Can a cornering motorcycle go faster if the rider puts a knee down?

[koodawg]

I remember this problem from my freshman physics class ~38 years ago. As I recall it was explained to us how a motorcycle rider could actually take a corner faster by putting his inside knee down on the ground. We see this in motorcycle racing where the riders have a knee pad that let's them place their knee on the ground, effectively sliding it along the pavement as they lean into turns..

What I remember and/or presume is that there is (1) the static friction between the tires and the road surface. The static friction would presumably increase/decrease proportionally with weight of the bike & rider. The static friction results in centripetal force keeping the bike in the turn. If rider takes the turn too fast then the inertial force (apparent centrifugal force) overtakes the static friction of the tires/pavement and the bike slides out of the turn.

Then there is (2) the apparent centrifugal force "pushing" the bike towards the outside of the turn along the turn radius.

So the idea is that, if the rider puts his inside knee down on the ground while in the turn, that corresponding amount of weight is removed from the apparent centrifugal force. So there's a little less centrifugal force so that allow the rider to go a little bit faster then when his knee was not sliding on the ground.

I'm ignoring the fact that the static friction would be reduced at the tires as well. But as I recall the way it works out the rider could take the corner faster.

Any insights on how this problem is solved and the result (however small an increase is possible, or not) would be appreciated. Just looking to resolve a friendly discussion.

Thanks
Mike

 

[russ_watters]

So the idea is that, if the rider puts his inside knee down on the ground while in the turn, that corresponding amount of weight is removed from the apparent centrifugal force.

I don't see how this can be true.

Unless tire performance is worse with a steeper bank because of the tread surface, I don't see how sticking the knee out could help. But here's what the first hit on google has to say about it:

But, the real reason why knee dragging exists is to provide a lean angle gauge. If your body position is consistent from corner to corner, all day long, then you can reliably use your knee as a measuring device.

https://www.ridinginthezone.com/knee-dragging-101/
Sounds plausible to me. When I ride a bicycle I am sometimes concerned about how much I lean in corners and not knowing if I'm going to slide out or catch a pedal on the ground. If I had a way to measure and ensure consistency I would think that would be a positive thing.

 

[koodawg]

Thanks but you didn't address what I suggested; by taking weight off the bike, the centrifugal force is reduced and therefore you could theoretically go a little bit faster. So what about that?

And no, the problem didn't involved different tire performance at different angles or anything more complex than the weight of the bike + rider, speed through turn, static friction, centrifugal force.

Clarification: you said "sticking the knee out", we're not talking about sticking it out. We're talking about actually putting the knee on the ground and letting it drag, thereby taking some amount of weight off the tires.

And BTW, for this problem I'm not interested in all the other reasons for hanging, leaning, putting a knee down for "angle guage" etc. I'm interested in whether or not you could theoretically take a corner faster.

Thanks

 

[jbriggs444]

Thanks but you didn't address what I suggested; by taking weight off the bike, the centrifugal force is reduced and therefore you could theoretically go a little bit faster. So what about that?

The centrifugal force is not reduced.

The centrifugal force is the fictitious pseudo-force that arises from adopting the rotating frame in which the motorcycle is at rest. Its magnitude is given by $m\frac{v^2}{r}$ (or $m\omega^2 r$). There is no term reflecting the presence of a knee on the ground.

Let us step back into the inertial frame. If you want to keep the motorcycle on a circular path, you have to apply an inward horizontal force of $m\frac{v^2}{r}$. Again the force of ground on knee has no inward horizontal component. It does not help.

 

[russ_watters]

Thanks but you didn't address what I suggested; by taking weight off the bike, the centrifugal force is reduced and therefore you could theoretically go a little bit faster. So what about that?

You're right, I wasn't explicit: centrifugal (centripetal) force is a function of mass, not weight, and you don't change the rider's mass by dragging a knee. You can reduce the weight pushing down on the tire, but not the cornering force it needs to apply to make the turn. This would make cornering worse, not better.

Consider the limiting case where the rider balances all the weight of the bike and himself on his knee (ouch). The cornering force applied by the tires is now zero and the bike/rider slide in a straight line. This is exactly what you are trying to avoid.

