# Calculate car acceleration from torque

I have data:

mass = 740 kg
wheel diameter = 670 mm
Rw = 0,335 m
power (max?) = 750 horsepower (551kW)


Now I would like to calculate car acceleration when throttle is max and speed in this moment = 100 km/h = 27,78 m/s

I calculate wheel RPM from this:

wheel speed(RPM) = v(km / h) * 25 / (3 * pi * r(m))


I get

WHEELrpm = 100 * 25 / (3 * 3,14 * 0,335) = 792


Next I calculate engine rpm:

RPMengine = RPMwheel * idifferential * igearbox * iclutch


where:

iidifferential  = 3,42
iclutch = 1
igearbox (gearbox ratio) = 2,55

RPMengine = 792 * 3,42 * 2,55 *1 = 6907


next I calculate torque from:

torque = (POWER * 5252) / rpm


I get

torque = (750 * 5252) / 6907 = 570


And now, apart from the resistance, I want to calculate drive force and acceleration.

I found this:

Fdrive = torque * gearboxRatio * iidifferential  * n / Rw
n - transmission efficiency (0,7?)


But I wonder if I can use it considering previous calculations. How to correctly calculate the acceleration now?

I try to base on this: https://engineering.stackexchange.com/a/22021 but I dont understand this formulas

• acceleration is a change of velocity but you fixed that at 100km/h – Solar Mike Jun 19 '20 at 15:04
• I mean this is speed at this specific moment of time – Mlody87 Jun 19 '20 at 15:14

## 1 Answer

You are fine. I'm not checking your work, but if you know engine torque, the using gear ratios you can calculate torque at the wheel. Force at the road is torque divided by wheel radius, and then A = F/M