# Calculating the propulsive force acting on a car's wheels

• Temp89

#### Temp89

I'm modelling a car in a simulator for fun. The sim's method of acceleration is to apply a force in Newtons on a selected wheel. I've browsed a few topics and whilst some come close there doesn't seem to be any equations that takes into account geartrains. Also I'm fuzzy on the relationship between torque and rpm. Equations seem to use one and exclude the other. I know that higher gears reduce torque and increase RPM but they shouldn't cancel each other out.

I have calculated the drag and rolling resistance in Newtons. I have the wheel radius, torque and RPM curves, the car's mass, the transmission gear and the differential/final drive gear ratios. The car is FWD. For simplicity, assume there is 1 gear ratio with a fixed rpm & torque output.

F = ma, naturally.

Here says we can get velocity using RPM
https://en.wikipedia.org/wiki/Gear_train#Example_2
v = [(wheel rad * 2 * pi) * engine rpm]/(trans gear * drive gear)

And looking at equations from here
http://www.engineeringtoolbox.com/cars-power-torque-d_1784.html
Force = [(Torque * gear ratio) * (Engine RPM / gear ratio) * efficency value]/(wheel radius * wheel RPM)

which does actually give a reasonable value except gear ratio has no impact and it tries to divide by zero if the car is still.

In practice, a motor is limited both in regard to max torque it can generate and max power. At low speeds, max torque is the limiting factor. As the speed increases, the max power limitation lowers the max torque that can be generated.

Did some more research. Have some better equations but still not quite right. Top speeds of low gears are too high and high gears too low.

Engine RPM is determined by accelerator input.

Wheel RPM = Engine RPM/(Gear Ratio*Final Drive)

This is the max speed the wheels can be turned by the engine and if the game detects it as higher due to downhill or whatever acceleration cuts to 0.

Engine Torque is taken from the point on the curve corresponding to the Engine RPM.

Wheel Torque = (Engine Torque * Gear Ratio * Final Drive * efficiency coefficient)/Wheel Radius

It accounts for both acceleration and velocity. Does that seem correct?

Engine rpm is not determined by throttle input: torque is determined by accelerator input.

It seems like you are trying to build a model that finds a way to ignore friction/wind resistance. I'm not sure there is a way to do that that will have any kind of realistic feel to it. Certainly you can't directly equate rpm with accelerator input, otherwise you'd have near instant speed changes.

Wheel Torque = (Engine Torque * Gear Ratio * Final Drive * efficiency coefficient)/Wheel Radius
That is dimensionally wrong. The left hand side has dimension force x distance, but the right has dimension of force. Have you conflated two equations?