# Which corners faster - car or motorcycle?

• seriously_tho
In summary, the conversation discusses the comparison between a car and a motorcycle in terms of their ability to travel fastest before their tires lose adhesion. The example given involves a painted line and a 90 degree arc, and the question is how to calculate this. The conversation also touches on other factors such as tire compounds, contact patch, and centrifugal force. Overall, the consensus is that in similar conditions, both vehicles would have similar cornering speeds and forces. The conversation also mentions the importance of aerodynamic downforce and the different dynamics between a car and a motorcycle.

#### seriously_tho

I've been turning this over in my head for a week & the answer is way beyond me, maybe y'all can help.

There's a painted line that arcs 90 degrees over say 200'. A car follows that line with it's outside tires. A moto does the same. Which vehicle can travel fastest before the tires lose adhesion? How would someone even calculate this?

The example can be tweaked into whatever is a more fair comparison, so if the car needs to straddle the line, etc. Also assume all other things are equal, like tire compounds etc. The question is really about how two wheels leaning into a turn differ from a 4-wheel flat car platform.

Here's what I'm thinking. First, I'm no engineer, just thinking out loud. Adhesion is a result of mass (centrifugal force here) vs the tire's friction coefficient. I would think the size of the contact patch would be relevant too but it would increase with mass so I'm thinking it's a non-issue.

So it seems the vector of the centrifugal force is the same with either a leaning bike or a flat car, right? And if so, they would both slide out at the same speed. Is this correct?

seriously_tho said:
I've been turning this over in my head for a week & the answer is way beyond me, maybe y'all can help.

There's a painted line that arcs 90 degrees over say 200'. A car follows that line with it's outside tires. A moto does the same. Which vehicle can travel fastest before the tires lose adhesion? How would someone even calculate this?

The example can be tweaked into whatever is a more fair comparison, so if the car needs to straddle the line, etc. Also assume all other things are equal, like tire compounds etc. The question is really about how two wheels leaning into a turn differ from a 4-wheel flat car platform.

Here's what I'm thinking. First, I'm no engineer, just thinking out loud. Adhesion is a result of mass (centrifugal force here) vs the tire's friction coefficient. I would think the size of the contact patch would be relevant too but it would increase with mass so I'm thinking it's a non-issue.

So it seems the vector of the centrifugal force is the same with either a leaning bike or a flat car, right? And if so, they would both slide out at the same speed. Is this correct?

A car typically has aerodynamic downforce, which increases its traction capabilities versus a motorcycle.

Assume downforce isn't an issue here.

Hmmm... maybe I don't know what I'm talking about(certainly possible!) but I thought that a motorcycle can turn much more acutely than a car.
With a motorcycle, one has the potential benifit of "leaning into the curve" which is not possible with a car.
A car without lean will flip over durring a sharp curve.
A motorcycle, leaned properly, will not flip on that same curve.

But again, I could be wrong.

Edit: Note that a motorcycle leaning places the center of gravity(COG) closer to the gound, making it more difficult to "flip" This dynamic does not afford itself in a standard 4-wheeled vehicle.

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I'm not sure, but I think a motorcycle will lose traction first as it has much less surface contact with its tires. But don't quote me on that.

pallidin said:
Hmmm... maybe I don't know what I'm talking about(certainly possible!) but I thought that a motorcycle can turn much more acutely than a car.
With a motorcycle, one has the potential benifit of "leaning into the curve" which is not possible with a car.
A car without lean will flip over durring a sharp curve.
A motorcycle, leaned properly, will not flip on that same curve.

But again, I could be wrong.

Leaning into a curve is something you MUST do to avoid falling over as you turn. A car will flip before a motorcycle will because it cannot lean into the turn. Motorcycles typically lose traction before they can flip.

Assuming no downforce, then it's an issue of coefficient of friction and dynamic issues related to the size of the contact patch and how "clean" the road is (like dust).

