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Subject: Re: LED light pipe tail light.
From: Jeff Peterson <jeffreyb.peterson@gmail.com>
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Does this meet the angular spread requirements for the FAA? I forget the
particulars, but the white light pattern has to be seen across a broad
swath to the rear and sides of the aircraft, as I recall.

Douglas W. Johnson MD, FACR

--------
Douglas,

My calculations indicate that the system meets the minimum intensity
requirements but I have not
measured this to confirm the calculations.

Here is the calculation....

The FAA requires at least 20 candela for the azimuth range 110 degrees to
250 degrees.
(FAR 23.1391)

The LED I used, LZ4-40CW00 ($15.20  at Mouser),
uses 14 V, drawing 700 mA and puts out 680 lumens.

1 Candela = 1 Lumen/Steradian

The aft-facing hemisphere has 2 pi steradians, so assuming the lightpipe
transmits about 75%
of the light the average brightness is 0.75 x 680 / (2 pi) = 81 candela


I sanded the output end of the lightpipe flat, which should make the source
 approximately "lambertian", which means the amount of light you see at
each angle is given just by the projected
area of the sanded end that you see.  This means the intensity pattern is
an approximate cosine function of the azimuth, peaking in the aft direction.

At 180 degrees azimuth the flux is higher than the 81 candela average, by a
factor close to pi/2 so the peak intensity is around 127 candela.  At 110
degrees (and 250) measured from the nose, the intensity is reduced to 127 x
cosine (70 degrees) = 43 candela.

This is more than twice the 20 candela requirement so yes, the LED/light
pipe is bright enough.

If I recall the old Whelen aft-facing white light uses 2 amps, so it is
impressive that a little LED drawing 700ma can match it.





