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How Fast Can You Go Round A Corner?

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This may seem like an odd question but bear with me. Assuming the track is warm, the tyres are up to temperature, the bike is well setup and most importantly the riders’ technique is bang on. At what point does it all get too much for the tyres resulting in a crash?

 

The reason I ask this is that at the moment I feel like I'm at a bit of a plateau and if I could just get over it I would probably be on a rapid improvement curve again. My overriding stumbling block is an unwillingness to push harder for fear of tucking the front. If the brakes are off and the power is being rolled on will the front wash out before the pegs are scraping on the ground? Obviously rider error like poor throttle control, trailing the brakes into the corner hard enough to overwhelm the front tyre etc. would somewhat compromise this!

 

While riding my old SV650 I couldn't reach the limit of traction in the middle of a corner because everything was scraping on the ground long before the tyres got worried. On my new bike (track prepared ZX10r) I get my knee down round every corner and I do press on but I can tell I am MILES away from the limit of traction and lean angle.

 

So I suppose the distillation of this question is:

 

“In perfect conditions is it possible to lose the front due to mid corner speed?”

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given if the max load of both tire and suspension is X thru a specific corner

if you overload ( X+1 ) , then yes.

 

better tires and tuned suspension based on rider weight helps alot imho. (makes the x value larger)

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Another way of asking this can fall along what another school touches on "How fast is the SLOWEST point in the corner?"

 

Figuring out how slow you are traveling at that moment when you are 100% off the brakes and transitioning into maintenance throttle or roll-on will ultimately give you an accurate idea of just how fast that corner can be taken. With that said, it should be as simple as watching a GPS layout of the lap record holder to see what their lowest speed is for a given corner and there ya go!!

 

However, it's what leads up to and after that point that is the tricky part, lol.

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There is a limit to available traction. Whether you hit that limit before you run out of ground clearance on your bike is going to depend on your bike, your suspension settings, your tires, rearset position, the track, your body position, and a multitude of other factors.

 

A better question might be: how can you explore the available cornering speed of your new ride without wadding it up in a corner in the process? :)

 

The best thing would be to get to a school and work with a coach and sort this out; but in the meantime, there is a very useful exercise in "A Twist of the Wrist II" in Chapter Six, in a section called "Discharging". It gives a straightforward process to appoach a corner, bringing the speed up gradually, so you can feel out the bike's limits (and yours) in a systematic manner. With this approach, assuming good technique (good throttle control, no unwanted bar input, etc.) and an absence of SRs (the drill helps with this part especially), it is possible to explore the limits and start getting feedback from the bike to warn you when you are getting close to the limits of the tire.

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With high-grip tires on a high-grip surface that is flat, smooth, with a fairly even radius, you are going to corner at a maximum of just under 1g of lateral acceleration. Past that you are putting more sideways force on the tire than gravity is pulling the bike down. If we were on a heavier planet with say, 2g's of gravity relative to earth, then you could corner much faster. Here on earth if you go through a corner that is banked, you will be able to corner even faster with more than 1g of lateral force.

 

A bump, poor tires, poor application of throttle/lean/braking, poor surface, etc could foil your plans for a fast pass through a corner.

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Someone correct me if I'm wrong but... I thought the actual speed in the corner was not as important as the speed you get going out of the corner by using correct throttle control and good drive... Slow in fast out as they say...

 

I'm pretty darn good at the slow in part myself. Just have to get that fast out perfected a bit more. :)

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MotoGP bikes lean over to 64 degrees, which I believe is around the 2g mark.

For an airplane yes, not for a motorcycle.

 

 

Can you be a little bit more specific?

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I will not go slippery-slop again with my limited math, but I belive I have seen this calculated. And the combined lean is even greater than 64 degrees due to the rider hanging off. Must do some more searching and see what I can dig out from somebody who know how to calculate these things.

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From Da Man himself

 

 

The barrier then is both physical sensation and visual orientation and I believe there is a make/break point in it. That point is 45 degrees of lean. At 45, the forces are a bit out of the ordinary. Along with the normal 1g down we now have a 1g lateral load as well. As a result the bike and our bodies experience an increase in weight. That’s not native to us and acts as a distraction and as a barrier.

Once we finally become comfortable with 45 and attempt to go beyond, the process begins to reverse. Immediately we have more lateral load than vertical load and things begin to heat up. Riders apparently have difficulty organizing this. Suddenly we are thrust into a sideways world where the forces escalate rapidly. While it takes 45 degrees to achieve 1g lateral, it takes only 15 degrees more to experience nearly double that, depending on rider position and tire size.