Race cars go the other way and try to maximize down force (similar to weight) with spoilers and wings

 

[berkeman]

Summary: Does the rider benefit from putting a knee down by being able to take the corner faster?

So the idea is that, if the rider puts his inside knee down on the ground while in the turn, that corresponding amount of weight is removed from the apparent centrifugal force. So there's a little less centrifugal force so that allow the rider to go a little bit faster then when his knee was not sliding on the ground.

The knee down is a "feeler" to help the rider judge their lean angle. It does nothing for corner speed directly, but helps the rider fine-tune the throttle setting and lean angle.

http://www.cornercarving.com/6-reasons-you-should-be-dragging-your-knee/

 

[koodawg]

You're right, I wasn't explicit: centrifugal (centripetal) force is a function of mass, not weight, and you don't change the rider's mass by dragging a knee. You can reduce the weight pushing down on the tire, but not the cornering force it needs to apply to make the turn. This would make cornering worse, not better.

Consider the limiting case where the rider balances all the weight of the bike and himself on his knee (ouch). The cornering force applied by the tires is now zero and the bike/rider slide in a straight line. This is exactly what you are trying to avoid.

Race cars go the other way and try to maximize down force (similar to weight) with spoilers and wings

Right I see this now. Apparently my memory was wrong and the problem showed that putting a knee down can actually make things worse, i.e could theoretically make you slide!

Thanks

 

[koodawg]

The knee down is a "feeler" to help the rider judge their lean angle. It does nothing for corner speed directly, but helps the rider fine-tune the throttle setting and lean angle.

http://www.cornercarving.com/6-reasons-you-should-be-dragging-your-knee/
View attachment 244631

Yes, as I stated I understand that there are various reasons riders like to touch their knee down, i.e. to feel their lean angle etc. I intended to make clear that I wasn't interested, for this discussion, in these touchy feely reasons for putting the knee down. What I am interested in, what I am asking for is the actual physics involved in putting a knee down and actually bearing *some* weight on the knee - what happens to the friction and centrifugal forces and russ_watters just gave a great explanation.

Thanks

 

[berkeman]

what I am asking for is the actual physics involved in putting a knee down and actually bearing *some* weight on the knee

You don't put weight on your knee. Except for Reason #6 of course...

 

[koodawg]

The knee down is a "feeler" to help the rider judge their lean angle. It does nothing for corner speed directly, but helps the rider fine-tune the throttle setting and lean angle.

http://www.cornercarving.com/6-reasons-you-should-be-dragging-your-knee/
View attachment 244631

Yes, as I stated I understand that there are various reasons riders like to touch their knee down, i.e. to feel their lean angel etc etc. I attempted to state in my original post that I wasn't interested, for this discussion, in these touchy feely reasons for putting the knee down. What I am interested in, what I am asking for is the actual p

 

[DaveC426913]

The biggest risk in a turn is a slide. That's the thing that limits a tighter turn.

And the rate-limiting factor is going to be traction on the wheels.

Any weight on the knee will reduce weight on the wheels and reduce traction, risking a slide.

Fairly straightforward, it seems to me.

 

[koodawg]

The biggest risk in a turn is a slide. That's the thing that limits a tighter turn.
And the rate-limiting factor is going to be traction on the wheels.

Thanks but I didn't ask anything about risk

Any weight on the knee will reduce weight on the wheels and reduce traction, risking a slide.

Yes thanks, this already has been established above.

 

[rcgldr]

It should be pointed out that riders don't hang out or use their knees as pavement feelers in high speed turns. They stay tucked in. Extreme examples are the two high speed banked turns used at Daytona, or Isle of Mann high speed turns (some at 200 mph). Skip forward to 1:10 into this video:

 

[DaveC426913]

Thanks but I didn't ask anything about risk

Not risk to life and limb; I mean risk to control.

In a turn, your goal is to make the best time / fastest speed-made-good.
Losing traction is the biggest risk to that goal, and makes traction the rate-limiting factor for the turn radius/speed.

Yes thanks, this already has been established above.

Yes. I was just boiling it down to a simpler conceptual explanation.
It doesn't really require appeal to centrifugal or centripetal forces; it simply requires an understanding of weight and traction.

