# Motor calculations for go-cart / go-kart

I built a basic wooden go-cart and I want to convert it to electric power, and my question is how to calculate the motor. I searched here and apart from this 24V 250W motors I can't see any similar questions. The go-cart is not intended to be high performance. Details are:

• It has 4 wheels which rotate independently on two axles, the front axle is for steering and rear axle fixed.
• It's intended for paved or mostly-smooth and mostly-level surfaces
• For simplicity I planned one motor driving one rear wheel, or two identical motors driving two wheels.
• The wheels are 23cm diameter (0.72m circumference) and I realize gearing is needed between the wheels and the motor.
• Total mass of go-cart, passenger and motor <= 50 kg
• Maximum speed of say 4 m/s, go-cart doesn't need to accelerate faster than 2 m/s/s
• The max speed and acceleration are very approximate and I don't mind if they are greatly different from the above. I based the max speed on the speed of a running person
• Motor to be controlled by controller or even a large rheostat https://surplussales.com/Potentiometers/Rheostats/PotsRheost-1.html

So my approach is to calculate the kinetic energy (KE = 1/2 M V^2) at different speeds to see what power is needed:

• Speed of 1 m/s = 2.2 mph (equivalent to walking). KE = 25 x 1^2 = 25 Joules
• Speed of 2 m/s = 4.5 mph (fast walk). KE = 25 x 2^2 = 100 Joules
• Speed of 3 m/s = 6.7 mph (jogging?). KE = 25 x 3^2 = 225 Joules
• Speed of 4 m/s = 9 mph (running). KE = 25 x 4^2 = 400 Joules
• To acquire a velocity of 2 m/s in 1 second = 100 Joules in 1 second (requires 100 watts)
• To acquire a velocity of 4 m/s in 2 second = 400 Joules in 2 second (requires 200 watts)
• Power = V x A, so assuming a 200 watt motor, this needs 200/12 = 17A from the battery.
• This website https://www.powerstream.com/battery-capacity-calculations.htm says (step 3) if we drain a lead-acid battery in 1 hour we get about half of the rated capacity. So to get 17A for 1 hour would need a 12 volt 35 A/hr battery
• When we know the required current (eg 17A above) this would be the minimum current handling capacity of the motor controller or variable resistor

I realize this method is very approximate, the KE isn't dissipated in 1 second, and the calculations don't allow for friction, gearing, motor or other losses. So my question is: how easiest to calculate the required motor for the go-cart as described?

• Comments are not for extended discussion; this conversation has been moved to chat. Oct 7 '20 at 20:08