 

Noam wrote:

 

 

tan(0 degrees lean) = 0 lateral G's
Tan(10 degrees lean) = 0.176 lateral G's
Tan(30 degrees lean) = 0.577 lateral G's
Tan(45 degrees lean) = 1 lateral G's
Tan(60 degrees lean) = 1.73 Lateral G's
Tan(63.3 degrees lean) = 2 Lateral G's

 

Full article http://forums.superbikeschool.com/index.php?showtopic=3723 where you can see yours truly again showing his ignorance, a habit I really could do without :rolleyes:

 

 

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Fact is I don't know what 63 degrees on a motorcycle is, however I do know that 54 degrees on a motorcycle has been measured right at 1g with instruments. The banking and g-force figures come from aviation. Different factors. For that matter cars do not lean 45 degrees at 1g either. Apples and oranges thing.

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I'm going to check with my go-to physics expert and see about settling this matter of lean angle and g-force. A Ferrari F40 can't break 1G on the skidpad. The idea that a motorcycle leaned over at 63 degrees can just over double that does not make sense. I'll probably come back with a very long and detailed explanation from my expert, but it seems some of the readers of this thread would like that.

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Here's some data to consider. Just a piece of the picture but it shows that the location of the contact patch changes the actual lean angle vs a zero width tire. This is also a clue to why Moto3 bikes don't lean as much as bigger bikes but corner very quickly.

post-9398-0-45914800-1394039748_thumb.jpg

post-9398-0-51388200-1394039926_thumb.jpg

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While I am very interested in what Dylan's goto Physics guru has to say on this subject but I'm pretty sure its going to boil down to a "Spherical Chicken in a Vacuum". Motorcycles are very complex things that are constantly moving and changing and trying to express that in a neat tidy equation is impossible, and requires that you ignore numerous other phenomena that are effecting the action you are trying to explain with your tidy formula. There's a neat tidy formula that some people have tried to argue means the size of your contact patch has nothing to do with your available traction, but it's not the case in the real world most notably due to the non linear elasticity of rubber, which said formula fails to account for.

 

to expand on this, there is the subject of "Lean angle" which we have discussed in several other threads,

 

First you have the "Apparent lean angle of the bike, say 45°, but that's not the real lean angle of the bike, because your tires aren't infinitely thin so you adjust your lean angle for the location of the contact patch and the CoG of the bike, so you lose a few degrees, but now you have to account for the rider who with good body position moves the CoG of the bike in and down, so you gain back a few of the degrees you lost to your contact patch, possibly even more increasing your lean angle to higher that the apparent lean you started with,

 

I previous threads we had referred to all of that as the "Effective Lean Angle" but this is still not the true lean angle, as you are trying to explain a 3D object moving through space with a 2D diagram, there's a entire second wheel involved here, and to complicate matters its not the same width, and depending on throttle application its not a 50/50 split between them, so now you have to calculate the "effective lean angle" for both tires, relevant to the actual CoG in 3D space, and then come up with some kind of weighted average between the two based on the distribution of the cornering load.

 

so after all that perhaps you end up with exactly 63.3° of entire "combined system lean angle" which the neat formula says is exactly 2 G's, is that ~1 G per tire which would line up neatly with Dylan's statement on being limited to 1 G of cornering force, or are both tires carrying a full 2 G ?

 

at the end of the day is knowing the mathematical theoretical limit that can be achieved going to improve your confidence in a corner ?

 

Tyler

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It should be 2g in that you would feel 2g going through your spine if you were sitting in line with the centreline of the bike and the tyres had no width and you were leaned over 63.3 degrees. So that should make the load 2g on both tyres, twice what it would be at 45 degrees.

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at the end of the day is knowing the mathematical theoretical limit that can be achieved going to improve your confidence in a corner ?

 

Tyler

 

That was a great summation, Tyler, and I couldn't agree more that this is the bottom line in all of this. While this is all an interesting debate for the geek in many of us including myself, I don't think that any of the resultant information will make any of us better riders in the end. How would you even apply the data if you could calculate or measure it real-time? You'd be staring at your speedo and lean angle data and comparing that to the calculated limit all the way through the corner and not watching your line. How comfortable would that be? If you weren't watching where you're going, how confident would you feel going fast through a corner? This isn't an effective approach to improving your riding, just an interesting, theoretical debate.

