Method of calculations

 Method of calculations

For lighting distribution calculations, two methods are introduced:

(1) VA method.
(2) Lux method.

(i) The VA method

The procedures:

(1) Determine the area of the room, (A) =width X length.
(2) Identify VA/m2 according to the room purpose.
(3) Total VA = (VA/m2) x area (A).
(4) Identify the used luminary type.
(5) Calculate the output VA of one luminary.
(6) Number of luminaries = (total VA) / (VA of one luminary).
(7) Calculate the proposed number of luminaries.
(8) Calculate the new total VA.
(9) Distribute the number of luminaries on the area

Table - VA per square meter [NEC]

(ii) The lux method

The lumen method is used in calculating the average luminance on the working plane in an interior. This is defined as:

where: 

 is the lighting flux [lumen]

is the working plane area.

A coefficient of utilisation (CU ) gives the fraction of lamp lumens that reach the workplane, directly from sources and from inter-reflections. The CU takes into account the efficiency of the luminaire and the impact of the luminaire distribution and the room surfaces in its derivation. Thus the number of lumens produced by the lamps, multiplied by this CU , determines the number that reaches the workplane:

Since the design objective usually is maintained illuminance, a light loss factor LLF  must be applied to allow for the estimated depreciation in lamp lumens over time, the estimated losses from dirt collection on the luminaire surfaces (including lamps), and other factors that affect luminaire lumen output over time. The formula thus becomes:

Although design calculations are based on the LLF using both non-recoverable and recoverable factors, it is sometimes necessary to calculate illuminance in a new lighting installation. In such cases, repeat the calculation using the non-recoverable losses, since the recoverable losses do not occur at 100 hours, the time at which lamps are nominally at rated lumens.The lamp lumens in the formula are most conveniently taken as the total rated lamp lumens in the luminaries. If the desired maintained illuminance is known, this equation can be solved for the total number of luminaries needed:

where N is the number of Luminaries.

(A) Limitations

The illuminance computed by the lumen method is an average value that is representative only if the luminaries are spaced to obtain reasonably uniform illuminance. The calculation of the coefficients of utilisation is based on empty interiors having surfaces that exhibit perfectly diffuse reflectance. The average illuminance determined by the lumen method is defined to be the total lumens reaching the workplane divided by the area of the workplane. The average value determined this way might vary considerably from that obtained by averaging discrete values of illuminance at several points.

(B) Cavity Ratios

The radiative exchange between the top and the base of a rectangular space is a function of the proportions of its length, width, and height. Cavity ratio values approximate this effect by combining these proportions into a single quantity. In the Zonal-cavity method, the effects of room proportions, luminaire suspension length, and workplane height upon the coefficient of utilisation are respectively represented by the room cavity ratio, ceiling cavity ratio, and floor cavity ratio. These ratios are determined by dividing the room into three cavities, and substituting dimensions (in m or ft) into the following formula:

where CR  is the cavity ratio, h is the cavity height, l is the cavity length, and w  is the cavity width. The illuminance in rooms of irregular shape can be determined by calculating the room cavity ratio using the following formula and solving the problem in the usual manner:

where CA  is the cavity base area, and CC is the cavity circumference.

(C) Effective Cavity Reflectance's

It provides a means of converting the combination of wall and ceiling or wall and floor reflectance's into a single effective ceiling cavity reflectance, ρcc  ,and a single effective floor cavity reflectance, ρcc. In lumen method calculations, the ceiling, wall, and floor reflectances should be initial values. Note that for surface-mounted and recessed luminaries, the ceiling cavity ratio equals zero and the actual ceiling reflectance may be used for ρcc.

Luminaries coefficient of utilization: Absorption of light in a luminaire is taken into account in the computation of coefficient of utilisation (UC) for that luminaire. Appendix A is a tabulation of coefficients of utilisation calculated by the Zonal-cavity method for representative luminaire types. These coefficients are for an effective floor cavity reflectance of 20%, but any UC obtained from the table may be corrected for a different value of ρFC by applying the appropriate multiplier from table Since the light loss factor includes the effect of dirt deposited on wall surfaces, the selection of the proper column of wall reflectance’s, ρw, should be based on the initial values expected. The wall reflectance should also represent the weighted average of the  reflectance's of the painted areas, fenestration or daylight controls,

chalkboards, shelves, and so forth in the area to be lighted. The weighting should be based on the relative areas of each type of surface within the cavity being considered. In using, it is often necessary to interpolate between room cavity ratios CR and effective ceiling cavity reflectance's. This is most easily accomplished by interpolating first between room CR to obtain CU for effective ceiling cavity reflectances that straddle the actual ρcc, and then interpolating between these CU values. As a guide line the following utilisation factors can be adopted with good accuracy for most applications:

Utilization factor table