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                           DEVELOPMENT, AND DISSEMMINATION
                               Samuel F. Baldwin
                             Princeton University
                        Support for the publication of
                          this volume was provided by
                            the Directorate General
                          for Development Cooperation
                          Ministry of Foreign Affairs
                         Government of the Netherlands
                       1600 Wilson Boulevard, Suite 500
                         Arlington, Virgnia 22209 USA
                     Tel: 703/276-1800 . Fax: 703/243-1865
                  Center For Energy and Environmental Studies
                             Princeton University
                        Princeton, New Jersey 08544 USA
Biomass Stoves
Copyright [sup.c] 1987 Volunteers in Technical Assistance
All rights reserved. No part of this publication may be produced or transmitted
in any form or by any means, electronic or mechanical, including photocopy,
recording, or any information storage and retrieval system without the written
permission of the publisher.
Manufactured in the United States of America.
Published by
                       1600 Wilson Boulevard, Suite 500
                         Arlington, Virgnia 22209 USA
Library of Congress Cataloging-in-Publication Data
Baldwin, Samuel F., 1952-
  Biomass stoves.
  Bibliography: p.
  Includes index.
  1. Biomass stoves--Design and construction.
  2. Biomass energy--Developing countries. 3. Fuelwood--
  Conservation--Developing countries. I. Title
  TH7436.5.B35 1987   683'.88 87-6107
  ISBN 0-86619-274-3
                                                     To my sister, Hannah
The work presented in this volume began in West Africa, under the auspices
of a long-term project implemented by Volunteers in Technical Assistance
(VITA) and the Comite Permanent Inter-etats de Lutte Contre la Secheresse
dans le Sahel (CILSS). Since then, numerous people and organizations have
assisted at every step in its development. Many of the contributors have
been carefully noted in the detailed references and so will not be
repeated here.  However, special thanks are due the following:
For financial support while in Africa: United States Agency for International
Development and IBM-Europe.
For institutional support while in Africa: CILSS, Ouagadougou; l'Institut
Burkinabe de l'Energie (IBE), Ouagadougou; Mission Forestiere Allemand
(MFA), Ouagadougou; Laboratoire d'Energie Solaire (LESO), Bamako; Centre
des Etudes et des Recherches des Energies Renouvelables (CERER), Dakar;
Association Bois de Feu, Marseille; Association pour le Developpement des
Energies Renouvelables en Mauritanie (ADEREM), Nouakchott; Church World
Service (CWS), Niamey; United States Agency for International Development
(USAID); and United States Peace Corps.
For partial financial support in the U.S.: World Resources Institute and
the Rockefeller Brothers Foundation, The Hewlett Foundation, the Center
for Energy and Environmental Studies of Princeton University, and VITA.
For illustrations and graphics assistance:  Ellen Thomson, Thomas O.
Agans, and Mike Freeman.
For editorial and production assistance:  Julie Berman, Margaret Crouch,
Juleann Fallgatter, Maria Garth, and Jim Steward of VITA.
For review comments and suggestions:  Alfredo Behrens, Margaret Crouch,
Gautam Dutt, Eric Larson, Cliff Hurvich, Eric Hyman, Willett Kempton,
Robert Morgan, H.S. Mukunda, Tom Norton, Kirk Smith, Bob Williams, and
Timothy Wood.
For providing optical scanning equipment: Charles Creesy of Princeton
For preparation and publication support: The Hewlett Foundation, the
Center for Energy and Environmental Studies, and VITA.
Simply listing those who have helped, however, does not adequately
describe the critical role that so many have played in this work.   The
original improved stoves project with CILSS began in 1980 when IBM-Europe
approached VITA with a request to design a program with CILSS for the
research and development of improved stoves as a way to combat deforestation.
USAID later provided funds to keep this program going. It was the
foresight and unwavering support of these two organizations -- the aid
agency and the corporation -- that allowed this work to take place at all.
Timothy Wood was the first Technical Coordinator of the VITA/CILSS
improved stove project and it was his fine work in organizing many of the
national projects and in beginning the development of fired clay stoves
that, in large part, paved the way for the work described here.
Following my arrival in West Africa as the second Technical Coordinator,
the work described was made possible only through assistance far above and
beyond the call of duty by: Issoufou Ouedraogo, Georges Yameogo, Frederic
Yerbanga, and Stephen and Cornelia Sepp in Burkina Faso; Yaya Sidibe,
Cheick Sanogo, and Terry Hart in Mali; Massaer Gueye, Lamine Diop, and
Susan Farnsworth in Senegal; Ralph Royer in Niger; Bill Phelan in Mauritania;
and above all, Moulaye Diallo of CILSS and Sylvain Strasfogel of
Association Bois de Feu. At the same time, I received superb support from
Paula Gubbins and Juleann Fallgatter at VITA headquarters.  Many, many
others also helped significantly and to them I must apologize for not
specifically citing their names here.
With my return to the United States I have continued to receive invaluable
assistance from many sources.  Among those listed above, special thanks
are due Margaret Crouch, Gautam Dutt, Eric Larson, and Ellen Thomson.   In
particular, Margaret and Gautam have provided countless hours of editorial
and production assistance, and unflagging support in this long endeavor.
To all of these people I give a heartfelt thanks.  Those mistakes that
remain in the text are mine alone and somehow remain despite all the
patient editorial assistance that I have received.  Similarly, several
illustrations of lower quality remain -- they are due to my shaky hand and
somehow remain despite the professional assistance available to me.   I
hope the reader will understand the underlying themes of this work despite
these shortcomings.
I would also like to thank my sister, Hannah, for first making me aware of
the problems in developing countries.  This book is testimony to the
profound impact a simple trip to visit her in Senegal in 1972 has had on
my career.
Finally, I would like to thank my wife, Emory, for her love, patience, and
understanding during the long months while what was intended to be a 50-page
technical report turned into a 300-page book.
                                   Sam Baldwin
                                  November 1986
                              TABLE OF CONTENTS
Table of Contents
     Environmental Impacts
     Economics and Policy Options
     Other Aspects of Stove Efficiency
     Construction Options
     Template Design: Cylindrical Stoves
     Metal Stove Production
     Fired Clay Stove Production
     Laboratory Tests
     Controlled Cooking Tests
     Production Tests
     Field Tests
     Marketing Tests
     Charcoal Stoves
     High Temperature Furnaces
     A. Conduction
     B. Convection
     C. Radiation
     D. Combustion
     E. Heat Exchangers
     F. Financial Analysis
     G. Statistical Methods
     H. Testing Equipment
     I. Units and Conversions
     J. Institutions
Developing countries are now suffering serious and increasingly rapid
deforestation.   In addition to environmental degradation, loss of forest
cover removes the wood energy resources on which traditional rural
economies are based. In response to the increasingly serious shortages,
programs to conserve fuelwood supply and to expand fuelwood production
have multiplied, but have frequently been ineffective due to a lack of
understanding of the economic, political, social, and technical complexities
of these problems.
The primary intent of this book is to resolve some of the technical
problems of conserving fuelwood supply(1).  This is done by using the
principles of modern engineering heat transfer to redesign traditional
energy technologies. As shown, this unlikely marriage of the modern and
the traditional is a powerful tool for improving the lives of the Third
World's poor.
The book is divided into two parts, the text and the technical appendixes.
The text is written for generalists who need a qualitative yet detailed
understanding of stove design and testing. The appendixes are written for
specialists who need an introduction to the application of the principles
of combustion and heat transfer to stove design. The two parts are combined
into a single volume so as to emphasize the importance of technical
analysis to stove design, development, and dissemination.  In brief, the
contents are as follows.
(1) A companion volume discusses policy aspects of using biomass energy
resources for rural development (1). Stove program planning and implementation
are discussed at length in reference (2).
Chapter II, Fuelwood, Charcoal, and Deforestation, reviews the role of
fuelwood in traditional societies, and the environmental, economic, and
policy considerations of increasing deforestation and worsening fuelwood
shortages.   Although fuelwood demand is not a primary cause of deforestation
on the global scale, it can significantly increase pressures on
forest resources locally, particularly around urban areas in arid regions
where the fuelwood demand is large and the biomass productivity of the
land is small.  In turn, deforestation places an enormous financial and
physical burden on hundreds of millions of people in developing countries
as they struggle to obtain vital supplies of fuel with which to cook their
food and heat their homes.
Responses to these problems might include tree planting programs, improved
land management, or the importation of fossil fuels for cooking. All of
these may be important components of any long-term strategy to meet the
energy needs of developing countries (1).  Yet in many rural and urban
areas such programs cannot be implemented quickly enough or are too
expensive to overcome the rapidly growing fuelwood deficits.
Improving the energy efficiency of biomass burning stoves potentially
offers a highly cost-effective alternative for easing the burden of buying
fuel by urban poor and collecting fuel by rural poor. Better stoves also
promise important health benefits to their users by reducing smoke
emissions. Finally, stoves may ease pressures on forests as well as help
maintain long-term soil productivity by reducing the need to burn crop
residues and dung.
Chapter III, Stove Design, discusses the technical aspects of combustion
and heat transfer as applied to improving biomass burning cookstoves(2). The
following points are emphasized:
o   Conduction processes in the stove require the stove to be as lightweight
   as possible to minimize stored heat in the walls and, where
   possible, to be lined with lightweight, high temperature insulants to
   reduce heat loss to the outside. Their light weight and easy transportability
   allow centralized mass production with distribution through
   existing commercial channels or decentralized mass production with
   distribution by informal sector artisans.
(2) "Biomass" as used in this book refers to raw or unprocessed biomass
fuels such as wood, agricultural wastes, or dung.  In contrast, fuels such
as charcoal, ethanol, methanol and others that are derived from raw
biomass are termed "processed biomass" fuels.
"Cookstoves" (or simply "stoves") refers primarily to stoves designed for
heating water.  Uses could include domestic, restaurant, or institutional
scale cooking (boiling) or hot water heating; commercial and industrial
uses such as beer brewing, cloth dyeing, or food processing (boiling); and
others.   It does not refer to stoves for frying foods or to woodburning
ovens, nor does it apply to space heating stoves, although many of the
same considerations will generally be applicable.
o   Convection processes in the stove require very precise control over the
   stove dimensions and precise matching of the stove to the pot.  The
   high degree of precision needed necessitates mass production based on
   standard templates.
Thus, because of fundamental principles of heat transfer, site-built or
massive stoves are unlikely to show acceptable performance; mass produced
lightweight stoves with carefully optimized and controlled dimensions are
much preferred.
In addition, combustion and radiation heat transfer processes are discussed
in Chapter III and  opportunities are presented for further research to
increase efficiency and reduce emissions.
Chapter IV, Stove Construction, applies the technical findings of Chapter
III to the practical aspects of actual stove construction. Template design
and step by step production are described in detail for several metal and
fired clay stoves recently developed and now being disseminated in West
Africa.   Additionally, suggestions are made for a variety of other stove
configurations that may better suit conditions in other areas.
In Chapter V, Stove Testing, step-by-step procedures are recommended for
testing stove prototypes and establishing a rudimentary stove industry. In
brief, laboratory and controlled cooking tests are used to select particularly
promising prototypes.  From these tests, standard templates are
developed that conform to the local pot sizes and shapes. A production
test is then run producing 50, 100, or more stoves for each of the most
popular pot sizes.  During this production test, a detailed analysis is
performed of the costs, the problems encountered, and potential improvements
in the production method.
Some of the stoves produced are distributed on a short-term, temporary
basis to selected families for field testing to determine both their
acceptability and their actual performance.
Another portion of those stoves is put on display in local commercial
outlets and sold on a commission basis.  Such simultaneous marketing may
allow some indirect feedback on how neighbors of the selected families
perceive the stoves' potential.  Marketing techniques such as radio and
newspaper advertising, billboards and other publicity, and public demonstrations
at social centers, schools, religious centers, and elsewhere
should also be attempted.  As interest develops, the stove promoter can
gradually withdraw, leaving the stove producer in direct contact with the
various commercial outlets.  If interest does not develop, modifications
will be necessarily based on the field and market surveys and any other
information that is available.
It must be emphasized that detailed, methodical testing of prototype
stoves; careful financial and statistical analysis of the results; and use
of these results to improve subsequent prototypes is crucial if improved
stoves are to be disseminated successfully and widely. In some areas the
testing prescriptions provided will need to be modified; in other areas
they will need to be completely reworked.  But everywhere, careful,
methodical testing and use of the results are crucial to understanding and
overcoming obstacles to good stove performance and acceptability.
Chapter VI briefly examines improvements in Charcoal Fueled Systems such
as stoves and high temperature furnaces that may save large amounts of
fuelwood when developed.
Technical Appendixes document the text in detail and provide the technical
reader the foundation for more detailed understanding.  Topics discussed
include conductive, convective, and radiative heat transfer processes;
principles of combustion; air to air heat exchanger design; and techniques
for financial and statistical analysis of test data.  Analytical and
numerical solutions to heat transfer equations are described in detail and
the results are presented in the text.  Extensive references are noted for
those who wish to do more detailed work and a list of institutions is
provided for contact with ongoing programs.
The specific technologies discussed in this book are by no means finalized:
rather they are beginnings.  Each has certain advantages, such as
fuel efficiency or safety, compared to traditional forms, but also brings
with it certain disadvantages such as reduced flexibility or increased
cost. Whether or not the improved technology is adopted in any area will
depend on the local fuel supply, the local economy, and a host of other
factors.   Further, the response will be dynamic, changing as conditions
change.   As biomass energy resources decrease, however, the demand for
more fuel efficient technologies must grow.  Adaptation and further
development of the technologies described here can provide the vital
energy services needed by the world's poor in an increasingly resource
limited world.
Similarly, this book is by no means a completed study but rather is an
introduction to the application of modern scientific analysis to traditional
technologies. In the examples discussed below, when modern engineering
heat transfer is applied to traditional energy technologies, new
technologies are developed with enormous potential to improve the lives of
the world's poor. Combined with modern mass production techniques that can
carry the fruits of a single dedicated engineering effort to the entire
world, this enormous potential can be realized. There is not time to
Ever since people learned to control fire they have been actively deforesting
their environment, initially using fire to aid in the hunt and
later to clear land for agriculture.  Tierra del Fuego or "Land of Fire"
was so named by Magellan in 1520 because of the numerous fires he saw
there set by indigenous South Americans.  Tropical savannahs and temperate
grasslands are, in large part, a consequence of such repeated burnings.
An estimated half of the world's deserts were similarly created (1).
Recorded history has numerous examples of such deforestation. Crete, once
heavily forested, suffered severe wood shortages by 1700 BC due to the
demands of a growing population. Cyprus provided the bronze needed by the
ancient Greeks for weaponry. Wood shortages are a likely cause for the reduction
in bronze smelting there by 1300 BC which forced rationing on the
Greek mainland and weakened the Mycenaeans to outside attack.   Aristotle
and Plato both documented the destruction of forests in Greece and the
consequences.   The Romans were forced to import wood from North Africa,
France, and Spain to keep their industries, public baths, and military
operational.   England suffered severe deforestation in many areas during
her early industrial period -- citizens even rioted over rising wood
prices -- until the transition to coal was made (2,3).
Today, the world's forests face unprecedented pressures. While potentially
a renewable resource, forests are disappearing faster than they are being
replaced. The United Nations Food and Agriculture Organization estimates
that forests are being lost to agriculture, grazing, commercial timber,
uncontrolled burning, fuelwood, and other factors at a rate of more than
11 million hectares per year, with 90% of the cleared land never replanted
(1) The author would like to acknowledge the assistance of Timothy Wood
in preparing portions of this chapter.
As forests disappear, the financial and physical burden of obtaining wood
fuel for cooking and space heating increases for the world's poor.   In
response, many turn to crop wastes and dung as an alternative, but one
that has potentially serious consequences for future soil fertility (6,7).
This is not a small or isolated problem.  Nearly two million metric tons
(tonnes) of wood, charcoal, crop wastes, and dung are burned daily in
developing countries, or approximately one kilogram each day for every
man, woman, and child. Although the energy obtained represents only about
10% of the energy consumed worldwide, it is over half the energy consumed
in some 50 to 60 developing countries and is as much as 95% of the
domestic energy used there (6-9).
Biomass fuels thus play a critical role in the economies of the developing
countries.   In this chapter the supply and demand of these fuels, their
production and economics, and the environmental consequences of their use
are reviewed in detail.  Although the extensive statistics presented are
themselves unemotional, one cannot be unemotional about the awesome toll
on human well-being that they represent.  The high cost of fuelwood
represents food, medicine, and clothing that the urban poor must forego.
The long distances walked and heavy loads carried by the rural poor
foraging for fuel represent time and labor better spent growing food or
producing goods for sale in village markets.  The large amounts of smoke
emitted by traditional stoves represent the discomfort and disease that
this smoke can cause the user. Only in such a broad context can the full
impact of traditional fuels and stoves on human life and well-being be
The total global annual growth of forest biomass has been variously
estimated to be about 50 times annual wood consumption and five times
total annual energy consumption including fossil fuels (Note 142)(2) (10).
Despite the large average global supply, there are acute and growing
shortages of fuelwood regionally and locally. Some regions, such as Asia,
have very little per capita forest growing stock (Note 143).   Within
regions, some countries are well endowed with biomass energy resources,
and others have totally inadequate supplies, (Table 1); and within
countries themselves, there are similar local abundances and shortages.
Zaire, for example, consumes only 2% of its sustainable yield of forest
biomass but has serious deforestation around Kinshasa (12).
In areas where forest resources cannot meet the demand, crop residues and
animal dung are marginally sufficient substitutes at best. In Bangladesh,
for example, crop residues and animal dung can supply about 300 watts per
capita (Table 1). This is barely enough to meet minimum needs.
(2) So as to not overburden the text yet still provide the reader with
detailed information, a number of Tables are given as Notes beginning on
page 251.
                                   TABLE 1
          Biomass Energy Resources in Selected Developing Countries
                                 Sustainable Yield in Watts/capita of
                     Population                     Crop        Animal
      Country         (millions)        Wood      Residues       Dung
      Congo                1           18100         35          n.a.
      Brazil             116           11100        257           507
      Zaire               30            4300         29            35
      Argentina           27            3900        793          1270
      Thailand            48            1170        295           124
      Nepal               14             666        225           412
      Burkina Faso         7             317        162           231
      India              694             222         174          200
      Bangladesh          89              63        136           162
      China              970            n.a.        216           108
      Adapted from reference (20) ; n.a. -- not  available
Estimates such as these are, of course, only very crude approximations.
As these traditional fuels do not usually move through monitored commercial
markets, estimates of their production and use can only be made by
detailed measurements at the locale in question.  Further, there is
considerable confusion in the literature over the units used to measure a
given quantity.  For example, foresters generally use volumetric units to
measure wood but sometimes fail to specify whether it is in units of solid
cubic meters or stacked cubic meters (steres).  Nor is the species and
density specified.  Note (144) gives very rough equivalences between the
two volumetric units for different classes of harvested wood. Similarly,
charcoal is usually measured by volume, but its energy content is determined
by its mass, which in turn is determined by the species from which
it was carbonized (14), the temperatures at which it was carbonized, i.e.,
its residual volatile content (15), and its packing density.
When estimates of energy content are based on weight, the preferred
method, it is similarly vital to know the moisture content of the fuel and
whether the weight is on a wet or dry basis (see Chapter III).
Estimating biomass energy resources should therefore be done by direct
measurement.   Forest resources can be measured by estimating standing
volumes or by cutting an area and making a direct weight or volume
measurement (16-19). Crop residues from the same species can vary widely
by soil type and rainfall as shown in Note (145) and similarly should be
directly weighed.  Growth rates can be estimated by numerous repetitions
of such measurements on comparable, adjacent samples over a period of
time. Finally, where animal dung is, or could be, used as an energy
resource, it, too, should be measured directly.  Estimates of dung
production rates are given in Note (146).  Calorific values for a number
of different biomass fuels are given in Appendix D.
Biomass energy resources have been estimated for a variety of local,
national, and regional cases as described in references (4,7,9,13,20-28).
Fuelwood Demand
Numerous estimates of biomass fuel demand have been made on the local,
national, and regional scale (29-59).  The rate of energy use by the
typical villager is usually in the range of 200-500 watts per person and
can vary dramatically with the season, climate, and general availability
of various fuels. Energy survey results are given for nearly 40 towns and
villages in Note (147). Much of this energy is used for domestic cooking
(Tables 2,3,6) and these values are much higher than the amounts of energy
used in developed countries for cooking (Table 4).  This is due to the
inefficiency of traditional fuels and stove technologies as well as
changes in diet and lifestyle that are possible with higher incomes.
Globally, biomass fuels are the principal source of cooking energy for
most developing countries (Table 5).  Additionally, they provide energy
for household needs such as heating bath water, ironing, and other uses.
Though perhaps atypical, 60% of domestic wood consumption in Bangalore,
India, is used to heat bath water (45).
Although their principal use in developing countries is domestic, biomass
also fuels much of the industry. As seen in Tables 7 and 8, biomass fuels
two-thirds of Kenyan industry and commerce and it is used for such things
as beer brewing, blacksmithing, crop drying, and pottery firing.
                                   TABLE 2
                   Total Power Consumption, Ungra, India
Source\Use       Agriculture     Domestic   Lighting     Industry       Total
Human              7.26          17.08         --         4.52         28.86
   Man            (5.11)        (6.01)        --         (3.92)       (15.04)
   Woman          (2.15)        (8.70)        --         (0.56)       (11.41)
   Child           --           (2.36)        --         (0.04)        (2.41)
Animal(**)        12.0             --          --         1.11         13.11
Firewood           --           222.8          --        36.85       259.7
Agro-waste         --            23.2          --          --          23.2
Electricity       3.18            --          1.17        0.37          4.72
Kerosene           --            0.19         6.88        0.97          8.04
Diesel            0.04           --            --           --          0.04
Coal               --             --           --         1.41          1.41
Total            22.5          263.3          8.05       43.23        339.
(*) Based on a total village population of 932 people in 149 households
(**) Provided by 111 bullocks, 143 cows, 93 calves, 113 buffalo and 489
     sheep and goats.
Reference (50)
Estimates of the energy intensity of commercial uses vary widely, but all
indicate substantial amounts of fuelwood used and often at very low
efficiencies.   One stacked cubic meter of wood, for example, is required
to cure 7-12 kg of tobacco leaf.  The efficiency of tobacco drying barns
in Tanzania has been estimated to be as low as 0.5% (49).  Tobacco curing
uses 11% of all fuelwood in Ilocos Norte, Philippines and 17% of the
national energy budget in Malawi (34,39,47,56,59).
Tea processing requires roughly 9.5 GJ or 500 kg of dry wood to produce 30
kg of dry tea leaves from 150 kg of green leaves (45,47).  Fish smoking/
drying is variously estimated to require from 0.25 kg (39) to 3 kg (40) of
fuelwood per kilogram of fish dried (47,59).  Brickworks require roughly
one stacked cubic meter of fuelwood to fire 20-25 pots (39) or 1000 bricks
(59).   In Bangalore, dyeing a tonne of yarn requires some 8.3 tonnes of
fuelwood; bakeries use 0.58 kg of fuelwood per kilogram of traditional
bread produced (45).  In Tanzania, beer brewing requires a stacked cubic
meter to produce 180 liters (59), and the brewing industry in Ouagadougou
uses 14% of the total fuelwood used (60).  Other major users include
institutional kitchens, wood processing (45), and sugar production, for
which the bagasse itself is used.  Overall, biomass fuels supply up to 40%
of the industrial energy used in Indonesia, 28% in Thailand, 17% in
Brazil, and similarly large fractions in many other countries (9)(3).
                                    TABLE 3
               Domestic Power Consumption, Taruyan, West Sumatra
                    Labor(*)    Firewood   Bagasse  Kerosene     Total
Cooking                8.6        181.        2.9        --        193.
Water Collection      2.6           --        --        --          2.6
Laundry                2.0           --       --         --         2.0
Wood Collection       1.9           --        --        --          1.9
Delivering Food       0.6           --       --         --          0.6
Lighting                --           --       --         52.1       52.1
Total                 15.7         181.        2.9        52.1     252.
Percentage             6.2%         71.9%      1.1%      20.7%    100.%
(*)Calculated at 1.05 MJ/man-hour; 14.9 MJ/kg firewood; 37.7 MJ/liter
Kerosene; 9.2 MJ/kg bagasse.
Reference (58)
      (3)A variety of units, GJ (giga-joules), kg., [m.sup.3] , tonnes, etc. , are
used here to correspond to the literature rather than using a single set
of units -- preferably GJ and watts.  Conversion tables for all these
units are given in Appendix I, approximate stacking factors for wood and
charcoal are given in Notes (144,149), and calorific values are given in
Appendix D. The author regrets the inconvenience.
                                    TABLE 4
                         Power Consumption for Cooking
                     Country             Fuel            W/cap
                     Brazil              LPG              55
                     Brazil              Wood            435
                     Canada              Gas              70
                     Cameroon           Wood           435
                     France              Gas              55
                     West Germany        Gas              30
                     Guatemala           Propane          50
                     Guatemala           Wood            425
                     India               Kerosene         50
                     India               Wood            260
                     Italy               Gas              55
                     Japan               Gas              25
                     Sweden              Gas/kerosene     40
                     Tanzania            Wood            590
                     United States       Gas              90
                     References (63,64)
                                    TABLE 5
               World Population by Principal Cooking Fuel, 1976
                             (millions of people)
                                       (fossil)                 Dung and
                               Total     Energy       Fuelwood   Crop Waste
Africa South of Sahara           340        35         215           90
India                             610        60         290          260
Rest of South Asia               205        25          95           85
East Asia-Developing Pacific     265        95         110           60
Asia, Centrally Planned
  Economies                       855      190        435           230
Middle East, North Africa        200       105          35           60
Latin America and Caribbean      325       230          85           10
North America - OECD Pacific     365       365           0            0
Western Europe                   400       400           0            0
European, Centrally Planned
  Economies                       340      340          0             0
Total                            3905       1845       1265          795
Reference (11)
                                    TABLE 6
                          Energy Consumption in Kenya
                     Percent of National Total(*) by End-use
                        Non-                 Biomass
                        Fuel         Wood   Charcoal  Other
Urban Household
  Cooking/Heating        0.8%         1.0%    3.3%      --
  Lighting               0.6          --      --         --
  Other                  0.2          --      0.5        --
Rural Household
  Cooking/Heating        0.2         45.3      2.8       2.7%
  Lighting               1.1          --      --         --
  Large                  8.6          5.3     0.3        --
  Informal  Urban       --            0.1      0.6       --
  Informal  Rural       --            9.1      0.1       --
Commerce                 0.6           0.5     0.1        --
Transportation          13.7           --      --         --
Agriculture              2.5           --      --         --
Total                   28.4%         61.3%     7.6%      2.7%
(*)Total National Energy Consumption = 332 million GJ
   Per Capita Power Consumption = 658 W
   Reference (24)
                                    TABLE 7
             Annual Consumption of Fuelwood and Charcoal in Kenya
                   by Rural Cottage Industries, Watts/Capita
                                     Fuelwood    Charcoal
                 Industry              W/cap       W/cap
                 Brewing               33.9         --
                 Brick firing           1.9         --
                 Blacksmithing          --          1.9
                 Crop Drying            1.3         --
                 Fish Curing            0.6         --
                 Tobacco Curing         1.3         --
                 Butchery               7.6         1.9
                 Baking                 4.1         --
                 Restaurants            5.4         1.3
                 Construction Wood     15.9         --
                 Total                 72.          5.1
                Reference (24)

Biomass fuels are crucial to the economies of most developing countries.
Note (148) lists 60 countries in which biomass fuels provide 30-95% of the
total energy used.  The energy these fuels provide, however, is only a
fraction of that used by fossil fuel based economies (8,31).   In the
developed world, average per capita energy use is about 6 kW while in
Africa and Asia it is barely one tenth of this (8); in North America,
energy use is over 10 kW, while in Africa it is about 450 W (8,31).
With these rates of biomass energy use and supply there is a serious and
growing shortage of fuelwood in many areas.  The UNFAO has estimated that
the number of people suffering an acute shortage of fuelwood will increase
from about 100 million in 1980 to over 350 million in the year 2000 (Table 9).
Such shortages increase costs for urban dwellers, lengthen foraging
for fuel by rural dwellers, and rob the soil of nutrients as people switch
to crop wastes and dung.
                                    TABLE 8
                         Fuelwood Consumption in Kenya
                        by Large Industry, Watts/Capita
                      Industry                      W/cap
                      Tea (average)                   8.9
                      Tobacco                         2.5
                      Sugar                           1.6
                      Wood Processing                 9.5
                      Wattle                          1.3
                      Clay Brick                      1.0
                      Baking                          9.5
                      Total                          34.3
                      Reference (24)
                                    TABLE 9
                 The Fuelwood Shortage in Developing Countries
                         (millions of people affected)
                               1980                    2000
                          acute       deficit      acute     deficit
                         scarcity                scarcity
            Africa             55      146          88          447
            Near East &
              North Africa    --       104          --         268
            Latin America      15      104         30          523
            Asia & Pacific     31      645        238         1532
            Total             101      999        356         2770
            Reference (6)
                                   TABLE 10
                  Fuelwood in World Power Consumption (1978)
                             Fuelwood        Commercial       Percent
               Population     Consumed      Power Consumed   wood/total
                millions     per capita       per capita
World             4258          110 W         1913 W           5.4%
  market           775          21           5946              0.3
  planned          372          73           5118              1.4
  Africa           415         254            185              58.
  Asia            2347         101            508              17.
   America         349         232            1028              18.
Reference (8)
Charcoal is produced by heating wood in the absence of oxygen until many
of its organic components gasify, leaving behind a black porous high
carbon residue.  The charcoal thus produced retains the same shape as the
original wood but is typically just one fifth the weight, one half the
volume, and one third the original energy content.  A more precise
relationship is given in Note (149).
The charcoal has a calorific value of 31-35 MJ/kg, depending on its
remaining volatile content, compared to 18-19 MJ/kg for oven-dry wood.
Table D-2 illustrates how the temperature history of the carbonization
process affects the volatile content and calorific value of the resulting
There are two different classes of carbonization equipment, kilns and
retorts.   Kilns burn part of the wood charge being carbonized to provide
the heat necessary for the carbonization process.  Retorts use a separate
fuel source to provide heat and thus can conserve the higher quality
product being carbonized by using a lower quality fuel such as twigs and
branches for the heating.  An extensive review is given in reference (156).
The most widespread system used in the developing world is a kiln made of
earth.   In this case the wood is stacked compactly either in a pit or on
the flat ground, covered with straw or other vegetation, and, finally,
buried under a layer of soil.  It is ignited with burning embers introduced
at one or more points at the bottom of the stack.  The task of the
charcoal-maker throughout the ensuing "burn" is to open and close a
succession of vent holes in the soil layer to draw the fire evenly around
the wood stack, heating the wood while burning as little of it as possible.
Other systems in use include brick kilns, which are used extensively
in Brazil (66,67).
The size of the kiln can be as much as 200 stere (68) and the energy
efficiency of the conversion process is variously given as 15% in Tanzania
(47), 24% in Kenya with an additional loss of 5% of the charcoal itself
during distribution (24), 29% in Senegal (69) and Ethiopia (70), and over
50% in Brazil with brick kilns (67).  Advanced retorts are claimed to be
capable of achieving 72% energy efficiencies in converting wood to charcoal
if there is complete recovery of all of the gaseous by-products (67).
The large variation in reported kiln efficiencies may be due in part to
confusion about units -- energy, weight, or volume, and wet or dry basis.
When side-by-side tests are done, energy efficiencies are typically in the
30-60% range as indicated in Table 11 (71,72).  The relative economic
performance of a few types of kilns is given in Table 12.  The poor economics
of the earthen kiln listed in Table 12 may be due to the very small
size studied.  Others have found traditional earthen kilns to have fairly
high performance and a good financial return with relatively little labor
(71).   Their disadvantages, however, include a variable yield and quality,
slow burns, and seasonal availability (not during the rainy season).   No
matter what system is used, however, producing charcoal results in a very
large net energy loss.  In terms of conserving forest resources, it is
always better to use wood rather than first converting it to charcoal.
Charcoal Transport
It has been frequently argued that it is cheaper and more efficient to
transport charcoal than wood because of its higher energy content per unit
mass.   As shown below, however, the amount of energy, whether in the form
of wood or charcoal, that can be carried per truckload is about the same.
As transport costs are primarily due to vehicle depreciation and maintenance,
the cost of hauling wood or charcoal is about the same per unit
of energy carried (150).
By assuming transport costs at a fixed US$0.10 per metric ton-kilometer,
Earl found that it was cheaper to transport energy in the form of charcoal
than in the form of wood for distances greater than 82 km (13).   Chauvin
similarly used a fixed cost per ton-km. in his analysis of the economics
of transporting charcoal from the Ivory Coast to Burkina Faso by rail (60)
Expressing transport costs in terms of ton-km's is a standard practice in
aggregated transportation statistics, but is not applicable in this
situation.   Most of the energy is used to move the vehicle itself, to
overcome wind resistance, internal friction and so forth.  Thus, an empty
truck uses nearly as much energy as one that is full.  A linear regression
on data presented in reference (73) shows that the energy intensity of
transport by tractor-trailers in the USA is related approximately to the
payload for the range 8-25 metric tons by the equation
        E = 23.6/M + 0.476
where E is the energy intensity in MJ per metric ton-km the load is moved,
and M is the mass of the load in metric tons.  Transport is more often
limited by volume than by weight and this is particularly true in the
developing world where vehicles are usually filled to overflowing.   In
this case of volume limited transport, Table 13, 13% more energy can be
transported per truckload of wood than of charcoal at a cost of a 21%
increase in fuel use.
Fuel costs, however, are only a small part of the total transport costs
and at least in some cases, do not substantially increase even on unimproved
roads (74).  Maintenance and repair of vehicles is a large factor
(74) and vehicle depreciation and labor are even larger (75).
                                   TABLE 11
             Energy Efficiencies of Assorted Carbonization Systems
                                Thailand, 1984
                       Total        Charcoal as      Charcoal    Number
                        Volume      Energy % of     Production     of
                      [m.sup.3]      Dry Wood       Rate kg/hr   Trials
Brick Beehive 1          8.3            61%          11.1          3
Brick Beehive 2          2.0            63            5.6         35
Brazilian, modified      8.3            55            10.7          2
Mark V(2)                2.6            43            10.1          7
Mud Beehive 3            2.2            56             5.1         27
Single Drum              0.2            38             5.9          7
Earth Mound              0.7            51             4.6          5
Reference (72). Also see (72) for data on 12 other types of kilns.
                                   TABLE 12
                         Charcoal Production Economics
                                Thailand, 1984
Per Burn                 Wood(*)     Capital(**)    Labor(***)   Charcoal
                                  Investment                  US$/tonne
Brick Beehive 1         $52.         $1.67          $9.00        $65.
Brick Beehive 2          15.         0.66           3.70          75.
Brazilian, modified      54.         1.13            9.80          71.
Mark V(2)                33.         3.15            4.70          90.
Mud Beehive 3            16.         0.17            4.10          74.
Single Drum               1.80       0.18            1.95         195.
Earth Mound               3.70        --             2.35         114.
(*)Wood costs US$8.30/stere; (**)Interest rate is 15%; (***)Labor is
Reference (72).  Also see (72) for data on 12 other types of kilns.
                                   TABLE 13
                Energy Required to Transport Wood and Charcoal
            Factor                        Wood          Charcoal
Assumed volumetric gravity               0.7              0.33(a)
Assumed packing density                  0.7              0.7 (b)
Effective volumetric gravity             0.49              0.23
Energy content per truckload           390. GJ(*)       345. GJ (c)
Weight per truckload                    24.5 MT(**)      11.5 MT (d)
Transport energy per truckload-km       35.3MJ/km        29.1 MJ/km
Transport energy per km/energy
content of load                         91x[10.sup.-6]    84x[10.sup-6]
(*)GJ is a gigajoule or 1 billion joules; (**)MT is a metric ton, 1000 kg
a)   Based on (14).
b)   For wood based on (13). Charcoal may have a higher or lower packing
    density depending on its size and whether or not it is bagged for
    transport.   It is normally bagged for transport.
c)   Assumed calorific value for wood, 16 MJ/kg; charcoal, 30 MJ/kg;
    both including moisture.
d)   Based on a payload volume of 50 [m.sup.3].  This is less than a standard
    tractor trailer, but was chosen so as to remain within the limits
    of the correlation of weight to transport energy, yet correspond
    to the case for most developing countries of volume limited transport
    for either wood or charcoal.
                                    TABLE 14
                     Transport Costs of Wood and Charcoal
                               Percent of Total
                                            Wood       Charcoal
               Labor and management           12%         12% (a)
               Fuel                           18          15  (b)
               Maintenance and repair         40          30  (c)
               Licenses and tolls              1           1
               Vehicle depreciation           42          42
               Total costs                   113         100
               Energy hauled                 113          100 (b)
a)   From reference (75) using charcoal as the baseline.
b)   From Table 21.
c)   Estimated from reference (75) data on tire depreciation and
    vehicle repair charges assuming that these costs increase proportionately
    to the total vehicle weight.
When these costs are considered, Table 14, the cost of hauling energy,
whether in the form of wood or charcoal, is virtually identical.   In
practice, factors such as vehicle size, labor and fuel costs, part-load or
back-haul of goods, and many others will complicate this analysis.
When production costs are included, charcoal is more expensive than
fuelwood.   These costs are reflected in their relative prices: the price
per GJ of charcoal is typically twice that of fuelwood (76).
Charcoal Demand
Despite its higher price, charcoal is a very popular fuel, particularly in
urban areas where people have a cash income.  According to a 1970 report
from Thailand, 90% of the wood cut for urban markets was converted into
charcoal (34).  In Tanzania that figure is 76%, with 10-15% of all wood
cut converted to charcoal (40,59).  In Senegal, 15% of all wood cut is
converted to charcoal for Dakar alone, transported to Dakar from as far as
600 km away, and used there by 90% of the households at a rate of 100
kg/person-year (77,78).  In Kenya, 35% of the wood cut is converted to
charcoal (24).
Although traditional charcoal stoves have an efficiency (15-25%) somewhat
higher than the open wood fire (15-19%), this does not compensate for the
drastic energy loss in the initial conversion from wood (79,80).
There are a variety of reasons for this popularity despite high cost and
energy inefficiency.  Unlike some wood species that must be used within as
little as a month of drying to avoid significant losses to termites,
charcoal is impervious to insect attack (21).  It can, therefore, be
prepared far in advance of, for example, the rainy season when other fuels
are unavailable.  Even more important is that charcoal is a very convenient
fuel to use.  Charcoal is nearly smokeless.   Cooking can be done indoors
in relative comfort without blackening the walls with soot.   Metal pots
stay relatively clean, and there is no smoke irritation to eyes or lungs.
Although there can be a high output of dangerous carbon monoxide, which is
a health hazard in poorly ventilated kitchens, this does not cause as
obvious discomfort to the user.  Additionally, once it is lit, a charcoal
fire needs little further attention from the cook, while a wood fire
requires frequent adjusting of the fuel.
The willingness of urban dwellers to purchase expensive charcoal should
thus encourage designers of improved stoves who are attempting to eliminate
smoke, ease the drudgery of cooking, and further reduce fuel costs.
At the same time, it should serve as a warning to those who pay attention
only to fuel efficiency.
Charcoal is also extensively used commercially.  In Brazil, some 19
million cubic meters of charcoal were used during 1983 to produce pig
iron, 2.5 million were used to produce cement, and 600,000 were used for
metallurgy.   Overall, about 18% of the energy used in the Brazilian steel
industry is from charcoal.  About 17% of this charcoal was generated from
plantations (43,67,82).
Large amounts of charcoal are traded internationally as well.   In 1981,
Indonesia, Thailand, and the Philippines each exported 44-49 thousand
tonnes of charcoal.  Large importers include Japan, with 52,000 tonnes,
and Hong Kong, with 23,000 tonnes (65).
There is now rapid and increasing deforestation around the world.   The
UNFAO (5,83) has estimated total annual global deforestation at about 11.3
million hectares (Table 15).  Others have estimated it to be as high as 20
million hectares and more per year (7).  Among the causes are the following.
Shifting agriculture damages or destroys about 0.6% of tropical
forestland annually and accounts for some 70% of forest loss in Africa
(84).   Opening pastureland to grow beef for export annually clears some 2
million hectares per year in Latin America (85-87).  Commercial timber
operations clear roughly 0.2% of tropical forestland annually (84), and
timber access roads open the areas to farmers leading to additional
degradation (87).  The Ivory Coast, for example, is losing some 6.5% of its
forests annually (5,83).  Finally, uncontrolled burning is believed
responsible for the creation of much of the world's savannah and grassland
(1,88,89).   Such brushfires in the African grasslands burn more than 80
million tons of forage annually, cause volatilization of organic nitrogen,
and allow excessive leaching of valuable salts (90).  This may be particularly
damaging in much of the Sahel where growth is already strongly
limited by the small available quantities of nitrogen and phosphorus (91).
The use of fuelwood increases pressures on forest biomass and can lead to
local deforestation (12,88), particularly in arid regions around urban
areas where demand is high and biomass growth rates are low.  Generally,
rural subsistence farmers cause relatively little damage to forests as
they take only small limbs, etc., and these often from hedgerows or from
near their farmlands.  For example, in Kenya, trees outside the forest
supply half the wood demand (37); in Thailand in 1972, 57% of the wood
consumed came from outside the forests (40).  In contrast, commercial
fuelwood and charcoal operations, even relatively small-scale ones, cut
whole trees and can damage or destroy large areas of forest.
Among the potential impacts of deforestation are erosion, flooding,
climatic changes, desertification, and fuelwood shortages (92-94).   Essentially
no soil or rainfall is lost from naturally forested areas.   However,
when tree cover is removed, massive amounts of soil can be washed away as
the rainfall flows across the surface.  Measurements in Tanzania indicated
that up to half the rainfall was lost as run-off from bare fallow (3.5[degrees]
slope), carrying some 70 tonnes/ha of soil with it (95).   Similar impacts
have been noted elsewhere (5,81,87,88,96,97).
Erosion chokes downstream waterways and reservoirs with silt, making them
even less capable of handling the increased volumes of water running
directly off the watersheds (2,7).  In 1982, flood and erosion damage due
to clearing India's forests was estimated to total $20 billion over the
previous 20 years.  This estimate included loss of top soil, loss of
property to floods, and shortened reservoir lifetimes (5).  Other estimates
place the direct costs of repairing flood damage at more than $250
million per year (98).  A general review of this problem in India is given
in reference (99).
As two-thirds of all rainfall is generated from moisture pumped back into
the atmosphere by vegetation, deforestation may cause serious climatic
change (1,100).  The surface reflectance is also changed and may affect
climate (1).  With no shading, soil temperatures rise dramatically and can
greatly reduce the vital biological activity in the soil (87,101).
Following deforestation, overgrazing and trampling can quickly destroy the
grass layer.  Without the protection of ground cover, the soil receives
the full force of pounding raindrops, bringing clay particles to the
surface and causing surface hardening and sealing that seeds cannot
penetrate (102,103).  The end result is often desertification.  During the
past fifty years, an estimated 65 million hectares of once productive land
have thus been lost to desert along the southern edge of the Sahara alone
(104,105).   Additional data for Africa are given in references (90,106).
As forest resources are lost, whether to agriculture, timber, brush fires,
or as fuelwood, villagers are increasingly forced to use lower quality
fuels such as crop wastes and dung to meet their minimum needs for cooking
and other purposes.  Globally, an estimated 150 to 400 million tonnes of
cow dung are now burned annually.  The burning of each tonne of dung
wastes enough nutrients potentially to produce an additional 50 kg of
grain.   The cow dung now burned in India wastes nutrients equal to more
than one-third of the chemical fertilizer used (7).
Increasing use of agricultural residues for fuel may cause serious damage
to soils.  Organic matter in soils provides most of the nitrogen and sulfur
and as much as half the phosphorus needed by plants.  It increases the
cation exchange capacity of the soil, binding important minerals such as
magnesium, calcium, potassium and ammonium that would otherwise be leached
away.   It buffers the pH of soils, and it improves the water retention and
other physical characteristics (151).
                                   TABLE 15
               Estimated Average Annual Rate of Deforestation of
             Tropical Forests, 1980-1985, in Millions of Hectares
                     and Percent of Total Standing Forest
                     Tropical      Tropical      Tropical        Total
Category              America        Africa        Asia      (76 countries)
Closed forest          4339         1331         1826           7496
                     (0.64%)       (0.62%)        (0.60%)       (0.62%)
Open forest            1272          2345           10           3807
                     (0.59%)       (0.48%)        (0.61%)       (0.52%)
All forests            5611          3676          2016         11303
                     (0.63%)       (0.52%)        (0.60%)       (0.58%)
Reference (31)
The destruction of forests may also have serious consequences in terms of
loss of genetic resources, loss of potential new medical products, and
others.   These are reviewed in reference (5).
The burning of biomass fuels has serious environmental impacts due to the
smoke released (107-112).  Although there have been numerous anecdotal
accounts of ill health associated with indoor biomass combustion, only
recently have systematic scientific studies of the problem begun (112).
Results to date indicate that in village homes, indoor concentration of
carbon monoxide, particulates, and hydrocarbons can be 10-100 and more
times higher than World Health Organization (WHO) Standards (111).
Further, cooks using traditional biomass burning stoves can be exposed to
far more carbon monoxide, formaldehyde, carcinogenic benzo(a)pyrene, and
other toxic and carcinogenic compounds than even heavy cigarette smokers.
From this it is expected that smoke is a significant factor in ill-health
in developing countries.  The diseases implicated range from bronchiolitis
and bronchopneumonia to chronic cor pulmonale to various forms of cancer
(110,111).   Indeed, the WHO now cites respiratory disease as the largest

bsex21.gif (600x600)

cause of mortality in developing countries (112).  Table 16 lists air
pollution emission factors for a variety of fuels and combustion systems.
Reducing and controlling exposure to biomass fuel emissions must be a
primary consideration in any stove program.  Further information is
available from the East-West Center (Appendix J).
The growing fuelwood shortage has a variety of economic impacts on both
rural and urban dwellers, the rural labor force, and the national economy.
For the rural subsistence dweller, depletion of local fuelwood resources
means ever longer foraging times.  There are numerous estimates of these
times ranging as high as 200-300 person days per year per household in
Nepal or 7% of all labor (22,46,98) and similarly high labor rates in
Tanzania (59) and other countries (99).  Approximate correlations relating
foraging distance to the local population density are easily developed by
equating the average consumption by a population to the area required to
provide a sustained yield, as shown in note (114).  A second example is
given in reference (115).  In arid regions with a low biomass growth rate a
village of as few as 500-1000 people can use up all the fuelwood within a
walking distance.  Foraging is also heavy work; in Burkina Faso, typical
headloads weigh 27 kg (113).
When wood becomes scarce, crop wastes and dung are the villagers' only
alternative; there is no cash for commercial fuels, nor do the long-term
environmental costs of using agricultural wastes outweigh their immediate
value as fuel.  In India, it has been estimated that a tonne of cow dung
applied to the fields would result in increased grain production worth
US$8, but if burned would eliminate the need for firewood worth $27 in the
market (116,117). Some have argued that due to the relatively low efficiency
of cow- dung in providing nutrients such as nitrogen, phosphorus,
potassium, and zinc to the soil in a useable form, it makes better sense
to burn it (117).  This, however, ignores other important contributions of
organic materials to soil fertility (151).
With a high market value for biomass fuels, the poor and landless are
sometimes denied access to their traditional fuel sources (118).   It has
even been reported that farm laborers in Haryana, India, formerly paid
cash wages, are sometimes instead paid crop residues to be used for fuel
(99) -- fuel they previously received free.
In contrast, urban dwellers often have no choice but to purchase their
fuel.   Again, there are numerous estimates of the financial burden this
imposes ranging up to as high as 30% of total family income in Ouagadougou
(34), to 40% in Tanzania (39), to nearly half in Bujumbura, Burundi (36).
During the 1970s the cost of wood and charcoal increased at a rate of 1-2%
per year faster than other goods (76).  Due to their rapid price escalation
during the 1970s, fossil fuels are often not viable alternatives.   In
Malawi, the use of kerosene declined 24% between 1973 and 1976, allegedly
due to higher prices (34).  Others have noted similar impacts (71).
The use of traditional fuels is important in stimulating the rural
economy.   The value of fuelwood and charcoal exceeds 10% of the Gross
Domestic Product in countries such as Burkina Faso, Ethiopia, and Rwanda,
and exceeds 5% in Liberia, Indonesia, Zaire, Mali, and Haiti (76).   This
pumps large amounts of cash into the rural economy and provides much
needed employment to rural dwellers (Table 17).  To supply Ouagadougou with
wood during 1975, for example, required some 325,000 person-days of labor
and generated over $500,000 in income directly and an additional $2.5
million in income through transport and distribution (34).   In Uganda, an
estimated 16 tonnes of charcoal are produced per person-year (13).   Other
estimates are given in Table 18 and references (71,72).  In many countries,
people in the poorest areas, where conditions do not permit
expansion of crop or animal production and the natural woody vegetation is
the only resource, depend heavily on sales of firewood for their income
(34,99).   Whatever program is put in place to meet the fuelwood shortage,
it will be necessary to take the employment impacts into account.
To meet the growing fuelwood shortage (Table 9), governments could import
fossil fuels as a substitute; plant fast-growing trees and improve the
management of existing forests; and develop more fuel efficient stoves and
other woodburning equipment, among other actions.
If every person now using fuelwood switched to petroleum based fuels, the
additional consumption would be just 3.5% of 1983 world oil output.   The
cost of kerosene and liquified petroleum gas (LPG) for all household needs
would be 15% of total merchandise exports or less for Kenya, Thailand,
Zimbabwe, and many other countries.  Importing fuels for cooking may then
be an important response in such areas (152).
In contrast, for Niger, Burundi, and others, a switch to petroleum fuels
for household energy needs would absorb almost all merchandise export
earnings (152).  Efforts to stimulate use of butane gas through subsidies
have begun in West Africa but have proven to be a heavy financial burden
(34,119).   There is also evidence that such subsidies benefit the wealthy
far more than the poor.  In West Sumatra in 1976, the poorest 40% of the
population used only 20% of the kerosene even though it was heavily
subsidized (58).  Yet without such subsidies, petroleum fuels are beyond
the reach of the poor.  In these areas, other actions are needed.
As a second response, plantations of fast-growing tree species can be
developed to provide fuel (123-126).  Extensive data on species, their
growth patterns, and their uses are given in references (5,12,102,123,124)
Donor agencies are now spending some $100 million per year on forestry
projects (116), and additional large funding is provided by the national
governments themselves.  The U.N., however, has estimated that $1 billion
per year is needed to meet the minimum needs of the year 2000 when a
shortage of about 1 billion cubic meters per year is expected with no
intervention (6).  To keep this sum in perspective, however, it must be
compared to the $130 billion per year needed for all energy sector
development in developing countries (154).
                                   TABLE 17
             Breakdown of Fuelwood Cost Factors for Niamey, Niger
             Labor for cutting, bundling, and
                     hauling to road (roadside price)      8.30
             Labor for loading/unloading                    2.80
             Transport permit                                .35
             Transport                                      5.30
             Cutting permit                                 5.50
             Profit                                         5.50
             Total                                        $27.75
             Reference (121); (*) Assumes 450 CFA/US$
                                   TABLE 18
           Labor Requirements for the Production of Fuel from Forest
                          Person-days/Hectare, Uganda
                                             Maximum   Minimum
                 Fuelwood                       120        50
                 Charcoal (portable kilns)     210         88
                 Charcoal (earth kilns)         308        128
Reference (38)
Plantations can provide rural employment (115) of some 150-500 person-days/hectare
during the first three years and almost twice that amount
during harvesting (127).  Additionally, plantations and planting trees
generally can provide very important environmental benefits.  Among these
are stabilizing and protecting soils from wind and water erosion, providing
protection to birds (which may eat crop-destroying insects -- or
the crops themselves) and other animals, and providing important soil
nutrients.   These are reviewed in (155).
Monocropping plantations, however, ignore the many traditional non-fuel
uses of forests such as food, fiber, medicines, and others (128).   Some
fast-growing species such as Eucalyptus, though productive and hardy, may
also deplete ground water supplies and soils, be inedible as livestock
fodder, and impede neighboring crop growth (5,99).  For other species,
however, interplanting with crops can be valuable.  Acacia albida can
increase yields of millet and sorghum by up to 3-4 times by fixing nitrogen
and by pumping other nutrients from deep within the soil.   Additionally
it provides large amounts of cattle fodder during the dry season
(102).   Other valuable species include the Tamarisk, used in southern Iran
to control salinity (129).
Some countries have begun to develop substantial plantations.   Brazil, for
example, has successfully planted 5 million hectares, mostly fast-growing
Eucalyptus, for fuel and pulp since 1970 (67).  In contrast, in Tanzania
an estimated 200,000 hectares of plantation were needed in 1983 to meet
the country's needs, but only 7300 were to be planted (47).  Substantial
progress is being made, despite sometimes high costs -- over $1000 per
hectare in places, yields that have sometimes been far below expectations
(127,130), and numerous other problems (5,99,116,125,131,132,155).   In
parts of Kenya, for example, individual woodlots are now being established

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widely (140).  In Table 19 several fossil and renewable fuels are compared
on the basis of their cost and the performance of the stoves used with
them.   As seen there, fuelwood is far less expensive than petroleum based
fuels or other renewable energy options.  Although this cost advantage
will decrease in arid regions, it will likely still be significant.
Village woodlots may further reduce the cost of fuelwood (Note 157-C).
Thus, wood will be a primary energy source in developing countries for the
foreseeable future.
As a third response, improving the efficiency with which biomass fuels are
used could greatly extend forest resources and at a very low cost.   In
this case, the cost advantage of wood as a cooking fuel becomes even more
apparent (Table 19).  The importance of the results shown in Table 19
cannot be overemphasized.  No other energy resource comes close to the
cost advantage of wood used in fuel efficient stoves.   Certainly, as
incomes rise the cleanliness and convenience of higher quality fuels such
as kerosene, LPG, or ethanol will be gladly paid for; but this is not now
a viable option for many of the world's poor.  Thus, a significant effort
must be focused on the development of stoves that burn wood, but do so
cleanly and safely, with high efficiency, and that are easily controlled.
The cost of saving energy by using an improved stove can also be compared
to the cost of producing fuelwood.  A typical household of eight people
who use fuelwood for cooking on a traditional stove (thermal efficiency of
17%) at a rate of 300 watts/person will consume about 150 GJ of energy in
a two-year period.  Alternatively, if this same household did their
cooking on two $3 improved channel-type woodstoves, which have observed
fuel savings of 30-40% in the field (thermal efficiency of 30%, Chapter
V), they would only consume 90-105 GJ over the two-year life of these
stoves.   The energy savings would be achieved at a cost of just $0.10-0.13/GJ
-- a factor of 10 less than the cost of plantation produced
fuelwood (Table 19).  The energy needed to produce these stoves does not
change this result.  Currently, 0.022-0.027 GJ/kg is needed to produce
steel from raw ore and new industrial processes could reduce this to
0.009-0.012 GJ/kg (136).  A typical stove might use 2-3 kg of steel and
thus require 0.1 GJ to produce while saving 25 GJ or more over its
Comparing these options in this manner is not intended to argue that
improved stoves are a substitute for planting trees.  Both are needed now
and both are important components of any longer-term energy strategy.
The cost of providing such fuel efficient stoves to every family on earth
now using biomass fuels for cooking would be less than a typical 1 GW
nuclear power plant, yet save some 10-20 times as much energy each year as
the reactor would produce during its entire lifetime (153).   The design,
production, and dissemination of low-cost, fuel efficient biomass stoves
and other technologies are the subjects of the following chapters.
In this chapter the basic physical principles of combustion and heat
transfer will be applied to the design of cookstoves burning raw biomass
fuels such as wood and agricultural wastes and guidelines for improving
their efficiency will be developed.  These guidelines form the basis for
the development of highly fuel efficient stoves.  These are, however,
guidelines only.  To determine accurately the effects on performance of
various design modifications and to optimize a design requires painstaking
testing as described in Chapter V.  The actual combustion and heat transfer
processes occurring in a stove are too complicated, too highly interdependent,
and too variable to model and predict easily.  Testing is a must.
To begin understanding how to improve the performance of a stove, both the
theoretical limits as well as the current practical limits to stove
performance must be understood.  The theoretical limits are examined first.
Consider, for example, cooking rice or porridge.  As shown in Table 1,
heating the appropriate amounts of dry grain and water to boiling and
inducing the necessary chemical reactions requires, in this ideal case,
the equivalent of about 18 grams of wood per kilogram of cooked food.   Yet,
controlled cooking tests with the open fire have required some 268 grams
of wood per kilogram of food cooked and even improved metal stoves have
used some 160 grams -- nine times the theoretical requirement.   (Chapter V
and reference 2).
To determine where the rest of this energy is lost requires detailed
experimental work, including monitoring stove wall temperatures, flue gas
temperatures and volumes, and emissions, and has only been done in a few

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special cases (3-5).  Some of these are sketched in Figure 1 below.
                                    TABLE 1
                          Energy Required For Cooking
            Specific             Temperature       Energy Required    Total     Wood Equivalent
              Heat                                  for Chemical      Cooking       (grams)
Food         kJ/kg[degrees]C    Change [degrees]C      Reactions       Energy       per kg Food
                                                      kJ/kg          kJ/kg          Cooked
Rice          1.76-1.84               80                 172           330(*)           18
Flour         1.80-1.88               80                 172           330(*)           18
Lentils          1.84                 80                 172            330(*)          18
Meat          2.01-3.89               80                 --           160-310          9-17
Potatoes         3.51                 80                 --            280              16
Vegetables       3.89                 80                 --             310             17
(*) This includes sufficient water for cooking but none for evaporation
(**) For wood with a calorific value of 18 MJ/kg.
References (1,3).
From these heat balances, several observations can be made.
  o Generally the largest loss, 14-42% of the input energy, is by beat
    conduction into and through the walls.  In massive stoves

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    stove (Figure lb) it is conducted through and lost from the outside

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  o The loss of energy in hot flue gas accounts for some 22-39% of the
    total input to the woodstove.   The energy efficiency of a stove can be
    dramatically increased by making use of the energy in this hot flue gas
    through improved convective heat transfer to the pot.
  o Although not explicitly detailed in Figure 1a, in open fires radiant

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    heat transfer is the mechanism for two-thirds of the heat transfer to
    the pot and cannot be greatly increased (7).
  o The energy losses due to incomplete combustion are relatively small,
    typically less than 8% of the input energy.  The greater problem with
    incomplete combustion is the emission of poisonous carbon monoxide and
    hydrocarbons -- many of which are toxic, even carcinogenic (8).
  o Typically half the energy entering the pot is lost in the form of steam

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    losses also occur in getting that energy into the pot.  Eliminating this
    steam loss by more carefully controlling the fire could, in principle,
    reduce total energy use by half.   Similarly, convective heat losses from
    the surface of the pot are quite important (Figure 1d).  For typical pot

