So far I have:

• selected a motor characteristic to represent the motor in the Tamiya Grasshopper
• used theory to produce a general mathematical model
• used data on the selected motor to customise the general mathematical model into one specifically for the selected motor

How good is our model?

Conveniently the Mabuchi website gives us more data than we need for developing our model. We can use the left-over data to check – at one point at least.

To get the coefficients in our model we needed the stall data and the no-load data.

The website also gave us the speed for maximum efficiency and the torque and power at that condition, as shown in the table:

quantity	Mabuchi data
supply voltage	6V
n, maximum efficiency	15220rpm
I, max efficiency	4.38 A
T, max efficiency	11.7 mNm
Power, max efficiency	18.6 W

We will compare these data with what our model predicts.

Last time I calculated the current, torque, power and efficiency over the operational speed range of the motor to produce the graph. 

All I had to do now was look at the column of efficiencies and find the maximum. Here is what I found.

quantity	Mabuchi data	my prediction
supply voltage	6V	6V
n, maximum efficiency	15220	15120
I, max efficiency	4.38 A	4.51 A
T, max efficiency	11.7 mNm	11.7 mNm
Power, max efficiency	18.6 W	18.5 W

The predicted current is too high by 3%, probably because of the way I handled no load torque, but it’s still pretty good. 

That’s about as far as I can take the theory at this stage. 

It’s time for some tests.