Interior Lighting for Designers

illuminance at the target is equal to thesine
of the angle of incidence or tilt.

fc=×

I

D^2

sinθ

whereIis theintensity of the source (in can-
delas) in the direction of the light ray,θis the
angle of tilt between nadir and the direction
of the target, andDis thedistance from the
source to the target (figure 10.7).
In figure 10.7,His the vertical mounting
height of the light source above the target
andRis the horizontal distance (run) from
the light source to the target.

Example
A 60PAR/HIR/SP10 lamp is tilted at a 30°
from nadir to cast light on a vertical surface
6 ft away. To determine illuminance on the
surface, follow these steps:

1. From an intensity distribution chart (figure
   10.3, left), find that the 60PAR/HIR/
   SP10 lamp produces 20,000 cd at 0°
   (the direction of the ray).


2. From the table of trigonometric functions
   (table 10), find that the sine of 30° is
   0.500

fc =

20,000

12

2 ×=^069 .500

Source at nadir, target on vertical
surface located to one side
If the source is aimed straight down but a
vertical target is located to one side of the
light ray, the illuminance at the target on the
vertical surface will be reduced by the sine of
the angle between nadir and the target.
To calculate illuminance from a source
at nadir to a target located to one side on a
vertical surface, the same formula is used:

fc=×

I

D^2

sinθ

whereIis theintensity of the source (in can-

delas) in the direction of the light ray,θis the

angle between nadir and the direction of the

target (to one side), andDis thedistance

from the source to the target surface (figure

10.8).

Example

A 60PAR/HIR/FL30 lamp is pointed straight

down. To determine the illuminance at a

target that is 10° to one side of nadir on a

vertical surface 12 ft away, follow these

steps:

1. From an intensity distribution chart (figure
   10.3, right), find that the 60PAR/HIR/
   FL30 lamp produces 2,800 cd at 10°
   (the direction of the ray).


2. From the table of trigonometric functions
   (table 10), find that the sine of 10° is
   0.174.

fc =

2,800

12

2 ×=^03 .174

Shortcomings

The inverse-square method yields only a

rough idea of what is perceived. Its chief use

is for comparison, as when establishing the

illuminance ratio between an object and its

surround. Even here, the inverse-square

method fails to account for any inter-

reflections within the space. And more sig-

nificantly, perceived brightness depends on

the reflectance of the surface and the posi-

tion of the observer.

Average Illuminance Calculations

To ensure that adequate illuminance is pro-

vided over a large area, thelumen method,

orzonal-cavity calculation, is used. This cal-

culation is performed by hand or generated

by computer; it predicts the average

illuminance incident on a horizontal work

surface, usually the workplane.

PHOTOMETRICS