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Friction when wheel slip is zero

  1. Mar 20, 2014 #1
    Most graphs show that when wheel slip is zero then the friction is zero. But I can't get it, as when the vehicle stand still on slope, the friction keeps the vehicle from going down hill

    Could someone explain for me?

    http://www.albi-engineering.nl/Electronics/Traction_Control/slipgraph.jpg [Broken]
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Mar 20, 2014 #2
    The slip ratio is (car speed - wheel speed)/(car speed), so when the car and wheels are stopped the slip ratio doesn't really make sense to define. The above graph above will only help you when you know the slip ratio, if not you'll need another graph (maybe someone else measured the static friction of the tyre?).
  4. Mar 20, 2014 #3

    So let say car speed and wheel speed are not zero, slip ratio is still zero when car speed equals wheel speed, and friction is zero. I can't get it, how can friction be zero?
  5. Mar 20, 2014 #4
    Friction of zero means that whatever the normal load on the tyre, it cannot generate any longitudinal force. Or another way to look at it, in order for the tyre to generate a non-zero longitudinal force the slip ratio must be non-zero.
  6. Mar 20, 2014 #5
    Yes, I knew that, but the problem is, I can not get it.

    Imagine a car moving at a constant speed with no slip on tire. So there is only static friction, no kinetic friction.

    Now the engine accelerates the wheel and the wheel should rotate faster. If this accelerated force is under the static friction limit, then the wheel will not slip, and it will rotate faster. The problem is that is model is completely wrong according to the above graph, no slip means no acceleration, but why? That is how I cant get it
    Last edited: Mar 20, 2014
  7. Mar 21, 2014 #6
    The instant the engine makes the wheel rotate faster, the wheel will then be rotating faster than the car so you will have a non-zero slip ratio. This then gives a non-zero coefficient of friction from your chart above and allows the tyre to generate a longitudinal force causing a forward force to act on the car to accelerate it. Depending on how hard you accelerate there will be an equilibrium at some point on your graph where the wheel is always rotating a bit faster than "it should" (ie how fast the wheel would be rotating if it were free to rotate).

    Maybe there are a couple of points you are missing:

    1) The tyre is not infinitely stiff, the wheel hub can be spinning faster than a free wheel would be without significant slip. This works because the bits of the tyre tread not in contact with the road have a higher angular velocity than the bits of tyre tread in contact with the road. Under acceleration the rubber slows down when it hits the road to match the speed of road, then speeds up again as it leaves the road. Then, the *average* angular velocity of the tread (and wheel hub) can be higher than normal "rolling".

    2) Under any acceleration there will be a small area of sliding between the tyre and road. The contact area of the rubber and the road has a finite area, and the normal loading on this area is not constant. Specifically around the leading and trailing edge the normal load is very low (going to zero as the rubber hits and leaves the road). Near this area it is easy for the rubber to slip without any noise or much force or wear. From 1), when the rubber starts to come in contact with the road it is going too fast for the road so it slips for a fraction of a second then grips. As you accelerate harder each bit of rubber takes longer to match the road speed, so the area that is slipping against the road grows. Eventually the whole contact area will be slipping, and you'll be past the peak in your graph, you'll be doing a burn-out :-)

    It's a bit like wearing shoes with very thick, very soft rubber soles, and trying to run in them. As you hit the ground with one step your foot itself will be lined up with the sole in contact with the ground, but to extert a force to push you forwards you need to push backwards which will cause your foot to move back faster than the road. When you lift your foot at the end of the step the rubber sole will spring back to it's normal position.
  8. Mar 23, 2014 #7


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    You can see static friction as a static activation force that must be overcome to enter the regime of dynamic friction. Since with static friction there is by definition no relative movement, no work is being done. Once the static friction threshold has been overcome, dynamic friction will begin to generate heat at the sliding contact.
  9. Mar 24, 2014 #8


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    I would expect those curves were not measured for a car driving on a road. It is more likely they were just one wheel running on a rolling road, with the motors adjusted to drive the wheel and the road at a constant relative speed, while measuring the motor torques to calculate the friction.

    In that situation, if there was no slip the motor torques would be very small, so the curve looks like it goes through zero, even if it doesn't go exactly through zero.

    The first part of the curve says is that to maintain a constant very small amount of slip (say 1%) and driving at constant speed, you can only apply a very small amount of engine power.

    To relate these curves to the performance of a real car on a real road, you also need to factor in the mass of the car and the friction force required to accelerate the car. If you did that, the curves would look different, but the basic message remains the same, to get maximum acceleration, you need a small but controlled amount of slip.

    The control system on the car probably doesn't use the "curve" to do any clever math. I expect it just measures what the car is doing, and adjusts the gas pedal to keep the slip from getting too big, rather like an ABS braking system but for acceleration not braking.

    from http://www.albi-engineering.nl/Electronics/Traction_Control/body_traction_control.html [Broken] (which is where the OP's graph came from)

    Some SUVs with 4WD already have similar systems, but they are designed to control the vehicle at low speeds driving off-road, not for road racing.
    Last edited by a moderator: May 6, 2017
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