This is best described with a picture.
The following image represents a flying airplane. It illustrates how the light gets darker as you approach the rear. Note that the lines represent the required intensity of the light, and is to scale.
The goal is to create a simple, reliable and light position indicator. It shoud be cheap, aesthetically pleasing, and exceed the performance mandated by the FAA or available on certified aircraft.
FAR 23 lays out the light requirements for aircraft tail and positional lights. The text reads:
Sec. 23.1387 Position light system dihedral angles. [(a) Except as provided in paragraph (e) of this section, each position light must, as installed, show unbroken light within the dihedral angles described in this section.] (b) Dihedral angle L (left) is formed by two intersecting vertical planes, the first parallel to the longitudinal axis of the airplane, and the other at 110° to the left of the first, as viewed when looking forward along the longitudinal axis. (c) Dihedral angle R (right) is formed by two intersecting vertical planes, the first parallel to the longitudinal axis of the airplane, and the other at 110° to the right of the first, as viewed when looking forward along the longitudinal axis. (d) Dihedral angle A (aft) is formed by two intersecting vertical planes making angles of 70° to the right and to the left, respectively, to a vertical plane passing through the longitudinal axis, as viewed when looking aft along the longitudinal axis.
(e) If the rear position light, when mounted as far aft as practicable in accordance with Sec. 23.1385(c), cannot show unbroken light within dihedral angle A (as defined in paragraph (d) of this section), a solid angle or angles of obstructed visibility totaling not more than 0.04 steradians is allowable within that dihedral angle, if such solid angle is within a cone whose apex is at the rear position light and whose elements make an angle of 30° with a vertical line passing through the rear position light.
Sec. 23.1385 - Position light system installation.
(a) General. Each part of each position light system must meet the applicable requirements of this section and each system as a whole must meet the requirements of 23.1387 through 23.1397.
(b) Left and right position lights. Left and right position lights must consist of a red and a green light spaced laterally as far apart as practicable and installed on the airplane such that, with the airplane in the normal flying position, the red light is on the left side and the green light is on the right side.
(c) Rear position light. The rear position light must be a white light mounted as far aft as practicable on the tail or on each wing tip.
(d) Light covers and color filters. Each light cover or color filter must be at least flame resistant and may not change color or shape or lose any appreciable light transmission during normal use.
[Doc. No. 4080, 29 FR 17955, Dec. 18, 1964, as amended by Amdt. 23-17, 41 FR 55465, Dec. 20, 1976; Amdt. 23-43, 58 FR 18977, Apr. 9, 1993]
Sec. 23.1387 - Position light system dihedral angles.
(a) Except as provided in paragraph (e) of this section, each position light must, as installed, show unbroken light within the dihedral angles described in this section.
(b) Dihedral angle L (left) is formed by two intersecting vertical planes, the first parallel to the longitudinal axis of the airplane, and the other at 110 degrees to the left of the first, as viewed when looking forward along the longitudinal axis.
(c) Dihedral angle R (right) is formed by two intersecting vertical planes, the first parallel to the longitudinal axis of the airplane, and the other at 110 degrees to the right of the first, as viewed when looking forward along the longitudinal axis.
(d) Dihedral angle A (aft) is formed by two intersecting vertical planes making angles of 70 degrees to the right and to the left, respectively, to a vertical plane passing through the longitudinal axis, as viewed when looking aft along the longitudinal axis.
(e) If the rear position light, when mounted as far aft as practicable in accordance with 23.1385(c), cannot show unbroken light within dihedral angle A (as defined in paragraph (d) of this section), a solid angle or angles of obstructed visibility totaling not more than 0.04 steradians is allowable within that dihedral angle, if such solid angle is within a cone whose apex is at the rear position light and whose elements make an angle of 30° with a vertical line passing through the rear position light.
[Doc. No. 4080, 29 FR 17955, Dec. 18, 1964; 30 FR 258, Jan. 9, 1965, as amended by Amdt. 23-12, 36 FR 21278, Nov. 5, 1971; Amdt. 23-43, 58 FR 18977, Apr. 9, 1993]
Sec. 23.1389 - Position light distribution and intensities.
