Originally posted by SSGGeezer So, doubling speed requires an logarithmic increase in power, similar to audio measurements which I thought were more like exponential increases when doubling the audible signal, with a Log scale for noticeable increases in sound, >3db.

Technically speaking, the kinetic energy in a moving system scales quadratically (x^2). Thus, a mirror going 2X the speed required 2^2 = 4X the energy, a mirror going 3X the speed has 3^2 = 9X, 4X speed has 4^2 = 16X, etc.

BTW, a logarithmic increase in power (power increase = log(x)) would imply a 10X increase in speed only takes 100% more power, a 100X increase in speed only takes 200% more power, and a 1000X increase in speed might only take a 300% increase in power.

An exponential increase would have the power required equal to c^x, where c is a constant that depends on the specifics of the system. If c=2, then 2X the speed takes 2^2 = 4X, 3X the speed takes 2^3 = 8X, 4X the speed takes 2^4 = 16X, etc. The relationship between exposure stops and total light, for example, is exponential with c=2. Thus, designing a photoflash system that gives 3 stops more light means using a flash capacitor and flash tube with 8X the power rating.