Track-Lighting Fixture Math

It's time to order the track (really cable) lighting system for Terry's studio, and I had to do some math to determine exactly what kind of fixtures to order. Terry didn't understand what needed to be calculated so I had to do it myself.

Terry had already calculated that he'd need about 250 watts of light based on the square footage of the room. The calculation is simple, for halogen lights you should have 1-3 watts per square foot. For us that work out to 128 - 383 watts, so 250 is a reasonable number.

The halogen bulbs come in various watts, for the fixtures we selected we can choose 20, 35, or 50 watt bulbs. They also come with various degrees of light spread, the options are 24, 36, or 60 degrees.

So first I had to calculate how big the circle of light would be per bulb, based on the width of its spread. I used the Right Triangle Calculator to figure this out. I knew that the bulb would be 88" above the floor, and I knew the degree-spread for each option. So a 24 degree bulb would illuminate a 39" diameter circle at floor level, the 36 degree bulb would illuminate 57", and the 60 degree bulb will illuminate 102". Armed with this information, I could calculate how many bulbs it would take to illuminate the room, and based on that number I would know the highest wattage per bulb we can use.

I determined that the 60 degree bulbs would be best for overall illumination, since we only need two to just about light the whole area. They are only available in 50 watt versions, so that leaves 150 watts left for other bulbs.

Both the piano keyboard and Terry's drum kit are in the 5' range for width, and that matches up pretty well with the spread of the 36 degree bulb. So we'll add a fixture to shine on each piece of equipment. For simplicity and symmetry I'm actually going to order three of those bulbs, in 50 watts to match the large-spread fixtures.