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                           A Design Manual
                           for Water Wheels
                           with details for applications to
                           pumping water for village use and
                           driving small machinery
                            WILLIAM G. OVENS
                      1600 Wilson Boulevard, Suite 500
                        Arlington, Virgnia 22209 USA
                    Tel: 703/276-1800 . Fax: 703/243-1865
                           [C]VITA, Inc. 1975
                 March 1977
                 June 1981
                 January 1989
                           TABLE OF CONTENTS
  I    Introduction
  II   Formulation of the Problem                                       
  III Design Limitations - Advantages and Disadvantages              
  IV   Theoretical Considerations for Design                            
      A.   Stall Torque                                                 
      B.   Power Output vs. Speed; Required Flow Rates                 
      C.   Bucket Design                                                
      D.   Bearing Design                                              
      E.   Shafts                                                      
      F.   Minor Considerations                                        
  V    Practical Considerations for Design                             
      A.   Materials                                                   
      B.   Construction Techniques                                     
      C.   Maintenance                                                 
PART TWO: APPLICATIONS                                               
  I   Water Pumping                                                   
     A.   Pump Selection Criteria                                     
     B.   Attachment to Wheel                                          
     C.   Piping                                                      
  II   Other Applications                                              
APPENDIX I   Sample Calculation                                      
APPENDIX II  An Easily Constructed Piston Pump:                     
             by Richard Burton
                            LIST OF TABLES
Table I            Stall Torque per Foot of Width                    
Table II           Horsepower output for a Constant Torque          
                   Wheel per RPM per Foot of Width
Table III          Water Power Input to Wheel per RPM per           
                   Foot of Width to Maintain Constant Torque (hp.)
Table IV           Flow Rate in Imperial Gallons per RPM            
                   per Foot of Width of Wheel Required to
                   Maintain Constant Torque
Table V            Estimated Maximum Output Horsepower for           
                   Constant Input Water Flow Rate Condition
Table VI           Upper Limits on Useable Flow Rates for           
                   Various Size Wheels
Table VII          Approximate Weight Carted by Each Bearing        
Table VIII         Maximum Bearing Diameter Required for            
                   Various Loadings
Table IX           Standard Pipe Sizes for Use as Axles with        
                   Bearing at 12 inches from Wheel Edge
Table X            Estimated Friction Factors                       
Table XI           Peak Pump Piston Velocities for Pump Rod Attached Directly to a Crank on the Wheel
Table XII          Peak Force on the Pump Rod of a Piston           
                   Pump for Various Bores and Heads
Table XIII         Volume of Water in Various Sized Delivery        
                   Pipes ([ft.sup.3])
Table XIV          Inertial Force per Inch of Stroke for Various    
                   Volumes of Water at Various Pump Cycle Speeds
Table XV           Horsepower Required for Water Pumping at         
                   Various Flow Rates and Heads
Table XVI          Quantities of Water Pumped per Stroke for        
                   Various Bore and Stroke Sizes
                            LIST OF FIGURES
Figure 1           Schematic Side  View of Bucket Shape               
Figure 2           Schematic View of Water Distribution on Wheel    
Figure 3           Schematic View of a Slider-Crank Mechanism       
Figure 4           Schematic View of a Trunnion-mounted Pump        
                   and Crank
Figure 5           Schematic View of a Scotch Yoke Mechanism        
Figure 6           Schematic Views of a Suitable Cam-activated      
                   Pump Rod
                       PART ONE: THE WATER WHEEL
     Supplying power to many remote locations in the world from central
generators using customary distribution methods is either economically
unfeasible or will be many years in coming.   Power, where desirable, will
therefore need to be generated locally.  Various commercial machinery
is marketed, but the required capital expenditure or maintenance/running
cost is beyond the capability of many potential users.   Some effort has
been expended at the Papua New Guinea University of Technology to devise
low cost means of generating modest amounts of power in remote locations.
This paper reports on one such project involving the development of low
cost machinery to provide mechanical power.
Regardless of the final use to which the power is put the natural sources
of energy which can be utilized are fairly readily categorized.   Among
           1.            Falling water
           2.            Animals
           3.            Sun
           4.            Wind
           5.            Fossil fuels
           6.            Nuclear fuels
           7.            Organic waste
Sun, wind and water are free and renewable in the sense that by using
them we do not alter their future usefulness.   From continually operating
cost considerations, a choice from among these is attractive.   From
capital cost consideration hydro-power may be very unattractive.   Sun
and wind have obvious natural limitations based upon local weather
conditions.  Furthermore, for technological and economic reasons, solar
power use is presently limited to applications utilizing the energy
directly as part of a heat cycle.  Animals require specialized care and
continuous food sources.  Conversion of organic waste to useable energy
is being experimented with, with varying success, in several parts of
the world.
Whatever the form of the naturally occurring energy, it may be transformed,
if necessary, into useable power in a wide variety of ways.
The choice of method depends upon a complex interaction of too many considerations
to enumerate fully here, but among them are:
       1.         the use to which the power will be put;
       2.         the form in which it will be utilized.   This
                 generally, but not exclusively, falls into the
                 broad categories of mechanical and electrical;
       3.         the economic and natural resources available;
       4.         availability of suitable maintenance facilities;
       5.         whether the machinery must be portable or not.
    In the absence of a specific request from government or any outside
body, the decision was taken based primarily on the obvious abundance of
available water power to investigate broadly the design possibilities for
low cost machinery to produce small amounts of mechanical power.   One
immediately obvious potential application is the generation of electric
power, but for reasons mentioned under "Other Applications" in Part Two
this has not been pursued.  However, in many places, villages are
located at some distance from the traditional source of drinking water.
The principal intended use for the power generated by the machine discussed
in this manual has been the pumping of potable water for distribution
to a village.  The project, thus, has included construction
of a simple pump attachment also.  Several other potential uses are
discussed later.
Limits on the scope of the project were decided based upon numerous
     1.          Minimum of capital expenditure indicated a device
                which could be constructed locally of inexpensive
                materials with no specialized, expensive components
                or machinery required.
     2.          Local construction suggested the desirability of
                design details requiring only simple construction
     3.          Since the installation was likely to be remote (indicating
                a probable shortage of local skilled tradesmen)
                maintenance, if any, would have to be minimal and
     4.          The device should be such that repair, if any, could
                be carried out on-site with parts and necessary tools
                light enough to be carried easily to the site.
     5.          The usual considerations of safety must apply with the
                knowledge that the village children could not/would not
                be kept away from the device.
I decided to concentrate on investigating the feasibility of using the
water wheel, it being the device which seemed most likely to optimize
the criteria set out above.  There are other types of machines suitable
for creating mechanical power from hydro sources, but none, known to me,
can be constructed with such simple techniques requiring so low a level
of trade skills as the wooden water wheel.
Water wheels are in use in various parts of the world now.   Many have
been constructed on an ad hoc basis and vary in complexity, efficiency
and ingenuity of design and construction.   The basic device is so simple
that a workable wheel can be constructed by almost anyone who has the
desire to try.  However, the subtleties of design which separate adequate
from inadequate models may escape those without sufficient technical
training.  The number of projects abandoned after a relatively short life
attests to the fact that designers/builders often have more pluck than
skill.  It seems desirable to attack the problem in a systematic fashion
with an objective of establishing a design manual for the selection of
proper sizes required to meet a specific need and to set out design
features based on sound engineering principles.   I offer the following
as an attempt to meet that objective.
The wheel consists of buckets-to hold the water-fixed in a frame and
arranged so that buckets and frame together rotate about a centre axis
which is oriented perpendicular to the inlet water flow.   Traditional
designs employ the undershot, overshot or breast configurations.   In the
undershot wheel, the inlet water flows tangent to the bottom edge of the
wheel.  In the overshot wheel, the water is brought in tangent to the top
edge of the wheel, partially or fully filling the bucket.   It is carried
in the buckets until dumped out somewhat before reaching the lowest point
on the wheel.  The breast wheel has water entering the wheel more or
leas radially, filling the buckets and then again being dumped near the
bottom of the wheel.  Typical efficiency values vary from as low as 15%
for the undershot to well over 50% for the overshot with the breast
wheel in-between.
We shall concentrate on the overshot wheel as being the most likely choice
to give maximum power output per dollar cost, or per pound of machine, or
per manhour of construction time based upon expected efficiences.   Mitigating
against this choice is the need for a more complex earthworks
and race way with the overshot wheel where the water must be guided in
at a level at least as far above the outlet as the diameter of the
wheel.  The undershot wheel, of course, may be merely set down on top of
the stream with virtually no preparation of raceway necessary.   But in
many streams the rise and fall with heavy local rainfall is spectacular,
so flood protection would be a major consideration for any type of device.
The simplest flood protection is a channel leading from the river to the
installation, with inlet to the channel controlled to keep flood water
in the main stream.  Since a diversion channel would probably be required
anyway, the odds are very good that a suitable location to employ an
overshot wheel can be found for most installations.   In the event that
the overshot installation is impossible, the undershot wheel straddling
the diversion channel is simple to use.
Another consideration which makes the overshot wheel attractive is the
ease with which it can handle trash in the stream.   First, the water
shoots over the wheel and so trash tends to get flung off into the tail-race
without catching in a bucket.  Secondly, there are not usually the
tight spaces between race and wheel in which trash can jam.   Somewhat
closer fitting arrangements are required with breast and undershot
wheels to get good efficiency.
     The wheel is a slow speed device limited to service roughly between
5 and 30 rpm.  Consequently this limits its usefulness as a power source
for electricity generation or any other high speed operation because of
the step up in speed required.  Although not a great problem from an
engineering viewpoint, adequate gearing or other speed multiplying
devices involve increasing complexities in terms of money, potential
bearing problems, and maintenance.
The slow speed is advantageous when the wheel is utilized for driving
certain types of machinery already in use and currently powered by
hand.  Coffee hullers and rice hullers are two which require only
fractional horse-power, low speed input.  Water pumping can be accomplished
at virtually any speed.  Slow speed output of a wheel cannot of
course, directly power a centrifugal or axial pump.   The positive displacement
"bucket pump" or suction lift pump already in use in various
villages normally operates at well under 100 cycles per minute and can
be adapted for use in conjunction with a wheel at slow speed.   This of
course, has been done for hundreds - maybe thousands - of years elsewhere.
Devices of this type have relatively low power output capability.   The
power output depends upon the dimensions of the wheel, the speed and
the useable flow rate of water to the wheel.   As an example, a reconstructed
breast wheel installed in a museum in America of 16 ft. outside
diameter and with bucket depth of 12 in. operating at 7 rpm, with
flow rate of 28 cubic feet of water per second had an estimated power
output of 18.5 hp (14 kw) (calculated at an efficiency of 100%).   Actual
output on that wheel has not been measured but would be less than 10 hp
(7.5 kw).  A 3 ft. OD, 1 1/2 ft. vide model constructed by the author is
in the fractional horse-power range.
Already mentioned once, it is worth emphasizing that a useable water
wheel can be built almost anywhere that a stream will allow, with the
crudest of tools and elementary carpentry skills.
A.  Stall Torque
    The stall torque capacity of the machine, ignoring the velocity
    effect of the water impinging on the stalled buckets, is easily
    calculated by a simple summation of moments about the shaft due
    to the weight of water in each filled or partially filled bucket.
    Obviously this will depend in part on the amount of spillage
    from the bucket which in turn depends on bucket design.  Bucket
    configurations used in the 18th and 19th century varied depending
    on the skill of the builder.  They were empirically determined
    on the criterion of maximizing torque by maximizing water retention
    in the buckets while recognizing that optimum design on this
    criterion also required increased construction complexities.
    Buckets of shape shown schematically in a side view, Fig. 1,

