# 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

Mentor
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

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Homework Helper
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.

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DannoXYZ, QuantumQuest, Ibix and 2 others
Mentor
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

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DannoXYZ, mfb, QuantumQuest and 2 others
Mentor
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/

DannoXYZ, Nik_2213, QuantumQuest and 1 other person
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

russ_watters
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

Mentor
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

davenn
Gold Member
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.
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.

Homework Helper
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:

QuantumQuest, berkeman and gmax137
Gold Member
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.

... 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.

Mentor
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.

QuantumQuest
Homework Helper
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.

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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?

Motore
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.

Motore
Homework Helper
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?

Motore
Homework Helper
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.

cjl, DannoXYZ and russ_watters
Gold Member
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."

Homework Helper
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.

Mentor
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).

Mentor
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

Homework Helper
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.

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russ_watters
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.

Mentor
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...

russ_watters
Homework Helper
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):

berkeman
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.

Homework Helper
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.

Homework Helper
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.