 

[gmax137]

... Skip forward to 1:10 into this video...

Thanks @rcgldr ! That is outstanding video. I spectated at Daytona a number of times back in the 1980s and 90s, that video really brings it home. I can't imagine running like that for 200 miles.

 

[berkeman]

It should be pointed out that riders don't hang out or use their knees as pavement feelers in high speed turns.

For sure not the high speed banked turns like Daytona. I've read that the g-forces in those banked turns are high enough that the riders have to rest their helmets on a small pad on the tank, because they cannot hold their heads up against those strong g-forces. Yikes!

Even at 150+mph, though, riders will generally put a knee down on un-banked turns. An example would be Turn 1 near the end of the front straight at Laguna Seca (or whatever its commercial name is now) in Monterey.

 

[rcgldr]

Even at 150+mph, though, riders will generally put a knee down on un-banked turns. An example would be Turn 1 near the end of the front straight at Laguna Seca (or whatever its commercial name is now) in Monterey.

I forgot to mention that aerodynamics becomes an issue at 150+ mph, an issue with overall drag and apparently an issue with upsetting then handling balance of the bike, so the riders stay tucked in at 150+ mph, even while turning.

At Laguna Seca, turn 1 is a high speed slight kink, no one is hanging off there. From the start/finish line, the riders don't hang off until the very tight turn 2.



At Isle of Man TT, the riders stay tucked in at 150+ mph, but as speeds decrease below 150 mph, the riders increasingly hang off.

 

[Quasimodo]

Dear community,

A motorcycle rider sticks out his knee on the road for the same reason the passenger rider in a sidecar race leans out his body inwards as far as he can

to bring the center of gravity of rider-machine system as lower to the ground he can thus allowing faster speeds while cornering without toppling off!

Ok?

 

[MikeeMiracle]

Yes I was going to say that also, lower center of gravity allows for faster cornering speeds just as it does with cars also. The knee touching the ground is just a by-product of the leaning required to lower the center of gravity.

 

[rcgldr]

Yes I was going to say that also, lower center of gravity allows for faster cornering speeds just as it does with cars also. The knee touching the ground is just a by-product of the leaning required to lower the center of gravity.

Lower center of gravity on cars reduces the roll torque, reducing the imbalance of downforce on the tires, which results in better overall grip, since tires coefficient of friction decreases with the vertical load on the tires.

For bikes, a lower center of gravity doesn't help with overall grip. The prior posts links discuss the reasons that racers hang off in turns.

 

[Quasimodo]

REeally, @rcgldr Have you ever tried to take a corner standing upright with legs on the pedals on a bike? Have you ever ridden a bicycle ever?

 

[jbriggs444]

REeally, @rcgldr Have you ever tried to take a corner standing upright with legs on the pedals on a bike? Have you ever ridden a bicycle ever?

On a bicycle, the pedals are an important limitation in a hard turn. Normally, the pedals will touch down before the wheels will slide out. I've experienced both failure modes. The ends of my pedals and the sides of my seat reflect it. I will often stop pedaling in order to maximize turn rate. If one has stopped pedaling, there is no motivation to stand upright. It would not hurt the cornering ability (it would actually help slightly -- putting the center of gravity closer to the center of the turn and thereby decreasing centrifugal force). But it would increase wind resistance. Bicycles are power-limited. You don't want to scrub away velocity if you can help it.

The ability to corner has little to do with the height of the center of gravity and much to do with lean angle.

 

[Spinnor]

I read the 6 reasons to hang out your knee above in post 6, maybe there is a 7th reason, there should be some down-force , maybe of order 10 to 20 pounds at race speed?

 

[Quasimodo]

The ability to corner has little to do with the height of the center of gravity and much to do with lean angle.

Yes, center of gravity has much to do with cutting corners.
When you are turning, the torque caused by two opposing forces (the horizontal component of the weight acting on the center of gravity and the horizontal component of the reacting force to the tires this being not vertical but on the axis joining tip of the tires to CoG as in the case of grip) must be minimized not for the sake of turning itself (always 0 since the bike is in balance) but for the sake of stability.
And the way to do this is by lowering the CoG. The slightest bump of the road or touch of the throttle overturns this balance and the bike turns over. You have to minimize the torque to remain stable that's where the CoG comes into play.
And that's the way the bikers do it in the picture of #18 because "nature cannot be fooled."