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    were used for overshot and breast configurations.  The straight
    sided buckets are less efficient but simpler to construct.  The
    width of the bottom of the bucket was typically 1/4 of the width
    of the annulus where that configuration was chosen.  Purely
    radial buckets were used in undershot wheels.
    It is convenient to use three of the wheel's dimensions for
    calculation of the torque capacity of the wheel: the outside
    radius, r; the wheel width, w, i.e., from side to side; and the
    annulus width, t, defined as t = (outside diameter - inside
    diameter)/2. See Fig. 1.
    The ratio of the annulus width, t, to the outside radius, r, is
    important to wheel design as there are practical limits to the
    useful values which may be employed.  In this paper only ratios
    0.05 t/r < 0.25 are considered.  For smaller ratios, the potential
    output per foot of diameter of the wheel is considered too low to
    be practical.   For larger values, the buckets become so deep that
    there is insufficient time to fill each one as it passes under the
    race exit.   Also, since the torque and power depend upon having
    the weight of water at the greatest possible distance from the
    wheel axis, increasing annulus depths increases total wheel weight
    faster than it increases power output.  The result is that if more
    power is needed it is better to increase the O.D. than to increase
    the annulus width to values exceeding t/r = 0.25.  In this way the
    wheel weight and the structural components to support that weight
    remain economically most advantageous for a given power output.
    Historically, wheels have tended to have t/r values around 0.1 to
    Upper limits on wheel width have tended toward approximately 1/2
    the O.D. because of structural problems with wider wheels.
    It can be estimated that the overshot wheels operate with the
    equivalent of approximately 1/4 of the buckets full.  That is, the
    total weight of water doing useful work on the wheel is 1/4 of
    the total that would be contained in an annular solid of dimensions
    the same as the O.D., I.D. and width of the wheel.  The actual
    weight distribution of the water is as shown schematically in
    Fig. 2a because of spillage from the buckets as they approach

dmf2x11.gif (600x600)

    the tail race.   If we assume the water is concentrated in the
     annular quadrant shown in Fig. 2b, the stall torque can be estimated
    more easily.   A suitable correction factor could be applied
    to account for actual bucket design, if that refinement were considered
    Results for wheels of various dimensions are given in Table 1.

dmft1120.gif (600x600)

    Experience has shown that many non-technically trained users of
    this information will be more confident of their ability to use
    data given in tabular than in graphical form.  Both will be presented
    here when appropriate.
B.  Power Output
    Power output is the product of the torque on the output shaft and
    the rotational speed of the shaft.  On the assumption that there
    is sufficient inlet water flow to keep the buckets full, thereby
    keeping the torque constant, the power output increases linearly
    with speed.   In a location where there is virtually an unlimited
    inlet water supply, this calculation will give an upper limit to
    the power output that can be expected.
The horsepower output per rpm per foot of width is shown in Table II.

dmft2150.gif (600x600)

     the Table II entry appropriate to the size wheel used times the
     actual speed in rpm times the Width Of the wheel in feet.
     The water power input is the maximum power which the wheel could
     achieve if it were 100% efficient.  It is calculated as the product
     of the water's specific weight, the volume flow rate, and head and
     is given in Table III for comparison.  This entry is also in horsepower

dmft3170.gif (600x600)

     that required to keep the buckets full and is given in Table IV.

dmft4190.gif (600x600)

     by the bucket wall thickness.  This can be corrected for later if
     desired.   The head is assumed here to be the diameter of the wheel.
     The lower edge of the wheel is the highest elevation permission for
     tailrace water without interfering with the wheel and is a logical
     datum.   Inlet raceways are seldom found with a significant slope so
     that velocity effects of raceway water are small.  It seems sufficiently
     accurate to estimate the inlet elevation as the top of the
     wheel.   Any error thereby introduced will be on the conservative
     side anyway.
     Theoretical efficiency values for the wheel using the assumptions
     adopted so far can be found by taking the ratio of the power output
     from Table II and the corresponding power input of Table III.  These
     values, for the water weight distribution assumed before, are about
     50% for the narrow annulus wheels and drop to just under 45% for
     the wider annulus wheels.  As mentioned previously, a well designed
     and constructed wheel will give efficiencies better than this.  This
     comparatively modest value is primarily the result of not considering
     the effect of the water still in the buckets below the
     horizontal centerline.   It reflects the fact that the simplifying
     assumption that the buckets remain full half way down the wheel
     and suddenly dump all their water is not accurate.  That inaccuracy
     is tolerable because 1) it makes the analysis so simple
     and 2) it gives slightly conservative figures for power so that
     almost every reader will be assured of getting sufficient power
     even from wheels of relatively amateurish construction.
     When the water flow is less than the required to fill each bucket
     completely as may be the case for a stream of limited size, the
     power characteristics are altered in that the torque now is a
     function of speed.   Using the assumption of one annular quadrant
     working, but not full, the volume of water, V, in the quadrant is
                   V = Q/4N
           where    Q = volume flow rate ([ft.sup.3]/min)
                   N = speed (rpm)
The weight of water in the annular quadrant at any speed is then
pgV where
                   p = density of water
                   g = gravitational acceleration
With units in feet, pounds, and minutes, the horsepower to be expected
from this annulus working is
                  hp = 2[pi] NT
            where T = pgV[bar]x = pgQ[bar]x
[bar]x is the distance to the centroid of the annular quadrant from the
rotation axis.  It is equal to average diameter.  [D.sub.av], of the annulus
divided by [pi].
           hp = 2[pi]NpgQ[D.sub.av] =  pgQ[D.sub.av]
                -------------------    -------------
                   4[pi]Nx33,000           66,000
     The power is independent of the speed.  The efficiency is the same
     as calculated previously.  It is because the output power is a
     function of the average diameter, that the efficiency drops off for
     wide annulus wheels of a fixed outside diameter.  Potential power
     output from a wheel operating under the conditions of constant flow
     may be estimated most easily by the equation for water input power,
     assuming 50% maximum efficiency and head equal to the outside
     Power under constant flow conditions for various diameter wheels
     is shown in Table V for likely attainable flow rates.  The values

