Light Distribution Analysis
Light in a vacuum obeys an inverse square law. This means that if it takes a given output I to illuminate an area 1 foot away, it takes 4*I to illuminate an area 2 feet away, and 9*I to illuminate an area 3 feet away. It turns out that light traveling in air can be modeled as light traveling in a vacuum, and thus, obeys the same inverse square law.
Modeling light sources is a task that defies hand calculation. Due to that, we have found a product that allows us to computerize the process. Lambda Research Corporation's TracePro software allows us to import geometry from Pro/ENGINEER models and assign properties to the surfaces.
Once the geometry is imported, we can assign certain surfaces as emitters. Using Lambda's Source Property Generator and the manufacturer's data sheet, the Property Generator can create a raytracing spectrum for an LED.
Following this process for a recent benchmarking board using 6 120-degree viewing angle LEDs from Avago (the ASMT-MW00 model) on a board gave the following output irradiance map on a target 14 feet away.
Actual real-world testing of this board gave an output of 1.1 ft-cd at the center of the lit area, with the following progression of light intensities: 1ft from center (1.0ft-cd), 2ft (0.9ft-cd), 5ft (0.87ft-cd), 10ft (0.57ft-cd), 15ft (0.38ft-cd), 20ft (0.27ft-cd).
In order to find the angles needed for our fixture, we created a series of simple geometric checks in Pro/ENGINEER. Using the following image, we showed the needed angle at the base of the light pole:
The above shows the need for a roughly 44-degree viewing angle on the down-facing LEDs.
Next, we had to examine the angle needed to reach the far distance.
This shows that the outer set of LEDs need to be pointed at a 70-degree angle to reach the 40-foot lateral distance.
Finally, we had to find the angle required to cover the sidewalk width at the far distance:
This shows that the LEDs on the angled boards needs to be approximately 15 degrees.
As we have access to LEDs with 120-degree, 30-degree, and 15-degree viewing angles, we were able to come up with a concept using 18 LEDs. Six LEDs face straight down, and have 120-degree viewing angles. The other 12, in two groups of six, face the far distances and have 15-degree viewing angles.
Further testing showed that the Avago LEDs and collimating lenses did not perform to spec. Further research revealed LEDs that matched spec much more closely: CREE XLamps. These LEDs have been included in the final design.