Electric Vehicle Speed Distance Formulas

Prob'ly can. (I don't think the speed/torque curve of the motor's going to come into it too much (just a feeling)).

Problem with the "each second" approach is that doing it incrementally means any little error at each step will be propagated to the next, so it could end up introducing a BIG error at the end.

If you can handle the sums, I think the maths (analytic) route would be a better way to go.

Thanks. Once I get the overall sheet worked out I will substitute constant torque/speed/force/acceleration values and see how much the answers deviate from ideal. I think it will only cover the first minute of acceleration in any case. BTW, the accel curves seem to generally follow an 1-[e^-t] form.

Of course you can do this in a discrete time analysis approach instead of an analog approach. You need to learn about the Z transform to properly explore this. For most motor performance curves though I expect that a Δt of one second will be too coarse of a unit step size.

IF you understand the system variables, use the correct equations (always double check your units), and choose the time-increment wisely, a discrete time or time-step simulation can provide very precise results. Hint: Air drag losses typically dominate above ~35 mph for most common vehicles.

Smaller time-steps provide the best solution, but the computation time becomes excessive. I've run many of these simulations and suggest you start at 10ms for this particular application. I'd expect you could increase dt to 100ms with little loss of accuracy. While a dt of 1 second should work fine during steady-state "cruise" conditions, it may be too large during periods of acceleration/deceleration.

The dt is the diminishing limit of delta t.

So barring round off errors etc, the result should be the same as the integrals.

I have modelled some pretty fancy veneer lathe systems with wide field range motors and very fast accel decel times. The "closed" equations were brutal and still boundary limited.

Another solution was done with excel with 10ms sample intervals and it yielded essentially the same results. Both were close enough to reality to be valid.

Good luck with the project.

That's a good way to model a system, especially where nonlinearities are involved. You probably need to model your battery pack (discharge rate vs capacity, etc) and your motor contoller (and driver commands) as well, to give you a complete picture.