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    loss rates of 700 W/[m.sup.2] (42,43), a 28-cm-diameter cylindrical pot with
    10-cm exposed to ambient air will lose energy at the rate of 100 W.
    Over an hour, this is energetically equivalent to 20 grams of wood.
FIGURE 1: Heat Balances In Cooking Stoves
Figure 1a: Traditional Open Fire
Final Energy Balance:
8% absorbed by water and food
10% lost by evaporation from pot
82% lost to environment
Reference (6)
Figure 1b: Two pot uninsulated metal
wood stove with chimney.
Final Energy Balance:
17.6% absorbed by first pot
10.3% absorbed by second pot
      the fraction lost by evaporation
      from pots is unknown
   2% absorbed by stove body
40.4% lost by convection and radiation
      from stove body
22.2% lost as thermal energy in
      flue gases
 7.8% lost due to incomplete combustion
Reference (5)
Figure 1c: Two pot massive wood
stove with chimney.
Final Energy Balance:
11.8% absorbed by first pot
 3.6% absorbed by second pot
29.2% absorbed by stove body
 1.9% lost by convection and radiation
      from stove body
39.0% lost as thermal energy in
      flue gases
 2.7% lost due to incomplete combustion
11.8% unaccounted for
Reference (5)
Figure 1d: Three pot mass wood
stove with chimney.
Final Energy Balance:
   6% absorbed by water and food
   4% lost by evaporation from pots
 2.1% lost from pot surfaces
13.9% absorbed by stove body
30.2% lost as thermal energy in
      flue gases
 1.1% lost as carbon monoxide
 1.9% lost to evaporate moisture in
 5.9% lost as latent heat of vaporization
      of water produced
      by combustion
 11.% lost as charcoal residue
Reference (3)
Figure 1e: Thai charcoal stove.
Final Energy Balance:
 3.1% absorbed by water and food
 4.6% lost by evaporation from pot
 0.2% lost by convection and
      radiation from pot lid
13.0% absorbed by stove body
 1.3% lost by convection and radiation
      from stove body
 2.1% lost as thermal energy in
      flue gases
 0.7% lost as carbon monoxide due
      to incomplete combustion
 75.% lost in the conversion of
      wood to charcoal
Reference (4)
Improving the fuel efficiency of a stove thus requires attention to a
number of different factors.  Among these are:
    Combustion Efficiency: so that as much of the energy stored in the combustible
    as possible is released as heat.
    Heat Transfer Efficiency: so that as much of the heat generated as
    possible is actually transferred to the contents of the pot.  This
    includes conductive, convective, and radiative heat transfer processes.
    Control Efficiency: so that only as much heat as is needed to cook the
    food is generated.
    Pot Efficiency: so that as much of the heat that reaches the contents
    of the pot as possible remains there to cook the food.
    Cooking Process Efficiency: so that as little energy as possible is
    used to cause the physico-chemical changes ocurring in cooking food.
The combustion and heat transfer efficiencies are often combined for
convenience and are then termed the thermal efficiency of the stove.   When
they are also combined with the control efficiency, the three together are
termed the stove efficiency.  Different tests measure different combinations
of these factors.  High power water boiling tests, for example,
measure the thermal efficiency.  High/low power water boiling tests and
controlled cooking tests are two different methods of measuring the stove
The heat transfer efficiency will be discussed first in terms of the
conductive, convective, and radiative processes going on in and around the
stove.   These processes are sketched in Figure 2.  The other aspects of

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efficiency will be discussed in turn.  The appendixes document the text in
detail and provide extensive references for further reading.
The temperature of a solid, liquid, or gas is a measure of how rapidly the
atoms and molecules within it are moving:  the faster they are moving the
hotter the substance is.  In gases and liquids, conductive heat transfer
occurs when high velocity molecules randomly collide with slower molecules,
giving up some of their energy.  In this way, heat is gradually
transferred from higher temperature regions to those at lower temperatures.
Because of their low density and the consequent low collision rate
between molecules, gases have a low thermal conductivity.   High quality
insulators take advantage of this by trapping millions of miniscule air
pockets in a matrix of (very porous or spongy) material: most of such
insulators is in fact air.  The solid material is there only to hold the
air in place -- to prevent currents of air that would increase the heat
transfer rate.  Thus, such insulators lose some of their insulating value
if they are compressed, which reduces the size of the air pockets, or get
wet, which fills the air pockets with higher conductivity water.
                                    TABLE 2
                    Typical Property Values at 20[degrees]C
Material                  Thermal             Density         Specific Heat
                       Conductivity        kg/[m.sup.3]       J/kg[degrees]C
Metals                   W/m[degrees]C(*)
  Steel Alloys            35 (10-70)        7700-8000         450-480
Nonmetallic solids
  Cement                  0.8-1.4           1900-2300           880
  Fiberglass               0.04                200              670
  Water                    0.597               1000             4180
  Air                      0.026               1.177            1000
(*) See Appendix I for the definition and conversion of units.
Reference (9). A more complete table is given in Appendix A.
In a solid, heat is conducted as more rapidly vibrating atoms excite and
speed up the vibration rate of more slowly moving neighbors.   Additionally,
in metals heat is conducted as free electrons with a high velocity move
from regions at a high temperature into regions at a lower temperature
where they collide with and excite atoms.  In general, heat conduction by
such electrons is much more effective than that by adjacent atoms exciting
each other.  For this reason, metals (which conduct electricity) have much
higher thermal conductivities than electrically insulating solids.
A brief table of thermal conductivities and other factors is presented in
Table 2 above.  The points just made about the low conductivity of gases,
the high conductivity of metals, and quality insulators being mostly air
(notice the low density) can be clearly seen in this table.
Calculating Thermal Conductivity

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The thermal conductivity of an object can
be expressed approximately by the equation
       kA([T.sub.1] - [T.sub.2])
   Q= ---------------------------            (1)
where Q is the rate of heat transfer, k is
the thermal conductivity of the material,
A is the area, s is the thickness of the
object across which heat is being conducted,
and ([T.sub.1-[T.sub.2]) is the temperature difference
between the hot and cold sides.  Thus, we see that if the plate is
large and thin (A/s large) the rate of heat tranfer will be large. If the
plate is small in area and thick, more like a rod (A/s small), the rate of
heat transfer will be small.  The heat transfer also varies directly with
the thermal conductivity and the temperature difference across the object
(Appendix A).
However, using this equation alone for the heat transfer across a stove
wall would lead to values that are many times too large.  The heat transfer
into and out of an object depends on the conductivities to and from the
surfaces as well as the conductivity within the object itself (Appendix
A).   In some cases, dirt or oxide layers may reduce the heat transfer
across the surface; in other cases, the air at the surface itself significantly
reduces the heat transfer.  Taking this into account then gives
           A([T.sub.1] - [T.sub.2])
       Q = ------------------------
           1          s        1
           -       +  -   +     -
        [h.sub.1]     k     [h.sub.2]                                         (2)
where [h.sub.1] and [h.sub.2] are the inner and outer surface heat transfer coefficients
(Appendix B).  Typical values for h are 5 W/[m.sup.2][degrees]C in still air to over 15
W/[m.sup.2][degrees]C in a moderate 3 m/s wind.  The inverse values 1/h and s/k are the
thermal resistances to heat transfer.  Typical values of the thermal
resistances (s/k) for different stove walls are 0.0000286 [m.sup.2][degrees]C/W for 1-mm-thick
steel, 0.04 [m.sup.2][degrees]C/W for 2-cm-thick fired clay, and 0.10 [m.sup.2][degrees]C/W for a
10-cm-thick concrete wall.  In contrast, the thermal resistance of the air
at the surface of the stove wall (1/h) is 0.2 [m.sup.2][degrees]C/W for still air and
0.0667 [m.sup.2][degrees]C/W for a 3 m/s wind.  These values must then be doubled to
account for both the inside and outside surfaces.
Thus, it is the surface resistance, not the resistance to heat transfer of
the material itself, that primarily determines the rate of heat loss
through the stove wall.  This is true until very low conductivity (high
thermal resistance) materials such as fiberglass insulation are used.
Fiberglass, for example, has a thermal resistance (1/k) typically about 25
m[degrees]C/W or, for a 4-cm-thick lining, a total resistance (s/k) of about I
[m.sup.2][degrees]C/W.   In this case the insulation, not the resistance of the surface
air layers, is the primary determinant of the stove's rate of heat loss.
The steady state rate of heat loss through a metal stove wall can now be
crudely estimated.  If the wall has an area of 1mx0.2m-0.2[m.sup.2], a temperature
difference of 500[degrees]C between the inside and outside, and is in still air
         Q= ------------------------   = 250 watts
            (.2) + (0.0000286) + (.2)
If the resistance of the surface boundary layer of air had been ignored, a
rate of heat loss 14,000 times greater would have been calculated -- an
absurdly large value.
Conductive heat transfer also carries heat through the pot to its contents.
High conductivity aluminum pots can save energy compared to clay
pots because they more readily conduct the heat of the fire to the food.
At the same time, however, aluminum pots will suffer greater heat loss
than clay pots from the warm interior to the portions of the exterior exposed
to cold ambient air.  These portions of the pot could be insulated to
reduce this heat loss.  The overall heat transfer coefficient of aluminum
pots has been estimated to be about 18 W/[m.sup.2][degrees]C compared to 9.7 W/[m.sup.2][degrees]C for
clay pots (3,10).  In controlled cooking tests with aluminum pots, fuel
savings were about 45% (3) compared to using clay pots.  Coating aluminum
pots with mud to protect their shine, or allowing a thick layer of soot to
build up on the outside reduce the pots' energy efficiency and should be
discouraged.   In addition to their high performance and ease of use cooks
prefer aluminum pots because, unlike traditional fired clay pots, they
won't break.  In a very few years the production and use of aluminum pots
has spread widely in many developing countries.
Calculating Thermal Storage
Another factor of importance in conductive heat transfer calculations is
the ability of a material to store thermal energy, measured as its
specific heat.  The specific heat of a material is the amount of energy
required to raise the temperature of 1 kg of its mass by 1[degrees]C.   For a given
object, the change in the total heat stored is then given by
        dE - [MC.sub.p](dT)                                                    (3)
where M is the object's mass, [C.sub.p] is its specific heat, and (dT) is its
change in temperature.  Thus, if the wall of a 3 kg metal stove increases
by 380[degrees]C during use, the change in energy stored in its wall is
      dE = (3kg)(480Ws/kg[degrees]C)(380[degrees]C) = 547200 Ws or 547.2 kJ
Thus, the thermal conductivity carries thermal energy through a material;
the specific heat and mass of an object store this heat energy.   The
larger the mass and specific heat of an object the more energy it can
store for a given change in temperature.  Thus a thermally massive (large
[MC.sub.p]) object warms up slowly; a thermally lightweight (small [MC.sub.p]) object
will warm rapidly.   This is called the thermal inertia of an object and is
an important design parameter in stoves.
Wall Loss Calculations
Reducing the heat loss into and through the stove walls to the outside
requires a detailed analysis of the conduction process, which is presented
in Appendix A.  In reviewing these calculations, it is important to note
first that they are based on a particular assumed combustion chamber
geometry and heat flux from the fire.  Because of this, the values listed
below are in watts, degrees, etc., rather than in dimensionless units.
Second, for simplicity and convenience the calculations were done assuming
that the fire is kept at a single power level all the time.  Thus, the
results listed are intermediate between those observed in practice for the
high power boiling phase and the low power simmering phase due to the
assumed values for the heat fluxes.  Although the values given are shifted
by these factors, they nevertheless show trends that will remain the same
for any combustion chamber.
When cooking begins, the walls of the stove are cold.  With time they warm
up at a rate determined by their mass and specific heat as discussed
above.   Lightweight walls have a low thermal inertia and warm quickly.
Thick, heavy walls warm more slowly.  Heat loss from the combustion chamber
is determined by how quickly these walls warm and subsequently how much
heat the wall loses from its outside surface.  This is shown clearly in

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Figure 4, where the thicker the wall the more slowly it warms.
Although a thick wall of dense high specific heat material may have
slightly lower heat loss than a thinner wall after several hours (See
Appendix A), it takes many hours more for the eventual lower heat loss of
the thick wall to compensate for its much greater absorption of heat to
warm up to this state.  Thus, it is always preferable to make the solid
(non-insulator) portion of the wall as thin and light as possible.
Additionally, the use of lightweight insulants such as fiberglass or

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double wall construction can dramatically lower heat loss (Figure 4B).
Materials such as sand-clay or concrete, which have a high specific heat
and density, and which must be formed in thick sections to be sufficiently
strong to support a pot or resist the fire, should therefore be avoided.
Heat Recuperation
It has frequently been argued that the large amounts of heat absorbed by
the walls of a massive stove should be utilized by either extinguishing
the fire early and using this heat to complete cooking or by later using
it to heat water.  Water heating tests on hot massive stoves, however, have
shown that only 0.6-1.3% of the energy released by the fire, of which
perhaps one-third was stored in the massive wall, could be recuperated -- heating
the water by typically 18-19[degrees]C (2).  What is often thought to be
heating or cooking by heat recuperation is actually done by the remaining
coals of the fire.
That heat recuperation from massive walls is so difficult can be easily
understood by considering the following.  First, heat conduction through
the wall is slow (Appendix A) so that little energy can be transported to
the pot directly.  Second, air is a relatively good insulator.  Thus, little
heat can be carried from the wall into the air space inside the stove and
then to the pot.  Third, both of these heat paths are further slowed by the
relatively small temperature difference between the wall and the pot.   The
low temperature of the wall also reduces the radiant transfer to the pot.
Finally, the heat stored in the wall tends to equilibrate within the wall
and then leak to the outside.  The result of all these processes is shown

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in Figure 6 and agrees very well with the experimental data cited above.
Rather than depending on low efficiency massive stoves (Table V-1) for
cooking and then attempting to recuperate heat for hot water, such water
heating can be much more efficiently done directly with a high performance
stove.   Further, it can then be done when needed rather than being tied to
the cooking schedule.  Similarly, using stored heat to complete cooking is
an extremely inefficient technique compared to using a high efficiency
lightweight stove and possibly a "haybox" cooker (discussed below under
Heat recuperation is clearly desirable, however, when it can be done
efficiently, cost effectively, and without excessively interfering with
the primary purpose of the device.  For example, heating water by heat
recuperation might be efficiently done by forming the wall of a high
performance metal stove itself into a water tank.  Heat that would otherwise
be lost into and through the wall would then instead be directly
absorbed by the water.  Whether   or not the lower average combustion
chamber temperatures would significantly reduce the pot heating efficiency
or interfere with combustion would need to be tested.
Thus, lightweight walls have the intrinsic potential for much higher
performance than massive walls due to their lower thermal inertia.   This
does not, however, necessarily mean that a lightweight stove will automatically
save energy or that a massive stove cannot.  For a lightweight
stove to save energy its heat loss to the exterior must also be minimized
and the convective and radiant heat transfer to its pot must be optimized.
Conversely, massive stoves can and sometimes do save energy despite their
large wall losses.  Such stoves can save energy if the convective and
radiative heat transfer to the pot is carefully optimized.
Reducing Wall Losses
If a lightweight single wall (metal) stove is heavily tarnished and sooted

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on the outside its exterior heat loss can be quite large (Figure 5).   This
heat loss is due to the emission of radiant energy (see Appendix C) and
can be reduced by chemically or mechanically polishing or coating the
exterior surface to leave a bright metallic finish.  Although such a finish
may have commercial appeal, its effectiveness in reducing heat loss will
last only so long as it is kept relatively clean and free of soot and
rust, etc.  It should be noted that most paints, even white paint, will
actually increase the radiant heat loss from a stove and should be
avoided; to decrease radiant heat loss, the surface must be metallic.
Lighweight single wall stoves are easy to construct, are low cost, and
have relatively high performance when convective heat transfer is optimized.
However, during use they can be quite hot on the outside and can

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burn the user as well as be uncomfortable to use (Table 3).  To reduce heat
loss and thus reduce this hazard, either double wall construction and/or
lightweight insulants such as fiberglass or vermiculite can be used.
Double wall construction with metal alone can significantly reduce heat
loss (Figure 5), user discomfort, and the hazard of burns (Table 3).   The
double wall serves two functions in reducing heat loss.  First, the dead
air space between the two walls is a moderately good insulator.   It should
be noted, however, that increasing the thickness of this dead air space
does not improve its insulating value.  This is due to the convection
currents, which flow more freely the larger the space, carrying heat from
one wall to the other.  Second, the inner wall acts as a radiation shield
between the fire and the outer wall.  Both of these factors can be seen in
Figure 5. There, the emissivity or, more accurately, the radiant coupling
between the inner and outer walls is the prime determinant of heat loss.
The exterior surface emissivity is less important due to the lower temperature
of that wall.  As the temperature of the exterior wall increases due
to greater radiant heat transfer from inner to outer wall ([[epsilon].sub.i] increasing)
the exterior emissivity, [[epsilon].sub.e], becomes more important (Appendix C).
In practice there are several potential difficulties:
o   Although it is preferable to minimize radiant coupling between the two
   walls by giving them a bright, long-lasting metallic finish, they will
   tend to rust, tarnish, and soot over time.  Keeping them clean would be
   difficult.  Even in the worst case ([[epsilon].sub.1] = .9, [[epsilon].sub.e] .9), however, the double
   wall still performs better than the best ([epsilon].sub.e] = .9) single metal wall.
o   The dead air space is a good insulator on its own, but attaching the
   inner wall to the outer will tend to short circuit its insulating value
   due to the high thermal conductivity of metal.  It is necessary that the
   two walls together be mechanically rigid, but they should not easily
   conduct heat from one to the other.   This might be done by using nonmetallic
   spacers or fasteners, or tack welding the walls together at
   selected points.   Long continuous welds should be avoided if possible.
o   The insulating value of the dead air space is reduced if air is allowed
   to flow through.   Thus, the dead air space should be closed at the top.
Double wall metal stoves are now being developed and commercialized in
Botswana (11,12) and Guinea (13).
Better yet is to use a high quality insulant such as fiberglass or
vermiculite with the double wall to hold it in place and protect it.   As
seen in Figure 5, layers of insulation as thin as a few millimeters are
effective in reducing heat loss.  Such stoves have been tested in Mali
(14).   Other lightweight insulants worth investigating include wood ash,
diatomaceous earth, and, possibly, chemically treated (to reduce its
flammability) straw or charcoal among others (see Table A-1).
Just as insulated walls reduce the exterior temperatures (Table 3), they
increase the inner wall temperature.  This can increase heat transfer to
the pot by convective heat transfer, by radiative heat transfer from the
inner wall surface, and possibly by improving the quality of combustion.
Convective heat transfer occurs when a gas or liquid is forced or flows
naturally into a region at a different temperature and then exchanges heat
energy by conduction - - by the interaction of individual particles.   It is
by convective heat transfer that the hot gas leaving the fire heats the
pot, or that the wind cools a hot stove.  In open fires and many traditional

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stoves much of the heating potential of this gas is lost (Figure 1).
Increasing convective heat transfer to the pot is the single most
important way to increase the thermal efficiency of a woodburning stove.
Increasing Convective Heat Transfer
In general, convective heat transfer is given empirically by the equation:
         Q = hA([T.sub.1]-[T.sub.2])                                    (4)
For the case of a pot being heated by hot gas leaving the fire, Q is the
heat transferred from the gas to the pot, h is the convective heat
transfer coefficient, A is the area of the pot across which the heat
exchange takes place, and ([T.sub.1]-[T.sub.2]) is the temperature difference between
the hot gas and the pot.
To increase the heat transfer Q to the pot there are then, in principle,
three things one can do.  First, the temperature [T.sub.1] of the hot gas can be
increased.   This can be done only by closing the stove and controlling the
amount of outside air that enters.  This is often impractical as it
requires manipulating a door on the wood entry, prevents easy visual monitoring
of fire, and usually requires cutting the wood into small pieces so
that the door can be closed behind them.  Further, the user must consistently
close the door.  Stoves with enclosed fireboxes are, however, being
developed and disseminated in India (15-18).  If successful on a large
scale, this is an important innovation.
Second, as much of the area A of the pot should be exposed to the hot gas
as possible.  This is very important.   The pot supports, for example, must
be strong enough to support the pot but should be kept small in area so as
not to screen the hot gas from the pot.  The gas should be allowed to rise
up around the pot and contact its entire surface.
Third, the convective heat transfer coefficient h should be increased.
This can be done by increasing the velocity of the hot gas as it flows
past the pot.
In convective heat transfer, the primary resistance to heat flow is not
within the solid object (unless it is a very good insulator), nor within
the flowing hot gas.  Instead, the primary resistance is in the "surface
boundary layer" of very slowly moving gas immediately adjacent to a wall.
Far from a wall, gas flows freely and readily carries heat with it.   As the
pot wall is approached, friction between the pot and the gas prevents the
gas from flowing easily, Within this region, heat transfer is primarily by
conduction and, as previously noted, the conductivity of gases is quite
low.   It is this surface boundary layer of stagnant gas that primarily
limits heat transfer from the flowing hot gas to the pot.
To improve the thermal efficiency of a stove, the thermal resistance of
this boundary layer must be reduced.  This can be accomplished by (among
others) increasing the flow velocity of the hot gas over the surface of
the pot.   This rapid flow helps "peel" away some of this surface boundary
layer and, thinner, the boundary layer of stagnant gas then offers less

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resistance to conductive heat transfer across it to the pot (Figure 7).
Fundamental Stove Types
Efforts to improve convective heat transfer have resulted in three
fundamental types of biomass stoves, which will be generically termed
multipot, channel, and nozzle (Figure 8).  In each of these, the flow

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velocity of the hot gas over the pot is increased by narrowing the
channel(1) gap through which the gas must flow past the pot.   (Because the
volume of hot gas flowing past any point is constant, its flow velocity
through a narrow gap must be faster than through a wider one).   This,
however, results in a serious handicap inherent in any improved stove
program.   As these channel gaps must be precise to within a few millimeters
to be effective, stove and pot dimensions must correspond and be precisely
determined - - greatly complicating both production and dissemination.
Multipot stoves heat two or more pots from a single fire.   In principle,
this increases the pot surface area exposed to the fire and hot gas and
raises the thermal efficiency.  In practice, however, it is difficult if
not impossible to individually control the heat input to each of the pots
(see OTHER ASPECTS).  The resulting stove efficiency is then usually lower
than channel or prototype nozzle stoves now under development.
Channel stoves increase the pot area exposed to the hot gas by forcing the
gas over as much of the surface of a single pot as practicable.   Radiant
transfer is maximized by placing the pot close to the firebed yet without
excessively interfering with the combustion.  Channel stoves offer higher
    (1) The channel dimensions are called "length" for the direction of gas
flow, "width" for the circumference of the pot or stove, and "gap" for the
space between the pot and stove walls.
efficiencies, better control, and lower cost than most multipot stoves.
Emissions from channel stoves, however, are often no less than from
multipot stoves and in some cases may be worse.
The development of nozzle type stoves has only recently begun (18,19), yet
they appear to offer considerable promise.  As for channel stoves, nozzle
stoves have a single pot, the entire surface of which is exposed to the
f ire and hot gas.  Similarly, as for both channel and multipot stoves,
nozzle stoves increase the velocity of the hot gases flowing past the pot
by forcing them through a narrow channel.  Additionally, the large height
and the narrowing throat of the nozzle stove's combustion chamber accelerate
the gases to a higher velocity before they contact the pot.  This is
done, however, at the expense of reduced radiant transfer.
Prototype nozzle stoves have achieved efficiencies of 43% in laboratory
tests (18,19), comparable to the best multipot stoves (15-17) and channel
stoves (14).  Further, because the shape of the combustion chamber improves
combustion, nozzle stoves have much lower emissions than other types.
Recent tests of nozzle stoves have shown emissions of carbon monoxide (CO)
to be just 5-6 ppm at peak power and of soot, less than 2.5 mg/[m.sup.3] (18,19).
These are far less than the open fire.  By comparison, typical emissions
from kerosene stoves at peak power are 25 ppm of CO and 0.2 mg/[m.sup.3] of soot.
Current prototypes, however, suffer the severe handicap of accepting only
very small pieces of biomass.  Whether or not this can be overcome remains
to be seen(2).
    (2) For further information, readers should contact H.S. Mukunda and U.
Shrinivasa at ASTRA (See Appendix J).
Modeling Convective Heat Transfer
Understanding convective heat transfer underpins all efforts to improve
the efficiency of biomass burning stoves.  A detailed empirical model of
convective heat transfer in channel stoves is developed in Appendix B;
references to an empirical model of multipot stoves are also provided
there.   Numerical analysis of convective heat transfer in channel and
nozzle stoves is now underway by the author and will be presented elsewhere.
Because channel stoves generally have much better performance than
multipot stoves and because they are more fully developed and tested than
nozzle stoves, critical elements in their design will be presented here.
The empirical model of convective heat transfer in channel stoves developed
in Appendix B provides considerable insight into their performance
and limitations.  This model is not sufficiently precise to be used to
predict the absolute quantitative performance of a real stove -- that can
only be done by detailed testing as discussed in Chapter V.  Nevertheless,
the model is useful in illustrating general trends in the performance of
this type of stove and its sensitivity to dimensional changes.
From the above discussion of convective heat transfer and surface boundary
layers one expects narrower channels to have higher rates of heat transfer
to the walls.  This is clearly seen in the model predictions presented in
Figure 9.  In fact, the channel efficiency, defined as the fraction of
energy in the hot gas entering the channel that is transferred to the pot,
is extremely sensitive to changes in the channel gap.  For a 10-cm-long
channel, the channel efficiency drops from 46% for an 8-mm gap to 26% for
a 10-mm gap.  Thus the stove and pot dimensions must be very precisely
controlled.   Multipot and nozzle stove performance is similarly sensitive
to the channel gap.
The lower efficiency of wide channel gaps can be partially compensated for

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by making the channel longer (Figure 9) or by closing the combustion
chamber to control excess air and thus raising the average gas temperatures
(Appendix B).  However, closing the firebox is often not practical,
as discussed below under Radiation, and longer channels can seldom fully

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compensate (Figures 9,11).  As seen in Figure 9B, additional channel length

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is also less and less effective.  As the gases in the channel rise and
give up their heat, their temperature drops.  Additional channel length is
trying to recuperate energy from this increasingly lower temperature
(lower quality) heat source.  For the 4-mm gap, effectively all the energy
in the gas that can be is recuperated in the first 2 cm length of the
channel.   Channels longer than 5 cm are useless.   For the 6-mm gap, the
first 5 cm length recuperates 57% of the energy in the gas, the next 5 cm
recuperate an additional 16%, the next 5 cm an additional 8%, and so on.
Whether the additional length is worthwhile depends on local fuelwood
prices, the construction costs for longer channels, and other factors.
This can only be determined by careful testing of the stove to determine
the actual performance tradeoffs of channel width and length and the
resulting financial benefits.
Although narrow channels have high efficiencies, they also reduce the
amount of gas that can flow through the channel and thus limit the

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firepower (Figure 10).  With a too narrow channel or a too large fire
either the smoke will pour out the stove door, or else the fire will be
choked and suffer poor combustion or simply not build up to the desired
power.   In either case, stove efficiency suffers.   Additionally, with a
too narrow channel, there will be such a small fire that the pot cannot be
heated in a reasonable length of time.  Thus, the choice of optimum
channel width is a compromise between high efficiency and rapid heating.

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Figure 11 illustrates this compromise.
To translate the above results into a total stove efficiency, it will be
assumed here that the efficiency for the pot alone (due to radiation and
convection on its bottom) is 20% and that a third of the total firepower
is available in the hot gases entering the channel.  The total stove
efficiency is then 20% plus one-third of the channel efficiency.
With these assumptions the total stove efficiency can be graphed versus
the total heat flux to the pot (Figure 11).  Now the tradeoffs between
channel gap and length and between stove efficiency and heating rate can
be clearly seen.  For example a stove (0.3-m diameter) with about a 40%
total efficiency could have a channel gap of 6 mm and length of 5 cm or
one of 8 mm by 20 cm.  However, the 6-mm stove would have a peak heat flux
to the pot of 1.3 kW while the 8-mm stove would provide nearly 3 kW.   In
fact, for reasonable channel lengths, the 6-mm channel could never reach 2
kW.   Similarly, if a stove capable of providing 4 kW to the pot was needed,
a channel gap of about 9-10 mm would be necessary (4 kW will raise 10
liters of water to boiling in about 14 minutes).  Thus, higher total stove
efficiencies can be achieved but must be balanced with the heating rate
and possibly the cost of constructing a long channel.  It should be
remembered, however, that all of these efficiencies and resulting heating
rates are higher than those of the protected open fire.
To this point, the hypothetical stove model has been operated at its
optimum power level.  At powers greater than the optimum the combustion
gases cannot all escape out the channel and instead must flow out the door
or perhaps suffocate the fire and lower the combustion quality.   At powers
below the optimum, the gas flow through the channel will remain about the
same but will be at a lower temperature due to more entrained air (less
gas at a higher temperature will accelerate due to its larger buoyancy and
pull in cold air until it reaches a new, lower temperature equilibrium
flow rate).  In either case, the efficiency drops.  Experimental work has
shown that for a variety of stoves the efficiency has a maximum at a
particular fire power (5).
From Figure 11, it can be seen that to allow rapid initial heating, a
larger channel gap may be needed: during simmering, the stove efficiency
then suffers.  Alternatively, if a slightly narrower channel gap is chosen,
the higher efficiency during the simmering phase will be at the expense of
slower initial heating.  A variable channel gap would be desirable, but is
difficult to realize in practice.  Depending on how sensitive the stove
efficiency is to the power level, a compromise between rapid heating and
efficient simmering may be necessary.  This choice must be determined in
part by the types of food to be cooked.  If cooking times are short,
heating should be emphasized; if long, simmering efficiency may be more
important.   Fortunately, these tradeoffs are not usually very severe.
For any estimated heat flux from Figure 11, the time required for the pot
to come to a boil is given by
        t = 4.186x[10.sup.3]V[delta(difference)]T
            ------------------------------------- minutes
where V is the volume of water in the pot in [m.sup.3], [delta(difference)]T is the temperature
change in the water to reach boiling, and P is the heat flux to the pot in
kW from Figure 11.  Additionally, the heat loss of approximately 0.7 kW/[m.sup.3]
from the lid (at T-100[degrees]C) should be subtracted from P (39) but is ignored
here.   Thus, for an industrial stove with G=14mm, L=0.5m, V=0.5 [m.sup.3] and
[delta]T=80[degrees]C, the time to reach boiling is t=71 minutes.
Finally, it is important to note that insulating the walls assists

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convective heat transfer (Figure 12).  For stoves with dimensions optimized
for convective heat transfer, this can be a significant potential.
The necessary precision of a few millimeter in the channel gap dimensions
found above has some very important consequences.  Such high precision in
stove and pot dimensions requires centralized artisanal or industrial mass
production based on standardized templates and molds.  Owner-built or
site-built stoves can rarely be made so precisely.  In those few cases
where they are, it is all but impossible to replicate the feat on a large
scale involving many thousands of stoves and stove builders in widely
separated locations.  Such precision also implies that stoves should not
be made of sand-clay, concrete, or other materials in which dimensional
control is difficult.  For these materials, walls of sufficient strength
to support the pot are also so thick that they shield much of the pot from
the hot gas -- reducing convective heat transfer.
Many design variations are possible that will help reduce these problems.

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Vertical walls, as shown for the channel stoves in Figure 8 and the inset
diagrams of Figures 9 and 11, strictly limit the acceptable pot size to
within a few millimeter of the optimum.  Nor can this limitation be avoided
if the stove and pot walls have the same shape.  In many cases, however, a
spherical pot will be used with a straight-sided stove wall (Chapter IV--Template
Design: Cylindrical Stoves).  In this case, if the walls where the
pot sits are steeply sloped (Figure 8 nozzle stove) and a strip of metal
is used to support the pot the desired channel width from the stove wall,
large variations in pot size can be accommodated.  Larger pots will sit
further from the fire, but the decrease in radiant heat transfer will be
in part compensated by the increased surface area for convective transfer.
All objects (materials) continuously emit electromagnetic radiation due to
internal molecular and atomic motion.  The higher the object's temperature,
the greater the amount of energy so radiated.  The warmth felt on one's
skin when standing near a fire (but not in the hot gases) is due to
infrared radiation from the fire.  The temperature of the object can also
be estimated by its color, ranging from 500[degrees]C when glowing dark red to
800[degrees]C when bright cherry red to 1100[degrees]C when yellow and to 1500[degrees]C and more

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when white.  Figure 13 shows the amount of energy radiated by a "black
body" (an object that absorbs or emits radiation perfectly regardless of
wavelength) as a function of temperature.
Similarly, all objects absorb radiation, exciting their internal molecular
and atomic motion.  The ability of a specific material to absorb radiation
is equal to its ability to emit it.
Most real materials, however, are not perfect emitters or absorbers.
Metals, for example, are very poor absorbers (emitters) because the free
electrons within them that give rise to large electrical and thermal
conductivities also couple tightly to impinging radiation and screen its
penetration into the material -- causing it to reflect instead.   Gases such
as water vapor and carbon dioxide have strongly frequency-dependent
absorption in the infrared corresponding to excitation of vibrational and
rotational motion of individual molecules.  Typical emissivities range
from 0.05 for well polished metals to 0.95 for carbon black.  Table C-1
lists the (frequency independent) emissivities for a variety of materials.
In woodburning cookstoves, radiative heat transfer is an important factor
in the transfer of heat from the firebed and flames to the pot; from the
flames to the fuel to maintain combustion; from the firebed and flames to
the stove wall; from the stove wall to the pot; and from the stove wall to

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ambient (Figure 2).
In traditional stoves, typically 10-12 PHU(3) percentage points (out of
perhaps 17 total) are due to radiative heat transfer directly from the
firebed to the pot bottom (7).  This is the primary heat transfer mechanism
for the traditional open fire.
Calculating Radiative Heat Transfer
The radiative heat transfer from the firebed to the pot is determined by
the firebed temperature (Figure 13) and by the view factor between the
firebed and the pot (Figure 14).  The view factor is the fraction of energy
emitted by one surface that is intercepted by a second and is determined
entirely by the relative geometry of the two surfaces.
Consider, for example, a 30 cm diameter pot that is 12 cm above a 15 cm

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so that 57.5 percent of the radiation emitted by the firebed strikes the
pot.   If the firebed is at an average temperature of 1000 K, Figure 13
shows that it will emit about 56 kW/[m.sup.2].  Multiplying the firebed area
(0.0752 [m.sup.2]) by (56 kW/[m.sup.2]) and by (0.575) gives the energy intercepted by
the pot as 0.57 kW.
To heat the pot more effectively by radiation directly from the fuelbed,
the average fuelbed temperature could be increased (without increasing
fuel consumption).   Alternatively, the view factor could be increased by
lowering the pot closer to the fire or increasing the size of the pot
relative to the firebed.
  (3) PHU is Percent Heat Utilized, that is, the thermal efficiency of the
stove.   This is discussed in detail in Chapter V.
Closing the firebox and controlling the air supply could increase the
average firebed temperature but present numerous difficulties in practice.
With the firebox closed it is difficult to monitor the size and condition
of the fire.  It is also difficult to chop the wood into sufficiently small
pieces to fit inside.  Finally, many cooks will not bother to control the
air supply.
Moving the pot closer to the fire can also increase the radiative heat
transfer from the fire to the pot as seen in Figure 14.  For example, for
the firebed, [r.sub.1] = 7.5 cm, the pot [r.sub.2]=15 cm, and the height between them h=15
cms, [r.sub.2]/[r.sub.1]=2, h/[r.sub.1]=2 and F=0.47.   Reducing the height h to 12 cms, h/[r.sub.1]=1.6
and F=.57.  This is a substantial increase in the fraction of radiant heat
transferred from the fire to the pot.  Reducing the height, however, may
interfere with the combustion processes and increase CO and hydrocarbon
emissions; if too close the fire will be quenched.  In practice, channel
stoves with distances as small as 6 cm between the firebed (with a grate)
and a 27-cm-diameter pot have been tested and been shown to give increased
heat transfer and overall thermal efficiency, but the effect on the
combustion quality is unknown (20,21).  Traditional artisans have typically
set the distance between the firebed and pot at one-half the pot
diameter (22).  Until there are reliable experimental data correlating the
firebed to pot height with smoke and carbon monoxide emissions, it is
rather arbitrarily recommended that the pot to grate distance be no less
than 0.4 times the pot diameter.
The effect of radiative heat transfer from the firebed to the stove wall
and from the stove wall to ambient temperature has already been modeled

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and discussed in detail (Figures 4,5).  Similarly, measuring or calculating
(Appendix B) the inner wall temperatures enables one to estimate
(Appendix C) that a metal wall with 2 cm of fiberglass insulation can
provide up to 50% more radiant heat flux to the pot than a bare metal
wall.   The increased radiative and convective heat transfer possible when
wall losses are reduced by insulation can substantially increase overall
stove performance.  For example, insulating the exterior wall of a
prototype channel stove increased the stove's efficiency from about 33% to
about 41% and increased its predicted fuel economy relative to the open
fire from about 48% to about 57% -- a substantial improvement (14).
Using radiative transfer to heat a pot, as in channel stoves, has both
advantages and disadvantages.  The primary advantage is that radiative
transfer is insensitive to the pot shape and depends only on the view
factor between the firebed and pot(4).
One of the primary disadvantages of using radiative transfer to heat a pot
is that this heat loss reduces the average combustion chamber temperature
and can thus lower the quality of combustion and increase emissions.
Efforts have been made to avoid this problem by reducing radiative transfer
  (4) The potential of improved radiative and convective heat transfer is
indicated by development work on an advanced gas stove in which efficiencies
of 70% have been reached with very low outputs of CO and [NO.sub.x] (23).
out of the combustion chamber to the pot while increasing convective
heat transfer to the pot in compensation.  For channel stoves, although the
efficiency could be maintained the same, the increased reliance on convective
heat transfer reduced the peak fire power that could be reached (24).
For nozzle stoves, both high efficiencies (43%) and reasonable firepowers
(1-2 kW) have been achieved in prototypes (18,19), but further development
and testing is needed before field tests can begin.
Biomass combustion is an extremely complex process and its study involves
chemical kinetics; conductive, convective, and radiative heat transfer
processes; molecular diffusion; and other physical phenomena.   Realistic
modeling of these processes is not yet possible and useful results are
still almost entirely empirical (25).  Thus, experimental measurements of
biomass stove performance are always necessary and are discussed in detail
in Chapter V.  Because of the complexity of wood combustion, the following
will be limited to a brief and simple description of the chemical and
physical properties of wood and how it burns.  A somewhat more detailed
description along with extensive references is given in Appendix D.   As
noted in Figure 1, however, incomplete combustion typically accounts for
less than 10% of the energy losses in a stove.  Improving combustion in a
stove is therefore more important in reducing the health hazard of smoke
than in increasing overall stove efficiency.
Calorific Values
There are a variety of ways to evaluate wood as a combustible.   Of the
greatest practical importance are its calorific value and its moisture
content.   Calorific values are normally expressed as either gross calorific
value, also known as the higher heating value, or as the net calorific
value, also known as the lower heating value.  The gross calorific
value is defined as the heat liberated when the material is completely
burned to carbon dioxide and liquid water at 25[degrees]C.   The net calorific
value is the same except that the water is assumed to remain in the
gaseous phase (i. e., steam) at 100[degrees]C.  For cookstove designers and
testers, the net calorific value is the more useful.  As dry wood typically
is about 6% hydrogen by weight, about 0.54 kg of water will be
produced per kilogram of dry wood burned.  The heat absorbed to warm and
vaporize this water will then reduce the net calorific value about 1390
kJ/kg as compared to the gross calorific value.
Because all woods are similar in structure and chemical composition, their
calorific values are likewise comparable.  On the average, dry wood is
composed of 49.5% carbon, 6% hydrogen, 43.5% oxygen, and 1% mineral salts
by weight.  On a dry basis, the gross calorific value for hardwoods is
about 19,734[-or+]981 kJ/kg (over 268 species) and for softwoods is about
20,817[-or+]1479 kJ/kg (over 70 species).  Values for heartwood, sapwood, and
barks are within about 5% of these values (26).
The observed variation among species, given by the standard deviations
above, can be accounted for by slight differences in the proportions and
calorific values of the five main wood components: cellulose (17,500
kJ/kg), hemicellulose (17,500 kJ/kg), lignin (26,700 kJ/kg), resins
(34,900 kJ/kg), and mineral salts (0 kJ/kg) (18).  On the average, woods
are composed of roughly 40-50% cellulose, 15-25% hemicellulose, and 20-30%
lignin, with the other components comprising small percentages.   Calorific
values for other biomass materials are listed in Appendix D.
It is important to note that although wood densities can vary enormously,
their calorific value per kilogram does not.  Experimentally, the wood
density does not appreciably affect stove efficiency (27,28).   However,
for the same amount of energy, a very large volume (but roughly the same
mass) of low density woods or biomass materials such as corn or millet
stalks is required.  For a given combustion chamber volume, low density
fuels will need to be fed in much more frequently.
Moisture Content
The second most important way to evaluate biomass is by its moisture
content.   All biomass contains some water which must be evaporated before
the biomass can burn, thus reducing its effective calorific value.
However, tests have shown that net stove efficiency is improved slightly
if the wood has a moisture content of 10-20% (28,29).  This may be due to
the moisture helping to localize the fire and reducing the escape of the
volatiles out of the combustion zone before they can completely burn (29).
Alternatively, the water may provide additional OH radicals which assist
Moisture content (M.C.) can be expressed as either a percentage of the
total wet wood mass (oven dry wood plus water), or as a percentage of the
oven dry wood mass.  These can be written as follows and are graphed in

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Figure 15 below (30).
        [M.C..sub.wet] = water (kg)/[dry wood + water] (kg) x100% = water (kg)/wet wood (kg) x 100%
        [M.C..sub.dry] = water (kg)/dry wood (kg) x100%
Even when protected from the rain and air dried for a long period of time,
wood and other biomass can have a large amount of water in them.   The
moisture content of air dried wood has been estimated to be (31,32):
        [M.C..sub.dry] = 0.2 RH
where RH is the average relative humidity.  A much more detailed analysis
correlating the moisture content of the wood with both the relative
humidity and the temperature is given in (32).  Thus, in a tropical area
where the relative humidity averages 90%, the moisture content by this
equation will be 18% on a dry basis.  This equation is only indicative at
best, however.  Exposure to the rain, sun, or numerous other variables can
alter the moisture content.  For best accuracy, direct moisture content
measurements should be made by drying the wood in a kiln (Appendix F).
Knowing the moisture content is important.  In testing stoves the moisture
content strongly affects the estimated calorific value.   In using stoves,
it strongly affects the ease of burning.  The moisture content reduces the
effective calorific value of wood by just 2575 kJ/kg water -- the amount
of energy needed to raise the temperature of water to boiling and evaporate
it.   This should be compared to an oven dry calorific value for wood
of about 18000 kJ/kg.  However, it dramatically reduces the apparent
calorific value based on the weight of wet biomass (Figure 15).   For
example, a kilogram of wood with a 20% moisture content will have just
(0.8)(18000)-14,400 kJ of energy in it, of which about 515 will be used to
evaporate the water.  Instead of a presumed 18000 kJ of energy in the
kilogram of wood, there are only 13,900 kJ.  Thus, field measurements,
which are normally of only partially dried biomass, will significantly
overestimate the energy use by a family unless corrections for moisture
content are made.
A third manner in which biomass fuels are characterized is by their
volatile fraction.  Wood is typically composed of about 80% volatile
material and 20% fixed carbon.  In contrast, charcoal produced by traditional
kilns will typically be 80% fixed carbon and 20% volatiles, with
relative amounts of fixed carbon and volatiles depending strongly on the
manner in which it was made, particularly the maximum kiln temperature and
duration at that temperature (Table D-2).
Other chemical and physical properties of wood and biomass are discussed
in Appendix D.
The Combustion Process
The combustion of wood and other raw biomass is very complicated but can
be broken down crudely into the following steps:
o   The solid is heated to about 100[degrees]C and the absorbed water is boiled
   out of the wood or migrates along the wood grain to cooler areas and
   recondenses.   At slightly higher temperatures, water that is weakly bound to
   molecular groups is also driven off.  Heat transfer through the wood is
   primarily by conduction.
o   As the temperature increases to about 200[degrees]C, hemicellulose begins to
   decompose followed by cellulose.   (See Appendix D for a brief description
   of these materials).   Decomposition becomes extensive at temperatures
   around 300[degrees]C.   Typically only 8-15% of cellulose and hemicellulose
   remain as fixed carbon, and the remainder is released as volatile
   gases.  Roughly 50% of the lignin remains behind as fixed carbon.
   The volatiles produced by this decomposition may escape as smoke or may
   recondense inside the wood away from the heated zone.  This can often be
   seen as pitch oozing out the non-burning end of the wood.  Heat transfer
   into the wood is still primarily by conduction, but the volatiles
   flowing out of the heated zone carry some heat away by convection.
o   As the volatiles escape the wood, they mix with oxygen and, at about
   550[degrees]C (27), ignite producing a yellow flame above the wood.  Although
   radiant heat from the flame itself (not counting radiant emission from
   the charcoal) accounts for less than 14% of the total energy of combustion
   (33), it is crucial in maintaining combustion.  Some of the radiant
   heat from this flame strikes the wood, heating it and causing further
   decomposition.   The wood then releases more volatiles, which burn,
   closing the cycle.   The rate of combustion is then controlled by the
   rate at which these volatiles are released.  For very small pieces of
   wood, there is a large surface area to absorb radiant heat compared to
   little distance for the heat to penetrate or for the volatiles to
   escape.  Thus, fires with small pieces of wood tend to burn quickly.
   This is also why it is easier to start a small piece of wood burning
   than a large thick one.   A thick piece of wood has less area to absorb
   the radiant heat from the flame compared to the greater distances
   through which the heat and volatiles must pass within the wood and the
   larger mass that must be heated.
   The temperature of the hot gas above the wood is typically around
   1100[degrees]C and is limited by radiant heat loss and by mixing with cold
   ambient air.   As the volatiles rise they react with other volatile
   molecules forming soot and smoke and simultaneously burning as they mix
   with oxygen.   Some 213 different compounds have so far been identified
   among these volatiles (25).
   If a cold object, such as a pot, is placed close to the fire it will
   cool and stop the combustion of some of these volatiles, leaving a
   thick black smoke.
   Overall, these burning volatiles account for about two-thirds of the
   energy released by a wood fire.   The burning charcoal left behind
   accounts for the remaining third.   Because the volatiles are released
   as long as the wood is hot, closing off the air supply stops combustion
   alone.  The heat output of the fire is then reduced but the wood
   continues to be consumed for as long as it is hot, releasing unburned
   volatiles as smoke and leaving charcoal behind.
o   As the topmost layers gradually lose all their volatiles only a porous
   char is left behind.   This hot char helps catalyze the breakdown of
   escaping volatile gases, producing lighter, more completely reacting
   gases to feed the flames.   In some cases, the volatiles cannot easily
   escape through this char layer.   As they expand and force their way out,
   they cause the burning wood to crack and hiss or spit burning embers.
   The char layer also has a lower thermal conductivity than wood.  This
   slows conduction of heat to the interior and thus slows the release of
   volatiles to feed the flames.
   At the surface of the char carbon dioxide reacts with the char's carbon
   to produce carbon monoxide.   Slightly further away (fractions of a
   millimeter) the greater oxygen concentration completes the combustion
   process by reacting with the carbon monoxide to produce carbon dioxide.
   The temperature near the surface of the burning charcoal surface is
   typically about 800[degrees]C.   The endothermic (heat absorbing) dissociation of
   carbon dioxide to carbon monoxide and oxygen, and radiant heat loss,
   limit higher temperatures.
   When all the carbon has burned off only mineral salts remain as ash.
   This ash limits the flow of oxygen to the interior and so limits the
   combustion rate.   This is an important mechanism controlling the
   combustion rate in charcoal stoves.
o   The entire process uses about 5 [m.sup.3] of air (at 20[degrees]C and sea level
   pressure) to completely burn 1 kg of wood.  To completely burn 1 kg of
   charcoal requires about 9 [m.sup.3] of air.  Thus, a wood fire burning at a
   power level of 1 kW burns 0.0556 grams of wood/second and requires
   about 0.278 liters of air per second.   Additional, excess air is always
   present in open stoves and is important to ensure that the combustion

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   process is relatively complete.   Figure 16 sketches these processes.
A complete description of the combustion process is further complicated by
such factors as the inhomogeneous structure of wood and charcoal -- such
as pores, cracks, wood grain, and anisotropic properties; and the presence
of moisture.  For example, because of the long fibers and pores running
through the wood, the thermal conductivity and transport of volatiles is
much easier along the grain than crosswise.  This assists combustion.  In
contrast, the pore structure is disrupted in briquetted fuels, making them
generally more difficult to burn.
Improving Combustion Quality
A variety of techniques are being developed to improve the efficiency and
the quality of combustion in stoves.  Among them are the following:
o   Using a grate will often increase efficiency and may reduce emissions
   as well.  Tests of traditional stoves, for example, have shown that the
   use of a grate alone could increase the efficiency from about 18 to
   nearly 25 percent (34).
   Grates appear to perform several functions in improving stove performance.
   By injecting air below the fuelbed they provide better mixing of
   air with both the fuelbed and the diffusion flame above -- likely
   improving the combustion of both.   This may allow the pot in multipot
   and channel stoves to be placed closer to the fire -- improving radiant
   heat transfer -- without significantly interfering with combustion.
   Grates with a high density of holes (high fraction of open area) can
   also achieve high firepowers due to the improved mixing of air with the
   fuelbed (14).   This allows a more localized fire and in multipot and
   channel type stoves, better radiant heat transfer (due to a higher view
   factor) to the pot.
   In practice, it is important that grates be frequently cleaned of ashes
   so that air flow is not blocked.
o   Controlling excess air can increase efficiency but may also increase
   emissions if too little oxygen enters the combustion chamber or if the
   fuel-air mixing is poor.   Excess air is that which flows into the combustion
   chamber in excess of that needed for stoichiometric combustion
   (Appendix D).   There are numerous practical difficulties in controlling
   excess air as well; these were previously noted under RADIATION.
o   Injecting secondary air into the diffusion flame may, in some cases,
   allow more complete combustion than would otherwise be possible (35).
   (Secondary air is the air that enters the diffusion flame from above
   the fuelbed -- this is in contrast to primary air which enters the
   combustion zone at the level of the fuelbed, or from below when a grate
   is used.) This may be particularly important when excess air is
   controlled.   Where an open firebox is used, however, secondary air may
   lower efficiency by cooling the hot gases (20, 34).
o   Preheating incoming air may also improve the quality of combustion and
   the efficiency by raising average combustion chamber temperatures.
   Preheating, however, can only be done in stoves where excess air is
   controlled; otherwise the air will bypass the preheating ducts and flow
   directly in the door.   Further, to achieve significant preheating of the
   air entering the stove, it is necessary to pass the air through a
   narrow channel bounded by the hot combustion chamber wall.  This is the
   exact converse of using the hot combustion gases to heat the pot.
   Preheating in this manner may, however, cause a significant pressure
   drop and reduce the air flow.   In a stove driven by natural convection
   this may starve the fire, reduce the peak firepower possible, or reduce
   the pressure available to drive convective heat transfer to the pot.
   Chapter VI discusses the use of preheating in high temperature furnaces
   and the theoretical analysis is presented in Appendix E.
o   Optimizing the shape of the combustion chamber may affect the combustion
   quality and stove efficiency in a number of ways.  As already
   discussed, in multipot and channel stoves, the height chosen for the
   pot above the fuelbed is a compromise between the radiant heat transfer
   to the pot and the combustion quality.   The overall volume of the
   combustion chamber may be determined in part by the type of fuel used.
   Low density fuels such as agricultural waste may need a larger volume
   or else require frequent stoking.   Baffles can be added to promote
   recirculation of and turbulence in the combustion gases to improve

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   overall combustion.   The nozzle stove (Figure 8), for example, uses a
   section of a cone just above the fuelbed to establish zones in which
   gases from the edge of the diffusion flame can recirculate until they
   diffuse to the center of the flame and burn completely.  Additionally,
   this prototype nozzle stove injects primary air at an angle to the
   combustion chamber to promote swirl and thus improve fuel-air mixing
   (18, 19).
o   Insulating the combustion chamber raises interior temperatures and can
   thus reduce emissions.
With each of these techniques, a careful balance must be found between the
efficiency, emissions, ease of use, firepower, and cost.  This balance can
only be determined by detailed testing as described in Chapter V.
There are several other ways in which fuel use can be reduced.   Among
these are improving control of the stove, improving the pot, and speeding
up the cooking process itself.
Control Efficiency
How well the fire in a stove is tended can strongly influence fuel use.   In
Burkina Faso, daily weighing of the fuel during a survey sufficiently
sensitized the cooks that they reduced fuel consumption by 25% (36).
A typical cooking process will use high fire powers to bring a pot to a
boil, then low powers to simmer it.  The amount of fuel used then depends
on both the stove's and the cook's "dynamic power range" -- that is, their
ability together to provide a high fire power and then rapidly make the
transition to a low power as needed, never using more fuel than absolutely
necessary to reach boiling and then maintain a light simmer.   In simpler
terms, the stove must be controllable; the cook must, in fact, control it.
Note (42) discusses control efficiencies in more quantitative terms.
The type of stove and fuel both influence the potential and manner of
controlling the firepower.  Multipot stoves suffer because it is impossible
adequately to control the heat input to several pots from one fire.   A fire
just large enough to cook the first pot provides insufficient heat to the
second; a fire large enough to cook the second pot will overcook the
first.   Although this problem can be reduced by making all the pots the
same size and thus interchangeable, it cannot be eliminated.  Perhaps only
a single pot meal is desired, or perhaps a large pot is needed for the
rice and a small one for the sauce.  The precise demands will change with
every type of meal.  Thus, multipot stoves are intrinsically less efficient
than single pot stoves.
Numerous groups have attempted to circumvent the problem of control by
using adjustable dampers.  However, these tend to be very difficult to
maintain and use, are often ineffective, and can considerably alter the
combustion and heat transfer characteristics to all the pots in the stove,
not just the individual one for which the damper was intended.   Further,
because of the circuitous path the gases must then follow through the
stove, it is often difficult to start a fire.
Certain other types of stoves are also hard to control.  Stoves that first
gasify the wood and then burn the gas directly under the pot must heat a
charge of wood to temperatures as high as 1000[degrees]C and more in a reduced
oxygen atmosphere.  The rate of gas production is sensitive to this operating
temperature, yet the temperature is hard to control, let alone
rapidly increase or decrease as needed for cooking.  Efforts to develop
satisfactory gasifier type stoves for the individual household have so far
been unsuccessful due to the difficulty of controlling them (18, 19).   In
contrast, large gasification systems using coal as a feedstock and piping
gas to individual households have been in use for many years and are still
being used in India and China (40).  Due to the high CO content of the gas,
the safety of gasification systems remains an important issue (41).
Control of a fire may be assisted by having a stove with a very high
thermal efficiency.  In this case, failure to reduce the fire power could
cause the food to burn.  Such feedback can sometimes be an important
element in sensitizing the cook to controlling the fire.
The control of a stove also depends on the type of fuel being used.   For
example, simply cutting the air supply to a wood fire will control the
combustion and heat output but still allows consumption of the wood by
release of volatiles as long as the wood is hot.  Therefore, wood fires
should be controlled by removing the wood from the fire and quickly extinguishing
it.   In contrast, hot charcoal does not release large quantities
of volatiles and so cutting its air supply is an effective control.
The condition of a fuel is also a factor.  Wet fuel burns with difficulty
and may not sustain a small fire.  In this case reducing the fire power
during simmering can be difficult.  The unavoidably larger fire then
wastes fuel and evaporates excessive amounts of water from the food.
A high quality stove and fuel both assist control of the fire and will
usually each provide fuel savings.  However, taking best advantage of
potential fuel savings requires that the cook carefully control the fire.
To do this close individual follow-up is important:  showing users that
proper control does save fuel and how to control the fire; that it is not
necessary to boil the food violently and that a light boil is adequate;
and that even such simple acts as pushing the wood into the stove when it
begins to burn outside, or extinguishing it.
Such training of stove users is a very important aspect of stove dissemination.
One of the most important factors determining field performance of
a stove is the fire power it is run at during the simmering phase.   Because
simmering times tend to be long, quite modest increases in fire power
above the minimum needed can greatly increase total fuel consumption (Note
42).   There are very good reasons, however, for sometimes running a stove
at a higher fire power.  When a stove smokes excessively, increasing the
fire power will usually reduce this smoke by raising average combustion
chamber temperatures and improving the quality of combustion.   Users must
then choose between the discomfort of more smoke while cooking or the
discomfort of gathering additional fuel.  The automatic reaction of most
is to blow on the fire, add more fuel, and avoid the smoke.  For many this
becomes a deeply ingrained habit.  When using an improved stove such a
reaction should no longer be necessary and users must be retrained
It is not realistic, however, to expect cooks to control their stoves
perfectly; they have far too many other tasks to take the time.   A stove
that saves fuel anyway and that needs little oversight is highly desired.
Further, in some cases it is not in the cook's interest to use a stove
efficiently.   In Niamey, Niger, for example, hired cooks traditionally
have the right to the charcoal remaining at the end of the cooking to sell
or to use for themselves.  In this case there may be resistance to the use
of an efficient stove that produces little charcoal or to using it
Pot Efficiency
Fuel use can also be reduced by improving the "pot efficiency."   As seen
earlier in the heat balance for cooking food on a stove, a very large
amount of energy is lost through excess evaporation (Figure 1).   Use of a
tightly fitting lid and reducing the excess firepower can therefore
greatly reduce fuel consumption.  Heat is also lost from the pot lid and
the portion of the pot exposed to ambient air.  Insulating them can reduce
this loss (37).
Another method of improving the "pot efficiency" is to use a "haybox
cooker."   In this case, the pot of food is heated to boiling and then
quickly transferred to a highly insulated box.  The food is then cooked by
the "retained heat," that is, by its own heat, which is held in by the
high quality insulation of the "haybox" (38).
Finally, the cooking process itself can be speeded up by use of a pressure
cooker.   Pressure cookers raise the pressure and thus the boiling temperature
of the pot.  Raising the temperature speeds the physico-chemical
processes of cooking.  For long cooking times this may save energy and,
perhaps more importantly for the cook, can save large amounts of time.
Pressure cookers may be especially useful at high elevations or in areas
where cooking times are long.
In closing this chapter the human element must be re-emphasized.   The goal
of applying engineering heat transfer to biomass stove design is not an
academic exercise to determine what the limits in thermal efficiency may
be.   Rather, the goal is to better the lives of the two billion people who
now use fuelwood to meet their domestic needs.  Improving stove efficiency
is important to the extent that it reduces the cost of buying fuel or the
burden of foraging for it.  Improving combustion is important to the extent
that it reduces the exposure of women and children to toxic emissions.
Closing stoves is important to the extent that it prevents burns.   It is on
these human needs that stove programs must be focused and that the stoves
themselves must satisfy.  In many areas of the world, there is no likely
alternative to biomass stoves for the foreseeable future (Table II-19).
Engineering design, and similarly, anthropology, economics, ergonomics,
sociology, and many others, are all tools to be used to design, develop,
and disseminate biomass stoves that truly meet these human needs.   There is
not time to waste.
In the last chapter, design principles showed that of the numerous
possible combinations of stove type(1) (multipot, channel), construction
material (sand-clay, concrete, metal, ceramic), and fabrication technique
(owner, artisan, factory), lightweight channel stoves that are mass
produced by artisans or in factories have the highest efficiency.
Constructing stoves of lightweight materials at central locations offers a
number of advantages in addition to potentially high efficiency.   Mass
production from standardized templates allows all the attendant advantages
of rapid production, reduced cost, improved quality control, and the
additional market advantage of a professional finish.  Although assembly-line
production of stoves generates fewer jobs than individually handcrafting
each, the increased productivity, reduced training and production
costs, and generally higher quality will usually more than compensate.
As they are lightweight, such stoves can be disseminated through the
existing market system and carried home by the client personally.   This
greatly simplifies the logistics of stove production and dissemination and
lowers transport costs of both raw materials and finished products.
Stoves, then, become a standard consumer product no different than the
pots used on them or the spoons used to stir the food.  Artisan or factory
produced stoves, however, do cost money.  This can be a very serious
handicap in cash poor areas.
In contrast, due to their fragility, massive stoves of sand-clay must be
built on site by their owner or by an artisan.  Such stoves offer several
important potential advantages.  They can be constructed of local materials
(1) Nozzle stoves are not considered in this chapter as, at the time of
this writing, further development and testing were needed before large
scale field tests could begin.  Interested parties should contact ASTRA.
(when available); if owner built with minimal outside supervision
they cost little or nothing -- a very important asset in rural areas; or
if artisan built, they provide local employment.  Their potential disadvantages
include often low fuel economy even compared to the open fire
(Tables V-1, V-2) due to their large mass and due to dimensional errors in
their construction; short lifetimes (typically less than two years) due to
cracking in the heat of the fire or exposure to water; and slow production
(often less than 1 stove per day per person), among others.
Massive stoves of concrete could in principle be manufactured at a central
location and transported to the site rather than being constructed at the
site itself.  This would reduce some of the problems of quality control
and slow production but they would still have generally lower performance
and be more difficult to transport than lightweight stoves.
In attempting to replace traditional stoves with more efficient designs it
must be recognized that traditional stoves have a number of positive
attributes and only with considerable effort will they be displaced.
Traditional stoves cost little or nothing; they have a long lifetime; and
they are portable or easily built at each desired cooking location by the
owner or by a local artisan.  They typically have a respectable thermal
efficiency of 15-19% (1); they adjust to a variety of pot sizes and shapes
with little change in performance; they are relatively insensitive to
errors in construction; and they provide light.  When developing improved
stoves it is necessary to take these advantages as well as many other
factors into account.
A variety of configurations of lightweight channel stoves are possible,
some of which are listed below.  Detailed testing techniques in Chapter V
assist the stove developer to choose among these options on the basis of
efficiency, cost, ease of use, and other factors.
Wall Materials
Possible wall materials include metal, usually sheet steel, and ceramic,
or fired clay.  Insulants include materials such as fiberglass and vermiculite.
Metal walls might be alloys, electroplated, or given a heat
resistant coating to help reduce rust or corrosion.  Electroplating,
certain types of coatings, or polishing may also give a lower emissivity
surface and improve market appeal at the same time.
Reducing heat loss from metal walls was discussed at length in the
previous chapter.  Two possible construction options, using double or
insulated walls, are shown in Figure 1.  The slightly tapered insert
fitting into the combustion chamber alone is particularly appealing due to
its simplicity.  It also helps center the fire in the combustion chamber.
Ceramic (fired clay) stoves must be highly resistant to thermal and
mechanical shock.  This requires a careful choice of refractory clays; the
addition of materials such as rice husk or powdered pottery shards (grog),
which disrupt the structure of the ceramic and prevent cracks from
propagating; and good firing.  In some cases it may be desirable to pack
mud around the stove.  Although this may lower the performance of the
stove somewhat by increasing the mass of its wall and will reduce its
portability, it may significantly increase the lifetime of the stove by
reducing the thermal stress on its wall.  (When the exterior is packed in
mud, the temperature change across the fired clay portion of the wall is
less than in the case when the exterior wall is directly exposed to
ambient air.  This reduces the stress on the wall due to temperature dependent
thermal expansion.)
The choice of channel gap and length must be based on the need for efficiency,
high fire power, and low cost (long channels require more material).
The choice of channel gap must also, in part, be based on the local
ability to maintain precise dimensions.  For example, beginning with a 6-mm
channel, a 2-mm error (i.e. , to 4 mm) might result in a stove that would
not heat well.  This could seriously damage the credibility of a stove
program.   In contrast, beginning with an 8-mm channel, a 2-mm error (i.e.
to 10 mm) could lead to a lower efficiency stove but it would still work.
Similarly, the choice of channel gap will depend on how the stove is
maintained.   If soot is allowed to build up, or the pots are coated with
mud, the channel gap will be reduced and the stove may not work.
Stove Shapes
The type of material used and the choice of channel length will, in part,
also be based on the pot shape.  For example, a cylindrical stove made of
fired clay may easily break because the forces on it from the pot are
expansive or shear rather than compressive; a contoured form is preferred