(a) General. The intensities prescribed in this section must be provided by new equipment with each light cover and color filter in place. Intensities must be determined with the light source operating at a steady value equal to the average luminous output of the source at the normal operating voltage of the airplane. The light distribution and intensity of each position light must meet the requirements of paragraph (b) of this section.
(b) Position lights. The light distribution and intensities of position lights must be expressed in terms of minimum intensities in the horizontal plane, minimum intensities in any vertical plane, and maximum intensities in overlapping beams, within dihedral angles L, R, and A, and must meet the following requirements:
(1) Intensities in the horizontal plane. Each intensity in the horizontal plane (the plane containing the longitudinal axis of the airplane and perpendicular to the plane of symmetry of the airplane) must equal or exceed the values in 23.1391.
(2) Intensities in any vertical plane. Each intensity in any vertical plane (the plane perpendicular to the horizontal plane) must equal or exceed the appropriate value in 23.1393, where I is the minimum intensity prescribed in 23.1391 for the corresponding angles in the horizontal plane.
(3) Intensities in overlaps between adjacent signals. No intensity in any overlap between adjacent signals may exceed the values in 23.1395, except that higher intensities in overlaps may be used with main beam intensities substantially greater than the minima specified in 23.1391 and 23.1393, if the overlap intensities in relation to the main beam intensities do not adversely affect signal clarity. When the peak intensity of the left and right position lights is more than 100 candles, the maximum overlap intensities between them may exceed the values in 23.1395 if the overlap intensity in Area A is not more than 10 percent of peak position light intensity and the overlap intensity in Area B is not more than 2.5 percent of peak position light intensity.
(c) Rear position light installation. A single rear position light may be installed in a position displaced laterally from the plane of symmetry of an airplane if --
(1) The axis of the maximum cone of illumination is parallel to the flight path in level flight; and
(2) There is no obstruction aft of the light and between planes 70 degrees to the right and left of the axis of maximum illumination.
[Doc. No. 4080, 29 FR 17955, Dec. 18, 1964, as amended by Amdt. 23-43, 58 FR 18977, Apr. 9, 1993]
Sec. 23.1391 - Minimum intensities in the horizontal plane of position lights.
Each position light intensity must equal or exceed the applicable values in the following table:
------------------------------------------------------------------------
Angle from right or
left of longitudinal Intensity
Dihedral angle (light included) axis, measured from (candles)
dead ahead
------------------------------------------------------------------------
L and R (red and green)............. 0° to 10°... 40
10° to 20°.. 30
20° to 110°. 5
A (rear white)...................... 110° to 180° 20
------------------------------------------------------------------------
[Doc. No. 4080, 29 FR 17955, Dec. 18, 1964, as amended by Amdt. 23-43, 58 FR 18977, Apr. 9, 1993]
This is best described with a picture.
The following image represents
a flying airplane. It illustrates how the light gets darker as
you approach the rear. Note that the lines represent the required intensity of the light, and is to scale.
Sec. 23.1393 - Minimum intensities in any vertical plane of position lights.
Each position light intensity must equal or exceed the applicable values in the following table:
------------------------------------------------------------------------
Intensity,
Angle above or below the horizontal plane l
------------------------------------------------------------------------
0°..................................................... 1.00
0° to 5°.......................................... 0.90
5° to 10°......................................... 0.80
10° to 15°........................................ 0.70
15° to 20°........................................ 0.50
20° to 30°........................................ 0.30
30° to 40°........................................ 0.10
40° to 90°........................................ 0.05
------------------------------------------------------------------------
[Doc. No. 4080, 29 FR 17955, Dec. 18, 1964, as amended by Amdt. 23-43, 58 FR 18977, Apr. 9, 1993]
Again, the light gets darker as you move up and down.
Sec. 23.1395 - Maximum intensities in overlapping beams of position lights.
No position light intensity may exceed the applicable values in the following equal or exceed the applicable values in 23.1389(b)(3):
------------------------------------------------------------------------
Maximum intensity
-----------------------
Overlaps Area A Area B
(candles) (candles)
------------------------------------------------------------------------
Green in dihedral angle L....................... 10 1
Red in dihedral angle R......................... 10 1
Green in dihedral angle A....................... 5 1
Red in dihedral angle A......................... 5 1
Rear white in dihedral angle L.................. 5 1
Rear white in dihedral angle R.................. 5 1
------------------------------------------------------------------------
Where --
(a) Area A includes all directions in the adjacent dihedral angle that pass through the light source and intersect the common boundary plane at more than 10 degrees but less than 20 degrees; and
(b) Area B includes all directions in the adjacent dihedral angle that pass through the light source and intersect the common boundary plane at more than 20 degrees.
