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The illuminance required in a room or at a working place must be realized - according to the respective visual task - by a suitable number and type of lamps and lighting fittings and their arrangement. For this purpose it is to be calculated how many lighting fittings and lamps are necessary. This can be done by finding the required luminous flux first.
Through the luminous flux of the individual lighting fitting the required number of lighting fittings can be found out. This is called luminous flux method. It is also possible to proceed this way: Calculation from a given arrangement of illuminators and the given luminous flux per illuminator taking into consideration the light distribution of the illuminators the illuminance, for instance at a certain point of the working area. Here, one speaks of the luminous intensity method. Then, the lamp supply of each illuminator or the arrangement of the illuminators must be altered by the difference between the required and the calculated illuminance. It was refrained from an accuracy not required in practice in favour of a more facile application of many calculating methods. The accuracy of the calculated luminous flux or of the calculated illuminance is influenced by the tolerances of the individual calculation factors such as the luminous flux of the illuminator, illuminator efficiency, light distribution curve. Unfortunately, the tolerances of the most important value - the luminous flux of the illuminator - are within wide limits; with gas-discharge light sources the tolerance amounts to 10 or even 15 % of the nominal value. Another source of inaccuracy consists in the tolerances of the illuminator efficiency, mainly with the gas-discharge lamps, which in their efficiency depend on temperature. Here, the respective efficiency for a certain surrounding temperature must be indicated in connection with correction factors considering the different thermal behaviour of the illuminators and the illuminator equipment.
To calculate the required number of illuminators that shall be symmetrically distributed in a room the following details must be given:
1. The required medium illuminance depending on the visual task
Table 11. Minimum illumination
|
Place to be lighted |
Illumination in lx |
|
Traffic roads |
50 |
|
Stairs |
100 |
|
Office rooms |
500 |
|
Assembly work at consumer goods |
1000 |
|
Goldsmith’s work |
1500 |
|
Sales rooms |
300 |
|
Locksmith’s work (fine) |
300 |
|
Locksmith’s work (rough) |
100 |
|
Building sites |
20 |
|
Filling stations |
100 |
|
Canteens |
200 |
|
Schoolrooms |
250 |
|
Rough work |
100 |
2. Colour of the ceiling and walls
Table 12. Reflection factors (selection)
|
Reflecting object |
Reflection factor | |
|
Paper (white) |
0.84 | |
|
Wood |
(spruce) |
0.50 |
| |
(plywood) |
0.38 |
|
Bricks |
(yellow) |
0.32 |
| |
(red) |
0.18 |
|
Lime plaster (grey) |
0.42 | |
|
Dry concrete (grey) |
0.32 | |
|
Asphalt (wet) |
0.05 | |
|
Paints |
(chalk-white) |
0.80 |
| |
(lemon yellow, ivory, creme) |
0.70 |
| |
(medium ochre) |
0.52 |
| |
(lime green, pastel) |
0.50 |
| |
(silver-grey) |
0.35 |
| |
(beige) |
0.25 |
| |
(vermilion, grass-green) |
0.20 |
| |
(carmine) |
0.10 |
3. Surface of the room (dimensions)
4. Suspension height of
the illuminators
5. Measuring plane (height of floor)
6. Cleaning cycle,
degree of getting dusty
Table 13. Depreciation factor with indoor lighting installations
|
Type of illumination |
Getting dusty | ||
| |
slightly |
normal |
much |
|
Direct |
0.9 |
0.8 |
0.6 |
|
Mainly direct |
0.9 |
0.8 |
0.6 |
|
Uniform |
0.8 |
0.8 |
--- |
|
Mainly indirect |
0.8 |
0.7 |
--- |
|
Indirect |
0.8 |
0.7 |
--- |
7. Type of illumination
Table 14. Types of illumination
|
Type of illumination |
Luminous flux emittance |
Material of the lighting fitting | |
|
Direct |
|
|
light-tight, reflecting |
|
Mainly direct |
|
|
transparent, partially reflecting |
|
Indirect |
|
|
light-tight, reflecting |
|
Mainly indirect |