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(Figure 2) and can be formed rapidly.
In contrast, forming a contoured stove from sheet metal, though possible,
requires expensive spinning or stamping equipment and dies.   The increase
in performance, even over a spherical pot in a cylindrical metal stove,
may not be worth the increased cost and production difficulty (Figure 2).
In considering a spherical pot in a cylindrical stove it should be noted
that the channel gap varies continuously, and that its narrow portion,
where the greatest heat transfer takes place, is very short.   Such a short
section can give high efficiency if very narrow, but this strongly limits
the fire power and total heat flux to the pot.  Lengthening the channel is
ineffective as the gap becomes increasingly large.  High efficiencies at
reasonable firepowers have been achieved with this combination of pot and
stove shape nonetheless (Table V-1).
Another important factor in construction is that the stove must be truly
round and the pot properly centered.  In places where the channel is wider
than average, such as a deformed ceramic wall or where a metal wall is
welded or folded together, excessive heat can flow out, lowering the
efficiency.   Figure III-9 and Table B-4 demonstrate this point in detail.
One should therefore pay particular attention to the manner and the
precision with which the wall is formed and to use tabs to center the pot.
Supports that rest against the wall of a metal stove may also push the
wall outwards under the weight of a heavy pot, deforming the wall and

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allowing excessive heat loss at these points (Figure 3).
To reduce smoke levels and improve cleanliness in the kitchen, chimneys

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are an option that should always be considered and encouraged.   The same
design principles apply as before, with the important addition of a gas
manifold at the top of the stove to allow gas to flow freely around the
pot before exiting out the chimney.  In addition, the chimney should have
a break in it and be open to room air at a point somewhat above the stove.
This will prevent the chimney from drawing too much draft through the
stove following a reduction in the fire power while the chimney is still
hot.   It is also important that the design include provision for cleaning
the chimney.  Cleaning must be done periodically to prevent creosote and
soot build-up inside the chimney from creating a fire hazard.
Cooks often prefer spherical pots as there are no corners for food to get
stuck in and the lip helps curl the food back in when mixing.   Stoves with
chimneys, however, may need a very wide top rim on such pots for them to
fit on the stove and not fall in.  Traditional green sand casting techniques
are usually unable to cast such a wide flat surface and thus
present a bottleneck for their introduction with chimney designs.
Other possibilities to improve the usefulness of a stove include clamps to
hold the pot or stove more rigidly when mixing foods.  This might take the
form of bars or a forked stick placed through the pot handles and held
down by a foot to fix the pot and stove together into place.   For use on
sandy soils, the stove can be given a wider base to help stabilize it or
to prevent it from sinking into the ground.  A hole at the center will
allow the ashes to fall out so that the stove is cleaned automatically
when moved.  Alternatively, a removable ash tray could be placed below the
grate.   Handles are also often useful additions, particularly for stoves
that run hot such as those with single bare metal walls.  Numerous other
options are, of course, possible and are limited only by the ingenuity of
the designer and their utility to the user.
Template design for a cylindrical, open firebox, channel type metal stove
is straightforward.  Such stoves are best used with cylindrical pots, but
have also been used with spherical pots with good results.   Dimensions
listed below are nominal and need to be optimized through laboratory
testing.   Laboratory and controlled cooking test data for this type of
stove are given in Tables V-1 and V-2.
1.   The width of the cylindrical stove template is given by

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         W = C + 2[pi]G + [O.sub.s] + [pi]S <see figure 1>
where C is the measurement of the pot around its widest circumference.   G
is the desired pot-to-wall channel gap.  For a gap of 4 mm, 2[pi]G=2.5 cm; for
6 mm, 2[pi]G=3.8 cm; for 8 mm, 2[pi]G=5.0 cm, and so on.   [O.sub.s] is determined by
the amount of overlap in the seam.  It is preferable to weld the stove
together end to end (thus [O.sub.s]=) to prevent the creation of a small
vertical channel by which the heat can bypass the pot.  If the seam is
crosswelded or folded, typical values for [O.sub.s] will be 1 cm. S is the
thickness of the metal used.  One typically uses 1 mm ([pi]S=0.3 cm) or 1.5
mm ([pi]S=0.47 cm) thick metal.  Thus, for a 90-cm-circumference pot, a 6-mm-channel
gap, an end to end welded seam, and 1-mm-thick metal:
W = 90 + 2[pi](0.6) + [pi](0.1) = 90 + 3.8 + 0.3 = 94.1 cm
2.   The template height H is determined by the sum of the airhole height A,
the grate-to-pot height P (measured from the top of the grate), and the
channel length L or, for spherical pots, the amount necessary to extend a
few centimeters above the pot's maximum circumference.   For cylindrical

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pots, L is determined by the desired channel length (chapter III) <see figure 2>
      H = A + P + L
Typical values for A are 3 to 5 cm and for P, 0.4 of the pot diameter.
For small cylindrical pots the height L is typically 5 to 10 cm.   Larger
institutional or industrial stoves may
have channel lengths L of 50 cm and
more.   The best height L is determined
more precisely by comparing the
increased efficiency and reduced fuel
use caused by the additional height
versus the increased cost of the extra
metal.   Additional height can also be
provided at the top and bottom of the
template, typically 1 cm each, to allow
the edge to be folded over to protect
against cuts on the sharp edges and to
increase the stove's rigidity and

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strength. <see figure 3>
3.   Stoves should have a total
air inlet of at least half the
area of the pot to wall channel
gap.   For the above stove 94 cm
in circumference and with a gap
of 6 mm this is 56 [cm.sup.2].  A
convenient size, then, is to
have four airholes, about 3 cm
by 4 cm each (A=3 cm) or 48 [cm.sup.2]
in area, spaced symmetrically
around the stove, but far
enough away from the door and
the seams to avoid weakening
the wall.  The airholes are cut
on two sides only so that when bent upward and inward they can act as
supports for the grate.  Larger airholes may be necessary if large
pots are used or if the stove is used on soft soil where the stove
will sink into the ground and block the airholes.  Alternatively, for
soft soil conditions a ring-shaped platform can be cut and attached

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to the stove. <see figure 4>
A fifth airhole (tab) can be cut opposite the door and bent to be above
the grate.  This will prevent the grate from tipping upwards when wood is
pressing down too heavily at the doorway.
4.   Pot supports are similarly spaced evenly around the stove, but offset
from the door and edges so as not to weaken the wall.  The height P for
the pot supports above the top of the airholes (where the grate will rest)
is given roughly by
      P = 0.4C/[pi] = 0.4D
where D is the pot diameter.  The best distance will vary somewhat with
the size of wood used locally, its moisture content, and other factors. <see figure 5>

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Pot supports should support the pot stably, yet be small in area so as not
to shield the pot from the hot gases -- reducing heat transfer.   Pot
supports should not cause the stove wall to bend when heavily loaded as
this can change the effective channel width and reduce performance.
5.   The size of the door is somewhat arbitrary and is determined in part by
the locally available wood size.  Typical door sizes for use with a 90-cm-circumference
pot are 12 cm wide by 9 cm high.  The bottom of the door is
placed at the grate position -- the top of the airholes.  The top of the
door is made several centimeters below the bottom of the pot so that the
hot gases are guided up around the pot rather than out the door.   If
necessary, the door height can be decreased to ensure that it is below the
bottom of the pot.
6.   The grate is a circle of sheet metal cut to fit snugly into the
finished cylinder.  Recuperated scrap metal is often used.  The center
half diameter is punched with a 30% hole density of 1 cm holes.   Grates
should not have any holes much larger than 1 cm in diameter, since large
holes in the grate will allow the charcoal to fall through and burn below
the stove, reducing efficiency.  Holes
of too small a diameter will easily
clog and reduce air flow into the

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charcoal bed. <see figure 6>
In some cases it may be useful to form
a conical grate.  This will both better
localize the fuel to improve combustion
and provide an insulating dead air

bse75b.gif (230x230)

space along the stove wall. <see figure 7>
7.   Spacers, used to center the pot
evenly, are also often needed. <see figure 8>

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Templates for tapered pots can be developed geometrically from conic
sections.   Dimensions are developed in the same manner as above.  Other
features such as double walls, insulation, chimneys, or others can be
included as desired.  Attachments might include handles for carrying the
stove or clamps for holding the pot firmly in place while stirring thick
Production test data for this type of stove, including production rates
and costs, are given in Tables V-3 and V-4.  The general procedure used is
the following, with specific tasks divided among different workers.
1.   The template is traced out on the

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metal sheet as shown in Figure 1 and
cut out in outline.  The door and pot
support holes are cut out, and the
strips for the airholes and to support
the grate are cut.
2.   The metal is rolled into a cylinder -- it should be as smooth, round,
and straight as possible.  If a sheet metal roller is used, the top and
bottom can be folded over before rolling.  If bent by hand, they can be
folded after rolling.  This provides additional rigidity and prevents the

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user from being cut on sharp edges. <see figure 2>
3.   Other components such
as the pot supports and
the grate are cut out
and the holes punched in

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the grate. <see figure 3>
4.   The stove is welded together and pot
supports are welded into place.  Alternatively,
the stove walls can be locked

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together by folding. <see figure 4>
5.   The grate is placed in the stove, and the
tabs for the airholes are bent inward and
upward to support the grate.  Pot supports are
slid and folded or welded into place.
6.   The stove is given the desired surface finish (electroplating, painting
with heat resistant paint, etc.) to improve its rust resistance and market

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appeal, and to reduce its heat loss by lowering its emissivity. <see figure 5>

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Artisanal production techniques can produce durable, highly efficient, and
very low cost fired clay stoves at a rapid rate.  To do so, however,
requires very careful attention to and painstaking quality control at each
step of the production process.  The optimal mix of clays must be chosen
to ensure durability and to provide a high level of mechanical and thermal
shock resistance.  Preparation of the clay (grinding, pounding) and the
proportion of water added must be standardized to ensure a uniform
product.   Templates must be carefully sized to take into account the
shrinkage of the clay during drying and firing while maintaining the
desired pot to wall gap, etc.  (Shrinkage is most easily determined by
rolling long rods of clay; measuring their length when wet, dry, and
fired; and calculating the percentage change).  Finally, the optimum
firing techniques and temperatures must be determined.
Each of these steps requires careful testing and optimization.   The
overall effort required usually limits production to centralized large-scale
facilities; only the most highly skilled potters could potentially
produce quality fired clay stoves on their own.  Within these constraints,
however, fired clay stoves may be an important alternative for potters who
are losing their traditional markets.
The production steps using traditional West African pot production
techniques are described below.  Typical production costs are given in
Table V-5.  Alternatively, casting, throwing (on a potter's wheel) or
other techniques could be used instead.  In particular, the use of
internal molds (which are interlocking and can be disassembled internally)
and potter's wheels have been used with some success in Thailand (2).
Flywheel presses (3) or hydraulic presses used with internal molds may be
even better (2).
1.   Clays are mined, prepared, mixed, etc., according to the need for
durability, firing, thermal shock resistance, and other factors.   Grog
(finely ground pottery shards), rice husk, or other materials are often
added to improve durability.  These inclusions prevent cracks from
propagating in the finished product.

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2.   The clay is kneaded, rolled, and flattened.  <see figure 1> Dried, powdered clay can
be used to reduce the surface stickiness of the wet clay.  As the clay is
worked, air pockets are lanced and bled out.  Flattened, the clay should
be a uniform thickness, perhaps 2 to 3 cm thick or as needed for durability,
etc.   A template is used to cut out a rectangle of clay that is
then rolled into a cylinder and the ends melded together.  This cylinder
forms the combustion chamber of the stove and its dimensions must be
chosen accordingly, taking into account such factors as the desired grate
to pot height of 0.4(pot diameter), and the need to place the combustion
chamber walls directly under the pot so that the walls are under compressive
rather than expansive forces, yet without the wall obscuring too much

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of the pot from direct radiant heat transfer from the firebed. <see figure 2>
3.   More clay is kneaded, rolled into a
ball, and somewhat flattened into a
circle.   This is then placed in an
appropriately sized spherical mold and
continuously turned (using lots of
dried, powdered clay) and worked to
form the upper part of the stove.  The
dimensions are checked frequently with

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a template to ensure accuracy. <see figure 3>
4.   The spherical
section is placed
on the cylinder,
the center of the
spherical section
is cut out, and the
two are melded

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together. <see figure 4>
5.   Small pot supports, 6-8 mm thick or as desired and 2-3 cm square, are
placed in line with the cylinder so as to direct the pot weight downward.
Such supports are most easily melded to the stove by lightly scratching
and moistening the mating surfaces.
6.   Supports for a metal grate are added
at the bottom of the stove.
7.   The doorway is cut out.   Holes for
air flow under the grate are cut out.
Cuts should be rounded; sharp corners
tend to generate greater stress and

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more frequent breakage. <see figure 5>
8.   All the surfaces of the stove, especially those cut, are lightly

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moistened and smoothed to reduce cracking. <see figure 6>
9.   The stove is placed in a cool location and allowed to dry slowly over a
several week period.  Finally, the stove is fired in a kiln.
10.   A metal grate is fitted to the stove.
In this chapter laboratory, controlled cooking, production, field, and
marketing tests are described in detail.  Techniques for financial and
statistical analysis of the data are presented in Appendixes F and G.   In
areas where surveys or other analysis have demonstrated the need for safer
and more efficient biomass burning stoves, tests such as those described
here are essential for their development.
In brief, the total testing program recommended is this:
o   Laboratory and controlled cooking tests are used to select particularly
   promising stove prototypes and to optimize their dimensions.
o   From these tests standard templates are developed that conform to the
   local pot sizes and shapes.
o  A production test is run with these templates producing 50-100 or more
   stoves for each of the most popular pot sizes.  During this production
   test a detailed analysis is performed of the costs, problems encountered
   and potential improvements in the production method.
o   Some of these stoves are then distributed on a short-term, temporary
   basis to selected families for field testing to determine both their
   acceptability and their actual measured performance in day to day use.
   Another portion of these stoves is put on display in local commercial
   outlets and sold on a commission basis.  Such simultaneous marketing
   allows some indirect feedback on how neighbors of the selected families
   perceive the stove's potential.
o   On the basis of the production and field testing results, modifications
   can be made to the templates and production system as needed and the
   process repeated.   A similar laboratory, production, field, and market
   testing effort can be used for commercial or industrial applications.
o   When a suitable model has been developed and fully tested in the field,
   larger-scale dissemination can begin.   Various marketing techniques
   such as radio and newspaper advertising, public demonstrations at
   social centers, and others can be done.
o   As interest develops, the stove promoter can gradually withdraw from
   the role of commissioning both production and sales, leaving the stove
   producer in direct contact with the various commercial outlets.
Increasing the fuel efficiency and safety of a stove may require the
concession of some of the advantages of traditional stoves, particularly
their lower initial cost, their flexibility to fit different pots, and the
lighting they provide.  As fuel costs rise, however, improved stoves will
become increasingly attractive.  Detailed testing, as described below,
permits the determination the performance and attractiveness of a particular
stove at any particular time in any given area.  Further, such
testing provides a means to launch rudimentary mass production, marketing,
and dissemination.
The testing of improved stoves, however, is not an end in itself.   It is
only a means to developing stoves that save users time, money, and labor,
and protect their health and safety.
In recent years a variety of laboratory testing methods have been used.
All of these methods simulate the high power (to bring to a boil)/low
power (to simmer) process of cooking while using water to simulate food.
The stove's performance is measured by its Percent Heat Utilized, PHU, or
by its Specific Consumption, SC.  The PHU of a stove is the percentage of
heat released by the fire that is absorbed by the water in the pot.   The
SC is the total quantity of wood used for the simulated cooking process
divided by the amount of water "cooked."  Results from different tests of
this general type are similar but not always precisely comparable.
The Provisional Draft International Standards developed in December 1982
standardize this type of method (1).  The procedure, as updated since, is
listed below (2) and a discussion of useful laboratory equipment is given
in Appendix H.  A more detailed discussion of the relative merits of
different testing methods is given in Note (2).
Lab Testing Procedure
1.   The test conditions are recorded including air temperature, wind, and
    relative humidity.   The stove and pot(s)(1) are described and sketched in
    detail including careful measurements of their relevant dimensions.
    These dimensions should include the grate to pot and pot to wall
    distances when the pot is in place on the stove.
   (1) The (s) in pot(s) and (first) pot in point 5 refer to the testing
of multipot stoves.
2. A quantity of wood no more than twice the estimated amount needed for
   the test is weighed, the weight recorded, and the wood set aside.  The
   moisture content and calorific value of the wood should be known.
   Testing standards for measuring the specific gravity, moisture content,
   ash, volatiles, and calorific values of wood or related materials are
   given elsewhere (22).   If possible, the wood should be of the same
   species and relatively uniform in size.  Buying sufficient wood of the
   same species for all the tests and then storing it in the same well
   protected location will aid in maintaining the moisture content at the
   same value.   Periodic rechecks will still be necessary.
3. The pots should be scrubbed clean both inside and out, and thoroughly
   dried before each test.   The pots must be identical in shape and size
   for all the tests to prevent these factors from skewing the test
   results.  The dry pot(s) and thermometer(s) are weighed together.   Then
   a fixed amount of water is added to the pot(s) that is roughly equal to
   two-thirds of the pot(s)'s capacity but exactly the same for each test
   for all the stoves, i.e., 5.000 kg.   The pot(s) with water and thermometer
   is weighed.   The water temperature should be within a few
   degrees of ambient air temperature.   Lids should not be used at any
   time (Note 2).
4. High Power Phase:  The stove must be at room temperature.  Then, the
   fire is lit in a reproducible manner (i.e., by using a measured amount
   [5 ml] of kerosene), the pot(s) is quickly placed on the stove, and the
   (first) pot is brought to a boil as rapidly as possible without being
   excessively wasteful of heat.   Water temperatures are recorded every
   five minutes.   Actions to control or relight the fire, observations of
   excessive smoke, high wind, or any others should also be recorded.
5. When the (first) pot comes to a full boil the water temperatures and
   time are recorded.   Then the following are done rapidly:
   o The wood is removed from the stove, any charcoal is knocked off, and
     all of the wood is weighed.
   o The charcoal is weighed.   With a large capacity balance and a lightweight
     stove, it is often easier to weigh the stove empty before the
     test, and then weigh the stove with the charcoal in it to determine
     the charcoal weight.   This speeds the process and reduces the disruption
     of the fire.
   o The pot(s) with water and thermometer(s) is weighed.
6. Low Power Phase:  The charcoal, wood, and pot(s) are returned to the
   stove and the fire relit.   The fire is then maintained for 30 minutes
   at the lowest power possible that is sufficient to keep the water
   preferably within 2[degrees]C (and not more than 5[degrees]C) of boiling yet not
   boiling excessively.   Water temperatures are again recorded every five
   minutes along with any actions to control the fire or observations.  As
   before, no lids are used at any time.
7. At the end of this 30-minute period of simmering, the wood, charcoal
   (or stove and charcoal together), and pot(s) with water are again
   weighed and the values recorded.
8. Finally, the following indices of stove performance are calculated.
       Firepower = P = [M.sub.w] [C.sub.w] - [M.sub.c] [C.sub.c]
                       -----------------------------------------   (kilowatts)
   where [M.sub.w] is the mass of dry wood burned, [C.sub.w] is the calorific value of
   the dry wood in kJ/kg. [M.sub.c] is the net increase or decrease in charcoal
   and [C.sub.c] its calorific value in kJ/kg.  I is the length of time in
   The specific consumption is given by
              [M.sub.w] - 1.5[M.sub.c]
         SC = ------------------------
   where [W.sub.f] is   the mass of the water remaining at the end of the period.
   It is often more convenient to express this as grams wood equivalent
   consumed/kilograms water cooked rather than kg wood/kg water (3).
   If there is a large variation in starting water temperature from day to
   day, the SC can be normalized by water temperature (23).  That is,
         SCN =       [M.sub.w] - 1.5[M.sub.c]
              [W.sub.f][([T.sub.f] - [T.sub.i])/75]
   Finally, the PHU can be calculated using
       PHU = --------------------------------------------------------------
  where [W.sub.i] is the mass of the water in kilograms at the start, ([T.sub.f]-[T.sub.i]) is
  the temperature change of the water in degrees celsius during that
  period, and ([W.sub.i]-[W.sub.f]) is the mass of the water evaporated.  The factor
  4.186 kJ/kg[degrees]C is the specific heat of water, and the factor 2260 kJ/kg
  is the latent heat of vaporization of water.  Additional terms are
  added as needed for multipot stoves.
Typically, a minimum of four tests per stove will be necessary.   The test
procedure should then be repeated as needed to provide statistically
significant data as discussed in Appendix G.
Laboratory Test Precautions
In performing laboratory tests there are a number of cautions:
o Considerable time and effort must be spent with the people doing the
  testing to ensure that the procedure is followed correctly and consistently,
  and that the data are accurately recorded.  It is frequently
  useful to design double checks into the procedure in order to catch
  common errors such as misweighing the wood or incorrectly recording the
  values.  As an example, under "remarks" on the sample laboratory test
  data sheet, all weights of the individual pieces of wood added to the
  fire can be recorded.   These values can be compared with the totals to
  ensure no wood was lost and no weight misrecorded.  If there is doubt
  about a measurement it should be discarded.
o In varying one parameter, it is vital that there be no other differences.
  Thus, in testing the effect of the channel length on performance,
  the different stoves must have identical diameters, grates, and
  doors, etc.  This is crucial.
o Testing should be done in an enclosed or well protected area to reduce
  the effect of the wind.   Even small amounts of wind can appreciably
  affect the results -- particularly for open fires and traditional
o If there is more than one tester, each person should test each stove
  the same number of times to eliminate any bias.
o The order of testing the stoves should be completely random.   Otherwise,
  for example, there will be a tendency to consistently test stove
  A in the late morning when the air is calm and stove C in the late
  afternoon when the wind is blowing strongly or to do all the tests of
  stove A first during a dry period and all tests of stove C later when
  the rainy season begins.   Using a random testing order will reduce such
  potential biases.
o High altitudes will have a small effect on water boiling tests, and
  will have a large effect on field tests due to the longer cooking times
  at the lower boiling temperatures due to lower atmospheric pressure.
Design Parameters to be Tested
A number of parameters that should be investigated in performing lab

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tests, including the following: <see worksheet 1>
o The channel gap, length, and shape, and the manner of its fabrication,
  such as overlapped or butt-welded joints.  These affect convective heat
o The grate-to-pot height.  These affect radiant heat transfer and
  combustion quality.
o The hole density (the fraction of open space) in the grate, the shape
  of the grate (conical to center coals and fuel, holes only toward the
  center, etc.), and the type of material used for the grate.  The hole
  density affects the possible firepower and the thermal mass and insulation
  of the grate partially control the heating rate and efficiency.
o The type of insulation and how it is placed (over the entire outside,
  inside the combustion chamber only, etc.), or the use of double walls.
  These are important in determining both the overall heat loss through
  the walls and, to a lesser extent, the radiant transfer to the pot and
  the combustion quality.   The size, shape, and insulation of the
  combustion chamber are also important considerations.  A smaller chamber
  may allow higher average temperatures and a higher chamber may allow a
  longer residence time -- both assisting more complete combustion.
o The control of primary or secondary air.  These may affect the combustion
  quality in some cases.
o The size and shape of the doorway, or the use of a closeable door or
  flapper for air control.   These will help determine the ease of use of a
  stove, e.g., ease of loading, monitoring the fire, etc.
o The type, size, and shape of pot supports.  Large pot supports will tend
  to screen the pot from the fire but may support the pot more stably.
o The use of various types (heights, widths, contours, etc.) of baffles
  to improve convective heat transfer or to cause recirculation in the
  combustion zone to improve combustion.
o The use of various heights, diameters, and materials for the chimney.
o The pot shape and material.
o The performance of the system with scale changes (e.g., doubling of the
  pot and stove size).
In planning a series of lab tests, it is often useful to do a few dozen
preliminary tests in order to determine the actual situation and the
desirable range of the parameters to be tested.  Once the parameter range
is determined the testing can begin.  Testing is most often done by
varying one parameter, such as the channel gap, at a time.  In rare cases,
carefully controlled factorial type experimental designs can be followed
which allow several variables to be varied simultaneously.  An example of
such an experimental design would be to vary the channel gap and length
simultaneously, as discussed in Appendix G.
Data Analysis
To analyze the data, the averages, standard deviations, and confidence
limits are calculated for each type of stove or variation.   The t-test is
used to differentiate between stoves.  Finally, regressions are used to
determine the influence of any particular parameter being varied.
Following extensive laboratory testing, several models are selected for
controlled cooking tests.  The models chosen, however, should not just be
those with the lowest SC or highest PHU.  In some cases, these performance
indices may not correspond to the actual cooking process or may be
misleading.   Thus, stove models covering the entire range of performance
are selected foor both controlled cooking tests and field tests.   With
those additional results the usefulness of the laboratory indices, PHU and
SC, can be determined and modified as needed.  Similarly, the laboratory
procedure itself can be modified to better correspond to actual cooking.
Both the PHU and SC appear to be fairly reliable laboratory indicators of
a woodstove's field performance (5,6).
                                  TABLE 1
                      Laboratory Tests of Woodstoves
                         PHU      PHU     PHU       PHU                # of
Stove                    POT 1    POT 2   POT 3     Total              Tests
Traditional Stoves (one pot):
Three Stone Fire        17.0                     17.0[- or +]1.0        9
Metal "Malgache"        18.2                     18.2[- or +]1.3        9
Metal " " with grate    24.7                     24.7[- or +]1.7        6
One-Pot Massive Stove with Chimney:
Nouna 31                 16.9                     16.9[- or +]1.0       10
Two-Pot Massive Stoves with Chimneys:
AIDR 2                   15.8      5.8             21.6[- or +]1.0      10
CATRU                    14.3      6.1             20.4[- or +]5.3       8
Kaya 2                   13.6      6.2             19.8[- or +]1.9      10
Nouna 2                  15.2      6.9             22.1[- or +]1.5      10
Nouna 3/2               16.3      5.1             21.4[- or +]1.0      10
Titao                    11.2      4.2             15.4[- or +]0.9      10
Three-Pot Massive Stoves with Chimneys:
AIDR 3                   14.8      4.5     2.5    21.8[- or +]0.8       10
Kaya 3                   10.2      5.9     4.0    20.1[- or +]1.6       10
One-Pot Massive Chimneyless Stove:
Louga                    19.0                     19.0                 n.a.
Two Pot Massive Chimneyless Stove:
Banfora                  18.8      7.9             26.7[- or +]1.3      10
One-Pot Lightweight Chimneyless Channel Stoves:
Metallic(*)              29.1                     29.1[- or +]:1.3      10
Ceramic(**)              31.9                    31.9[- or +]2.2      10
Ceramic(**)long channel 36.1                    36.1[- or +]1.9      14
Insulated Metal(*)      42.6                     42.6                 n.a.
References (5,7,8,9).  Note that values here are recalculated from
reference (5) and include charcoal.  All pots were spherical.
(*) cylindrical stove.  (**)spherical stove.
Examples of laboratory test data are given in Table I.  In particular, the
relatively low performance of the massive and multipot stoves compared to
the lightweight channel stoves should be noted.  This corresponds to the
theoretical analysis presented in Chapter III.  Additional preliminary
test data showing the influence of channel gap and of insulation on the
performance of lightweight channel type woodstoves are given in (9).
Although not discussed here, the measurement of stove emissions is as
important as the measurement of efficiency.  Readers are strongly urged to
contact the East-West Center in Honolulu, Hawaii, for information on
emission testing methods.
Controlled cooking tests (CCTs) are useful in demonstrating that the model
stoves are easy to use and perform well in actual cooking.   In addition,
they help verify that laboratory tests are measuring parameters relevant
to actual cooking.  Although they are more difficult to conduct than
laboratory tests, they are an important intermediate step before production
and field testing are begun.
The general steps for performing controlled cooking tests follow.
1. A standard meal, typical for the area, is chosen and several tests are
   performed in order to standardize precisely the type and quantity of
   each ingredient.   Standardizing quantities prevents the occasional need
   for excessive boiling to eliminate extra water that might have been
   added by mistake or perhaps consistently by just one of the cooks.
   Standardizing quantities also reduces the effects of scale that
   otherwise might skew the test results.
   Wood is chosen to ensure that it is of a consistent type and moisture
   content, and its calorific value and moisture content are measured.
   All other factors, including pots, lids, and cooking equipment, are
   standardized to the extent possible.   If there is to be more than one
   cook, each cook should test each stove the same number of times to
   eliminate any possible bias due to different cooking habits.
2. Test conditions are recorded, the stove and pot(s) are described in
   detail, the stoves are cleaned of ash, and the wood is weighed and
   recorded.  Pot lids are used if done so typically in the region.   If
   used, they are weighed with the pot.   The food is prepared for cooking.
   Food is precisely weighed out as indicated in the sample CCT test sheet

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   shown in Worksheet 2.
3. The fire is lit and the cooking begun.  The cook does the cooking in
   the usual manner and decides when the food is done.  Cooking times and
   any relevant observations are recorded, including comments by the cook
   on difficulties encountered in using the stove or other observations
   such as excessive heat, smoke, or instability.
4. The charcoal and remaining wood are weighed and the cooked food is
   weighed.  The specific consumption is calculated by:
         SC =  [M.sub.w] - 1.5[M.sub.c]
                 (Total Food Cooked)
   where [M.sub.w] and [M.sub.c] are as previously defined.  If desired, this can also be
   normalized to ambient temperature as for the laboratory test.
   If the wood and charcoal species, moisture contents, and calorific
   values are known, they should be reported so as to allow standardization
   of the SC.
5. The tests are repeated at least three times or as needed to get sufficiently
   precise statistics to make reliable distinctions between the
   various stoves.
   The average, standard deviation, and confidence limits are calculated
   for each stove from its test results.   Stoves are then distinguished by
   use of the t-test.   If a particular parameter has been varied, linear
   regression can be done between that parameter (or its square, cube,
   etc., if it has a nonlinear influence) and the SC.  Many of the other
   cautions cited above for laboratory tests are also applicable for
   cooking tests and should be reviewed.
An example of CCT data is shown in Table 2.  The high fuel economy of the
lightweight channel type metal stove relative to both the traditional
stoves and to these particular massive multipot stoves is quite striking.
It is also important to note that even though the laboratory PHUs of the
multipot stoves were significantly higher than that of the traditional
open fire, their CCT fuel economies were only marginally better and
sometimes worse.  The reason for this is that the additional heat recuperated
by the second and subsequent pots increases the laboratory PHU, but
is ineffective in actually cooking food because it is too low in temperature
and because it cannot be easily controlled.  An analysis of the data
in Table 2 and those for other stoves has shown that the performance of
multipot stoves in actual cooking of food is better predicted by their
first pot PHU than by their total PRU (5).  This strongly supports the
discussion in Chapters III and IV concerning the poor control efficiency
of multipot stoves.
On the basis of the results from the laboratory and controlled cooking
tests, models must be selected for production and field testing.   The
choice should not be made solely on their relative fuel efficiency,
however.   Instead, it must be based on the entire range of factors that
will eventually determine the consumer's choice.  High cost, for example,
may be a far more significant barrier to the rural dweller than the urban
dweller.   The smoke from a high efficiency chimneyless stove may be far
more annoying to the user of a stove with a chimney, though perhaps an
inefficient one, than for the user of an open fire.
Quantifying the subjective factors that determine stove acceptability

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through the use of a scorecard is difficult, but may help indicate the
acceptablity of a stove in the field.  Of greater importance is that the
scorecard reminds the stove developer to pay attention to more than just
fuel efficiency.
                                  TABLE 2
              Controlled Cooking Test Results for Woodstoves
BURKINA FASO, 1983          Laboratory                Controlled Cooking
                             (Table 1)            Specific
                       PHU      PHU     # of   Consumption      # of    Economy
STOVE                  Pot 1    Total   tests   grams wood       tests   
Traditional Stoves
  Three Stone Fire      17.0    17.0        9     268[- or +]21      4       0
Massive Multipot Stoves
  Nouna 2               15.2    22.1      10      244[- or +]19       5     +9
  AIDR 3                14.8    21.8      10      304[- or +]29       4    -13
  Banfora               18.8    26.7      10      213[- or +]29       6    +14
Lightweight Channel Stoves
  Metallic              29.1    29.1       9      161[- or +]5        3    +40
NICER, 1983            PHU Total
                      (High Power)
Traditional Stoves
  Metal Malgache        21.5[- or +]1.76   6     392[- or +]129      4      0
Lightweight Channel Stoves
  Metallic              31.2[- or +]4.3   14     228[- or +]57       4     42
References: (5,6)
After stove prototypes are optimized in laboratory tests and their fuel
saving potential is verified in controlled cooking tests, the next step is
to distribute such stoves to a large group of families in the field to
observe the stoves' performance, acceptability, lifetime, and other
characteristics in day-to-day use.  At this point a production test can be
run to construct the stoves necessary for field tests as well as to
provide valuable information as to their ease of production, production
costs, quality control, and other factors.
A production test is done simply by producing a large number of standard
sized stoves as rapidly as possible while timing the various steps,
evaluating the cost of all the inputs, observing the quality of the stoves
produced, and determining possible ways to improve the process in terms of
cost, quality, rapidity, or other factors. Additionally, local technical,
managerial, and extension abilities and needs should be evaluated.
The procedure will vary depending on the type of stove as well as the
material used.  Ceramic stoves will require extensive material preparation,
molding on standard forms, drying, and firing, each of which are
distinct steps requiring separate evaluations.  Described briefly below
are the steps used in a production test of metal channel type stoves.
1. The most popular pot sizes and shapes are determined through surveys of
   local pot makers, merchants, and households. The pots made by different
   pot producers are precisely measured to determine if they are standardized.
   If the pots vary sufficiently in size to affect performance
   significantly when used on a standard sized stove, it may be necessary
   to sell stoves designed for each specific pot at the site of the
   producer, i.e., stove-pot packages. For example, if the comparable 0.3-m
   pots of two producers differ by 8 mm in diameter, then from
   Figure III-11, the performance of a stove designed to have a channel gap of 8
   mm (by 10 cm long) with the larger pot and a fuel savings of roughly
   43% would decrease to a 20% savings with the smaller pot.  This is a
   drop in expected fuel savings of over one-half, a significant decrease.
   Alternatively, a stove designed for the smaller pot would be too tight
   and not function with the larger.
2. Once optimum stove dimensions are determined through laboratory and
   controlled cooking tests, and once stove sizes are chosen based on the
   results of the pot surveys, templates are prepared on paper and then
   transferred to sheet metal to provide a permanent copy. (To prevent the
   template's loss through use itself for a stove, metal bars can be
   welded across it to prevent rolling it into a cylinder.) An example of
   template design for cylindrical or spherical pots was given in Chapter
   IV.  Dimensions there were nominal and will have to be adjusted based
   on laboratory data and the pot size.   Dimensions may also have to be
   adjusted to minimize material costs.   For example, the height of the
   template might be adjusted to squeeze one additional stove out of a
   standard sheet of metal.   The question then is what is the loss in
   performance with the lower stove wall versus the decrease in material
   costs.  Whether the lowered cost is locally perceived to be worthwhile
   is often very hard to determine. In some cases the purely psychological
   advantage of, for example, keeping the finished stove price under an
   even amount, e.g., $5.00, will make the adjustment worthwhile in terms
   of increased public interest and sales.
3. When the template has been developed, various metal shops are contacted
   and commissioned to make several stoves each.  One or two shops are
   chosen for the production test based on their construction quality,
   price, and other desirable factors. A minimum of 50-100 stoves in each
   of the chosen pot sizes should be ordered from each shop.  Production
   is then run along the general format indicated in Chapter IV.
4. Finally, the production process is analyzed to determine how it might
   be improved. Among the factors to be evaluated are:
   o The production rate as a function of each step in the production line
     as well as the total process and how to optimize this rate.  The
     example in Table 3 shows that cutting the stove form out of sheet
     metal and then later welding it and the pot supports into place were
     by far the slowest steps in the production process.  The addition of
     better or additional metal cutting and welding equipment and jigs may
     then offer an opportunity to increase shop productivity considerably.
   o The costs of production as a function of material, labor, electricity,
     rent, amortization of equipment, profit, etc., and how to
     minimize this cost.   Examples are given in Tables 4-6.   As seen in
     Table 4, the    cost of metal accounts for over half the total stove
     cost.  The use of lower cost alternatives such as recuperated scrap
     or lighter gauge metal may therefore offer a significant opportunity
     to reduce costs. It should also be noted that labor is a very small
     component of the total costs; increasing shop productivity by
     purchasing better metal cutting and welding equipment may then be a
     less important consideration in this case.  In contrast, the very
     large labor and transportation costs of producing massive stoves on
     site should be noted in Table 6.
   o The quality of the finished product in terms of respect for dimensions,
     roundness, professional finish, etc., and how to monitor and
     regulate quality control.
   o The possibility of introducing a professional finish for these stoves
     such as heat resistant paint, electroplating, electropolishing, or
     others to improve the stove's lifetime, performance, and saleability.
Options might include modifying the form of the stove away from its
thermal performance optimum, as already discussed, in order to reduce
material costs; simplifying the curves of the conical template in order to
maximize production rates; or substituting recuperated metal or lighter
weight metal to minimize the material costs and/or improve the stove's
cost/benefit, marketability, or lifetime.
                                    TABLE 3
           Production Times for Metal Stoves, Burkina Faso, 1983(*)
    Production Step                                 Time (minutes)
                                                    for 8 stoves
    1.  Tracing stove from template                     10
    2.  Cutting stove                                   49
    3.  Bending/hammering into cylinder                 15
    4.  Cutting pot clamps and pot supports             18
    5.  Cutting and/or punching grate                  12
    6.  Bending the air holes                           14
    7.  Welding                                         64
    8.  Painting                                        30
        TOTAL                                          212 minutes
        Per Stove                                       26.5 minutes
(*) The design was a single wall, chimneyless channel type stove as described
in Chapter IV; Template Design: Cylindrical Stoves and Metal
Stove Production.
References (11,12). See also reference (6) for similar data from Niger
                                    TABLE 4
        Lightweight Metal Stove(*) Production Costs, Burkina Faso, 1983
           Material costs per stove                  US$
              metal sheet                           1.41
              pot supports and clamps               0.24
              grate                                 0.19
              welding                               0.08
              paint                                 0.11
                   Subtotal                              2.03
           Labor costs per stove
                   (four employees)                      0.14
           Operating costs per stove
              rent of hut                           0.03
              electricity                           0.02
              transport to market                   0.03
                   Subtotal                               0.08
           Total Production Costs                         2.25
              profit: owner                         0.37
              profit: project                       0.13
           Sale price by project                          2.65
(*) The design is as described in Table 3.
References (11,12). See also reference (6) for similar data from Niger
                                     TABLE 5
               Lightweight Fired Clay Stove(*) Production Costs
                              Burkina Faso, 1983
              Labor costs per stove(**)                0.13
              Firing                                   0.06
              Metal grate                              0.25
              Transport to market                      0.13
              Total production costs                   0.57
              Profit                                   0.93
              Sale price                               1.50
(*) The design was a single wall, chimneyless channel type stove as
described in Chapter IV; Fired Clay Stove Production.
(**) Material costs per stove are included under labor for digging clay.
Reference (13)
                                    TABLE 6
                    Massive Multipot Stove Production Costs
                              Burkina Faso, 1983
                Material costs per stove           US$
                  Bricks                           1.20
                  Cement                           2.88
                  Chimney                          1.01
                  Sand and gravel                  0.63
                      Subtotal                    5.72
                Labor costs per stove              8.86
                Transport costs to site            7.92
                Total production costs            22.50
                Subsidy by project                11.25
                Sale price by project             11.25
                (*) 400 CFA - US$ 1
                References (11, 12)
Field tests, or kitchen performance tests, of improved stoves are critical
to determining how well stoves perform in actual use and how acceptable
they are to local cooks.  In designing the tests and choosing participants,
it is important to consider a wide range of socioeconomic data and
other factors (14-16).  A particularly useful review of rural energy
surveys and techniques is given in (14) and additional information is
given in (15,16).  Examples of sociological surveys are given in (17,18).
In recent years greater attention has been focused on the interconnections
between energy use in households, smallholder agriculture and farm
animals, and informal commerce and industry, among others.  Such surveys
are proving crucial to the understanding of the dynamics of rural economies;
relevant studies are cited in Note (24).
Researchers examining hazardous smoke emissions from stoves may want to
include medical questions such as the incidence of eye and lung disease,
i.e., eye irritation, coughing, etc.  Relevant information can be obtained
from the East-West Center (Appendix J).
While a detailed review of survey techniques as applied to traditional
energy in developing countries is far beyond the scope of the presentation
here, there are a number of useful questions that should be asked.   Some
of these are listed below:
o   Who cuts the   wood and how?  Who produces charcoal and how?  What are
   the labor and transport techniques and costs for these fuels? Are fuels
   carried only in backhaul that would otherwise be empty cargo space? Is
   this activity the domain of a particular ethnic group, economic class,
   sex, or age?   Are these activities considered socially demeaning?   Is
   it a social activity?   Do children collect fuel? -- and does this
   encourage larger families or deprive children of their education?  Is
   the use of dung considered socially demeaning?
   How do all these factors change with the shift from subsistence
   foraging to commercial production and marketing?
o   What fuels are used and at what time during the year -- crop residues
   following harvest, dung, wood, etc.?   What are the competing uses for
   the fuels -- fuel, fodder, fertilizer, construction-material, artisanal
   uses, industrial heating, domestic heating?  Are the higher quality
   fuels sold to urban areas leaving lower quality fuels for rural use?
   Is wood green or thoroughly air dried before use?
o   Where is the fuel taken from? Who owns the land -- government, wealthy
   absentee landlord, peasant, community?   Who gathers the fuel from this
   land?  Are permits required?  How are they obtained?  What are the
   competing uses for that land -- trees or fuel crops, food crops,
   fodder?  Are trees killed when fuel is taken or are only branches
   pruned? Are trees replaced?
o   What is the history of the region -- the trends in its population
   density and distribution, farming techniques and intensity, forest
   density, building of roads, development of commercial timber harvesting,
   etc.?  What is the nature of the local community -- its size,
   sources of income, growth rate?
In performing surveys a few potential biases must be kept in mind as well.
These include:
o   Cultural perceptions of time, distances, and other factors can vary
   dramatically. Direct observation is needed.
o   Field research should include all seasons -- not just the dry season,
   nor just the "academic" season.
o   Respondents often exaggerate their personal situation or say what they
   think the interviewer wants to hear.   To avoid this, questions should
   focus on specific past actions, for example, "Have you ever used a type
   X woodstove?."   Alternatively, questions might be posed in a negative
   or leading manner to offset a respondent's tendency to answer affirmatively.
   Whether or not this is useful will depend strongly on the
   local culture.   Negative or leading questions must be used with great
   care to prevent them from introducing a bias in their own right.
o   Some questions should be left open-ended so that the respondent can
   provide some direction or provide types of information not initially
   anticipated.   Otherwise the results will tend to reflect the preconceived
   notions of the person writing the questionnaire.  As an example,
   one could ask an open-ended question such as "what did your household
   like (dislike) about the stove?"
o   People near rural roads, the most frequently visited, tend to be
   wealthier, more experienced, and more integrated into the market
   economy than those with less access to roads.
o   Key informants are unusual people and often do not represent the norm.
o   People reporting on social behavior often cite the ideal and not the
   norm. Their comments are useful but must be independently checked.
Given these general questions and considerations, the following are
specific proposals for determining the acceptability and performance of
improved stoves.  Countless variations of these are possible and should be
developed in order to respond well to local conditions.  For any survey
method, however, a preliminary test should be run to determine if it is an
effective approach before beginning a full-scale effort.
The families involved should not, under most conditions, be given the
stove free of charge on a permanent basis as this will bias potential
buyers to wait for the next giveaway.  Instead, for the acceptability and
wood consumption surveys, the stoves can be distributed on a trial basis,
at the end of which either the user buys the stove at a slightly reduced
rate consonant with the degree to which they were disrupted during the
survey, or they return the stove and are in turn themselves paid for their
trouble in assisting during the survey.  This also indicates somewhat the
value they place on the improved stoves.  For families that do not buy the
stove there should be a follow-up a few days later to observe how they are
adapting to the traditional stove.
Finally, when conducting surveys generally, it is important to be highly
suspicious of any and all data.  Frequent, independent verification of
results by varying the questions and the survey technique is an important
component of a field program.
Acceptability Surveys
Acceptability surveys normally consist of:
o   A background sociological, economic, and cultural survey with questions

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   such as those indicated in Worksheets 4, 5, and 7.
o  Distribution of stoves (produced in a production test) on a trial basis
   to perhaps 100 families for a three- to six-month period, or longer;
o   Visits every week or two to determine the condition and status of the
   stoves and what difficulties users of the stoves have.  Typical

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   questions are given in Worksheets 5 and 7.  It is particularly important
   to note whether or not the stove is in fact used.  For this,
   visits at mealtimes are useful; the stove can be inspected to see if it
   is warm or not, or if the ashes are fresh or not.  If still in doubt, a
   piece of straw or other material can be covertly placed in the stove to
   indicate later whether or not the stove was used during the interim.
   Additionally, it is important to estimate the lifetime of the stoves by
   monitoring their condition over a long period.
o   A final questionnaire, like those in Worksheets 5 and 7, to determine
   the general user response to the stove and why.  With care, the
   questions may be posed in a leading or negative manner as necessary.
Wood Economy Surveys
Wood economy surveys normally consist of all the components of an acceptability
survey and, additionally, include regular (i.e., daily) weighing
of the fuel used by a family to determine fuel consumption using both
traditional and improved stoves. The financial impacts, among others, on
a family using an improved stove can also be determined.   Typically, a
wood economy survey will require monitoring the fuel use of at least 40
families or as needed to generate statistically significant results.
Because wood economy surveys attempt to be quantitative, they are much
more complicated than acceptability surveys.  A number of errors are
possible that reduce the usefulness of the data.  Typical errors include
the following: The loss of fuelwood by loaning or trading it to neighbors
or carrying it off elsewhere for other uses (such unexpected and diverse
uses could include hitting goats to drive them out of the garden).   The
addition of unweighed fuel to the kitchen pile.  The family giving the
same response each day regardless of the real situation (for example
saying the number of people eating at a meal is the same when it is known
to vary).  The seasons changing during the course of testing (e.g., the
winter heating season or the rainy season beginning or ending), or
religious holidays taking place.  The family being wealthy and not
worrying about reducing wood consumption or the families compared being
from markedly different economic levels. Simply the act of weighing the
wood daily may sensitize the user and tend to cause the amount used to
decrease (19).  In addition, in many cases the family will not use the
improved stove part or all of the time, giving a wood economy that is a
corresponding fraction of the true potential of the stove.
Several different approaches are possible that reduce these problems.   For
all surveys generally, an attempt is made to test the same family with
both the traditional and the improved stove, to instruct families carefully
on the importance of using weighed wood for cooking only and to
cook only with weighed wood.  Additionally, families are chosen that are
reasonably homogeneous in economic level, size, living situation, etc.
Beyond that are the following options, among others:
o   The tester can remain with the same family for the entire day observing
   all fuel uses and manners of use.   The stove tested can be varied as
   desired.  Such rigid control eliminates many of the problems listed
   above, but is an exceedingly tedious method of gathering very few data.
   Such an effort is recommended once or twice in any survey, but is too
   expensive and time consuming for large-scale surveys.
o   For the same family, the tester can weigh fuel on a meal by meal basis.
   In some regions where fuel is gathered before every meal, this is
   unavoidable.   This is somewhat less tedious than the method above and
   it still allows reasonably good control over both fuel and stove use.
   The stove tested can be varied as desired. Stoves can be switched
   (i.e., traditional stove to improved stove and back) on a weekly or a
   daily basis.   Frequent switching of stoves (i.e., daily, or even meal
   by meal [20]), however, can seriously disrupt a household.  In areas
   where extra food is prepared for guests who may come later, data from
   daily or meal by meal switching of stoves can also be skewed by the
   amount of leftovers.   Finally, with any stove there is a certain
   natural learning time before the optimum use is achieved.  Switching
   stoves too frequently will tend to reduce use below optimum.
o   The stoves can be switched back and forth with the same family on a
   weekly basis.    A few days to a week are provided between weighings to
   give the user time to readjust to each type of stove.  This procedure
   is listed in Table 7.
Of these methods, switching stoves back and forth with the same family on
a weekly basis is preferred.  Such a procedure is particularly valuable
because it eliminates potential biases created by comparing different
families.   Additionally, it compensates for the automatic reductions in
consumption regardless of stove as the stove user becomes sensitized to
daily wood use by the act of daily weighing.  The major difficulty is
ensuring that a particular stove and only that stove is used during its
proper week.
If there is difficulty in getting a family to switch back and forth
between stoves, other families can serve as a control group for those
receiving the improved stove. These data can then be used to subtract the
effect of the act of measuring itself on fuel consumption or the effects
of seasonal change, etc.  In this case the procedure might be as shown in
Table 8.
Whatever the precise methodology chosen, the steps in the process are then
o   Interview the families who may participate to obtain background data as

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   shown in Worksheet 4.   Families should be chosen in order to be as
   homogenous as possible -- similar income level, family size, etc.
o   Weigh the wood in participating households on a daily basis as in

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   Worksheet 6.   The tester should arrive at roughly the same time each
   morning at a particular house, weigh the amount of fuel left from the
   day before, and weigh the amount of fuel to be added to the kitchen
   pile for that day. It is helpful if the "kitchen" pile is no more than
   twice the daily fuel consumption.   The fuel in the kitchen pile must
   not be used for any purpose other than cooking in that kitchen with the
   stove being evaluated.   If it is used with a variety of stoves, then
   the final numbers will be some average of the performance of the
   various stoves used.   The number of people eating at each meal the
   previous day is determined and from this the number of adult equivalents
   is calculated using Worksheet 6. Other questions can be asked as
   desired as indicated at the end of Worksheet 6.
o   Follow (daily fuel use) data collection with summary questionnaires as

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   illustrated in Worksheet 5.   Results should be shared with each family
   at the end of the testing and families should be thanked.  Final disposition
   of the stoves -- sold at a reduced price to the family or
   returned -- should be done and tabulated.
A number of sample biomass stove survey forms and questions are included
below.   In many cases it may also be useful to conduct surveys of the
fuelwood and charcoal producers and sellers as discussed in reference
(21).   Before beginning a full-scale survey, each question and each survey
form should be pretested to ensure that it is useful for that region, and
that it gives reliable responses.  If desired, questionnaires can be
numbered for computer tabulation (this will not be worthwhile except in
the largest of studies).
                                    TABLE 7
                             Preferred Methodology
                 Alternating Stoves Used By Each Family Weekly
     Time                   Activity/Stove
     Week  1          Daily wood weighings with stove A
     Week  2          No wood weighings, learning to use stove B
     Week  3          Daily wood weighings with stove B
     Week  4          No wood weighings, relearning to use stove A
     Week  5          Daily wood weighings with stove A
     Week  6          No wood weighings, relearning to use stove B
     Week  7          Daily wood weighings with stove B
                      Etc., as desired
                                    TABLE 8
                 Using Control Groups While Alternating Stoves
Time Period                  Group A                     Group B
                                                  (Control Group for A)
Week 1:
Daily wood weighing.   On the stove currently      On the stove currently
                       used by the family.        used by the family.
Week 2:
Sensitizing the        Provide the family          Family continues to
family on the need     with the new stove          use current stove.
to reduce wood use     to be evaluated;
and how to do it;      teach them how to
no daily weighings.    use it.
Week 3:
Daily wood weighing.   On new stove.               On current stove.
Week 4:
Sensitizing as in      No further work             Provide the family
week 2                  with this family.           with the new stove;
                                                  teach them how to
                                                  use it.
Week 5:
Daily wood weighing       - - - -                  On new stove.
Marketing tests follow the successful completion of field tests.   A major
component of marketing is promotion and among promotional possibilities
are radio and newspaper advertising, billboards, printed fabrics and
buttons, songs and sound trucks; public demonstrations at social centers,
schools, religious centers, and other public places; and stove sales by
commission at various commercial outlets.  A particularly effective
technique for public demonstrations is to provide enough wood to complete
the cooking when using the improved stove but not enough when using the
traditional stove. When public demonstrations are made it is important to
have stocks of improved stoves available for immediate sale; otherwise
potential customers can become frustrated.  In areas with relatively small
markets and a well-established traditional stove, rapid marketing can be
done by commissioning all traditional stove producers and commercial
outlets to make and sell only the improved version during a trial period.
Much of the focus of any marketing effort must be to train users how to
select the best stove for their purpose.  Such factors as recognizing the
importance of the channel gap and how wide it should be are crucial.
Additionally, it may be necessary to provide independent quality control
of stove production, providing an easily and (by educating the user)
widely recognizable stamp of certification or warranty for stoves that
meet the requirements.
Users must similarly be taught how to use the stove correctly.   This was
discussed in Chapter III under Control Efficiency.  Failure to train users
how to minimize fuel consumption can greatly reduce the potential savings
of any stove.
Initial marketing efforts are best directed at urban areas where there is
already a cash economy and where fuel costs are highest.  Once an urban
stove market is established, the stove may then spread more easily to
rural areas, driven in part by the prestige of being a modern (urban)
stove.   The general problem of stove dissemination in rural areas is,
however, a particularly difficult one (25) and much additional study is
Marketing efforts should also attempt, to the extent possible, to use
existing avenues to disseminate the improved stove.  Traditional metal
artisans or potters should be included at every step of the design and
development effort.  Market vendors should be used to sell the improved
stove.   Finally, existing neighborhood organizations should be included in
the dissemination effort, particularly for user training.   In all of these
cases, as much responsibility as possible should be given to individuals
to promote stoves in their area.
Studies should be done of the stoves' cost/benefit ratio based on production
and field tests and the local fuel costs.  Marketing efforts may
point out the need for changes in the form of the stove such as putting a
professional finish (electropolishing, electroplating, heat resistant
paint) on the stove to increase consumer appeal, or reducing the cost
through use of lighter components even at the expense of decreased stove
life. Different approaches can be tried in different areas such as using
social centers for sales in one area, commercal outlets in another, and
the results compared.  In all these cases, a record should be kept of the
date, client, address, family income, stove cost, stove size, etc. , so
that followup can be done later and to provide an understanding of the
dynamics of selling the stoves.  For example, sales at social centers
might prove to be to women who require an emphasis on speed and ease of
use, while sales at commercial outlets may be more frequently to men who
are more concerned about the potential financial savings.
Finally, the reader is once again urged to examine closely and use
regularly the financial and statistical techniques presented in Appendixes
F and G for the analysis of stove testing data.
In this chapter, the design and testing of fuel efficient charcoal stoves
and foundries are discussed in general terms.  No prototypes are presented,
only guidelines for their development.  Charcoal stoves have been
the focus of intense research, development, and dissemination efforts in
Kenya (1-5) and Thailand (6-8).  Detailed performance and production data
for Kenya, including breakdowns of manufacturing costs, are given in (3).
In Kenya, sales of improved charcoal stoves have grown rapidly and are far
above the original project goals.  By mid-1985, nearly 100,000 improved
charcoal stoves had been disseminated (3).  Those who are considering
working on charcoal stoves are strongly urged to contact KREDP or KENGO,
ITDG, E/DI, or the Thai group (6) (Appendix J) for design, testing, and
dissemination data.
Design Considerations
Charcoal stoves should be lightweight to minimize their absorption and
storage of heat.  Designs that thermally isolate tbe combustion chamber
from the rest of the stove may further reduce this stored heat.
Convective heat transfer can be optimized in charcoal stoves by fitting
the stove to the pot with an optimized pot to wall channel gap through
which the hot gases must flow.  The higher average combustion temperatures,
however, reduce the relative importance of convective compared to
radiative heat transfer.  Further, in Kenya channel designs have met
consumer resistance and most development and dissemination work has
focused on insulating the combustion chamber with durable fired clay or
cement/vermiculite linings (4).
Radiative heat transfer is much more important in charcoal stoves than in
wood stoves due to the higher combustion temperatures.  Further, burning
the volatiles given off by wood requires a large combustion volume.   In
contrast, because there are few volatiles in charcoal, radiative transfer
can be maximized by setting the pot as close to the fire as possible with
little concern about interfering with the combustion of volatiles.
Charcoal beds, however, have one complication not found when burning wood.
Wood volatiles burn above the fuel bed and the wood thus tends to burn
from the top down.  Radiative transfer is then directly from the flames to
the pot. In contrast, the charcoal fuel bed tends to burn from the bottom
and center upwards, as this is the area with greatest oxygen flow and is
the best insulated from the outside world, achieving the highest temperatures
for combustion.  Burning charcoal thus tends to radiate heat away
from the pot toward the stove bottom, and the charcoal next to the pot
tends to insulate the pot from both radiative and convective heat transfer.

