Coefficient of Utilization, Lumen Method
The lumen method is an indoor lighting calculation methodology that allows a quick assessment of the number of luminaires necessary to achieve a given average illuminance level or alternatively the average illuminance level that will be achieved for a given number of luminaires. It is valid for empty rectangular rooms with simple three-surface diffuse reflectances for ceiling, wall, and floor.
When an electric lamp is turned on, it emits light and it is possible to quantify the amount of light by measuring it, the result being given in the units of lumens. In itself this is a useful piece of information, but what would be more useful would be to have a method of converting this into a measure of the amount of light that would be received onto a desk from one or more luminaires or alternatively the number of luminaires necessary to achieve a given quantity of light on the desk. This calculation is known as the lumen method.
However, luminance is a difficult quantity to measure and changes with viewing position. Imagine a day-lit room with resultant shadows and patches of light reflected from polished surfaces. As the observer position moves within the space, the shadows and patches of light change with viewing position. As vision is essentially viewing luminance, this means that the luminance is view dependent. This makes it a difficult design quantity, so for ease, common practice is to design using illuminance which is view independent as the amount of light falling onto a surface does not change with viewing position. (There are a few exceptions, an example being traffic routes, where design may use luminance, in this case the light that is reflected from the road surface).
Calculating the Maximum Achievable Illuminance
Frequently in large spaces, it is not known where tasks such as desks will be positioned and may not be even clearly known what tasks will be performed within the space. Even if the task types and locations are known, most spaces and how they are used change through time. This means that, within reason, lighting has to be flexible enough to preserve the correct lighting conditions for changing requirements.
Calculating the illuminance level for a particular area within a larger space is generally beyond the ability of a quick and easy calculation method. For lighting the calculation of an average illuminance across a space is relatively easy, while the calculation of the illuminance across a desk located in a room would normally require the use of a computer calculation program.
For a given number of luminaires, Nlum
Where each luminaire contains a given number of lamps, Nlamp
And each lamp produces a given quantity of lumens, lmlamp
This value assumes all the light produced by the lamps will be received onto the task, with no losses. This is generally not possible or even desirable.
As this is the maximum illuminance theoretically (but not practically) achievable, if the illuminance is too low, at this point more luminaires and, hence more lumens, will be required.
Losses within the light fitting
Losses through aging and dirt
Losses through light not going directly to the task plane but via reflection from room surfaces
Accounting for Losses Within the Light Fitting
The luminaire has its own microclimate, the temperature inside the fitting generally being different to that of the air outside. Designing a fitting so that the internal temperature is the optimum for the light source it contains requires skilled design, and the larger the difference between the optimum light source conditions and the actual luminaire conditions results in an increasing reduction in lumen output from the light source and/or reduced operating life expectancy for the source.
An optic, no matter how well designed, has an element of inefficiency. No surface will reflect 100 % of any light incident upon it and losses are cumulative. So, for example, if a metal reflector has a reflectance of 92 %, then light that bounces once off the reflector before exiting the luminaire loses 8 % of its initial lumens. If it requires two bounces to exit the fitting, only 0.92 * 0.92 = 0.85 or 85 % of the initial lumens exit the fitting, 15 % being lost. Similarly optics that rely on transmission of light, such as diffusers or prismatic controllers, absorb some of the light, no material being 100 % transmissive.
Components within the luminaire will obstruct light, and this light may become trapped and never exit the fixture. For example, light emitted from the light source upwards into a ceiling recessed luminaire will need to be reflected around the light source, and some light will be lost in this process, trapped behind the source. (This can cause extra problems if the light is absorbed by the source, causing it to heat up further). Many reflectors trap light in their back which may be open and shaped as the inside of a V with low reflectance.
Therefore, a measure is needed to quantify how all of these situations affect the lumen output of the luminaire. This is the light output ratio (LOR). Essentially the LOR is the ratio of light emitted from the luminaire to the light emitted by the light source, and the value of LOR is luminaire specific.
Accounting for Losses Through Aging and Dirt
When a lighting system is first installed, the lamps are new and all functioning, the luminaires are clean, and generally the room surfaces (floor, walls, and ceiling) are clean. However, through time the condition of the installation will deteriorate. As light sources age, their lumen output reduces (lumen depreciation) and some lamps will fail completely. Dust and dirt will gather on the reflecting surfaces of the luminaires, reducing how efficiently light is directed from the light source out of the fitting, and room surfaces will become dirty and marked through everyday wear and tear. All of these will reduce the amount of light reaching the task plane.
Accounting for Reflection Losses from Room Surfaces
Equation 4 still makes one major assumption that all of the light from the luminaires goes directly onto the working plane.
An example utilization factor table
Ceiling 70 %
Walls 50 %
Floor 20 %
Length 12 m
Width 12 m
Height 3 m
(Values used in the calculation are always percentages, so in this case, 69 % = 0.69. Some tables may already show the values as fractions, in this case 0.69).
Calculating the Number of Luminaires Required in a Room
- 1.CIE Publication 40: Calculations for interior lighting – basic method (1978)Google Scholar
- 2.CIE Publication 52: Calculations for interior lighting – applied method (1982)Google Scholar
- 3.CIE Publication 97: Guide on the maintenance of indoor electric lighting systems (2005)Google Scholar
- 4.ISO 8995-1:2002(E)/CIE S 008/E: 2001: lighting of work places part 1: indoorGoogle Scholar