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

#### koodawg

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

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#### russ_watters

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.

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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#### jbriggs444

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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#### russ_watters

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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#### berkeman

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.

#### 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.

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

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.

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

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.

#### rcgldr

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:

#### DaveC426913

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.

#### 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

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.

#### rcgldr

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?

#### 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

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?

#### jbriggs444

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.

#### Spinnor

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."

#### jbriggs444

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.

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

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