 

[jbriggs444]

When you are turning, the torque caused by two opposing forces (the horizontal component of the weight acting on the center of gravity and the horizontal component of the reacting force to the tires this being not vertical but on the axis joining tip of the tires to CoG as in the case of grip) must be minimized not for the sake of turning itself (always 0 since the bike is in balance) but for the sake of stability.

Right. The torque due to weight must match the torque doe to lateral friction, else the bike tips over.

All other things being equal, the torque due to weight is given by the mass times the acceleration of gravity times the distance from the center of gravity to the road surface multiplied by the sine of the lean angle (referencing lean angle to the vertical).

$$\tau_g=mgh \sin\theta$$

The torque due to lateral friction is given by the mass times the lateral acceleration of the bike times the distance from the center of gravity to the road surface multiplied by the cosine of the lean angle.

$$\tau_f=mah \cos\theta$$

Since the two torques must match and since they are oppositely directed, one can equate the two right hand sides and obtain:

$$a = g \tan\theta$$

It's all about the lean angle. How high you stand up on the pedals is irrelevant.

 

[russ_watters]

Yes, center of gravity has much to do with cutting corners.
When you are turning, the torque caused by two opposing forces (the horizontal component of the weight acting on the center of gravity and the horizontal component of the reacting force to the tires this being not vertical but on the axis joining tip of the tires to CoG as in the case of grip) must be minimized not for the sake of turning itself (always 0 since the bike is in balance) but for the sake of stability.
And the way to do this is by lowering the CoG.

While it is true that a bike is more stable with a lower center of gravity, that has nothing to do with this discussion. This discussion is about how you generate traction to "hold" the corner. For the purpose of this discussion, the resulting force vector is a straight line through the center of gravity and tire contact patches (or, rather, a point on the curve between the tires) and the net torque is zero. There is no net torque when you are properly balanced and if you are fighting a torque, then you are doing something wrong (and probably in the process of falling).

 

[berkeman]

At Laguna Seca, turn 1 is a high speed slight kink, no one is hanging off there. From the start/finish line, the riders don't hang off until the very tight turn 2.

You might be right. I remember watching the Superbike races there many years ago, and I thought I remembered them getting knees down in Turn 1. But looking at Google Images now, it does seem like they do have a knee out a bit, but are not hanging all the way off. You do lift a bit going through Turn 1 (at least I do, but I only got up to about 120mph through that turn at my track days), so staying tucked in through the turn isn't super-important. Braking for Turn 2 starts pretty much as you are leaving Turn 1.

BTW, funny story about those short red marker rods on the left side of Turn 1 (they separate the track from the pit exit lane). The first year we went to watch the Superbike races there, during the first practice several riders kept grazing the rods with their helmets (the rods were taller at first). You can imagine how distracting that is at 140+mph. Before the next practice, the track workers went out and cut all of the rods down to that lower height. LOL

https://www.motorcycle.com/blog/wp-...4-MazdaRacewayLagunaSeca-WSBKWeekend-6882.jpg

 

[rcgldr]

Yes, center of gravity has much to do with cutting corners. When you are turning, the torque caused by two opposing forces (the horizontal component of the weight acting on the center of gravity and the horizontal component of the reacting force to the tires this being not vertical but on the axis joining tip of the tires to CoG as in the case of grip) must be minimized not for the sake of turning itself (always 0 since the bike is in balance) but for the sake of stability. And the way to do this is by lowering the CoG.

The lower the center of mass, the greater the amount of lateral force required to change lean angle at a certain rate. The guys who run torpedo bikes for top speed runs at Bonneville often have to add balast to the top of the frame to raise the center of mass from being too low. If the center of mass of the bike is too low, it takes too much lateral force to get the bike to lean.

For "flickability", the idea is to have a reasonably high center of mass on a bike and to have much of the mass located near the front to back line of the center of mass to reduce angular inertia. Some superbikes rotate the engine backwards (which requires internal gearing to "unreverse"), in order to reduce the rotating angular momentum of engine and tires.