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     entries by factors as shown at the bottom of the table for various
     practical t/r values.   The author's prototype with t/r = .17 tested
     at approximately 150 gpm, gave output power of approximately .06 hp
     in reasonable agreement with the values predicted in Table V.
     Blank spaces are left where flow rates are impractical for the
     wheel size given.   Upper bounds to practical flow rates for various
     wheel sizes are found by multiplying the entry from Table 1 by the
     practical upper limit of speed and width for the O.D. and are
     shown in Table VI.   Lower bounds are subject to considerably more
     guesswork.   On the assumption that it would be uneconomical to
     construct a wheel of width less than 1 ft. and to operate it at
     less than 25% capacity (completely arbitrary choice) for the
     speeds quoted in Table VI the useful lower bounds may be estimated.
     These are indicated by blank under the 100 gpm and
     200 gpm columns in Table V.
                                   TABLE VI
Upper Limits on Useable Flow Rates for Various Size Wheels in Imperial Gallons Per Minute (assuming
        wheel width = 1/2 (O.D.) and peripheral velocity is 5 ft/sec.)
                                    Outside Diameter (ft.)
                  3        4          6         8           10        14        20
Width                    RPM at 5 ft/sec peripheral velocity
+(in.)   32        24         16        12          10         7         5
  2              500       625      1000
  3              700        900       1400      1900         2500
  4              900      1150      1800       2400         8000     
  6                       1650      2600      3500         4500       6000      9500
  8                                 3400       4500        6000       8500     12000
 10                                           5500         7500      10500     15500
 12                                           6500         9000      12500     18500
 16                                                                17000      24000
 20                                                                20000     30000
 24                                                                          35000
     The upper limit to the speed at which the wheel will operate depends
     primarily upon the rate at which the wheel slings the incoming
     water off so that it is not utilized.  This depends primarily
     upon the speed and radius of the wheel and secondarily upon the
     bucket configuration and its relation to the inlet water.
     The figures quoted in Table VI are based on the rule of thumb
     peripheral velocity of 5 ft/sec.  With smaller wheels this is a
     bit high, based on prototype tests.  With the larger wheels the
     peripheral velocity may be as high as 8 ft/sec.
     In summary, the type of power vs. speed curve that one can expect
     from a water wheel is as follows for fixed flow rates: Linearly
     increasing from zero speed up to the speed at which the buckets
     can no longer be completely filled by the prevailing flow, then
     constant up to the speed at which significant amounts of water are
     rejected from the wheel by slinging action, thereafter decreasing
     in proportion (roughly) to the square of the speed.
C.  Bucket Design
     The optimum bucket design is taken to be that which produces the
     greatest torque on the wheel shaft.  The upper limit to this condition
     is that the buckets fill completely at the top, carry the full
     water weight with no spillage to the bottom and dump their loads
     there.   There is not a practical method of achieving this maximum.
     With fixed buckets, the best we can do is minimize spillage from
     the buckets as they travel from the top, where they are filled,
     to the bottom where they should be empty (so as to limit losses
     incurred by carrying water up the back side of the wheel).
     There are broadly two styles of bucket as shown in Fig. 1.  In the

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     straight sided bucket the limits on the angle the bucket makes
     with the tangent at the O.D. or I.D.  (See Fig. 1) are from tangential
     (0[degrees]) to radial (90[degrees]).  With tangential buckets, the filling
     process is slow at the top because of the very shallow angle with
     respect to the incoming(nearly horizontal) water.  Furthermore the
     emptying process at the bottom is not complete until after the
     bucket passes bottom dead centre.  This carries some water up the
     back side and consequently reduces the efficiency.  At the other
     extreme, radial buckets are nearly empty by the time they have gone
     1/4 turn from the top because the bucket wall is then horizontal.
     We can estimate the optimum angle by assuming that the greatest
     effect will be due to the bucket whose weight is acting at the
     greatest distance from the shaft.  By drawing buckets of various
     angles we can estimate, graphically, the optimum.  While the
     tangential bucket carries the greatest amount of water, its centroid
     distance is not a maximum The maximum occurs at a bucket
     angle (to the tangent at the I.D.) of about 20[degrees].  While the
     amount of water still retained at 90[degrees] after top dead centre by
     this bucket shape is about 20% less than for the tangential bucket, the
     loss is compensated for in the early filling and early emptying.
     Especially on emptying, the 20[degrees] inclination is a major factor
     since the length of the bucket (distance from I.D. edge to O.D. edge) is
     more than 30% shorter than the tangential bucket.  With a 30[degrees]-bucket,
     the weight carrying capacity at 90[degrees] after top dead centre is down
     to about 65% of the tangential, a figure which is so low that it
     cannot be compensated for by the secondary effects on efficiency
     such as filling and emptying.  This graphical technique, while of
     no additional value in designing any individual wheel, also shows
     that the assumption of the distribution of water over an upper
     quadrant is a reasonable one for estimating torque.
     I recommend the bucket wall angle be kept between 200 and 250 to
     the I.D. tangent.
     The use of flat bottomed buckets does not significantly change the
     water carrying capacity for wall angles of 20[degrees].  The purpose is
     to decrease the distance the water must travel to empty the bucket.
     Its use is increasingly beneficial at large t/r ratios but the
     builder must accept that the construction is somewhat more complicated
     than that of the straight sided bucket.  Bottom widths should
     be approximately 1/4 of the annulus width, t.  This will cut 25%
     off the side width with the attendant saving in travelling distance
     to empty the bucket.   The significance of this is that less water is
     carried up the back side of the wheel.  Any water carried up the
     back side lowers the efficiency.  I cannot give figures for the
     improvement of efficiency using flat bottomed buckets but it seems
     hard to imagine as much as ten percentage points.
     Historically, bucket shapes have varied considerably.  They were,
     as far as I can determine, chosen emperically.  (In a historical
     sense this is a euphemism for "arbitrarily" or "by educated guesswork").
     By the time engineers, rather than carpenter-craftsmen,
     were considering the problem the water wheel's usefulness was
     already on the decline).   Even in relatively recent manuals for
     construction, circa 1850, while wheels were still in general use
     in the U.S., bucket side angles of 45[degrees] were recommended - a choice
     which can easily be shown to be less efficient than smaller angles.
     The 20[degrees] - 25[degrees] figure is, however, in close agreement with the
     design of two wheels that I know are still in use in the U.S.
     The number of buckets to use depends upon the volume consumed by
     the bucket wall material.  The ideal wheel has closely spaced
     buckets of very thin wall thickness.  A reasonable figure to design
     by is that not over 10% of annular volume should be consumed in
     bucket material.   Typical values for the size wheels discussed here
     would be 25 - 30 - 1/4 in. thick buckets on a 3 foot wheel and
     50 - 1-1/4 in. thick buckets on a 14 foot wheel.
D.  Bearing Design
     The wheel itself has only one rubbing or sliding part subject to
     wear, viz.   the bearings upon which the axle is supported.  Standard
     bearing design is covered in almost any machine design text.  In
     the manufacture of such a device as is discussed here, the value
     of such   standard" bearings is questionable.  Fully weather-proofed
     ball or roller bearings are too expensive and complicated to satisfy
     the initial criteria.
     Bronze bushings with suitable shaft material would be satisfactory
     but lubrication and replacement both present problems.  The use of
     wooden bearings is, I think, the best alternative for several reasons:
        1.   Simplicity of manufacture with local skills.
        2.   Availability of replacement parts.
        3.   Negligible cost.
     Wooden bearings are used commercially for such applications as washing
     machine wringer bearings under conditions simulating those proposed for
     the wheel.   Rock maple, lignum vitae, and various species of oak are
     used commercially, but when these are not native to the country of
     intended use, substitutes may be found.  Among woods with fairly
     widespread distribution, others which may reasonably be expected to be
     satisfactory are beech and red mangrove.  Forestry departments, when
     they exist in a country are generally in a position to make useful
     In the absence of any specific knowledge, the general rule is "the
     harder, the better".
     An estimate of allowable loading based on experience with commercially
     available wooden bearings would be around 75 psi (for oak) to 150 psi
     (for lignum vitae) for orientations with the sliding surface parallel
     to the grain and about 150 to 300 psi respectively for end grain use.
     If the wood used has strength and density properties comparable to
     those mentioned above, it is likely that safe loading would be about
     100 psi parallel to the grain and 200-250 in end grain usage.  It
     remains to be seen what the wear resistance at these pressures will
     be, but structurally the figures given can be used with confidence.
     Length to diameter ratios of bearings in this application would
     reasonably be expected to be about unity and on that basis the
     sizes of the bearings can be estimated for wheels operating at
     maximum output.   An allowance for the weight of the wheel itself
     is made on the basis that the volume of wood required is approximately
     equal to the volume of water carried at stall and that the specific
     gravity of wood operating constantly in water is about unity.
     Table VII shows the approximate weight on each bearing per foot of
     width of wheel.   Total weight carried on each bearing is then the
     product of the Table entry and the width of the wheel in feet.  This
     of course assumes that the wheel is simply supported at each end of
     the shaft and does not allow for additional loads imposed by the
     attached machinery.   It is important that significant loads due to
     the Table VII values for the purposes of determining bearing size
     from Table VIII for the side of the wheel where the machinery is
     attached.   In this event the bearings will apparently need to be of
     different sizes.   In practice, unless the indicated sizes are very
     different, we usually make both the size indicated by the larger load.
     Thus one is really longer than it needs to be.
     Bearing diameters required to support the various loads are given in
     Table VIII calculated on the basis of 100 psi in parallel useage and
     200 psi for end grain useage and L/D = 1.  Values are given to
     20,000 lb. to allow for the largest reasonable bearing loads.
                                   TABLE VII
Approximate Weight Carried by Each Bearing Excluding Loads Due To Attached Machinery
(per foot of width of the wheel) (lb.)
                                 Outside Diameter (ft.)
                 3       4         6        8         10         14          20
  2               24      32       50
  3               35      47       70        95        120
  4               44      60       89       125        160
  6                       86      140      185        235         335        470
  8                               180       240       305         440         675
 10                                        290        370         530        765
 12                                        330        445        635         920
 16                                                             820       1215
 20                                                            1020       1500
 24                                                                       1760
                              TABLE VIII
     Minimum Bearing Diameter Required for Various Loadings (in.)
                                        Load (lb.)
                       100    200   500   ]000    2000   5000   10000    20000
     Parallel Useage    1     1-1/2 2-1/4 3-1/4  4-1/2   7      10      14
     End Grain Useage   1/2   1     1-3/4 2-1/4   3-1/4  5      7        10
     These bearings are assumed to be steel on wood. In the likely event
     that, especially in larger sizes, the bearing is considerably larger
     than the required shaft size, a "built up and banded" bearing may be
     used. A wooden cylinder is built onto the shaft at the bearing location
     such that the cylinder O.D. is the necessary size. Then steel bands
     are bent and fastened to the cylinder. The criterion for design in
     this case is that the product of the diameter and the total width (sum
     of the individual widths) of the bands equals or exceeds the square
     of the entry in Table VIII for the corresponding load and grain
     If it is possible to arrange for and be certain of, suitable maintenance,
     a steel shaft in bronze bushings mounted in commercial
     plummer blocks (available from hardward suppliers) is probably the
     best choice. Proper alignment may be a minor problem but is usually
     fairly easy to overcome. This choice involves additional initial
     expense and is justified only if maintenance can be guaranteed
     regularly and frequently.
E.   Shafts
     Shafting may be wooden or steel. The diameter is of course dependent
     upon which material is used and the dimensions of the wheel. Minimum
     permissible shaft diameters d, may be estimated from the equation
     for stress for solid metal shafting
            [d.sup.3] = 16 [square root][M.sup.2] + [T.sup.2]
     In this equation M is the maximum bending moment occuring where
     the wheel sidewall attaches to the shaft. It can be estimated as
     the product of the bearing load (entry in Table VII for the appropriate
     wheel) and the distance from the wheel side wall to the
     centre of the bearing. In the interest of keeping the shaft as
     small as possible, it is therefore desirable to locate the bearings
     as close to the side of the wheel as possible. (Note that in most
     cases, it is not critical to include the additional machine load
     on the bearing, discussed in connection with the use of Table VIII.
     It must be included only when the external machine load times the
     distance along the shaft from the point of application of the load
     is larger than the bearing load from Table VII times the distance
     along the shaft from the bearing to the point where the wheel is
     T is the torque acting on the shaft and a conservative estimate
     is found from Table I. S is the allowable shear stress of the metal.