bse1x117.gif (600x600)

This is illustrated in Figure 1.
To reduce this effect and to allow the hot gas to flow freely along the
pot bottom, it may help to support the pot slightly (2-3 cm) above the
f ire bed.  An insulated grate, insulated combustion chamber wall, and
insulated stove bottom or radiation shield may help reduce radiation loss
toward the bottom and sides of the stove.  Insulating linings have been
generally well received in Kenya (4).  Fired clay grates in particular,
however, tend to crack in just 2-3 months.  And because of their insulating
ability it is more difficult to light the charcoal by burning paper
or straw below the grate (4).
Finally, additional controls are needed despite the fact that burning
charcoal tends to self regulate its rate of combustion by forming a layer
of ash that slows the flow of oxygen to its burning interface.   A tightly
fitting door to regulate the flow of oxygen into the stove is desirable.
Contrast this with wood stoves where the firepower is best controlled by
removing the wood and extinguishing it directly.
Each of these factors will need to be carefully tested when developing a
practical charcoal stove.
Laboratory Testing Procedure
A number of slightly different lab testing methodologies have been
proposed for testing charcoal stoves of which several are reviewed in (9).
The testing procedure described below is almost identical to that for
woodburning stoves in Chapter V.  The two primary differences are that the
initial quantity of charcoal must be standardized and that lids are used
to better define the low power capability of the stove (10).  Controlled
cooking and field testing procedures are the same as for wood stoves.
1. Test conditions are recorded and the stove and pot are described in
   detail.  The stove and pot are thoroughly cleaned and dried.   The

bsexws10.gif (600x600)

   testing area should be well protected from the wind. <see worksheet 1>
2. A standard amount of charcoal, for example 0.500 kg, is weighed out for
   each test.  The moisture content and calorific value should be known and
   sufficient charcoal for the entire series of tests should be available,
   all of the same type, and stored in the same place so as to have a
   uniform moisture content.   If possible, the stove is weighed when empty
   and then with the charcoal.   This will prevent the loss of charcoal
   that could occur when transferring from the stove to the balance pan.
   This also reduces the disruption of the fire.
   It is important that the initial mass of charcoal be the same for each
   test in every stove.   Tests have shown that the calorific value of
   charcoal increases as it is burned in a stove - - probably due to the
   removal of low energy volatiles (9).
3. The pot, lid, and thermometer are weighed, and then a fixed amount of
   water is added, roughly equal to two-thirds the pot capacity but
   exactly the same for each test and all the stoves, (i.e., 5.000 kg).
   The lids should close snugly and the thermometers should sit well
   immersed in the water.
4. A measured amount of kerosene (i.e. 15 ml) is added to the charcoal,
   the fire is lit, and the pot put in place the moment that the kerosene
   itself goes out.   A delay in placing the pot on the stove to allow the
   fire to establish itself better can cause a large and varying amount of
   charcoal to burn during this period, increasing the scatter of the
   data.  Timing begins when the pot is put on the stove.   The fire is
   fanned as needed.   The door is left open throughout the high power
5. The temperature of the water and any actions to control the fire are
   recorded every five minutes.
6. The moment that the pot comes to a vigorous boil, the pot with lid and
   thermometer and the stove with the charcoal are each weighed and their
   weights recorded.   If the balance capacity is insufficient to weigh the
   stove with the charcoal, the charcoal must be removed and weighed
   alone.  This, however, is more difficult and also disrupts the fire.
7. As quickly as possible the pot is put back on the stove, the door is
   closed for the low power phase, and temperatures are again recorded
   every five minutes.   If the temperature drops more than 5[degrees]C below
   the boiling point, the coals should be stirred to improve their burning
   and/or the door should be opened a crack to increase air flow.
8. After thirty minutes the stove and charcoal, and the pot and water are
   again weighed and the values recorded.
In analyzing the data, three parameters are calculated for each phase:
the firepower P, the percent heat utilized PHU, and the specific consumption
The firepower is given by:
   P = -------------------- (kilowatts)
where [C.sub.c] is the calorific value of the charcoal in kJ/kg, [M.sub.c] is the amount
of charcoal consumed during that phase of the test in kg, and I is the
elapsed time in minutes. Again, it should be noted as in point 2 of the
procedure above, that the calorific value of charcoal increases upon
burning.   This often causes serious discrepancies, for example, between
the high power and low power phases of the test.  In this case, the low
power phase has a calculated PHU that is unreasonably high.
The percent heat utilized PHU is calculated by:
       4.186[W.sub.1]([T.sub.f]-[T.sub.i]) + 2260([W.sub.i]-[W.sub.f])
PHU = --------------------------------------------------------------- x (100%)
                            [M.sub.c] [C.sub.c]
where [W.sub.i] and [W.sub.f] are the masses of the water at the beginning and end of
that phase in kg, ([T.sub.f] - [T.sub.i]) is the temperature change of the water during
that phase in [degrees]C. The constant 4.186 kJ/kg is the specific heat of water
and the constant 2260 kJ/kg is its latent heat of vaporization.
The specific consumption is given by (11):
    SC = ---------
where [M.sub.c] and [W.sub.f] are the same as above.  For convenience, the specific
consumption defined here can be expressed in terms of grams of charcoal
consumed per kilogram of water "cooked."
Alternatively, a specific consumption that does not penalize the stove for
evaporating water can be used.  Its definition uses instead the initial
water quantity:
     [SC.sub.2] = ---------
Finally, if there is a large variation in starting water temperatures from
day to day, the water temperature can be normalized, giving an SCN, as
done in Chapter V.
The best measure for the stove's performance, PHU, SC, or [SC.sub.2], must be
determined by comparing laboratory data to controlled cooking and field
testing data.  At present, such data are not generally available.
Design Parameters To Be Tested
A number of different parameters affecting stove performance should be
examined.   Among these are the following.
o   pot to wall channel gap;
o   pot to wall channel length;
o   use and placement of insulation;
o   use of an insulated stove bottom or radiation shield below the grate;
o   hole density of the grate;
o   mass of the grate and the possible thermal isolation of the grate from
   the rest of the stove;
o   use of low cost bellows to achieve high fire powers quickly;
o   grate-to-pot height (leaving a small space for free airflow between the
   charcoal and the pot);
o   form of the grate -- conical, flat, etc.; and
o   injection of secondary air to reduce of carbon monoxide.  Tests of a
   west african charcoal stove have shown that secondary air could reduce
   CO emissions by 25% (11).
Sample Data
Tables 1-5 summarize test data from (9) and are presented here as examples
of the type of data that are generated by the charcoal testing procedure.
These data are particularly useful in demonstrating differences between
wood and charcoal stoves.  Additionally, these data illustrate aspects of
both test methodology and data analysis that may mislead the unwary.
Four tests were done for each combination of channel gap, length, and the
use of insulation.  The coefficient of variation (Appendix G) was typically
0.1 or less.  Several comments can be made about these data:
o   There is a dramatic increase in the PHU between the high and low power
   phases.  This is due to both thermal inertia and a varying calorific
   value of the charcoal in the stove.   The energy needed to warm the
   stove during the initial high power phase (the stove is cold at the
   start) will lower the PHU compared to the later, low power phase.
   Further, the charcoal burns its lower energy volatiles at the start of
   the test.  Using an average calorific value will then cause the
   calculated PHU to be overstated during the high power phase and
   understated during the low power phase.
o   The observed PHU during the high power phase is independent of the
   channel gap and length and the use of insulation.  This suggests that
   the dominant factor here is the thermal inertia of the stove.
o   Large increases in PHU occur during the low power phase with the use of
   insulation and longer and narrower channels.  This is expected from
   consideration of conductive and convective heat transfer processes.  A
   multiple linear regression on this data is presented in Appendix G.
   These efficiency increases, however, have little effect on the overall
   PHU because little energy is used during the second phase.
o   The total PHU increases weakly with increasing channel gap, channel
   length, and use of insulation.   The rather odd result that a wider
   channel gap should give a higher PHU is in fact due to that stove
   burning a large amount of charcoal during the second phase and thus
   more heavily weighting that higher efficiency phase in the total.  In
   other words, the stove with the wide channel gap burned too much fuel,
   but the PHU showed this not as a loss, but as a gain.  The PHU is,
   then, a poor indicator of the fuel efficiency of a charcoal stove.
o   The specific consumption shows no effect for varying channel length or
   insulation; only the channel gap reduces consumption, and the 3-mm gap
   has a significant savings over the stoves with 5- or 8-mm gaps or the
   traditional malgache stove.
o   The SC shows little change over [SC.sub.2] for the 3-mm gap but a significant
   increase in consumption for the 5-mm and 8-mm gaps.  This indicates, as
   did the PHU, that, for whatever reason, the control of air flow through
   these latter stoves is much less efficient than for the 3-mm stove.
   That is, the larger channel gap results in much greater firepowers and
   excess evaporation.   This also indicates that SC is a more sensitive
   measure of stove performance than [SC.sub.2].  The importance of air supply on
   the high and low power performance of charcoal stoves has also been
   noted in (12) with regard to testing of the Umeme stove.
                                    TABLE 1
                   Charcoal Stove(*) Tests, Senegal 1983-84
                       High Power Phase: Summary of PHUs
                                      Channel Length
                       No Insulation                   With Insulation
    Channel         5 cm    10 cm     15 cm            5 cm    10 cm      15 cm
     3 mm           25.9     27.0      26.0            26.0     26.2      26.9
     5 mm           25.0     23.8      25.7            24.2     25.2      24.5
     8 mm           24.7     25.1     25.1           25.9      24.9      25.6
    Traditional West African "Malgache" Stove: 23.0
                                    TABLE 2
                   Charcoal Stove(*) Tests, Senegal 1983-84
                       Low Power Phase: Summary of PHUs
                                      Channel Length
                       No Insulation                   With Insulation
    Channel         5 cm   10 cm     15 cm            5 cm    10 cm    15 cm
     3 mm           41.4    36.5      62.2            57.5     68.6     78.4
     5 mm           36.9    43.9      47.7            50.2     71.9     77.3
     8 mm           39.1    46.1      54.3            48.8     61.7     64.9
    Traditional West African "Malgache" Stove: 24.0
                                    TABLE 3
                   Charcoal Stove(*) Tests, Senegal 1983-84
                       Both Phases: Summary of PHUs
                                        Channel Length
                          No Insulation                  With Insulation
    Channel           5 cm    10 cm     15 cm           5 cm    10 cm     15 cm
     3 mm             27.4    28.0      29.0           28.8     30.3      31.3
     5 mm             27.3    26.7      28.9           29.5     32.6      31.9
     8 mm            28.1     29.9      32.6          31.3     33.3      35.5
    Traditional West African "Malgache" Stove: 23.4
                               TABLE 4
                 Charcoal Stove(*) Tests, Senegal 1983-84
                    Summary of Specific Consumption SC(**)
                                      Channel Length
                        No Insulation                  With Insulation
    Channel         5 cm    10 cm     15 cm           5 cm    10 cm     15 cm
     3 mm           66.7      65.0     65.4          66.0      66.0     65.1
     5 mm           79.0     76.7      72.6           84.5     76.6      77.0
     8 mm           85.2     86.9      89.3           82.8     88.1      89.5
    Traditional West African "Malgache" Stove: 95.8
                                    TABLE 5
                   Charcoal Stove(*) Tests, Senegal 1983-84
                Summary of Specific Consumption [SC.sub.2](**)
                                  Channel Length
                    No Insulation                  With Insulation
    Channel      5 cm   10 cm     15 cm           5 cm    10 cm     15 cm
     3 mm        64.7    63.2      63.0           63.7     63.1      62.1
     5 mm        74.5    72.8      68.7           77.8     70.3      71.2
     8 mm       79.0     79.3     79.8           75.7      78.4     78.2
Traditional West African "Malgache" Stove: 23.0
(*)Tests are based on a conical type charcoal stove with a constant pot-to-wall
channel gap; an operable door; a grate with a 30% hole density; and a
pot-to-grate distance of approximately 5 cm.  (**)Calculations presented
here are normalized with respect to initial water temperatures (13).
These results contrast sharply with the case for woodstoves.  The PHU for
woodstoves was found to be a reliable indicator of their cooking performance
in tests in West Africa (14).  Further, tests there found the
performance of channel type woodstoves to be highly dependent on the
channel dimensions and the use of insulation, as discussed in Chapter III
(15).   These differences between charcoal stove and woodstove performance
are due primarily to differences in the combustion characteristics of
these fuels.  In particular, heat transfer in charcoal stoves is due
primarily to radiation; convection is predominant in woodstoves.   Control
of a charcoal stove is a function of the airtightness of the door and
other factors within the stove itself, while woodstoves are controlled
simply by removing the wood.
A large amount of charcoal is used by artisans in fabricating metal
objects such as aluminum pots.  In the region of San, Mali, for example,
preliminary estimates by the Mali Solar Energy Laboratory (16) are 155,000
kg of wood used for cooking and other purposes and 31,000 kg of charcoal
used for blacksmithing work each year.  If the conversion efficiency of
wood to charcoal is assumed to be 20%, then 155,000 kilograms of wood were
used to produce this charcoal.
Traditional forges are flexible and easy to make and maintain but they are
inefficient.   By shielding against radiant heat loss and by using counterflow
heat exchangers to recuperate waste heat, such forges could be made
much more efficient.
A typical traditional foundry for aluminum pot production consists of a
metal barrel sunk into the ground for insulation and lined on the inside

bse2x126.gif (480x480)

with a banco mixture to protect the metal from corrosion (Figure 2).
Leaving a space below for the plenum chamber (air entry and ash collection),
heavy iron rebar is laid horizontally to act as a grate.  The top
of an old barrel is laid over the entire system to reduce radiant heat
losses.   The forge is activated by a small hand driven blower forcing air
through a 5-cm-diameter pipe into the plenum chamber below the grate and
then into the charcoal bed.
The use of an air-to-air heat exchanger design may significantly improve
the efficiency of these foundries.  An example design consists of two

bse3x126.gif (540x540)

dependent parts (Figure 3): a tightly fitting insulated lid to reduce
radiant heat loss and to seal the top of the furnace from air leaks, thus
forcing the hot gases to go through the heat exchanger; and a counterflow
heat exchanger to recuperate waste heat by capturing it in the incoming
combustion air.  The lid can be made of metal and whatever high temperature
insulation is available.  However, the lid and the top of the heat
exchanger must be carefully matched so that they seal and prevent the
combustion gases leaving the furnace from bypassing the heat exchanger.
Banco could be used to improve the matching of the cover and the top of
the heat exchanger in sealing.  Additionally, allowance must be made for
thermal expansion of the metal, parts and easy access to the interior so
that fouling residues can be removed.  Details of the mathematical analysis

bse4x127.gif (600x600)

are given in Appendix E and results are shown in Figure 4.  As an example,
a 2-m long heat exchanger with an 8-mm gap can potentially recuperate 68%
of the energy of the fire, or 6.8 KW in this case, at the cost of 3.7 W in
additional effort needed to operate the fan.  That is a return of nearly
2000 to 1.
Such heat exchangers may also be useful in improving the efficiency of
ovens, crop dryers, and other such devices.  For example, the use of heat
exchangers in tobacco curing sheds in Malawi reduced fuel use by 27% and
drying time by 20% (17).  Additional references on the technical aspects
of heat exchanger design and development are listed in Appendix E.
For heat conduction in isotropic materials, assuming no heat generation

bsexeq1.gif (101x528)

within the material itself, the differential equation is: <see equation 1>
where T is the interior temperature distribution, t is the time, and
[alpha]=k/[[rho]c.sub.p] is called the thermal diffusivity where k is the
thermal conductivity, [rho] is the density, and [c.sub.p] is the specific
heat (1,2).
The operator [Laplacian operator] is given in various coordinate systems
by: <see equations below>

bsexeq2.gif (200x600)

Heat Flow Through An Infinite Slab
Consider an infinite (in y and z directions) slab with thickness s in the
x direction and temperatures [T.sub.1] and [T.sub.2] on its two faces.   In the steady
state the heat conduction equation for this system becomes <see equation 5>

bsexeq5.gif (84x600)


bsexeq6.gif (60x600)

This has solutions of the form <see equation 6>
Applying the boundary conditions <see equations below>

bsexeq7.gif (145x600)

The Fourier conduction law gives <see figure 9> <see figure 1 to 4>

bsexeq9.gif (84x600)

bsex130.gif (600x600)

where n is the surface normal. Thus, in this case <see equation 10>

bsexeq10.gif (75x600)

where (s/ka) is a thermal resistance.
Now consider the case of an infinite slab with a hot gas on one side and a
cold gas on the other.
Beginning again with <see equation 5>

bsexeq5a.gif (94x600)

there are solutions of the form <see equation 6>

bsexeq6a.gif (84x600)

Now the boundary conditions for convective heat transfer, discussed in
Appendix B, are applied: <see equation 11>

bsexeq11.gif (84x600)

where [h.sub.1] and [h.sub.2] are the surface convective heat loss coefficients (Appendix
B) and the equations are to be evaluated at x=0 and x=s, as indicated.
The difference in sign between the two surfaces is determined by whether
heat flow is in the direction of or opposite to the surface normal.
Applying (dT/dx)=a from equation (6) and evaluating T-ax+b at x=0, x=s <see equation 12 and 13>

bsexeq12.gif (145x600)

Applying the Fourier conduction law <see equation 14>

bsexeq14.gif (117x600)

where q is the heat flux. Typical values for the surface heat loss
coefficient h for low temperature differences are 5 W/[m.sup.2][degrees]C in still air to
over 15 W/[m.sub.2][degrees]C in a more moderate 3 m/s wind (3). Thus for values of k of
roughly 1.0 W/mK and values of [h.sub.1] and [h.sub.2] of 5 W/[m.sub.2][degrees]C, the surface heat
loss coefficient plays a major, if not dominant, role for thicknesses s up
to 0.50 m and more. However, for this geometry, increasing s reduces heat
loss over the entire range of values, unlike other geometries presented
                                   TABLE 1
                   Typical Property Values at 20[degrees]C
                                k             [rho]           [C.sub.p]
   Material                     W/mk          kg/[m.sup.3]   J/LGK
     aluminum alloys          110-200        2600-2800       850-900
     steel alloys              12-70         7700-8000       450-480
                            average 35
   Nonmetallic Solids
     brick                   0.38-0.52       1760-1810         840
     clay                      1.28             1460            880
     cement                  0.8-1.4         1900-2300         880
     hardwood (ash)          0.17-0.21        609-800         2390
     sandstone               1.6-2.1         2160-2300         710
     cardboard                0.064             --             --
     charcoal                 0.05           0.3-0.5           670
     cotton                   0.059               80          1300
     fiber board
     (insulating)            0.048            237             --
     glass wool               0.04             200            670
     wood felt                0.05              330              --
     water                    0.597           1000           4180
     air                      0.0262           1.177          1005.7
   Reference (1)
Two other brief points. First, it should be noted that, comparing
equations (10) and (14), thermal resistances can be added generally in the
manner <see equation below>

bsex132.gif (97x285)

Where [delta]T is the temperature difference.
Secondly, the small surface heat loss coefficient h and its extreme
sensitivity to the wind are both features of it being determined by a
surface boundary layer of still air with thermal conductivity k=.026 W/mK.
Heat Flow through the Walls of a Cylindrical Combustion Chamber
Equations (1) and (3) give for the steady state of an infinite cylinder: <see equation 15>

bsexeq15.gif (67x600)

which has solutions of the form <see equation 16>

bsexeq16.gif (84x600)

Where 1n is the natural logarithm.
For inner and outer wall temperatures of [T.sub.1] and [T.sub.2]
respectively, then <see equation 17>

bsexeq17.gif (94x600)

where L is the length of the portion of the cylinder considered and the
cylinder is assumed to be infinitely long (no end losses).
For the case where there is a gas at temperature [T.sub.1] inside the cylinder
and one at [T.sub.2] outside, with surface heat loss coefficients of [h.sub.1] and [h.sub.2],
and T=a1n(r)+b <see equation below>

bsexeq18.gif (145x600)

with solutions: <see equation 19>

bsexeq19.gif (200x600)

The heat loss from this cylindrical combustion chamber per unit length and
temperature difference is given by: <see equation 21>

bsexeq21.gif (94x600)

Assuming that [h.sub.1] = 15 W/[m.sup.2][degrees]C; [r.sub.1]=0.1 m; [h.sub.2]=5 W/[m.sup.2][degrees]C; k=1.0 W/n[degrees]C then
equation (21) gives the values shown in Table 2.
It is interesting to note (Table 2) that the heat loss Q actually increases
for 0.12<r<0.30 m and does not fall below its value at [r.sub.2]=0.12
until [r.sub.2][nearly equal to]0.37 or a 27 cm thick wall. However, to reach this steady state
condition itself requires a tremendous amount of heat, an amount increasing
with wall thickness. Thus, as shown in more detail below, it is
preferable to keep such walls thin.
One can similarly look at the functional dependence of Q on other parameters:
for [h.sub.1] = 15 W/[m.sup.2][degrees]C; [r.sub.1] = 0.12 m; [h.sub.2] = 5 W/[m.sup.2][degrees]C, equation (21) gives the
values shown in Table 3.
Thus, to significantly reduce the heat loss by the wall, the conductivity
of the material in the wall must be made quite low, i.e., k<[near equal to]0.1 W/m[degrees]C.
                   TABLE 2
          Values For Equation (21)
        [r.sub.2]        --------------
          (m)            (W/m[degrees]C)
          0.12              .398
          0.14              .411
          0.16              .419
          0.18              .423
          0.20              .424
          0.25              .420
          0.30              .411
          0.35              .401
          0.40              .392
          0.45              .382
          0.50              .374
          0.60              .358
          0.70              .345
          0.80              .334
          1.00              .315
                   TABLE 3
          Values For Equation (21)
            k                 Q
     (W/m[degrees]C)    (W/m[degrees]C)
      0.1                    .241
      0.5                    .371
      1.0                    .398
      5.0                    .422
     10.0                   .425
     50.0                    .428
Spherical Geometry
A similar set of calculations can be done for a closed sphere (i.e., a
closed massive stove with a proportionately small pot).
In this case <see equation 22>

bsexeq22.gif (84x600)

and has solutions of the form <see equation below>

bsex134.gif (87x317)

Using the same boundary conditions as (11) above, this gives solutions of
the form <see equation below>

bsexeq23.gif (200x393)

With [h.sub.1] = 15 W/[m.sub.2][degrees]C; [h.sub.2]=5 W/[m.sub.2][degrees]C; [r.sub.1]=0.1 m;
k = 1.0 W/m[degrees]C as parameters, equation (24)
gives the values shown in Table 4.
In this case, the heat loss with increasing
radius is even more severe than in the case
of the cylinder above. The reason is that
the surface heat loss is now increasing at
a rate of [r.sup.2] [sub.2] for the sphere compared to a
rate of [r.sub.2] for the cylinder. Further, the
insulating value of the wall <see equation below>

bsexeq24.gif (84x256)

is increasing only very slowly compared to the cylinder's insulating
value: <see equation below>

bsex135.gif (108x150)

Knowing the temperature distribution the energy required to reach that
steady state level can also be calculated.
The change in heat stored in a body is generally given by: <see equation 25>

bsexeq25.gif (84x600)

where dV is a volume element and [T.sub.2] is the initial temperature of the
volume element.
For a typical metal stove, for example, one might find: <see equation below>

bsexeq26.gif (145x600)

                   TABLE 4
          Heat Loss From a Sphere
          As a Function of Radius
       [r.sub.2]               Q
         0.12          0.565
         0.14          0.638
         0.16          0.689
         0.18          0.723
         0.20          0.754
         0.25          0.793
         0.30          0.808
         0.35          0.814
         0.40          0.815
         0.45          0.814
         0.50          0.813
         ....          .....
         0.70          0.804
         ....          .....
         1.00          0.793
Wood has roughly 18,000 kJ/kg of energy in it so this is the equivalent of
22.5 gm of wood in energy to heat the stove to its steady state condition.
In contrast, for a typical cylindrical massive stove one might find <see equation below>

bsexeq27.gif (105x393)

Again using L=0.3 m; [rho]=2000 kg/[m.sup.3]; [c.sub.p]=0.880 J/kgK; one finds dE-22 MJ
or the equivalent of 1.22 kg of wood in energy.
Transient Heat Loss Calculations
The above calculations for beat loss were based on the steady state
condition which for massive walls can only be achieved after several hours
of operation. The time to reach this steady state condition can be easily
estimated in the special case of the metal cylinder where there are no
thermal gradients of significance.  In this case the temperature rise of
the metal cylinder can be calculated by comparing its specific heat to the
total heat gain -- the heat flux in minus the heat flux out. Thus <see equation below>

bsexeq28.gif (94x353)

where V is the volume of metal in the stove with a density [rho] and a
specific heat of [c.sub.p], and [A.sub.1] and [A.sub.2] are the inner and outer surface areas,
[A.sub.1][nearly equal to][A.sub.2]; [T.sub.1] and [T.sub.2] are the interior and exterior gas temperatures with
surface convective heat loss coefficients of [h.sub.1] and [h.sub.2]. Solving for T
gives <see equation 29>

bsexeq29.gif (67x600)

Where e is the base for natural logarithms, e=2.71828.
The characteristic time for this system, the time for it to reach (1- 1/e)
of its steady state value, is given by the inverse of the exponent of (29) <see equation below>

bsexeq30.gif (94x600)

For the same stoves as in Table 5 with [h.sub.2]=5 W/[m.sup.2][degrees]C; [[rho].sub.massive]=2000 kg/[m.sub.3];
[c.sub.massive]=0.880 J/kg[degrees]C; [rho].sub.metal]=8000 kg/[m.sup.3]; [c.sub.metal]=450 J/kg[degrees]C.
    [t.sub.c] = 6 minutes         metal stove
    [t.sub.c] = 4.9 hours         massive stove
Certainly, this approach is not correct for the massive stove as there are
significant temperature gradients within its walls, but it does indicate
the rough order of time needed to reach steady state in a massive stove.
A more general calculation which takes into account the thermal gradients
in the massive stove walls is given below.
Numerical Techniques
Consider now the more general case of transient heat loss where the
temperature gradients in the wall are included. Returning, <see equation below>

bsex137.gif (121x600)

where [T.sub.g] is the temperature of the hot gas and [T.sub.a] is ambient temperature.
Such equations and non-homogenous boundary conditions are straight forward
to solve using integral transform techniques. Reference (4) gives their
general solution in several different coordinate systems. However, these
solutions are generally transcendental equations and it is easier to
simply generate a numerical solution directly from equations (1) and (11).
The numerical analysis is begun by dividing a cylindrical wall into small
concentric sections. The cross section of the wall is shown in Figure 4.

bse4x130.gif (437x600)

Ignoring end effects, the heat conduction equation for this cylindrically
symmetric geometry becomes <see equation 31>

bsexeq31.gif (105x600)

Standard numerical procedures (4) give for the temperature [mm] at point i
(figure 4 indicates how i is determined) and time n <see equation below>

bsexeq32.gif (200x600)

Where [omicron]() is the order of the truncation error resulting from terminating
the series expansion.
Using these <see equations 35> equations, for points inside the wall

bsexeq35.gif (105x600)

where the value [r.sub.i] is given by i[delta]r or, equivalently, <see equation 36>

bsexeq36.gif (60x600)

At the surface the boundary conditions, equation (11), are, <see equation below>

bsex138.gif (167x437)

to get at the inner surface, i=[i.sub.1] <see equation 37>

bsexeq37.gif (75x600)

and at the outer surface i-[i.sub.2] <see equation 38>

bsexeq38.gif (75x600)

rather than equation (36).
Several simple modifications of this are possible to more accurately
reflect the conditions within a stove.
First, at both the inner and outer surfaces the convective heat transfer
boundary conditions can be modified to include radiant heat transfer.
Modifying equation C-12, this can be written as <see equation 39a>

bsexeq39.gif (75x600)

where i=[i.sub.1], that is, i is the inner surface; and <see equation below>

bsexeq40.gif (84x437)

for i=[i.sub.2], the outer wall. In these equations, [sigma] is the Stefan-Boltzmann
constant, A is the area of the pot bottom and firebed, and [F.sub.fw] is the view
factor between the firebed and the combustion chamber wall. The factor [beta]
reduces the effective size of the fire as it does not generally cover the
entire firebed but more usually only the center half diameter. [T.sub.f] is the
temperature at which the firebed radiates and [T.sub.p] is the pot temperature.
In the second equation, [[epsilon].sub.w] is the emissivity and A is the area of the
wall. The emissivity is missing in the first equation because it is
assumed equal to 1. This is reasonable as the interior will be blackened
and further this assumption avoids the complications of multiple reflections
on the inside surfaces. The view factor F is missing in the second
equation because it is equal to 1.0 -- the stove is radiating uniformly
out in all directions. Finally, it should be noted that the temperatures
and heat losses predicted by this program are for the combustion chamber
only and only for a single stove power -- usually high. To predict the
values for an entire stove the exterior area and interior area exposed to
the hot gases must be increased appropriately while keeping the interior
area exposed to the radiant heat of the fire the same.
The second modification accounts for the increasing heat loss from the
exterior surface as it warms due to increasing convective heat transfer.
Warm air rises. The hotter the exterior wall the more it warms the
adjacent ambient air and the faster it rises, increasing the convective
heat transfer to it even more. Correlations for this factor, natural convection
by a heated vertical plate or cylinder, are given in most basic
texts and are listed in Appendix B. The form used here for the exterior
convective heat transfer coefficient is from reference (5): <see equation below>

bsex139.gif (108x393)

where i=[i.sub.2], and L is the height of the plate, or in this case, the combustion
The performance of the bare metal stove, in particular, will be affected
by this variable exterior heat transfer coefficient due to its generally
higher temperatures. Similarly, the performance of the bare metal stove
will be more strongly affected by the wind than will the performance of
insulated metal, fired clay, or concrete stoves. However, as cooking is
almost always done in protected locations this is not expected to be an
important consideration.
To reduce the heat loss of the bare metal wall, double wall geometries
with a dead air space can be considered. For this case the same equations
as above apply for each wall separately, but the boundary conditions
between the two walls must be modified. In particular, the effective heat
transfer coefficient across a dead air space is given empirically by
reference (5). <see equation 41>

bsexeq41.gif (117x600)

where [delta] is the space between the two walls, CH is the combustion chamber
height, and [T.sub.1] and [T.sub.2] are the surface temperatures of the two facing
Alternatively, lightweight insulants can be used. Again the above equations
are used twice, first to calculate the heat conduction through the
first wall, then through the insulation. In this case, the boundary
condition between the walls and insulant is given by setting their facing
surfaces at the same temperature (removing the radiative and convective
heat transfer terms), and setting their heat fluxes equal at the surface
between the two walls; <see equation 42>

bsexeq42.gif (94x600)

where [k.sub.1], [T.sub.1] and [k.sub.2], [T.sub.2] are the thermal conductivities and temperatures of
the wall and insulant at the point of contact.
Computer programs in Microsoft basic for the Apple Macintosh are listed
below along with a table (Table 5) of the parameters used. The output is

bsextab5.gif (600x600)

presented in the figures in the text, chapter III, and discussed there.
In addition, to the graphs of computer output presented in Chapter III,
other data of interest that has been generated by this numerical routine
include: The integrated wall loss as a function of time; The wall loss
as a function of different levels of interior wall convective or radiative
heat loads; and radiant transfer from the wall to the pot (Appendix C).
The numerical routine discussed above is stable (4) if <see equation 43>

bsexeq43.gif (84x600)

The numerical routine was also tested to ensure that it converged to exact
steady-state analytical solutions and did so independently of the size of
the time step, t, or node size, r. Convergence was excellent in all cases
tested. The primary drawback of this numerical routine, however, was the
very small time steps necessary when [alpha] was large -- such as for metal
stoves. This led to run times of several hours in such cases. Among the
methods available for speeding up this calculation in such cases are using
"compiled" rather than "interpreted basic" and by careful optimisation of
the computer code itself. These tasks are left to the interested reader.
Program 1:
    5 CLS: BEEP
    7 CLEAR
    50 OPEN "LPT1:" FOR OUTPUT AS #1
    100 DIM TT(S), TN(S)
    151 INPUT "ENTER RA, RZ, CH"; RA, RZ, CH
    153 PRINT #1, "RA="; RA, "RZ="; RZ, "CH="; CH
    200 INPUT "ENTER HA, EE"; HA, EE
    202 PRINT #1, "HA="; HA, "EE="; EE
    210 INPUT "ENTER HC, HD, HK"; HC, HD, HK
    212 PRINT #1, "HC="; HC, "HD="; HD, "HK="; HK
    220 INPUT "ENTER DT, NT, PT"; DT, NT, PT
    222 PRINT #1, "DT="; DT, "NT="; NT, "PT="; PT
    510 PRINT #1, "THE STABILITY FACTOR IS", USING "##.### ^^^^"; BB
    520 IF BB)=.5 6070 220
    530 INPUT "ENTER TA, TG, TF"; TA, TG, TF
    532 PRINT #1, "TA=";TA, "TG="; TG, "TF="; TF
    533 REM TYPICAL VALUES ARE TA=300, TG=700, AND TF=1000
    550 SGM=.000000056697# 'THE STEFAN-BOLTZMANN CONSTANT 5.6697D-08
    552 FV1=(CH/RA)^2+2!
    561 TT(I)=TA
    562 TN(I)=TA
    563 NEXT I
    652 PRINT #1, "TEMP";JS;
    653 NEXT JS
    710 TN(0)=BB*((1-1/(2*11))*(TT(1)+BAR+BA*(TG-TT(0)))-2*TT(0)+(1+1/(2*I1))*TT(1))+TT(0)
    740 SM=S-1
    760 TN(I)=BB*((1-1/(2*I2))*TT(I-1)-2*TT(I)+(1+1/(2*I2))*TT(I+1))+TT(I)
    765 NEXT I
    790 19=I1+S
    795 TN(S)=BB*((1-1/(2*I9))*TT(SM)-2*TT(S)+(1+1/(2*I9))*(TT(SM)-BZR+BZ*(TA-TT(S))))+TT(S)
    800 QQ=-CH*HK*RA*6.283185#*(TN(1)-TN(0))/DR
    900 X=P*PT
    925 PRINT #1, USING "####.##"; QT;
    930 FOR IZ=0 TO S STEP 1
    936 PRINT #1, USING "#####.#"; TN(IZ);
    937 NEXT IZ
    938 PRINT #1, USING "#######.##"; QQ;
    940 PRINT #1, USING "########.#"; TOTQ
    1000 FOR 1=0 TO S STEP 1
    1020 NEXT I
    1100 NEXT N
    1499 BEEP
    1500 END
    Program 2:
    5 CLS
    7 CLEAR
    50 OPEN "LPT1:" FOR OUTPUT AS #1
    100 DIM TT(S), TN(S), ZTT(ZS), ZTN(ZS)
    151 INPUT "ENTER RA, RZ"; RA, RZ
    153 PRINT #1, "R4="; RA, "RZ="; RZ
    158 PRINT #1, "ZRA="; ZRA, "ZRZ="; ZRZ
    161 INPUT "ENTER CH"; CH
    171 INPUT "ENTER HA"; HA
    178 PRINT #1, "EE="; EE, "ZEE="; ZEE
    181 INPUT "ENTER HC, HD, HK"; HC, HD, HK
    183 PRINT #1, "HC="; HC, "HD="; HD, "HK="; HK
    193 PRINT #1, "ZHC="; ZHC, "ZHD="; ZHD, "ZHK="; ZHK
    201 INPUT "ENTER TA, TG, TF"; TA, TS, TF
    203 PRINT #1, "TA="; TA, "TG="; TG, "TF="; TF
    211 INPUT "ENTER DT, NT, PT"; DT, NT, PT
    213 PRINT #1, "DT="; DT, "NT="; NT, "PT="; PT
    421 QI1P=1+1/(2*I1) : ZQI1P=1+1/(2*ZI1)
    422 GI1M=1-1/(2*I1) : ZQI1M=1-1/(2*ZI1)
    423 GI2P=1+1/(2*(I1+S)) : ZQI2P=1+1/(2*(ZI1+ZS))
    424 QI2M-1-1/(2*(I1+S)) : ZQI2M=1-1/(2*(2I1+ZS))
    426 SM=S-1 : ZSM-ZS-1
    520 IF BB>=.5 GOTO 211
    521 IF ZBB>=.5 GOTO 211
    550 SGM=.000000056697# 'THE STEFAN-BOLTZMANN CONSTANT 5.6697D-08
    552 FV1=(CH/RA)^2+2!
    561 TT(I)=TA
562   Tn(I) =TA
563   NEXT I
571   ZTT(ZI)=TA : ZTN(ZI)=TA
572   NEXT ZI
649   SZS=S + ZS + 1
652   PRINT #1, "TEMP";JS;
653   NEXT JS
710   TN(0)=BB*(QIIM*(TT(1)+BAR+BA*(TG-TT(0)))-2*TT(0)+Q11P*TT(1))+TT(0)
740   SM=S-1
755   12=1/(2*(I1+I))
760   TN(I)=BB*((1-12)*TT(I-1)-2*TT(I)+(I+I2)*TT(I+1))+TT(I)
765   NEXT I
792   BZ=(2!*DR/HK)*3.93*(ZRA-RZ)^-.1389*CH^-.1111*(TT(S)-ZTT(0))^.25/(TT(S)+ZTT(0))^.3171
795   TN(S)=BB*(QI2M*TT(SM)-2*TT(S)+QI2P*(TT(SM)-BZR+BZ*(ZTT(0)-TT(S))))*TT(S)
810   ZTN(0)=ZBB*(ZQI1M*(ZTT(1)+ZBAR+BZ*(TT(S)-ZTT(0)))-2*ZTT(0)+ZQI1P*ZTT(1))+ZTT(0)
855   Z12--1/(2*(ZII+I))
860   ZTN(ZI)=ZBB*((I-ZI2)*ZTT(2I-1)-2*ZTT(ZI)+(1+Z12)*ZTT(ZI+1))+ZTT(ZI)
865   NEXT ZI
901   QQ=-CH*HK*RA*6.283185#*(TN(1)-TN(0))/DR
905   X=P*PT
925   PRINT #1, USING "####.##" ; QT;
930   FOR IZ=O TO S STEP 1
936   PRINT #1, USING "#####.#" ; TN(IZ);
937   NEXT IZ
939   PRINT #1, USING "#####.#" ; ZTN(ZI);
940   NEXT ZI
948   PRINT #1, USING "#######.##"; QQ;
949   PRINT #1, USING "#######.#"; TOTQ
1000   FOR I=O TO S STEP 1
1020   NEXT I
1030   FOR ZI-0 TO ZS STEP 1
1032   ZTT(ZI)=ZTN(ZI)
1034   NEXT ZI
1100   NEXT N
1499   BEEP
1500   END
Program 3:
100   DIM TT(S), TN(S), ZTT(ZS), ZTN(ZS)
153   PRINT #1, "RA="; RA, "RZ="; RZ
158   PRINT #1, "ZRA="; ZRA, "ZRZ="; ZRZ
178   PRINT #1, "ZEE="; ZEE
183   PRINT #1, "HC="; HC, "HD="; HD, "HK="; HK
193   PRINT #1, "ZHC="; ZHC, "ZHD="; ZHD, "ZHK='; ZHK
203   PRINT #1, "TA="; TA, "TG='; TG, "TF="; TF
213   PRINT #1, "DT="; DT, "NT="; NT, "PT="; PT
421   QI1P--1+1/(2*11) ; ZQI1P=1+1/(2*ZI1)
422   QI1M=1-1/(2*I1) ; ZQIIM=I-I/(2*ZLL)
423   GI2P=1+1/(2*(I1+S)) : ZQ12P-1+1/(2*(ZII+ZS))
424   Q12M=1-1/(2*(I1+S)) : ZQ12M-1-1/(2*(ZII+ZS))
426   SM=S-1 : ZSM=ZS-1
520   IF BB)=.5 GOTO 1499
521   IF ZBB)=.5 GOTO 1499
550   SGM.000000056697# 'THE STEFAN-BOLTZMANN CONSTANT 5.6697D-08
552   FVI=(CR/RA)^2+2!
561   TT(I)=TA
562   TN(1) =TA
563   NEXT I
571   ZTT(ZI)=TA : ZTN(ZI)=TA
572   NEXT ZI
649   SZS=S + ZS + 1
650   PRINT #1, " TIME    "; 'A COLUMN HEADING
652   PRINT #1, "TEMP";JS;
653   NEXT JS
710 TN(0)=88*(QI1M*(TT(1)+BAR+BA*(TG-TT(0)))-2*TT(0)+QI1P*TT(1))+TT(0)
755   12=I/(2*(I1+I))
760   TN(I)=BB*((1-I2)*TT(I-1)-2*TT(I)+(1+I2)*TT(I+1))+TT(I)
765   NEXT I
795   TN(S)=BB*(Q12M*TT(SM)-2*TT(S)+QI2P*(TT(SM)+DR*ZHK*(ZTT(1)-TT(SM))/(ZDR*HK)))+TT(S)
800   ZTN(0)=TN(S)
855   ZI2=1/(2*(ZII+I))
860   ZTN(ZI)=ZBB*((1-Z12)*ZTT(ZI-1)-2*ZTT(ZI)+(1+ZI2)*ZTT(ZL+1))+ZTT(ZI)
865   NEXT ZI
901   QQ=-CH*HK*RA*6.283185#*(TN(I)-TN(0))/DR
905   X=P*PT
925   PRINT #1, USING "####.##"; QT;
930   FOR IZ=O TO S STEP 1
936   PRINT #1, USING "#####."# TN(IZ);
937   NEXT IZ
938   FOR ZI-0 TO ZS STEP 1
939   PRINT #1, USING "#####.#" ; ZTN(ZI);
940   NEXT ZI
948   PRINT #1,USING "#######.##" QQ;
949   PRINT #1, USING "#########.#" ; TOTQ
1000   FOR I=O TO S STEP 1
1020   NEXT 1
1030   FOR ZI=O TO ZS STEP 1
1032   ZTT(ZI)-ZTN(ZI)
1034   NEXT ZI
1100   NEXT N
1499   BEEP
1500   END
There are numerous texts, such as those listed as References (1-5), which
discuss convective heat transfer in detail.
As described in Chapter III, convective heat transfer occurs when a liquid
or gas flows, carrying heat from one point to another followed by conductive
heat transfer between the newly arrived gas or liquid and the materials
previously there.  Contrast this with conductive heat transfer which
is due to direct interaction between individual particles only.   Analyzing
convective heat transfer is therefore much more difficult than analyzing
conductive heat transfer because both the motion of the fluid itself and
the energy transfer processes must be studied simultaneously.
Analysis of convective heat transfer begins by deriving the continuity,
and the momentum and energy conservation equations for the fluid.   Due to
the complexity of the resulting set of equations, they are usually
simplified to the "boundary layer" equations, so called because the
simplification is based on the observation that most of the resistance to
heat transfer between a fluid and a solid is concentrated in a thin
"boundary layer" next to the solid.  The velocity of the fluid varies
dramatically across this layer, from zero at the wall to the mainstream
value at its outer edge.  This is shown in Figure III-7.  Within this
boundary layer, heat transfer is by a complex interaction of heat conduction
and energy transport by the moving fluid.  Once across this boundary
layer the heat is rapidly carried away by the solid, or alternatively by
the mainstream flow of the fluid.
With these simplifications, <see equations below> for two-dimensional boundary

bsex149.gif (207x600)

layer natural convective heat transfer become (1-5):
where u and v are the velocities of the gas in the x and y directions; T
is the temperature of the gas and p is its density -- [rho][infinity] is the ambient
density; [mu] is the dynamic viscosity of the gas; k is the conductivity of
the gas; [p] is the pressure and g is the acceleration due to gravity.   The
geometry is shown in Figure 1.

bse1x152.gif (437x540)

Boundary   conditions in the case with one bounding surface are typically:
u(at) wall)=0            u(at [infinity])=0                            (4a)
v(at) wall)=0            v(at [infinity])=0                            (4b)
T(at wall)=[T.sub.wall]  T(at [infinity])=[T.sub.ambient]              (4c)
Initial conditions are used to set the average initial temperature and
velocity of the gas entering the region being analyzed.
Even in the above simplified form, these equations are difficult to solve
and particularly so in the case of natural convection dominated flows.   In
natural convection, the case of interest for improved stoves, the force
driving the flow of the hot gas is its higher temperature and resulting
lower density compared to its surroundings.  In short, hot air rises.  But
as it rises, it gives up some of its energy to its surroundings, such as
the pot or stove wall.  As its temperature thus decreases, so does the
force propelling it upwards.  As its velocity then decreases, so does the
rate at which it gives up heat to its surroundings, and so on.   It is this
coupled nature of natural convection flows -- the gas temperature determining
its flow and heat transfer rates which in turn determine its
temperature -- that make such systems so difficult to solve analytically
or numerically.  For these reasons, empirical correlations developed from
experimental observations are extensively used to analyze and predict the
behavior of natural convection systems.  These will be discussed before
returning to analytical and numerical techniques of analysis.
A variety of parameters and correlations are used regularly in describing
convective heat transfer.  Some of these are listed in Table 1.  Empirical
correlations for a variety of different situations are listed in Table 2.
Complete tables of such correlations are given in (9-10).
In improved stoves, flow regimes of interest include:
o   The plume of hot gas rising from the fire;
o   The stagnation point where the hot gas first encounters the pot;
o   The wall jet where the hot gas flows outwards and upwards along the pan
   bottom; and
o   The duct flow where the hot gas is channeled through a narrow gap
   between the pot and stove wall before leaving the stove.
These different flows are illustrated in Figure 2.

bse2x152.gif (486x486)

The first three of these, the plume, stagnation point, and wall jet, may
be the basis for part of the efficiency improvements found in nozzle type
stoves (See Figure III-8).  The fourth, duct flow, is a primary factor in
the efficiency improvements found in all three types -- multipot, channel,
and nozzle stoves.
o   For the interested reader, fire plumes are discussed extensively in
   (3,5,11-13,16).   The velocity of the gas in the plume initially increases
   with height within the flame but then decreases slowly above
   the flames.   The heat transfer at the stagnation point and along the
   pan bottom then increases somewhat with increasing pot height above the
   fire; reaching a maximum just when the flame tip touches the pot (11).
   This partially compensates the reduction in radiant heat transfer from
   the firebed to the pot that occurs with increasing pot height.  Experimentally,
   it has been found for channel and multipot stoves that the
   radiative heat transfer is more important and that better heat transfer
   is achieved by placing the pot close to the fire (17,18).  This may,
   however, increase dangerous smoke emissions.
   In contrast, nozzle type stoves combine increasing gas velocity within
   the fire plume with reduced stove diameter (Figure III-8) in order to
   sufficiently augment gas velocity and convective heat transfer on the
   pot bottom that it compensates for reduced radiative heat transfer.
o   Stagnation point heat transfer is discussed in (3,5,11,12,19).  Analytical
   solutions have been developed for nonreacting flows and are found
   in most textbooks as well as in Table 1.  When combustion is taking
   place simultaneously, the situation is greatly complicated.  Dissociated
   and intermediate chemical species are present and have a strong temperature
   dependence.   Significant heat transfer can take place due to
   diffusion-recombination processes leading to heat transfer rates much
   higher than that predicted in the case of nonreacting flows (12).  The
   structure of the flames (turbulent or laminar, etc.) can also strongly
   influence heat transfer rates (19).   Finally, the shape of the pan
   bottom influences the heat transfer somewhat (Table 2).
o   Wall jets, the free flow of hot gas over a wall with no other bounding
   surfaces, are discussed in (1-5,11,14).   Again, analytic solutions are
   readily available but must be used with caution in the present case of
   high temperatures, large temperature differences, and a reacting flow.
   In principle at least, adding fins or other devices to the pan bottom
   could also increase the heat transfer.   In practice, such devices would
   quickly soot and probably result in lower overall heat transfer rates.
o   Duct or channel flow heat transfer is discussed extensively in Chapter
   III.  An empirical model for convective heat transfer in multipot
   stoves is presented in reference (21) and gives results generally
   similar to those found for channel type stoves.  A simple empirical
   model for convective heat transfer in channel type stoves follows.
Empirical Analysis of Convective Heat Transfer In Channel Stoves
The convective heat transfer is given by
        Q - hA([T.sub.1]-[T.sub.2])                              (4)
where h is the heat transfer coefficient; A is the surface area of contact
between the hot gas and the object being heated, and ([T.sub.1]-[T.sub.2] is the
temperature difference between the hot gas and the object -- in this case
the pot or stove wall.
The parameter h is determined either experimentally or, in special cases,
theoretically.   Here the relation
        Nu = hG/k                                                (5)
will be used, where Nu is the Nusselt number, k is the conductivity of air
and G is the width of the channel gap through which the hot gas is
flowing.   For low velocity natural convection in a vertical channel,
reference (8) uses Nu=1.0.  Forced convection heat transfer results show
Nu=7.541 (3.77 per wall) for fully developed flow between constant
temperature walls and Nu=4.861 when one wall is perfectly insulated (Table 2).
In the entrance region of a duct the value of Nu is higher still
(1,2,4,9,10) but such entrance region effects will be ignored here as the
flow velocities are low and the channel is narrow ([Re.sub.G]Pr(G)l is small (4).
Now consider the case of a one pot chimneyless stove as shown in Figure 3.

bse3x152.gif (600x600)

Gas at temperature [T.sub.a]  leaves the fire and enters the space between the pot
and the stove wall.  This annular space will be treated as planar in the
model.   The high temperature of the gas and thus low density give it a
tendency to rise and a certain pressure is generated.  At the same time,
friction between the gas and stove wall and pot will counter this tendency
to rise with a corresponding pressure drop.  The gas velocity will
increase or decrease till these two competing pressures exactly balance.
In flowing past the pot and stove walls, a certain amount of heat will be
transferred from the hot gas -- thus changing the pressure drops, velocities,
and convective heat transfer, which again changes how much heat is
lost from the gas, how much its temperature changes, etc.
Consider now a very small segment of the cylinder, [X.sub.i], with entering gas
temperatures of [T.sub.h] and exiting gas temperatures of [T.sub.j].   A pressure drop is
generated in this segment due to friction of the gas with the walls over
the length [X.sub.i].  Assuming a gas velocity [U.sub.i] and assuming a kinematic
viscosity [v.sub.i], and density [[rho].sub.i], which are determined by the average temperature
in that segment
        [T.sub.i] = [[T.sub.h]+[T.sub.j]/2                      (6)
The pressure drop is then given by (Table 2 and references 4,9) <see equation 7>

bsetab20.gif (600x600)

bsex153a.gif (77x660)

Corrections due to entrance region effects will again be ignored for [delta][P.sub.i]
as they were for the value of the Nusselt number.
This pressure drop is balanced by the pressure generated due to the
density difference of the hot gas, [[rho].sub.i], compared to gas at ambient, or <see equation 8>

bsex153b.gif (69x660)

where g is the gravitational acceleration, g=9.8 m/[s.sup.2], and [rho][infinity] is the
density of ambient air.
The heat loss of the gas to the pot and stove walls is <see equation 9>

bsex153c.gif (165x660)

where it has been assumed that G<<[r.sub.p][perspective to][r.sub.w] [perspective to]r.
Finally, the heat lost to the walls per unit time is the same as the heat
lost by the flowing hot gas which determines its temperature change.   Thus <see equation 10>

bsexx.gif (78x600)

where [c.sub.i] is the specific heat of the gas at temperature [T.sub.i] in this section
of the duct.
The unknowns in the above equations can now be solved for.  Setting the
equations for pressure drop equal and for heat transfer equal, and using <see equation below>

bsex154.gif (600x600)

Should one wish to account  for entrance region effects, the values of
[beta](fRe), [Nu.sub.p] , and [Nu.sub.w] can be appropriately adjusted.
The thermal conductivity, k, kinematic viscosity, m, and v, specific heat,
[c.sub.p] of air are temperature dependent as shown in Table 3.   Fitting an

bsextab3.gif (600x600)

exponential to this data around T-800K gives <see equation below>

bsex16a.gif (348x660)

Inserting this into (15) gives <see equation 17>

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For a gas temperature, [T.sub.h], entering a segment [x.sub.i], the average temperature
[T.sub.i] and hence the exiting temperature [T.sub. ]can now be determined by selecting
the physically reasonable roots of equation (17).  Determining the heat
transfer for an entire duct is now simply a process of iterating over each
of the [x.sub.i] to determine the entrance conditions ([T.sub.h])i+1 for the next
section [x.sub.i+1].  From these temperatures, one can calculate the average gas
velocities, temperatures,  heat transfers, etc., over the entire length of
the stove.  A useful check on the solution is that the flow of mass <see equation 18>

bsex18.gif (106x660)

is constant for the entire length of the duct.  Considerable care must also
be taken to choose the physically reasonable root [T.sub.i] of equation (17).
The above model determines the flow rates and heat transfers in the
channel assuming an initial gas temperature at the channel entrance.   In
turn, the gas temperature and flow rates determine the combined fire power
and excess air factor.  For example, if it is assumed that a third of the
energy released by the fire is in the hot gases as they enter the channel,
the excess air factor, [lambda], can be determined by solving <see equation 19>

bsex19.gif (104x726)

Here, a third of the energy released by burning 1 kg of dry wood has been
set equal to the mass of the hot gases times their specific heat and
temperature above ambient.  The factor 5 comes from the volume of air
needed for stoichiometric combustion with 1 kg of wood.  With the calculated
flow rates and the above excess air factor, the fire power is <see equation below>

bsex20.gif (118x660)

A simple computer program that solves this system is attached and the
output data is shown in the text (see note 20).  Due to the lack of
precision in the correlations used and to the excessive simplification of
the model itself, there tend to be some deviations from the requirement
that the mass flow be constant, particularly for very narrow channels
where the heat transfer is most abrupt.  These variations are usually less
than 10%.  For very narrow channels, typically 3 mm or less, there are
also often problems in finding the physically reasonable roots [T.sub.i] of
equation (17).  Finally, these same simplifications and approximations
caused the model to approach the efficiency limit suddenly rather than
asymptotically (Figure III-9A).  Practically, these are of little interest.
The baseline parameters for this model were [Nu.sub.p]=4.86; [Nu.sub.w]=0; fRe=24; and
[T.sub.g] =900 K and output for these parameters is shown in Chapter III.   That
the model is generally robust was verified by varying convective heat
transfer coefficients for the pot and the wall, inlet gas temperatures,
numerical step size, and a variety of other factors.  In all cases the
behavior of the model remained generally the same.  For example, changing
the Nusselt number for the pot from 1.0 to 8.0 had essentially no effect
on the form of the curve, e.g. , Figure III-9A, but the channel gap for a
50% channel efficiency varied from 4.3 mm ([Nu.sub.p]=1) to 7.2 mm ([Nu.sub.p]=8).
Both of these are quite close to the channel gap of 6.4 mm for the case of
[Nu.sub.]p=4.86 (L=5 cm, [T.sub.g]=900 K).  Similarly, increasing the inlet gas temperature
from 700 K to 1300 K did not change the general shape of the curve
(Figure III-9A); but only shifted its position.  For example, the channel
gap for 50% channel efficiency changed from 7.0 mm (700 K) to 8.9 mm (1300
K) for a 10 cm long channel.
The above model assumes a constant channel gap.  In practice, the pot will
not be perfectly centered nor the stove perfectly round.   As discussed in
Chapter III, this can strongly reduce the heat transfer as the slightly
wider sections tend to lose very large amounts of heat.   The reason for
this is the large variation in pressure drop with channel gap (equation
7).   A wedge of the duct with a slightly larger gap will suffer much
smaller pressure drops, 1/[G.sup.2], so that the hot gases will flow out of the
stove much easier at that point.  Table 4 lists these points in detail.

bsextab4.gif (600x600)

A related calculation has been done for the convective heat transfer to
the second and subsequent pots of a multipot stove and is described in
detail in (21).  In general, however, multipot designs are not recommended
even when their total thermal efficiency is high because it is very
difficult to effectively control the heat input to each of the pots
individually from one fire.
Although the above empirical model is useful in describing the expected
trends in the performance of the duct with dimensional changes, gas
temperatures, and other factors, it is not expected to be an accurate
predictor of performance.  To more accurately do that, numerical analysis
of the boundary layer equations (1-3) is necessary.  References (3,22-25)
are particularly useful reviews of this.
For low temperature differences, the Boussinesq approximation, which sets
[rho], [micro], k, and [c.sub.p] constant everywhere except the term g([rho][infinity][lambda]-[rho]) is used.
Numerical solutions in this case for particular geometries are given by
(26-27), and with time dependence by (33).  For improved stoves, temperature
differences of several hundred degrees are found over distances of a
few millimeters.  Under these conditions, the Boussinesq approximation is
less accurate (6) and other techniques are necessary, as described in
In addition, flows in improved stoves are driven by buoyancy forces which
presents additional difficulties in obtaining stable numerical solutions.
Various techniques used to handle these difficulties are described in
references (3,23-25,28,30-32).
In particular, for duct flows only the duct geometry is known and the
pressure in equation (2) above is a variable.  This requires an addition
to equations (1-3) for there to be a solution and is usually done by
requiring the mass flow in the duct to be constant (3). <see equation 21>

bsexe21.gif (102x798)

