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How do I calculate forces acting on bicycle axle?

  1. Sep 29, 2015 #1
    Hey everyone,

    I am trying to figure out how to calculate how much total force is being applied to the wheel axle on a bicycle. I'm focusing on the rear wheel for the moment. For the sake of simplicity, let's say that the bike and rider together weigh 100kg and that 60 percent of that is going to the rear wheel. Let's also say that the bike is traveling at up to 10 meters per second. I know that 60kg of force is being applied in a downwards direction on the axle , but I am uncertain as to how I calculate the backwards force being applied when traveling at that speed.
    I wondered if it were simply the weight × the speed in m/s ? But this would give 660kg of total force on just the rear axle alone, and that seems rather high to me. And what about the traction of where the bicycle tyre touches the ground? Does that make a difference and if so wouldn't different tyre widths and different levels of inflation affect that.

    If it's not already obvious, I am an amateur when it comes to engineering, so go easy on me. Any help is much appreciated.

    P. S If your curious, I am considering what material other than metal might be used for the wheel axles, and would like to know how much force is being applied to them and hence whether the material would be strong enough.
  2. jcsd
  3. Sep 29, 2015 #2


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    Staff: Mentor

    Welcome to the PF.

    It sounds like you should be looking into torque as well as force. What reading have you been able to do so far online about axle forces and torques?
  4. Sep 30, 2015 #3


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    Staff: Mentor

    For linear force (which I guess gives you the shear on the axle at the forks, but I'm not sure how useful that is...), you need to know how much force is required to keep a constant speed. Newton's laws tell you the net force is zero, but that just means the forces sum to zero. So, what are the forces propelling and opposing a bike's motion? How do they vary?

    For a simple estimate, you might start by estimating the power input from pedaling and use the definition of work to calculate the force applied to the ground.

    Ps: you'll need to pay better attention to units because the calculation you did doesn't work.
    Pps: what happens to the force when you hit a bump...?
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