2. Lumen Method Calculations   The lumen method is based on fundamental lighting calculations. The lumen method formula is easiest to appreciate in the following form. (1) where E = average illuminance over the horizontal working plane      n = number of lamps in each luminaire      N = number of luminaire     F = lighting design lumens per lamp, i.e. initial bare lamp luminous    flux      UF = utilisation factor for the horizontal working plane      LLF = light loss factor           A = area of the horizontal working plane   2.1 Light Loss Factor Light loss factor (LLF) is the ratio of the illuminance produced by the lighting installation at the some specified time to the illuminance produced by the same installation when new. It allows for effects such as decrease in light output caused by (a) the fall in lamp luminous flux with hours of use, (b) the deposition of dirt on luminaire, and (c) reflectances of room surfaces over time. In fact, light loss factor is the product of three other factors: (2) where LLMF = lamp lumen maintenance factor LMF = luminaire maintenance factor RSMF = room surface maintenance factor   2.1.1 Lamp Lumen Maintenance Factor Lamp lumen maintenance factor (LLMF) is the proportion of the initial light output of a lamp produced after a set time to those produced when new. It allows for the decline in lumen output from a lamp with age. Its value can be determined in two ways: (a) by consulting a lamp manufacturer's catalog for a lumen depreciation chart, and (b) by dividing the maintained lumens by the initial lamps.   2.1.2 Luminaire Maintenance Factor   Luminaire maintenance factor (LMF) is the proportion of the initial light output from a luminaire after a set time to the initial light output from a lamp after a set time. It constitutes the greatest loss in light output and is mainly due to the accumulation of atmospheric dirt on luminaire. Three factors must be considered in its determination: (a) the type of luminaire, (b) atmospheric conditions, and (c) maintenance interval.   2.1.3 Room Surface Maintenance Factor Room surface maintenance factor (RSMF) is the proportion of the illuminance provided by a lighting installation in a room after a set time compared with that occurred when the room was clean. It takes into account that dirt accumulates on room surfaces and reduces surface reflectance. Figure 4 shows the typical changes in the illuminance from an installation that occur with time due to dirt deposition on the room surfaces.   2.2 Utilisation Factor Utilisation factor (UF) is the proportion of the luminous flux emitted by the lamps which reaches the working plane. It is a measure of the effectiveness of the lighting scheme. Factors that affect the value of UF are as follows: (a) light output ratio of luminaire (b) flux distribution of luminaire (c) room proportions (d) room reflectances (e) spacing/mounting height ratio   2.2.1 Light Output Ratio of Luminaire Light output ratio of luminaire (LOR) takes into account for the loss of light energy both inside and by transmission through light fittings. It is given by the following expression. (3)   Example 1 The total, upward and downward lamp output from a lamp are 1000 lm, 300 lm and 500 lm respectively. Calculate upward light output ratio (ULOR), downward light output ratio (DLOR), light output ratio (LOR) of luminaire and percentage of light energy absorbed in luminaire. Amount of light energy absorbed in luminaire = 100 - 80 = 20 % A greater DLOR usually means a higher UF. A simple classification of luminaires according to their distribution is based on flux fractions, as shown in Figure 5. Upward flux fraction (UFF) and downward flux fraction (DFF) are used as a basis of comparison.   Example 2 For data given in Example 1 determine upward flux fraction (UFF), downward flux fraction (DFF) and flux fraction ratio (FRR).   Figure 5 Flux Fraction of Various Luminaires   2.2.2 Flux Distribution of Luminaire Direct ratio is the proportion of the total downward luminous flux from a conventional installation of luminaires which his directly incident on the working plane. It is used to assess the flux distribution of luminaire. Since the intensity distribution pattern of the light radiated from a luminaire in the lower hemisphere will affect: (a) the quantity of the downward flux falls directly on the working plane and (b) the quantity of flux available for reflection from the walls in a given room, Direct ratio depends on both the room proportions and the luminaires. Direct ratio has a low value with a narrow room (small room index) and a luminaire which emits most of its light sideways (BZ 10), and on the contrary, a high value with a wide room (large room index) and a luminaire which emits most of its light downwards (BZ 1).   2.2.3 Room Proportion   Room index (RI) is the ratio of room plan area to half the wall area between the working and luminaire planes. (4) where L = length of room W = width of room Hm = mounting height, i.e. the vertical distance between the working plane and the luminaire.   2.2.4 Room Reflectances The room is considered to consist of three main surfaces: (a) the ceiling cavity, (b) the walls, and (c) the floor cavity (or the horizontal working plane). The effective reflectances of the above three surfaces affect the quantity of reflected light received by the working plane.   2.2.5 Spacing to Height Ratio Spacing to Height ratio (SHR or S/Hm) is defined as the ratio of the distance between adjacent luminaires (centre to centre), to their height above the working plane. For a rectangular arrangement of luminaires and by approximation, (5) where A = total floor area                 N = number of luminaires                 Hm = mounting height Under a regular array of luminaires the illuminance on the working plane is not uniform. The closer spaced the luminaires for a given mounting height, the higher the uniformity; or the greater the mounting height for a given spacing, the greater the uniformity. If uniformity of illuminance is to be acceptable for general lighting, (a) SHR should not exceed maximum spacing to height ratio (SHR MAX) of the given luminaire as quoted by the manufacturer, and (b) geometric mean spacing to height ratio of the luminaire layout should be within the range of nominal spacing to height ratio (SHR NOM) of the given luminaire as quoted by the manufacturer, i.e. (6)