Typically motorcycle tires used on sport bikes (the most common type of motorcycle) have more effective grip than the tires commonly used for sedan type cars, but not much more, if any, over the high performance tires used on sports cars. So sport motorcycles will out corner econoboxes and heavier sedans, but not the better sports oriented cars.

Drakkith said:
Motorcycles typically lose traction before they can flip.

Ah, indeed. Perhaps that's why some of the supersport motorcycles races on curved tracks have special tires with significant tread on the sides?

Too many variables. Light, overpowered car with rear-wheel drive? You can drift a turn, letting the rear slide around and then hammer the throttle. Think MGA on this one, especially on loose road surfaces, like gravel. Change road surface, tires, power-balance, or geometry (or many other variables) and everything is up in the air.

pallidin said:
Ah, indeed. Perhaps that's why some of the supersport motorcycles races on curved tracks have special tires with significant tread on the sides?

Yep. That's because those bikes lean SOOOO far over, and are going SOOO fast around a curve that they need as much tread on the side of the tire (which is where the tire is touching the ground in the turn) to avoid losing traction.

Seriously tho, you have it right. Given similar tire compounds, no aero downforce and reasonable tire width to mass ratio, the cornering speeds and forces will be very similar. That happens to be around the 1.3 G mark for both.

The dynamics are different but the physics isn't.

P.S. "centrifugal force" doesn't enter into this unless the corners are banked. Then it will again be the same for both vehicles.

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pallidin said:
A car without lean will flip over during a sharp curve.

Lean has nothing to do with it; centre of gravity does.

Given the average C of G location on a typical passenger car, that cornering force would have to exceed 2 gs before being in danger of flipping from the cornering force. That or trip on a curb.

mender said:
Lean has nothing to do with it; centre of gravity does.

Given the average C of G location on a typical passenger car, that cornering force would have to exceed 2 gs before being in danger of flipping from the cornering force. That or trip on a curb

Leaning changes your center of gravity on a bike.

Drakkith said:
Leaning changes your center of gravity on a bike.

The centre of gravity of a bike is always acting through the centre of the tire contact patch when cornering steady state.

mender said:

I saw the quote, I didn't realize you were only referring to the car. I was just throwing that out there.

mender said:
Seriously tho, you have it right. Given similar tire compounds, no aero downforce and reasonable tire width to mass ratio, the cornering speeds and forces will be very similar. That happens to be around the 1.3 G mark for both.

The dynamics are different but the physics isn't.

P.S. "centrifugal force" doesn't enter into this unless the corners are banked. Then it will again be the same for both vehicles.

Thank God someone read the question :tongue:

I was thinking that a square-shaped tire on a car that doesn't lean still has the same forces applied to it, that is a combination of 2 vectors - downward force from mass & lateral force from...something... centrifugal, centripetal...I don't know all the terms.

A leaning moto seems like an excellent illustration of exactly how those two vectors affect each other. More lean means more lateral force, etc. But the car, while not leaning, sees the same vectors affecting the tire, it just ain't visible the same way.

One last question, how does the ratio of mass to contact area affect tire adhesion?

So for example, two identical bikes & riders with a weight total of 500# each but one has tire contact patches twice the size of the other due to wider tires. Assuming everything else being the same, would they both lose traction at the same speed?

seriously_tho said:
So for example, two identical bikes & riders with a weight total of 500# each but one has tire contact patches twice the size of the other due to wider tires. Assuming everything else being the same, would they both lose traction at the same speed?
The larger contact patch results in less load per unit area of the tire, and less deformation of the contact patch. Tires have a load senstivity, where the coefficient of friction decreases with the load, so a larger contact patch increases grip, but there's a limit to that where there's almost no gain with further contact patch size increase.

The other reason for a larger contact patch inherent with a tire with more surface area is heat dissipation and wear.

If the tire pressure is the same for both bikes, the area of the contact patch will also be the same. Divide the weight by the tire pressure to get the contact patch area.

