|MadSci Network: Physics|
Question: Does knee dragging affect turn radius?
When a motorcycle rider leans into the turn and drags his knee slider, does the friction change the radius of the turn?
An interesting question and a well-defined one. It helps to limit the scope of the answer. I'll still need to make some assumptions. I'll assume that the bike is being ridden near the limit of adhesion in a circle and that the friction between the knee and the road is significant. I suspect that normally the friction is small compared to the other forces in operation. You probably know more about riding a bike than I do, though it was my only transport for a few years. My impression is that the rider uses the knee slider to feel the road and if necessary provide a force to keep him on the bike as he strives to move his body in order to shift the centre of gravity down and to the inside of the bend. This allows the bike itself to be more upright.
Your question though is that if the friction is significant, will the radius be reduced or increased. My first instinct was to say that it will be reduced and that the bike will turn inside the path it would otherwise take. However, I think it depends on the position of the point where the knee contacts the road in relation to the centre of gravity along the line between the bike and the centre of the circle described by the path of the bike.
To find out what a steady frictional force would do qualitatively let's imagine the force of the knee on the road was suddenly very high ie the rider's knee hits a heavy object ( ouch! ). Looking down on the bike we can imagine the big circular path of the bike with the tyres on it and the bike inside the circle at whatever angle is needed to keep it on the circle. The centre of gravity of the bike will be inside the circle as will the point of contact of the knee on the road.
When the knee hits the object which is heavy enough to stop the knee for a moment ( and assuming the rider's body is strong enough to transmit the force to the bike ) the bike will tend to rotate around the knee, but which way ? Will it rotate towards the centre of the circle or away from it ? This will depend on whether the point of contact of the knee is inside or outside the centre of gravity, that is whether it is nearer the centre of the circle or further away than the bike's centre of gravity.
I wonder whether the rider instinctively positions his knee directly below the centre of gravity, the position at which there will be no rotational effect in the plane of the road. Then, any variable friction will not affect his steering. He may place it nearer the centre of the circle so that if he needs to apply a force to keep up-right it will be more effective. In that case, the bike will tend to rotate in the direction which will help to tighten the radius of the circle.
I usually try to think of an experiment to test my answer. I don't think I will on this occasion !
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