-- 
Jeff Peterson

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<span style=3D"font-family:&#39;Gill Sans&#39;,&#39;Helvetica Neue&#39;,Eri=
eLight,Erie,&#39;Eras Medium&#39;,Verdana,Tahoma,Arial,helvetica,sans-serif=
;font-size:15px;background-color:rgb(252,252,252)">Does this meet the angul=
ar spread requirements for the FAA? I forget the particulars, but the white=
 light pattern has to be seen across a broad swath to the rear and sides of=
 the aircraft, as I recall.</span><br style=3D"font-family:&#39;Gill Sans&#=
39;,&#39;Helvetica Neue&#39;,ErieLight,Erie,&#39;Eras Medium&#39;,Verdana,T=
ahoma,Arial,helvetica,sans-serif;font-size:15px;background-color:rgb(252,25=
2,252)">
<br style=3D"font-family:&#39;Gill Sans&#39;,&#39;Helvetica Neue&#39;,ErieL=
ight,Erie,&#39;Eras Medium&#39;,Verdana,Tahoma,Arial,helvetica,sans-serif;f=
ont-size:15px;background-color:rgb(252,252,252)"><span style=3D"font-family=
:&#39;Gill Sans&#39;,&#39;Helvetica Neue&#39;,ErieLight,Erie,&#39;Eras Medi=
um&#39;,Verdana,Tahoma,Arial,helvetica,sans-serif;font-size:15px;background=
-color:rgb(252,252,252)">Douglas W. Johnson MD, FACR</span><div>
<font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight, Eri=
e, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-serif" si=
ze=3D"3"><br></font></div><div><font face=3D"&#39;Gill Sans&#39;, &#39;Helv=
etica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, A=
rial, helvetica, sans-serif" size=3D"3">--------</font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3">Douglas,</font></font></div><div><font face=3D"&#39;Gil=
l Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#3=
9;, Verdana, Tahoma, Arial, helvetica, sans-serif"><font size=3D"3"><br>
</font></font></div><div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica =
Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, =
helvetica, sans-serif"><font size=3D"3">My calculations indicate that the s=
ystem meets the minimum intensity</font></font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3">requirements but I have not</font></font></div><div><fo=
nt face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight, Erie, =
&#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-serif"><font=
 size=3D"3">measured this to confirm the calculations. =A0</font></font></d=
iv>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3"><br></font></font></div><div><font face=3D"&#39;Gill Sa=
ns&#39;, &#39;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, =
Verdana, Tahoma, Arial, helvetica, sans-serif"><font size=3D"3">Here is the=
 calculation....</font></font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3"><br></font></font></div><div><font face=3D"&#39;Gill Sa=
ns&#39;, &#39;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, =
Verdana, Tahoma, Arial, helvetica, sans-serif"><font size=3D"3">The FAA req=
uires at least 20 candela for the azimuth range 110 degrees to 250 degrees.=
</font></font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3">(FAR 23.1391)</font></font></div><div><font face=3D"&#3=
9;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medi=
um&#39;, Verdana, Tahoma, Arial, helvetica, sans-serif"><font size=3D"3"><b=
r>
</font></font></div><div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica =
Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, =
helvetica, sans-serif"><font size=3D"3">The LED I used, LZ4-40CW00 ($15.20<=
/font></font><span style=3D"font-size:medium;font-family:&#39;Gill Sans&#39=
;,&#39;Helvetica Neue&#39;,ErieLight,Erie,&#39;Eras Medium&#39;,Verdana,Tah=
oma,Arial,helvetica,sans-serif">=A0 at Mouser),=A0</span></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3">uses 14 V, drawing 700 mA and puts out 680 lumens.</fon=
t></font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3"><br></font></font></div><div><font face=3D"&#39;Gill Sa=
ns&#39;, &#39;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, =
Verdana, Tahoma, Arial, helvetica, sans-serif" size=3D"3">1 Candela =3D 1 L=
umen/Steradian</font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f" size=3D"3"><br></font></div><div><font face=3D"&#39;Gill Sans&#39;, &#39=
;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, Verdana, Taho=
ma, Arial, helvetica, sans-serif" size=3D"3">The aft-facing hemisphere has =
2 pi steradians, so assuming the lightpipe transmits about 75%</font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f" size=3D"3">of the light the average brightness is 0.75 x 680 / (2 pi) =
=3D 81 candela</font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f" size=3D"3"><br></font></div><div><font face=3D"&#39;Gill Sans&#39;, &#39=
;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, Verdana, Taho=
ma, Arial, helvetica, sans-serif"><font size=3D"3"><br>
</font></font></div><div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica =
Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, =
helvetica, sans-serif"><font size=3D"3">I sanded the output end of the ligh=
tpipe flat, which should make the source =A0approximately &quot;lambertian&=
quot;, which means the amount of light you see at each angle is given just =
by the projected</font></font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3">area of the sanded end that you see. =A0This means the =
intensity pattern is an approximate cosine function of the azimuth, peaking=
 in the aft direction.</font></font></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3"><br></font></font></div><div><font face=3D"&#39;Gill Sa=
ns&#39;, &#39;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, =
Verdana, Tahoma, Arial, helvetica, sans-serif"><font size=3D"3">At 180 degr=
ees azimuth the flux is higher than the 81 candela average, by a factor clo=
se to pi/2 so the peak intensity is=A0</font></font><span style=3D"font-siz=
e:medium;font-family:&#39;Gill Sans&#39;,&#39;Helvetica Neue&#39;,ErieLight=
,Erie,&#39;Eras Medium&#39;,Verdana,Tahoma,Arial,helvetica,sans-serif">arou=
nd 127 candela. =A0At 110 degrees (and 250) measured from the nose, the int=
ensity is reduced</span><span style=3D"font-size:medium;font-family:&#39;Gi=
ll Sans&#39;,&#39;Helvetica Neue&#39;,ErieLight,Erie,&#39;Eras Medium&#39;,=
Verdana,Tahoma,Arial,helvetica,sans-serif">=A0to 127 x cosine (70 degrees) =
=3D 43 candela.</span></div>
<div><span style=3D"font-size:medium;font-family:&#39;Gill Sans&#39;,&#39;H=
elvetica Neue&#39;,ErieLight,Erie,&#39;Eras Medium&#39;,Verdana,Tahoma,Aria=
l,helvetica,sans-serif"><br></span></div><div><span style=3D"font-size:medi=
um;font-family:&#39;Gill Sans&#39;,&#39;Helvetica Neue&#39;,ErieLight,Erie,=
&#39;Eras Medium&#39;,Verdana,Tahoma,Arial,helvetica,sans-serif">This is mo=
re than twice the 20 candela requirement so yes, the LED/light pipe is brig=
ht enough.</span></div>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f"><font size=3D"3"><br></font></font></div><div><font face=3D"&#39;Gill Sa=
ns&#39;, &#39;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, =
Verdana, Tahoma, Arial, helvetica, sans-serif" size=3D"3">If I recall the o=
ld Whelen aft-facing white light uses 2 amps, so it is impressive that a li=
ttle LED drawing 700ma=A0</font><span style=3D"font-family:&#39;Gill Sans&#=
39;,&#39;Helvetica Neue&#39;,ErieLight,Erie,&#39;Eras Medium&#39;,Verdana,T=
ahoma,Arial,helvetica,sans-serif;font-size:medium">can match it.</span></di=
v>
<div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight=
, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-seri=
f" size=3D"3"><br></font></div><div><font face=3D"&#39;Gill Sans&#39;, &#39=
;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras Medium&#39;, Verdana, Taho=
ma, Arial, helvetica, sans-serif" size=3D"3"><br>
</font></div><div><font face=3D"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#3=
9;, ErieLight, Erie, &#39;Eras Medium&#39;, Verdana, Tahoma, Arial, helveti=
ca, sans-serif"><font size=3D"3"><br></font></font></div><div><font face=3D=
"&#39;Gill Sans&#39;, &#39;Helvetica Neue&#39;, ErieLight, Erie, &#39;Eras =
Medium&#39;, Verdana, Tahoma, Arial, helvetica, sans-serif"><font size=3D"3=
"><br clear=3D"all">
</font></font><div><br></div>-- <br>Jeff Peterson<br><br>
</div>

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