 

As Hotfoot mentioned, the better way to learn to find your limit in a corner is by taking a step-by-step approach to learning/improving each of the individual skills that go together to make up a good corner. By learning to consistently set the proper entry speed, then geting proper timing of the throttle application followed by proper throttle control and relaxing on the bars... you will create a stable contact patch that will give you predictable traction. Once you've learned to create that predictable traction, you can develop a feeling for your level of grip. Finally, you can begin to increase your entry speed methodically & learn to feel the cues it gives when it begins to slide and how to handle it. Twist of the Wrist II covers each of these individual skills well, and CSS teaches them in class one session/skill at a time and then reinforces them with on track coaching from really talented coaches like Hotfoot and Dylan, among many. In fact, these are all level 1 skills.

 

Unfortunately, there is no easy answer to your original question of dragging hard parts before losing traction... as has been clearly demonstrated here. :blink: If you really want to learn to explore that limit as safely as possible, get to a school. At least read and apply the skills in Twist II (book or DVD) to your own riding and it will help you move in that direction. Best of luck however you choose to learn your limits.

 

Benny

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While I am very interested in what Dylan's goto Physics guru has to say on this subject but I'm pretty sure its going to boil down to a "Spherical Chicken in a Vacuum". Motorcycles are very complex things that are constantly moving and changing and trying to express that in a neat tidy equation is impossible, and requires that you ignore numerous other phenomena that are effecting the action you are trying to explain with your tidy formula. There's a neat tidy formula that some people have tried to argue means the size of your contact patch has nothing to do with your available traction, but it's not the case in the real world most notably due to the non linear elasticity of rubber, which said formula fails to account for.

 

Tyler

Very well put. I totally agree with your summation. Could not have said it better. What I would find interesting is listing out the various things that one would have to consider to try to figure out how fast a bike could corner. It would be a list but going through the exercise of naming all the physics/mechanics involved would be illuminating.

 

Things like:

Friction coefficient of tires.

Actual lean angle/vs theoretical "zero width" tire.

Combined CofG of bike/rider.

Throttle application.

Acceleration.

Contact patch sizes.

G forces created.

Suspension.

Tire spring rate.

Tire temp.

Road surface (bumps).

Friction coefficient of road.

Camber.

Elasticity of rubber on tire.

Tire width.

Tire profile shapes in relation to each other.

Slip angle, front and rear tires.

Radius of turn.

Radius of rider's line.

Bar tension from rider.

Weight distribution of rider's body.

 

anyone want to add to the list?

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It should be 2g in that you would feel 2g going through your spine if you were sitting in line with the centreline of the bike and the tyres had no width and you were leaned over 63.3 degrees. So that should make the load 2g on both tyres, twice what it would be at 45 degrees.

 

I'm not physics expert but I disagree, assuming the combined mass of rider and bike is say 500 Lbs , and perfect 50/50 weight distribution, a stationary upright bike would apply 250 lbs of force to each contact patch, at 2g of cornering force the bike would be applying 1000 lbs of force, but its still split between the 2 contact patches 500 Lbs of force,

 

 

 

Dylan,

 

all the environmental factors

 

Ambient Humidity,

Ambient Temperature

Road Temperature,

Wind speed

 

 

Steering geometry factors

 

Rake

Trail

Offset

Head Angle

Wheelbase

Ride Height

 

Ground Clearance

Rate of Steering application

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My addition.

 

How well insured the rider is. :)

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I didn't see mass of bike and mass of rider on the list, those would be factor for sure.

 

Proportion of unsprung weight would probably figure in, at some point, too...

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I asked Eric, my go-to physics guy, to comment on a few points. Here's his response which I find very helpful in painting a more complete picture.

 

Dylan:

 

Well, the tangent of 63° = 1.96, which should mean that a bike/rider assuming zero width tires, infinite traction, and rider center of mass in the plane of the bike should be able to corner at 1.96G with a lean angle of 63°. And tan(45°) = 1, so under the same assumptions a bike leaned over at 45° should yield 1G turns. That’s just pure mathematical physics, and there is zero controversy about the math or physics of it. There is only room for questioning the assumptions.