References (26-27) then solve the system of difference equations generated
from equations (2,3,21) and use the results in equation (1) to determine
the velocity v.  Such a procedure is not fully self consistent.  In
contrast, references (3,31-32) solve equations (1-3) and vary p iteratively
until equation (21) is satisfied.  For the interested reader,
detailed computer programs solving these equations are given in (3).
Finally, it is useful to note from the above analysis that there are a
number of "scale" factors which enter into stove design.   Some of these
are listed in Table 5.  As an example, consider what happens when a stove
and pot and all the associated dimensions are changed in scale by a factor
of two -- that is, they are all doubled (or halved) in size.   In that case,
the energy needed to heat the pot increases by its volume or [D.sup.3]=[2.sup.3]=8 times
where D is the pot diameter, but the energy available from the fire only
increases by its surface area or [D.sup.2]=4 times.  This is a result of the heat
required being determined by the volume of the pot while the heat supplied
is determined roughly by the area of the fire.  The effect on various other
aspects of stove performance can be similarly estimated from Table 5.
                               TABLE 1
Correlations, Definitions, and Parameters in Convective Heat Transfer
Characteristic length--the primary dimension determining system behavior:
   For a flowing fluid bounded on only one side, the characteristic length
   of the system would be the distance from the leading edge of the
   bounding wall; for flow between two walls it would be the distance
   between them; and for flow in a pipe it would be the inner diameter.
Developed flow:  When the fluid first enters the duct, there are rapidly
   changing fluid velocities very close to the duct wall, and a relatively
   constant unperturbed flow velocity at the center of the duct.  This is
   known as the entrance region and heat transfer coefficients are somewhat
   higher than further downstream.   With distance into the duct, these
   surface boundary layers of fluid (with rapidly changing velocity
   according to the distance from the duct wall) grow thicker until they
   merge at the center of the duct.    That is, the flow across the entire
   duct has been perturbed by the friction with the wall.  This point on
   is known as the developed region.   In this region the flow velocity has
   a parabolic profile.   More precisely, a duct flow is said to be fully
   developed when the relative flow velocities across the channel width
   are no longer changing along the length of the duct.
Grashof number, Gr: Gr-g[beta]([T.sub.w]-[T.sub.[infinity])[x.sup.3]/[v.sup.2] where g is the acceleration due
   to gravity, [T.sub.w] is the wall temperature, and [T.sub.[infinity] is the fluid temperature
   far from the wall, and x is the characteristic dimension of the system.
   Gr gives the magnitude of the buoyant force relative to the viscous
   force.  Buoyant forces are generally only important in natural convection
Ideal Gas Law: PV-nRT where P is the pressure, V is the volume, and T is
   the-temperature of n, moles of the gas. R is the universal gas constant
   R=8.314 J/[degrees]Kmole.
Kinematic Viscosity, v: v=[mu]/[rho] where [rho] is the fluid density. v gives the
   rate at which momentum diffuses through a fluid due to molecular motion
Laminar flow:  A flow is termed laminar when its layers of flow, or
   streamlines, are smooth, even, well ordered, etc.  This condition
   normally occurs for relatively low fluid velocities.
Newtonian Fluid: [tau]=[mu]u(du/dy) by definition of a newtonian fluid where [tau] is
   the shear stress or force per unit area on a bounding fluid layer or
   surface and is in the direction of fluid flow; u is the velocity in the
   direction of fluid flow, x, Figure 1; and [mu] is the dynamic viscosity.
Nusselt number, Nu: Nu(x)=[h.sub.x]/k where [h.sub.x] is the local convective heat
   transfer coefficient, x is the characteristic length of the system, and
   k is the thermal conductivity of the fluid.  Because h is approximately
   given by k/[delta] where [delta] is the thickness of the local thermal boundary
   layer, the Nusselt number is x/[delta] or the ratio of the characteristic
   length of the system to the local thermal boundary layer thickness.
Peclet number, Pe:  Pe-RePr The Peclet number is a measure of the
   relative importance of convection versus conduction mechanisms within
   the fluid.
Prandtl number, Pr:  Pr=v/[alpha] Pr is a measure of the fluid's ability to
   diffuse momentum, v, compared to its ability to diffuse heat, [alpha].  For
   gases, the Prandtl number is nearly constant with temperature and is
   about .68 for air.
Rayleigh number, Ra:  Ra=GrPr
Reynolds number, Re(x): Re(x)=[u.sub.[infinity]x/v] where [u.sub.[infinity] is the free stream velocity
   of the fluid and x is the characteristic length of the system.  The
   Reynolds number is the ratio of inertial forces in the fluid to the
   viscous forces.   The transition from laminar to turbulent flow is
   described by a critical value of Re(x).  For flow along a single wall
   this critical value is typically Re=5x[10.sup.5]; for flow in a pipe it is
   typically Re-2300.
Stanton number, St:  St=h/[[rho]c.sub.p][u.sub.[infinity]=[Nu/Pe gives the ratio of convected heat
   transfer to that virtually transferable if temperatures were equalized.
Thermal Diffusivity, [alpha]:  [alpha]-k/[rho]c where k is the thermal conductivity, [rho] is
   the density, and c is the specific heat of the fluid.  [alpha] gives the rate
   at which heat can diffuse through a substance.
Turbulent flow:  A flow is termed turbulent when its streamlines are
   randomly intermixed and disordered.   This condition normally occurs for
   relatively higher fluid velocities.
Volume Coefficient of Expansion, <see equation>

bsex158.gif (135x230)

For ideal gases [beta]=1/T.
                                    TABLE 5
                      Some Scale Factors in Stove Design
               Pot diameter/fire diameter                     D/D
               Pot to stove wall channel gap/length          G/L
                    FACTOR                               SCALES AS
             Energy needed to heat a pot to boiling      [D.sup.3]
             Energy rate available from the fire         [D.sup.2]
             Maximum fire size (limited by gas escape)   D
             Heat transfer within channel                 DL/G
             Pressure drop in channel                     L/[G.sup.3]
20 S=200*L
25 DIM QQ(S), VV(S), TT(S)
110 D=.3 `diameter of pot
112 TW=373 : TP=373 : TA=300 `temperatures of wall, pot, and ambient
120 NUP=4.86 : NUW=O! : FR=24! `NUW=O corresponds to a perfectly insulated wall
130 DA=1.1774 `ambient air density
200 TB=TG 'sets temperature at bottom of first segment equal to entering gas temperature
300 XI=L/S `length of segment
310 B=39.2*DA*LL'4/(FR*XI)
400 FOR J=1 TO S STEP 1
500 Y=10 `increments temperature by 10 degrees in search for root
510 T1=TB
520 F1=1.78E-15*(NUP+NUW)*T1'4.2-1.78E-15*(NUP*TP+NUW*TW)*T1'3.2+B*T1'2-B*<TB+TA)*T1+B*TB*TA
600 FOR 1=1 TO 60 STEP 1
610 T2=T1-Y*I
620 F2=1.78E-15*(NUP+NUW)*T2'4.2-1.78E-15*(NUP*TP+NUW*TW)*T2'3.2+B*T2'2-B*(TB+TA)*T2+B*TB*TA
640 G=F1*F2
650 IF G<=0 GOTO 700 'check to see if have crossed root, F=0, between F1 and F2
660 F1=F2 'sets up for next check to determine crossover
670 NEXT 1
700 IF Y<=1 GOTO 750
710 Y=1 'iterates by one degree increments
720 T1=T2+10 'raises temperature to that at crossover of root
730 GOTO 520
750 T2=T2+ABS(F2)/(ABS(F1)+ABS(F2)) 'linear interpolation of T2 root from function values
810 VI=.0000823*(T2/800)'1.626
820 KI=.05779*(T2/800)'.746
900 QI=3.14*D*XI*KI*NUP*(T2-TP)/LL 'average heat flux in section
910 UI=19.6*LL'2*(T2-TA)/(FR*VI*TA) 'average velocity in section
1000 QQ(J)=QI : VV(J)=UI : TT(J)=T2
1100 TB=2*T2-TB 'calculates temperature at top of current section and bottom of next section
1200 NEXT J
1290 SQ=O : SM=O
1400 PRINT #1, "L="; L, "LL="; LL, "D="; D
1410 PRINT #1, "TG="; TG, "NUP="; NUP, "NUW="; NUW, "FR="; FR
1450 REM PRINT #1, "  TEMP " ; " HEAT  "; "   VEL  "; " MASS "
1500 FOR IP=1 TO S STEP 1
1510 MF=3.14*D*LL*VV(IP)*DA*TA/TT(IP) 'mass flow in each section
1520 GOTO 1530 'this bypasses the step by step printout
1521 PRINT #1, USING "#######.##"; TT(IP);
1522 PRINT #1, USING "######.###"; QQ(IP);
1523 PRINT #1, USING "#####.####"; VV(IP);
1524 PRINT #1, USING "####.######"; MF
1530 SQ=SQ+QQ(IP) 'sum of heat fluxes in each section
1535 SW=SM+MF 'sum of mass flow in each section
1540 NEXT IP
1545 MFA=SM/S 'average mass flow rate
1550 CG=1097.8*(TG/800)'.176 'specific heat of gas entering channel
1555 XSR=.17*(6000000!/(CG*(TG-TA))-1) 'excess air if .33 fire energy in hot gases entering channel
1560 PF=18000*MFA/(1+5.885*XSR) 'total fire power for average flow rate and assumed excess air factor
1561 PFQ=MFA*CG*<TG-TA) 'total energy of gases in channel based on average flow rate
1565 EFT=(TG-TT(S))/(TG-TA) 'efficiency based on temperature change of gas
1570 EFG=SQ/PFQ 'heat flux to pot obtained by adding the Q=hAdT of each segment
1575 MFA=SM/S 'average gas flow rate
1580 SQT=EFT*PFQ 'heat flux to pot (nuw=0) based on temperature change in gas
1601 PRINT #1, "PF=";
1602 PRINT #1, USING "###,####"; PF;
1603 PRINT #1, "  EFT=";
1604 PRINT #1, USING "#. #####"; EFT;
1605 PRINT #1, "  EFQ";
1606 PRINT #1, USING "#.#####"; EFQ;
1607 PRINT #1, "  QF=";
1608 PRINT #1, USING "#####.####"; SQ;
1609 PRINT #1, "  MFA=";
1610 PRINT #1, USING "##.#######"; MFA
1620 PRINT #1, "PFQ=";
1621 PRINT #1, USING "######.###"; PFQ;
1622 PRINT #1, "  QFT=";
1623 PRINT #1, USING "#####.####"; SQT
1700 BEEP
1800 END
All substances continuously emit electromagnetic radiation due to the
molecular and atomic motion associated with the internal energy of the
material. In the equilibrium state, this internal energy is proportional
to the temperature of the substance. Basic texts that discuss radiation
and radiation heat transfer in detail are listed as references (1-3).
For electromagnetic radiation in a vacuum, the wavelength and frequency
are related by the equation <see equation 1>

bsexe1.gif (92x798)

where c is the speed of light, c=2.998x[10.sup.8] m/s. Figure 1 relates the

bse1x168.gif (600x600)

various bands of radiation to their wavelength. The energy in a single
photon of radiation is related to its frequency by the equation <see equation 2>

bsexe2.gif (90x877)

where h is Planck's constant, h=6.6256x[10.sup.-34] Js.
The ability of an object to emit radiation is given by its emissivity [epsilon]
and is usually a function of the wavelength of the radiation. Table 1
lists the average (frequency independent) emissivities for a variety of
common materials. Similarly, the ability of an object to absorb radiation
is usually wavelength dependent and is given by [alpha]([lambda]). The emissivity and
absorptivity of a material are equal, [alpha]([lambda])= [epsilon]([lambda]).
Objects that are perfect absorbers (emitters), [alpha]-1.0, of radiation
regardless of wavelength are known as blackbodies. If they only absorb a
fraction 0<[alpha]<1.0 of the impinging radiation they are known as graybodies.
Perfect reflectors have [alpha]=0.0.
For a black body, heat energy is radiated at a rate given by the Stefan-Boltzmann
law <see equation 3>

bsexe3.gif (93x726)

where [sigma] is the Stefan-Boltzmann constant, [sigma]=5.6697x[10.sup.-8] W/[m.sup.2] [K.sup.4], A is the
emitting area of the object in square meters, and T its temperature in
degrees Kelvin.  This emitted radiation has a maximum intensity at the
wavelength given by Wien's law <see equation 4>

bsexe4.gif (92x798)

For graybodies, the Stefan-Boltzmann law is modified as <see equation 5>

bsexe5.gif (92x798)

As can be seen, the total energy radiated by a black body (or gray body)
is strongly temperature dependent.  Increasing the temperature just 10
percent increases the heat output by [(1.1).sup.4] or nearly 50 percent.
                                    TABLE 1
Emittance [epsilon] [perpendicular to] In The Direction Of The Surface Normal
Material                               [degrees]C    [epsilon] [perpendicular to]
Aluminum, bright rolled                  170          .039
        , paint                           100          .2-.4
        , oxidized at 600[degrees]C       300          .13
Chrome, polished                         150          .058
Iron, bright etched                      150          .128
    , bright abrased                       20         .24
    , red rusted                           20          .61
    , hot rolled                           20          .77
        "  "                              130          .60
    , heavily crusted                      20          .85
    , heat resistant oxidized              80          .613
Nickel, bright matte                     100         .041
Stainless steel 301                      260          .18
Stainless steel 347, oxidized
   at 1100[degrees]C                      300         .87
Tin, bright tinned iron sheet             38          .08
  White                                   100          .925
  Black matte                              80         .970
  Lampblack                                52          .94
  Candle soot                              52          .95
  Red ([Fe.sub.2][O.sub.3])                52          .96
  Brick, mortar, plaster                   20          .93
  Concrete                                 30          .94
  Fired clay                               67          .91
  Refractory  brick, ordinary           1100         .59
                     white               1100         .29
                     dark chrome         1100          .98
  Sand                                     25          .90
 References (1,2)
At the same time that an object is emitting radiant energy it is also
absorbing energy emitted by other objects. A "view factor" [F.sub.12] can then
be defined as the fraction of total energy radiated by surface 1 which is
intercepted by surface 2.
In the simplest case of a point source radiating spherically outwards, a
small section of a surrounding spherical shell will intercept a fraction
([A.sub.2]/4[pi][r.sup.2]) of the energy radiated by this source (Figure 2). Thus, in this

bse2x168.gif (486x486)

case, [F.sub.12=A.sub.2/4[pi]r.sup.2] and the heat from point 1 arriving at
surface 2 is <see equation 6>

bsexe6.gif (116x726)

where [epsilon][sub. perpendicular to], is the emissivity at right angles (normal) to the surface.
It should be noted that this heat transfer is very sensitive to the
distance between the two; doubling the distance r reduces the heat
transfer by four times.
In the more general case, the radiant heat transfer must be calculated by
integrating the "view" one surface element has of the other over both
entire surfaces. With the parameters as defined in Figure 3, <see equation 7>

bse3x168.gif (540x540)


bsexe7.gif (116x726)

For the case of two flat disks facing each other on the same axis, Figure 4,

bse4x172.gif (437x437)

this integral gives <see equation 8>

bsexe8.gif (129x726)

Graphs of this function are given in Chapter III. The view factors for
other particular geometries are given in references (1-4).
From the definition of the view factor as the fraction of the total energy
radiated by surface 1 which is intercepted by surface 2, an enclosed
surface i gives the identity <see equation 9>

bsexe9.gif (127x798)

where the surfaces k are all the other surfaces which enclose surface i.
The net radiant heat lost or gained by surface i is the difference between
the heat it radiates and that which it absorbs from other radiating
surfaces. Thus, for blackbodies (see equation 10>

bsexe10.gif (129x726)

Finally, by symmetry there is the relation between surface i and surface k
<see equation 11>

bsexe11.gif (129x726)

With these equations the radiant transfer for a variety of simple geometries
can be determined. Consider, for example, the heat balance on the
inner surface of the cylindrical combustion chamber shown in Figure 5. As

bse5x172.gif (486x486)

the wall itself intercepts much of the heat it radiates, its net heat gain
must be written as the difference between that which the wall radiates
specifically to the pot and fire and that which is radiated by the pot and
fire to the wall. It is assumed that the surfaces are all perfect
absorbers, [epsilon]=1. For the interior of a woodburning stove this is a good
approximation as the walls and pot will be heavily sooted. Thus, <see equation 12>

bsexe12.gif (116x726)

Using equation (11) and noting that symmetry gives [A.sub.f][F.sub.fw] = [A.sub.p][], this
simplifies to <see equation 13>

bsexe13.gif (127x798)

Finally, by equation (9) <see equation 14>

bsexe14.gif (104x726)

and [F.sub.fp] is given by equation (8). The results of calculations based on
equations (3,5,8,13,14) and the wall temperatures as determined by the
model developed in Appendix A are presented in figure 6. As seen, well

bse6x172.gif (600x600)

insulated walls can substantially increase radiant heating of the pot.
In the more general case [epsilon][not equal to]1 and multiple reflections between the different
surfaces must be considered.
For the interested reader there are numerous additional factors in radiant
heat transfer from fires worthy of consideration. Although the radiation
from the flames is a small portion of the total energy released by the
fire, typically less than about 14% (5), it plays a crucial role in the
combustion process itself. Radiant energy from the flames heats the wood
and releases more volatiles that burn in the flame, maintaining the
combustion and controlling, in part, its rate.
To understand the emissivity of a flame requires knowledge of the luminous
(yellow) emissions of the burning soot which acts as a cloud of miniscule
blackbodies as well as of the infrared molecular band emissions of the
combustion products, primarily [CO.sub. 2] and [H.sub.2]O. Reference (6) calculates the
detailed extinction and scattering coefficients for a cloud of soot
particles. Reference (7) develops approximate techniques for calculating
the total flame emissivity including the black body spectrum of soot, the
molecular band emission of the gases, and, additionally, the overlapping
and interactions of the bands themselves. Reference (8) details the
importance of flame dimensions on the relative magnitudes of soot versus
molecular band emissions.  Reference (9) presents experimental results
which show that the presence of water vapor in a flame in addition to that
generated by the combustion itself can greatly reduce the emission of the
soot particles and the total flame emissivity. This may be a dominant
factor in controlling the burning rate of wet fuel. An excellent review
of flame radiation is given by reference (10).
In addition to the above complexities of strongly wavelength dependent
emissivities, the calculation of radiant heat transfer is also complicated
by the transfer of energy taking place between widely separated elements.
This is to be contrasted with the case of conduction and convection for
which it is adequate to consider only adjacent volume elements. As a
consequence, a complete description of radiant heat transfer requires the
solution of systems of nonlinear integrodifferential equations. Reference
(2) discusses the formulation of such systems of equations and presents a
few case studies. References (11-13) present additional examples of this
type of analysis.
In this appendix various chemical and physical properties of biomass and
its combustion will be discussed in somewhat more detail than was possible
in the text.  Due to the complexity of the subject, however, extensive
references will be given for further reading rather than attempting to
provide an exhaustive review here.  The topics discussed below include:
chemical and physical properties of biomass and its chars, the pyrolysis
of wood, the combustion of charcoal, diffusion flames, soot and air
Chemical and Physical Properties of Biomass and Biomass Chars
As mentioned in the text, there are a variety of ways to characterize the
chemical and physical properties of biomass and its chars.  These include
the following:
Proximate analysis of biomass lists the fractions of biomass in terms of
moisture, volatiles, fixed carbon, and ash.  Such analysis is usually
performed by slowly heating the material to 950[degrees]C in an inert atmosphere
and examining the material released as a function of temperature.   Table 1
lists typical values from proximate analysis for raw biomass.   Table 2
shows the effect of pyrolysis temperature on the final char yield (3).
Ultimate analysis determines the elemental composition of the material.
Beginning with catalytic combustion or pyrolysis, biomass is broken down
into carbon dioxide, water, hydrogen sulfide, and nitrogen.   These gases
are then measured by gas chromatography using flame ionization or thermal
conductivity detectors (1).  Typical values are listed in Tables 3 and 8
below.   To convert the values in Table 3 into molar ratios, the weight-percent
must be divided by their respective atomic weights given in Table 4.
Results are shown in Table 5.  From this, the amount of oxygen needed
to completely burn the material, assuming perfect mixing or in other words
the stoichiometric ratio of oxygen, can be calculated as shown in Table 6.
For charcoal, 8.3 [m.sup.3] of air are needed to burn 1 kg; for wood, 5.5   [m.sup.3] air
are needed per kilogram.
The ash remaining following combustion is typically composed of CaO, [K.sub.2]O,
[Na.sub.2]O, MgO, SiO, [Fe.sub.2][O.sub.3], [P.sub.2][O.sub.5], and [SO.sub.3]. CaO generally represents about half
the ash and [K.sub.2]O is about 20 percent (1).  The potassium carbonate, in
particular, is useful in making soap.
Calorific values were briefly mentioned in the text and more extensive
lists are given in Tables 2, 7 and 8 and in references (3-7).   The
calorific value can also be estimated from the results of ultimate
analysis using standard correlations available in the literature and have
errors of typically less than 2 percent.  However, it is generally easier
to perform bomb calorimetry measurements and determine the calorific value
of biomass directly rather than circuitously do ultimate analysis followed
by the use of such correlations.
The density of wood is determined by the numbers and sizes of the pores
within it and can vary dramatically as seen in Table 9 (1,8).   Wood, and
biomass generally, consists of long fibers of cellulose ([C.sub.6][H.sub.10][O.sub.5]).sub.m] and
hemicellulose ([C.SUB.5][H.SUB.8][O.sub.4]).sub.n] cemented together by lignin ([C.sub.9][H.sub.10][O.sub.3]([CH.sub.3]O)[sub.9-1.7)p]
For both hard and softwoods, cellulose is about 43 percent of the total.
Hemicellulose, however, forms about 35 percent of the typical hardwood
compared to 28 percent of softwood while lignin is about 22 percent of
hardwood and 29 percent of softwood (1).  Calorific values for each of
these components are given in the text.
Because woods consist of these long fibers running lengthwise, their
properties are highly anisotropic.  Their permeability, for example, can
be 10,000 times (and more) greater in the longitudinal direction than in
the transverse (1,9).  This is important because the permeability controls
                                TABLE 1
                   Proximate Analysis of Raw Biomass
Material                 Volatiles(*)    Fixed Carbon(*)       Ash(*)    Reference
Oven Dry Woods
  Western Hemlock           84.8%           15.0%             0.2%         1
  Douglas Fir               86.2            13.7              0.1          1
  Ponderosa Pine            87.0            12.8              0.2          1
  Redwood                   83.5             16.1               0.4         1
  Cedar                     77.0            21.0              2.0          1
Oven Dry Barks
  Western Hemlock           74.3            24.0              1.7          1
  Douglas Fir               70.6            27.2               2.2         1
  Ponderosa Pine            73.4            25.9              0.7          1
  Redwood                   71.3            27.9              0.8          1
  Cedar                     86.7            13.1              0.2          1
Oven Dry Bagasse           85.7             11.5               2.8         2
(*) weight percent,   dry basis; Reference (1)
                                TABLE 2
                 Australian Eucalyptus Retort Charcoal
Temperature         Yield %    Approximate    Volatile    Ash by     Calorific
   of             by Weight      Fixed        Matter      Weight       Value
Carbonizing        of Dry       Carbon, by    by Weight     %          MJ/kg
  [degrees]C     Wood Sample    Weight %        %
  400              40             78            21.5        0.5         31.5
  450              35             82            17.5        0.5         33.1
  550              31.5           88.5          11.0        0.5         33.9
  650              28             95             4.5        0.5         34.7
Reference (56)
the movement of water vapor and volatiles away from the combustion zone
out of the wood or into cooler parts of it.  Materials such as biomass
briquettes or sawdust may burn with greater difficulty than wood because
their long fibrous nature is disrupted and air pockets within the material
insulate and localize the combustion zone (57).  Similarly, thermal
conductivities of wood are about twice as big in the longitudinal direction
as in the transverse (8).  Representative values are listed in Table 9.
Additionally, these properties vary with the moisture content in fresh
biomass and degree of charring in burning biomass.  Even the growth rings
and grain structure can strongly affect the combustion characteristics of
wood (10-12).  Much more detailed discussions of the physical and chemical
structure of biomass and biomass chars can be found in references (1,8).
                                TABLE 3
                     Ultimate Analysis of Biomass
Material           C(*)      H(*)   N(*)     S(*)     O(**)    Ash
Charcoal           80.3%     3.1%   0.2%     0.0%     11.3%    3.4%
Douglas Fir       52.3      6.3    0.1      0.0      40.5     0.8
" " " " Bark      56.2      5.9    0.0     0.0       36.7     1.2
Hickory            49.7      6.5    0.0      0.0      43.1     0.7
Rice Hulls        38.5      5.7    0.5     0.0       39.8    15.5
Rice Straw        39.2      5.1    0.6     0.6       35.8    19.2
Animal Waste      42.7      5.5    2.4     0.3       31.3    17.8
(*) Weight percent, dry basis; (**) By difference;  Reference (1)
                                TABLE 4
                            Atomic Weights
Element            C       H (H2)(*)    N (N2)    S        O (02)
Atomic weight    12.0       1.0         14.0     32.0      16.0
(*) The form in parentheses is the molecular form in which the chemical
  species is normally found in air at atmospheric pressure and 20[degrees]C.
                                TABLE 5
                    kmoles of element/kg of biomass
Material            C          H        N          S         O
Charcoal          .0669(*)    .031    .00014      0.0-     .0071
Douglas Fir      .0436       .063    .00007      0.0-     .025
Animal Waste     .0356       .055    .002       0.0001    .020
(*) Calculated by dividing values in Table 3 (fractional basis) by respective
atomic weights, Table 4.
                                TABLE 6
Stoichiometric Amounts of Oxygen Needed for Combustion per Kg Biomass(*)
Material          C[right arrow][CO.sub.2]    H[right arrow]H.sub.2]0    less 0 in    Total 0 Needed     Air Volume
                                                                         biomass        (kmoles)        ([m.sup.3])(**)
Charcoal                   .134                         .015                 .0071          .142              8.3
Douglas Fir               .087                         .032                 .025            .094              5.5
Animal Waste              .071                         .028                 .020           .079              4.6
(*) Based on molar values from Table 5
(**) Air is 78 percent [N.sub.2] and 21 percent [O.sub.2]. At 27 C and sea level
     pressure, the density of air is about 1.177 kg/[m.sup.3] and air thus
     has about 8.6 moles [O.sub.2] per [m.sup.3].
                                TABLE 7
                           Calorific Values
Material                  Gross Calorific Value                Reference
Hardwood Average         19.734 [- or +] 0.981  MJ/kg             4
Hardwood Bark            19.343 [- or +] 1.692                   4
Hardwood Sapwood         20.349 [- or +] 0.791                   4
Hardwood Heartwood       20.683 [- or +] 0.961                   4
Softwood Average         20.817 [- or +] 1.479                   4
Softwood Bark            21.353 [- or +] 1.221                   4
Rice Straw                        15.21                           1
Rice Hulls                        15.37                           1
Dung Cakes                        17.17                           1
Corn Cobs                         18.9                            5
Coconut Shells                    20.1                            5
Coconut Husks                     18.1                            5
Cotton Stalks                     15.8                            5
Alfalfa Straw                     18.4                            5
Barley Straw                      17.3                            5
Charcoal                         Table 2
Material                  Gross Calorific Value(*)          Density(*)
n-Butane                           45.72 Mj/kg              548 kg/[m.sup.3]
Diesel: light                     42.37                     876
        medium                     41.87                     920
        heavy                      41.37                    960
Ethanol                            26.80                     789
Gasoline (73 Octane)              44.13                     720
Kerosene                           43.12                     825
Methane                            50.03                    - - -
Methanol                           19.85                     793
Propane                            46.35                     508
(*) Reference (13)
Because of the various complications it is extremely difficult to model
realistically the combustion of wood.  Thus, the following will only
present very simple models of particular aspects of wood combustion and
then extensively reference the literature for more detailed investigations
by the interested reader.  As background, general texts on combustion are
listed as references (13-16).
                                TABLE 8
       Ultimate Analysis and Calorific Values For Biomass Chars
Material                  C      H     N     S     O     Ash    Calorific
Redwood Charcoal                                            Value MJ/kg
 (pyrolized at 550 C)   75.6   3.3   0.2    0.2  18.4    2.3      28.8
Redwood Charcoal
 (pyrolized at 940 C)   78.8   3.5   0.2    0.2  13.2    4.1      30.5
Oak Charcoal
 (pyrolized at 570 C)   64.6   2.1   0.4   0.1    15.5   17.3    23.0
Fir Bark Char          49.9    4.0   0.1   0.1    24.5   21.4    19.2
Rice Hull Char         36.0    2.6   0.4   0.1    11.7   49.2    14.2
Grass Straw Char       51.0    3.7   0.5   0.8    19.7   24.3    19.3
Animal Waste Char      34.5   2.2    1.9   0.9    7.9    48.8    12.7
Reference (1)
                                TABLE 9
Densities, Conductivities, and Thermal Diffusivities For Various Woods
                                                     Thermal     Thermal
                       Conductivity  Conductivity   Diffusivity Diffusivity
              Density   Transverse   Longitudinal   Transverse   Longitudinal
Wood           kg/[m.sup.3]   W/mC            W/mC     [m.sup.2]/s        [m.sup.2]/s
Fir           540           0.14            0.34          18.7X[10.sup.8]      45.9X[10.sup.8]
Mahogany      700           0.16           0.31         16.6                  32.3
Oak           820           0.21           0.36         18.7                  32.1
White Pine   450           0.11           0.26         17.8                  42.1
Teak          640           0.18           0.38         20.1                  43.5
Reference (8)
Wood Pyrolysis <see figure 1>

bse1x184.gif (486x486)

Wood pyrolysis was described qualitatively in Chapter III.   Briefly, as
wood is heated it undergoes chemical reactions in which volatile gases are
evolved and escape the wood, leaving a porous char behind.  Among the
earliest quantitative models to describe this phenomena was that of
reference (17).  Other, more recent and more complete models are listed as
references (18-26).
The typical model is based on the transient heat conduction equation,
equation (A-1), to account for heat being conducted into the wood.
Additional terms are added to account for the heat carried out of the wood
by the escaping volatiles and to account for the energy absorbed or
released by the pyrolysis reaction itself.  Other constraints include
accounting for the decomposition process and for the change in the thermal
conductivity, density, specific heat and any other relevant properties of
the wood/char as the decomposition process progresses.
The form of the pyrolysis equations in one dimension is then: <see equation below>

bsex180.gif (313x660)

In equation (1), the first two terms [delta]([[rho].sub.s][c.sub.s]T)/[delta]t=[delta]{[delta]T/[delta]x)}/[delta]x is simply
the equation for transient heat conduction, equation (A-1), for materials
with variable thermophysical properties.  The variables [[rho].sub.s],[c.sub.s],k, and T
are the density, specific heat, thermal conductivity, and temperature of
the pyrolyzing solid, i.e. the charring wood.  The third term [delta]([[rho].sub.g][V.sub.g][C.sub.g]T)/[delta]x
is the heat carried out of the pyrolyzing solid by the volatile gases of
density [[rho].sub.g] moving with a velocity [V.sub.g] and having a specific heat [C.sub..g]. Extensive
data on the magnitude of internal convection is given in reference
(19).   It is assumed that the gases are in thermal equilibrium with the
solid.   The final term of equation (1), [Q.sub.p][delta][[rho].sub.s]/[delta]t , is the energy absorbed
(or released) by the pyrolysis of [delta][[rho].sub.s]/[delta]t of material per unit time.
Equation (2) describes the pyrolysis process itself in terms of a single
first order, Arrhenius type (13-16) rate law.  The factor A is the
frequency, or pre-exponential, factor, E is the activation energy for the
pyrolysis reaction, and R is the universal gas constant; R=1.987 cal/mole[degree]C-8.314
J/mole[degree]C.   Again, [[rho].sub.s], is the density of the pyrolyzing solid while
[[rho].sub.a] is the density of the portion of the solid which gasifies.
Equation (3) is the continuity equation expressing the change in density
with time, [delta][[rho].sub.s]/[delta]t, in terms of the flow of mass, [[rho].sub.g][V.sub.g], out of the pyrolyzing
In all these equations, the pyrolyzing solid is assumed to consist of a
char matrix, density [[rho].sub.c], and an active or gasifiable portion of density
[[rho].sub.a].   The thermophysical properties of the pyrolyzing solid are assumed to
be given by linear interpolation between those of the virgin wood and
those of the char as a function of density.  For example, the thermal
conductivity of the pyrolyzing solid is given by <see equation below>

bsex180a.gif (204x594)

where the subscripts, c, s, and w, are char, pyrolysing solid, and virgin
Typical boundary conditions for this set of equations are to set all the
temperatures to ambient and all the properties to that of virgin wood at
time t=0. At t=0 a heat flux Q(t) is then applied to the exposed surface <see equation 4>

bsex181.gif (75x726)

which raises the temperature of the system and begins the decomposition
process.   Additionally, at some point, x=s, into the wood it is assumed to
be perfectly insulated, [delta]T/[delta]x=0, and that there is no further flow of
volatiles, [[rho].sub.g][V.sub.g]=0
Equations (1-3) and boundary conditions (equation 4 plus the above
discussion) can be formulated into a set of finite difference equations
and solved as done in (22) and others.  Typical values used are listed in
Tables (1,9, 10) but vary dramatically between studies (1,8,9,17-33).
Numerous additional considerations can be taken into account in modeling
pyrolysis.   Among these are adapting to different geometries (23,25);
accounting for radiant and convective heat losses from the surface (26);
and accounting for the volatiles that escape into the virgin wood as well
as through the char (26).  Other factors that should be considered include
                               TABLE 10
           Constants for the Pyrolysis of Wood, Equation (2)
     A                            E                   Ref
 5x[10.sup.9] g/[cm.sup.3] s     35 kcal/mole         33 path 1
 3x[10.sup.17]                   55                   33 path 2
 5x[10.sup.7](*)                 30                   22
2.5X[10.sup.4]                   18                   20, 26
 5x[10.sup.8]                    33                   17
(*) In this case A is expressed in terms of 1/sec rather than gm/[cm.sup.3]s
so that other factors must be adjusted accordingly.
                               TABLE 11
              Pyrolysis Yield For Different Contaminants
                                 Charcoal     Tar   [H.sub.2]O   [CO.sub.2]     CO
No additive                       30%(*)     46%     19%           4%           1%
.14% Wt/Wt [Na.sub.2][CO.sub.3]   85           3       8           2             2
8% Wt/Wt NaCl                     51           6      29           7             7
(*) By weight percent
Reference (3)
the effects of char cracking, multiple chemical decomposition (or pyrolysis)
pathways and energetics, shrinkage of the char matrix, simultaneous
char combustion, and simultaneous char-volatile reactions.
In particular, it is important to note that there are at least two
chemical decomposition paths (9,28,33) for cellulose alone.  The first
predominates at low temperatures, 200-280[degrees]C, and consists of "dehydration"
or the removal of water from the cellulose leaving considerable char and
producing little combustible gas.  The second predominates at higher
temperatures (280-340[degrees]C) and is a depolymerization process producing
mostly combustible gases with little or no char left behind (28,33).
Because of the presence of alternative pyrolysis paths, relatively low
concentrations of contaminants can shift the relative yield of char
considerably depending on which path is emphasized.  This is illustrated
dramatically in Table 11 and examined in greater detail in reference (18).
In the absence of contaminants, however, the yield of char from the
pyrolysis of wood is relatively insensitive to its temperature history (3)
with only its volatile content varying with temperature as already
discussed.   For further information on the chemistry of pyrolysis the
interested reader is referred to reference (33); on the thermodynamics of
pyrolysis, (30), and on the kinetics of pyrolysis, (31).
Charcoal Combustion
Following (and during) loss of the volatiles by pyrolysis, the remaining
char burns by oxidation at its surface. Basic reviews of this process are
given in references (13,14) and are summarized below.
The most simple model of carbon combustion considers only the two following
     2CO + [O.sub.2] [right arrow] 2[CO.sub.2]                           (5a)
     C + [CO.sub.2]   [right arrow] 2CO                                    (5b)
Experimentally, it has been found that carbon leaves the surface of the
charcoal primarily in the form of CO.  Diffusing away from the surface,
the CO encounters and burns with [O.sub.2] through a variety of intermediate
reactions(1) in the gas phase to form [CO.sub.2] (reaction 5a).   This reaction can
sometimes be seen as a faint bluish flame just above the surface of the
charcoal.   Part of this [CO.sub.2] diffuses back to the surface where it is
reduced to CO by the solid carbon (reaction 5b) thus closing the cycle.
The mass fractions for these various reactants are shown schematically in
Figure 2.

bse2x184.gif (600x600)

(1) A variety of reactions with OH, [HO.sub.2], [H.sub.2][O.sub.2], and other intermediate
hydrogen-oxygen radicals are necessary to fully explain the observed
behavior of carbon and carbon monoxide combustion (47). Modeling of this
system is also discussed in (47).
The law of conservation of species in spherical coordinates for this
highly simplified system is then <see equation 6a>

bsex6a.gif (95x660)

for oxygen, subscript o, and <see equation 6b>

bsex6b.gif (95x660)

for carbon dioxide, subscript d.  The variable [[rho].sub.g]. is the density of the
gas; [R.sub.c] is the radius of the carbon sphere; [Y.sub.o] or [Y.sub.d] is the mass fraction
of that chemical species, [Y.sub.o]=[P.sub.o][M.sub.o]/PM, where P is the pressure and M is the
molecular weight; [W.sub.o] or [W.sub.d] is the rate of reaction (moles/volume-sec) of
that species; [M.sub.c] is the mass flux (mass/area-sec) of carbon from the
surface of the charcoal sphere; and [D.sub.o] or [D.sub.d] is the species diffusivity.
If [f.sub.c] grams of carbon react with 1 gram of [CO.sub.2] at the surface of the
charcoal to form (1+[f.sub.c] grams of CO, if [f.sub.m] grams of CO react with 1 gram
of [O.sub.2] to form  1+[f.sub.m]) grams of [CO.sub.2], and if the species diffusivities are
equal, [D.sub.o]=[D.sub.d]=D, then the burning rate of the charcoal can be calculated
(13) and is given by <see equation 7a>

bsex7a.gif (104x726)

and the particle lifetime (characteristic time until it burns
up) is <see equation 7b>

bsex7b.gif (204x660)

where [[rho].sub.c] is the density of the carbon sphere.
In reality, there are numerous complications to this simple theory
(34-42).   Among these are: the presence of volatiles and char-gas reactions
(30,31); the presence of water vapor speeding the conversion of CO
to [CO.sub.2] (35,47); radiant heat loss which in some cases leads to spontaneous
extinction of combustion for small particle sizes (36); the effect of
pores and cracking on diffusion rates (37,38); the effect of varying
reaction rates, and of heat and mass transport (38,40); the effect of
thermal inertia (39); the effect of the outer ash layer slowing diffusion
of gases to the burning surface (10,11); and the departure from equilibrium
In particular, the ash layer of non-combustible salts remaining on the
surface of burning charcoal is an important factor controlling its rate of
combustion (10,11).  In turn, this regulates the power level of charcoal
stoves and does so in a useful manner: providing high power levels at the
early part of cooking and then lower power levels as the ash forms (43).
Raising the power level again is done simply by moving the pot and
knocking off the ash layer.
A variety of things can be done to improve the combustion quality of a
stove.   Among these are insulating to raise combustion chamber temperatures;
increasing the volume (and particularly the height of the combustion
chamber) so that there is more complete burn-up before the hot gases
come into contact with the pot and combustion is quenched (this does,
however, reduce radiant heat transfer to the pot); provide swirl to the
incoming gases to improve mixing; provide baffling in the combustion zone
to create recirculation zones to better burn the gases; and to use a grate
to provide the charcoal firebed oxygen with which to burn (this improves
the overall combustion, reduces the wasted charcoal, and can raise fire
powers (44,45)).  A number of these were discussed in Chapter III.
Diffusion Flames, Soot, and Air Quality
When pyrolysis gases, or volatiles, leave the wood they either escape as
smoke or they burn in the yellow flame above the wood.  Such flames are
known as diffusion flames because their overall speed of combustion is
controlled by the rate at which oxygen can diffuse to the burning volatiles
rather than being controlled by the rate of the oxygen-hydrocarbon
kinetics themselves.  Diffusion flames are discussed in detail in basic
combustion texts (13-16).  Due to the complexity of flaming combustion of
wood, the topic will only be briefly surveyed here.
The pyrolysis gases consist of over 200 different compounds (46).   In the
lower part of the flame, these gases react to produce free carbon in the
form of soot and carbon monoxide which then burn in the upper part of the
flame. The combustion of carbon monoxide generally occurs through carbon-hydrogen-oxygen
reactions including primarily CO+OH-[CO.sub.2] + H which is much
slower than the rate of reaction between OH radicals and typical hydrocarbon
species (47).  Thus, although much CO is produced in the lower part
of the flame its subsequent combustion to [CO.sub.2] is retarded until most of
the hydrocarbons have been consumed (47).  Although, as already discussed,
wood with a moisture content of 20 to 30 percent has better overall
combustion efficiency than oven dry wood, this may not be due to catalysis
by OH radicals or other mechanisms (48) but perhaps simply to limiting the
migration of volatiles out of the combustion zone.  In fact, measurements
have shown that higher wood moisture contents can lead to greater CO
production (49).
Because CO is preferentially burned in the upper part of the flame,
bringing the pot too close to the flames may then quench the combustion of
carbon monoxide and cause larger amounts to be emitted, increasing the
health hazard.  What very little data there is on this factor suggests
that for some stoves, CO production does increase when the pot is brought
very close to the fire (49).  This is an important factor that needs to be
examined much more carefully.
The carbon that agglomerates into soot burns in the manner already
discussed above under Charcoal Combustion and gives off the characteristic
yellow flame of a wood fire (Appendix C).  The estimated time to burn up a
carbon particle, equation (7b), can be balanced against the average time
that that particle is in the combustion zone (height of combustion zone
divided by average velocity) to determine, simplistically, whether or not
it burns up completely or escapes as soot.  Moving the pot closer to the
fire then reduces the time for combustion and can quench soot combustion
before it is complete.  This will increase the amount of soot/smoke that
escapes the fire.  A particularly simple example of this can be observed
by placing an object in the flame of a candle to produce candle black.
The mechanisms leading to soot production are not yet well understood (50-52).  
For thoroughly premixed fuel-air flames, the production of soot is
determined by the rate at which the volatile gases pyrolyze leaving carbon
behind which then subsequently agglomerate and grow into large soot particles
and the rate at which these soot particles burn up by oxidation.
In general, as the temperature is raised the particles burn (oxidize)
faster than they pyrolyze and agglomerate (51).  Thus, in this case,
higher temperatures reduce soot.
In contrast, under some diffusion controlled conditions, raising the
temperature increases the rate of pyrolysis and increases the tendency to
soot (51).  In general, the tendency to soot will depend on the fuel flow
rate, flame temperature, oxygen diffusion and the particular molecule
involved (51).
In woodstoves, as the flame height (and contact with the pot) increases
with the firepower, the amount of soot produced can be expected to
increase with firepower as well.  Under typical operating conditions for
small stoves, as much as 40 grams and more of particulates can be released
per kilogram of wood burned with values of 5 g/kg more typical (53) (see
Table II-16).
In terms of overall stove efficiency, incomplete combustion, as evidenced
by carbon monoxide, soot, and smoke production, has little effect.
However, these are very important in terms of user health (53).   A number
of compounds emitted by wood fires have been identified as carcinogenic
and the total exposure to particulates, carbon monoxide, and carcinogens
such as Benzo-a-pyrene suffered by users are often considerably above
recognized health standard recommendations (53).  Raising the average
combustion zone temperature can reduce these emissions - - with the
greatest reduction occuring for temperatures in excess of 600[degrees]C (44).
For the interested reader, information on modeling diffusion flames is
given in references (13-16,54) and the case of the open wood fire is
specifically treated in reference (45).
Detailed information on heat exchanger design is given in (1-6) and the
interested reader is urged to consult these sourcebooks.  Although the
following calculation is for the case of forced convection, the concept of
counterflow heat exchange can be similarly applied to flows driven by
natural convection.  As the example below clearly indicates, the potential
of heat exchangers to improve the performance of traditional energy
technologies is enormous.
The air-to-air heat exchanger discussed in Chapter VI for the high
temperature foundry is an especially simple form to analyze.   Effectively,
it consists of two parallel streams of gas moving in opposite directions,
bounded and separated by thin sheets of steel.  Because it is a closed
system, the air flow in this heat exchanger is constant and the same going
in and out.  The situation is illustrated in Figure 1.

bse1x188.gif (540x540)

In this figure, T is the temperature, the subscripts h and c refer to the
hot and cold gas streams, and i and o refer to the streams incoming to and
outgoing from the heat exchanger.  The heat exchanger itself is L long, W
wide, and formed of two adjacent ducts each with a gap G.   The ducts are
bounded by steel of thickness [s.sub.m] and conductivity [k.sub.m].
Then, the following equation is used for the change in air temperature: <see equation 1>

bsex187a.gif (129x726)

where dE is the change in heat energy of an object of mass m and specific
heat [c.sub.p] due to a temperature change within that object of dT.   Applying
this equation to a volume element WGdL with a constant mass flow through
it of m[.], where the dot indicates a time derivative, (dm/dt)=m[.], the heat
exchange per unit time is Q=(dE/dt), or <see equation below>

bsex187b.gif (199x798)

with [bar] V and [bar] [rho] being the average gas velocity and density within that volume
Since this is a closed system and ignoring the roughly five to ten percent
increase in the mass of the gas when the combustion products are added,
m[.]h=m[.]c.   Further, the external walls of the heat exchanger are assumed to
be perfectly insulated and the gas properties, such as [c.
sup.p], constant.  In
this case, the cold and hot gas streams have equal and opposite temperature
changes and ([T.sub.h]-[T.sub.c]) is constant and the same for all dL.
Next, the convective heat transfer can be written
     Q = d (hAT) = hAdT                                            (5)
This equation gives the heat transfer per unit time from one object to
another when they have a common surface area of A, a heat transfer
coefficient of h and a temperature difference dT.
In this system, typical gas velocities are low resulting in laminar flow.
As the temperature difference between the hot and cold streams is everywhere
constant, there is a constant heat flux.  The Nusselt number then
used is (Appendix B): <see equation 6>

bsex188a.gif (95x660)

where G is the characteristic dimension of the duct, k is the thermal
conductivity of air, and h is the convective heat transfer coefficient
between the gas and the wall.
For an area element dA, the heat transfer from one gas stream to the other
can now be written as: <see equation 7>

bsex188b.gif (106x660)

where the Fourier conduction law has been used.  As the thermal conductivity
of air is typically [10.sup.-3] that of steel, this reduces to: <see equation below>

bsex189a.gif (181x726)

     [bar] k [approximate] 1/1/[k.sub.h] + 1/[k.sub.c] [equivalent] k  t
Now using equations (2,3,8) the following can be written for the entire
heat exchanger: <see equation below>

bsex189b.gif (224x726)

The inlet temperatures [] and [T.sub.h1] can be assumed to be known.   Then, []
and [T.sub.ho] can be solved for to find: <see equation 10>

bsex189c.gif (278x726)

and the efficiency of the heat exchanger is given by: <see equation 11>

bsex189d.gif (181x726)

A kilogram of charcoal requires roughly 9 [m.sup.3] of air at standard temperature
and pressure (STP) for stoichiometric combustion.  A one kW fire
then burns 3.45x[10.sup.-5] kg/s of charcoal and 3.1x[10.sup.-4] [m.sup.3]/s of STP air.  With
an excess air factor of 2, 7.3x[10.sup.-4] kg/s of air flow into the heat
exchanger and 7.65x[10.sup.-4] kg/s of combustion products flow out.   Averaging,
roughly 7.5x[10.sup.-4] kg/s of mass flow through the heat exchanger for a 1 kW
fire.   For the effective specific heat, an average value of 1.1x[10.sup.3] J/kgK
is used and for the effective thermal conductivity [bar] k an average value of
0.027 W/mK is used (Table A-4) which is relatively constant independent of
the temperature difference between the gas streams.
From equation (11) it can be seen that the efficiency of heat recuperation
is improved by making the duct gap G thinner and the duct area LW larger.
However, the thinner and longer the duct, the greater the pressure drop
and the more work that is needed to force the gas through the system.
Additionally, as the pressures increase, the more air that will leak
directly out of the furnace and completely bypass the heat exchanger.
The pressure drop in laminar forced convection is (Table B-2, page 159,
and equation (4) above): <see equation 12>

bsex190a.gif (116x726)

where (2L) is the total duct length and [bar][nu] is the kinematic viscosity of
the gas and for convenience here is averaged over the entire length of the
hot and cold streams.  For assumed inlet temperatures of 300 and 1,300 K,
[bar][nu]=89x[10.sup.-6] [m.sup.2]/s and [bar][rho]=0.724 kg/[m.sup.3].  Using the relation Power-forcexvelocity
we then find: <see equation 13>

bsex190b.gif (93x726)

Graphs based on equations (11) and (13) are presented in Chapter VI.
As can be seen from Figure VI-4 and from equations (11) and (13), the
pressure drop increases very rapidly with the duct gap, the efficiency
only moderately so.  As the gap is reduced, the point where large amounts
of fan power are needed is quickly reached.  As the available fan technology
in most developing countries is limited and the motive power is
usually human, it is important to minimize the pressure drop that must be
overcome within the heat exchanger.  An improved fan technology may be
needed regardless.  A typical starting point might be a heat exchanger 2 m
long, 0.5 m wide and with a duct gap of 6 mm.  This would provide, in
principle, a 70 percent heat recovery at a cost of 12 watts in blower
power.   A much wider duct, W, could be used but ensuring that the gas
flows uniformly across the entire area is difficult.
It should also be noted here that with heat recuperation, the necessary
mass flow in through the system is reduced roughly proportionally, which
further improves the efficiency of heat recuperation and reduces the power
needed for the fan.
With the above parameters the Reynold's number is: <see equation 14>

bsex190c.gif (114x798)

which gives laminar flow.
The steady state gas temperature can also be estimated.  With an excess
air factor of 2, 1 kg of charcoal requires 21 kg of air for combustion and
provides 29,000 to 34,000 kJ of energy.
Assuming an average specific heat of 1.2x[10.sup.3] J/kgK, there will be a
temperature rise of: <see equation below>

bsex190d.gif (135x600)

This, however, ignores a number of large losses including the dissociation
of the combustion products which will be significant at these temperatures.
For a more precise calculation, the reader should consult a text
on combustion.
Finally, because of the high temperatures within the system, there can be
significant thermal expansion of the metal and possibly warping and
buckling.   As the thickness of the ducts is important, the effect of this
thermal expansion should be taken into consideration.
The coefficient of thermal expansion, [alpha],ranges from about 11x[10.sup.-6]/[degrees]C at
room temperature to about 15X[10.sup.-6]/[degrees]C at 750[degrees]C for steel (7).  Consider,
for example, an air to air heat exchanger formed from three concentric
cylinders for which at room temperature the inner wall has an outer
diameter of 1 meter and the outer wall is of 2 mm thick metal with an
outer diameter of 1.016 meters (or a duct gap of 6 mm).
If when in operation, the inner wall has a temperature of 530 [degrees]C, its
diameter will be 1.0063 meters ([alpha]=12.5x[10.sup.-6]).  If the middle wall is
instead at 330 C, its outer diameter will be 1.0197 meters.   Thus, instead
of a 6 mm gap there is a 4.7 mm gap.  This could make an important difference
in the performance of the furnace.
To avoid this problem it is then preferred to make the heat exchanger out
of parallel sheets of metal as described in the text, with spacers between
the shells to maintain the desired duct gap.  To prevent the assembly from
warping due to differential expansion during operation, the individual
sheets can be left free to slide back and forth past each other with a
rigid external frame holding the entire assembly in place.   This will also
allow easy disassembly and cleaning.
                                TABLE 1
               Linear Thermal Expansion Coefficients
[degrees]C    Aluminum               Steel             Steel             Steel               Steel
                                   (.1% C)           (hard)             (Ni)                (soft)
  50         .0234x[10.sup.-3]       --                 --                --                 --
 100         .0238               .012x[10.sup.-3]   .01170x[10.sup.-3]   --                  --
 200         .0245                      --          .01225               --                  .01255x[10.sup.-3]
 300         .0255                      --          .01277                .00933x[10.sup.-3]    .01307
 400         .0265                      --          .01328                .01000                .01360
 500         .0274                      --          .01382                .01050                .01412
 600         .0283                      --          .01433               .01042                .01465
 700           --                       --           .01486                .01114               .01519
 800           --                       --              --                 .01156                   --
 900           --                        --              --                .01167                  --
1000            --                        --              --                .01185                  --
Reference    (7)
Simple financial analyses of improved stoves can only provide a general
indication of potential benefits.  Numerous factors such as reduced smoke
inhalation, greater convenience in cooking, and a modern image may well
prove to be more important in the decision to purchase an improved stove
than the potential financial savings for those who purchase fuel.   And even
for those who purchase fuel, it is difficult to realistically estimate the
barrier posed by the first cost of the stove.  Among the factors that tend
to raise this barrier are a short-term view -- no longer than through the
next harvest and often considerably shorter; a narrow margin of survival
-- so that risks must be very carefully weighed; and a simple lack of cash
to invest.  World Bank data for commercial interest rates for agricultural
credit show rates as high as 192 percent, with most countries falling in
the 20 to 66 percent range (cited in 1).  Thus, the first cost of an
improved stove can be a truly formidable barrier and must be taken into
The first cost of a stove can be an even greater barrier to those who
forage for fuelwood or other fuel rather than purchasing it, In this
case, the monetary cost of a stove is balanced against the labor of the
forager -- in many cases a child who may not have any other immediately
useful task to perform in place of foraging.  Obviously, the head of the
household will often choose against such a purchase when there are ready
hands available.
Financial analyses of projects which receive government or international
donor support and which do not themselves earn revenue must also take into
account that it is often easier to get one-time funds to install project
equipment than it is to get recurrent funds for operation and maintenance
(2).   Initial capital investment can often be obtained through aid programs,
liberal financing, or one-time budgeting, while recurrent costs
must come out of the regular budget and must compete against all the other
needs of education, rural assistance, and infrastructure development.   The
ability to meet recurrent costs is often far more important than minimizing
life cycle costs as measured in a single present value (2).   Combining
initial capital and recurrent costs into a single present value
ignores the crucial differences between their funding sources and restrictions.
In many cases it may be better to perform undiscounted comparisons
of capital and recurrent costs separately (2).  Developing countries are
littered with projects and equipment in which recurrent costs could not be
met.   In stove projects, an extra effort must be made to ensure that sales
can meet recurrent costs.
With these caveats, simple financial analysis techniques will now be
considered.   As a simple first example, consider the case of a traditional
stove and two improved models (ignoring effective interest rates) as
listed in Table 1.  As seen there, at the end of the first year both
improved models have nearly identical financial savings relative to the
traditional stove despite widely differing first costs and efficiencies.
Because the lifetimes and other characteristics of stoves can vary so
dramatically, it is often convenient to spread their cost over their
entire lifetime.  The results in this same case with no interest rate, are
presented in Table 2.  Additional costs to be spread over the lifetime of
the stove include maintenance.
Calculations such as these with no interest factors are extremely simple
and numerous variations can be tried to observe the relative importance of
different parameters such as the cost of fuel, the cost of the stove, the
energy savings of the stove, and so on.  As the interest rate is assumed
zero, each of these factors will have a linear interdependence.
                                 TABLE 1
             Financial Analysis of Three Hypothetical Stoves
                                 Daily Accounting
                                       EXPENDITURES, US$
                       Traditional         Improved            Improved
                       Metal Stove         Stove A             Stove B
                                         (30% Savings)      (40% Savings)
                Day     Daily    Total      Daily    Total      Daily    Total
Installation      0    -$0.50   -$0.50    -$6.50   -$6.50    -$15.5    -$15.5
Fuel              1     - 0.25   - 0.75    -  .175  - 6.675    -   .15  - 15.65
Fuel              2     - 0.25     1.00    -  .175  - 6.85     -   .15  - 15.80
Fuel              3     - 0.25   - 1.25    -  .175  - 7.025    -   .15  - 15.95
Fuel              4     - 0.25   - 1.50    -  .175  - 7.20     -   .15  - 16.10
....             ...    ...      ...       ...      ...       ...       ...
                365    - 0.25   -91.75    -  .175  -70.375    -   .15  - 70.25
Simple payback time (days)                       80                 150
Savings over one year                           21.38              21.50
                                 TABLE 2
             Financial Analysis of Three Hypothetical Stoves:
                                   Daily Totals
                                Traditional      Improved      Improved
                                Metal Stove     Stove A        Stove B
Installation   US$)                 0.50           6.50         15.50
Lifetime (years)                  1               2             4
Installed cost/day(*) (US$)       0.00137         0.008904       0.0106
Energy savings relative to
traditional stove (percent)       --             30             40
Fuel cost/family-day (US$)        0.25            0.175          0.15
Total operating cost/day (US$)    0.25137         0.1839         0.1606
(*) Interest rate is assumed zero.
In the more general case, the effective interest rate must be taken into
account.   The effective interest rate can be thought of as a quantitative
representation of the barrier opposing the purchase of a stove by a poor
person.   The higher the interest rate the greater the value placed on
having the money in hand at the moment rather than investing it in something
that will only provide a financial return in the future.
To calculate simple interest, the formula
     F = P(1+ni)                                                                     (1)
is used, where P is the present value of the investment, i is the interest
rate per time period, and n is the number of time periods.  The factor F
is the value of the investment n time periods into the future.   Thus, if
$10 are put into the bank at a simple annual interest rate of 20 percent,
then the future worth, F, of that investment one year in the future is
F=$10(1+0.2)=$12; two years in the future F=$14, and so on.
To calculate compound interest (the more general case), the formula
     F = P[(1+i).sup.n]                                                (2)
is used.   Thus, at the end of each time period, the entire investment P
plus interest i gained during that time period is reinvested at that
interest rate i.  For the above example, the future worth F of the $10
investment at the end of each year is given in Table 3.
Alternatively, the present value P of some worth is given by P=F/[(1+i).sup.n].
Thus, at an interest rate of 20 percent, being promised $24.88 in five
years is the same as being given $10 immediately.
If n equal payments, E, are regularly made over a period of time, then the
future worth F of these payments is simply the sum <see equation 3>

bsex195a.gif (165x660)

The corresponding present worth P is <see equation 4>

bsex195b.gif (93x726)

where n is the number of periods over which the payments E are made and i
is the interest rate over each period.  This can also be expressed as
spreading a single down payment P over a number of smaller payments E out
into the future.
As an example, the above case can be considered with a nominal annual
interest rate of 40 percent or a nominal daily rate (40/365) of 0.11
percent.   Spreading the cost P of the traditional stove A and stove B into
n equal daily payments E over the lifetime of the stove, the daily cost of
operating the stove can be calculated as shown in Table 4.

bsex196.gif (600x600)

It should be noted that the effective annual interest rate, when compounded
over a period of less than a year, is <see equation 5>

bsex196a.gif (75x726)

for compounding the nominal interest rate, r, (c) times during the year.   As
c becomes very large, compounding every week or less, this can be written <see equation 6>

bsex196b.gif (85x660)

where e is the base for natural logarithms, e=2.71828.  In the above case,
the nominal annual interest rate of 40% becomes, with daily compounding,
an effective annual rate of approximately
     [e.sup.0.40] -1 = 0.4918 or 49%
                                 TABLE 3
                             Compound Interest
Year         [(1+i).sup.n]            F
 0           1                   $10.00
 1          [1.2.sup.1]           12.00
 2          [1.2.sup.2]           14.40
 3          [1.2.sup.3]            17.28
 4          [1.2.sup.4]           20.74
 5          [1.2.sup.5]           24.88
With these formulas, a wide variety of situations can be analyzed.   More
complicated situations, such as with inflation, can similarly be analyzed
using standard interest rate formulas presented elsewhere (3).
For the calculations above, an effective interest rate must be assumed and
is often based on very dubious assumptions.  To avoid this, a factor termed
the internal rate of return is calculated which does not depend on any
particular assumed interest rate.  Its disadvantage is that it is usually
more difficult to calculate.
The internal rate of return is the interest rate that sets the total
present worth, receipts plus disbursements, to zero.  As an example, for
stove model A listed in Tables 1, 2, and 4, there is a disbursement of
$6.50 on day zero and receipts of $.075 each day in fuel savings over a
two year period.  The internal rate of return is that interest rate which
gives a present value of $0.00 for all these costs. <see equation 7>

bsex197a.gif (116x726)

Because the interest rate is so high, this can be solved directly.   Thus, <see equation 8>

bsex197b.gif (118x660)

