A number of methods have been employed for lighting calculations, among which may be mentioned: 1. Watts per Square Metre Method 2. Lumen or Light Flux Method 3. Point to Point or Inverse-Square Law Method.

#### 1. Watts per Square Metre Method:

This is principally a “rule of thumb” method, very handy for rough calculation or checking. It consists in making an allowance of watts per square metre of area to be illuminated according to the illumination desired on the assumption of an average figure of overall efficiency of the system.

#### 2. Lumen or Light Flux Method:

This method is applicable to those cases where the sources of light are such as to produce an approximate uniform illumination over the working plane or where an average value is required.

From the size of lamp or lamps employed and from their efficiency total lumens output are determined. Multiplying the total lumens output from the source by coefficient of utilization, the lumens received on the working plane are determined. If the lamps and surroundings are not perfectly clean, then in determination of lumens received on working plane, the depreciation factor or maintenance factor should be included, i.e.,

Also Lumens received on working plane = Number of lamps x wattage of each lamp x efficiency of each lamp in terms of lumens per watt x coefficient of utilization x maintenance factor.

Coefficient of Utilization or Utilization Factor:

The whole light radiated by the lamps does not reach the working plane. The ratio of lumens reaching the working plane to the total lumens given out by the lamp or lamps, is known as utilization factor or coefficient of utilization. Higher the value of utilization factor, more lumens will reach the working plane for the given lumens output of the lamps.

The value of utilization factor depends upon:

(i) The mounting height of lamps—utilization factor decreases with the increase in mounting height of lamps

(ii) Area to be illuminated—for given height, proportion of direct light becomes more and more if floor area increases, i.e., utilization factor increases with the increase in area to be illuminated

(iii) Type of lighting—more for direct lighting and low for indirect lighting and

(iv) Colours of surroundings etc.— more for light colours and less for dark colours. Its value varies from 0.25 to 0.5 and from 0.1 to 0.25 for direct and indirect lighting schemes respectively.

Maintenance Factor:

The illumination produced by a lighting installation is considerably less after a year or two of use than it was initially. The loss is due partly to the aging of the lamps and partly to the accumulation of dust on the lamps, on the reflecting and transmitting surfaces of the fixtures and on the ceiling and walls. This fact is taken into account by including the maintenance factor, which is defined as the ratio of the ultimate maintained metre-candles on the working plane to the initial metre- candles. Its value is more if the lamp fittings are cleaned regularly, say 0.8, and less if there is much dust etc. say 0.6.

Depreciation Factor:

This is merely the inverse of the maintenance factor and is defined as the ratio of the initial metre- candles to the ultimate maintained metre-candles on the working plane. Its value is more than unity.

#### 3. Point to Point or Inverse-Square Law Method:

This method is applicable where the illumination at a point due to one or more sources of light is required, the candle powers of the sources in the particular direction under consideration being known.

If a polar curve of lamp and its reflector giving candle powers of the lamp in different directions is known, the illumination at any point within the range of the lamp can be calculated from the inverse square law. If two and more than two lamps are illuminating the same working plane, the illumination due to each can be calculated and added. This method is not much used because of its complicated and cumbersome applications. It is employed only in some special problems, such as flood lighting, yard lighting etc.

Example 1:

A small assembly shop 16 m long, 10 m wide and 3 m up to trusses is to be illuminated to a level of 200 lux. The utilization and maintenance factors are 0.74 and 0.8 respectively. Calculate the number of lamps required to illuminate the whole area if the lumen output of the lamp selected is 3,000 lumens.

Solution:

Working area, A = 16 x 10 = 160 m2

Required illumination level, E = 200 lux

Total lumens required = E x A = 200 x 160 = 32,000 lumens

Total lumens to be given out by the lamp

Example 2:

A minimum illumination of 80 lumens/m2 is required in a factory shed of 100 m x 10 m. Calculate the number, location and the wattage of the units to be used. Assume that the depreciation factor is 0.8, coefficient of utilization is 0.4 and efficiency of the lamp is 40 lumens/watt.

Solution:

Area to be illuminated, A = 100 x 10 = 1,000 m2

Illumination required, E = 80 lumens/m2

Total lumens required = A x E = 1,000 x 80 = 80,000

Utilization factor = 0.4

Depreciation factor = 0.8

42 lamps of 150 W rating in 2 rows, each row having 21 lamps, can be used giving spacing of 4.76 m in length and 5 metres in width.

Disposition of lamps is shown in Fig. 7.45.

Example 3:

An illumination on the working plane of 75 lux is required in a room 72 m x 15 m in size. The lamps are required to be hung 4 m above the work bench. Assuming a suitable space- height ratio, a utilization factor of 0.5, a lamp efficiency of 14 lumens per watt and a candle power depreciation of 20%, estimate the number, rating and disposition of lamps.

Solution:

Area to be illuminated, A = 72 x 15 = 1,080 m2

Illumination required, E = 75 lux

Total lumens required = A x E = 1,080 x 75 = 81,000

Utilization factor = 0.5

Maintenance factor = 1 – candle power depreciation = 1 – 0.2 = 0.8

80 lamps in 4 rows, each row having 20 lamps, can be used giving spacings of 3.6 metres in length and 3.75 metres in width and space- height ratios of 0.9 and 0.9375 respectively.

Wattage of each lamp = 14,464/80 = 180.8 ≃ 200 W (say) Ans.

Disposition of lamps is shown in Fig. 7.46.