 

You may recall my discussion of the effect of tire width on the effective lean angle. Tire width has a big impact here. I think I recall estimating that a 600cc bike with fairly high CG and ~5” wide tires would have an effective lean angle of ~41.5° at a measured bike lean angle of 45°. Doesn’t sound like much, but if the rider keeps his center of gravity in the plane of the bike, then an effective lean angle of 41.5° will only get you ~0.88G in a coordinated turn. With the same geometry assumptions, a bike leaned at 63° would experience a greater “lean angle penalty” than at 45° for two reasons: (1) The bike is riding on a fatter part of the tire profile at 63° measured lean angle than at a 45° measured lean angle, and (2) The bike is riding on a part of the tire that is at a smaller radius from the center of gravity. I haven’t run the numbers, but suspect that the lean angle penalty could be in the neighborhood of 10° or more at a measured lean angle of 63°, which would bring the effective lean angle down to ~53° or less, or ~1.33G or less in a coordinated turn. Since street tires can’t possibly deliver 1.33G cornering force, there’s not much point in providing the ground clearance for a 63° measured lean angle.

 

With a wider tire and a lower bike/rider center of gravity, as you would expect in racing, the lean angle penalty would be even more pronounced. It wouldn’t greatly surprise me if the lean angle penalty got upwards of 15°, before accounting for the beneficial effect of rider hang-off. If that’s in the ballpark, then a 63° measured lean angle would only provide ~48° of effective lean angle (or 1.11G in a coordinated turn) if the rider stayed centered on the bike, maybe recoverable to ~53° of effective lean angle (or 1.33G in a coordinated turn) with good rider hang-off.

 

I don’t know whether motorcycle race tire compounds can deliver 1.33G of turning force or not—that’s about as far as I can possibly stretch my head. But there are a couple of experiments you could try to see if my explanation is just bogus or maybe not so bogus.

 

Experiment 1:

Get two good riders, a 125CC racer, and an R1000SS out on a track. Station a camera on a tripod at the tangent to the apex of a turn. Use your radar gun to train both riders to go through the turn at exactly the same speed, such spped to require ~55° lean angle on the R1000SS. Also train the riders to ride exactly the same line and to not hang off the bike (i.e., stay on the bike’s centerline.)

I’m betting you will find, if you compare photos of the bikes at the apex of the turn, that the 125 will require ~4° less lean angle than the R1000SS. Admittedly, that’s a pretty small angle to measure, given all the variability you’ll see from lap to lap, but if you average over 20 – 30 laps, I think the difference will be apparent.

 

Experiment 2:

Set up your camera and radar gun as before, but at the apex of a perfectly flat turn. (Use a carpenter’s level.) Paint or tape a constant radius arc through the apex, and measure its radius exactly. (Use a stake at the center of the turn and a piece of string to make sure the radius is constant. Train the rider to not hang off the bike at all, and to track as close to 12” outside the arc as possible. ((We don’t want the tire contact patch on the tape.) Using any bike of your choice, but with aggressive tires, send the rider around the track, and measure the rider’s speed at the exact instant you photograph the bike from exactly behind its rear wheel. Speed in the turn can vary a fair amount, but should require fairly aggressive lean angles (but, again, no hanging off!) Do this for 20-30 laps, making sure that you take photos and speed exactly when the camera is in the plane of the rear wheel.

We can then measure the lean angle and estimate the effective lean angle from the photographs, and we can measure the exact G’s of the bike in every pass by comparing the bike’s speed with the turn radius. We will then be able to compare measured and effective lean angles against the actual Gs, and see if my explanation accounts for your concern. I’m betting it will.

 

Finally, while I agree that braking or accelerating at much more than 1G is just not happening, I think that’s because the center of gravity of the bike/rider is so high that the G limit is imposed by wheelies or stoppies rather than tire traction. When stopping in a straight line, the G-limit is set by the ratio of the height of the combined bike/rider center of mass to the horizontal distance between the combined bike/rider center of mass and a vertical line drawn through the center of the front tire’s contact patch. If those distances were exactly equal, then the maximum braking Gs you could develop, even with infinite tire-pavement friction, would be 1G. (And, remember, you have to measure these distances when the front forks are compressed by the weight transfer!)

 

In contrast, when in a turn, the combined bike/rider center of mass gets lower as the lean angle increases. So in a coordinated turn, you don’t high-side—and the G-limit is set by tire-pavement traction, not vaulting laterally over the tires.

 

This is just a long-winded way of saying that you should not try to reason that cornering Gs on a bike would be no better than driving or stopping Gs. The G-limits of cornering are different from those of driving and stopping.

 

Does this help?

 

-Eric

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