This is a nominal annual rate of 365(0.0115)=420 percent.   In this particular
case, the internal rate of return decreases almost linearly with the
decreasing price of fuelwood, the decreasing fuel efficiency of the stove,
or the increasing initial cost of the stove.
As a second example, more typical of rate of return calculations, consider
a stove which costs $20.00 and saves $0.20 worth of fuel per week the
first year.  Due to losses in performance, the stove saves $0.16 per week
the second year, $0.12 per week the third year, $0.08 the fourth year, and
$0.04 the fifth year.  When the stove is purchased, its present value is
then <see equation 9>

bsex197c.gif (106x660)

where (Fuel X) is the present value of the fuel used during the year X at
the beginning of that year, the factor N is given by N=[(1+i).sup.52], and i is
the weekly interest rate.  The factor N discounts the value of the fuel
during any particular year to its present value at the time the stove is
purchased.   The present value of the fuel during any particular year X is
given by equation (4); <see equation below>

bsex198a.gif (204x660)

and so on .....
For each weekly interest rate the present value is then calculated from
equations (9) and (10).  Results are shown in Table 5.  As can be seen, the
internal rate of return is between 25 and 30% and can be roughly estimated
to be 27%.
In closing this section it is important to note that it has dealt with
financial analysis for the individual stove user only.  In determining the
value of a stove program it is also important to consider the economics,
that is, the national environmental costs of doing nothing; the impacts of
stove programs on rural and urban employment; the national costs of
importing substitute fuels or subsidizing stove dissemination; the cost of
infrastructure development; and many others.  Some of these were briefly
discussed in Chapter II.
                                 TABLE 5
                         Internal Rate of Return
Interest      Capital                    Savings(**) (by year)
Rate(*) %    Investment       1          2        3         4          5      Total
0.002        -$20.00        $9.87     $7.12     $4.81    $3.01     $1.30    +$6.10
0.003         -20.00          9.62      6.58      4.23     2.41      1.03     +3.87
0.004         -20.00          9.37      6.09      3.71     2.01      0.82     +2.01
0.005         -20.00          9.14      5.64     3.26     1.68       0.65    +0.36
0.006         -20.00          8.91      5.22      2.87     1.40      0.51     -1.08
0.007         -20.00          8.69      4.84      2.53     1.17      0.41     -2.36
(*)These are weekly interest rates and correspond to nominal annual
    interest rates of approximately 10, 15, 20, 25, 30, and 35%.
(**)Savings are due to reduced fuel costs.  Column 1 is given by
     (Fuel 1) above; column 2 is given by (Fuel 2)/N; column 3 by (Fuel
     3)/[N.sup.2]; etc. corresponding to the terms in equation (9).
This appendix is a brief "how to" review of a number of basic statistical
techniques including the average, standard deviation, coefficient of
variation, confidence limits, t-test, and linear regression.   Those
interested in more detailed information or more advanced techniques should
consult a basic text on statistics such as reference (1).
Statistical techniques are very useful in quantifying data and can
sometimes assist one's understanding of the physical or social processes
that are occurring.  However, these techniques are not a substitute for
understanding these processes.  Such understanding is developed instead,
for example, by analyzing the combustion and heat transfer processes in a
stove or the cultural and social response in adapting to a new stove.
When statistical analysis of the data is done mechanically, without an
understanding of these underlying physical or social processes, important
factors may be obscured that might otherwise be seen by carefully reviewing
the raw data.  Thus, statistical techniques are a tool to be used with
Finally, it is important to note that most of the following statistical
techniques are based on certain simplifying assumptions about the nature
of the test data being analyzed.  In particular, it is assumed that the
test data are always a random sample of an underlying "normal" or gaussion
distribution.   Although this is usually a reasonable approximation, it is
not guaranteed, and applying the following statistical techniques to data
that are not "normal" can sometimes lead to significant errors.   These
techniques should therefore be used with caution.  For the interested
reader, reference (1) discusses various tests to determine whether or not
a sample can be treated as "normal" and, if not, alternative statistical
techniques that can be used.
The average of a set of data [x.sub.i] is defined as <see equation 1>

bsex199a.gif (146x726)

where[sigma] is the sum of all the n individual test values [x.sub.i].   More precisely,
X[bar] is an estimator of the true average value of the underlying
"normal" distribution of which the test data are a random sample.   As the
number of tests, n, increases to infinity, X[bar] converges to the true average
value of the distribution.
As an example, assume that three different stoves, A, B, and C, are tested
in the laboratory with the results shown in Table 1.  The average for
stove A is <see equation below>

bsex199b.gif (165x660)

                                  TABLE 1
                     Hypothetical Laboratory Test Data
                 Test       A (PHU)       B (PHU)      C (PHU)
                   1         204(*)       13%          15%
                   2         17           16            14
                   3         16           17            17
                   4         18           18            15
                   5         14           14            16
                   6         17           16            13
                   7         18           17            17
                   8        19           18            16
                   9         18           17            --
                  10         15           16            --
       (*) For ease of illustration, values are only given to two
       significant figures.   In practice, a third significant figure,
       i.e. 20.3 will usually be included, assuming that the test
       procedure is sufficiently reliable to justify that precision.
the average for B is: <see equation below>

bsex200a.gif (87x486)

and for C is: <see equation below>

bsex200b.gif (97x600)

Standard Deviation
The standard deviation, [sigma], is a measure of how much variation there is
from one test to another within the "normal" distribution underlying the
observed test data.  The sample deviation is an estimate of the standard
deviation based on the observed test data.  If the tests were repeated an
infinite number of times, the sample deviation would approach and, in the
limit, be equal to the standard deviation (2).
The sample deviation for a test series is defined as: <see equation below>

bsex200c.gif (186x486)

and for ease of calculation this is written as: <see equation below>

bsex200d.gif (146x726)

For the test series on stove A above, [S.sub.A], is then calculated as
follows: <see equation below>

bsex201a.gif (317x600)

This calculation can be repeated for test series B and C, giving:
        [S.sub.B] = 1.6193
        [S.sub.C] = 1.4079
Test results are normally expressed an the average plus or minus the
sample deviation: <see equation below>

bsex201b.gif (150x317)

The sample deviation, S, can also be used to predict the approximate range
over which the data will lie if further tests are done -- assuming the
same conditions hold.
For a set of n data points [x.sub.i], assuming they are a random sample of a
normal distribution, the estimated average X[bar] and sample deviation [S.sub.x] can
be found as discussed above.  The number of degrees of freedom of this
data set is then given by:
        f = [n.sub.x] - 1                                        (3)
From the t-Table, Table 2, a t-value can be found for f degrees of freedom
and various levels of confidence/levels of significance, 100(1-[alpha])/[alpha].   The
range <see equation 4>

bsex201c.gif (67x726)

then holds approximately 100(1-2[alpha])% of all the data points.
As the sample size n becomes very large so that X[bar] converges with the true
average value of the "normal" distribution and [S.sub.x] converges with the
standard deviation, [sigma], of the distribution then 68.27 percent of all tests
done will have a value lying within [- or +]1[sigma] of the average.   Similarly, 95% of
the data points will lie within [- or +]1.96[sigma] of the average, and 99% of the data
points will lie within [- or +]2.57[sigma] of the average.  This can be seen in Table 2
for an infinite number of degrees of freedom.
For the more common case of finite sample size n, as in the case of
hypothetical stoves A, B, and C above, equation (4) must be used.
As an example, the test data for stove A has f-10-1-9 degrees of freedom.
Thus, for f=9 and [alpha]=2.5%, the t-table indicates that the interval <see equation below>

bsex202a.gif (78x600)

holds approximately 100(1-2[2.5])-95% of all expected data points if
testing were to continue indefinitely (generating sample sets of 10 data
Similarly, <see equation below>

bsex202b.gif (63x486)

holds approximately 99% of all expected data points.
For stove C with f=8-1=7 degrees of freedom, the interval <see equation below>

bsex202c.gif (87x486)

holds approximately 95% of all expected data points, and so on.
Coefficient of Variation
The coefficient of variation CV simply normalizes the sample deviation by
dividing it by the average: <see equation 5>

bsex202d.gif (85x660)

For the test series on stove A: <see equation below>

bsex202e.gif (108x486)

The coefficient of variation and the sample deviation are measures of the
quality of the data.  The smaller the CV, the more tightly grouped the
data are and the less important the uncontrolled variables.  A very large
coefficient of variation means that the experimental conditions are not
adequately controlled.  For example, there may be too much wind, the
balance may be sticking, or different testers may perform the tests in far
different manners.  Regardless, if the CV is large, greater effort must be
made to better control the experimental conditions and reduce the variability
of the data.
                                       TABLE 2
Degrees of    Level of Confidence     [100(1-[alpha])]/Level of Significance [[alpha]]
 Freedom         90/10      95/5          97.5/2.5            99/1     99.5/0.5
    1            3.078      6.314         12.706            31.821      63.657
    2           1.886       2.920           4.303            6.965      9.925
    3            1.638      2.353          3.182             4.541       5.841
    4            1.533      2.132          2.776             3.747       4.604
    5            1.476      2.015          2.571             3.365      4.032
    6            1.440      1.943          2.447             3.143       3.707
    7            1.415      1.895          2.365             2.998       3.499
    8            1.397      1.860          2.306             2.896       3.355
    9            1.383      1.833          2.262             2.821       3.250
   10            1.372      1.812          2.228             2.764       3.169
   11            1.363      1.796          2.201             2.718       3.106
   12           1.356       1.782           2.179            2.681      3.055
   13            1.350      1.771          2.160             2.650       3.012
   14            1.345      1.761          2.145             2.624       2.977
   15            1.341      1.753          2.131             2.602      2.947
   16            1.337      1.746          2.120             2.583       2.921
   17            1.333      1.740          2.110             2.567       2.898
   18            1.330      1.734          2.101             2.552       2.878
   19            1.328      1.729          2.093             2.539       2.861
   20            1.325      1.725          2.086             2.528       2.845
   21            1.323      1.721          2.080             2.518       2.831
   22            1.321      1.717          2.074             2.508       2.819
   23            1.319      1.714          2.069             2.500       2.807
   24            1.318      1.711          2.064             2.492       2.797
   25            1.316      1.708          2.060             2.485       2.787
   26            1.315      1.706          2.056             2.479       2.779
   27            1.314      1.703          2.052             2.473       2.771
   28            1.313      1.701          2.048             2.467       2.763
   29            1.311      1.699          2.045             2.462       2.756
   30            1.310      1.697          2.042             2.457       2.750
   40            1.303      1.684          2.021             2.423       2.704
   60            1.296      1.671          2.000             2.390       2.660
  120            1.289      1.658          1.980             2.358       2.617
[infinity]       1.282       1.645          1.960            2.326       2.576
   Reference (1)
When analyzing data, a test value quite different from all the others,
called an "outlier", may be found, yet there may be no obvious reason to
disqualify that particular test, e.g. no water was spilled, wood was
neither "lost" nor misweighed, values were not misrecorded, etc.   The
presence of such an outlier virtually guarantees that the distribution
with it included is not "normal" and analyzing it correctly can therefore
be quite difficult.
One way to avoid these complications is simply to arbitrarily ignore
outliers if they are sufficiently different from the other data.   The
consequencies of incorrectly throwing out a "good" data point are insignificant;
the consequences of not throwing out a "bad" data point can be
quite adverse.  One useful criterion for deciding whether or not to
include an outlier is to calculate how many sample deviations it lies from
the average of the other test data.  It is important that this sample
deviation and average not include the outlier.  If it lies more than, for
example, four sample deviations away, the outlier should be discarded.   In
some cases it may be desirable to use the more strict criterion of three
sample deviations.
As an example, consider the case where a ninth test is done on Stove C
(Table 1) and a value of 9% is found.  As already shown, the average and
sample deviation for the first eight tests on Stove C=15.4[- or +]1.41.   The
value 9% is more than four sample deviations from the average, that is,
15.4-4(1.41)=9.76, so it could be discarded.  Alternatively, consider the
case where the ninth test gave a value of 20 percent.  A value of 20
percent is just slightly more than [3S.sub.C] from C[bar].   Discarding this value may
be desirable in some cases, but is not so clearly "bad" as the value 9%.
Confidence Limits
Confidence limits give a range of values within which the true average
value for the data is expected to lie.  As before, a t-value is found for
the test data with f degrees of freedom and a level of significance, [alpha].
The confidence interval: <see equation 6>

bsex204a.gif (97x486)

is then 100(1-2[alpha])% certain (see note 3) to hold the true average value of
the underlying normal distribution from which the test data are a random
sample.   Note the difference of 1/[radical]n compared to equation (4).  As the
number of data points, n, gets large, the confidence interval narrows down
on the true average value even while the scatter of data, equation (4),
remains the same.
As an example, for Stove A (Table 1), the range <see equation below>

bsex204b.gif (97x486)

is 100(1-2(2.5))%=95% certain to hold the true average.   Similarly, <see equation below>

bsex204c.gif (87x486)

is 99% certain to hold the true average.
The t-test is used to determine if two data sets differ in a statistically
significant way.
Comparing stoves A and B, their average and standard deviation are given
by: <see equation below>

bsex205a.gif (97x486)

and their 95 percent confidence ranges (within which there is a 95 percent
probability of finding their true average values -- See Note 3) are:
        [A.sub.g5] = 15.9 to 18.5 and [B.sub.g5] = 15.0 to 17.4
Thus, their 95 percent confidence limits overlap from 15.9 to 17.4.   How,
then, does one know that stove A is actually better than stove B?   To
determine this a t-test is used.  For two data sets x and y the t-value is
defined as (4): <see equation 7>

bsex205b.gif (127x798)

where [S.sub.p] is the pooled sample deviation, <see equation below>

bsex205c.gif (150x486)

[n.sub.x] and [n.sub.y] are the number of tests used for calculating the average and
standard deviations of data sets X and Y respectively, and the number of
degrees of freedom is given by
        f = [n.sub.x] + [n.sub.y] - 2                             (8)
If the value of t calculated by Equation (7) is larger than the value
listed in Table 2 for that number of degreas of freedom and a certain
level of significance, [alpha], then the data sets X and Y are said to be
different at the 100(1-2[alpha])% level of confidence (see note 4).   It is
important to note that the value [alpha] must be chosen from Table 2 in order to
have a 100(1-2[alpha])% confidence that the means (or averages) are different.
This is known as a two-sided t-test of the means.
Thus, comparing stoves A and B (Table 1) <see equation below>

bse205d0.gif (167x486)

From the t-table, for f=18 degrees of freedom and a 100(1-2[alpha])-90 percent
level of confidence, [alpha]=5 and t=1.734.  Since the calculated t-value above,
t=1.30, is less than this, one says that the two stoves, A and B, do not
meet the 90 percent level of confidence requirement -- that is, there is
less than a 90 percent chance that the performance of the two stoves
differ, or equivalently, there is more than a 10 percent chance that the
average PHU performance of stove A is the same as that of stove B (see
note 5 for a more detailed discussion).
Comparing stove B to stove C (Table 1): <see equation below>

bsex206a.gif (285x486)

for f=10+8-2=16 degrees of freedom the t-value for a 90 percent level of
confidence ([alpha]=5) is 1.746 so again [t.sub.BC]=1.10 is less than 1.746=[t.sub.90] and
there is greater than a 10 percent chance that the true average value of
performance for stove B will be the same as that of stove C.
Similarly, stove C and stove A can be compared to find:
        [S.sub.P] = 1.65      t = 2.30       f=16
From Table 2, the t-value for f-16 and a 95 percent level of confidence is
([alpha]=2.5) [t.sub.g 5]=2.12; for a 98 percent level of confidence ([alpha]-1) [t.sub.g 8]=2.583.
The t-value for Stoves A and C is then; <see equation below>

bsex206b.gif (97x540)

Thus, there is a 95 percent level of confidence that the performance of
Stove A is different than that of Stove C.  Alternatively, it can be said
that there is an approximately 2 to 5% chance that their performances are
the same.  This does not state, however, what their relative performance
is.   Their relative performance is somewhere in the range of values given
by their confidence levels.  For example, it is 95 percent probable that
their true performance lies in the ranges given by: <see equation below>

bsex206c.gif (87x600)

In the case of stoves A and B, the data was insufficient to show a
significant performance difference between them.  Additional tests are
To determine the number of tests n required to show a significant difference
between two data sets each of n data points, the following formula is
used: <see equation 9>

bsex207a.gif (121x600)

where [bar]X and [bar]Y are the averages for the two data sets, [S.sub.P] is the pooled
sample deviation for sets X and Y, and u is given by, for 90 percent
confidence levels, u=1.293; for 95 percent, u=3.61, and for 99 percent,
u=4.90 (see note 6).
For example, to be 90 percent confident that stoves A and B had different
performances, the number of tests needed would be approximately <see equation below>

bsex207b.gif (121x540)

or about 25 tests of each stove.  The 99 percent confidence level requires
about 71 tests of each.  Clearly, if possible, it is preferable to more
carefully control the tests so that there is less variation between tests;
that is, to reduce the sample standard deviation.  Thus, reliable testing
results are more easily achieved by better controlling the variables such
as wood moisture content, wind, etc., than by trying to overpower them by
"endlessly" repeating tests.
Linear Regression
Linear regression is used to find the "best" linear relationship between
two variables.  If the relationship between the variables is not linear,
then the linear regression should be done with the appropriate combination
of variables so that it is as close to a linear relationship as possible.
For example, if y is approximately equal to [x.sup.2] then the linear regression
should be done between the variable y and the variable [x.sup.2] rather than
between y and x itself.  The approximate form to use can usually be
roughly estimated by quickly graphing the data values, x, [x.sup.2], etc. versus
y and observing which is most nearly linear.
The formulas for doing a linear regression are the following:
Given n data pairs (x,y), the best linear fit to these data points is
given by the line: <see equation 10>

bsex207c.gif (70x600)

where m is the slope and ([bar]Y-mX[bar]) is the y intercept.   The coefficient [bar]X of
this equation is given by the average: <see equation below>

bsex208a.gif (162x726)

With the definitions: <see equation below>

bsex208b.gif (600x600)

The correlation coefficient is then given by <see equation 14>

bsex208c.gif (129x726)

and is a measure of how well the line y=m(x-X[bar])+Y[bar] actually fits the data:
[- or+]1 in a perfect fit; 0 indicates there is no correlation between the
variables x and y in the data pairs ([x.sub.i],[y.sub.i]).
A confidence region can also be determined for the regression line and is
similar to the confidence limits for an average value discussed above.   The
confidence region is given by the equation: <see equation below>

bsex208d.gif (230x600)

is the estimated variance of residuals and F(2,n-2) is the upper (1-[alpha])
percentage point of the F distribution for 2 and n-2 degrees of freedom at
the desired confidence level (1-[alpha]).  The F distribution is listed in Table 5
This is the equation for an ellipse in variables (a,b).  Lines y =
a'+b'(x-X[bar]) with (a',b') within this ellipse fit the regression line with
the level of confidence given by the choice of F.  Lines with (a',b')
outside this ellipse do not fit the data to that level of confidence.
As an example of the use of linear regression, suppose that a series of
tests is done to determine the effect of the grate-to-pot height (all
other factors remaining precisely the same) with the results for stoves D
and E as shown in Table 3.
                                 TABLE 3
        Hypothetical Stove Data of PHU versus Grate To Pot Height
                  H (height)      D (PHU)      E (PHU)
                    10 cm        30%          17%
                    11            28           14
                    12            27           16
                    13            25           17
                    14            24           18
                    15            23           16
                                  TABLE 4
                     An Example Linear Regression Worksheet
               H     D      E      HD       HE     [H.sup.2]       [D.sup.2]       [E.sup.2]
              10     30     17     300      170    100      900     289
              11     28     14     308      154    121      784     196
              12     27     16     324      192    144      729     256
              13     25     17     325      221    169      625     289
              14     24     18    336      252     196     576     324
              15     23     16     345      240    225      529     256
Sum [sigma] = 75    157     98    1938     1229    955    4143     1610
Clearly, the performance of this hypothetical stove D is very sensitive to
the grate-to-pot height while that of stove E is not.   A linear regression
can be done to determine what the best linear relationship is between the
stove performance and the height in centimeters and to determine how
accurately this linear relationship represents the data.
From the data set above for stoves D and E the sums and sums of squares
and products can be formed as indicated in Table 4.
Then <see equation below>

bsex210a.gif (600x600)

Thus, the best linear fit to the data for stove D is
        [PHU.sub.D] = -1.4(H-12.5) + 26.1667
and there is a very good correlation, |R|=0.99, between these data points
as shown in Figure 1.

bse1x213.gif (600x600)

For stove E, the best linear fit is given by
        [PHU.sub.E] = 0.229(H-12.5) + 16.333
but the correlation is not very good, |R|=0.313, as can also be seen in
Figure 1.
Similarly, confidence regions can be determined for the above regression
lines.   With a desired level of confidence of 95 percent, the F value with
n=4 is 6.94.  For stove D, the confidence region is then given by: <see equation below>

bsex210b.gif (230x600)

For stove E the confidence region in given by:
        [(a-16.333).sup.2] + 2.9167[(b-0.229).sup.2] = 4.863
                                    TABLE 5
                              F(2, n) DISTRIBUTION
                   level of confidence/level of significance
 n                90%/10%      95%/5%      97.5%/2.5%       99%/1%
 1                 49.5        199.5          799.5         4999.5
 2                  9.00        19.00          39.00         99.00
 3                  5.46          9.55           16.04        30.82
 4                  4.32         6.94          10.65         18.00
 5                  3.78         5.79           8.43         13.27
 6                  3.46         5.14           7.26         10.92
 7                 3.26          4.74            6.54         9.55
 8                  3.11         4.46           6.06          8.65
 9                  3.01         4.26           5.71          8.02
10                  2.92          4.10            5.46         7.56
11                  2.86         3.98           5.26          7.21
12                  2.81          3.89            5.10         6.93
13                  2.76          3.81            4.97         6.70
14                  2.73          3.74            4.86         6.51
15                  2.70          3.68            4.77         6.36
16                  2.67          3.63            4.69         6.23
17                  2.64          3.59            4.62         6.11
18                  2.62          3.55            4.56         6.01
19                  2.61          3.52            4.51         5.93
20                  2.59          3.49            4.46         5.85
21                  2.57          3.47            4.42         5.78
22                  2.56          3.44            4.38         5.72
23                  2.55          3.42            4.35         5.66
24                  2.54          3.40            4.32         5.61
25                  2.53          3.39            4.29         5.57
26                  2.52          3.37            4.27         5.53
27                  2.51          3.35            4.24         5.49
28                  2.50          3.34            4.22         5.45
29                  2.50          3.33            4.20         5.42
30                  2.49          3.32            4.18          5.39
40                  2.44          3.23            4.05         5.18
60                  2.39          3.15            3.93         4.98
120                 2.35          3.07           3.80         4.79
[infinity]          2.30          3.00           3.69          4.61
Reference (1)
These are graphed in Figure 2 below (7).  As can be seen, the confidence

bse2x213.gif (600x600)

region for stove E is much larger than for stove D.  That is, there is a
considerable latitude in possible choices for the line parameters for
stove E for a given level of confidence.  Stated another way, there is
considerably less certainty about what the regression line should really
be for stove E than for stove D.  This corresponds to the much smaller
correlation coefficient for stove E data than stove D.  Thus, the calculated
regression line for stove E, for example, is the best fit to the
given data, but other regression lines with parameters given within the
ellipse provide nearly as good a fit (95 percent confidence level for the
given data) to this data.
Comparing Linear Regression Lines
It is frequently necessary to compare two regression lines to determine
whether or not they are parallel or perhaps even statistically indistinguishable.
To do this, a technique similar to the t-test can be used.
Given two sets of data: <see equation below>

bsex212a.gif (121x600)

were the subscripts 1 and 2 on the brackets refer to the respective data
First, regression lines are fit through each separate data set as described
above. <see equation 18>

bsex212b.gif (230x600)

where the subscripts distinguish between data sets I and 2.
Second, the estimated residual variance, [S.sup.2.sub.r], is calculated for each data
set as given in equation (16).
Third, the pooled estimated residual variance, [], is calculated for the
two data sets. <see equation 19>

bsex212c.gif (150x600)

where the subscripts again distinguish between the data sets.
Fourth, the pooled t-value [t.sub.p] is calculated for the two regression lines <see equation 20>

bsex214a.gif (167x600)

This can now be compared to the t-value for ([n.sub.1]+[n.sub.2]-4) degrees of freedom
and the desired level of significance, [alpha], from the t-table.   If [t.sub.p] is
greater than that given for [t.sub.[alpha]] in the t-table then the lines are said to
have different slopes at the level of confidence 100(1-2[alpha])%.
If the slopes are not statistically distinguishable then they can be
tested to determine if they are also coincident.  To do this, a common
slope must next be calculated for all the above data.  Thus, the fifth
step is to estimate a common slope, [m.sub.c], and a common residual variance,
[S.sub.c] for the two data sets together. <see equation below>

bsex214b.gif (230x600)

Sixth, calculate the corresponding common t-value, [t.sub.c]: <see equation 23>

bsex214c.gif (207x600)

As above, if [t.sub.c] is greater than the t-value for ([n.sub.1]+[n.sub.2]+3) degrees of
freedom at the desired level of significance, [alpha], then the two lines are
parallel but statistically distinguishable.  If [t.sub.c] is less than the
t-value then they are statistically indistinguishable at the level of
confidence 100(1-2[alpha])%.
An idealized field study will be analyzed to illustrate the technique.
The first week, daily wood weighings are done for each of the eight
families using their traditional stove.  For each family, the number of
adult equivalents eating and the fuel consumption per adult equivalent are
calculated for each day and then averaged over the week.  The second week,
the process is repeated with the families using improved stove model A;
the third week with improved stove model B.  The fourth week, the families
again use their traditional stoves so as to check that the performance is
the same; that is, to verify that the conditions, weather, wood moisture
content, and other variables that could affect the stove performance, have
remained the same during the entire period of testing.  The data are
summarized in Table 6.
These data are plotted in Figure 3.  Although it is easy to see that stove

bse3x217.gif (600x600)

A consumes less fuel than the traditional stove, it is not easy to see any
difference between stove B and the traditional one.
The first step is to calculate [bar]X, [bar]Y, [S.sub.xxn], etc.   The results are listed in
Table 7.
The regression lines are given by (Table 7 and equations 11 to 14 above):
Traditional stove: Y = -28.6(x-10.25) + 625.    R = -0.84
Model A stove:     Y = -19.4(x-10.25) + 387.5   R = -0.56
Model B stove:     Y = -29.0(x-10.375) + 575.   R = -0.89
where Y is the fuel consumption per person per day, x is the family size
in adult equivalents, and R is the correlation coefficient.   Clearly,
stove A has a lower fuel consumption than the others.  However, its change
in fuel consumption with family size is also significantly different.   To
compare these stoves, the fuel consumption per person for the average size
of family can be used.  At x = 10. 25, the traditional stove uses 625
grams/person-day, stove A uses 387.5 grams/person-day, and stove B uses
578.6 grams/person-day.  Because of the strong correlation between family
size and fuel consumption usually observed in the field, it is important
that stove performance be compared on the basis of the same family size.
The regression lines for the traditional and model B stoves have similar
slopes and can be compared.  Calculating the residual variance, equation
(16), for each data set <see equation below>

bsex215a.gif (150x600)

From this the pooled residual variance is given by [] = 4820.
The corresponding pooled t-value is <see equation below>

bsex215b.gif (87x600)

From the t-table, for (8+8-4)-12 degrees of freedom, the 80 percent level
of confidence ([alpha]-10) is (1.356).  Thus, the slopes of these two lines are
statistically indistinguishable.
Now a common slope and common sample variance for the two data sets
combined can be calculated.
    [m.sub.c] = 28.8 and [S.sub.c] = 66.7
                                    TABLE 6
                     Data From A Hypothetical Field Study
               Week 1                           Week 2                         Week 3
         Traditional Stove                     Model A                        Model B
          Equivalent    Fuel per      Equivalent      Fuel per       Equivalent       Fuel per
FAMILY      Adults      person-day       Adults       person-day        Adults        person-day
  A         4            800               4             600               5             800
  B         7            700               7             400              6            700
  C         9            600               9             500              9            600
  D        10            700              10            400               9             500
  E        11            700              11             300             11            600
  F        11            600              12             400             12            500
  G        14            400              14             300             15            500
  H        16            500              15             200             16            400
                                    TABLE 7
                Regression Analysis Of Hypothetical Field Study
                     Traditional      Stove A          Stove B
[bar]X                   10.25              10.25           10.375
[bar]Y                  625.               387.5           575.
[S.sub.xxn]              99.5               91.5           107.875
[S.sub.yyn]         115,000.           108,750.       115,000.
[S.sub.xyn]           -2850.             -1775.         -3125.
The corresponding t-value is <see equation below>

bsex216.gif (167x600)

For (8+8-3)=13 degrees of freedom, the t-table gives a t-value of 1.35 for
the 100(1-2[alpha])=80 percent confidence level ([alpha]=10) and 1.771 for the 90
percent confidence level ([alpha]=5).  Thus, 1.771 > [t.sub.c]-1.39 > 1.35, that is,
there is greater than an eighty percent chance, but less than 90 percent,
that these two stoves have a different level of performance (although it
has already been shown that the change in their performance with family
size, i.e. the slope of their regression lines, is the same).   The beat
estimate of their relative performance vas given above for the family size
of 10.25, that is 625 grams/person-day versus 578.6 grams/person-day or
stove B uses 7.5 percent less fuel than the traditional stove.
In analyzing real field data there are numerous complications.   The fuel
consumption and/or the numbers of people fed can vary dramatically from
day to day for an individual family.  In this case, it may be better to do
the linear regressions or other analyses on the daily data from all the
families combined rather than first averaging it over the time period
(week) for each family.  The fuel consumption will often tend to decrease
somewhat with time as the families become more sensitive to fuel use or
better learn how to control their stoves.  Changes in weather, such as the
beginning or end of the rainy season, can sometimes dramatically affect
fuel consumption.  This factor, in particular, could be reduced by
monitoring the fuel moisture content.  The family's economic status can
also be a large factor in determining fuel use.  Such factors as these can
often be accounted for by doing a multiple regression on the data.
Linear Regression on Two Variables
In many cases there are two or more variables which determine the system's
response.   The laboratory PHU of a stove might be determined by both the
channel height and gap, or the fuel consumption per person might depend on
both the family size and income, or perhaps on the family size and day of
the test -- the fuel consumption decreasing as the family becomes more
sensitized to their fuel use.  To analyze such cases the following procedure
is used.
Given n triplets of observations ([y.sub.1], [x.sub.1i] [x.sub.2i]), the regression equation
which fits this data is <see equation below>

bsex218a.gif (600x600)

and the partial correlation coefficient between [x.sub.1] and y is given by <see equation below>

bsex218b.gif (600x600)

In the case where the variables [x.sub.1] and [x.sub.2] have no correlation ([S.sub.x1x2n]=0)
the formulas above for [m.sub.1] and [m.sub.2] reduce to that for linear regression on a
single variable.  In many cases, however, [x.sub.1] and [x.sub.2] will not be independent.
For example, consider the case where [x.sub.1] is the family size, [x.sub.2] is
the family income, and y is the fuel consumption per person-day.   Both [x.sub.1]
and [x.sub.2] will affect y.  Additionally, however, families with larger incomes
will frequently have fewer children.  Thus [x.sub.1] and [x.sub.2] are not independent
in this case.
As a final worked example, laboratory test data on insulated charcoal
stoves during the second, simmering phase and listed in Table VI-2 will be
analyzed.   The data is listed in Table 8 with y the PHU, [x.sub.1] the channel
gap in millimeters, and [x.sub.2] the channel length in centimeters.   The PHU is
extraordinarily high and is less sensitive to the channel dimensions than
would be expected from Chapter III for reasons discussed in Chapter VI.
From this data the sums, sums of squares, and sums of products can be
calculated as before.  The averages and other factors can then be calculated.
The results are listed below in Table 9.

bsex219.gif (600x600)

                            TABLE 8
             PHU Data for Charcoal Stoves, Simmering Phase
              Y (PHU)      gap [x.sub.1] (mm.)      length [x.sub.2] (cm.)
               57.5              3                           5
               68.6              3                          10
               78.4              3                          15
               50.2              5                           5
               71.9              5                         10
               77.3              5                          15
               48.8              8                          5
               61.7              8                          10
               64.9              8                          15
From Table 9, the slopes and partial correlation coefficients are calculated.
  [m.sub.1] = -1.997        [R.sub.x1y] = -0.776
  [m.sub.2] =  2.1367      [R.sub.x2y] =   0.934
Thus, the regression equation is given by:
  y = 64.4 - 2.0([x.sub.1]-5.3) + 2.1([x.sub.2]-10)
This equation is the best linear fit possible to the data.  The equation
says, for example, that decreasing the channel gap from 5.3 to 3.0 mm will
increase the PHU by about 4.6%; lengthening the channel from 10 to 15 cm.
will increase the PHU by about 10.5%.  As can be seen from the partial
correlation coefficients, the fit is quite good between the PHU, y, and
the channel length, [x.sub.2].  It is not as good between the PHU, y, and the
channel gap, [x.sub.1].
There are numerous other useful statistical techniques as well, such as
regression on more than two variables, analysis of variance, and many
others.   The interested reader should refer to a textbook on the subject
for details (1).
Useful instruments in stove design, development, and testing are listed
below.   A very extensive list of manufacturers for these and other
scientific instruments is given as reference (1).
o   Flexible metal tape measure: Used to measure template, stove, and pot
   dimensions, etc.
o   Balance: Used for laboratory, controlled cooking, and field tests.  In
   the laboratory and controlled cooking tests a balance with a precision
   of [- or +]1 gram is desirable.   The balance capacity should be at least 5 kg
   and preferably 10 kg or more.   With higher capacities, the entire stove
   can be weighed with charcoal in it, thus avoiding the complications of
   removing the charcoal from the stove, weighing it, and then restarting
   the fire.  The balance should be either a double or triple beam type
   balance, or electronic.   The electronic balances have the advantage of
   ease of use and reduced errors in measurement, but cost considerably
   more and are more fragile than the standard mechanical pan balances.
   In field tests, due to the need for portability, linear spring balances
   with a precision of at least [- or +]10 grams are preferred.
   No matter what balance is used, its calibration should be frequently
   checked over its entire range by weighing a set of standard weights.
   The balance should also be placed on a level platform where it will not
   be jarred and carefully protected from dust, extreme heat, and water.
o   Thermometers: Used to measure the water temperature during lab tests.
   Typically, mercury in glass thermometers with a length of 30 to 45 cm
   and a range of 0 to 105[degrees]C or 110[degrees]C with a precision of al least [- or +]0.5[degree]C
   are most useful.   Alternatively, thermocouples can be used.
o   Thermocouples: Used to measure temperatures of the water, or of the
   stove or hot flue gases.   A wide variety of thermocouple wires and
   probes are available for different temperature ranges.  In testing
   stoves, type K chromel-alumel thermocouple wire with high temperature
   ceramic or glass insulation is usually adequate.  If a direct temperature
   readout meter with a built in electronic cold junction is not
   available, then a digital volt meter that has a resolution of 0.1 mV
   and a reference junction, preferably in an ice bath, will be needed.
   For accurate measurements, the test junction must be in very good
   thermal contact with the temperature being measured.
   Direct readout digital thermometers with a built in reference can be
   very convenient, but the standard probes supplied with them may reduce
   the experimenter's flexibility to make a wide variety of measurements
   as they are often too large and unwieldy to be easily inserted in the
   region of interest -- such as the pot to wall channel.  In this case
   the experimenter will want to make a personal set of thermocouple
   probes from standard type K wire.
o   Kilns: Used to measure the moisture content of wood.  "Wet" wood is
   collected in the field and placed in air tight plastic bags and in a
   cool location until the moisture test can be done (Note that many types
   of plastics are somewhat permeable -- the test should be done as soon
   as possible).   The wood alone is then weighed and placed in the kiln to
   dry at 105[degrees]C until its weight becomes constant.  This can take several
   days depending on the size of the wood.  The difference between its
   initial and final weights is the moisture content.  Alternatively,
   though less precise, an electronic moisture meter can be used to
   estimate the moisture content.
o   Moisture meter: Used to measure the approximate moisture content of
   wood.  It consists of a calibrated four prong probe which is inserted
   into the wood.   The meter measures the electrical resistance of the
   wood through these probes and from that gives a readout of the moisture
   content.  Such moisture meters can have a reduced accuracy for moisture
   contents greater than 25%.   Further, as they only measure the surface
   moisture content, they can be seriously in error for the interior.
o   Bomb calorimeter: Used to measure the calorific value of the wood or
   biomass being used with the stove.
o   Gas analysis: Used to measure the carbon monoxide and other gases
   released by combustion in the stove.   A variety of portable personal
   monitors to determine individual exposures to smoke and suspended
   particulates have been developed by the Resource Systems Institute of
   the East-West Center.   Interested readers should contact them directly.
When purchasing laboratory or field testing equipment, it is important to
know how their precision will affect the overall quality of data.   For
such analysis the following rules can be used (2).
If m measurements with an apparatus give an estimated average reading and
sample deviation of [X.sub.m][- or +][], n measurements with a second apparatus gives
[Y.sub.n][- or +][S.sub.ny], and so on; then the sum of such measurements is
given by: <see equation 1>

bsex222a.gif (167x600)

where a, b, c, .... are constants; and the product of such
measurements is <see equation 2>

bsex222b.gif (167x600)

where i, j,... are exponents.  In both these cases it is assumed that the
variables X, Y,..., are uncorrelated.
Use of these formulas is straight-forward.  Consider, for example, the
errors in a laboratory PHU test if the thermometer has an error of [- or +]1[degree]C
(determined by repeatedly measuring the temperatures of e.g. boiling water
over a period of time and then calculating the sample deviation) and the
balance has a typical error of [- or +]2 grams.  Then from Chapter V, <see equation 3>

bsex223a.gif (167x600)

and with typical values of [W.sub.i]=5.000 kg; [W.sub.f]=4.700 kg; [T.sub.i]=30[degrees]C; [T.sub.f]=100[degrees]C;
[M.sub.i]=0.500 kg; [M.sub.f]=0.150 kg; [C.sub.i]=0 kg; [C.sub.f]=0.040 kg; [C.sub.w]=18000 kJ/kg; and
[C.sub.c]=29000 kJ/kg.  Inserting these assumed values along with the errors into
equation (3) gives <see equation below>

bsex223b.gif (600x600)

or, as a percentage <see equation below>

bsex223c.gif (70x600)

If a balance with a one gram precision is used instead, then the same
procedure can be used to find <see equation below>

bsex223d.gif (97x600)

If, in addition, a thermometer with a precision of 0.5[degree]C is used, the
error is further reduced to <see equation below>

bsex223e.gif (78x600)

Thus, by following a simple procedure such as this (see reference (2) for
a more rigorous discussion) the effect on data quality of different levels
of precision in any laboratory instruments can be quantified.   Whether or
not a more precise and expensive instrument is worthwhile can then be
determined directly.  In some cases it will be found that the errors due
to a previously overlooked instrument, such as a $5 thermometer, will far
outweigh the potential advantage of upgrading another instrument, such as
a balance.
Other factors that should also be considered include the variability of
the calorific value and moisture content of the fuel; the effect of the
wind on the balance; differences in the way personnel handle the fuel,
fire, pots, and water; and many others.  An analysis should be done of
each of these factors by first repeating measurements of each over a
period of time to determine the sample deviation and then performing an
overall error analysis such as the above.
The International System of Units (SI) is based on the units listed in
Table 1.   All other quantities are derived from these seven arbitrarily
chosen units and various examples are listed in Table 2.  Table 3 lists

bsex225.gif (600x600)

common prefixes used in the SI system.  Table 4 lists some physical
constants in SI units.  Table 5 lists common conversion factors between

bsex2270.gif (600x600)

