Basics of Selecting an Electric Motor

One of the first questions when planning an RC snow cat is: "Which motor should I choose?" or "Is this or that motor sufficient for my snow cat?". Here are the physical basics.

These are the forces acting on a snow cat when climbing a hill at constant speed.

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G = weight of the snow cat, acts downwards
G * sin alpha = weight portion acting against driving direction, alpha = gradient angle (slope)
F = driving resistance of the snow cat, i.e. resistances in powertrain and snow

The weight of the snow cat can easily be determined using a scale. The driving resistance is a different story. Here measurements would be necessary.

For the calculation example we took a typical 1:8 snow cat with a weight of 15 kg (= 147 N).
The driving resistance was chosen rather high with 50% of the weight (= 73.5 N).
The velocity is 0.7 m/sec, which corresponds with 20 km/h of the original.
Gradient angle = 45°, which is a 100% grade and very steep. Here even the original would not be able to climb without a winch. The sinus of 45° = 0.7

power = force x velocity (instead of "x" for "times" the "*" is often used in formulas)
power = (G * sin alpha + F) * v
power = (147 * 0.7 + 73.5) * 0.7 = 123 W

Torque is definde as: power = torque * rotational speed, which yields: torque = power / 2*Pi*speed, whereas the speed has to be given in revolutions/sec.

With a common speed of appr. 240 R/min (= 4 R/sec) the moment is calculated as 123 / (2 * 3.14 * 4) = 4.9 Nm, or rounded up to appr. 5 Nm.

The engine torque would be these 5 Nm divided by the gear box ratio. For example for a 1:50 gear box this would be 0.1 Nm or 10 Ncm. As we are using 2 motors, each motor only has to achieve half of this torque, which is 0.05 Nm (5 Ncm).

On the electrical side power = voltage x current, or current = power / voltage

With a 12 V battery the current is calculated as 123 / 12 = 10 A (without losses, in reality it will be higher)..

We want again make clear, that the big unknown is the driving resistance, which we therefore assumed rather high. Also one would possibly not be able to climb up a 100% grade. So this is also an worst case assumption. This means that the calculated numbers are rather on the safe side.

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