Elroch said:
Do you accept the point that if you pick your frame moving with the bike, so that the plane through the points of contact and the centre of gravity is considered as "vertical", then in this frame, the artificial centrifugal force (which results from the fact that the frame is rotating) and the gravity add to give a single perceived force in this "vertical line"?
The reason this viewpoint is useful is it is close to what the rider experiences. They experience something very close to an increased gravitational force which stays in the same direction relative to them and the ground becomes steeply sloping to the side. The effect of banking is to cancel out this slope in the ground. This is modified slightly by the choice of riders to shift their centre of gravity to the side, which means the tilt of the bike is lower (as the plane between the centre of gravity and the contact points is at an angle to the centre plane of the bike) . As far as I can see, this choice does not make it possible to go faster, as long as the tyre works over the full range of angles, which it should. It would be interesting to study whether riders really get any physical advantage out of changing their position on the bike, or whether (surprisingly) it just feels better.
Here I implicitly assume the rider is moving in a constant circle at a constant speed, but it is a very useful approximation.
Yes, that model works, but rider still experiences 2G of forces. Banking only cancels out lean-angle, but it doesn't cancels out cornering forces. While you may be able to take 1G corner without leaning, there is still 1G of gravity and 1G of cornering. Just happens that cornering-forces are in-line with bike; it's pushing up on tyre instead of sideways on it. In cases of Wall-of-Death, there can be unlimited "cornering" traction since there's no leaning whatsoever.
This is especially apparent on 2-wheel vehicles that don't have as high cornering forces as motorcycles... say bicycles on velodrome. These are banked at either 20 or 30-degrees depending upon tightness of curve. At tighter 0.25km velodromes such as Hellyer Park or Encino, you really can feel the extra G-forces on your neck. On 0.33km velodromes like Cal State Dominguez Hills, curve isn't as tight, so less G-forces, even though bike still stays straight & upright relative to track surface.
There is an advantage when you change angle between effective CoG and contact patch. It allows for higher cornering forces with less lean angle and you don't run off edge of tyre. There
IS an upper limit for lean-angles where you
WILL roll off and crash. None of this idealistic "assuming unlimited traction" stuff not connected to reality.
This is where testing part of scientific process comes into play to verify hypotheses. Numerous real-world experiments have been conducted to verify:
1. there is
not unlimited traction on tyres
2. there
is a lean-angle limit beyond which you'll roll off edge of tyre and crash
3. when at this lean-angle limit, separating body & bike to maintain lean-angle, yet increase angle between effective CoG and contact-patch
DOES allow for faster cornering without crashing.
This is typically what racers do in practice. They go faster and faster each lap and typically stay in-line with bike at lower-speeds. As you get up to lean-limit, you can feel bike starting to slide. Next laps around, you keep lean-angle, but hang off more. Suddenly, bike doesn't slide anymore. Then laps after that, you can continue with increasing speeds gradually again.