the SI system and other system of units. For a more complete discussion,
the reader should review references (1,2,3-6) from which the following
materials are extracted.
                                    TABLE 1
                      Fundamental Units In the SI System
                Quantity                   Name              Symbol
                length                     meter                m
                mass                      kilogram             kg
                time                       second               s
                electric current           ampere               A
                temperature                kelvin               K
                number of particles
                 (atoms, molecules)         mole              mole
                luminous intensity         candela             cd
                                    TABLE 3
                 Prefixes in the International System of Units
                  Multiplier            Symbol           Prefix
                    [10.sup.18]           E                exa
                    [10.sup.15]           P                peta
                    [10.sup.12]           T                tera
                    [10.sup.19]           G               giga
                    [10.sup.6]            M                mega
                    [10.sup.3]            k                kilo
                    [10.sup.2]            h                hecto
                    [10.sup.1]            da               deka
                    [10.sup.-1]           d                deci
                    [10.sup.-2]           c                centi
                    [10.sup.-3]           m                milli
                    [10.sup.-6]          [mu]              micro
                    [10.sup.-9]           n                nano
                    [10.sup.-12]          p                pico
                                    TABLE 4
                  Some Fundamental Physical Constants in the
                         International System of Units
                     Quantity                  Symbol        Value
           Speed of Light in a Vacuum            c             2.99792x[10.sup.8] m/s
           Stefan-Boltzmann Constant             [sigma]       5.66961x[10.sup.8] W/[m.sup.2][K.sup.4]
           Boltzmann's Constant                  K             1.380622x[10.sup.-23] J/K
           Avogadro's Constant                   [N.sub.A]     6.022169x[10.sup.2 6] 1/kmol
           Gas Constant                          R             8314.34 J/kmolK
           Planck's Constant                     h             6.626196x[10.sup.-34] Js
           Gravitational Constant                G             6.685x[10.sup.-5] [m.sup.3]/kg[s.sup.2]
           Gravitational Acceleration            g             9.8 m/[s.sup.2]
           Units and Conversions
Institutions active in tropical forestry are listed in reference (1). A
handbook listing governmental and nongovernmental natural resource management,
environmental and related organizations is cited as reference (2).
A number of other institutions involved in biomass energy research and
development are given in (3). Below are listed institutions involved with
fuel efficient stove development and dissemination.  Although many of the
larger organizations such as USAID, the United Nations, and the World Bank
are involved in stove projects in a variety of countries, only primary
addresses are listed.  This is neither a complete listing nor a listing of
the most important groups and should not be construed as such.   It is
simply a partial listing of institutions as were available at Press-Time.
Apologies go to all those who have been inadvertently omitted; and they
are requested to notify the author so that they may be included in future
listings of active institutions.  For additional information, readers
should also contact the Foundation for Woodstove Dissemination.
ACEEE (American Council for an Energy Efficient Economy), 1001 Connecticut
Ave., N.W. suite 535, Washington, D.C. 20036 USA. (attn: Howard Geller)
ADEREM (Association pour le Developpement des Energies Renouvelables en
Mauritanie) B.P. 6174, Nouakchott, Mauritania.
AIDR (Association Internationale de Developpement Rurale), 20 rue de
Commerce, Boite 9, B-1040, Brussels, Belgium.
ARD (Associates in Rural Development), 72 Hungerford Terr., Burlington,
Vt. 05401, USA.
ASTRA (Centre for the Application of Science and Technology to Rural
Areas), Indian Institute of Science, Bangalore, India 560-012.
ATI (Appropriate Technology International), 1724 Massachusetts Avenue,
N.W., Washington, D.C. 20036, USA.
ATOL (Appropriate Technology for Developing Countries), Blijde Irkomstraat
9, 3000 Leuven, Belgium.
Africare, 1601 Connecticut Avenue, N.W., Washington, D.C., USA.
Appropriate Technology Development Institute, P.O. Box 793, Lae, Papua New
Aprovecho Institute, 442 Monroe Street, Eugene, Oregon 97402, USA.
Association Bois de Feu, 73 Avenue Corot, 13013 Marseille, France.
Bellerive Foundation, Case Postale 6, 1211 Geneva 3, Switzerland.
Beijer Institute, The Royal Swedish Academy of Science, Box 50005,
S104-05, Stockholm, Sweden; and Scandinavian Institute of African Studies,
Bohuslaningens, AB, Uddevalla, Sweden.
BioEnergy Users Network, c/o International Institute for Energy and
Development, 1717 Massachusetts Ave. N.W., Washington, D.D. 20036. (attn:
Albert Binger)/P.O. Box 1660, San Jose, Costa Rica. (attn: Alvaro Unana).
Brace Research Institute, McDonald College of McGill University, P.O. Box
255, ste. Anne de Bellevue, Quebec, Canada H9X 1CO.
CDI (Centro de Desarrollo Industrial), A.P. 1626, Tegucigalpa, Honduras.
CEAER, Universite du Rwanda, Butare, Rwanda; (attn: Prosper Mpawenayo)
CEES (Center for Energy and Environmental Studies); Princeton University,
Princeton, New Jersey, 08544. USA. (attn: Sam Baldwin, Gautam Dutt, Eric
Larson, Bob Williams).
CERER (Centre d'Etudes et de Recherches sur les Energies Renouvelables)
Universite de Dakar, B.P. 476, Dakar, Senegal.
CEMAT (Center for Mesoamerican Studies on Appropriate Technology), P.O.
Box 1160 Guatemala.
CICON (Centro de Investigaciones de Ingenieria), Ciudad Universitaria,
Zona 12, Guatemala.
CILSS (Comite Permanent Inter-etats de Lutte Contre la Secheresse dans le
Sahel), Equipe Ecologie-Forets, B.P. 7049, Ouagadougou, Burkina Faso.
CISIR (Ceylon Institute for Scientific and Industrial Research), P.O. Box
787, 363 Bauddhaloka Mawatha, Colombo 7, Sri Lanka.
CORT (Consortium on Rural Technology), E-350, Nirman Vihar, Delhi 11092
CRES (Centre Regional Energie Solaire), B.P. 1872, Bamako, Mali.
CWS (Church World Service), B.P. 11624, Niamey, Niger (attn: Ralph Royer);
B.P. 3822 Dakar, Senegal (attn: Lionel Derenoncourt).
Center for Development Technology, Department of Technology and Human
Affairs, Washington University, St. Louis, Missouri 63130 USA. (attn:
Robert P. Morgan)
Center for the Study of Energy and Natural Resources, Universidad Catolica
Madre Y Maestra, Santiago de los Caballeros, Dominican Republic
Center for Energy Research, National Office for Scientific and Technical
Research, Yaounde, Cameroon.
Centre National des Energies Alternatives, BP 199, Nouakchott, Mauritania.
Centre National de Productivite, B.P. 811 Conakry, Guinea.
Centre Technique Forestier Tropical, 45 bis, avenue de la Belle Gabrielle,
94130 Nogent-sur-Marne, France.
Chemical Engineering Department, Bangladesh University of Science and
Technology, Dacca 2, Bangladesh.
DHV Consulting Engineers, P.O. Box 85, 3800 AB Amersfoot, The Netherlands
(attn: Gerhard van de Rhoer).
Department of Community Development, Banjul, The Gambia (attn: Bai
Bojang); Department of Forestry, No. 5 Marina, Banjul, The Gambia (attn:
Bymaas Taal).
Dian Desa, P.O. Box 19 Bulaksumur, Yogyakarta Dij, Indonesia.
Directorate of Research, N.W.F.P. University of Engineering and Technology,
Peshawar, Pakistan (attn: I.H. Shah).
EEC (European Economic Community); Directorate General for Energy; Commission
of the European Communities; Rue de la Loi 200; B1049 Brussels,
E/DI (Energy Development International), 1015 18th Street, N.W. Suite 802,
Washington, D.C. 20036. USA.
Earthscan, 10 Percy Street, London W1P ODR, United Kingdom.
East-West Center, Resource Systems Institute, 1777 East-West Road,
Honolulu, Hawaii, 96848 USA. Contact: Kirk Smith
Eglise Lutherienne Malgache, Foibe Fampandrosoana, Dept. of Development,
Antsirabe, Madagascar.
Energy Research Group, Carleton University, C.J. MacKenzie Building, Room
218, Colonel By Drive, Ottawa K1S 5B6 Canada.
Energy Research Institute, University of Cape Town, Private Bag, Rondebosch
7700, South Africa.
Energy Resources Group, University of California, Rm. 100, Bldg. T-4,
Berkeley, California 94720, USA.
Energy Unit, Ministry of Agriculture, Box 30134, Lilongwe 3 Malawi.
Environmental Studies Center, Wright State University, Dayton, Ohio 45435
USA. (attn: Timothy Wood).
FUNDAEC, Apartado Aereo 6555, Cali, Colombia.
Forestry Research Institute of Malawi, P.O. Box 270, Zomba, Malawi
Foundation for Woodstove Dissemination, Korte Jansstraat 7, 3512 GM
Uttrecht, the Netherlands. (attn: Ad Hordijk)
GATE (German Appropriate Technology Exchange) P.O. Box 5180. D6236
Eschborn 1, West Germany; See GTZ.
GRET (Groupe de Recherche et d'Echanges Technologies), 34 rue Dumont
d'Urville 75116 Paris, France.
GRUEA (Groupe de Recherche des Utilisations des Energies Alternatives),
Universite de Burundi, Faculte des Sciences, B.P. 2700, Burundi
GTA (Grupo Tecnologia Appropriada) Apartado 8046, Panama 7, Panama.
GTZ, (Deutsche Geseltschaft fur Technische Zusammerenarbeit), Postfach
5180, Dag-Hammerskjoldweg 1, D-6236 Eschborn 1, West Germany.
German Forestry Mission (Mission Forrestiere Allemand), BP 13, Ouagadougou,
Burkina Faso.
Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, 81
Martyr's Road, Guangzhou, Canton, People's Republic of China
IBE (Institut Burkinabe de l'Energie), BP 7047, Ouagadougou, Burkina Faso
ICAITI, Apartado Postal 1552, Avenida la Reforma 4-47, Zona 10, Guatemala,
Guatemala (attn: Marco Augusto Recinos).
IDRC (International Development Research Center), Box 8500, Ottawa,
Ontario, Canada K1G 3H9
IIED, International Institute for Energy and Development, 1717 Massachusetts
Avenue, N.W., Washington, D.C. 20036.
INE (Instituto Nacional de Energia), Italia No. 438 y mariana de jesus,
Quito, Ecuador
ITDG (Intermediate Technology Development Group), 9 King Street, London
WC2E 8HN, United Kingdon (attn: Yvonne Shanahan).
IT Power (Intermediate Technology Power, Ltd.), Mortimer Hill, Mortimer,
Reading, Berkshire, RG7 3PG United Kingdom.
IUFRO (Fuelwood Production Information Network), A-1131, Vienna, Austria.
(attn: Oscar Fugalli).
Institut du Sahel, BP 1530, Bamako, Mali
Instituto de Energia, Academy of Sciences, Casilla 5279, La Paz, Bolivia.
Instituto Mexicano de Tecnologias Apropriadas SC, Farallones 60-B, Col.
Acueducto de Gpe., C.P. 07270, Apdo. Postal 63-254, 02000 Mexico, D.F.
Instituto Nacional de Investigacao Tecnologica, C.P.  185, Praia, Cape
Instituto Tecnologico de Costa Rica, Centro de Informacion Technologica,
Apartado 159, Cartago, Costa Rica.
International Rice Research Institute, P.O. Box 933, Manila, Philippines.
KENGO (Kenya Energy Non-Governmental Organization Association),   P.O. Box
48197, Nairobi.
Kenya National Council for Science and Technology, Box 30623, Nairobi.
LESO (Laboratoire d'Energie Solaire), B.P. 134, Bamako, Mali.
Laboratorium voor Koeltechnik en Klimaatreling Katholieke Universiteit,
3030 Heverlee, Belgium (attn: G. de Lepeleire).
Mazingiri Institute, P.O. Box 14550, Nairobi, Kenya.
Ministry of Energy, P.O. Box 2256, Government Buildings, Suva, Fiji (attn:
Jerry Richolson).
Ministry of Energy, Government of Kenya, P.O. Box 30582, Nairobi, Kenya.
Ministry of Foreign Affairs, Section For Research and Technology, P.O.
Box 20061, 2500 EB The Hague, The Netherlands.  (attn: Joan Boer)
Ministry of Science and Technology, Department of Non-Conventional Energy
Sources, Government of India, C.G.O. Complex Block No.14, Lodi Road, New
Delhi, 110 003.
NAS/BOSTID; National Academy of Sciences, Board on Science and Technology
in Development, Room JH-213, 2101 Constitution Avenue, N.W., Washington,
D.C. 20418 USA.
OECD Club du Sahel, 2 rue Andre Pascal, 75775 Paris Cedex 16 France.
OLADE (Latin American Energy Organization), Casilla 119-A, Quito, Ecuador.
ONERSOL (Office de 1'Energie Solaire), B.P. 621, Niger.
OXFAM-America, Inc. 115 Broadway, Boston Massachusetts, USA.
Peace Corps, 806 Connecticut Avenue, N.W. Washington, D.C. USA.
Projet National Foyers Ameliores, B.P. 296, Niamey, Niger, (attn: Issaka
RECAST (Research Center for Applied Science and Technology) Tribhuvan
University, Kirtipur, Kathmandu, Nepal.
RETAIN, (Rural Energy Technology and Innovation Network) Science Policy
Research Unit, Mantell Building, University of Sussex, Falmer, Brighton
BN1 9RF, United Kingdom.
Rural Industries Innovation Center, Box 138, Kanye, Botswana.
Service Des Foyers Ameliores, Jeunesse Canada Monde, 4824 Cote des Neiges,
Montreal, Quebec, Canada H3V 1G4.
SKAT (Swiss Center for Appropriate Technology), Varnbuelstr. 14, Ch-9000
St. Gallen, Switzerland.
SIDA (Swedish International Development Authority), Birgir Jaris Gatan 61,
S-10525 Stockholm, Sweden.
Sarvodaya Institute, Palletalawinna, Katugastota, Kandy, Sri Lanka.
Service Nationale Projet Foyers Ameliores, Ministere de 1'Environnement et
Tourisme, B.P.14, Ouagadougou, Burkina Faso.
Silveira House, P.O. Box 545, Harare, Zimbabwe.
Societe de Vulgarisation du Foyer Ameliore, 985 Hotel de Ville, Montreal,
Quebec, H2X 3A4, Canada.
Somali National Committee for Alternative Energy, c/o The Foundry, P.O.
Box 1411, Mogadishu, Somalia (attn: Ali Dahir).
TATA Energy Research Institute, Bombay House, 24 Homi Mody Street, Bombay
TERI Field Research Unit, c/o Sri Aurobinda Ashram, Pondicherry 65002
India (attn: C.L. Gupta).
TOOL, Stichting TOOL, Mauriskade 61a, Amsterdam, The Netherlands.
UNDP (United Nations Development Program), one United Nations Plaza, New
York, N.Y. 10017
UNIDO (United Nations Industrial Development Organization), Lerchen Felder
Strasse 1, P.O. Box 707, A-1070 Vienna, Austria.
UNFAO (United Nations Food and Agriculture Organization), Via delle Termi
di Caracalla, 0100 Roma, Italy
UNEP (United Nations Environment Program), P.O. Box 30522, Nairobi, Kenya.
UNICEF: Eastern Africa Regional Office, P.O. Box 44145, Nairobi, Kenya.
Universidad Nacional Autonoma De Mexico, Facultad de Ciencias, Departemento
de Fisica (3er piso) Ciudad Universitaria 04510, Mexico, D.F. (attn:
Marco A. Martinez Negrete)
USAID Office of Policy and Planning, Room 3887, Washington, D.C. 20523 USA
USAID Office of Energy, DS/ST Room 306 SA-18, Washington, D.C. 20523, USA
USAID Office of the Sahel, AFR/SFWA Room 3491, Washington, D.C. 20523 USA
University of Dar Es Salaam, Forestry School, P.O. Box 643, Morogoro,
Tanzania, (attn: R.C. Ishengoma); Faculty of' Engineering, P.O. Box 35169
Dar Es Salaam, Tanzania (attn: Simon Nkonoki).
University of Khartoum, c/o DSRC, P.O. Box 321, Khartoum, Sudan (attn:
Edwin Hunley).
VITA (Volunteers in Technical Assistance), 1815 North Lynn Street, Suite
200, P.O. Box 12438, Arlington, Virginia 22209-8438 USA.
Village Industries Program, P.O. Box 464, Gaborone, Botswana.
Village Industry Service, P.O. Box 35500, Lusaka, Zambia
Volunteers in Asia, Box 4543, Stanford, CA 94305 USA
Wood Stove Group, T.H.E. Eindhoven, University of Technology, W&S, P.O.
Box 513, 5600 MB Eindhoven, The Netherlands.
World Bank, Science and Technology Unit, Room E1036, 1818 H Street, N.W.,
Washington, D.C. 20433, USA.
World Bank, Energy Department, Room D434, 1818 H Street, N.W., Washington,
D.C. 20433, USA.
World Bank, Energy Assessment Division, Room D446, 1818 H Street, N.W.,
Washington, D.C. 20433, USA.
World Environment Center, 605 Third Avenue, 17th Floor, New York, N.Y.
10158 USA.
World Resources Institute; 1735 New York Avenue, N.W., Washington, D.C.
Bangladesh: Chemical Engineering Department
Belgium: ATOL; AIDR; EEC; Laboratorium voor Koeltechnik en Klimaatreling
Bolivia: Instituto de Energia
Botswana: Rural Industries Innovation Center; Village Industries Program
Burkina Faso: CILSS; IBE; Service Nationale Projet Foyers Ameliores
Burundi: CRUEA
Cameroon: Center for Energy Research
Canada: Brace Research Institute; Energy Research Group; IDRC; Service Des
  Foyers Ameliores; Societe de Vulgarisation du Foyer Ameliore.
Cape Verde: Instituto Nacional de Investigacao Tecnologia
China: Guangzhou Institute of Energy Conversion
Colombia: FUNDAEC
Costa Rica: BioEnergy Users Network; Instituto Tecnologico de Costa Rica
Dominican Republic: Center for the Study of Energy and Natural Resources
Ecuador: INE; OLADE
Fiji: Ministry of Energy
France: Association Bois de Feu; Centre Technique Forestier Tropical;
  GRET; OECD Club du Sahel;
Gambia: Department of Community Development
Germany: GATE; German Forestry Mission; GTZ
Guinea: Centre National de Productivite
Honduras: CDI
India: ASTRA, CORT; Ministry of Science and Technology; TATA Energy
  Research Institute; TERI Field Research Institute
Indonesia: Dian Desa
Italy: UNFAO
Kenya: KENGO; Kenya National Council for Science and Technology; Mazingiri
  Institute; UNEP; UNICEF
Madagascar: Eglise Lutherienne Malgache
Malawi: Energy Unit; Forestry Research Institute
Mali: CRES; Institut du Sahel; LESO
Mauritania: ADEREM; Centre National des Energies Alternatives
Mexico: Instituto Mexicano de Tecnologias Apropriadas; Universidad
  Nacional Autonoma De Mexico
Netherlands: DHV Consulting Engineers; Foundation for Woodstove Dissemination;
  Ministry of Foreign Affairs; TOOL; Wood Stove Group
New Guinea: Appropriate Technology Development Institute
Niger: CWS; ONERSOL; Projet National Foyers Ameliores
Pakistan: Directorate of Research
Panama: GTA
Philippines: International Rice Research Institute
Rwanda: CEAER
Senegal: CERER; CWS
Somalia: Somali National Committee for Alternative Energy
South Africa: Energy Research Institute
Sri Lanka: CISIR; Sarvodaya
Sudan: University of Khartoum
Sweden: Beijer Institute; SIDA
Switzlerland: Bellerive Foundation; SKAT
Tanzania: University of Dar Es Salaam
United Kingdom: Earthscan; ITDG; IT Power; RETAIN
United States of America: Africare; ACEEE; ATI; Aprovecho; ARD; BioEnergy
  Users Network; Center for Development Technology; CEES; East-West
  Center; E/DI; Energy Resources Group; Environmental Studies Center;
  IIED; NAS BOSTID; Oxfam; Peace Corps; UNDP; USAID; Volunteers In Asia;
  VITA; World Bank; World Environment Center; World Resources Institute
Zambia: Village Industry Service
Zimbabwe: Silveira House
Chapter I
1.   Baldwin, Sanuel F., Domestic Energy For Developing Countries: Options
    and Opportunities, forthcoming.
2.   Joseph, S.D., Y.H. Shanahan, and W. Stewart, The Stove Project Manual:
    Planning and Implementation, Intermediate Technology Publications, 9
    King Street, London WC2E 8HW, U.K., 1985.
Chapter II
1.   Sagan, Carl, Owen B. Toon and James B. Pollack.  "Anthropogenic Albedo
    Changes and the Earth's Climate", Science Vol. 206, 1979, pp. 1363-1368.
2.   Eckholm, Erik P., Losing Ground: Environmental Stress and World Food
    Prospects, W.W. Norton and Company, NY, 1976, 223 pp.
3.   Perlin, John and Boromir Jordan,   "Running Out -- 4200 Years of Wood
    Shortages", Coevolution Quarterly, Spring 1983, pp. 18-25.
4.   UNFAO, Tropical Forest Resources, Forestry Paper No. 30, United
    Nations Food and Agriculture Organization, Rome, 1982, 106 pp.
5.   Technologies to Sustain Tropical Forest Resources, March 1984, 344
    pp.; Sustaining Tropical Forest Resources; U.S.  and International
    Institutions. Background paper #2, May 1983; and Sustaining Tropical
    Forest Resources:   Reforestation of Degraded Lands.   Background paper
    #1, May 1983.   Congressional Office of Technology Assessment; U.S.
    Government Printing Office, Washington, D.C.
6.   "Fuelwood and Charcoal, Report of the Technical Panel", Second
     Session, United Nations (A/CONF.100/PC/34) February 25, 1981.
7.   The Global 2000 Report to the President, Volume 2, Council on Environmental
    Quality and the Department of State, US Government Printing
    Office, Washington, D.C., 1980.
8.   Arungu-Olende, Shem.   "Rural Energy," Natural Resources Forum, Volume
    8, 1984, pp. 117-126.
9.   Dunkerley, Joy; Ramsay, William; Gordon, Lincoln; and Cecelski,
    Elizabeth.   Energy Strategies for Developing Countries, Resources for
    the Future, Johns Hopkins University Press, Baltimore, 1981, 265 pp.
10.   Hall, D.O. "Solar Energy Use Through Biology -- Past, Present and
     Future", Solar Energy, Vol.22, 1979, pp. 307-328.
11.   Hughart, David. Prospects for Traditional and Non-Conventional Energy
     Sources in Developing Countries, World Bank Staff Working Paper No. 346, 132
     pp., July 1979.
12.   Moss, R.P., and Morgan, W.B. Fuelwood and Rural Energy Production and
     Supply in the Humid Tropics, United Nations University, Tycooly
     International Publishing, Ltd., Dublin, 1981.
13.   Earl, D.E. Forest Energy and Economic Development, Clarendon Press,
     Oxford, 1975.
14.   Abe, Fusako.   "Manufacture of Charcoal from Fast Grown Trees" in W.
     Ramsey Smith, ed., Energy from Forest Biomass, New York: Academic
     Press, 1982.
15.   Harris, A.C.   "Charcoal Production", Eighth World Forestry Congress,
     Jakarta, Indonesia, 1978.
16.   Wegner, K.F., ed. Forestry Handbook, New York: John Wiley and Sons,
     1984, 1335 pp.
17.   Kuusela, K. and Nyyssonen, A.   "Quantifying Forest Energy", UNASYLVA,
     pp. 31-34.
18.   Openshaw, K. "Woodfuel Surveys: Measurement Problems and Solutions to
     these Problems", Stencil No. 799, Division of Forestry, University of
     Dar Es Salaam, Morogoro, Tanzania, July 10, 1980.
19.   Wood Fuel Surveys, UNFAO, Programme for Forestry for Local Community
     Development, GCP/INT/365/SWE, Rome, 1983, 202 pp.
20.   Hall, D.O.; Barnard, G.W.; and Koss, P.A. Biomass for Energy in the
     Developing Countries, Pergamon Press, Oxford, 1982, 212 pp.
21.   Nkonoki, Simon and Sorensen, Bent. "A Rural Energy Study in Tanzania:
     The Case of Bundilya Village," Natural Resources Forum, Vol. 8, No. 1,
     1984, pp. 51-62.
22.   Singh, J.S.; Pandey, Uma; and Tivari, A.K. "Man and Forests: A Central
     Himalayan Case Study", Ambio, Vol. 12, No. 2, 1984, pp. 80-87.
23.   Revelle, Roger. "Energy Use in India", Science, Volume 192, 1976, pp.
24.   O'Keefe, Phil, Paul Raskin, and Steve Bernow, eds. Energy and Development
     in Kenya: Opportunities and Constraints, Beijer Institute and
     Scandinavian Institute of African Studies, 1984, Bohuslaningens, AB,
     Uddevalla, Sweden, 1984.
25.   Keita, M.N. Les Disponibilites de Bois de Feu en Region Sahelienne de
     l'Afrigue Occidentale -- Situation at Perspectives, Rome: UNFAO, 1982.
26.   Alio, Hamadil.   Firewood Shortage in the Sahel Countries: A Niger Case
     Study, M.Sc. Thesis, University of Arizona, 1984.
27.   CILSS Equipe Regional Ecologio-Forets.   "Quantification des Besoins en
     Bois des Pays Saheliens: Une Analyse des Bilans/Programmes", Comite
     Permanent Interetat de Lutte contre la Secheresse dans le Sahel",
     Reunion de Banjul, October 18-22, 1982.
28.   Clement, Jean.   Estimation des Volumes et de la Productivite des
     Formations Mixtes Forestieres et Graminennes Tropicales, Centre
     Technique Forestier Tropical, 45 bis, avenue de la Belle Gabrielle,
     94130 Nogent-sur- Marne, France.
29.   See references (1-4,6,9,17-21); reference (17) is a particularly
     useful review of the literature.
30.   Islam, M. Nunil; Morse, Richard; and Soesastro, M. Hadi, eds. Rural
     Energy to Meet Development Needs:   Asian Village Approaches, Boulder,
     Colorado, and London: Westview Press, 1984, 561 pp.
31.   O'Keefe, Phil, and Kristoferson, Lars. "The Uncertain Energy Path -- Energy
     and Third World Development", Ambio, V.13, 1984, pp. 168-170.
32.   Munslow, Barry; O'Keefe, Phil; Parkhurst, Donna; and Philips, Peter.
     "Energy and Development on the African East Coast", Ambio, Volume 12,
     No. 6, 1983, pp. 332-337.
33.   Dunkerley, Joy. "Patterns of Energy Consumption by the Rural and Urban
     Poor in Developing Countries", Natural Resources Forum, Volume 3,
     1979, pp. 349-363.
34.   Arnold, J.E.M. "Wood Energy and Rural Communities", Natural Resources
     Forum, Volume 3, 1979, pp. 229-252.
35.   Goldemberg, Jose. "Energy Problems in Latin America", Science, Volume
     223, 1984, pp. 1357-1362.
36.   Dunkerley, Joy, and Rassay, William.   "Energy and the Oil-Importing
     Developing Countries", Science, Volume 216, 1982. pp. 590-595.
37.   O'Keefe, Phil.   "Fuel for the People:  Fuelwood in the Third World",
     Ambio, Volume 12, 1983, pp. 15-17.
38.   Earl, Derek.   "A Renewable Source of Fuel", UNASYLVA, Volume 27, No.
     110, 1975, pp. 21-26.
39.   Mnzava, E.M.   "Village Industries vs. Savannah Forests", UNASYLVA,
     Volume 33, No. 131, 1981, pp. 24-29.
40.   Arnold, J.E.M. and Jongma, Jules.   "Fuelwood and Charcoal in Developing
     Countries", UNASYLVA, Vol. 29(118), 1978. pp. 2-9.
41.   Bhagavan, M.R. "The Woodfuel Crisis in the SADCC Countries", Ambio,
     Volume 13, No. 1, 1984, pp. 25-27.
42.   Hinrichson, Don.   "Fuelwood and Charcoal: The Other Energy Crisis",
     Ambio, Volume 10, No. 5, 1981, pp. 234-235.
43.   Goldemberg, Jose; Hukai, Roberto Y.; et al. A Country Study -- Brazil,
     A Study on End-Use Energy Strategy, Global Workshop on End-Use
     Oriented Energy, Sao Paulo, Brazil, June 4-15, 1984.
44.   Servin, Jesus Cervantes; Negrete, Marco Antonio Martinez; Cerutti,
     Omar Masera; and Estrada, Fernando Shutz.  End-Use Oriented Energy
     Strategies for Mexico, Global Workshop on End-Use Oriented Energy
     Strategies, Sao Paulo, Brazil, June 4-15, 1984.
45.   Reddy, Amulya Kumar N.; and Reddy, B. Sudhakar. Energy in a Stratified
     Society -- A Case Study of Firewood in Bangalore, Indian Institute of
     Science, Bangalore 560 012, July 1982.
46.   Shrestha, Kedar Lal.   Energy Strategies in Nepal and Technological
     Options, Research Center for Applied Science and Technology, Tribhuvan
     University, Nepal, End-Use Oriented Global Energy Workshop, Sao Paulo,
     Brazil, June 1984.
47.   Mwandosya, M.J. and Luhanga, M.L. Energy Demand Structures in Rural
     Tanzania, Department of Electrical Engineering, University of Dar-Es- Salaam,
     P.O. Box 35131, Dar-Es- Salaam, Tanzania.
48.   Balanco Energetico Nacional, Republica Federativa do Brazil, Ministerio
     des Mines E Energia, Bloco J, 75.056-Brasilia-DF, 1983.
49.   Mwandosya, M.J. and Luhanga, M.L.P. Energy Use Patterns in Tanzania,
     Short form: Center for Energy and Environmental Studies Report No.
     180, Princeton University, Princeton, N.J., Feb. 1985.  Full length:
     Department of Electrical Engineering, University of Dar Es Salaam, Dar
     Es Salaam, Tanzania, Draft, 1984, 240 pp.
50.   Ravindranath, N.H.; Nagaraju, S.M.; Somashekar, H.I.; Channeswarappa,
     A.; Balakrishna, M.; Balachandran, B.N.; and Reddy, Amulya Kumar N.
     "An Indian Village Agricultural Ecosystem -- Case Study of Ungra
     Village, Part I:   Main Observations", Biomass, Volume 1, No. 1,
     September 1981, pp. 61-76.
51.   Reddy, Amulya Kumar N. "An Indian Village Agricultural Ecosystem -- Case
     Study of Ungra Village, Part II: Discussion", Biomass, Volume 1,
     No. 1, September 1981, pp. 77-88.
52.   Makhijani, Arjum and Poole, Alan. Energy and Agriculture in the Third
     World, Ballinger Publishing Company, Cambridge, Mass., 1975, 168 pp.
53.   Tiwari, K.M. "Fuelwood -- Present and Future with Special Reference to
     Conditions in Developing Countries", in Energy from Biomass, 2nd
     International Conference on Biomass, A. Strub, P. Chartier and G.
     Schleser, eds., London: Applied Science Publishers, 1982.
54.   Hall, D.O., and Moss, Patricia.   "Biomass for Energy in Developing
     Countries." Geojournal, Vol. 7.1, 1983, pp. 5-14.
55.   Cecelski, E., "Energy Needs, Tasks, and Resources in the Sahel:
     Relevance to Woodstove Programs," Geojournal, Vol. 7.1, 1983, pp.
56.   Hyman, E.L. "The Demand for Woodfuels by Cottage Industries in the
     Province of Ilocos Norte, Philippines,"  Energy, Vol. 9, pp. 1-13,
57.   Zhu, H., Brambley, M.R. and Morgan, R.P., "Household Energy Consumption
     In The People's Republic of China", Energy V.8, pp 763-774, 1983.
58.   Down, S.  "Household Energy Consumption In West Sumatra. Implications
     for Policy Makers", Energy, Vol. 8 pp 821-833, 1983.
59.   Mnzava, E. M.   "Fuelwood and Charcoal in Africa", in Energy from
     Biomass, First International Conference on Biomass, Brighton, East
     Sussex; W. Paley, P. Chartier, D.O. Hall, ads., London: Applied
     Science Publishers, Ltd., 1980.
60.   Chauvin, Henri. "When an African City Runs Out of Fuel", UNASYLVA,
     Vol. 33 (133) pp. 11-20., 1981
61.   Boureima, Issoufou and Gilles De Chambre.  "Rapport sur l'evaluation
     du programme foyers ameliores", Niamey, Niger: Association des Femmes
     du Niger and Church World Service, November 1982.
62.   Sassin, Wolfgang, "Energy," Scientific American, Sept. 1980, p. 119.
63.   Prasad, K. Krishna. Cooking Energy, Workshop on End-Use Focused Global
     Energy Strategy, Princeton University, Princeton, New Jersey, April
     21-29, 1982.
64.   Williams, Robert H. Potential Roles for Bioenergy in an Energy
     Efficient World, Princeton University center for Energy and Environmental
     Studies, Report No. 183, February 1985; Workshop on Biomass
     Energy Systems, Airlie House, Virginia, January 29-February 1, 1985.
65.   United Nations, Yearbook of World Energy Statistics, 1981, New York:
     United Nations, 1983.
66.   Booth, H.E.  "Realities of Making Charcoal", UNASYLVA, Volume 33, No.
     131, 1981, pp. 37-38.
67.   FLORASA, Man-Made Forests for Wood and Charcoal in Brazil, Minas Gerais,
     Brazil: Florestal Acesita, S.A., Belo Horizonte, Oct.1983, 53 pp.
68.   Uhart, E. Preliminary Charcoal Survey in Ethiopia, U.N. Economic
     Commission for Africa, FAO Forest Industries Advisory for Africa, Doc.
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69.   Karch, G.E. Calrbonization: Final Technical Report of Forest Energy
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70.   Wood, T.S. Report on Domestic Energy Use for Cooking (Energy Assessment
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71.   Wartluft, Jeffrey.   "Team Compares Charcoal Production Methods", VITA
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     Arlington, Virginia: VITA, March 1984.
72.   Charcoal Production Improvement For Rural Development In Thailand,
     Forest Products Research Division, Royal Forest Department, Ministry
     of Agriculture and Cooperatives, for the National Energy Administration,
     Ministry of Science, Technology, and Energy under the Renewable
     Nonconventional Energy Project, Royal Thai Government and U.S. Agency
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73.   Rose, A.B., Energy-Intensity and Related Parameters of Selected
     Transportation Modes:   Freight Movements, Oak Ridge National Laboratory,
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74.   Bonney, R.S.P. and Stevens, N.F. Vehicle Operating Costs on Bituminous,
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75.   Truck Operating Characteristics in the Sudan, Transport and Communications
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76.   Wardle, Philip and Palmieri, Massimo.   "What Does Fuelwood Really
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77.   Foley, Gerald, and van Buren, Ariane.   "Substitutes for Wood",
     UNASYLVA, Volume 32, No. 130, pp. 11-24.
78.   Weber, F., Economic and Ecologic Criteria of Forestry/Conservation
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79.   Baldwin, Sam. Technical Notes for the Senegalese `Ban Ak Suuf'
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80.   Yameogo, Georges; Bussman, Paul; Simonis, Philippe; and Baldwin, Sam.
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     from VITA.
     See also, Yameogo, Georges; Evaluation des differents Prototypes de
     Foyers Ameliores Existants en Haute Volta; Universite de Ouagadougou,
     Institut Superieur Polytechnique; Mamoire de fin d'Etudes. Juin 1983
     L'Institut Voltaique de L'Energie, rapport No.1, Etat de Developpment
     Technigue des Foyers Ameliores en Haute Volta, Ouagadougou, April 1983
81.   Smil, Vaclav.   "Deforestation in China", Ambio, Volume 12, No. 5, 1983,
     pp. 226-231.
82.   Brown, Lester R. ; Chandler, William; Flavin, Christopher; Postel,
     Sandra; Storke, Linda; and Wolf, Edward.  State of the World 1984.
     Worldwatch Insitute, New York:   W.W. Norton and Company, 1984.
83.   Jackson, Peter.   "The Tragedy of our Tropical Rainforests", Ambio,
     Volume 12, No. 5, 1983, pp. 252-254.
84.   Steinlin, Hans Jurg.   "Monitoring the World's Tropical Forest",
     UNASYLVA, Volume 34, No. 137, 1982, pp. 2-8.
85.   Myers, Norman.   "The Hamburger Connection:  How Central America's
     Forests Become North America's Hamburgers", Ambio, Volume 10, No. 1,
     pp. 3-8.
86.   Nations, James D.; and Komer, Daniel I. "Central America's Tropical
     Rainforests: Positive Steps for Survival", Ambio, Volume 12, No. 5,
     1983, pp. 232-238.
87.   Salati, Eneas and Vose, Peter B.   "Depletion of Tropical Rainforests",
     Ambio, Volume 12, No. 2, 1983, pp. 67-71.
88.   Finn, Daniel.   "Land Use and Abuse in the East African Region", Ambio,
     Volume 12, No. 6, 1983, pp. 296-301.
89.   Pratt, D.J. and Gwynne, M.D., eds., Rangeland Management and Ecology
     in East Africa, Huntington, New York:  Robert E. Kreiger Publishing
     Company, 1977.
90.   National Academy of Sciences. Environmental Change in the West African
     Sahel, Washington, D.C.:   Board on Science and Technology in Development,
     National Research Council, 1983, 86 pp.
91.   Breman, H. and deWit, C.T. "Rangeland Productivity and Exploitation in
     the Sahel", Science, Volume 221, 1983, pp. 1341-1347.
92.   Kartawinata, Kuswata, Seonartono Adisoemarto, Soedarsono Riswan, and
     Andrew P. Vayda.   "The Impact of Man of a Tropical Forest in Indonesia",
     Ambio, Volume 10, No. 2-3, 1981, pp. 115-119.
93.   Brown, Lester R. "World Population Growth, Soil Erosion, and Food
     Security", Science, Volume 214, 1981, pp. 995-1002.
94.   Grainger, Alain. Desertification, Earthscan, 1984, pp. 94.
95.   O'Keefe, Phil. "The Causes, Consequences and Remedies of Soil Erosion
     in Kenya", Ambio, volume 12, No. 6, 1983, pp. 302-305.
96.   Smith, Nigel J.H. "Colonization Lessons from a Tropical Forest",
     Science, Volume 214, 1981, pp. 755-761.
97.   Gentry, A.H. and J. Lopez-Parodi. "Deforestation and Increased
     Flooding of the Upper Amazon", Science, Volume 210, 1980, p.1354.
98.   Spears, John.   "Preserving Watershed Environments", UNASYLVA, Volume
     34, No. 137, 1982, pp. 10-14.
99.   The State of India's Environment 1984-84. The Second Citizen's Report
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     New Delhi 110 019.
100.   Shukla, J. and Y. Mintz. "Influence of Land-Surface Evapotranspiration
      on the Earth's Climate", Science, Volume 215, 1982, pp. 1498-1501.
101.   Dosso, Henri, Jean Louis Guillaumet, and Malcolm Hadley. "Land Use
      Problems in a Tropical Forest", Ambio, Volume 10, No. 2-3, 1981.
102.   National Academy of Sciences. Agro Forestry in the West African Sahel.
      Board on Science and Technology in Development, National Research
      Council, Washington, D.C. 20418. 1983. 86 pp.
103.   Novikoff, Georges and Mohamed Skouri. "Balancing Development and
      Conservation in Pre-Saharan Tunisia", Ambio, Volume 10, No. 2-3, 1981,
     pp. 135-141.
104.   Novikoff, G. "Desertification by Overgrazing", Ambio, Volume 12, No.
      2, 1983, pp. 102-105.
105.   Lamprey, H.F. and Hussein Yussuf. "Pastoralism and Desert Encroachment
      in Northern Kenya", Ambio, Volume 10, No. 2-3, 1981, pp. 131-134.
106.   Anderson, D. and R. Fishwick, Fuelwood Consumption and Deforestation
      in African Countries, World Bank Staff Working Paper No. 704, 1984.
107.   Smith, Kirk R.; Aggarwal, A.L.; and Dave, R.M. "Air Pollution and
      Rural Fuels: A Pilot Village Study in India", Working Paper WP82-17,
      November 1982. East-West Center, Honolulu, Hawaii
108.   Smith, Kirk R.; Ramakrishna, Jamuna; and Menon, Premlata. "Air
      Pollution from the Combustion of Traditional Fuels: A Brief Survey,"
      Conference on Air Quality Management and Energy Policies, Baroda and
      Bombay, India, February 16-25, 1981, WP 81-5.
109.   Smith, Kirk R.; Aggarwal, A.L.; and Dave, R.M. "Air Pollution and
      Rural Fuels: Implications for Policy and Research," Honolulu, Hawaii:
      Resource Systems Institute, East West Center, WP-83-2, November 1982.
110.   de Koning H.W., K.R. Smith and J.M. Last, "Biomass Fuel Combustion and
      Health", Bulletin of the World Health Organization 63 (1), pp. 11-26,
111.   Smith, K., Biomass Fuels, Air Pollution, and Health: A Global Review,
      Plenum Publishing Co., New York, (forthcoming).
112.   Smith Kirk R., "Biomss Fuels, Air Pollution and Health" included in
      Baldwin, Sam, Howard Geller, Gautam Dutt and N.H.  Ravindranath,
      "Improved Woodburning Stoves:   Signs of Success", Ambio Vol. 14, No.
      4-5, pp. 280-287, 1985.
113.   Ernest, E. "Fuel Consumption Among Rural Families in Upper Volta, West
      Africa." Eighth World Forestry Conference, Jakarta, Indonesia, 1978.
114.   If the total fuelwood demand (given by the population of village, P,
      times the demand per person, D) is set equal to the total renewable
      fuelwood supply (given by the average biomass productivity per area
      times the area available for woody biomass production - - and this area
      is given crudely by the total land area, [pi][R.sup.2], less that needed for
      crop production equal to population, P, times agricultural land needs
      per person, A).   Thus, <see equation below>

bsex249.gif (108x600)

      The average collection distance will be approximately the fraction of
      R that circumscribes half the area of radius R, or 0.707R.  More
      detailed correlations can be developed as desired, including variable
      biomass productivities, inefficiencies in biomass collection, and
      other factors.
115.   Prasad, K. Krishna. Woodburning Stoves: Their Technology, Economics,
      and Deployment, Geneva: International Labor Organization, 1983.
116.   Eckholm, Eric; Foley, Gerald; Barnard, Geoffrey; and Timberlake,
      Lloyd. Fuelypod: The Energy Crisis That Won't Go Away, Earthscan,
      1984, 105. pp.
117.   Aggarwal, G.C. and N.T. Singh,   "Energy and Economic Returns From
      Cattle Dung as Manure and Fuel"  Energy, Vol. 9, No. 1, pp.  87-90,
118.   Vidyarthi, Varun. "Energy and the Poor In An Indian Village" World
      Development Vol. 12, No. 8, pp. 821-836, 1984.
119.   Strasfogel, Sylvain.   "Au-dela du choix economique, le choix ecologique:
      le gaz butane au Senegal", Informations No. 3, November-December
      1982, pp. 4-7, Association Bois de Feu.
120.   Baldwin, Sam.   "New Directions in Woodstoves Development" VITA News,
      VITA, January 1984.
121.   Strasfogel, Sylvain and Gilles Dechambre.  Programme Regional Foyers
      Ameliores - - Le Niger, Aix-En-Provence, France: CILLS/Association Bois
      de Feu, July 1984.
122.   World Bank.  World Development Report, 1984, New York: Oxford University
      Press, 1984.
123.   Keita, J.D. "Plantations in the Sahel," UNASYLVA,  V.33,   N.134, pp.
124.   National Academy of Sciences.   Firewood Crops, Volume 1, 1980, 237 pp.,
      Volume 2, 1983, 87 pp.
125.   Noronha, Raymond.   "Why Is It So Difficult to Grow Fuelwood?",
      UNASYLVA, Volume 33, No. 131, 1981, pp. 4-12.
126.   World Bank. Forestry, Sector Policy Paper, February 1978.
127.   Pant, M.M. "Social Forestry in India", UNASYLVA, Volume 31, No. 125,
      1979, pp. 19-24.
128.   Poulsen, Gunnar. "The Non-Wood Products of African Forests", UNASYLVA.
129.   Salem, B. Ben and Van Nao, Tran. "Fuelwood Production in Traditional
      Farming Systems", UNASYLVA, Volume 33, No. 131, 1981, pp. 13-18.
130.   Digernes, T.H.   Wood for Fuels: Energy Crisis Implying Desertification:
      The Case of Bara, the Sudan,   thesis for the Geografisk
      Institutt, Bergen, Norway, 1977, 128 pp.
131.   Hyman, Eric L., "Loan Financing of Smallholder Treefarming in the
      Provinces of Ilocos Norte and Ilocos Sur, The Philippines," Agro-forestry
      Systems Vol. 1, 1983. pp. 225-243.
132.   Hyman, Eric L., "Pulpwood Treefarming in The Philippines from the
      Viewpoint of the Smallholder: An Ex Post Evaluation of the PICOP
      Project," Agricultural Administration. Vol. 14, 1983. pp. 23-49.
133.   Moreira, J.R. and J. Goldemberg, "Alcohols - - Its Use, Energy and
      Economics - - A Brazilian Outlook", Resource Management and Optimization
      Vol. 1 No. 3, pp. 213-279, 1981.
134.   Geller, H.S., "Ethanol Fuel From Sugar Cane In Brazil", Annual Review
      of Energy, Vol. 10, pp. 135-164, 1985.
135.   Rivera, S. , "Honduras, Country Study", Global Workshop on End-Use
      Oriented Energy Strategies, Sao Paulo, Brazil, June 1984.
136.   Williams, Robert H., A Low Energy Future For The United States, Center
      For Energy and Environmental Studies,  Report No.   186,  Princeton
      University, Princeton, New Jersey, U.S.A. February 1985.
137.   Gupta, R.K., Efficiency of Utilization of Domestic Fuels, Indian Oil
      Corporation, R & D Centre, Faridabad; International Seminar on Energy,
      Administrative Staff College of India, Hyderabad, January 1979.
138.   Shaikh, Asif M. and G. Edward Karch, "Will Wood Work? The Future of
      Wood Energy In The West African Sahel", Special Document, 9th World
      Forestry Conference, Mexico City, July 1985.
139.   Moundlic, Jean; "Can Fermentation Alcohol be Substituted For Wood As A
      Cooking Fuel?", Workshop on Fermentation Alcohol For Use As Fuel and
      Chemical Feedstock In Developing Countries, Vienna Austria, 26-30
      March, 1979.   U.N. I.D./WG.293/28, 22 February 1979.
140.   Bradley, P.N., N. Chavangi, and A. Van Gelder, "Development Research
      and Energy Planning In Kenya", AMBIO, V. XIV, N. 4-5, pp.228-236, 1985
141.   Baldwin, S.; "Domestic Energy For Developing Countries: Options and
      Opportunities", forthcoming.   Reference I-1.
                        Global Power Supply and Demand
              Global   photosynthesis              1X[10.sup.5] GW(*)
              Global   forest biomass growth       5X[10.sup.4]
              Global   energy consumption          1X[10.sup.4]
              Global   vood consumption            lX[10.sup.3]
              Global   fuelwood consumption        5x[10.sup.2]
              (*) 1 GW   = 1 billion watts of power.
              Reference (10)
More recent estimates of wood fuel consumption range from roughly 7% (6)
to 14% (20) of global energy consumption.  Thus, the fuelwood consumption
values presented in the Table above indicate only the magnitude of use.
                             Forest Growing Stock
                        Africa                    92
                        America, North           179
                        America, Central          50
                        America, South           428
                        Asia                      17
                        Europe                    27
                        USSR                     310
                        Reference (7)
                 Reducing Factors for Converting Stacked Wood
                             To Solid Wood Content
  Type                     Class                              Factor
Softwood     large, round, and straight                        0.80
            medium split billets, smooth and straight        0.75
            medium split billets, crooked                     0.70
            small, round firewood                             0.70
Hardwood     large split billets, smooth and straight         0.70
            large split billets, crooked                      0.65
            small round firewood, smooth and straight        0.65
            small round firewood, crooked                     0.55
     twigs  small  round   firewood, crooked                0.30-0.45
Brushwood    small round   firewood, crooked                0.15-0.20
Reference (13)
                 Production of Crop Residues from Cereal Crops
                            in Developing Countries
           Crop                Yield               Residue Production
                       Metric tons/ha-year        Metric tons/ha-year
                          Range    Average             Range   Average
           Rice           0.7-5.7    2.5           1.4-11.4     5.0
           Wheat          0.6-3.6    1.5            1.1-6.1      2.6
           Maize          0.5-3.7    1.7            1.3-9.3      4.3
           Sorghum        0.3-3.2    1.0            0.8-8.0     2.5
           Barley         0.4-3.1    2.0            0.7-5.4      3.5
           Millet         0.5-3.7    0.6            1.0-7.4      1.2
           Reference (20)
                   Manure Production by Donesticated Animals
                 Animal                          Metric tons/head-year
                 Cattle, buffalo, camels                1.00
                 Horses, donkeys                        0.75
                 Pigs                                   0.3
                 Sheep, goats                           0.15
                 Reference (20)
                        Fuel Use in the Village Sector
                                 Percent of
                                 Total from     W/cap
        Country          Village           Biomass       Total         Author
        Bangladesh       Dhanishwar          100          190       Bangladesh, 1978
                        Ulipur               100           238      Briscoe, 1979
        Bolivia          Altiplano                         352      World Bank, 1983
        Botswana         Matsheng                          523      White, 1979
        Burkina Faso     Ranga                             285       Ernst, 1978
        Cameroon         Ngaoundere                       571       Vennetier, 1979
        Chad             N'Djamena                        1395      Bertrand, 1977
        China            Peipan               87          666       Makhijani, 1975
        Congo            Brazzaville                       428      Gilbert, 1978
        Ethiopia         Addis Ababa                       333      FRIDA, 1980
        India            Pura                 96          285       Reddy, 1979
                        Injambakkam           95           159      Murugapa ..., 1981
                        Pemmadapalle(*)       97           112      Bowonder, 1985
                        Khurpatal                         233       Singh et. al., 1979
                        Bhalutia                          275       Singh et. al., 1979
                        Ungra                 95           285      Ravindranath, 1980
        Iran             Semnan                            571      Vojdani, 1978
        Kenya            Machakos                          476      Mutula, 1979
        Lesotho         Malefiloane          98           260       Best, 1979
        Mali             Deguela                           241      Caude, 1977
                        Sanzana                           349       Caude, 1977
                        Bamako                            713       Bertram, 1977
        Mauritania       Nouakchott                        713      FRIDA, 1980
        Mexico           Arango               33          412       Makhijani, 1975
        Nepal            Hill                 97           349      Hughart, 1979
        Niger            Niamey                            400      Pare, 1979
                        Niamey                            136       Boureima, 1982
        Nigeria          Batawagara           99          476       Makhijani, 1975
                        Kano                              571       Grut, 1973
                        Ibadan                            381       Ay, 1978
        Rwanda           Nyarugenge(**)       81         1617       Gatera, 1978
        Senegal         Dakar(**)                        698      Tall, 1974
        Sierra Leone     Waterloo                          571      Cline-Cole, 1979
        Sri Lanka        Anuradhapura                      168      Bialy, 1979
        Sudan            Khartoum(**)                      856       FRIDA, 1980
        Tanzania         Bundilya                          680      Nkonoki, 1984
        Togo             Lome                              174       Grut, 1971
        (*) Domestic cooking only.   (**) Charcoal.
        References primarily compiled and more completely documented by (20).
        Additional data from references (21,22,61,147B,147C)
147B. B. Bowonder, N. Prakash Rao, B. Dasgupta, S.S.R. Prasad, "Energy Use
      In Eight Rural Communities In India", World Development, V.13, N.12,
      pp.1263-1286, 1985.
147C. World Bank, "Bolivia: Issues and Options In The Energy Sector",
      UNDP/WB Energy Sector Assessment Program, Rpt. 4213-BO, April 1983.
           Power Consumption for Selected Developing Countries, 1981
                 Total     Fraction                     Total      Fraction
Country            GW         from        Country         GW         from
                          Biomass                                 Biomass
Angola             3.4        72%       Belize             0.2        57
Benin              1.3        89        Costa Rica        1.8        33
Burkina Faso      2.2        91        Cuba              19.         35
Burundi            0.3        76        Dominican
Cameroon           6.1        40          Republic        3.3        29
Central African                       El Salvador       2.1        53
  Republic         0.9       90         Guatemala          5.4       71
Chad               2.4        96        Haiti              1.9       83
Ethiopia           8.2        90        Honduras          2.3        64
Gabon              1.3        31        Mexico           121.          3
Ghana              3.6        63        Nicaragua         1.7        52
Guinea             1.4        72         Panama             2.4       29
Guinea-Bissau      0.2       77        Bolivia            3.6        44
Ivory Coast       3.4        65         Brazil          153.        44
Kenya             10.8        81        Colombia         33.         41
Liberia            2.0        65        Ecuador           6.8        26
Madagascar         2.4        76        Paraguay          1.8        73
Mali               1.1        84        Peru              12.         12
Mauritania         0.5        42        Uruguay           3.0       20
Mauritius          0.8        65
Mozambique         4.5        80        Afghanistan      3.0         72
Niger              1.1        79        Bangladesh       7.1         45
Nigeria           46.         64        Burma             9.7         78
Rwanda             1.7        95        China(*)       580.           9
Senegal            1.8        42        Kampuchea        1.4         99
Sierra Leone      2.7        89        India           196.          36
Somalia            0.7        38        Indonesia       77.         56
Sudan             12.         87        Republic of
Tanzania          12.         93          Korea         72.          29
Togo               0.5        34        Nepal             4.3         96
Uganda             1.7        83        Pakistan        24.         27
Zaire              4.5        58        Philippines     26.          38
Zambia             3.7        45        Sri Lanka        3.8         60
Zimbabwe           6.4        40        Thailand        27.          44
Reference (65);  (*) Reference (20) estimates the fraction as 29%.
149.    More precisely, in a test on eleven fast growing species the volumetric
gravity of the charcoal, Y, was found to be typically related to
the specific gravity of the air dry wood, X, by the equation (14)
    Y = 0.575X - 0.069
The volumetric gravity is the weight of a volume of material, including
pores within, compared to the weight of an equivalent volume of water.
This is to be contrasted with specific gravity where pores are often not
counted as part of the volume, only the material itself is.
150.   This analysis has been previously published in: T. S. Wood and S.
      Baldwin, "Fuelwood and Charcoal Use in Developing Countries," Annual
      Review of Energy, V.10 (1985), pp.407-429.
151.   Barnard, Geoffrey and Lars Kristoferson, Agricultural Residues As Fuel
      In The Third World, Earthscan, International Institute for Environment
      and Development, Energy Information Program, Technical Report No.4,
      London, 1985.
152.   Foley, Gerald, "Wood Fuel and Conventional Fuel Demands In The
      Developing World", AMBIO, V.14, N.4-5, pp.253-258, 1985.
153.   Baldwin, Sam, Howard Geller, Gautam Dutt, and N.H. Ravindranath,
      "Improved Woodburning Cookstoves: Signs of Success", AMBIO, V.14, N.4-5,
      pp.280-287, 1985.
154.   Energy Issues and Options In Thirty Developing Countries, UNDP World
      Bank Energy Sector Assessment Program, Report No. 5230, August 1984.
155.   Foley, Gerald and Geoffrey Barnard, Farm and Community Forestry,
      Earthscan, International Institute for Environment and Development,
      Energy Information Program, Technical Report No.3, London, 1984.
156.   Foley, Gerald, Charcoal Making In Developing Countries, Earthscan,
      International Institute for Environment and Development, Energy
      Information Programs, Technical Report No.5, London, January 1986
157.   Notes to Table 19.
  (a) Reference 48;
  (b) Reference 134;
  (c) Reference 133. Note that 11.8 [m.sup.3]/ha-yr is a high yield compared to
      those frequently observed, but is only a small fraction of what should
      be achievable.   An annual increment of 11.8 [m.sup.3]/ha-yr at a specific
      gravity of 0.8 is equivalent to an energy capture rate of 0.5 W/[m.sup.2]; or
      with an average insolation of 250 W/[m.sup.2], an energy conversion rate of
      just 0.2%.   The reason, in part for such low yields is the lack of
      inputs such as properly applied fertilizers and irrigation, or simply
      poor species choice for the local conditions.
Approximate yields for the West African Sahel (1981-1983) are given in
the Table below.
                    Wood Production and Yield In the Sahel
                               Cost to                          Yield
                           Establish(*) $/ha     Rainfall     [m.sup.3] /ha-yr
Commercial Plantations         630-1000            600 mm        1.5-3.0
                                                  800 mm       3.0-5.0
                                                 1000 mm       6.0-10.0
Village Woodlots                150-388                         1.5-3.0
Managed Natural Forest           80-150                         0.5-1.5
(*) Note that recurrent costs are  not included here but will average
    perhaps $100/ha-yr for commercial plantations and less for the other
Reference (138)
  (d) Reference 24
  (e) Reference 136
  (f) Reference 137
  (g) Shukla, K.C. and J.R. Hurley, Development of An Efficient Low [NO.sub.x]
      Domestic Gas Range Cook Top, Gas Research Institute, Chicago, Illinois,
      1983. Note that this advanced gas stove has efficiencies of 70%
      but is not yet commercially available.
      See also W.F. Sulilatu and C.E. Krist-Spit, "The Tamilnadu Metal
      Stove" in From Design to Cooking, Reference III-35.
  (h) Reference 139
  (i) See Chapter VI, Charcoal Stoves, and References therein.
  (j) See Chapter V, Table V-1.
  (k) See (g) and (j), also see Reference III-18.  Note that side by side
      tests in (g) showed wood stoves with thermal efficiencies of 49-54%
      and a natural gas burner in the same stove having an efficiency of
      54%. However, control of the natural gas burner will be somewhat
      better than of a wood fire.
  (1) Delivered Energy is that which is absorbed by the pot in order to cook
      the food.
1.   Geller, Howard S. and Gautam S. Dutt. "Measuring Cooking Fuel Economy"
    in Wood Fuel Surveys, pp. 147-172. See ref II-19.
2.   See Reference II-80.
3.   Geller, Howard S. "Fuel Efficiency and Performance of Traditional and
    Innovative Cookstoves", in Wood Heat For Cooking, Eds. K. Krishna
    Prasad and P. Verhaart, Bangalore:   Indian Academy of Sciences, pp.
    Geller, Howard S. "Cooking in the Ungra Area: Fuel Efficiency, Energy
    Losses, and Opportunities for Reducing Firewood Consumption", Biomass,
    V. 2, 1982, pp. 83-101.
4.   Dunn, P.D.; Samootsakorn, P.; and Joyce, N. "The Performance of Thai
    Charcoal Stoves". in Wood Heat for Cooking  (Ibid.), pp. 107-118. See
    also Dunn, P.D.; Samootsakorn, P.; and Joyce, N. "The Traditional Thai
    Cooker" in Energy from Bionamass, 2nd International Conference on
    Biomass, Eds. A. Strub, P. Chartier, and G. Schleser, London: Applied
    Science Publishers, pp. 748-752.
5.   Prasad, K. Krishna and Ernst Sangen (Eds.) Technical Aspects Of
    Woodburning Cookstoves, Woodburning Stove Group, Eindhoven University
    of Technology; and Division of Technology for Society, Apeldoorn, The
    Netherlands. September 1983.
6.   Calculated from controlled cooking test data in Yameogo, Bussmann,
    Simonis, and Baldwin, reference II-80.
7.   The heat gain of the pot on an open fire by radiant transfer can be
    directly extimated by examining the performance of sultipot massive
    stoves with excessive drafts. In such stoves, radiant transfer does
    not change but convective heat transfer is greatly reduced as the
    flames and hot gases are pulled out the rear of the stove with little
    or no contact with the first pot. Typical PHU's for the first pot in
    such stoves are 12 percent (Kaya 2 in Yaneogo, Bussmann, Simonis and
    Baldwin, Reference II-80). Alternatively, the radiant transfer can be
    directly estimated using the Stefan-Boltzmann law and view factor
    between the firebed and pot as discussed in Appendix C. Model
    calculations elsewhere (Bussmann, P.J.T.; Visser, P.; and Prasad, K.
    Krishna, "Open Fires: Experiments and Theory." pp. 155-188 in Wood
    Heat for Cooking (Ibid) ref 3) estimate the radiant heat transfer
    alone to account for about 10 PHU percentage points of the thermal
    efficiency of a pot on an open fire.
    The value 17% efficiancy for an open fire is chosen here to correspond
    to test results in the field, ref 6. This value can be higher if well
    protected from the wind, or lower if exposed to the wind.
8.   Saith, et al. References II-107 to II-112.
9.   Eckert, E.R.G, and Drake, Robert M., Jr.  Analysis of Heat and Mass
    Transfer, New York: McGraw-Hill, 1972, 806 pp.
10. Goller, H.S. and G.S. Dutt, "Measuring Cooking Fuel Economy", in Wood
    Fuel Surveys, See Ref. II-19.
11. Geller, Howard S.; Leteemane, Bai; Powers, Theresa A.M.; and Sentle,
    James.  Prototype Metal and Mud Wood-Burning Cookstoves for Botswana,
    Burlington, Vermont: Associates in Rural Development, May 1983.
12. Ashworth, John H. The Technology Adaptation Process:  Steps Taken to
    Transform the BRET Metal Stove Prototypes into Finished Commercial
    Models, Burlington, Vermont:   Associates in Rural Development, June
13. Brunet, Eric personal communication.
14. Sanogo, Cheick; Sidibe, Yaya; Strasfogel, Sylvain; and Baldwin, Sam.
    Results, Technical Notes and Proposals for the LES Improved Stove
    Program.  LES/CILSS/Association Bois de Feu/VITA, October 1983.
    Available from VITA.
15. Lokras, S.S., D.S. Sudhakar Babu, Swati Bhogale, K.S. Jagadish, and R.
    Kumar. Development of an Improved Three Pan Cookstove, Bangalore,
    India: ASTRA, Indian Institute of Science, 45 pp.
16. Shailaja, R. and N.H. Ravindranath.  Diffusion of an Efficient Wood
    Stove for Cooking in Rural Areas, Bangalors, India: ASTRA Indian
    Institute of Science, 22 pp.
17. Ravindranath, N.H. and R. Shailaja. A Field Evaluation of a Fuel-Efficient,
    Smokeless Woodstove; ASTRA OLE, Bangalore, India: ASTRA,
    Indian Institute of Science, 25 pp.
18. Mukunda, H.S. and U. Shrinivasa, Single Pan Wood Stoves of High
    Efficiency, ASTRA, Indian Institute of Science Bangalore, India 560
    012, July 1985.
19. Mukunda, H.S., U. Shrinivasa, S. Dasappa, and S.B. Sunil Lumar, Single
    Pan Wood Stoves of High Efficiency, Part II, ASTRA, December, 1985.
20. Yameogo, Georges; Ouedraogo, Issoufou; and Baldwin, Sam. Lab Tests of
    Fired Clay Stoves, the Economics of Improved Steady and State
    Heat Loss from Masive Stoves, CILSS/VITA, October 1982. Available
    from VITA.
21. Prasad, K. Krishna (Ed.). Some Studies on Open Fires, Shielded Fires,
    and Heavy Stoves.   Apeldoorn, The Netherlands:   Woodburning Stove
    Group, Department of Applied Physics and Mechanical Engineering,
    Eindhoven University of Technology and Division of Technology for
    Society, TNO, October 1981, 161 pp.
22. Baldwin, Sam. See Ref. II-120.
23. Shukla, K. C.  and J.R. Hurley, Development of An Efficient Low [NO.sub.x]
    Domestic Gas Range Cook Top, Gas Research Institute, Chicago, Illinois,
24. Christiaens,  M. and G. De Lapeleire, "Observations on Combustion and
    Heat Transfer" in Technical Aspects of Woodburning Cookstoves. See (5)
25. Emmons, Howard W. and Arvind Atreya. "The Science of Wood Combustion"
    in Wood Heat for Cooking, Prasad, Verhaart, Eds., Indian Academy of
    Sciences, 1983, pp. 5-14.
26. Harker, A.P., A. Sandels, J. Burley. "Calorific Values for Wood and
    Bark and a Bibliography for Fuelwood," London: Tropical Products
    Institute, August 1982.
27. Bussmann, P.J.T.,  P. Visser and K. Krishna Prasad. "Open Fires:
    Experiments and Theory" in Wood Heat for Cooking. See Ref. 3.
28. Sangen, E. "A Survey of Test Results in Wood Stoves" in Technical
    Aspects of Woodburning Cookstoves, Eindhoven, 1983. See ref 5.
29. Personal communication with Kirk Smith, 1984.
30. To calculate the calorific value of the wet biomass for the different
    moisture content definitions, tables as sketched below can be developed
    where the energy to evaporate water from 25[degrees]C is 2575 kJ/kg.
                                           Wood Moisture Content
                                               Measured on a
                                           Dry Basis     Wet Basis
  Moisture Content                             30%              30%
  Equivalent Dry Wood per kg of Biomass        1.0 kg          0.7 kg
  Water Content per kg of Biomass              0.3 kg          0.3 kg
  Total, equivalent dry wood plus water        1.3 kg          1.0 kg
  Gross Energy per kg of Biomass               18 MJ           12.6 MJ
  Less Energy To Evaporate Water
     per kg Dry Biomass                        17.227 kJ       11.827 kJ
  Net Energy per kg Wet Biomass                13.252 MJ       11.827 MJ
31. Shelton, Jay.  The Woodburners Encyclopedia, Waitsfield, Vermont:
    Vermont Crossroads Press, Ninth printing, 1979, 126 pp.
32. Stevens, W.C. and G.H. Pratt, Kiln Operators Handbook, Department of
    Scientific and Industrial Research, Her Majesty's Stationery Office,
    London, 1952, 138 pp.
33. Prasad, K. Krishna; Sangen, E.; Visser, P. "Woodburning Cookstoves",
    In Advances Tn Heat Transfer, Eds., James P. Hartnett and Thomas F.
    Irvine, Jr. Volume 17, pp. 159-317, Academic Press, N.Y. 1985.
34. Ouedraogo, Issoufou; Yameogo, Georges; and Baldwin, Sam. Lab Tests of
    Fired Clay and Metal One-Pot Chimneyless Stoves, IVE/CIIAS/VITA,
    February 1983. Available from VITA.
35. Krist-Spit, C.E., "The Combustion Quality of the Charcoal Stoves
    Sakkanal and Malgache" in From Design To Cooking, eds. C.E. Krist-Spit
    and D.J. vander Headen, Woodburning Stove Group Eindhoven University
    of Technology; and Division of Technology of Society, Apeldoorn, The
    Netherlands. January, 1985.
36. Wood, Timothy S., "Laboratory and Field Testing of Improved Stoves In
    Upper Volta", National Academy of Sciences, BOSTID, Washington, DC,
    1981, pp.23
37. De Lepeleire, G. and M. Christiaens. "Heat Transfer and Cooking
    Woodstove Modelling" in Wood Heat for Cooking. Ref. (3).
38. Waclaw Micuta, "Modern Stoves For All", Intermediate Technology
    Publications, London, and the Bellerive Foundation, 1985.
    The alternative of extinguishing the fire and placing a highly
    insulating jacket over the stove and pot together is a second possibility.
    In this case, the remaining coals would help maintain the
    temperature. However, even with a tightly fitting lid, there may be a
    problem due to excessive smoke and carbon monoxide entering the pot
    and contaminating the food. This needs to be tested.
39. The calculation was done using the conductive heat loss program for
    double walls (Appendix A), setting the initial temperature distribution
    of the massive outer wall to that for a single wall stove
    running for 60 minutes, and setting the parameters and temperatures of
    the inner wall to that for cold water.
40. Zhu, Brambley, and Morgan, Reference II-57.
41. Foley, Gerald, and Geoffrey Barnard, Biomass Gasification In Developing
    Countries, Earthscan, International Institute For Environment
    and Development, Energy Information Programme, Technical Report No.1,
    London, 1983.
42. As a more quantitative example of the importance of control, a simple
    illustrative calculation of energy use by two hypothetical stoves and
    pots is given below. Capabilities of these stoves and pots are given
    in Table A. Given these parameters, the time to reach a boil is given
    by <see equation below>

bsex260.gif (393x600)

For pot loss rates of about 700 W/[m.sup.2] (Reference 43) and an exposed pot
area of about 0.14 [m.sup.2], total pot losses are then 100 W/[m.sup.2]. This gives
     t = 8x[10.sup.5]/(800-100) = 1140 seconds
The total amount of energy used to bring the pot to a boil is then
     E = (1140 s)x(2000 W) = 2.28 MJ
The power level for simmering is determined by the minimum level
necessary to make up for the heat losses from the pot.  Lids are
assumed to be used, so steam losses are not included.  Such steam
                                    TABLE A
                    Hypothetical Stove and Pot Performance
                                                      Stove A       Stove B
                     High Power                         2 kW           4 kW
                     Thermal Efficiency                 40%            40%
                     Low Power                          0.5 kW         0.2 kW
                     Thermal Efficiency                 40%            30%
                                                       Pot 1          Pot 2
                     Heat Loss                          100 W         25 W
                                    TABLE B
                          A Hypothetical Cooking Task
          Stove/Pot                          A/1     A/2      B/1     B/2
          Time to Boil (minutes)             19       17       9       8
          Energy Used (MJ)                   2.29     2.06     2.13   2.03
          Simmering Power (kW)               0.5      0.5      0.3     0.2
          Excess Energy to Steam(*)(kW)      0.1     0.175    0.0     0.035
          Energy Used to Simmer (MJ)         1.8      1.8      1.08    0.72
          Total Energy Used (MJ)             4.09     3.86     3.21    2.75
          Actual Energy Needed(**)(MJ)       1.16    0.89     1.16    0.89
          Overall Cooking Efficiency         28%      23%      36%     32%
         (*) This is the difference between the energy input to the pot at the
         firepower closest to the minimum needed and the heat losses from the
         pot. Thus (0.5 kW)(0.4 efficiency) - (100 W pot loss) = (100 W to steam)
         (**) The actual energy needed for the cooking task is the energy
         required to bring the 10 kgs. of food to a boil and maintain that
         temperature for one hour.
losses are due to excessive fire powers.  The amount of energy then
used during one hour of simmering is the fire power times 3600
Total energy consumption for bringing the food to a boil and then
simmering it for one hour can then be calculated and the result
compared to the ideal case as done in Table B.
Several features in Table B stand out. First, although Stove A had a
higher efficiency than Stove B during the simmering phase, its overall
cooking efficiency was lower because its firepower could not be
reduced below 0.5 kW.  Second, insulation on the pot strongly influenced
the amount of energy used.  Third, the overall cooking efficiency
was not a good indicator of total energy consumption by the
stove.   Fourth, the ability to reach high power levels saved time,
typically about 10 minutes, and also saved energy due to a shorter
period that the pot could lose heat to the environment.
43. G. De Lepeleire and M. Christaens, "Heat Transfer and Cooking Woodstove
    Modelling", in Wood Heat For Cooking, eds. K. Krishna Prasad and
    P. Verhaart, Indian Academy of Sciences, Bangalore 560 080, 1983.
1.   Yameogo, Bussmann, Simonis, Baldwin, Ref. II-80.
2.   Improved Biomass Cooking Stove For Household Use, Forest Products
    Research Division, Royal Forest Department, Ministry of Agriculture
    and Cooperation; and National Energy Administration, Ministry of
    Science, Technology, and Energy, Royal Thai Government; and USAID,
3.   Selker, John S., Laurie F. Childers, and Peter J. Young. Development
    of Stoves For Use In Urban Areas of Sri Lanka: Interim Technical
    Report, ITDG, London, November, 1985
1.   Testing the Efficiency of Woodburning Cookstoves: Provisional International Standards.
    Arlington, Virginia: VITA, December 1982, 76 pp.
2.   Testing the Efficiency of Woodburning Cooktoves: Provisional International
    Standards. Arlington, Virginia: VITA, Revised, May 1985.
    There are several important changes in these updated procedures
    compared to reference (1). First, the 15 minute extension of the high
    power phase vas eliminated because it did not improve the resolution
    of the test, only its duration. Second, lids are not used. Lids proved
    to be cumbersome in practice and additionally did not reduce the
    scatter in the data but rather increased it.
    Additionally, in this book the index for evaluating the stoves'
    performance in the lab is changed from (wood used)/water evaporated to
    PHU or SC because these are better indicators of a stove's performance
    and because these indices better correspond to those for controlled
    cooking or field tests.
    It is important to note the interaction between the use of a lid on
    the pot and the index used to evaluate the stove's performance.  If a
    lid is used then the amount of water evaporated and escaping is
    somewhat dependent on the tightness of the lid's fit to the pot, and
    extremely dependent on the firepower.   If the firepower is low so that
    the temperature is maintained a few degrees below boiling, effectively
    no water vapor will escape.   If the firepower is high enough so that
    the water boils, the escaping steam will push the lid open and escape.
    (The partial pressure of the water vapor is greater than atmospheric
    pressure.) In this case there will be a large amount of water evaporated
    from the pot.   The index, wood/water evaporated, is then very
    sensitive to how well the firepower is controlled.  The PHU is
    similarly sensitive due to the measure of the heat absorbed by the pot
    being given in part by the water evaporated.  Heat is still absorbed,
    but is not measured as the water vapor condenses on the lid and falls
    back in.  The heat is instead lost by convection from the pot lid.
    Finally, for specific consumption defined as wood/(initial water), the
    amount of evaporation has no effect.   For specific consumption defined
    as (wood used)/(final water) or (wood used)/(water "cooked"), evaporation
    has an effect but a less significant one.
    When no lid is used, then the index (wood used)/(water evaporated) is
    still sensitive to the firepower while PHU and SC are relatively
    insensitive to it.
    By not using a lid, evaporation rates are higher and the stove must be
    run at a somewhat higher power to maintain the temperature than is the
    case with a lid.   Thus, when not using a lid the low power performance
    of the stove is not really being evaluated during the second phase.
    In this context, it is important to note the difference in control
    between wood stoves and charcoal stoves.
    Tests conducted by the author in collaboration with IBE, Burkina Faso
    unpublished) showed a large variation between tests in firepower and
    evaporation rates when operating the stove at a very low power level
    (with lids).   The reason for this was that without a consistent size
    of wood and precise fire feeding timetable, maintaining a very low
    power proved to be more a function of the tester's patience and
    conscientiousness and of the wood size and moisture content than of
    the stove design.   In daily use in the field, users certainly do not
    control woodstoves to this degree to optimize their low power phase
    fuel consumption.
    In contrast, the low power capability of a charcoal stove is a
    function of the air tightness of its door and additionally is determined
    by the formation of the ash layer on the surface of the burning
    charcoal, slowing its combustion (Appendix D).  Very low power tests
    of charcoal stoves (by using a lid on the pot), then, do directly test
    the stove itself (its airtightness) and thus &re recommended (Chapter
 3. The specific consumption is defined as (wood used)/(water remaining at
    end of test) rather than (wood used)/(water at start of test) because
    this index corresponds to the form used for the controlled cooking
    tests and to the concept of (wood used)/(water "cooked").  Although
    this index is sensitive to excess evaporation (see ref. 2) it is still
    sufficiently robust to be a useful indicator.
    In cases where there is a large daily or seasonal variation in ambient
    temperature it may be desirable to normalize the specific consumption
    according to the initial water temperature.
 4. Particularly useful is using a factorial design for the experiment and
    then performing an analysis of variance and a multiple regression on
    the data.  This however is beyond the scope of the section on statistics
    and the reader is referred to a basic text on the subject such as
    Reference (16) below.
 5. Yameogo, Bussmann, Simonis, and Baldwin.  Reference II-80.
 6. Strasfogel, Deschambre.   Reference II-121.
 7. Yameogo, Ouedraogo, Baldwin.   Reference III-20.
 8. Ouedraogo, Yameogo, Baldwin.   Reference III-34.
 9. Sanogo, Sidibe, Strasfogel, Baldwin.   Reference III-14.
10. Dutt, Gautam, M. Hassan.  "Efficient Cookstove Development in Somalia:
    A Progress Report".   Arlington, VA:   VITA, July 1984.
11. Sepp, Cornelia.  "Production and Dissemination of Improved Stoves -- A
    Case Study", Ouagadougou, Burkina Faso:  German Forestry Mission,
    September 1983, pp.17
12. Sepp, C.  "Un Foyer Metallique a un trou pour la Haute-Volta", Informations,
    Marseille, France:   Association Bois de Feu, No. 5, April-May-June
    1983, pp. 20-21.
13. Baldwin, reference II-120.
14. UNFAO.  Wood Fuel Surveys. ref II-19.
15. National Academy of Sciences.  Proceedings of the International
    Workshop on Energy Survey Methodologies for Developing Countries.
    BOSTID, National Academy Press, 1980.
16. Hyman, E.L., "How to Conduct A Rural Energy Survey In a Developing
    Country", Renewable Sources of Energy, Vol. VI, No.2, pp. 137-149
17. Smale,  Melinda;   Savoie,  Michelle;  Shirwa, Zahra Cabdi; and Axmed,
    Mohamed Cali.   Wood Fuels Consumption and Cooking Practices in Selected
    Sites of Lower Shabeelle, Banaadir, and Gedo Regions of Somalia.
    Arlington, Virginia:   VITA, July 1984, 151 pp.
18. Ki Zerbo, J.  Improved Wood Stoves:   Users' Needs and Expectations in
    Upper Volta.   Arlington, Virginia:  VITA, 1980.
19. Wood, Timothy, "Laboratory and Field Testing of Improved Stoves In
    Upper Volta" National Academy of Sciences (BOSTID), Washington, D.C.,
20. Dutt, Gautam; Field Evaluation of Woodstoves, VITA, Arlington,
    Virginia:  1981.
21. Hyman, Eric L., "Analysis of The Wood Fuels Market:   A Survey of
    Fuelwood Sellers and Charcoal Makers in The Province of Ilocos Norte,
    Philippines", Biomass V.3, 167-197.   (1983).
22. Cited in Michael R. Brambley and Thomas Medynski, Evaluation of
    Biomass Briquettes As Cookstove Fuel:   An Experimental Study, Department
    of Engineering and Policy, Center for Development Technology,
    Washington University, St. Louis, Missouri, July 1984.
    ASTM Standard D2395-69, Standard Method of Test For Specific Gravity
    of Wood and Wood Base Materials, American Society For Testing and
    Materials, Philadelphia, Pennsylvania, 1977.
    ASTM Standard D2016-74, Standard Method of Test For Moisture Content
    of Wood, 1974.
    ASTM Standard D1102-56, Standard Method of Test For Ash In Wood, 1978.
    ASTM Standard D2015, Standard Method of Test For Gross Calorific Value
    of Solid Fuel By The Adiabatic Bomb Calorimeter, 1972.
    ASTM Standard D3175-77, Standard Test For Volatile Matter In The
    Analysis Sample of Coal and Coke, 1977.
    ASTM Standard D3172-73, Standard Method for Proximate Analysis of Coal
    and Coke, 1979.
23. Although the natural scale for water to be normalized to is 100[degrees]C, it
    is convenient to divide instead by 75[degrees]C (i.e. normalize it to 25[degrees]C) so
    that the results don't differ too significantly from the unnormalized
24.   Examples of total village energy use studies include:  Nkonoki and
    Sorensen, reference II-21; Singh, Pandey and Tiwari, reference II-22;
    Ravindranath, et. al., reference II-50; Reddy, reference II-51; Down,
    reference II-58; Bowonder, et. al., reference II-147.  In particular,
    the interested reader should review Ravindranath et. al. and Reddy.
25. Agarwal, Bina, "Diffusion of Rural Innovations:  Some Analytical Issues
    and the Case of Wood-Burning Stoves", World Development, V.11, N.4,
    pp.359-376, 1983.
 1. Kinyanjui, M.   "The Kenya Cookstove Project, 1981-1983", UNFAO, October
    1983, 37 pp.
 2. M. Kinyanjui, "The Kenya Charcoal Stoves Program:  Interim Report",
    Energy/Development International, USAID, Washington, D.C. June 1984.
 3. Eric L. Hyman, "The Economics of Fuel-Efficient Household Charcoal
    Stoves In Kenya", Appropriate Technology International, Washington,
    D.C. 1985, to be published.
    Eric L. Hyman, "The Strategy of Decentralized Production and Distribution
    of Improved Charcoal Stoves In Kenya", Appropriate Technology
    International Washington, D.C., 1985, To be published.
    Eric L. Hyman, "The Experience With Improved Charcoal and Wood Stoves
    for Households and Institutions In Kenya", ATI, Washington, D.C.,
    December 1985.
 4. Simon Burne, "Charcoal Stove Developments In Kenya:  The Present and
    The Future", ITDG, Rugby, U.K., Aug. 1985.
 5. Joseph, Stephen; "Advisory Visit To The Stoves Project of MOERD/KENGO,
    Kenya", Intermediate Technology Development Group, London, England,
    September, 1984.
 6. Ministry of Science, Technology, and Energy, Royal Thai Government,
    Reference IV-2.
 7. Dunn, Samootsakorn, Joyce; Reference III-4.
 8. Sherman, Marcus, William Steward, and Banyat Srisom, "An Evaluation of
    Thai Cooking Fuels and Stoves", Renewable Energy Review Journal V.5,
    N.1 pp.60-65, April 1983.
 9. Baldwin, reference II-79.
10. See reference and note V-2.
11. C.E. Krist-Spit, reference III-35.
12. Dutt, Gautam.  "Efficient Cookstove Development in Somalia:  A Progress
    Report." VITA, 1984.
13. See ref V-3.
14. Yameogo, Bussmann, Simonis, Baldwin, reference II-80.
15. Sanogo, Sidibe, Strasfogel, Baldwin, reference III-14.
16. Koenig, Delores.  Laboratoire Energie Solaire, Bamako, Mali, 1983
17. National Academy of Sciences, Reference II-124.
 1. Eckert, E.R.G., and Drake, Robert M., Jr.  Analysis of Heat and Mass
    Transfer.  New York:  McGraw-Hill, 1972.
 2. For a discussion of the specific heat at constant pressure [c.sub.p], the
    specific heat at constant volume [c.sub.v], and their respective uses, see
    reference (1) above, F. Reif, Fundamentals of Statistical and Thermal
    Physics, McGraw-Hill, New York 1965, or other basic thermodynamics
 3. Duffie, John A., Beckman, William A.   Solar Energy Thermal Processes.
    New York:  John Wiley and Sons, 1974.
 4. Ozisik, M. Necati.   Heat Conduction.   New York:  John Wiley and Sons,
 5. Holman, J.P. Heat Transfer.   New York:  McGraw-Hill, 1981.
    [k.sub.e] is derived from the empirical equation <see equation below>

