**Cornell University Ergonomics Web**

DEA3500: Ambient Environment: Luminaires
and the Basics of Lighting Design

#### Distribution of Light

The light output of a uniform point source of light is 4piI lumens where
- I = intensity in candelas
- 4pi = complete surface area of a sphere of 1 meter radius

Thus if light source had an intensity of 10 candelas, total light output = 4piI = 4pi10 (4pi = 12.6) + 12.6 x 10 = 126 lumens.

Efficiency of lamp is Lumens watt -1, so if source is 40 watt and gets 126 lumens, efficiency would be only 3. However, luminaires seldom distribute light equally in all directions because of reflection and refraction. See diagram. Some measure of the distribution of light from a source is needed (polar curve).

**Polar curve **(for both up and down light sources)
Light distribution is commonly indicated graphically in the form of a polar curve. Here the intensity of light in a series of directions (usually at
10° intervals) is plotted. See diagram. For most luminaires the downward light flux greatly exceeds the upwards light flux.

**Rectilinear graph** - (for downward only light sources) - candlepower by distance.

**Linear luminaires **- e.g. fluorescent luminaires. Here it is usual to produce 2 polar curves, one for the long axis (axial) and one at 90o to this (transverse).

#### Light output from lamps and luminaires

Suppose a luminaire housing a lamp giving 1000 lumens has a light output of 300 lumens above the horizontal and 400 lumens below (see diagram).
Light output ratio

LOR = light from luminaire / light from lamp

= 300 + 400 / 1000

= 0.7 or 70%.

Upward light output ratio

ULOR = 300 / 1000 = 0.3 or 30%

Downward light output ratio

DLOR = 400 / 1000 = 0.4 or 40%.

Upper flux fraction

= Upward light / Total light from luminaire

= 300 / 300 + 400 = 3/7 or 43%

Lower flux fraction

= Downward light / Total light from luminaire

= 400 / 300 + 400

= 4/7 or 57%

Flux fraction ratio (fff)

= Upper flux ratio / Lower flux ratio

= 43/57 = 0.75

NB as output increases downwards fff decreases.

As output increases upwards fff increases.

As output balances fff = 1.0.

Light output ratios and flux fractions are involved in the calculation of glare indeces.

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