 

[Quasimodo]

The lower the center of mass, the greater the amount of lateral force required to change lean angle at a certain rate. The guys who run torpedo bikes for top speed runs at Bonneville often have to add balast to the top of the frame to raise the center of mass from being too low. If the center of mass of the bike is too low, it takes too much lateral force to get the bike to lean.

For "flickability", the idea is to have a reasonably high center of mass on a bike and to have much of the mass located near the front to back line of the center of mass to reduce angular momentum. Some superbikes rotate the engine backwards (which requires internal gearing to "unreverse"), in order to reduce the rotating angular momentum of engine and tires.

I really have no idea what are you talking about here. I googled Bonneville and found no racetrack, and what type of superbikes are you referring to?
One must notice that you are progressing to lean over ( lowering the CoG ) not at once but gradually from the entrance to the apex of the curve. The tilt of the bike generates angular momentum too, and since this must be conserved any further diminishing of the distance between CoG and point of touch of the wheels generates more "flickability" as you put it.

 

[berkeman]

really have no idea what are you talking about here. I googled Bonneville and found no racetrack, and what type of superbikes are you referring to?

They go very fast and (mostly) straight at the Bonneville salt flats. The "racetrack" is a straight line painted on the salt. If you've ever seen the classic movie "On Any Sunday", you'll remember a pretty comical failure to steer one of these "torpedo bikes" at low speeds...

https://cdn.gearpatrol.com/wp-content/uploads/2017/08/salt-flats-kit-gear-patrol-facebook.jpg

 

[rcgldr]

One must notice that you are progressing to lean over ( lowering the CoG ) not at once but gradually from the entrance to the apex of the curve.

On a long (time wise) curve, a lot of time is spent at max lean angle.

The tilt of the bike generates angular momentum too, and since this must be conserved

Angular momentum is only conserved if you include the reaction by the earth.

I googled Bonneville and found no racetrack, and what type of superbikes are you referring to?

They are called streamliners. Current record was set a few years ago, 376 mph average speed on a flying mile (peak speed 394 mph), two runs (both directions):

 

[Quasimodo]

@rcgldr
The situation is as follows:

1.Assuming that the radius of the curve remains constant throughout the turn, the motorcycle enters the curve.

2.Assuming unlimited grip of the tires, the lean angle is limited only by the frame of the motorcycle and the body of the rider of course.

3.The angular momentum of the system motorcycle-rider is constant throughout the bend, but the speed is not! The rider by jutting out his knee and bringing his whole body closer to the center of the curve and by lowering his center of gravity thus and bringing it closer to the center of the curve can manipulate his speed and ( yes! ) increase it at the apex of the curve ( no throttle ) which he could not do otherwise by increasing the lean angle because there is a physical limit to it as explained in 2.

As of the streamliners you are talking about, I know nothing about their geometry so I can't comment.

Thank you all for the beautiful discussion.

 

[jbriggs444]

The rider by jutting out his knee and bringing his whole body closer to the center of the curve and by lowering his center of gravity thus and bringing it closer to the center of the curve can manipulate his speed and ( yes! ) increase it at the apex of the curve ( no throttle ) which he could not do otherwise by increasing the lean angle because there is a physical limit to it as explained in 2.

Won't work.

Once you have fixed the radius of the curve, the mass of the bike+rider, the distance of the center of gravity from the wheel track and the angular momentum of the assembly as it rounds the curve, there are no more free parameters. The lean angle is locked in. You cannot stick a knee out one way without sticking something else out the other way -- else you blow the lean angle and fall over.

 

[Quasimodo]

Won't work.

Once you have fixed the radius of the curve, the mass of the bike+rider, the distance of the center of gravity from the wheel track and the angular momentum of the assembly as it rounds the curve, there are no more free parameters. The lean angle is locked in. You cannot stick a knee out one way without sticking something else out the other way -- else you blow the lean angle and fall over.

Look again at the picture post #18. The bike can be in a complete upright position and still negotiate the curve!

The torque of a weight put away at a distance from the wheels ( the knee and position of the body of the rider away from the saddle ) generates the extra centripetal force needed for the increased velocity at the apex of the curve.

