Good lighting design can improve worker efficiency and reduce a building owner’s operating costs.

Years ago, calculating the number of lighting fixtures for an indoor office space only required you to determine the average uniform horizontal illumination, in footcandles (fc) for the entire room, select a fixture from a catalog, and then uniformly space the fixtures throughout the room. However, now that many workstations are equipped with specialized task lighting fixtures and everyone is interested in the use of daylighting to reduce energy consumption levels, nonuniform lighting is a key criterium to address in modern office lighting design.

To help you determine the proper light levels for a given space, the Illuminating Engineering Society of North America (IESNA) Lighting Handbook, Ninth Edition, recommends illuminance levels, or lighting power density (LPD) values, for a variety of spaces. The guidelines extend from lighting a public area using 2 fc to 5 fc level, to lighting special visual task areas of extremely low contrast and small size using 1,000 fc to 2,000 fc. The recommendations consider factors like occupant age, room surface reflectance, and background reflectance.

However, to calculate your nonuniform lighting needs, you have to start with a uniform lighting measurement and then apply other formulas that take into account factors such as lighting cavities and obstructions. For the first half of the task, the lumen method allows you to determine the expected level of uniform illumination on an imaginary horizontal plane, 2.5 ft above the floor, which is the standard height of a desktop, for a specific lamp-fixture combination or luminaire.

### Understanding the lumen method.

The lumen method is based on the definition of a footcandle, or the illuminance on a surface area of 1 sq ft on which there is a uniform distributed flux of one lumen, expressed in the following equation:

E = Lu ÷ A

where E is the average illuminance in fc, Lu is the number of lumens, and A is the area in sq ft.

Once you know the number of lighting fixtures and the number and types of lamps installed in each luminaire in the room, you can calculate the total lumens generated by the lamps by multiplying the total initial lamp lumens by the initial lumens per lamp.

However, not all lamp lumens reach the workplane. Some are trapped in the fixture or blocked by obstructions, and some are absorbed by the room surfaces. Before you can calculate the true illuminance at the workplane, you need to find a factor that represents the ratio between the lumens reaching the workplane and the total lamp lumens produced. This factor is called the coefficient of utilization (CU).

### Coefficients of utilization.

CU is defined as the percent of rated bare-lamp lumens that exit the luminaire and reach the workplane. It accounts for light directly from the luminaire as well as light reflected off the room surfaces. There are several elements that impact the CU:

• Type of luminaire, including its efficiency and distribution pattern.

• Reflectance levels of the room surfaces. The higher the reflectance factor of the ceilings, walls, and floors, the greater the percentage of lamp lumens that will reach the workplane.

• Mounting height of the luminaires. Higher mounts mean more wall space between the luminaire and the workplane, and therefore more chance for the wall to absorb the light.

• Area of the room. The larger the room, the greater the number of luminaires needed. Note that the light distribution from each luminaire overlaps the output of adjacent luminaires, which in turn raises the total light level. In addition, there is less wall surface to absorb the light.

• Proportions of the room. The dimensions of a room directly affect the CU.

Manufacturers will supply each luminaire with its own CU table derived from a photometric test report. The effective cavity reflectance factors (CC) of the ceiling, walls, and floor are listed across the top of the table. These reflectance factors are based on the concept that a room has a series of cavities determined by the elevations of the luminaires and the workplane. And these cavities, or zones, have effective reflectances with respect to each other. The room cavity ratio (RCR) is determined by using the zonal cavity method.

In the zonal cavity method, the CU, the effects on light distribution of the luminaire mounting height, the room's size and proportions, and the height of the workplane are considered mathematically, using the following methods and formulas.

Divide the cross section of a room into three sections or cavities. The space between the ceiling and luminaire plane is the ceiling cavity. In the case of either recessed or shallow surface mounted fixtures, there is no ceiling cavity. The space between the luminaire plane and the workplane is the room cavity, and the space between the workplane and the floor is the floor cavity.

The cavity ratios (CR) for these three cavities are determined using the following formula:

CR = [5 x h x (room width + room length)] ÷ (room width x room length) where h is the CC for the ceiling cavity ratio (CCR), the CC for the room cavity ratio (RCR), and the CC for the floor cavity ratio (FCR).

Since the CU is based on the RCR, it's necessary to treat this cavity as if a ceiling surface existed at the luminaire plane and a floor surface existed at the workplane level, as shown in the Figure above. Therefore, it is necessary to convert the actual ceiling reflectance into an effective ceiling cavity reflectance, referred to as "pCC." In a similar way, the actual floor reflectance must be converted to an effective floor cavity reflectance, referred to as "pFC."

### Understanding light loss factor.

In addition to the reflectance of light in cavities and small spaces, it's also necessary to consider the life of your luminaires. As soon as a new lighting system is energized, the light level starts to gradually decrease because of various aging characteristics, so it's necessary to provide an initial illuminance level greater than the minimum specified level to compensate for light loss and to ensure light levels will remain above a minimum level over a specific time period.

The light loss factor (LLF) accounts for this depreciation. LFF is the ratio of the lowest level of illuminance before corrective action is taken, such as relamping, to the initial light level.

LLF is the product of all the factors that contribute to the loss of light, which are divided into two categories: unrecoverable and recoverable. The unrecoverable factors refer to equipment and site conditions that cannot be changed with normal maintenance. They are ballast factor, temperature factor, and line voltage factor. The three recoverable factors are lamp lumen depreciation, luminaire dirt deprecation, and room surface dirt deprecation.

After you obtain the CU from its appropriate CU table and determine the LFF, insert them in the lumen method equation to arrive at the following:

E = [(N x L) x CU x LLF] ÷ A

where E is the average illuminance in footcandles, N is the number of luminaires in the space, L is the total lamp lumens for all the lamps in a luminaire, CU is the coefficient of utilization, LLF is the light loss factor, and A is area of the room in sq ft.

If the average illuminance is already specified, the equation would be rearranged to solve for the number of luminaires (N).

N = (A x E) ÷ (L x CU x LLF)