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# Light: Lumen Method

Light is as much a 'material' as concrete, steel or glass for, whilst there would be no building were it not for its actual structure, we could never sense or appreciate it were it not for reflected light. Light is therefore a fundamental factor in any building design.

In recent years it has been realised that the intuition of the architect alone is not sufficient to fully comprehend the interplay of light and predict with certainty the amounts of illumination in all parts of the room. On the other hand, the computational tools available are also insufficient in themselves to achieve 'beautifully' lit buildings. Intuition and imagination are therefore very important in lighting design, but have no validity unless based on some level of objective analysis.

Early developments in artificial lighting were mainly concerned with quantity, gaining more light for less energy - an essentially engineered solution. Now the concerns are focused more on architectural function, not simple utility. With the huge range of lighting options available, it is now a design solution. However, the utility is taken for granted, with even the worst architect being required to at least meet the minimum lighting standards set in regulations.

### The Lumen Method

In rooms lit with a uniform array of luminaires and where the minimum lighting level in the room is not to be less that 70% of the maximum level, the lumen method of lighting design can be used. This is the simplest method of calculating the overall illumination level for such areas. It is accurate enough for the majority of purposes, and is the calculation most used by lighting engineers when determining the number of luminaires for a given lighting level. The simple formula is as follows:

$\large E = \frac{F}{A}$

Where:
E is the average (or minimum) illumination level at the work plane (lux) , F is the useful lumen output of all sources (lumens) and A is the total surface area of the working plane (mÃ‚Â²).

In terms of architectural design, solving for F allows the architect or engineer to determine the total amount of light required in the room. This is given by rearranging the formula as follows:

$\large F = A E$

It must be realised that the resultant value is not the total lamp lumens as not all of the light produced by each lamp actually reaches the work plane. Many factors affect the amount of light reaching the work plane:

• The size and proportion of the room.
• The height of the light fixtures above the work plane.
• The reflectance of wall and ceiling surfaces.
• The nature of the light fixture and its distribution of light.
• Light loss due to ageing, dust collection and yellowing.
• Atmospheric particles such as smoke or dust.

Some of the most efficient fixtures in the most effective layout can result in up to 80% if the installed flux reaching the work plane whilst ineffective fixtures in a dark-coloured room can result in only 2%. As a result, the steps required in using the Lumen Method of lighting design are as follows:

#### 1. Select Required Illumination

Most countries have a set of minimum lighting levels for various tasks. The designer must determine what the minimum required illumination level is for their particular application.

This is simply a matter of calculating the total surface area over which the required illuminance is to be distributed and multiplying this by the required illumination level using the formula F = AE. This gives the amount of Ã¢â‚¬ËœusefulÃ¢â‚¬â„¢ light required. From this, the total installed flux can be determined.

#### 3. Select a Light Fitting

A preliminary assessment must be made of the type of lighting required, a decision most often made as a function of both aesthetics and economics. This fitting may prove unsuitable for the lighting task, however, the next few steps are used to determine this.

#### 4. Determine Mounting Height

The distance from the source to the working plane is very important as it is a major determinant of the final illumination level. This is simply a function of the inverse square law.

#### 5. Determine Room Index

The Room Index is required when using tables to find the utilisation factor. It is given by:

$\large RI = \frac{(l x w)}{(l + w)} \times H_m$

Where l is the length of the room, w is its width and HM is the mounting height above the work plane.

#### 6. Determine Coefficient of Utilisation (UF)

Using tables available from manufacturers, all architects offices will have several, it is possible to determine the coefficient of utilisation for different light fittings if the reflectance of both the walls and ceiling is known, the room index has been determined and the type of luminaire is known.

#### 7. Determine Maintenance Factor (MF)

The maintenance factor is based on how often the lights are cleaned and replaced. It takes into account such factors as decreased efficiency with age, accumulation of dust within the fitting itself and the depreciation of reflectance as walls and ceiling age. For convenience, it is usually given as three options;

Maintenance Factor
Good = 0.70
Medium = 0.65
Poor = 0.55

#### 8. Determine Number of Fixtures

This is done by first applying the above factors to the received flux in order to determine the installed flux. This if achieved using the following formula;

$\large F_{installed} = \frac{F}{(UF * MF)}$

From the installed flux, the number of fixtures required can be determined by simply dividing by the total output of each selected light source.

#### 9. Check Spacing of Fixtures

Once the number of fixtures is known, they must be distributed uniformly throughout the enclosure. This is simply a matter of determining a grid based on the total number.

Once the spacing between grid lines is known, it is important to use a significant amount of imagination and common sense in order to visualise what the resulting light pattern will actually be like. The total number of fixtures may be correct but they would need to be spaced so far apart that there is a significant falloff in lighting levels between them. Conversely, they may need to be placed so close that their physical dimensions overlap. Either way, the selected fitting is going to be unsuitable for the required lighting task. Simply select a new fitting (based on the experience gained in this calculation) and perform steps 3-9 again.

Lumen Method Calculations
http://personal.cityu.edu.hk/~bsapplec/lumen.htm
Light: Lamp Selection
Light: Luminaires