bsex267.gif (135x540)

    where C=0.197, n=0.25, and m=0.111; and the temperatures are fit to
    exponentials as discussed in Appendix C.
 6. These and other numerical data are available from the author by
 1. Arpaci, Vedat S. , and Larsen, Paul S.  Convection Heat Transfer.
    Englewood Cliffs, New Jersey:   Prentice-Hall, Inc., 1984.
 2. Burmeister, Louis C.   Convective Heat Transfer.   New York:  John Wiley
    and Sons, 1983.
 3. Cebeci, Tuncer, and Bradshaw, Peter.   Physical and Computational
    Aspects of Convective Heat Transfer, New York, Springer-Verlag, 1984.
 4. Eckert, ref A-1.
 5. Jaluria, Y.   Natural Convection:  Heat and Mass Transfer, Volume 5 of
    The Science and Applications of Heat and Mass Transfer.  Oxford:
    Pergamon Press, 1980.
 6. Gray, Donald R., and Giorgini, Aldo.   "The Validity of the Boussinesq
    Approximation for Liquids and Gases", Int. J. Heat and Mass Transfer,
    Volume 19, 1976, pp. 545-551.
 7. Holman, J.P.   Heat Transfer.  New York:  McGraw-Hill, 1981.
 8. Kanury, A. Murty.   Introduction to Combustion Phenomena.   New York:
    Gordon and Breach, 1975.
 9. Rohsenow, Warren M., and Hartnett, James P.,  Eds. Handbook of Heat
    Transfer.  New York:  McGraw-Hill, 1973.
10. Shah, R.K., and London, A.L.  "Laminar Flow Forced Convection in Ducts"
    in Advances in Heat Transfer, J.P.  Hartnett and T.F. Irvine, Eds.,
    Supplement 1.   New York:  Academic Press, 1978.
11. Bussmann, P.J.T.;  Visser,   P.;  and  Prasad, K. Krishna.   "Open Fires:
    Experiments and Theory," in Wood Heat for Cooking, K. Krishna Prasad
    and P. Verhaart, Eds.,   Bangalore:  Indian Academy of Sciences, 1983,
    pp. 155-188.   See also Prasad, Sangen, and Visser, Reference III-33.
12. Conolly, R., and Davies, R.M.  "A Study of Convective Heat Transfer
    from Flames", in The International Journal of Heat and Mass Transfer,
    Volume 15, 1972, pp. 2155- 2172.
13. Cox, G., and Chitty, R.  "A Study of the Deterministic Properties of
    Unbounded Fire Plumes", in Combustion and Flame, Volume 39, 1980, pp.
14. Cairnie, L.R. and A.J. Harrison.  "Natural Convection Adjacent to a
    Vertical Isothermal Hot Plate with a High Surface-to-Ambient Temperature
    Difference", in The International Journal of Heat and Mass
    Transfer, 1982, pp. 925-934.
15. Petukhov, B.S. and A.F. Polyakov.  "Buoyancy Effect on Heat Transfer in
    Forced Channel Flows", Seventh International Heat Transfer Conference
    Proceedings, Volume 1, pp. 343-362, Washington:  Hemisphere Publishing
    Corporation, 1982.
16. Lee, Shao-Lin and H.W. Emmons.  "A Study of Natural Convection Above a
    Line Fire", in The Journal of Fluid Mechanics, Volume VII, 1961, pp.
17. Yameogo, Ouedraogo, Baldwin, ref III-20; Ouedraogo, Yameogo, Baldwin,
    ref III-34.
18. Sangen, E.  "A Survey of Test Results in Wood Stoves" in Technical
    Aspects of Woodburning Stoves, Prasad and Sangen, Eds. Eindhoven,
19. Horsley,  M.E.;   Purvis, M.R.I.; and Tariq, A.S.   "Convective Heat
    Transfer from Laminar and Turbulent Premixed Flames", Seventh International
    Heat Transfer Conference, Volume 3, pp. 409-415, Washington,
    D.C.:  Hemisphere Publishing Company, 1982.
20. Faster, more precise algorithms for finding the roots [T.sub.i] than used
    here are widely available.   See, for example, S.D. Conte and Carl de
    Boor, Elementary Numerical Analysis, 2nd Edition, McGraw-Hill, 1972,
    or Eugene Isaacson and Herbert Bishop Keller, Analysis of Numerical
    Methods, John Wiley and Sons, 1966.   Such techniques are not generally
    necessary for the simple case here.
21. Delepeleire, G., and Christiaens, M.  "Heat Transfer and Cooking
    Woodstove Modelling", in Wood Heat for Cooking, K. Krishna Prasad and
    P. Verhaart, Eds., Bangalore:   Indian Academy of Sciences, pp. 189-200.
22. Hughes, T.J.R., Ed.  Finite Element Methods for Convection Dominated
    Flows.  New York:  American Society of Mechanical Engineers, 1979.
23. Roache, Patrick J.  Computational Fluid Dynamics.  Albuquerque, New
    Mexico:  Hermosa Publishers, 1976.
24. Shih, T.M.  Numerical Heat Transfer.   Washington, D. C.:   Hemisphere
    Publishing Corporation, 1982.
25. Shih, T.M. , Ed.  Numerical Properties and Methodologies in Heat
    Transfer.  Washington, D.C.:  Hemisphere Publishing Corporation, 1983.
26. Bodoia, J.R. and J.F. Osterle.  "The Development of Free Convection
    Between Heated Vertical Plates", in The Journal of Heat Transfer,
    Transactions ASME, February 1962, pp. 40-43.
27. Aung, W.,  L.S.   Fletcher,  and V.   Sernas.  "Developing Laminar Free
    Convection Between Vertical Flat Plates with Assymmetric Heating", in
    The International Journal of Heat and Mass Transfer, Volume 15, 1972,
    pp. 2293- 2308.
    Aung, W.  "Fully Developed Laminar Free Convection Between Vertical
    Plates Heated Assymmetrically", in The International Journal of Heat
    and Mass Transfer, Volume 15, 1972, pp. 1577-1580.
28. Back, Lloyd H.  "Very High Temperature Laminar Flow of a Gas Through
    the Entrance Region of a Cooled Tube -- Numerical Calculations and
    Experimental Results", in The International Journal of Heat and Mass
    Transfer, Volume 15, 1972, pp. 1001-1021.
29. Bradley, D. and A.G. Entwistle.  "Developed Laminar Flow Heat Transfer
    from Air for Variable Physical Properties", in The International
    Journal of Heat and Mass Transfer, Volume 8, 1965, pp. 621-638.
30. Leonard, B.P.  "A Stable and Accurate Convective Modeling Procedure
    Based on Quadratic Upstream Interpolation," in Computer Methods in
    Applied Mechanics and Engineering, Volume 19, 1979, pp. 59-98.
31. Cebeci,  T.;   Khattals,  A.A.;   and Lamont, R.   "Combined Natural and
    Forced Convection in Vertical Ducts." Seventh International Heat
    Transfer Conference, Volume 3, pp. 419-424, Washington, D.C.:  Hemisphere
    Publishing Co., 1982.
32. Dalbert, A.M.  "Natural, Mixed and Forced Convection in a Vertical
    Channel with Assymmetric Uniform Heating." Seventh International Heat
    Transfer Conference, Volume 3, pp. 431-434, Washington, D.C.:  Hemisphere
    Publishing Co., 1982.
33. Kettleborough, C.F.  "Transient Free Convection Between Heated Vertical
    Plates Including Entrance Effects", Int, J. Heat Mass Transfer, Vol.
    15, pp. 883-896, 1972.
 1. Eckert and Drake, ref A-1.
 2. Ozisik, M. Necati.   Radiative Transfer and Interactions with Conduction
    and Convection.   New York:  John Wiley and Sons, 1973.
 3. Siegel, Robert, and Howell, John R.   Thermal Radiation Heat Transfer.
    2nd Edition.   New York:  McGraw Hill, 1981.
 4. See F.R. Steward and R. Gaulard in Blackshear, Perry L., Ed.  Heat
    Transfer in Fires:   Thermophysics, Social Aspects, Economic Impacts.
    New York:  John Wiley and Sons, 1974.
 5. Prasad, Sangen, Visser, ref III-33.
 6. Lowes, T.M., and Newall, A.J.   "The Emissivities of Flame Soot Dispersions",
    in Combustion and Flame, Volume 16, 1971, pp. 191-194.
 7. Felske, J.D., and Tien, C.L.   "Calculation of the Emissivity of
    Luminous Flames", in Combustion Science and Technology, Volume 7,
    1973, pp. 25-31.
 8. Sibulkin, Merwin.   "Estimates of the Effect of Flame Size on Radiation
    from Fires", in Combustion Science and Technology, Volume 7, 1973, pp.
 9. King, N.K.   "The Influence of Water Vapor on the Emission Spectra of
    Flames", Combustion Sci. and Tech., Volume 6, 1973, pp. 247-256.
10. Tien, C.L. and S.C. Lee. "Flame Radiation", in Prog. Energy Combustion
    Science, Volume 8, 1982, pp. 41-59.
11. Modak, Ashok T.  "Thermal Radiation from Pool Fires", in Combustion and
    Flame, Volume 29, 1977, pp. 177-192.
12. Modak, Ashok T.  "Nonluminous Radiation from Hydrocarbon-Air Diffusion
    Flames", in Combustion Sci, and Tech., Volume 10, 1975, pp. 245-259.
13. Kurosaki, Yasuo; Mishima, Hiroshi; and Kashiwagi, Takao.  "Heat
    Transfer Combined with Radiation and Natural Convection in a Rectangular
    Enclosure", in Seventh International Heat Transfer Conference
    Proceedings, Volume 2, pp. 215-220, New York:  Hemisphere Publishing
    Corporation and McGraw-Hill International, 1982.
 1. Graboski, M., and Bain, K.   "Properties of Biomass Relevant to Gasification"
    in Biomass Gasification.   Principles and Technology.   T.B.
    Reed, Ed.  Park Ridge, NJ:  Noyes Data Corporation.
 2. Stubington, J.F., and Fenton, H.   "Combustion Characteristics of Dried
    and Pelletized Bagasse" in Combustion Science and Technology, Volume
    37, 1984, pp. 285-299.
 3. See also C.A. Zaror and D.L.   Pyle, "The Pyrolysis of Biomass:   A
    General Review" in Wood Heat for Cooking, reference III-3.
 4. Harker, A.P.; Sandels, A.; and Burley, J.  Calorific Values for Wood
    and Bark and a Bibliography for Fuelwood. 56/62 Gray's Inn Road, WC1X
    8LU, London, England:   Tropical Products Institute, August 1982.
 5. Kjellstrom, B.   Producer Gas.  Stockholm:  Beijer Institute, 1980.
 6. National Academy of Sciences.   Firewood Crops:   Shrub and Tree Species
    for Energy Production.   Volume 1, 1980, Volume II, 1983, Washington,
    D.C.:  National Academy Press.
 7. Abe, Fusako.   "Manufacture of Charcoal from Fast-Grown Trees" in Energy
    from Forest Biomass, W. Ramsey Smith, Ed. New York:  Academic Press,
    1982, pp. 129-146.
 8. Kanury, A. Hurty, and Blackshur, Perry L.,  Jr.   "Some Considerations
    Pertaining to the Problem of Wood Burning" in Combustion Science and
    Technology, Volume VI, 1970, pp. 339-355.
 9. Roberts, A.F.   "A Review of Kinetics Data for the Pyrolysis of Wood and
    Related Substances" Combustion and Flame, Volume 14, 1970, pp. 261-272
10. Bhagat, Phiroz M.  "Wood Charcoal Combustion and the Effects of Water
    Application" in Combustion and Flame, Volume 37, 1980, pp. 275-291.
11. Bhagat, Phiroz M.  "Analytical Modeling of the Effects of Water
    Application on Burning Wood Charcoal Surfaces" in Combustion and
    Flame, Volume 47, 1982, pp. 93-98.
12. Atreya, Arvind.  "Fire Growth on Horizontal Surfaces of Wood" in
    Combustion Science and Technology, Volume 39, 1984, pp. 163-194.
13. Kanury, A. Murty.  Introduction to Combustion Phonomena.  New York:
    Gordon and Breach, 1982.
14. Glassman, Irvin.  Combustion.   New York:  Academic Press, 1977.
15. Buckmaster,  J.D., and Ludford,   G.S.S.  Theory of Laminar Flames.
    Cambridge University Press, 1982.
16. Toong, Tau-Yi.  Combustion Dynamics. New York: McGraw-Hill, 1983.
17. Bamford, C.H.;  Crank, J.; and Malan, D.H.   "The Combustion of Wood,
    Part I" in Proceedings of the Cambridge Philosophical Society, Volume
    42, Part 2, 1946, pp. 166-182.
18. Blackshear, Perry L., and Kanury, A. Murty.  "On the Combustion of Wood
    I:  A Scale Effect in the Pyrolysis of Solids" in Combustion Science
    and Technology, Volume 2, 1970, pp. 1-4.
19. Kanury, A. Murty, and Blackshear, Perry L., Jr.  "On the Combustion of
    Wood II:  The Influence of Internal Convection on the Transient
    Pyrolysis of Cellulose" in Combustion Science and Technology, Volume
    2, 1970, pp. 5-9.
20. Kanury, A.  Murty.   "Thermal Decomposition Kinetics of Wood Pyrolysis"
    in Combustion and Flame, Volume 18, 1972, pp. 78-83.
21. Kanury, A. Murty.  "Rate of Burning of Wood" in Combustion Science and
    Technology, Volume 5, 1972, pp. 135- 146.
22. Kung, Hsiang-Cheng.  "A Mathematical Model of Wood Pyrolysis" in
    Combustion and Flame, Volume 18, 1972, pp. 185-195.
23. Kung, Hsiang-Cheng and Ashok S. Kalelkar.  "On the Heat of Reaction in
    Wood Pyrolysis" in Combustion and Flame, Volume 20, 1973, pp. 91-103.
24. Havens, J.A.; Hashemi, H.T.; Brown, L.E.; and Welker, J.R.  "A Mathematical
    Model of the Thermal Decomposition of Wood" in Combustion
    Science and Technology, Volume 5, 1972, pp. 91-98.
25. Maa, Peter S., and Bailie, Richard C. "Influence of Particle Sizes
    and Environmental Conditions on High Temperature Pyrolysis of Cellulosic
    Material-I (Theoretical)" in Combustion Science and Technology,
    Volume 7, 1973, pp. 257-269.
26. Kansa, Edward J.; Perlee, Henry E.; and Chaikin, Robert F.   "Mathematical
    Model of Wood Pyrolysis Including Internal Forced Convection"
    in Combustion and Flame, Volume 29, 1977, pp. 311-324.
27. Roberts, A.F.  "The Heat of Reaction During the Pyrolysis of Wood in
    Combustion and Flame, Volume 17, 1971, pp. 79-86.
28. Broido, A.; and Nelson, Maxine A.  "Char Yield on Pyrolysis of Cellulose"
    in Combustion and Flame.   Volume 24, 1975, pp. 263-268.
29. Milne, T.  "Pyrolysis -- The Thermal Behavior of Biomass Below 600 [degrees]C"
    in Biomass Gasification.  Principles and Technology,   T.B. Reed, Ed.
    Park Ridge, New Jersey:   Noyes Data Corporation, 1981, 401 pp.
30. Desrosiers, R.  "Thermodynamics of Gas-Char Reactions" in T.B. Reed,
    ref 29.
31. Graboski, M.  "Kinetics of Char Gasification Reactions." in T.B. Reed,
    ref 29.
32. Williams, F.  "Condensed-Phase Mass and Energy Balances" in Heat
    Transfer in Fires:   Thermophysics, Social Aspects, Economic Impacts,
    Perry L. Blackshear, Ed.   New York:  John Wiley & Sons, 1974.
33. Williams,   F.  "Chemical Kinetics of Pyrolysis" in Heat Transfer in
34. Roberts,  O.C.,   and Smith, I.W.   "Measured and Calculated Burning
    Histories of Large Carbon Spheres in Oxygen" in Combustion and Flame,
    Volume 21, 1973, pp. 123-127.
35. Adomeit, G.; Mohiuddin, G.; and Peters, N.  "Boundary Layer Combustion
    of Carbon" in Sixteenth International Symposium on Combustion,
    Combustion Institute, 1976.
36. Ubhayakar, Shivadev K.  "Burning Characteristics of a Spherical
    Particle Reacting with Ambient Oxidizing Gas at Its Surface" in
    Combustion and Flame, Volume 26, 1976, pp. 23-24.
37. Beshty, Bahjat S.  "A Mathematical Model for the Combustion of A Porous
    Carbon Particle", in Combustion and Flame, Volume 32, 1978, pp.
38. Libby, Paul A., and Blake, Thomas R.  "Theoretical Study of Burning
    Carbon Particles" in Combustion and Flame, Volume 36, 1979, pp.
39. Libby, Paul A.  "Ignition, Combustion, and Extinction of Carbon
    Particles" in Combustion and Flame, Volume 38, 1980, pp. 285-300.
40. Kassoy, David R.; and Libby, Paul A.  "Activation Energy Asymptotics
    Applied to Burning Carbon Particles" in Combustion and Flame, Volume
    48, 1982, pp. 287-301.
41. Matalon, Moshe.  "Complete Burning and Extinction of a Carbon Particle
    in An Oxidising Atmosphere" in Combustion Science and Technology,
    Volume 24, 1980, pp. 115-127.
42. Matalon, Moshe.  "Weak Burning and Gas-Phase Ignition About a Carbon
    Particle in an Oxidizing Atmosphere" in Combustion Science and
    Technology, Volume 25, 1981, pp. 43-48.
43. Baldwin, Sam, ref II-79.
44. Prakash, C.B. and F.E. Murray.  "Studies on Air Emissions from the
    Combustion of Wood Waste" in Combustion Science and Technology, Volume
    6, 1972, pp. 81-88.
45. Bussmann, P.J.T.,  P.    Visser, and K.  Krishna Prasad.  "Open Fires:
    Experiments and Theory" in Wood Heat for Cooking.
    This is also presented in Bussman, P., and Prasad, K.  Krishna, "Model
    Predictions of Temperature and Velocity Profiles in Turbulent Diffusion
    Buoyant Flames." Proceedings of the Seventh International Heat
    Transfer Conference Vol. 12, pp. 401-406, 1982, Hemisphere Publishing
    Corp., N.Y. and McGraw Hill International.
46. Emmons, Howard W. and Armind Atreya.  The Science of Wood Combustion.
    In Wood Heat For Cooking.
47. Westbrook, Charles K. and Frederick L. Dryer.  "Chemical Kinetic
    Modeling of Hydrocarbon Combustion" in Proc.  Energy Combustion
    Science, Volume 10, Number 1, 1984, pp. 1-57.
48. Lee, Calvin K. and J. Rodney Diehl.  "Combustion of Irradiated Dry and
    Wet Oak" in Combustion and Flame, Volume 42, 1981, pp. 123-138.
49. Sangen. Ref. B-18.
50. Calcote, H.F.  "Mechanisms of Soot Nucleation in Flames -- A Critical
    Review" in Combustion and Flame, Volume 42, 1981, pp. 215-242.
51. Glassman, I. and P.  Yaccarino.   "The Temperature Effect in Sooting
    Diffusion Flames", Eighteenth Symposium (International) on Combustion,
    The Combustion Institute, 1981, pp. 1175-1183.
52. Kent, J.H. and H.G. Wagner.  "Soot Measurements in Laminar Ethylene
    Diffusion Flames", in Combustion and Flame, Volume 47, pp. 53-65,
53. Smith et al., refs II-107 to 112.
54.   Shih, T.M. Numerical Heat Transfer.   Washington, D.C.: Hemisphere
     Publishing Corporation, 1984.
55.   Wesson, H.R., J.R. Welker, and C.M. Sliepcevich.  "The Piloted
     Ignition of Wood by Thermal Radiation", in Combustion and Flame,
     Volume 16, 1971, pp. 303-310.
56.   Harris, reference II-15. See also Foley et. al., reference II-156.
57.   H.S. Mukunda has found (personal communication, October 27, 1986) that
     good combustion is possible with briquettes, sawdust, rice husk, or
     other materials if done in a properly designed combustion chamber.
     Several innovative stove designs for use with these materials are now
     under development.   For further information, he should be contacted
     directly at ASTRA.
1.    Kakac, S.; Shaw, R.K.; and Bergles, A.E. Eds. Low Reynolds Number
      Flow Heat Exchangers, Washington, D.C.: Hemisphere Publishing Company,
     1983, 1016 pp.
2.    Kakac, S.; Bergles, A.E.; and Mayinger, F. Eds. Heat Exchangers:
     Thermal-Hydraulic Fundamentals and Design, Washington, D.C.
     Hemisphere Publishing Company, 1983, 1131 pp.
3.    Kays, William Morrow, and London, A.L. Compact Heat Exchangers, Third
     edition, New York: McGraw-Hill, 1984, 335 pp.
4.    Walker, G. Industrial Heat Exchangers, Hemisphere Publishing Corporation,
     Washington, D.C., 1982, 408 pp.
5.    Taboreh, J.; Hewitt, G.F.; and Afgan, N., Eds. Heat Exchangers:
     Theory and Practice, Hemisphere Publishing Corporation, Washington,
     D.C., 1983, 979 pp.
6.    Heat Exchanger Design Handbook, 5 volumes, Washington, D.C.: Hemisphere
     Publishing Corp., 1983. Vol. 1: Heat Exchanger Theory, Vol. 2:
     Fluid Mechanics and Heat Transfer, Vol. 3: Thermal and Hydraulic
     Design of Heat Exchangers, Vol. 4: Mechanical Design of Heat Exchangers.
7.    Raznjevic, Kuzman. Handbook of Thermodynamic Tables and Charts. New
     York: McGraw-Hill, 1976.
1.    French, David. The Economics of Renewable Energy Systems for Developing
     Countries. Washington, D.C., June 1979.
2.    Baldwin, George B., "Why Present Value Calculations Should Not Be Used
     In Choosing Rural Water Supply Technology", World Development, V.11,
     N.12, pp.1075-1081, 1983.
3.    Thuesen, G.J., and Fabrycky, W.J. Engineering Economy. Englewood
     Cliffs, New Jersey: Prentice Hall, Inc., 6th Edition, 1984.
1.    Brownlee, K.A. Statistical Theory and Methodology in Science and
     Engineering. New York: John Wiley and Sons, 1965.
2.    The sample standard deviation, s, is based on a finite amount of test
     data representing a small fraction of the possible values were the
     testing to be continued indefinitely. The population standard deviation,
     [sigma], is based on all the possible values generated by testing
     forever.  The two are related by the equation <see equation below>

bsex276a.gif (167x486)

     so that the difference is significant only for small test series with
     few data points n.
3.    Note that this is not true but is a useful fiction.  Any particular
     interval will or will not hold the true average value.  Only by
     repeating a series of tests many times can such a statement of
     probability be made.    For example, if a series of 10 tests were
     repeated 115 times (for a total of 1150 tests), all under identical
     conditions with similar sample deviation, then a fraction 100(1-2[alpha])%
     of the ranges <see equation below>

bsex276b.gif (108x600)

     will include the true average.   The subscript i refers to the different
     test series above, not to individual tests.
4.    Dixon, Wilfred J. and Frank J. Massey, Jr., Introduction to Statistical
     Analysis, Third Edition, McGraw-Hill, New York, 1969.
     Note also that the more conventional notation denotes this as the
     [t.sub.[alpha]/2]-value rather than t-value.   The latter notation has been used
     here for consistency with the notation used for the confidence level,
     etc. and for convenience.
5.    Strictly speaking, this statement is wrong.  In fact, one can only say
     that if the average performances of stoves A and B were the same, the
     probability is more than 10 percent that the t-value would exceed the
     observed value of 1.30.
6.    More precisely, the u in equation (9) is u = ([u.sub.1 - [beta]] + [u.sub.1 - [alpha]/2]) for a
     two-sided test where [u.sub.1 - [beta]] is the probabilty of correctly rejecting a
     false hypothesis (the power of the test) and [u.sub.1-[alpha]/2] is the probability
     of correctly accepting the true hypothesis (converse of the level of
     significance).   The u are points of the cumulative normal distribution
     function.   It should also be noted that for convenience the pooled
     sample deviation has been assumed to be equal to the standard deviation
     of the underlying population distribution.   For further information
     see reference 1 above.   (Note that the statements concerning the
     number of tests needed in the draft standards, reference V-1, are
7.    Remember in solving this that the square root of a number can be both
     positive and negative. Thus, to form the ellipse both roots are used
     in the equation to find the different quarters of the ellipse.
1.    1984-85 Guide to Scientific Instruments.  Washington, D.C.: American
     Association for the Advancement of Science.
2.    Barford, N.C., Experimental Measurements: Precision, Error, and
     Truth, Addison-Wealey, London, 1967.
1.    Burmeister, ref B-2.
2.    Cebeci, ref B-3.
3.    Meinel, Aden B. and Marjorie P. Meinel; Applied Solar Energy,
     Addison-Wesley, Reading. Massachusetts, 1976.
4.    Duffie and Beckman. ref A-2.
5.    Handbook of Chemistry and Physics. 51st Edition. Chemical Rubber
     Publishing Company, 1970, 1971.
6.    Energy Factbook, Committee on Interstate and Foreign Commerce, Print
     96-IFC-60, November 1980, U.S.   Congress House of Representatives and
     U.S. Library of Congress, Congressional Research Service.
1.    U.S. Congressional Office of Technology Assessment, Reference II-5,
     background paper #2, May 1983.
2.    The World Environment Handbook, World Environment Center, New York,
3.    Hall, Barnard, and Moss, reference II-20.
                           INDEX, BY AUTHOR
Abe, F. (II-14) 7, 16; (II-149)
   253; (D-7) 175
Adisoemarto, S. (II-92) 18
Adomeit, G. (D-35) 183
Afgan, N. (E-5) 187
Agarwal, B. (V-25) 113
Aggarwal, A.L. (II-107,109) 20
Aggarwal, G.C. (II-117) 22
Alio, H. (II-26) 8
American Association for the
Advancement of Science, (H-1) 221
American Society for Testing and
Materials (V-22) 83
Anderson, D. (II-106) 19
Arnold, J.E.M. (II-34) 8, 17, 19,
   22, 23; (II-40) 8, 9, 17, 18
Arpaci, V.S. (B-1) 149, 151, 153,
Arungu-Olende, S. (II-8) 6, 12, 13
Ashworth, J. (III-12) 40
Atreya, A. (III-25) 55, 59; (D-12)
   177; (D-46) 185
Aung, W. (B-27) 156, 157
Axmed, M.C. (V-17) 101
Babu, D.S.S. (III-15) 41, 43
Back, L.H. (B-28) 156
Bailie, R.C. (D-25) 179
Bain, K. (D-1) 175-179, 181
Balachandran, B.N. (II-50) 8
Balakrishna, M. (II-41) 8
Baldwin, G.B. (F-2) 193
Baldwin, S.F. (I-1) 1; (II-79) 17,
   116, 117, 122-124; (II-80) 17,
   27, 29, 66, 90-93; (II-120) 54;
   (II-150) 14; (II-153) 26; (III-14)
   41, 43, 54, 60, 90, 91,
   151; (III-20) 54, 61, 90; (III-34)
   60, 61, 90, 151
Bamford, C.H. (D-17) 179, 181
Barford, N.C. (H-2) 222-223
Barnard, G.W. (II-20) 7, 8, 231,
   251-254; (II-116) 20, 22, 24;
   (II-151) 20; (II-155) 24; (III-41)
Beckman, W.A. (A-3) 131
Bergles, A.E. (E-1,2) 187
Bernow, S. (II-24) 8, 11, 12, 14,
Beshty, B.S. (D-37) 183
Bhagat, P.M. (D-10,11) 177, 183
Bhaghavan, M.R. (II-41) 8
Bhogale, S. (III-15) 41, 43
Blackshear, P.L. (D-8) 175, 177,
   179, 181; (D-18 179, 181; (D-19)
   179, 181, 182
Blake, T.R. (D-38) 183
Bodoia, J.R. (B-26) 156, 157
Bonney, R.S.P. (II-74) 15
Booth, H.E. (II-66) 14
Boureima, I. (II-61) 253
Bowonder, B. (II-147B) 253; (V-24)
Bradley, D. (B-29) 156
Bradley, P.N. (II-140) 24
Bradshaw, P. (B-3) 149-151, 156,
Brambley, M.R. (II-57) 8, 63; (V-22)
Breman, H. (II-91) 18
Broido, A. (D-28) 181, 182
Brown, L.E. (D-24) 179, 181
Brown, L.R. (II-82) 17; (II-93) 18
Brownlee, K.A. (G-1) 199, 203,
   211, 220
Brunet, E. (III-13) 40
Buckmaster, J.D. (D-15) 179, 180,
   185, 186
Burley, J. (III-26) 55; (D-3) 175
Burmeister, L.C. (B-2) 149, 151,
   153, 156, 157, 162, 225
Burne, S. (VI-4) 115-116
Bussmann, P.J.T. (II-80) 17, 27,
   29, 66, 90-93; (III-7) 28;
   (III-27) 56, 58; (III-33) 58;
   (B-11) 150, 151; (D-45) 185,
Cairnie, L.R. (B-14) 151, 156
Calcote, H.F. (D-50) 186
Cebeci, T. (B-3) 149-151, 156,
   157, 225; (B-31) 156, 157
Cecelski, E. (II-9) 6, 8, 9; (II-55)
Center for Science and Environment,
   India (II-99) 19, 20, 22,
Cerutti, O.M. (II-44) 8
Chaikan, R.F. (D-26) 179, 181
Chandler, W. (II-82) 17
Channeswarappa, A. (II-50) 8
Chauvin, H. (II-60) 9, 14
Chavangi, N. (II-140) 24
Childers, L.F. (III-3) 78
Chitty, R. (B-13) 150
Christiaens, M. (III-24) 55
CILSS Equipe Ecologie-Forets (II-27)
Clement, J. (II-28) 8
Conolly, R. (B-12) 150, 151
Conte, S.D. (B-20) 155
Council on Environmental Quality
   (II-7) 6, 8, 18, 251
Cox, G. (B-13) 150
Crank, J. (D-17) 179, 181
Dalbert, A.M. (B-32) 156, 157
Dasappa, S. (III-19) 41, 43, 53,
Dasgupta, B. (II-147B) 253
Dave, R.M. (II-107,109) 20
Davies, R.M. (B-12) 150, 151
de Boor, C. (B-20) 155
DeChambre, G. (II-61) 253; (II-121)
   23, 91, 93, 99
DeKoning, H.W. (II-110)20
De Lepeleire, G. (III-24) 55;
   (III-37) 64; (B-21) 151, 156
Desrosiers, R. (D-30) 181, 182
de Wit, C.T. (II-76) 17
Department of State (II-7) 6, 8,
   18, 251
Diehl, J.R. (D-48) 185
Digernes, T.H. (II-130) 24
Dixon, W.J. (G-4) 205
Dossi, H. (II-101) 19
Down, S. (II-58) 8, 9; (V-24) 101
Drake, R.M. (III-9) 33; (A-1) 129,
   149, 151, 153, 162, 163, 167,
   169, 170
Dryer, F. (D-47) 182, 183, 185
Dunkerley, J. (II-9) 6, 8, 9; (II-33)
   8; (II-36) 8, 22
Dunn, P.D. (III-4) 27, 30, 115
Dutt, G. (II-153) 26; (III-1) 28;
   (III-10) 35; (V-10) 96; (V-20)
  104; (VI-5) 123
Duffie, J.A. (A-3) 131, 225
Earl, D. (II-13) 8, 14, 16, 22,
   252; (II-38) 8
Earnest, E. (II-113) 20
Eckert, E.R.G. (III-9) 33; (A-1)
   129, 149, 151, 153, 162, 163,
   167, 169, 170
Eckholm, E.P. (II-2) 5, 18; (II-116)
   20, 24
Emmons, H.W. (III-25) 55, 59; (B-16)
   150; (D-46) 185
Entwistle, A.G. (B-29) 156
Estrada, F.S. (II-44) 8
Fabrycky, W.J. (F-3) 197
Felske, J.D. (C-7) 171
Finn, D. (II-88) 18
Fishwick, R. (II-106) 19
Flavin, C. (II-82) 17
Fletcher, L.S. (B-27) 156, 157
FLORASA (II-67) 14, 17, 24
Foley, G. (II-77) 17; (II-116) 20,
   24; (II-152) 23; (II-155) 24;
   (II-156) 186; (III-41) 63
French, D. (F-1) 193
Gaulard, R. (C-4) 170
Geller, H. (II-153) 26; (II-157/134)
   25; (III-1) 28; (III-3)
   27, 28, 30, 35; (III-10) 35;
   (III-11) 40
Gentry, A.H. (II-97) 18
Giorgini, A. (B-6) 156
Glassman, I. (D-14) 179, 180, 182,
   185, 186; (D-51 186
Goldemberg, J. (II-35) 8; (II-43)
   8, 17; (II-157/133) 25
Gordon, L. (II-9) 6, 8, 9
Graboski, M. (D-1) 175-177, 179,
   181; (D-31) 181, 182
Grainger, A. (II-94) 18
Gray, D.R. (B-6) 156
Guillaumet, J.L. (II-101) 19
Gupta, R.K. (II-157/137) 25
Gwynne, M.D. (II-89) 18
Hadley, M. (II-101) 19
Hall, D.O. (II-10) 6, 8, 251; (II-20)
   7, 231, 251-254; (II-54) 8
Harker, A.P. (III-26) 55; (D-3)
Harris, A.C. (II-15) 7, 176, 186
Harrison, A.J. (B-14) 151, 156
Hartnett, J.P. (B-9) 150, 153
Hashemi, H.T. (D-24) 179, 181
Hassan, M. (V-10) 96
Havens, J.A. (D-24) 179, 181
Hewitt, G.F. (E-5) 187
Hinrichson, D. (II-42) 8
Holman, J.P. (A-5) 139, 162
Horsley, M.E. (B-19) 151
Howell, J.R. (C-3) 167, 170
Hughart, D. (II-11) 10
Hughes, T.J.R. (b-22) 156
Hukai, R.Y. (II-43) 8, 17
Hurley, J.R. (II-157) 25; (III-23)
Hyman, E.L. (II-56) 8,9; (II-131)
   24; (II-132) 24; (V-16) 101;
   V-21) 104; (VI-3) 115
Isaacson, E. (B-20) 151
Islam, M.N. (II-30) 8
Jackson, P. (II-83) 18
Jagadish, J.S. (III-15) 41, 43
Jaluria, Y. (B-5) 149, 150, 151
Jongma, J. (II-40) 8, 9, 18
Jordan, B. (II-3) 5
Joseph, S.D. (I-2) 1; (VI-5) 115
Joyce, N. (III-4) 27, 30, 115
Kakac, S. (E-1,2) 187
Kansa, E.J. (D-26) 179, 181
Kanury, A.M. (B-8) 153, 162; (D-8)
   175, 177, 179, 181; (D-13) 179
   180, 182, 183, 185, 186; D-18;
   179; (D-19) 179, 181, 182; (D-20)
   179, 181; (D-21) 179, 181
Karch, G.E. (II-69) 14; (II-157/138)
Kartawinata, K. (II-92) 18
Kashiwagi, T. (C-13) 173
Kassoy, D.R. (D-40) 183
Kays, W.M. (E-3) 187
Keita, J.D. (II-124) 23
Keita, M.N. (II-25) 8
Keller, H.B. (B-20) 151
Kent, J.H. (D-52) 186
Kettleborough, C.F. (B-32) 156
Khattals, A.A. (B-31) 156, 157
King, N.K. (C-9) 171
Kinyanjui, M. (VI-1) 115; (VI-2)
KiZerbo, J. (V-18) 101
Kjellstron, B. (D-5) 175
Koenig, D. (VI-16) 125
Komer, D.I. (II-86) 18
Kristoferson, L. (II-31) 8, 12
Krist-Spit, C.E. (II-157) 25;
   (III-35) 61, 119
Kumar, R. (III-15) 41, 43
Kung, H.C. (D-22,23) 179, 181
Kurosaki, Y. (C-13) 173
Kuusela, K. (II-17) 7
Lamont, R. (B-31) 156, 157
Lamprey, H.F. (II-105) 19
Larsen, P.S. (B-1) 149, 151, 153,
Last, J.M. (II-110) 20
Lee, C.K. (D-48) 185
Lee, S.C. (C-10) 171
Lee, S.L. (B-16) 150
Leonard, B.P. (B-30) 156
Leteemane, B. (III-11) 40
Libby, P.A. (D-39,40) 183
Lokras, S.S. (III-15) 41, 43
London, A.L. (B-10) 153, 164; (E-3)
Lopez-Parodi, J. (II-97) 18
Lowes, T.M. (C-6) 171
Ludford, G.S.S. (D-15) 179, 180,
   185, 186
Luhanga, M.L. (II-47) 8, 9, 14,
   24; (II-49) 8, 9
Lumar, S.B.S. (III-19) 41, 43, 55,
Maa, P.S. (D-25) 179, 181
Makhijani, A. (II-52) 8
Malan, D.H. (D-17) 179, 181
Massey, F.J. (G-4) 205
Hatalon, M. (D-41) 183
Mayinger, F. (E-2) 187
Medynski, T. (V-22) 83
Menon, P. (II-108) 20
Meyers, N. (II-85) 18
Hicuta, W. (III-38) 64
Milne, T. (D-29) 181
Mintz, Y. (II-100) 19
Mishima, H. (C-13) 173
Mnzava, E.M. (II-39) 8, 9, 22;
   (II-59) 8, 9, 17
Modak, A.T. (C-11,12) 173
Mohiuddin, G. (D-35) 183
Moreira, J.R. (II-157/133) 25
Morgan, R.P. (II-57) 8, 63
Morgan, W.B. (II-12) 6, 18, 23
Morse, R. (II-30) 8
Moss, P.A. (II-20) 7, 8, 231, 251-254;
   (II-54) 8
Moss, R.P. (II-12) 6, 18
Moundlic, J. (II-157/139) 25
Mukunda, H.S. (III-18,19) 41, 43,
   55, 61, 62; (D-57) 177.
Munslow, B. (II-32) 8
Murray, F.E. (D-44) 185
Mwandosya, M.J. (II-47) 8, 9, 14,
   24; (II-49) 8, 9
Nagaraju, S.M. (II-50) 8
National Academy of Sciences (II-90)
   18; (II-102) 19, 23, 24;
   (II-124) 23, 127; (V-15) 101;
   (D-6) 175
Nations, J. (II-86) 18
Negrete, M.A.M. (II-44) 8
Nelson, M.A. (D-28) 181, 182
Newall, A.J. (C-6) 171
Nkonoki, S. (II-21) 8, 17, 253;
   (V-24) 101
Noronha, R. (II-125) 23, 24
Novikoff, G. (II-103,104) 19
Nyyssonen, A. (II-17) 7
O'Keefe, P. (II-24) 8, 11, 12, 14,
   17; (II-31) 8, 12, 19; (II-32)
   8; (II-95) 18
Openshaw, K. (II-18) 7
Osterle, J.F. (B-26) 156, 157
OTA (II-5) 5, 18, 23, 24, 231
Ouedraogo, I. (III-20) 54, 61, 90,
   151; (III-34) 60, 61, 90, 151
Ozisik, M.N. (A-4) 137, 140; (C-2)
   167, 169, 170, 173
Palmieri, M. (II-76) 16, 22
Pandey, U. (II-22) 8, 20, 253
Pant, M.M. (II-127) 24
Parkhurst, D. (II-32) 8
Perlee, H.E. (D-26) 129, 181
Perlin, J. (II-3) 5
Peters, N. (D-35) 183
Philips, P. (II-32) 8
Pollack, J. (II-1) 5, 18, 19
Poole, A. (II-52) 8
Postel, S. (II-82) 17
Poulsen, G. (II-128) 24
Powers, T.A.M. (III-11) 40
Prakash, C.B. (D-44) 185
Prasad, K.K. (II-63) 10; (II-115)
   20, 24; (III-5) 27, 29, 49;
   (III-7) 28; (III-21) 54; (III-27)
   56, 58; (III-33) 58, 151,
   171; (B-11) 150, 151; (D-45)
   185, 186
Prasad, S.S.R. (II-147B) 253
Pratt, D.J. (II-89) 18
Pratt, G.H. (III-32) 56
Purvis, M.R.I. (B-19) 151
Pyle, D.L. (D-3) 175, 181, 182
Ramakrishna, J. (II-108) 20
Ramsay, W. (II-9) 6, 8, 9; (II-36)
   8, 22
Rao, N.P. (II-147B) 253
Raskin, P. (II-24) 8, 11, 12, 14,
Ravindranath, N.H. (II-50) 8; (II-153)
   26; (III-16,17) 41, 43;
   V-24) 101
Raznjevich, K. (E-7) 191
Reddy, A.K.N. (II-45) 8, 9; (II-50)
   8; (II-51) 8; (V-24) 101
Reddy, B.S. (II-45) 8, 9
Reif, F. (A-2) 129
Revelle, R. (II-23) 8
Riswan, S. (II-92) 18
Rivera S. (II-157/135) 25
Roache, P.J. (B-23) 156
Roberts, A.F. (D-9) 176, 181, 182;
   (D-27) 181
Roberts, O.C. (D-34) 183
Rohsenow, W.M. (B-9) 150, 153
Rose, A.B. (II-73) 14
Salati, E. (II-87) 18
Salem, B.B. (II-129) 24
Samootsakorn, P. (III-4) 27, 30,
Sandels, A. (III-26) 55; (D-3) 175
Sangen, E. (III-5) 27, 29, 49;
   (III-27) 56, 58; (III-33) 58,
   151, 171; (B-18) 151, 185
Sanogo, C. (III-14) 41, 43, 54,
   60, 90, 91
Savoie, M. (V-17) 101
Selker, J.S. (IV-3) 78
Sentle, J. (III-11) 40
Sepp, C. (V-11,12) 99, 100
Sernas, V. (B-27) 156, 157
Servin, J.C. (II-44) 8
Shah, R.K. (B-10) 153, 164
Shaikh, A.M. (II-157/138) 25
Shailaja, R. (III-16,17) 41, 43
Shanahan, Y.N. (I-2) 1
Shaw, R.K. (E-1) 187
Shelton, J. (III-31) 56
Sherman, M. (VI-7) 115
Shih, T.M. (B-24) 156; (B-25) 156;
   (D-54) 186
Shirwa, Z.C. (V-17) 101
Shrestha, K.L. (II-46) 8
Shrinivasa, U. (III-18,19) 41, 43,
   55, 61, 62
Shukla, J.C. (II-157) 25; (III-23)
Shukla, J. (II-100) 19
Sibulkin, M. (C-8) 171
Sidibe, Y. (III-14) 41, 43, 54,
   60, 90, 91
Siegel, R. (C-3) 167, 170
Simonis, P. (II-80) 17, 27, 29,
   66, 90-93
Singh, J.S. (II-22) 8, 20, 253;
   (V-24) 101
Singh, N.T. (II-117) 22
Skouri, M. (II-103) 19
Sliepcevich, C.M. (D-55) 186
Smale, M. (V-17) 101
Smil, V. (II-81) 18
Smith, J.W. (D-34) 183
Smith, K.R. (II-107 to 112) 20,
   21, 28, 186; (III-29) 56
Smith, N.J.H. (II-96) 18
Soesastro, M.H. (II-30) 8
Somashekar, H.I. (II-50) 8
Sorenson, B. (II-21) 8, 17, 253;
   (V-24) 101
Spears, J. (II-98) 19, 20
Srisom, B. (VI-7) 115
Steinlin, H.J. (II-84) 18
Stevens, W.C. (III-32) 56
Steward, W. (VI-7) 115
Stewart, W. (I-2) 1
Stevens, N.F. (II-74) 15
Storke, L. (II-82) 17
Strasfogel, S. (II-119) 23; (II-121)
   23, 91, 93, 99; (III-14)
   41, 43, 54, 60, 90, 91
Sulilatu, W.F. (II-157) 25
Taboreh, J. (E-5) 187
Tariq, A.S. (B-19) 151
Thai Government, Forest Products
Division (II-72) 14, 22; (IV-2)
   78, 115
Thuesen, G.J. (F-3) 197
Tien, C.L. (C-7,10) 171
Timberlake, L. (II-116) 20, 24
Tiwari, A.K. (II-22) 8, 20, 253;
   (V-24) 101
Tiwari, K.M. (II-53) 8
Toon, O.B. (II01) 5, 18, 19
Toong, T.Y. (D-16) 179, 180, 185,
Ubhayakar, S.K. (D-36) 183
UN (II-6) 6, 12, 23, 251; (II-65)
   18, 254
UNDP (II-154) 23
UNFAO (II-4) 5, 8; (II-19) 7; (V-14)
Uhart, E. (II-68) 14
van Buren, A. (II-77) 17
van Gelder, A. (II-140) 24
Van Nao, T. (II-129) 24
Vayda (II-92) 18
Vidyarthi, V. (II-118) 22
Visser, P. (III-7) 28; (III-27)
   56; (III-33) 58, 151, 171; (B-11)
   150, 151; (D-45) 185, 186
VITA (V-1) 82; (V-2) 82
Vose, P.B. (II-87) 18
Wagner, H.G. (D-52) 186
Walker, G. (E-4) 187
Wardle, P. (II-76) 17, 22
Wartluft, J. (II-71) 14, 22
Weber, F. (II-78) 17
Wegner, K.F. (II-16) 7
Welker, J.R. (D-24) 179, 181; (D-55)
Wesson, H.R. (D-55) 186
Westbrook, C.K. (D-47) 182, 183,
White, S. (II-71) 14
Williams, F. (D-32) 181; (D-33)
   181, 182
Williams, R.H. (II-64) 10; (II-136)
   26; (II-157/136) 25
Wolfe, E. (II-82) 17
Wood, T.S. 5, (II-70) 14; (II-150)
   14; (III-36) 62; (V-19) 104
World Bank (II-154) 23; (II-126)
   23; (II-147C) 254
World Environment Center (J-2) 231
Yaccarino, P. (D-51) 186
Yameogo, G. (II-80) 17, 27, 29,
   66, 90-93; (III-20) 54, 61, 90,
   151; (III-34) 60, 61, 90, 151
Young, P.J. (III-3) 78
Yussuf, H. (II-105) 19
Zaror, C.A. (D-3) 175, 181, 182
Zhu, H. (II-57) 8, 63
                           INDEX, BY SUBJECT
Absorptivity, see emissivity
Acceptability surveys, 103
Airholes, 61, 73-74, 80
Air to air heat exchanger 125-127,
Altitude, effects on testing, 85
Animal Dung, 7, 19, 20, 22, 252
Arrhenius rate law, 180-181
Artisanal production, 49, 50, 65
ASTRA, 43, 65
Average, 92, 199-200
Baffles, 61, 86, 185
Balance, 83, 117-118, 221
Bangladesh, 6
Biases, in field surveys, 102
Black body, 50-52, 167-172
Biomass, 2, 6-13, 17-18, 23-25
   consumption, 6, 8-13, 17-18
   resources, 7,8
Bomb calorimeter, 175, 222
Boussiness approximation, 156
Boundary Layer, 42, 43, 160-162
Briquetted fuels, 60, 177
Calorific values, 55-57, 175, 178,
Carbon dioxide, 59, 182-186
Carbon monoxide, 59, 182-186
   in charcoal stoves, 17, 122
   in gasifiers, 63
   in nozzle stoves, 43
Cellulose, 56, 58, 176, 182
Ceramic stoves, 66, 78-80, 90, 100
Channel dimensions, 42, 123, 125
   efficiency, 45-48, 85
Channel stoves, 42-50, 65, 80, 90,
   93, 99, 151-166
Characteristic length, 157
Charcoal, 13-18, 182-185
   calorific value, 7, 176, 179
   combustion, 182-185
   conversion efficiency, 14-15
   demand, 17-18
   density, 7
   industrial uses, 17-18, 125-127
   kilns, 13-14
   transport, 14-17
   volatiles, 7, 176
Charcoal stoves, 115-125
   energy Balance, 30
   foundries, see foundries
   performance, 122-125, 219-220
Chimneys, 68, 71, 86
Coefficient of variation, 202-203
Combustion, 55-61, 175-186
   efficiency, 31
   losses, 28-30
Combustion chamber geometry, 61,
Common residual variance, 214
Concrete, 66
Conduction, 2, 31-41, 129-147
   of wood in a fire, 59
Conductivity, 33-35 132, 154, 163,
   179, 180
Confidence limits, 204-205
Confidence region, 208-210, 212-213
Contaminants, effect on pyrolysis,
Control efficiency 31, 62-64, 260-262
Control groups in field surveys,
Controlled cooking tests, 91-96
Convection, 3, 32, 41-50, 149-166
   Losses, 28-30
Cooking energy, 8-11 27-28
Cooking process efficiency, 31
Cookstoves, 2
Correlation coefficient, 208, 218
Crop Residues, 6-7, 10, 19
Dampers, 62
Data analysis, 86
Dead air space, 38-40, 139
Deforestation, 5, 6, 18, 19
Degrees of freedom, 201, 206
Density, 33, 129, 132, 163
Developed flow, 157
Dimensional errors, 3, 66-68, 70,
Domestic energy use, 8-10
Doors, 41, 60-62, 74, 86
Double walls, 38-40, 66-67
Dry basis, 56-57
Duct flow 150-157
Dung, see animal dung
East-West Center, 20, 101
E/DI, 115
Economics, 20, 22-23, 92, 193-198
Efficiency factors, 31
Electroplating, 66
Emissions, 19-21, 93, 151, 185-186
   of nozzle stove, 43
Emissivity, 38-40, 51, 167, 169-173
Energy balances, 28-30
Energy demand, 8-13, 17-18
Energy storage, 35, 135
Environment, 18-20
Errors in dimensions, 3, 66-68,
   70, 156
Errors in testing equipment,
analysis of, 222-223
Erosion, 18-19
Excess air, 60-61, 155
F-distribution, 209, 211
Fan power, 125, 127, 190
Fanning friction factor, 159, 153
Field test, 101-112
Financial analysis, 193-198
Fired clay -- see ceramic
Firepower, 84, 86, 89, 118, 155,
Flames, 150, 151, 171, 185, 186
Flywheel press, 78
Foraging, 20-22, 249
Forced convection 160-161
Forest, 5, 6, , 18-19, 251
Forges, 125-127
Fossil fuels, 22-23, 25, 178
Foundries, see forges
Friction factor, see fanning
Fuelwood, see woodfuel
Furnaces, see forges
Future worth, 195-198
Gap, 42
Gas analysis, 222
Gasifiers, 62
Grashof number 157, 159-162
Grate to pot height, 51-54, 85
Grates, 60, 75, 77, 80
Grog, 66
Gross calorific value, 55, 257
Haybox cooker, 36, 64
Heat exchangers, 125-127, 187-191
Heat recuperation, 36, 38, 39
   see also heat exchangers
Heat storage, 32, 135
Heat transfer correlations, 159-162,
Heating rate, 48-49, 136-140
Hemicellulose 56, 58, 178
Higher heating value, 55, 257
High power phase, 83, 89
Humidity, relative, 56
Hydraulic diameter, see characteristic
   length, 159
Hydraulic presses, 78
Ideal gas law, 157
Industry energy use, 9, 11, 12, 17
Insect attack of wood, 17
Institutions, 231-239
Insulants, 34, 86, 132
Interest rate, 193-198
Internal molds, 78
Internal rate of return, 197-198
International testing standards,
ITDG, 115
KENGO, 115
Kenya, 11, 12
Kilns for drying wood, 222
Kilns for producing charcoal, 13-15
KREDP, 115
Laboratory tests, 81-91
   parameters to be tested, 85-86,
        119, 122
   precautions, 85
   procedure, 82-84, 116-119
Laminar, 115, 158, 159-162
Level of confidence, 201, 203, 206
Lightweight stoves, 35-41, 65, 90
Lignin, 56, 58, 176
Linear regressions, 207-220
Lower heating value, 55, 257
Low power phase, 83, 89
Malgache, 90, 123, 124
Marketing tests, 113-114
Massive stoves, 29-30, 34-37, 65-66,
   90, 93, 100
Moisture content, 56-57, 259
Moisture meter, 222
Multipot stoves, 65-66, 90, 93,
   control, 62
   energy balance, 29-30
Natural convection, 161, 162
Net calorific value, 55, 257
Newtonian fluid, 158
Normal distribution, 199, 201
Nozzle stoves 42-44, 55, 65, 151
Numerical techniques, 137-140
Nusselt number, 151, 158, 159-162
Observables, 111
Outlier, 204
Peclet number, 158
PHU, percent heat utilized, 51,
   82, 84, 89, 92, 119, 122-124
Plantations, 23-24
Plenum chamber, 125-126
Plume, 150-151
Pooled sample deviation, 205
Pooled residual variance, 212
Pooled t-value, 214
   by cooking fuel, 10, 12
Pot, 31, 34-35, 64, 68
   efficiency, 31, 34-35, 64
   supports, 41, 74, 77, 80, 86
Potters wheels, 78
Power consumption, 8
Prandtl number 153, 158, 163
Preheating air, 61, 125-127
Present value, 195-198
Pressure cookers, 64
Pressure drop, 153, 164, 190
Production tests, 97-100
Promotion, 113
Proximate analysis, 175-176
Public demonstrations, 113
Pyrolysis, 179-182, 185-186
Radiation, 28-30, 38-41, 50-55,
   77, 138-139, 167-173
   in charcoal stoves, 116-117
   role in wood combustion, 58
Rayleigh number, 158
Recuperation, see heat recuperation
Regression, see linear regression
Relative humidity, 56
Retorts, 13-15
Reynolds number, 153, 158-162
Rollers, sheet metal, 76
Sample deviation, 200-202, 204
Sample size required, 207
Scale factors, 96, 157, 164
Scorecards, 93, 95-96
Secondary air, 61, 122
Single pot stoves, 62-63, 65-67,
Site construction, 49-50
Smoke, see emissions
Soils, 19
Soot, see emissions
Spacers, to center pot, 75
Specific consumption, 82, 84, 89,
   92, 94, 119, 123-124, 264
Specific daily consumption, 110
Specific heat, 33, 35, 129, 132,
   154, 163
Stagnation point, 150-151, 160-162
Standard deviation, 92, 200-201
Standard meal, 91
Stanton number 158
Steady state heat loss, 129-136
Steel, 17, 25-26, 66
Stefan-Boltzmann law, 167
Steres, 7
Stoichiometric air, 59, 155, 178
Stove efficiency, 31
   accessories, 68, 70
   adjustable to pot, 50
   construction, 65-70
   production, 76-80
   shapes, 67-69
   types, 42
Sumatra, west, 9
Surface boundary layer, see
   boundary layer
Surface heat loss, see wind, 139
Surveys, see field tests
Swirl, 61, 185
t-table, 203
t-test, 92, 205-207
Tape measure, 221
Temperature gradient, 67, 136
Template design, 72-75
Tests, 3, 81-114, 116-122
   controlled cooking, 81, 91-96
   field, 81, 101-112
   laboratory, 81-91, 116-122
   marketing, 82, 113-114
   production, 76-80, 81, 97-100
   results, 90, 93, 98-100, 123,
Thermal conductivity, 31-41, 129-147
Thermal diffusivity, 129, 158, 163
Thermal efficiency, 31
Thermal inertia, 35
Thermal mass, 35
Thermal storage, 32, 35
Thermocouples, 221
Thermometers, 83, 117-118, 221
Traditional stoves, 8-13, 17-18,
   20, 22, 25, 29, 66, 90, 93,
   123, 124
   energy balance, 29
Transient heat conduction in wood,
Transient heat loss, 136-140
Transportation energy, 14-18
Turbulent flow, 158, 160-162
Ultimate analysis, 175, 177, 179
Umeme, 123
Ungra, 8
Units, 7, 9, 225-230
Variance, see standard deviation
Variance of residuals, 208, 212
Vendors, 113
View factor, 51-54, 170-173
Viscosity, 154, 158, 163
   charcoal, 7, 182
   wood, 57-59, 179-182, 185-186
Volume coefficient of expansion,
Wall jet, 150-151
Wall losses, 28-30, 35-41, 129-147
Wall temperatures, 40
Walls, 35-41, 66-80
   double, 37-40, 66-67
   fired clay, 37, 39, 40, 41, 66-69,
   insulated, 37, 39-41
   lightweight, 37-41, 65-66
   massive, 36, 65-66
   single, 37-40, 66-77
Warranty, 113
Welding, 77
Wet basis, 56-57
Wind, 34, 85, 131
Wood economy surveys, 103-105
Woodfuel, 6-12
   consumption, 8-12
   deficits, by population, 12
   foraging, 20
   resources, 7