Re: Accelerated ageing of incandescent lamps at a higher voltage

I have worked with and tried to understand incandescent lamps for several decades, but I have never worked with the exact kind of problem that you ask about! It's a very good question, and I will make a stab at helping us all understand it.

At almost any lamp manufacturer's site you can find charts and/or graphs of the expected life of a bulb based on the operating voltage versus design voltage. One example is here. The nice part about this particular reference is that it gives us actual equations to work with. The equations are very similar to what other manufacturers could give us, with the main features that the input parameters are the design voltage (V2) and the operating voltage (V1).

For the benefit of those who don't go out to the site above, here is the equation we'll be using:
B1 = B0(V1/V2)^-12

But your question is basically a two-step question because you want to change the operating voltage before the lamp actually fails at the first voltage. Okay, let's think about that. The equation for lamp life multiplies a power (-12) of the voltage fraction (V1/V2) times the rated lamp life, B0. In your example you start off with V1 of 36 volts, and V2 of 28 volts. You didn't specify a rated lamp life, but I'll just pull a number out of the air and say the rated life B0 is 500 hours. Using the equation we find that the fraction (V1/V2)^-12 is 0.049!!! That means that the actual life is only 4.9% of the rated life, at 36 volts! (Keep in mind that the equations aren't very accurate when the actual voltages vary from the design voltage by more than 10%, but we can still get the flavor of what's happening.) At the rated life of 500 hours (my out- of-the-air number) the actual life would only be 24.5 hours, so we probably never get to the 100 hours you wanted! Hmmm....okay, to make the problem realistic lets say the rated life is 5000 hours, so the actual life at 36 volts would be given as 245 hours. After you have run the lamp for 100 hours, you have 145 hours left in its life, at 36 volts. Okay, let's now call B0 145 hours, and call 36 volts the design voltage!!

The actual voltage, in the second step of your problem, is now 28 volts. The fraction (V1/V2)^-12 is now 20.4, and multiplying that times the remaining life of 145 hours gives us 2960 hours left in the lamp's life. (Notice that 20.4 = 1 / 0.049)

So, you can see that, in our example, the lamp only gets a total of about 100 + 2960 hours, or 3060 hours, out of the rated life (at the original design voltage!) of 5000 hours. Running the lamp at the increased voltage takes its toll on the lamp!

Keep in mind three things:
a) The calculations are very approximate because we have exceeded the +/-10% utility of the equations.
b) The utility of the equations in a two-step process like this is questionable.
c) The rated life of lamps is a statistical average, with a wide variation (standard deviation) in the population. That is, you can make calculations but the actual performance of any one lamp can vary significantly from the average.

John Link, MadSci Physicist