As I have explained before, if the lean angle of the bike weren't limited by the frame of the motorcycle there wouldn't be any need for this and the turning speed would be as big as you like provided unlimited traction of course.

 

[jbriggs444]

Look again at the picture post #18. The bike can be in a complete upright position and still negotiate the curve!

The effective lean angle of that bike (the angle from the tire track to the center of gravity) is not vertical. And it is not even a two-wheeled vehicle. It does not count. Nor do I see a knee extended.

The torque of a weight put away at a distance from the wheels ( the knee and position of the body of the rider away from the saddle ) generates the extra centripetal force needed for the increased velocity at the apex of the curve.

It does not generate any centripetal force at all. It is responsible for a torque due to gravity that can counter the torque from the couple of friction and centrifugal force. Increasing this can allow an extra centripetal force.

As I have explained before, if the lean angle of the bike weren't limited by the frame of the motorcycle there wouldn't be any need for this and the turning speed would be as big as you like provided unlimited traction of course.

The specifications for your claim involved a fixed angular momentum. You cannot increase turning speed by increasing lean angle if you are holding angular momentum fixed. As I already pointed out and as you have failed to grasp.

 

[Quasimodo]

The specifications for your claim involved a fixed angular momentum. You cannot increase turning speed by increasing lean angle if you are holding angular momentum fixed. As I already pointed out and as you have failed to grasp.

What failure?

More weight towards the center of rotation, more speed.

You are right about the picture, the lean angle is not vertical, is not 0, is negative and away from the curve, this more support of my claim.

 

[Quasimodo]

And it is not even a two-wheeled vehicle. It does not count. Nor do I see a knee extended.

Yes, for the moment the third wheel doesn't touch the surface of the track the tricycle becomes a bicycle!

 

[jbriggs444]

What failure?View attachment 244751More weight towards the center of rotation, more speed.

You are right about the picture, the lean angle is not vertical, is not 0, is negative and away from the curve, this more support of my claim.

Read the specifications for my counter-claim again.

 

[Quasimodo]

@jbriggs444 You will never see a competitive racetrack rider in a very tight bend sticking out only his kneecap to feel the road as Google claims. He always leans his whole body towards the inside of the curve, literally dismounting from the saddle. It's a center of gravity thing. Those who are putting their knee down only to feel the road, simply don't win races!

 

[Quasimodo]

Here's another article in support of my claims by the same author: https://www.ridinginthezone.com/body-position-tips-2/

 

[rcgldr]

1.Assuming that the radius of the curve remains constant throughout the turn, the motorcycle enters the curve.

2.Assuming unlimited grip of the tires, the lean angle is limited only by the frame of the motorcycle and the body of the rider of course.

3.The angular momentum of the system motorcycle-rider is constant throughout the bend, but the speed is not! The rider by jutting out his knee and bringing his whole body closer to the center of the curve and by lowering his center of gravity thus and bringing it closer to the center of the curve can manipulate his speed and ( yes! ) increase it at the apex of the curve ( no throttle ) which he could not do otherwise by increasing the lean angle because there is a physical limit to it as explained in 2.

#2 is unrealistic, there's a limit to the grip. If the tires have a circular profile, then contact patch area remains the same regardless of the bikes lean angle. Some tires have a taller profile (similar to a parabola), where the contact area is largest at some specific lean angle.

#3 - the "closer to center of curve" effect is minimal. Other than hair pin turns, most turns have a radius of more than 100 ft (100 foot radius translates into ~ 40 mph 1 g turn). The inwards component of center of mass shift is only a few inches, as the rider's weight is 1/3rd or less than the total weight of bike and rider, and the riders's body shifting mostly moves the center of mass with respect to the contact patches radially, barely changing the distance from center of mass to contact patches.

 

[berkeman]

Apparently it also helps you go faster if you use your elbow as a feeler...

 

[DannoXYZ]

I race bikes, so I have some perspective on this. Here's start of race at Sears Point Sonoma Raceway.

While lots of ideas were covered relating to "knee out" physics those may more effect rather than cause. Also some are completely unrelated at all. That being 3-wheel side-cars vs. 2-wheel bike. With 3-wheels, it corners like car and requires turning steering into corner. The monkey hanging off side is to countreact lateral weight-transfer that's trying to tip it over. Moto on other hand only uses steering to initiate leaning and once desired angle is reached, steering is aimed straight ahead again. Centripetal force pushing bike into circular-path is generated by tyre's camber-thrust.

