Limit Cornering

[Erunanethiel]

When you are at the max lean angle and generating as much grip as the tires you have allow in a steady-state, long corner, how do you exit the turn? I think it is theoretically impossible.

You counter-steer into the turn to bring the bike up? That increases the lateral load on tires because you momentarily make the center of mass of the bike+rider system to make a turn, so you fall.

You accelerate? You fall.

You decelerate? You fall, no matter the method. Just shutting down the throttle a bit would increase the lateral force on the tire espically over 45 degrees of lean angle.

Pushing down on the outside peg? The outside peg pushes you up, and since you are leant over, when you go "higher" your center of mass tries to take a tighter turn around the center of the corner. Since "up" is "in" when leaned over. And also the force on the motorcycle by that downward force on the peg increases lateral force on the tires and well, you fall.

Any upper body movement you make that would be of any benefit, could also have been used to take the corner at a higher speed.

 

This really bugs me as a thought.

 

Am I missing something?

 

[Hotfoot]

On ‎12‎/‎29‎/‎2019 at 9:47 PM, Erunanethiel said:

You counter-steer into the turn to bring the bike? That increases the lateral load on tires because you momentarily make the center of mass of the bike+rider system to make a turn, so you fall.

 

I do not understand this statement, can you restate it or explain it more?

If I understand your question about how to exit a corner, you are talking about coming out of the corner onto a straight(er) part of track, and you are asking how to change the arc to put the bike in a straighter line, is that right? 

If so, then the answer is yes, you would counter steer to bring up the bike. The momentary instability caused by the countersteering effort is overcome right away by the increased grip afforded by getting the bike more upright (primarily due to your suspension being able to work more effectively). In other words even if the front tire DID slide a little, it would recover, and in fact that is often how riders recover when a tire starts to slide - by standing the bike up. (Sometimes they recover by just staying loose on the bars and the tires regain grip either because they reach better pavement - like a slide on a greasy spot in the road - or because the bike has slowed some.)

Keep in mind, though, that the rider must make a reasonably controlled steering input - a death grip on the bars that restricts bar movement, or a rider pushing on BOTH bars, or an extremely rough bar input could indeed cause a fall.

[Erunanethiel]

On 12/31/2019 at 11:31 PM, Hotfoot said:

I do not understand this statement, can you restate it or explain it more?

If I understand your question about how to exit a corner, you are talking about coming out of the corner onto a straight(er) part of track, and you are asking how to change the arc to put the bike in a straighter line, is that right? 

If so, then the answer is yes, you would counter steer to bring up the bike. The momentary instability caused by the countersteering effort is overcome right away by the increased grip afforded by getting the bike more upright (primarily due to your suspension being able to work more effectively). In other words even if the front tire DID slide a little, it would recover, and in fact that is often how riders recover when a tire starts to slide - by standing the bike up. (Sometimes they recover by just staying loose on the bars and the tires regain grip either because they reach better pavement - like a slide on a greasy spot in the road - or because the bike has slowed some.)

Keep in mind, though, that the rider must make a reasonably controlled steering input - a death grip on the bars that restricts bar movement, or a rider pushing on BOTH bars, or an extremely rough bar input could indeed cause a fall.

Edited the OP, you are right regarding what I am asking. 

 

But I do not think you'd be able to bring the bike up at all since the moment you put in extra countersteering (turning the bars in to the corner) the bike would start to fall since it would switch to kinetic friction from rolling friction.

[Hotfoot]

18 minutes ago, Erunanethiel said:

But I do not think you'd be able to bring the bike up at all since the moment you put in extra countersteering (turning the bars in to the corner) the bike would start to fall since it would switch to kinetic friction from rolling friction.

It sounds to me as though you might not be taking into account how suspension affects tire grip. Are you, for example, assuming a completely rigid connection between the wheel and motorcycle, with no suspension action and a non-deformable tire? Are you assuming that the grip of tire to pavement is constant, and is at the theoretical maximum friction of rubber to asphalt? There is more grip available when the bike is upright because the suspension is more effective at keeping the tire consistently in contact with the pavement. There is a theoretical maximum friction that you can calculate but in real-world riding, the pavement is not perfectly flat or perfectly consistent so the theoretical grip (calculated from formulas, with assumptions and simplifications made - usually a LOT of them) is NOT the same as actual real-life grip.

