This isn’t choosing a car for the Grasshopper – we took what we were given in the kit.

No, what we are doing here is finding a suitable motor to represent the one in the kit when we create the mathematical model.

On the motor in the Grasshopper kit  is inscribed:
STANDARD MOTOR
RP 380-ST/4440 SM14N 22290 1

If I could have found information for this motor on the web, then all would have been well. But I found very little . 

But I  did find the Mabuchi website, which gave me  details of these motors:

RS-380SH 4535 
and
RS-380PH 4045

They were quite different. In fact the main thing they shared was the 380 code. This meant it was the correct physical shape, which was a start. The most obvious difference between them was the no-load speed, 18000 rpm and 12500 rpm respectively. From what I could find on the web, 18000 rpm was the most likely figure for the motor in the Grasshopper, so I selected the RS-380SH 4535 for my mathematical model. The data for this are given below.

supply voltage	6 V
stall torque	75.6 mNm
stall current	24 A
no load speed	18 000 rpm
no load current	0.8 A
Max efficiency: speed	15 220 rpm
Max efficiency: current	4.38 A
Max efficiency torque:	11.7 mNm

This is a start, but it is all for 6 V, and just three conditions – stall, no load and maximum efficiency. We will need performance for other voltages, and loading conditions.  To predict this I used the basic theory I remembered from the textbook I bought in 1965 for a first year mechanical engineering class.

For  permanent magnet motors I could use the equations there for a ‘shunt wound’ motor.

The equation for torque is:

T = K1*I        where I is current, K1 is a constant

The equation for current is:

I = (V-E)/R       where I is current, V is supply voltage, E is back emf and R is resistance

E is curious. Even though we are looking at a motor, because the windings are moving in a magnetic field they generate a voltage – a back ElectroMotive Force. This can be represented by:

E = K2*n       where E is back emf, n is rpm and K2 is a constant

With the data from the Mabucci website we can find the coefficients we need from these equations.

The stall test gives us:

K1=Ts/Is                        where subscript s denotes stall

The no load test gives us (with a bit more rearranging):

K2 = (V-I0*R)/n0         where subscript 0  denotes zero load

That’s enough for now. Next time I will substitute the data and find the coefficients . And I will check the results against the Mabucci data for maximum efficiency.