|
|
transparent, partially reflecting |
|
Uniform |
|
|
transparent |
8. Type of light source
Table 15. Survey of light sources
|
General-service lamps |
Fluorescent lamps | ||||||||
|
Wattage rating |
Clear glass bulb |
Internally coated |
Duro-life lamp |
Wattage rating |
Twin-tube |
Rod shape diameter (mm) 16 |
U-shapes 26 |
|
Ring shape |
|
(W) |
(lm) |
(lm) |
(lm) |
(W) |
(lm) |
(lm) |
(lm) |
(lm) |
(lm) |
|
25 |
220 |
218 |
190 |
4 |
- |
150 |
- |
- |
- |
| | | | |
5 |
250 |
- |
- |
- |
- |
|
40 |
430 |
395 |
360 |
6 |
- |
300 |
- |
- |
- |
| | | | |
7 |
400 |
- |
- |
- |
- |
|
60 |
730 |
680 |
620 |
8 |
- |
450 |
- |
- |
- |
| | | | |
9 |
600 |
- |
- |
- |
- |
|
75 |
960 |
900 |
825 |
10 |
600 |
- |
- |
- |
- |
| | | | |
11 |
900 |
- |
- |
- |
- |
|
100 |
1380 |
1280 |
1170 |
13 |
900 |
950 |
- |
- |
- |
| | | | |
15 |
- |
- |
900 |
900 |
- |
|
150 |
2200 |
-- |
-- |
16 |
- |
- |
900 |
900 |
- |
| | | | |
18 |
1200 |
- |
1450 |
950 |
- |
|
200 |
3100 |
-- |
-- |
20 |
- |
- |
- |
- |
1100 |
| | | | |
22 |
1800 |
- |
- |
- |
- |
|
300 |
5000 |
-- |
-- |
24 |
- |
- |
- |
- |
- |
| | | | |
26 |
1800 |
- |
- |
- |
- |
|
500 |
8400 |
-- |
-- |
30 |
- |
- |
1700 |
- |
1700 |
| | | | |
32 |
- |
- |
- |
- |
- |
|
1000 |
19000 |
-- |
-- |
36 |
2900 |
- |
3450 |
- |
- |
| | | | |
38 |
- |
- |
2700 |
2700 |
- |
|
1500 |
29000 |
-- |
-- |
40 |
- |
- |
- |
- |
2800 |
| | | | |
50 |
- |
- |
5400 |
- |
- |
|
2000 |
40000 |
-- |
-- |
65 |
- |
- |
- |
4500 |
- |
The calculation of an interior space illumination shall be demonstrated by an example of the luminous flux method. The result is of sufficient accuracy.
A classroom shall be illuminated by fluorescent lamps. The double-lamp illuminators are evenly distributed in the room. The room is 7.00 m wide and 12.00 m long. The illuminators shall be suspended at a height of 2.60 m. The measuring plane is supposed to be 0.75 m (level of the desks). The degree of contamination is normal. The ceiling is chalk-white, the walls have an ochre painting. Illumination is direct, the illuminators are not screened on their lower ends but have reflectors on top. The degree of efficiency is supposed to be 1.
Solution: Parameters
|
Ceiling reflection |
|
according to Table 12 |
: 80 % |
|
Wall reflection |
|
according to Table 12 |
: 52 % |
|
Required illuminance |
|
according to Table 11 |
: 250 lx |
|
Type of illumination |
| |
direct |
|
Depreciation factor |
(V) |
according to Table 13 |
: 0.8 |
|
Length of the room |
(L) | |
: 12.00 m |
|
Width of the room |
(B) | |
: 7.00 m |
|
Measuring plane |
(ME) | |
: 0.75 m |
|
Suspension height |
(hA) | |
: 2.60 m |
Solution: Calculating steps
1. Surface of the room
A = L x B = 12m x 7m =84.00 square metres
2. Useful height
hN = hA - ME = 2.60 m - 0.75 m = 1.85 m
3. Room factor
K = 4.3
4. Determination of the illumination efficiency with the help of Table 16: Basis is the rubric ‘direct’. Under the term of ceiling reflection 70 % (the nearest to 80 %), that column is chosen which comes next to the wall reflection, i.e. 50 %. This column is gone down until the value of K = 4 is reached.
Here, the value 0.45 (45 %) is to be found. This is the degree of room efficiency. Since the efficiency degree of the illuminator was supposed to be 1, it appears that the illumination efficiency is equal to the degree of room efficiency (0.45).
5. Determination of the total luminous flux
PHIges approximately 58,340 lm
6. Calculation of the number of lamps
7. Illuminator arrangement
The result is that double-lamp illuminators have to be evenly distributed in the room.
Hints concerning the selection of the lamps:
According to the principle of assigning lamps of a certain light colour to the individual activities, it has to be decided about the colour of light after having calculated the number of lamps required.
There are the following colour shades: white, warm-tone, warm-tone extra or white, warm-white, warm-white de luxe as well as universal-white, white de luxe and daylight.
