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Wheel acceleration in relation to vertical LOAD and current speed

  1. Jun 10, 2012 #1
    Hello everybody!

    I'm trying to write a car simulation but I'm having problems with precisely calculating the acceleration / velocity of the car's wheel. Currently the simulation works as if the Car was lifted in the air, so there is no load (vertical force) on the Wheel. What I have so far:
    - the applied torque (engine torque multiplied with appropriate values)
    - mass moment of inertia of the wheel

    Now I would like to take into account the weight Load on the Wheel. How do I do this?
    Currently the wheel spins up pretty fast even in 5th gear (well not at low RPM, but once the engine and axle are rotating together), but in reality I know it should be accelerating slower at high speeds - but it accelerates at the same speed as in 1st gear. I assume this is normal for no load on the wheel (though I might be wrong!!).

    Any help would be appreciated! :)

    Also this is my first post and this is not a homework assignment.
  2. jcsd
  3. Jun 10, 2012 #2


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    The only significance of the vertical load on the wheel is that it permits a frictional force to develop between road and wheel. This applies a torque to the wheel, leading to a forward force on the wheel axle. This is what propels the car. If the frictional force is sufficient, the torque from the road balances the torque from the engine sufficiently that the wheel rolls instead of skidding.
    Your observation re accn versus gear is correct. If the engine is working at constant power then the kinetic energy will increase at a constant rate, regardless of the gearing. A low gear just means the engine spins faster. In practice, engines work best within certain ranges of spin, hence the need for gears.
  4. Jun 11, 2012 #3
    Thank you, it was really helpful for understanding how things work!

    However I would really like to know the exact formula to calculate the torque loss (?) due to wheel load, but can't find anywhere on the internet. So if we have:

    - torque applied to the wheel axle
    - moment of inertia of the wheel
    - mass or vertical force of load on wheel
    - road friction maybe

    how do I change the formula which I currently have:

    velocity = velocity + (torque / inertia)

    Does the load somehow reduce the torque? Change the moment of inertia? Reduce acceleration? If so, how? (just to be accurate with the weight + weight distribution of the car, I don't really want random numbers)

    Edit: velocity is in rad/s, torque is in N-m
    Last edited: Jun 11, 2012
  5. Jun 16, 2012 #4


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    You say I've helped, but from your latest questions I'm not sure. You're still fixated on vertical load, though I already pointed out this is mostly of interest in ensuring there's no skidding. It does not act to reduce torque or slow the vehicle. What matters is inertia.

    Let the mass of the vehicle (including wheels) be M, the moment of inertia of the wheels (all 4 combined) be I, torque (total for driving wheels) T, wheel radius R.
    The linear acceleration A of vehicle = TR/(MR2+I)
    For normal road cars, I is fairly insignificant, simplifying it to A = T/(MR). I guess I matters for dragsters.
    I'm assuming road friction is adequate to prevent skidding, and I've ignored rolling resistance. Rolling resistance deducts a constant amount from the acceleration, so long as the velocity is nonzero.
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