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     (13,000 is used in the example in Appendix 1.)
     For solid wooden shafts two equations are used and the larger diameter
     of the two results is chosen as the diameter of the shaft.
          [d.sup.3] = 16T
          [d.sup.3] = 32M
     where S, T and M have the same meaning as before. However, the value
     of S is typically 150 to 300 psi for hardwoods. B is the allowable
     bending stress and has a value of about 1500 psi for typical hardwoods.
     If wood is used it must be sound and free from longitudinal cracks.
     For hollow shafting like a pipe, the equation to determine the outside
     diameter is:
            [d.sup.3] = 16[square root][M.sup.2] + [T.sup.2]
                                [pi]S(1 - [k.sup.4])
     where K = Ratio of inside to outside diameter.
     The values of O.D. and I.D. are standardized for pipes. For bearing
     loads tabulated in Table VIII, on the assumption that the centre of
     the bearing is 1 foot from the edge of the wheel, the standard pipe
     sizes shown in Table IX should be satisfactory. Table IX automatically
     allows for torque that would be reasonable to expect from a wheel of
     such a size that the bearing load would be given in Table VIII.
     The values are approximate only since exact values cannot be given
     until all the details concerning the loads due to the attached pump
     or machine are known. The values given should serve as a guide only
     and the final decision should be checked against the equation to be
     sure. When making substitutions, in assembly, of one pipe size for
     another, it is permissable to use larger pipe than shown in Table IX
     but not smaller pipe.
                                TABLE IX
     Minimum Standard Pipe Sizes for Use as Axles with Bearings at 12
                         inches from Wheel Edge
     Bearing load (lb)   100   200    500    1000   2000   5000    10000
     Pipe Diameter (in) 1"  1 1/2"   2 1/2"    3"     4"      6"       8"
     Comparing these figures with the required bearing diameters of Table VIII,
     it is obvious that when using pipe or solid steel shaft, the
     bearing will need to be of the build up type when using wooden
     bearings. An alternative is to use a shaft whose size is selected
     according to the needs of the bearing size. It will be much stronger
     (and heavier) than necessary but may save some work. With wooden
     shafts, the required shaft diameter will usually exceed the required
     bearing diameter and then one has the choice of reducing the shaft
     diameter at the bearing location (but only there) or of using larger
     bearings. In either case the shaft must be banded with steel, sleeved
     with a piece of pipe or given some similar protection against wear
     in the bearing.
F.   Minor Considerations
     We have considered all the major theoretical aspects of selection of
     sizes etc. to meet specific requirements. All have been based on an
     assumed efficiency of 50% - a figure which is readily achievable in
     practice with an overshot wheel. There is one minor consideration
     over which the design/builder has control which may affect the
     effiency slightly. The raceway exit should put water onto the wheel
     slightly before top dead centre. The exact location is a function of
            1.   flow rate and raceway inclination which affect
                the inlet water velocity; and
            2.   the bucket sidewall angle and peripheral velocity
                which affects how smoothly the inlet water comes
                onto the wheel.
     Exact calculations hardly seem justifiable for a machine which by
     its very nature is as crude and (relatively) inefficient as this.
     Let it be sufficient that the designer-builder get the water in
     approximately tangent to, and at the top edge of, the wheel.
A.   Materials
     Most wheels are wood, of course, though they need not be. Among
     the considerations for selection of the proper material are the
     ease of working, cost, availability and durability. The average
     carpenter can make a proper choice on all these except perhaps the
     latter. Forestry departments in many countries can provide this
     information on potentially useful species. Others which would
     probably be suitable are mentioned in the section on bearing design.
     Builders of water wheels may naturally consider a "marine" plywood
     as a likely material. It is convenient to work with but the quality
     varies widely around the world. Because even the best grades have
     a doubtful durability when operating continuously in water unless
     painted, plywood should be chosen only when it can be well cared for
     or when a relatively short life is anticipated
     Regarding the framework to mount the wheel on, bamboo might seem a
     logical choice in many countries but the durability is such that
     it probably would require more long term care and replacement than
     other materials. The species listed for the bearings in section
     IV D are all fairly durable under constantly wet conditions and
     should be the first to be considered.
B.   Construction Techniques
     Any person sufficiently skilled to build a water wheel will probably
     also be sufficiently knowledgeable to work out most of the construction
     details. This manual is intended to give the engineering groundwork
     necessary to select the proper overall size of wheel to meet a given
     need and to make sure that prevailing water supplies are, in fact,
     adequate. However, a few general suggestions may help the reader
     avoid some pitfalls.
     Attachment of the wheel sides to the shaft, whether the sides are
     spoken or solid, can be accomplished in many ways. If a steel shaft
     is used, a thin flange plate can be welded to the shaft (if such
     facilities are available) and this greatly facilitates the attachment.
     With a solid side plate there is no further problem but if
     the spokes are used, the bending in the spokes at the flange must
     not be so great as to break the spokes. The spokes should be
     attached to the flange with two or more bolts and the distance
     required between the bolt holes to support bending varies with wheel
     diameter and the rigidity of the spoke/wheel joint. For a flexible
     joint the required a distance would be approximately 1/10 to 1/12
     of the outside diameter of the wheel. For example, on a 12 foot
     wheel, when using radial spokes attached to a flange by 2 bolts
      and to the wheel side plate (annular ring) by one, the flange
     bolts should be about a foot apart on each spoke.
     Alternatively if the spokes are quite rigid and firmly attached to
     annular ring of the wheel as with 2 or more bolts, the bolt hole
     separation can be reduced to 1/20 of the diameter of the wheel at
     the flange.
     A simple spoke arrangement to use is pairs of spokes, (one spoke
     of each pair on each side of the shaft) crossing at right angles
     to make a shape like the tic-tac-toe or noughts and crosses symbol.
     The wheel axis runs through the centre square and the extremities
     of the lines are attached to the wheel annulus.
     Any glue used should be highest quality waterproof glue for obvious
      reasons. Resorcinol glue is probably the best choice.
     Bucket attachment to the side wall may be made by either grooving
     the side wall to receive the bucket edge or by attaching strips to
     the inside of the side wall to fasten the buckets to. There is an
     advantage to the annulus shape of side wall in that the inside of
     the bucket is accessible from the I.D. This makes closing off the
     inside of the bucket simpler because the necessary pieces can be
     inserted through the I.D. With solid sidewalls, the buckets must
     be made complete and non-leaking before the sidewall is attached.
     This is by no means impossible but may be more difficult.
     If a solid sidewall is used, holes should be drilled adjacent to
     the bucket bottom into the space between the bucket and the haft
     to let any leakage water out. A solid side wall would not commonly
     be used. Spokes offer several advantages.
     Numerous books are available to give helpful hints on various
     construction techniques for the truly amateur builder.
C.   Maintenance
     The wood used may be painted or varnished for a protective coating.
     This will obviously extend the life of the wheel. Periodic repainting,
     if desired, can be carried out. The decision on painting
     must be made on purely economic grounds. If a very durable wood has
     been used initially, painting is a luxury. If a somewhat less durable
     species is used, painting is probably cheaper and easier than early
     replacement or repair of the wheel.
     The only major maintenance problem is in bearings. Generous allowances
     have been made in the figures in Table VIII but the bearing
     will still ear. This will drop the wheel from its original position.
     Shimming under the bearing block will compensate for this. Bearing
     replacement, when the block is completely worn through is a simple
     Lubrication is totally unnecessary with lignum vitae or commercially
     processed maple, if available. With the other species, we can not make
     such a flat statement. Generally speaking the bearing should be made
     from the hardest wood available and lubricated as needed. Oils and
     grease in small amounts will probably do no harm and may slow the wear
     rate. Pig grease and tallow would certainly be harmless and might help.
                        PART TWO: APPLICATIONS
A. Pump Selection
   The only type of pump which is reasonable to use at the slow speed
   of the wheel is a positive displacement pump.  They are called by
   various names such as bucket pump, lift pump, piston pump, windmill
   pump and occasionally even simply by brand name such as "Rocket"
   pump.   Numerous models are available commercially and vary in cost
   from a few dollars for small capacity pumps to several hundred for
   high capacity, high head, durable, well manufactured units.  Units
   can be manufactured at low cost in the simplest of workshops.
   Details are given in Appendix II.
   Such pumps may vary in bore size, stroke length and head capacity.
   There is a practical limit to the speed at which they can operate.
   This is usually above the frequency of the fastest of wheels.  A
   frequency of speed multiplier such as a multi-lobed cam or a gear
   set may be used, but these more complicated pumps and mechanisms,
   while increasing the efficiency of the pumping process, contravene
   the criteria of Section II, Part One for simplicity and will not
   be discussed.  We will discuss only very simple pumps.
   Even with simple single or double acting pumps there are certain
   problems.   one single acting pump attached to the wheel will cause
   speed surges on the wheel because of the fact that actual pumping
   takes place only half the time.  The other half is spent filling
   the cylinder.   During this filling stage considerably less wheel
   torque is required than when actually pumping.  The speed surge
   can be partially overcome by using
        1. two single acting pumps 180[degrees] out of phase so that one
           of the pumps is always doing useful work;
