I came across a problem that got me confused about the difference between RMS and the arithmetic average. Let's say I have a conveyor belt that starts and stops periodically throughout the day. It moves at a constant speed and then stops for a time. If I measure the distance the conveyor moves over the day and then divide by the time elapsed, I get an average speed. Pretty simple.

Because the graph of the speed of the conveyor over time looks like a pulse wave, and I'm used to doing RMS calculations for that kind of electrical signal to find mean voltage, I thought that it might be interesting to try the RMS of the speed. I used sqrt((1/t2-t1)speed^2*dt) and summed the whole sequence of start and stop times together for the whole day.

Basically, I found that the RMS value was too high. If the Peak was 100ft/minute with a duty cycle of 50%, it's effectively an average speed of 50ft/minute over the day. The RMS of this function is 70.71ft/minute. This does not correspond seem to correspond to any real quantity.

Why does RMS work for something like voltage, but not for a conveyor belt?