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The closest question I could find with regards to this subject was this one:
Countersteering a motorcycle

However, it does not address the specific physics of what I would like to know.

There are 3 ways to lean when turning a motorcycle:

  1. Upper body remains upright while the bike leans.
  2. Whole body remains aligned with bike.
  3. Most of the body "hangs off" the side leaning in.

I'm trying not to make any assumptions to allow for detailed and proper answers addressing issues I may not have considered; hopefully, without being too generic.

So to summarize, I would like to know whether the first 2 items are sufficient for all conditions or whether the 3rd has some physical properties necessary in certain conditions.

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    $\begingroup$ Somewhat related: physics.stackexchange.com/q/132449 and physics.stackexchange.com/q/506 $\endgroup$ – Brandon Enright Sep 3 '14 at 15:49
  • $\begingroup$ I noticed that riders in Le Tour de France do #3, and it got me wondering ... $\endgroup$ – garyp Sep 3 '14 at 17:27
  • $\begingroup$ @garyp Yep, and it's to keep the tire's best tread region in contact with the road. $\endgroup$ – Carl Witthoft Sep 3 '14 at 18:12
  • $\begingroup$ Well, the riders on Le Tour just rotate their hip so that the knee juts out toward the ground. The bicycle does not appear to be more upright. I guessed that it lowers the center of mass. I'm both a road cylclist and a mountain biker. I find better control on my road bike if I extend my knee like that. But on my mountain bike I find better control if I keep my body upright causing my bike to tilt more. Mountain bike tires are knobby, and pressure is kept low. So perhaps this posture keeps better tread contact. In any event, I've had this question also ... but without too much thought. $\endgroup$ – garyp Sep 3 '14 at 20:38
  • $\begingroup$ as an advanced motorcyclist, and not a physicist, the only correct procedure option is 2. Its worth noting to the uninitiated, that you dont lean to turn a motorcycle, you countersteer. Option 3 has no advantage whatsoever on the road, however on the track riders do this so they are able to judge the amount of lean, normally with their knee, or in some loony cases, their elbows. $\endgroup$ – DevDonkey Apr 5 '16 at 8:27
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The point of lean is to keep the center of mass aligned with the force vector which sums gravity (purely perpendicular to the horizon) with the acceleration forces created by the turn. Traveling in a straight line, the only force is gravity, so you center yourself upright over an upright bike. As you initiate a turn, you lean at some angle; the more aggressive the turn, the greater the angle from vertical. At some point, you will either exceed the limits of the tire's grip, or some part of the bike will contact the ground. In either case, the most likely outcome is a spill.

If you have very grippy tires, the limit of the bike's lean could will be interference with the road from some part of the bike. That's when the rider would want to hang off the bike - to increase the effective lean of the bike i.e. move the center of mass further - without a further increase in lean of the bike.

Apart from bike part contacts road, another consideration may be the design of the tires and the geometry of a sharply inclined rotating tire on the road; that the tire tread may no longer be simply planting itself on the road but squirming around. If that is happening, one would expect a few not-so-nice things to go along with it - wasted energy, wear on the tire, loss of effective grip because of opposing forces, and loss of grip because static friction between tire and pavement has been replaced by dynamic friction.

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All the force to accelerate or turn a motorcycle come from the wheel/ground interface. So to turn a bike quickly means a larger force on the wheel (from friction on the ground).

If the bike were upright when a strong sideways force were applied, it would quickly rotate the bike around its center of mass and dump the rider. Instead, the rider leans into the turn so that the sum of the friction and normal forces go through the center of mass and there is no torque to flip the bike.

The harder the turn, the more the center of mass must be displaced from the vertical. So the hardest turn possible would be limited either by the static friction of the tires, or by the amount the center of mass could be displaced. Hanging off allows for greater displacement.

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    $\begingroup$ That's not answering the question. The reason to hang out rather than lean is related to a desire to keep the main part of the tread in contact with the road. If the bike itself leans, you better have proper competition tires with tread up the "sidewall," as do motorcycle racers, who lean the bike over so far they use skid plates on their inside knee. $\endgroup$ – Carl Witthoft Sep 3 '14 at 18:11
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    $\begingroup$ Just to make what @CarlWitthoft said a bit more explicit; when the rider "hangs off" to the inside of the turn, then the bike does not have to lean over quite as far in order to put the combined bike/rider center of mass in the right place. Not leaning the bike as far is what keeps the right part of the tires in contact with the road. $\endgroup$ – Solomon Slow Aug 26 '15 at 16:16
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The important thing about leaning in is that it puts you closer to the road so you don't have so far to fall when you exceed the stickiness of your tires.

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