        2. a double acting pump which has the same effect as 1.
           but is built in one unit; or
        3. best of all two double acting pumps 90[degrees] out of phase.
   Such use of multiple simple pumps will also improve the overall
   efficiency of the system.   (In general one unit can be attached
   easily to a crank at each end of the wheel shaft).
   There are pressure variations in the delivery line which depend
   on several factors.   As long as the peak pressures do not exceed
   the capacity of the pump and related mechanism, nor stall the
   wheel, such variations will cause no harm.  The pressure peaks
   can be damped with an air chamber in the delivery line or smoothed
   by using two or more simple pumps as mentioned in the preceeding
   paragraph.   The possibilities are so numerous and the details
   sufficiently complex that they cannot all be included here.  A
   pump expert or pump design manual should be consulted if the design
   ideas given here seem insufficient for the user's needs.
   In general the pressure peak will be a function of the peak piston
   velocity, the pump bore size, the delivery pipe size, the length
   of the delivery pipe and the type of pipe used.  When speaking of
   pump performance and design requirements, the term "head" is
   encountered often.   It is a means for visualizing the fluid pressures
   involved in the pump or attached pipes.  It means the height
   of water in a vertical pipe necessary to produce, at the bottom
   of the pipe, the pressure being referred to.  The pressure is an
   actual system will not, in general, be produced just by a static
   column of water but it will be the same as if it were.  It's
   just a handy shortcut often used by fluids engineers.  The head
   The head required at the pump outlet will be made up of two main
       1. the actual change in elevation to the delivery pipe
          exit, i.e. the (vertical) height of the hill; and
       2. friction loss in the pipe which is given by the
                            L V
          friction loss = f - -
                            D 2g
          where f = friction factor obtainable from handbooks or
          Table X
          L = length of pipe
          D = inside diameter of pipe
          V = velocity of water in the pipe
          g = gravitational acceleration
   (Note: Units for dimensions must be consistent. See Appendix I
   for an example of the use of this equation).
                                TABLE X
           Estimated Friction Factors for Cool Water
               Water    Velocity   (ft/sec.)
                     1         5          10
   Old Iron Pipe    .045     .040         .038
   New Iron Pipe    .030     .023         .021
   Plastic Pipe     .025     .017         .015
   It is evident that this becomes a major factor in very long pipes,
   in small diameter pipes, or with high velocities.  The water velocity
   in the delivery pipe is a function of the peak pump piston
   velocity and the ratio of the pump bore size and the delivery pipe
   size.   Peak piston velocity for pumps attached directly to the
   wheel is given in Table XI for various strokes and wheel speeds.
   From Table XI, the delivery line velocities can be estimated
   simply by multiplying the Table XI entry by the ratio of the pump
   bore area and the delivery pipe area.  That is, piston velocity
   times piston area = water velocity in delivery pipe times pipe bore
   As a rule of thumb, this resulting delivery pipe velocity should
   be a maximum of 10 ft/sec. in short runs, and even smaller for
   very long pipes.   The peak head required of the pump will be the
   sum of the two different heads mentioned, i.e., elevation change
   plus friction loss head.
   The bore size (piston area) and peak head occurring during pumping
   will determine the force required at the pump rod since force on an
   area is the product of the area and the pressure acting on that
   area.   Figures for force at the rod are given in Table XII.   No
   allowance is made for rod diameter so the figures given are conservative.
   Bore sizes quoted are commercially available.
                               TABLE XI
Peak Pump Piston Velocity (ft/see) for a Pump Rod Attached Directly to a Crank on the Wheel
Wheel Speed                 Stroke (in.)
              2 1/4       4        6              8        10      12
     5         0.048    0.087     0.129           0.172    0.216   0.260
     6          .059     .104      .156            .208     .259    .310
     8          .078     .138      .207            .276     .345    .414
    10          .097     .173     .259           .345      .432    .518
    12          .117     .208      .312            .416     .520    .624
    15          .147     .260      .390            .520     .650    .780
    20          .195     .345      .518            .690     .865   1.04
                               TABLE XII
Peak Force on the Pump Rod of a Piston Pump Required for Various Bores and Heads (lb.)
               Peak Head (ft.) change in elevation and friction loss
Pump Bore (in.)    50    100    200    300     400    500
  1 1/4                     30    60    110     370    220    280
  1 1/2                     40    80    160     240    320    400
  1 3/4                     60   110    220     320    430    540
  2                         70   140    270     420    560     700
  2 1/2                    110   220    440     660    880   1100
  3 1/4                    185   370    740    1120   1480   1850
  4 1/4                    315   630   1260    1890   2520   3150
   These figures are required to design such parts as clevis pins
   (if used) and to determine that, if the pump rod is attached directly
   to the wheel, that the crank arm length times the entry in Table XII
   does not exceed the torque capacity of the wheel as given by
   Table I.
   Of course, if levers or other torque/force multiplying devices are
   used, appropriate calculations at the wheel can be made.  The force
   at the pump rod still remains as given in Table XII.  The velocity
   given in Table XI must be adjusted for the change in crank arrangement.
   Additionally, if the line is very large so that a large mass of water
   must be accelerated on each stroke, the inertial forces can become
   greater than the pressure forces.  The inertial forces can be
   estimated with the aid of Tables XIII and XIV.
                                  TABLE XIII
         Volume of fluid in various sized delivery pipes ([ft.sup.3])
                           Pipe length  (ft.)
   Nominal pipe size      50    100    200     500   1000
          1"             .3     .6     1.2      3      6
          2"            1.16    2.32    4.65   11.6   23.2
          3"            2.46    4.91    9.82   24.6   49.1
          4"            4.38    8.78   17.50   43.8   87.5
                               TABLE XIV
   Inertial force (lb.) per inch of stroke for various volumes of fluid at various pump cycles speeds
   Pump Cycles per
   Minute            Volume of Fluid in delivery pipe([ft.sup.3])
                .5         1        2      5        10      50     100
      5              .133     .266    .533    1.33    2.66    13.3     26.6
     10              .577    1.14    2.29     5.77   11.4     57.7    114
     15             1.20     2.40    4.80     12.0   24.0    120      240
     20             2.14     4.27    8.33    21.4    42.7    214     427
     25             3.31     6.61    13.2     33.1   66.1    331      661
     30             4.78     9.65    19.1     47.8   96.5    478      965
   This inertial force is at its peak just as the piston starts its
   pumping stroke.   At this time the friction loss is zero because
   the delivery pipe velocity is zero.  Hence the total rod force at
   the start of the stroke ill be equal to the force due to the
   static head plus the inertial force.  It should be compared with
   the rod force when the friction loss is a maximum and the components
   designed to withstand the larger of the two.
   We can calculate the power required to accomplish pumping under
   various conditions of head, flow rate and pump type.  These figures
   are given in Table XV for steady flow and are adjusted for unsteady
   flow explained below.
   This is the theoretical minimum power input required to the pump
   under steady conditions.
   Under the unsteady conditions of a piston pump, to estimate the
   water wheel power capacity required, multiply the table entry by
   2 1/2 for one single acting pump, by 2 for one double acting pump
   or two single acting pumps 180[degrees] apart or by 1.5 for 2 double acting
   pumps 90[degrees] apart.   This will give an estimate of the size of wheel
   and flow rate required to the wheel.
   As mentioned near the beginning of this section, there will be
   speed fluctuations in the wheel which may be pronounced in smaller
   wheels working near their capacity.  This is no particular disadvantage
   so long as the stall torque capacity of the wheel exceeds
   the minimum torque necessary to keep the pump moving.  The magnitude
   of the fluctuations decreases with double acting or multiple
   pumps installations and where the mass of the wheel is such that
   a flywheel action begins to take place.
                               TABLE XV
   Horsepower Required for Water Pumping at Various Flow Rates and Heads (both assumed steady)
                               Total Head (ft.)
     Flow Rate
   (      50          100   200        300     400       500
         5                 0.00125    0.0025   0.0050   0.0070     0.01     0.0125
        10                  .0025      .0050    .01      .015       .02      .025
        25                  .00625     .0125    .025     .0375      .05      .0625
        50                  .0125      .025     .05      .075       .1       .125
       100                  .25        .50      .1        .15        .2       .250
       150                  .0375      .0750    .15      .225       .3       .375
       200                  .05        .1       .2        .3         .4       .500
       250                  .0625      .125     .25      .375       .5       .625
       300                  .075       .15      .3       .45        .6        .75
       500                  .125       .25      .5       .75       1.0      1.25
      1000                  .25        .5      1.0        1.5       2.0      2.5
   "See text for correction factors for various types of pump sets."
   The volume pumped per stroke varies slightly with the design of
   the pump and with the bore and stroke sizes.  One commercial
   manufacturer quotes figures which can be taken as representative.
   These are given in Table XVI.
   B. Method of attachment to wheel
   In activating any piston pump, it is done ideally, such that
   straightline motion of the piston rod is achieved.  Any bending
   in the rod puts undue side loads on the discharge head seal and
   on the piston bucket.   Straightline motion mechanisms are described
   and discussed in textbooks, so I will not endeavor to
   give details of the common mechanisms.  The books seldom mention
   however, the practical problems which arise when trying to use
   such mechanisms.   Nor do they usually compare advantages and disadvantages.
   I will mention some possible mechanisms along with
   the advantages and potential problems.
   A slider and crank mechanism (See Fig. 3) is attractive as a simple