Does it make sense to you, in your actual riding experience, that you have more grip when the bike is more upright than when you are at maximum lean angle? If so, does it follow that as you stand the bike up, you HAVE more grip available, so that even though you were at the max (for that lean angle) a millisecond before, you now have MORE grip available because the bike is coming up, and any tiny slide that would have begun from the countersteering effort would be halted by that additional grip?

One must be very careful when attempted to use physics formulas to calculate grip. There are MANY factors that are ignored, assumed constant, or simplified in order to make formulas or concepts easier to understand, but trying to apply theories that don't take into accounts the LARGE number of variables present in real-world riding can lead to some confusions. You can find numerous examples on this board.

[Lnewqban]

On 12/30/2019 at 12:47 AM, Erunanethiel said:

When you are at the max lean angle and generating as much grip as the tires you have allow in a steady-state, long corner, how do you exit the turn? I think it is theoretically impossible.

You are correct, but only if such motorcycle is neutral steering-wise.  As you know, many bikes have a natural tendency to either understeer or oversteer (if the rider releases the handlebar while the bike is leaned on a curve).  Those tendencies depend mainly on geometry and profile of tires.  The front contact patch of an understeering bike will "feel" less lateral force when coming out of a lean/corner as it had been forced to over-steer during the curve.

In the steady conditions that you have described (while keeping zero angular input on the steering), the sliding force on each contact patch remains constant and it depends on the square value of the forward velocity of the bike and the inverse of the radius of the trajectory.  As you properly have explained, any counter-steering input will instantaneously increase the value of that lateral or sliding force (especially for the front contact patch).

The lean angle (and linked lateral forces) can remain constant along a curve, but real conditions of the road make it maximum only intermittently.  Maximum grip or friction depends on the force that is normal or perpendicular to the surfaces in contact.  The undulations of the road and the instantaneous accelerations that add to and subtract from the natural acceleration of gravity, induce a fluctuating amount of that normal force or available maximum friction or grip.  Each tire has more available traction each time it rolls over a crest: that instantaneously increased normal force deforms the tire and partially compresses the springs, which push and accelerate the rider and the rest of the mass of the bike and fluids upwards.  Exactly the opposite happens when the tire "falls" into a valley of the track's surface: less available traction for a fraction of a second.

In other words, assuming a perfectly horizontal traverse surface of the curve (no sectional slant, slope or crown), which makes the value of the normal force that induces grip equal to the value of the weight supported by one tire, the undulating nature of that surface will make that tire and its suspension alternatively support more and less weight than normal (for a perfectly ideal flat surface).  Hence, more that having a sharp value, the available grip of each tire constantly rises and falls / pulses / swings / oscillates around an average value.

Similar effect (although at much higher frequencies) is produced by the vibrations coming from the rubber compound of the tire when supporting strong lateral forces (getting deformed, twisted, overheated, sheared) and when crabbing or sliding off the trajectory (while keeping grip).  At microscopic level, things are changing at a very rapid rate and the surfaces are gripping each other and letting go in a very rapid sequence.

Consider also that all the disturbances described above induce minimal steering inputs.  Because of the trail of the front tire, while it is leaned, any close to vertical force has a perturbing effect (torque that is equivalent to a sideways force times trail distance) when the bike is in vertical position.  A torque is induced into the steering, which can be over or under-steering, which significantly modifies the radius of the trajectory, which momentarily changes the magnitude of the lateral forces.

Hotfoot's excellent post has perfectly explained the Physics of real life.

 

 

[Erunanethiel]

On 12/31/2019 at 11:31 PM, Hotfoot said:

 

Thank you guys both for the great responses.

 

Do you reckon the great guys of bike racing are able to get as close to the "theoretical maximum grip" of their tires mid-corner as their car racing counterparts? Or would the necessity of bringing the bike up at the end cause any conservation? (Apart from psychological response due to danger)

 

Very nice forum this is!

[Hotfoot]

Keith asked me to add a little more info about grip:

The point on max grip is another many faceted process. Due to the slip angle tires never do have 100% mechanical grip, they actually are sliding. That is a prophylactic process as it cleans the spent rubber off the tire's surface but is ALWAYS happening, in every corner. It's sometimes overlooked in the traction arguments.

 

In the end it's more to less, less to more SLIDE rather than more to less, less to more traction. Maybe that's just another way of looking at the same issue.