Interior Lighting for Designers

Source aimed at an angle to a
horizontal surface
If the source is aimed at an angle toward the
target instead of being perpendicular to the
target, the light will spread over a greater
area, reducing the illuminance at a specific
point. For ahorizontalsurface, the reduction
is equal to thecosineof the angle of inci-
dence or “tilt.”
To calculate illuminance from a source
at an angle to a horizontal surface:

fc=×

I

D^2

cosθ

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 light ray, andDis thedistance from
the source to the target surface (figure
10.5).
In figure 10.5,His the vertical mounting
height of the light source above the target of
measurement, andRis the horizontal dis-
tance (run) from the light source to the
target.

Example

A 60PAR/HIR/SP10 lamp is tilted at 30° from
nadir (straight down) to cast light on a hori-
zontal surface 12 ft away (D). 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 in the Appendix), find that the
   cosine of 30° is 0.866.

fc =

20,000

12

2 ×=^0 .866^120

Source at nadir, target on

horizontal surface located

to one side

If the source is aimed straight down but the

target is located to one side of the central

ray, the illuminance at the target on a hori-

zontal surface will be the intensity of the

beam at nadir reduced by the cosine of the

angle from the source to the target.

To calculate illuminance from a source at

nadir to a point located to one side on a hori-

zontal surface, the same formula is used:

fc=×

I

D^2

cosθ

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, andDis thedistance from the source

to the target surface (figure 10.6).

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

horizontal 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 cosine of 10° is
   0.985

fc =

2,800

12

2 ×=^019 .985

Source aimed at an angle to a

vertical surface

If the source is aimed at an angle toward a

target on averticalsurface, the reduction in

INTERIOR LIGHTING FOR DESIGNERS