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I can get a simple linear model if I make the "reasonable" assumptions:
1) e=C1*omega: back emf is proportional to angular velocity, and
2) omega=C2*I: angular velocity is prop to current.
Then the terminal voltage equation: V=e - Ir becomes
V = C1*C2*I - IR, or [equation 3]
V=C*I, a straight line in V/I space.
How realistic is this (and for what type motors)?
(Obviously, I also assume a constant mechanical load.)