[Doc. No. 4080, 29 FR 17955, Dec. 18, 1964, as amended by Amdt. 23-43, 58 FR 18977, Apr. 9, 1993]
A properly designed and positioned reflector should make this a non-issue. Bascially, you don't want people on your right seeing your green light. The only time this would be an issue is if the lens gets scratched and dirty. We'll avoid scratched and dirty lenses.
Sec. 23.1397 - Color specifications.
Each position light color must have the applicable International Commission on Illumination chromaticity coordinates as follows:
(a) Aviation red --
y is not greater than 0.335; and
z is not greater than 0.002.
(b) Aviation green --
x is not greater than 0.440 - 0.320y;
x is not greater than y - 0.170 and
y is not less than 0.390 - 0.170x.
(c) Aviation white --
x is not less than 0.300 and not greater than 0.540;
y is not less than x - 0.040 or y - 0.010, whichever is the smaller; and
y is not greater than x+0.020 nor 0.636 - 0.400x;
Where y0 is the y coordinate of the Planckian radiator for the value of x considered.
[Doc. No. 4080, 29 FR 17955, Dec. 18, 1964, amended by Amdt. 23-11, 36 FR 12971, July 10, 1971]
That is somewhat difficult to interpret without a picture, but a simple diagram makes the intent clear. The obvious goal of the FAA is to mold the light output so that an airplane's position and direction can be interpreted by an observer from the visible lights. It's important to remember that what is not showing is just as important as what is, and that is provided for in the maximum intensity sections.
The conventional method of achieving this goal is to create lots of light by heating a filament in an omni-directional bulb, and then use a reflector to block and direct the light in the proper direction. To create the different colors, gobs of full-spectrum light are created and then a colored lens traps all but what needs to be presented. At multiple points, light energy is created and then thrown away as heat. Not very efficient, but it worked well enough to make Thomas Edison rich and famous. To produce enough light, the conventional tail light bulbs run about 25W and the wing tips are around 40W.
The light emmitting diode is a solid state device that converts electric energy directly into light. Some energy is lost as heat as the electric current flows through the device, but it is only a fraction of what the conventional bulb produces. The light is also directional and its color is nearly pure, being determined by the chemicals used in creating the diode material and the casing. The result is that the energy is nearly all used to produce light where it is needed instead of heat.
The goal is now reduced to engineering a device to direct enough light in the proper direction to satisfy the FAA and make the airplane visible. Until recently, LEDs produced only a miniscule amount of light, making it difficult to pack enough together to be useful for anything other than panel indicators; however, recent introductions have changed that. SuperBright LED are cheap and bright. Determining how many are necessary is a difficult exercise due to the multiple ways of measuring a device's light output and then converting one to another, but the math can be simplified if we just ignore the unecessary distractions and concentrate on the goal of dumping enough light in the proper direction.
I have spent a lot of time trying to bend my brain around all of the calculations with steradians, luminous flux, inverse square laws, etc, ad infinitum, before I finally realized that most of that stuff is simply a distraction. The FAA specifies the required light intenities in 'candles' which is not equivalent to the 'candela', and that is the unit that is used to specify the intensity of LEDs . The candela is a a measurement of a lights intensity at a point source. More area will produce more light, but only insanity ensues if we go that way. The road is simple if we stick to the requirements...a point source that produces the appropriate intensity.
A moments consideration will make it clear why the FAA chose the point source intensity vs the total output to specify the requirement. A 6ft flourescent tube may produce the same amount of total light as a standard bulb, but at a distance the flourescent tends to wash out and blend with the background. The standard bulb will look more like a sparkle that is more likely to draw the other pilot's attention. And the whole point of a marker light is to get attention. I strongly disagree with anyone who claims that the apparent brightness of various lights do not matter as much as what can be measured by various devices. Unless those devices are to be mounted in the airplane and used as a primary scan device, it will be a set of human eyes that are used for collision avoidance. At the end of the day (pun intended), it will be the apparent brightness as measured by a set of eyes that keeps airplanes off one another. That being said, we have little choice but to use a measurement tool to specify the intensity of a device if we are to use any type of unit like the candle. The method I propose is to calculate what should be necessary and then compare that to other devices currently in use that do meet the requirements (or have at least passed through the FAA approval process).