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   device with the advantage of requiring no special techniques to
   prevent bending moments on the pump plunger.  Stroke is easily adjustable
   by attaching the crank pin to the wheel shaft via a flange
   plate with holes drilled at various distances from the rotation axis,
   through which the crank pin can be fixed.  Unless a double acting
   pump is used, the pumping stroke and return stroke will have different
   forces on the crank pin resulting in non-uniform wheel rotational
   speed (unless compensated for by other means - such as attaching
   single acting pumps operating 180[degrees] out of phase).  This non-uniform
   motion can be alleviated to an extent by attaching the slider
   (pump axis) offset from the wheel axis.  It then becomes a form of
   quick return mechanism.   This, however, increases the side load on
   the slider during the return stroke, which necessitates moving the
   slider bearings apart (increasing the slider length) to maintain
   the same slider bearing pressure as with the symmetrical arrangement
   if bearing pressure and the resulting frictional drag on the slider
   become large enough to cause a problem.  Lubrication of the slider
   bearing presents a problem.  Although precautions can limit somewhat
   the exposure to water in the bearing, it is unlikely that the
   bearing can be completely protected.  Pressure grease fittings
   using a suitably wash-resistant grease might prove suitable.
   Packing box style lubrication with oily felt or rags could also
   be successful.   Both methods rely on periodic attention, which could be
   of an intolerable frequency.  There are also the crank pin and clevis
   pin at the slider to be lubricated.  Finally, alignment is a potentially
   tricky problem because of the narrow tolerance allowable on
   parallelism of the wheel shaft and crank pin and on perpendicularity
   of the plane of the slider crank mechanism with the wheel shaft.
   One major advantage compared with the next method discussed is that
   since the pump body can be fixed if the alignment is sufficiently
   accurate, the connection with the distribution pipe can be rigid.
                               TABLE XVI
  Quantities of Water Pumped per Stroke for Single Acting Pumps of Various Bore and Stroke Sizes
                              (Imperial Gallons)
                             Stroke (in.)
Bore (in.)     2 1/4        4         6       8         10         12
      1 1/4             .009       .016     .023     .032      .040      .049
      1 1/2             .013       .023     .035     .045      .057      .069
      2                 .023      .040     .062     .082      .102      .122
      2 1/2             .035       .064     .095     .127      .159      .191
      3                 .052      .092     .139     .184      .230      .278
      3 1/2             .070       .125     .187     .248      .312      .276
      4                 .092      .163     .245     .227      .410      .489
      5                 .143      .255     .382     .510      .638      .765
   A second method of attachment is to pivot the pump body about an
   axis parallel to the wheel shaft (as on trunnions), attach the
   pump rod end to the same kind of crank pin as before and let the
   pump oscillate side to side as the piston goes up and down.  (See
   Fig. 4).   This eases the difficulty of the alignment problem involving