In any case it is advisable - due to the variety of international manufacturers - to use the respective colour temperature for selection, (e.g. warm-white 2900 K; white 4300 K). Furthermore, the starting behaviour of the lamps should be considered. In a cool ambient temperature, fluorescent lamps of the standard type start very bad. In such case, cold-proof lamps should be used.
As has been stated, the calculation according to the luminous flux method includes the reflection capacity of ceiling and walls in the design of the lighting installation. No daylight support is added! It is also supposed that the colour of the ceiling and the walls remains unchanged, because otherwise the initial parameters of the illumination would change.
By this method, the illuminance on a surface to be illuminated is calculated, with direct irradiation by the light source and without consideration of reflecting surrounding surfaces (spotlight effect). With the illuminance given the light source can be found.
The following details are required for the calculation:
1. Average illuminance required for the visual task.2. Type of illuminator with the appertaining light distribution curve indicated by the manufacturer.
3. Suspension height
4. Measuring plane
5. Degree of getting dusty
6. Type of light source
7. Angle of irradiation (indirect by lengths of reference)
Figure 15. Light distribution curve
(rotational symmetrical representation)
1 light intensity in cd
Example of a calculation task concerning a lighting installation for an assembly surface (open-air surface). The result is of sufficient accuracy.
An assembly surface shall be illuminated by downlighters equipped with high-pressure mercury vapour lamps. Rough work - locksmith’s work - shall be carried out. The dimensions of the surface are 10 x 10 m. The downlighters shall be installed at a height of 4 m. The required lamp performance has to be found out, if 4 illuminators shall be used.
|
Solution: |
Parameters | |
|
According to Table 11 for rough work: |
100 lx | |
|
According to Ill. 15: |
illuminator, general | |
|
Light source: |
suspension height: |
4.0 m |
| |
measuring plane: |
0 m |
|
Degree of getting dusty, depriciation factor: |
0.6 | |
|
Type of light sources |
high-pressure mercury vapour lamp | |
Angle of irradiation: This has to be calculated with the help of Pythagoras and function of angles according to the space dimensions, (acc. to Fig. 16). It amounts to approximately 41.2 degrees.
Figure 16. Dimensional sketch
1, 2, 3, 4, 6 suspension and/or mounting frames of the lighting fittings, 5, 6, 7 lighting points resulting from the angle of arrival alpha, 8 (2.5 m), 9 (10.0 m), 10 (4.0 m), primed 1 and 3 vertical rotation point below the lighting fitting.
Solution: Steps of calculation
1. To 41.2 degrees the corresponding cosine has to be determined. It is approximately 0.425.
2. From the light distribution curve, Fig. 16, approximately 350 cd (candelas) appear.
Application: At 41.2 degree, the curve is intersected.
From the point of intersection, the value is read radially on the vertical axis.
3. In order to be able to calculate the required luminous flux, the two formulae for Ep and la must be linked. If the respective values are put in as follows
Luminous flux of lamps in lumen (lm)
Illuminance in point ‘P’ in lux (lx)
Useful height in square metres
Light intensity from the light distribution curve in candela (cd)
Solid angle ratio for rotation-symmetrical light distribution
Depreciation factor (degree of getting dusty in %)
the result is a luminous flux of the lamps of 17930 lm
4. Determination of lamps
Selection:
High-pressure mercury vapour lamp 400 W = 23.000 lm
High-pressure sodium vapour lamp 250 W = 25.000 lm
5. Counter calculation:
Since the rated luminous flux is greater than the calculated one, it derives for the illuminance in point ‘P’:
for high-pressure mercury vapour illumination 128 lx
and for high-pressure sodium vapour illumination 139 lx
6. The illuminance adds in the middle of the working surface to 4 x Ep = 512 and 556 lx, respectively.
7. Directly under the illuminator the following illuminance is calculated:
Ep approx. 302 lx
With high-pressure sodium vapour lamps it would be
Ep approx. 328 lx
The illumination distribution, for instance with high-pressure sodium vapour lamps, would be as follows:
|
+ 139 lx | |
| |
139 lx + |
| |
+ 328 lx | |
328 lx + | |
| | |
+ 556 lx | |
|
| |
+ 328 lx | |
328 lx + | |
|
+ 139 lx | |
| |
139 lx + |
Questions for repetition and knowledge test
1. By what methods a lighting installation can be calculated?
2. What importance does the type of illumination have for the determination of the number of lamps?
3. What is the importance of the light distribution curve?
4. What is understood by the term of ‘illuminance shape’?
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