So, we start with the FAA requirements and LED specifications. We just have to bring the two together in a reasonable fashion. The LED manufactures specify the intensity with a measurement in candela and a spread in angles. The spread is an angle from the center of the light emission pattern out to the point where the intensity is half that of the center. The FAA specifies that the light intensity in foot candles, has a minimum intensity when viewed from a specified angle. It's just a matter of devising an arrangement whereby the intensity exceed the minimum from all appropriate angles. One of the assumptions I will use is that two point sources place close enough together will converge and their intensities will be additive.
First we have to convert from footcandles to candelas. There's a neat online calculator to help us with that. For the 40 footcandles specified, we will need 430 candelas. BestHongKong, as of 27 July 2006, has an excellent deal on some very powerful LEDs mounted on a 3/4" round substrate. They specify the light output for the green ones to have 130lm over a 35 degree spread. How to convert from lumens to candelas? We have a guide for that on the net also. His neat little table specifies a conversion for us. beam angle cd/lm 5 167.22 10 41.82 15 18.60 20 10.48 25 6.71 30 4.67 35 3.44 40 2.64 45 2.09 So with a 35 degree spread 3.44=Xcd/130lm. Solving for X, give us 447 candela, or 41 footcandles. Just a little more than enough for our purposes. Older stuff. Below was some design work I had done about a year ago (2005 timeframe). Even as I was working this out, the guys at BestHongKong were working hard to make it obsolete. The diagram below illustrates two arrangement of 10cd/15degree, 6cd/30degree and 2.5cd/45degree LEDs that will enable us to meet the vertical requirements.
The center facing LED (W10015) only produces 10cd, where the FAA asks specifically for 20cd. The difference is mostly covered by the contribution of the two W6030s facing only 10degree above and below the center line. The W6030 will only put out about 3cd when viewed from 15degrees off its center. Assuming a linear degradation, there will be about 18cd at the centerline (10 from W10015 and 4 from each of two W6030).
Not quite up to spec, but we're not done yet. Now we have to combine several of the vertical arrangements to provide horizontal coverage as specified by the FAR. The diagram below illustrates an arrangement that will do this nicely.
The vertical ...let's call them 'cards'.... are arranged such that the light from a W6030 in the first B card will flow into the field of the first A card. The second B card will actually be assisted by 4 W6030s, 2ea from the 2 A cards to each side.
(UPDATE: Ok. So I've been lax in working out the CAD views for the above text. The truth is that the keyboard on the laptop that was my CAD machine crapped out on me, and I haven't made it a priority to fix. (wing rib building has been my latest distraction) If anyone has a spare keyboard for an IBM 380Z Thinkpad laying around that you don't need...8*)
The pictures below are the ones that I have completed and should convey the necessary information on how to line up the lamps.)
Once the number of LEDs and the direction of each is known, it's necessary
to point them that way. One method is to mount the LED such that there is
a space between the legs and the circuit board. It can then be bent to the
proper direction. 'Potting' the board (encasing the whole thing in epoxy)
ensures that nothing ever moves out of place. Another method, the one I have
chosen and describe below, is to machine a structure that will hold the body
of the LED in the appropriate orientation. The legs can then be connected
as necessary. I have found this method to be attractive in the one-off situation
that most homebuilders find themselves in.
The first step is to select a suitable piece of 1/4" plexiglass or Lexan. The finished product will be very small, so start with a piece somwhat larger. The second piece needed is several angle blocks. A piece of 2x4 and a chop saw will give you what you need in just a second. My design used 30 and 45 degree blocks. Now just chuck a 3/16" bit in a drill press set for it's highest speed. If it isn't at least an eighty degree day, heat the plexiglass with a hair dryer for a while. Plexiglass gets brittle real fast with temperature drop and a little heat and high bit speed will make a special plexiglas bit unnecessary.
The physical arrangement doesn't necessarily have to follow directly from the logical diagram. As long as the LEDs are all located within a few inches of one another, they will converge to a single point past 50 ft or so. This point can be used to our advantage to construct slim, contour fitting lights that blend with our airframes. The pictures below details the construction of an arrangement for a tail light that is less than an inch wide.
