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Calculating driving force from wheel rpm, wheel radius and engine power

  1. Oct 13, 2009 #1
    I have spent a while trying to work out a simple equation to give me the driving force of the engine in a car using the inputs: Power, wheel radius and rpm but when I put in real numbers from a production car, I get low values of 2197N. The equation I have derived is:

    Driving force = 30*P/(rpm*r*pi) where P is the power of the engine in Watts, rpm is the rpm of the wheel after it is geared down, and r is the radius of the wheel.

    Assuming there are no passengers or even a driver and the effects of friction and drag etc. are neglected, by my calculation of the maximum acceleration in first gear, given a car mass of 1420kg, is 1.5ms-2 which seems to me to be too low even for a slow car.

    To derive the equation I just used, the equations P=Tw, Torque= Force*wheel radius and w = (rpm*pi)/30, where w is the angular velocity, T torque and P power.

    Can anyone verify if this equation is right and whether I have done something wrong?

    Many thanks


    Paul Harris
  2. jcsd
  3. Oct 13, 2009 #2
    The derivation is... different i'll give you that.

    A tip for deriving this sort of stuff, start from where the power and torque are made (ie the engine). Then trace it along to the wheels. It's not working becucase you are putting in wrong values into an equation that wont acutally give you what you want. Where did you get the values you are sticking into that equation?

    You dont even need power to calcualte the triving force, its all done with torque.

    Torque*gear ratios = wheel torque.
    Then WT= F* radius.

    Convert power to torque at the start if you dont have a torque figure.

    If you are using power to determine acceleration, and therefore force you need a velocity.
    Last edited: Oct 13, 2009
  4. Oct 13, 2009 #3
    Hi Paul Harris-

    First, the relation between force F and acceleration a is:

    F = ma

    Force times displacement dx is work (joules)

    Force times work per unit time dx/dt is power (watts)

    But dx/dt = velocity v

    So P = Fv = mav (Newton-meters per second) = watts

    You are already aware that it is easier to accelerate from zero to 10 mph than from 70 mph to 80 mph. The velocity v in this equation is why.

    Now, write power as torque T (Newtons) times angular velocity w (radians per second) where RPM is wheel RPM.

    P = 2 pi T RPM/60

    P = 2 pi T RPM/60 = mav.

    That's it. The wheel RPM is directly proportional to velocity, so once you know torque, mass and velocity, you can calculate acceleration. Note all units except RPM are metric.

    Bob S
    Last edited: Oct 13, 2009
  5. Oct 14, 2009 #4
    Thanks for your replies guys.

    I suppose I should have stated that I need to eliminate torque from the equation. This is because the force needs to be calculated from a Power vs. engine rpm curve. I have no direct information on the engine torque so it needs to be calculated from the power (P=Tw).

    Converting engine rpm to wheel rpm is simple enough (multiplying by the gear ratio). Acceleration does not really need to be calculated, it was just to check if my equation for force was producing sensible answers.

    I cancelled the 2/60 part of the equation to give 1/30 and eliminated T by using T=Fr. Is this right and does then then mean that my equation is in fact technically correct and producing correct answers? Doesn't 1.5ms-2 for a car's maximum acceleration seem a bit slow to anyone? The data I used was a max power of 124kW at 5900rpm (engine rpm) and a 1st gear ratio of 2.92:1 producing a wheel rpm of 2021rpm and according to my equation, 2197N of driving force. The wheel radius is 0.2667m.

    Thanks again

    Paul H
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