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   the plane of the crank mechanism previously discussed but
   introduces new complications.  The pump rod is subjected to side
   loads.   This is ordinarily intolerable at both the gland and the
   bucket but fortunately is easily overcome by a simple frame
   attached to the pump with sliding bearing surrounding the crank
   pin which the pump rod end (at the crank pin) then slides in.  The
   bearings absorb all the side loads required to cause the oscillation,
   leaving the pump rod loaded linearly only.  Side loads on
   these slider bearings would be smaller than the side loads on the
   slider in the slider crank mounting so that the sliding bearing
   problems with this technique are somewhat simpler.  A serious objection
   to this mounting method is the necessity for a flexible
   connection from the pump to the distribution pipe.  If the reader
   intends to build his own pump, which would be likely if considering
   this particular arrangement, plan to have the outlet of the
   pump colinear with the trunnion axis.  In this way a simple seal
   to allow the pump exit pipe to oscillate in the delivery pipe will
   suffice.   This method of flexible connection will probably be the
   most durable.
   The scotch yoke mechanism (See Fig. 5) is simple and direct but may

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   require more sophisticated machining than available equipment will
   allow.   Furthermore, there is the potential danger of excessive
   wear and short life if the lubrication is insufficient.  This is not
   generally a suitable mechanism for unattended use in harsh conditions.
     A cam activated pump rod is an attractive alternative.  It
     eliminates the need for any linkage, simplifying the alignment
     problem and eliminating some parts.  Side loads on a properly
     designed profile would be very small and a sliding bearing on
     the outboard end of the pump rod would easily absorb it.  A
     suitable cam profile is given schemetically in Fig. 6.  Force for

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     the return stroke can easily be supplied by a properly weighted
     pump rod and the simplest location for such weight would be
     immediately above the follower plate.  Solid mounting of the pump
     in this case allows rigid supply piping to be attached directly
     to the pump.
     A pump bought ready made with a handle can be attached quite simply
     by a rod suitably aligned between a crank on the wheel and the free
     end of the pump handle.   Then force and velocity calculations must
     be modified.
     Various straight line motion linkages are easily constructed.  They
     have the advantage of simplicity and durability even under harsh
     working conditions.   Many such linkages are discussed in books on
     Theory of Machines and Machine Design.
     One simple technique to achieve straight line motion seldom seen
     in texts on machine design is to run a cable over a pulley such
     that the end of the cable attached to the pump is colinear with
     the pump rod.   The other end can be attached to the wheel crank
     and the cable provides sufficient flexibility that no solid linkage
     is needed.   An alternative to this approach is to link the wheel
     crank to a sector of a pulley sheave in such a way that the sheave
     oscillates as the crank rotates.  With the cable wrapped far enough
     around the sector so that the cable always remains tangent to the
     sector and fixed there, the free end of the cable can be attached
     colinear with the pump rod to provide straight line motion.  This
     is the mechanism used on oil drilling rigs.
     The cable, as a part of the drive mechanism, can be made very long
     in order to drive pumps located at a considerable distance from
     the wheel itself.   Such a technique provides the means to power,
     for instance, a shallow bore pump in the middle of a village using
     power generated at a stream some distance away.
C.   Piping
     For any water distribution system where the water must be transported
     to a higher elevation, piping is usually required.  There
     are alternatives such as buckets on an endless belt, etc., but that
     is outside the scope of this manual.
     The choice will probably fall between polythene and galvanized
     iron pipe.   There are advantages and disadvantages to both.  I
     shall endeavor to give some helpful information to aid the designer
     in making the best choice.
     Polythene pipe is available in long (now around 200 meter) lengths
     so numbers of couplings and joints are greatly reduced compared to
     the iron pipe which comes in short lengths (21 1/2 ft typically).
     It is flexible (softer, weaker and more elastic in strict engineering
     terminology) and for this reason is more susceptable to damage
     from bush knives, rocks, pig hooves, etc.  Its strength is limited
     such that it is rated to support at best 300 foot normal working
     heads at standard conditions.  The strength is strongly temperature
     dependent however, and at 120[degrees] F head capacity is down to
     185 ft maximum.   It is not fire resistant.   Consequently in open
     country it would probably need to be buried.  If the local soil
     is very rocky, the burying process must be done with great care
     to keep the pipe from suffering rock (penetration) damage.  Sand
     is usually used as a bed and cover.
     Iron pipe can generally simply be laid on the ground with rock
     piles to support it through low spots.  It will support more than
     1000 ft heads with plenty of safety margin.  For heads to get
     that high, the system required will be more sophisticated than
     can be made by the techniques detailed in this manual.
     Prices for the two types are competitive in the higher strength
     grades of polythene but for low pressure systems, polythene may
     be substantially cheaper.
     Polythene has a smoother bore so that friction losses are less than
     with iron pipe, although this would not likely be a significant
     factor.   It becomes more important in long gravity feed systems.
     Weight of a given length is vastly different.  100 ft of high
     strength 2" polythene weighs 60 lb while 100 ft 2" standard iron
     pipe weighs 357 lb.   Therefore, long distance transport by hand to
     very remote areas might influence the decision for polythene even
     in spite of its other shortcomings.
     While water pumping is an obvious use for the water wheel, other
     machinery can be adapted to use the mechanical power output of the
     wheel.   It is not the intention of this section to attempt to
     enumerate all the possible applications.  Rather, I include this
     section to offset any impression that may have been given by the
     preceeding section that water pumping is the most important, or
     perhaps only use to which the wheel may be put.
     Generation of electricity is a possibility which will probably
     spring to the minds of most people reading this manual.  There
     are wheel driven electric generators in operation in Papua New
     Guinea today but the number of attempts and failures testify to
     the fact that it is not a simple, cheap task to make a successful
     rig.  The principal difficulties are the speed step-up required
     for generators and speed regulation.  Low voltage D.C. generation
     using readily available parts (old auto generators or alternators)
     avoids the speed regulation problem.  Simple starter-motor-pinion/
     flywheel-ring-gear sets could be adequate for speed step-up at a
     reasonable cost.   Typical ring gear sets have a lower limit of 10
     diametral pitch size teeth which gives a power rating of 10 R.P.M.
     of about 1/2 h.p.   It is, therefore, marginal to expect to produce
     continuous output from a 12 volt automobile generator at, say, 60
     amps for long periods of time without gear problems.  The small
     amount of power generated, the need for 12 volt bulbs, resistance
     losses in long distribution systems and other problems also mitigate
     against this being a useful bolt-on accessory.  Electricity generation
     is better left to the higher speed devices which are more amenable
     to speed regulation such as the Banki Turbine of a centrifugal
     pump being forced to run as a turbine.
     Attachment directly to other mechanical machinery can be accomplished
     by a variety of coupling devices described in various
     machine design books.   Two circumstances are likely to occur:
          1.   the machine to be driven will be located some
              distance from the wheel; and
          2.   the input shaft of the machine will not easily
              be aligned with the wheel shaft.
     Alignment difficulties are overcome simply and cheaply with old
     automobile drive shafts and their attached universal joints.
     Note that the use of one universal joint will not give constant
     speed on both sides.   For a constant input speed, the output is
     alternately faster and slower than the input depending upon the
     angle between the two shafts.  The speed variations are small and
     will generally not be of any consequence.  If the speed variations
     cannot be tolerated, either a special constant velocity joint (as
     from the front wheel drive automobile) or two ordinary U joints
     must be used, each to compensate for the non-uniform motion of the
     Flexible shafts are commercially available but are of limited
     torque carrying capacity.
     Solid shafts can transmit torque over considerable distance but
     require bearings for support and may therefore be expensive.
     Virtually any stationary machine which is currently hand-powered
     could be run by water wheel power.  The means to accomplish the
     attachment would vary from machine to machine of course, but only
     in the case of where the wheel and the machine are separated by long
     distances should there be any significant problem.
                               APPENDIX I
                 Sample Calculation for Wheel-pump set
The following is an example of the use of this manual to make decisions
relating to water wheel for use in water pumping.   The decisions made
must be consistent with the bounds placed upon the system by the village's
needs (how much power is required) and the geography and size of the
supply stream (how much power we can expect to get from the wheel).   If
the power required is greater than the power that can be generated by
the wheel, then the system cannot work.  This example is taken from
calculations made for Ilauru village, approximately 15 miles south of
Wau, New Guinea.  One of the possible locations for a wheel is in a stream
about 350 feet below the level of the village.   The hill is quite steep
and would require about 750 feet of pipe.   There is a place in the stream
where the water level drops quite rapidly through a vertical distance
of 8 or 10 ft.  The stream is about 10 ft. wide, averages 6 or 9 inches
depth and flows about between 1 and 2 ft. per second (estimated by measuring
the time for a leaf to travel a fixed distance).   That description
establishes the conditions to determine the maximum wheel size.
The village has about 300 people.  Each person now consumes less than
2 gallons of water per day in the village according to a rough estimate.
If the water were pumped into the village, experience in other countries
shows that the consumption would increase.   A minimum of 10 gallons per
day per person is sometimes quoted as a minimum viable scheme.   Let us
calculate for twice that to allow for expansion of population or of consumption.
      1.   Total water requirement in gallons per hour
          20 gal/person-day   x   300 people  x   day/24 hr  =  250 gal/hour
          assuming storage facilities at the village to allow larger
          draw at peak hours.
      2.   Power required to meet this pumping rate from Table XV.
          250 gal/hour at approx. 400 ft. head (350 actual ft. rise +
           some losses as yet uncalculated) requires about 1/2 h.p. under
          steady conditions.
      3.   Depending on the type of pump arrangement used, the wheel will
          need to be designed for 2 1/2 times that for a single acting pump,
          2 times that for double acting pump or 1 1/2 times that for 2
          double acting pump.   Assuming the simplest case of 1 single
          acting pump we need a wheel of 1 1/4 h.p. potential.
      4.   Can we get that much power from a water wheel under the stated
          conditions at the stream? The largest diameter possible is
          limited by the drop in the stream in a useable distance -- about
          8 feet.   An 8 ft. wheel will operate at about 12 rpm or less
          (Table VI).   The stream has a flow rate of at least
                    10 ft x 1/2 ft x 1 ft = 5 [ft.sup.3]
                                     -----     ---------    
                                     sec       sec
                          5 [ft.sup.3] x 6 1/4 gal x 60 sec =  1800 gal
                            ----------   ----------   ------    ---------                       --------   
                              sec        [ft./sup.3]      min      min
          At 1800 gal/min we should be able to produce 2 h.p. at least
          from an 8 ft. wheel (Table V) or slightly less depending upon
          the exact t/r values finally chosen.
          Therefore we conclude that the job, in theory, is possible.
          Had the flow rate been, for example, only 500 gallons per
          minute, the task of pumping 250 gal per hour to the village
          would probably have been impossible.
      5.   At an estimated 12 rpm and 4 ft. width (maximum usually used
          is half the diameter) we can estimate the annulus width necessary
          (Table II).
          1 1/4 h.p. needed
          ------------------   =  0.025 h.p. per rpm per ft of width
          12 rpm x 4 ft wide
          In the entry under 8 ft. diameter wheels we see that all annulus
          widths listed will provide at least that much power.  We
          now know we can make the wheel less than 4 ft. wide if desired
          and the annulus width can be between 3 in. and 12 in.
          It is now completely established that an 8 ft. diameter water
          wheel in this location will do the job required.
      6.   If the wheel operates at 12 rpm and the pump is directly
          coupled so that there is one stroke per rpm with no added
          leverage (for instance, as with the wire connection suggested
          in Part Two, Section IB), there will be one stroke per revolution.
          To accomplish 250 gal/hr we need:
          250 gal      hr        min
              --- x ------ x ---------- = .35 gal/stroke
              hr      60 min  12 strokes 
          From Table XVI that means we need 3 1/2 pump with 12" stroke
          or 4" pump with 9" stroke etc.
      7.   If we limit the velocity in the pipe to 10 ft/sec then the
          pipe size with the 3 1/2" pump (chosen because it is cheaper
          than the 4" pump) is related to the peak piston velocity and
          the pump size.   From Table XI the peak piston velocity at
          12" stroke 12 rpm is .624 ft/sec.  The delivery pipe cross
          section area must be approximately
          .624 x 11 [(3 1/2).sup.2]   1
                    --------------- x --  = Pipe area = .64 [in.sup.2]
                          4            10
          This would require a nominal 1" diameter pipe.
      8.   The pipe would need to be galvanized iron to withstand the pressure
          of heads exceeding 350 ft.  If a nominal 1" pipe is used,
          the actual peak velocity is about 7 ft/sec.
          The friction head loss would be (Table X)
          friction loss = 0.022 x 750    [7.sup.2]
                                  ---- x --------- = 150 ft
                                  1/12   2 x 32.2
          Thus the total peak head causing forces on the pump rod
          would be 350 (elevation) + 150 (loss) = 500 ft.
          Commercial 31/2 m. pumps are fitted with 2 in. pipe outlet
          holes and if 2 in. pipe is used the loss is much less
          because the velocity is less and the diameter is greater.
               friction loss = 0.028 x 750    [2.sup.2]
                                       ---- x --------- = 8 ft
                                       2/12   2 x 32.2
          The saving is obviously substantial but the cost of doubling
          the pipe size may be unattractive.
      9.   Assuming we use the 1" pipe we find the required pump rod
          force from Table XII is about 1850 lb.  For a 12" stroke a
          crank length of 6" is required and so the peak torque on
          the machine is 925 ft/lb.
          From Table 1 we see that this is well within the capacity
          of the wheel if it is 4 ft. wide.
     10.   To allow for reasonable future expansion of needs without
          adding unnecessary weight to the wheel I would select a 4"
          annulus.   Having done that, the bearing loads are (Table VII)
          about 500 lb. each.   Assuming the bearings can be located
          fairly close to the wheel, say 6" away, the solid steel
          shaft size required is found from:
               [d.sup.3] = 16[square root][(6 x 500).sup.-2] + [(925 x 12).sup.2]
                                                [pi] (13,000)
               d = 1.65 in
          Any solid steel shaft larger than this will be satisfactory.
                              APPENDIX II
                   An Easily Constructed Piston Pump

