φ
v
⎡
⎢
C
z
(
δ
)
all
δ
horizontal
⎣
m/2
≅
∑
bands with I
V
> 0
all
θ
within
horizontal band
∑
I (
θ
,
δ
)
⎥
V
n
⎤
⎦
C
z
(
δ
)
≅
4
π
2
cos (
δ
)
nm
Where:
Φ
v
= total luminous flux emitted by the light source
I
v
(θ,δ) = luminous intensity emitted at angular position
θ
degrees left/right and
δ
degrees up/down.
n
= number of horizontal divisions that an imaginary
sphere surrounding the signal lamp is subdivided
into. For example, for 5° increments, n =
360°/5° = 72.
m
= number of vertical divisions that an imaginary
sphere surrounding the signal lamp is subdivided
into. For example, for 5° increments, m =
360°/5° = 72.
δ
= vertical angle of midpoint of horizontal band.
For example, for 5° horizontal bands (i.e., m = 72),
the midpoint of the horizontal band covering
angles from –2.5° to 2.5° would have a value
of
δ
= 0° and the midpoint of the horizontal band
covering angles from 2.5° to 7.5° would have a
value of
δ
= 5°.
Since most photometric specifications are specified
in horizontal and vertical increments of 5°, the zonal
constant is equal to:
As an example of the
zonal constant integration technique,
consider the total luminous flux emitted by an automotive
amber rear turn signal (a similar example for an automotive
rear brake lamp is given in Stringfellow, HBLED, pp
246—247). The U.S. requirements for the rear amber turn
signal are contained in SAE J588 titled
Turn Signal Lamps
For Use On Motor Vehicles Less Than 2032 mm In Overall
Width.
The minimum photometric design guidelines are
shown in Table 1.1. Note that the minimum luminous intensi
ties are specified over a range of 10 degrees up and down
and 20 degrees left and right.
C
z
(
δ
)
=
4
π
2
cos (
δ
, in increments of 5
°
)
72
2
=
0.007615 cos (
δ
)
Tip: Since most automotive signal lamps are only specified
over a narrow range of up and down angles, typically 15U to
15D, in increments of 5 degrees left and right, then the zonal
constant, C
Z
(δ), is approximately equal to 0.0076.
For a detailed derivation of the
zonal constant
integration technique,
please see G. B. Stringfellow and
M. George Craford,
High Brightness Light Emitting Diodes,
pp. 233—246.1
Figure 1.2 Zonal Constant Integration.
SuperFlux LEDs in Automotive Application Brief AB20 1 (5/04)
6
LUMILEDS [ LUMILEDS LIGHTING COMPANY ]