Here's an overview of cornering angle, it's dictated by angle between effective COG of bike+rider and ground.

Note that distance (height) between effective COG and contact patch makes no difference. In steady-state cornering once lean-angle has been set, tyres ony notice that there's certain vertical-force from rider's weight+bike's weight, and lateral centripetal force from cornering. Rider can be sitting on 10-ft high-chair above bike, and it will still corner exactly at same speed as another bike with rider tucked in at same lean-angle. Obviously if lean-angle is 45-degrees, vertical and horizontal forces are identical and bike corners at 1G. Here's table of lean-angles and resultant cornering-G.

Notice that function is not linear? Well, up to 45-degrees, it's fairly linear, and increase even faster than that. Going from 45-degree to 60-degree lean generates double cornering force. Here's roughly lean-angle maximums for various types of tyres.

Different rim-wdiths, casing constructions and rubber compounds allow professional race-bikes to achieve extreme lean-angles and cornering speeds. Race-tyres only has to last about 100-miles, so their super-sticky rubber-compounds have incredible grip.

Now, why is there lean-angle limit and what happens if you go over?

You roll off edge of tyre and crash! Street tyres tend to have flatter profile and won't handle too much angle before rolling off. DOT-R tyres, soft-compound street-legal tyres tend to have more triangular profile so that when its leaned over, it has larger and flatter contact on ground. THIS is why racers stick out their knee, as an angle-feeler gauge to compliment the excellent angle and G-force measuring device known as ears.

You see street-riders street-riders trying to out-macho each other by seeing who has least amount of "chicken strips" on their tyres. These are those unused stripes on each side of tyre. And they brag about "getting their knee down", which is supposedly some indicator of skill.

For racers, it's exact opposite. We try to keep tyres off edge as much as possible to not go over and crash. Knees are used to gauge how close you are to edge, as such, it's only done at maximum lean-angle. In slow/medium-speed corners, where I may actually tip out knee tiny bit and if there's slight rub or kiss, then I pull it back in, once I know how much lean I have. For high-speed corners where I'm not even going to use fulll-lean (i.e. turn-1 @ Laguna Seca), the knee stays tucked tightly in for aerodynamics. Sticking knee out at those speeds, causes an immediate 3-6mph reduction in speed.

So how can you corner even faster once you've leaned up to tyre's edge? By recognizing that effective COG is combined system of bike AND rider.

By shifting entire body inside of bikes centre-line, you've effectively moved COG towards inside of bike. This bike+rider system at 39-degrees lean, has an effective lean-angle similar to previous picture of 52-degrees. It can corner at same speeds for less lean-angle! This gives you overhead to lean bike+rider more to limit of 55-degrees while not rolling off edge of tyre at 50-degrees like before. Here's some examples of moving entire body towards inside to keep bike as upright as possible for more cornering speed.

Another benefit of hanging off inside and keeping bike more upright, is you can use more throttle coming out of corners for higher top-speed down next straight. So really, knees touching is not cause of higher-speeds, it's just tool to allow rider to know how close they are to edge of tire and maximum lean-angle.

 

[cmb]

Excuse me if I missed any subtlety above which says the same as this, but, no, putting your knee down (resulting in a downward force, and thus friction forces on the knee pad) does nothing for cornering. Quite the opposite, it removes some of the vertical normal reaction so reduces the vertical load on the tyre edge, thus lowers its grip and ability to apply a centripetal force.

I used to ride bikes and never really understood the reason people would do this for cornering purposes on the road. Wanna-be road racers seemed to be aping racing riding, which is pointless.

I had a range of bikes from very large 1200cc stuff to two stroke race bikes, and there was really no issue in cranking the things over until bits of the bike started scraping along the ground. Road bikes tend to have foot peg sliders which are spherical headed bolts in the end of the foot pegs, and my right one tended to get a bit of abuse. (We drive on the left here, so taking left hand bends fast is just dangerous and silly, because the only way you are going to go if you get it a bit wrong is straight into the oncoming traffic. At least right hand bends you can be a bit safer if there is a ploughed field to your left!)

