The figure below describes the forces and torque that acts on the bike, with the frame of reference at the centre of combined mass (rider and bike).
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| Figure 1: Forces (blue) and Torque(red) acting on the bike in the 'counter-steering' step. Left image is top-bottom view, right image is rear-front view of the bicycle. Front wheel create lateral force (friction) that both 'yaw' and 'roll' the bike. |
Once the bike starts to roll (counter-clockwise as in Figure 1), rider starts to steer into the direction that they would like to go. The action once again create extra lateral force (friction) on the front tyre, which would create torque in roll-axis (clock-wise, to stop the bike from dropping) and to 'yaw' the bike to the direction rider wish to follow. At first, the front experiences more side-way friction than the rear. However, the rear and the front tyre will create equal lateral force (friction), to 1) stop the bike from rolling (roll-axis), and 2) creating centripetal force that is required for the cornering.
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| Figure 2: Forces (blue) and Torque(red) acting on the bike at the first step of steering. Left image is top-bottom view, right image is rear-front view of the bicycle. |
I was invited to comment from this stackoverflow question: http://bicycles.stackexchange.com/questions/39187/loading-front-wheel-in-a-sharp-turn/39190.
ReplyDeleteThe point about front tire experiencing more lateral force at the beginning of turn is true, but insignificant compared to forces during stable cornering. First, a balanced bike is either unstable or metastable, so it requires next to no force to tilt. Second, the angular velocity ("yaw") of the bike and rider during cornering is very slow, and because of this the initial angular acceleration is not large either.
there is no problem at the initial counter-steering step. However, let's consider the transition from 'counter-steering' to 'steering'.
Delete1) During the transition, the bike is 'unstable', and continue to roll (accelerating). This means that the bike also has less available grip. The front wheel transitioned from 'counter-steering' position to 'steering' position. This action generate a large slip-angle on the front wheel, relative to the rear wheel. This relatively rapid transition causes the front tire to experience fair amount of lateral force (recalling concept of slip-angle). This can be observed by the trail of the front wheel before the cornering, the curvature of the transition in the front wheel is relatively sharp, comparing to the curvature of the front wheel during stable cornering.
2) After the transition, I agree that the rear wheel would experience larger 'slip-angle'. This can be observed by the trail left by a bicycle after cornering.