[Kevin Sevcik]

I'm not holding out that it can't be done by FIRST students. I'm simply declaring that it's somewhat impractical and uneconomical... At least doing it in any of the straight-forward obvious ways the were first discussed here. I think Ken's suggestion of using known rotary inertias plus a large amount of math and testing is the most practical solution. Given the datalogging capabilities of the cRIO, you could probably pull it off with the right instrumentation and careful calibration. It wouldn't be quite as simple as he's hoping, I think. The motor would be accelerating the known inertia of your load, plus the unknown inertia of the motor's rotor. In fact, there's a fair few parameters you'd have to account for to model the motor better than a first order approximation. And if you only care to a first order approximation, why aren't you using the spec sheets? Anyways, here's the parameters I can recall/think of:

Motor torque constant
Motor emf constant (should ideally be the inverse of the above, not necessarily independent)
Motor armature resistance (can be tested at low voltages with locked rotor)
Motor armature inductance (ditto)
Motor rotor inertia
Motor static friction
Motor dynamic friction

I know there's possibly external magnetic field losses in there somewhere, but I think those might be negligible in the motors we work with. Anyways, ignoring the resistance and inductance as separate problems, that gives you 4 unknowns, so you'd want 4 independent data points at a minimum. I'm pretty sure it could be done with at least two different load inertias, and two different voltages applied as step functions to the system. That plus some educated initial guesses based on no-load speed, etc., and you could probably get some decent values. Once you've worked out all the non-linear regression stuff you'd be needing. But it could probably be done. It'd certainly make a heck of a capstone project for any FIRSTer that needed one.