The 250 two stroke I had was flat out a road legal race bike. It had no pegs and would in theory have happily scraped its chain on the floor before worse things happened. Anyway, the steering was extremely limited, only 15 degrees or so on the handle bars so the only way to get tight cornering was fast and deep! Forget a slow speed U turn, race bikes don't really do that. This steering was, however, extremely sensitive. The bike weighed about 100kg and the lightness and tall castor angle meant that you could literally lean your head to one side of the bike and it'd start turning in that direction! So there are a host of other reasons racers do the knee out thing, one is for sure the comfort thing and to be able to gauge where the bike's dangling bits are relative to the tarmac, but at high speed sticking a knee out also slows the bike down considerably. You'll see race guys popping up like meerkats as they approach corners, along with their inside knees popping out. If you are at a serious speed, this slows you down and pulls you into the corner without even thinking about steering. As they enter the corner, there's not much point pulling their knee back in because the next thing they do is move even more over on the bike and also hang off it, along with their knee!

So, does sticking a knee out in a race help them win? Yes, there are reasons why it might help (though it doesn't help every rider's style). Does it help on a road bike? No, just makes you look cool!

 

[DannoXYZ]

It was mentioned earlier that putting weight on knee would jack up bike, lowering vertical-loading on tyres and reduce grip. While this is true, you'd have to have super-human strength to push your knee out that hard.

What's more common is some hard non-yielding parts will touch down, such as kickstand bracket, or exhaust or footpegs. When these parts touch, further leaning WILL jack up bike on that point and lift rear tyre and cause crash. So I've cut off kickstand bracket on my bike, installed exhaust that sits higher and use folding pegs.

Having some fun at Laguna Seca (3 videos in playlist).

 

[berkeman]

Having some fun at Laguna Seca (3 videos in playlist).

Great stuff! The bigger bikes have the power to pass you in the straights, but you have the braking and cornering skills to pass them right back. Awesome

Was that at a track day? Keigwins or a different group?

 

[DannoXYZ]

the last video is mine and it was track-day practice with Pacifc Track Time.



Unfortunately, Keigwins is no more. Done in and bankrupted by idiot rider who crashed and sued them and Laguna Seca. However, it has been revived as Carters at the Track with previous GM as new owner. :)

 

[berkeman]

track-day practice

Nice riding! Gotta love that "pass on the outside" track day rule

 

[rcgldr]

Moto on other hand only uses steering to initiate leaning and once desired angle is reached, steering is aimed straight ahead again. Centripetal force pushing bike into circular-path is generated by tyre's camber-thrust.

Steering relative to a bike's path is always inwards. Both front and rear tire are angled slightly inwards of the bikes actual path, due to flexing at the contact patch, known as "slip angle". Flexing at the rear tire contact patch (slip angle) coexists with the overall bike's frame being oriented slightly inwards of the bikes path. While in a turn, the steering relative to the bike's frame may be inwards, straight ahead, or slightly outwards (relative to the frame), depending on the amount of inwards orientation of the bike's frame due to the rear tire contact patch flexing under load.

The contact patch on a tire flexes in response to a side load. Camber thrust is related to the net linear centripetal flexing of the contact patch. I'm not aware of a term related to the net twisting of the contact patch. Slip angle is related to the total (both linear and twisting) amount of flex of the contact patch, the angle between the actual path and the geometric path if there was no flex.

Sometime the term camber thrust is mis-used to describe an effect similar to a cone rolling on its side will roll in a circular path, but a two cone vehicle with one cone in front of the other cone, with parallel (no steering) axis, will travel in a (nearly) straight line, with a lot of skidding of the cones surfaces.

 

[sophiecentaur]

One thing that doesn’t seem to have been mentioned is that a small drag force on the knee could produce a torque (about a vertical axis). Depending on where this force acts relative to the CM of bike and rider, it could alter the forces on the tyres and tend to steer in or out of the curve.
With M/C combination racing, a brake applied to the third wheel could have a similar effect ( different for right and left hand turns, of course). If anyone knows about this they could put me right about whether or not it’s used in racing. (IMO it is the nuttiest form of racing ever invented!)