dmfspx71.gif (600x600)

                                 by R. Burton
This pump was designed by P. Brown (of the Mechanical Engineering Workshop
at the Papua New Guinea University of Technology) with a view to
manufacture in Papua New Guinea.  Consequently the pump can be built up
using a minimum of workshop equipment.  Most parts are standard pipe
fittings available at any plumbing suppliers.
To avoid having to bore and hone a pump cylinder, a length of copper
pipe is used.  Provided care is taken to select an undamaged length and
to see that the length is not damaged during construction this system
has proved quite satisfactory.
As can be seen from the cross-sectional diagram, the ends of the pump
body consist of copper pipe reducers silver soldered onto the pump
cylinder.  This does make disassembly of the pump difficult, but avoids
the use of a lathe.
If a lathe is available, a screwed end could be silver soldered to the
upper end of the pump to allow for simple disassembly.
The piston of the pump consists of a 1/2" thick P.V.C. flange with holes
drilled through it (see diagram).  A leather bucket is attached above
the piston and together with the holes serves as a non-return valve.
In this type of pump the bucket must be made of fairly soft leather,
a commercial leather bucket is not suitable.   Bright steel bar is
used as the drive rod and has to be thread cut at its ends using a die.
A galvanized nipple is silver soldered to the top copper reducer of the
pump to allow the discharge pipe to be attached.
An `O' ring seal of the type used to join P.V.C. pipe is used as a
seal for the foot valve. This seal does not require any fixing since
it push fits into the lower copper pipe reducer. A 1/2" screwed flange
with a plug in its centre forms the plate for the foot valve. This plate
must be restrained from rising up the bore of the pump by three brass
pegs fitted in through the side wall of the pump above the valve plate.
These pegs must be silver soldered in to prevent leakage or movement.
A parts list for a 4" bore x 9" stroke pump is set out below together
with a tool list.
              1 only 12" x 4" dia. copper tube
              2 only 4" to 1 1/2" copper tube reducers
              1 only 1 1/2" galvanized nipple
              1 only 1/2" screwed flange
              1 only 1/2" plug
              1 only 1/2" P.V.C. flange
              1 only Rubber `O' ring 4" dia.
              1 only piece of 4 1/2" dia. leather
              1 only 15" x 1/2" dia. bright steel bar
              1/8" dia. brazing rod
              Handi gas kit
              Silver solder
              Hand drill
              1/2" Whitworth die
              1/2" Whitworth tap
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