I'm really confused with resistor power rating and pulses. I'm trying to determine the power rating of a resistor that will receive pulses of potentially 40 volts for 15 milliseconds. During this pulse it is receiving high power. But it will only receive this pulse once every three seconds for a total of ten seconds. The resistance that will be seeing this is a 16 ohm resistor. What should be the power rating of the resistor in this situation? Or at least how would I go about seeing if a resistor would have sufficient power rating to sustain this situation?
So, 100W, 15ms at a time? And after the three pulses, there's plenty of time for it to cool back down to room temperature?
100W is the absolutely safe rating, of course. The question is, can less be used?
Most resistors carry an overload rating, something like 5x for 5s. This seems quite safe to use here, so a 20W resistor might be fine.
If we can use an energy argument, 100W * 15ms = 1500mJ. But be careful here: pulse-rated resistors are usually for a given waveform, e.g. 8/20µs (IEC 61000-4-5 surge), or 10/1000µs (some telecom standard), etc. If they give power/energy vs. time curves, you can find if this point is inside the curve. If not, extrapolating from a different waveform can be dubious.
A straight energy argument fails, because resistors aren't time-asymptotic energy reservoirs. Specifically, for short time periods, heat only flows into the resistive element, dissipating potentially quite high peak powers, but limited energy. Power drops and energy rises with time, as the heat spreads out into nearby materials. (It does happen to be near-proportional in semiconductors, probably due to thru-plane conduction -- more or less a one-dimensional heat flow.) How fast, depends on what materials. So you can get quite different curves for metal film, wirewound, metal-case, sand resistors...
There are also high-pulse "bulk" resistors, fairly specialty, but handy when you need only very little duty cycle:
They don't have much to say about them, so I assume they treat them as energy summed over some time period, with power (average over that time period) within ratings.