But I still maintain that torque is directly proportional to current. I though I would test our point of contention with real numbers so I went to myelectrical/tools/induction-motor-calculator.

Making the assumption that at constant excitation voltage power = voltage * current. I know the current has a real and imaginary part, however I going to assume that we are talking about the real part.

I ran the calculator through 4 different conditions (of power input) and recorded the resulting torque.

This is way I found

What was the point of this exercise? You'll find the equation is:

T = P * 9549 / N

Where

T = Torque in Nm

P = power in kW

N = speed

Of course this satisfies your requirement, it has a constant in the equation. But, I don't see amperage mentioned anywhere.

Jumping ahead, you said in this thread:

*"I know the current has a real and imaginary part, however I going to assume that we are talking about the real part."*Yes, that was exactly what I was talking about. The real part as found in the real world. A clamp on ammeter works for me.

If you had a 1 kW (or 1hp, doesn't matter) motor at the ready, I'd suggest measuring the amperage with the motor unloaded. You'll find the current to be about 50% of the full load rating. Load the motor to its rated torque at rated speed and the current should match the nameplate full load rating. Plot those two points. This is what you'll see:

Torque is X, Current is Y. Now, satisfy the requirement of y = kx and k = y/x with k being a constant.

That's my very simplistic point. Overly broad statements of motor behavior can appear to be incorrect when compared to real world measurements.

I fully understand the reasons why the measurements appear as they do. I've been explaining it plant electricians for more years than I'd like to admit.