Start with the straight through holes in the middle. Use a 3/16" bit and use the drill press' highest speed. The bit will walk through the plexiglass like it isn't even there.
Lay the piece on the angle blocks and tilt the drill press table as necessary to get holes that point in the appropriate direction. You can drill from the front or back. It takes a little bit of geometric mental gymnastics to imagine how to attack each hole, but it's not extremely difficult and each hole is reproduce across 4 quadrants. A 3D CAD program would help to space everything more symmetrically, but the completed example below was done on the fly. It's not exact, but back up 10ft and it won't matter. If the pilot behind you hasn't seen you by that point, you'll have to build a new one anyway.
Notice the tilt on the drill press table.
Now plug the holes with the LEDs. They'll be a tight fit, which is a good thing. Make sure you'll have clearance to solder the leads together. Now, pull them out, coat the sides with some epoxy, and shove them back in.
The last step is to shape the plexiglass carrier to a pleasing shape.
Electric connections.
The goal is to have a solid chunk of plastic with a connector or a group of wires sticking out to get electrons to the LEDs. My design foregoes circuit boards and such for the chunk-of-plastic simplicity.
LEDs like all diodes are constant voltage devices. Except for the effects of a small amount of internal resistance, they will drop the same amount of voltage across the leads, regardless of the voltage applied, until they burn up. This is not technically true as temperature and other factors have some small effect, but is close enough to design a reasonable system.
I aimed to design the system so that it would work within manufacturers specifications between 11 and 15 volts. The methodology was to subtract the diode's voltage from system's, and drop the rest across a resistor that would limit the current to an appropriate value. Checking the specs at SuperBrightLeds.com, I first notice that the price has dropped since I bought some last. Then I remember what I'm doing and note that the max forward current is 100mA, the max continous current is 30mA, and the forward voltage maxes out at 4 and is typically 3.5V. The operating temp is -20 to 80 degrees Celsius.
I went through several iterations, but what I ended with is two LEDs and a resistor in series. The LEDs will drop 7V leaving 4V to 8V to be dropped by the resistor. At the max 8V (system at 15V), the resistor must limit the current to 30ma. Since R=E/I or 8/.03, we'll need a 266.66ohm resistor. The RatShack doesn't carry that value, but since 15 is a rather high system voltage and the LEDs will have some internal resistance, we can compromise a little and use 240ohm. Power is I2*R or, 0.216W. A standard 1/4W, 240ohm resistor is cheap and easily available. Going to 1/2W is just as cheap and available, and will provide a ridiculously large safety margin under normal conditions. Since I=E/R, there will only be 12.5mA when the battery drops to 11V. The light output of the LED is linear with current, so it will only produce one third the rated light output on a 11V battery. Keep adding LEDs if you want to light up the city till the battery is down to around 7V, at which point it won't have enough potential left to jump the LEDs and the lights go out.
The LEDs are one way devices, so they have to be connected correctly. If they are connected in reverse they will not light up. There are a lot of places on the net that will tell you the 'cathode' and 'anode' and which is which, but I use that information just often enough to not be able to ever remember it. The easy way is to connect the lead next to the flat spot on the case of the first LED to the leg away from the flat spot on the next LED. Tie on a resistor and connect a battery across the leads. If it doesn't work, switch the leads around. You won't burn the LEDs up if you apply the current in reverse because they effectively turn the circuit off. Do that for each of the pairs in your lamp, then connect all the ends together. Wrap a piece of scotch tape around the side of the lamp to form a bowl. Arrange all the leads so that nothing is touching, and all of the components are below the top of the bowl, then pour in a glob of 5 minute epoxy. (Keep it cool at this point as that 5min stuff likes to heat up).
Boom! You're done.
I would like to thank Eric and other members of the Aerolectric Connection mailing list. Their input and corrections to my first prototype forced me (kicking and screaming) to investigate and better understand the more complicated issues in creating and distributing enough light to produce a safe tailight. That first prototype only used 9 LEDs and produce about 25% of the required output.
The cigarette lighter plug is NOT part of the lamp. It is just a convenient way to get electrons flowing through the circuit. The blue block in the lamps top left corner is the connector.