500lbs/(25 lbs/in^2) = 20 square inches

There will be no difference in area but the shape of the contact patch will change due to different construction of various tires.

Long narrow patches don't work as well as short but wide ones for a few reasons, the main ones being that wider contact patches are better controlled and the percentage of the contact patch that is experiencing slippage is reduced. That results in a higher level of grip.

To get the "wide tire" effect on motorcycle tires, the sidewalls have a larger radius than the centre - a parabolic shape as opposed to circular if you were to look at the tire from the back of the bike. As the bike is leaned over from vertical, the contact patch changes shape from an ellipse with the major axis in the fore-aft direction to one in the side to side direction. That mimics what the contact patch of a wide car tire looks like and gives the same benefits.

Here's a traction circle for a bike:
http://www.sportrider.com/riding_tips/146_0909_traction_circle_riding_skills/photo_02.html
Given what I said above, can you guess why the bike has less traction in a straight line when exactly vertical, as mentioned in the footnote and demonstrated by the graph?

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I'm guessing b/c a parabolic shape with a narrower vertical profile yields less actual contact patch than when the bike's off-center & into the meat of the parabola - no?

So (tall & narrow) < (short & wide) since the area of slippage vs area of controlled contact is proportionally smaller, as mentioned above.

Thanks for the thoughtful answers Mender, much appreciated.

I'm curious about something: When a bike is steeply leaned in a turn, the radius of the outermost portion of the tire that is in contact with the road is somewhat longer than the radius if the innermost portion of the tire that contacts the road. This implies that the inner and outer portions of the tire are skidding a bit in the turn, and only a small portion of the tire in the middle part of the tire track is not skidding. Given that static friction is greater than sliding friction, would this not be a disadvantage to a bike vs. a car?

That's interesting. Most bike tires have a width greatly larger than the width of the rim it's mounted to which I would think would increase the radius to something very close to center tread. I've never researched that tho, just guessing.

But if what you're saying is correct, a car tire would be subject to the same thing in that the outer edge in an arc would need to travel faster than the inner edge. In fact it seems the car tire would have a lot more of this "turning differential scrubbing" than the bike since the car tire contact patch is wider. Please adjust my new term there accordingly, making this up as I go.

Well, tho, (heh...) with the turning radius being 1529 inches, and assuming a car tread width of ten inches, the inner radius is five inches from the (non-skidding) center of the tire track, same for the outer edge. It's hard for me to believe that this results in a TDS anywhere comparible to the TDS of a leaned bike. Just sayin'...

seriously_tho said:
I'm guessing b/c a parabolic shape with a narrower vertical profile yields less actual contact patch than when the bike's off-center & into the meat of the parabola - no?

So (tall & narrow) < (short & wide) since the area of slippage vs area of controlled contact is proportionally smaller, as mentioned above.

Thanks for the thoughtful answers Mender, much appreciated.

seriously_tho,

Hi Rhody here, first do you ride sport bikes, and is this a theoretical or practical issue ? See http://www.google.com/images?hl=en&...&btnG=Search+Images&gbv=2&aq=f&aqi=&aql=&oq=". Turbo is correct. It is complicated and many factors contribute to the tires ability to stick, slip or slide on pavement and what that means to a car or bike being quicker in the same situation.

Modern sticky bike race tires are taller with a longer wearing harder material in the center. The main reason they are this way is to allow the tire to transition to the side of the tire quickly/smoothly and not to become flat easily which adverse affect the ability the snap into the corner quickly. The outer one third of the tire is much softer, second it heats quicker, providing maximum grip based on the number of heat cycles in the tire. My understanding is that once leaned over assuming that the corner is a smooth, a race tire will stick the best with the chassis of the bike balanced and at approaching maximum lean angle (around 50+ degrees) the throttle must be in maintenance mode (slightly open, sort of at idle). The siping or cuts in the tire are for funneling water to keep the tire from hydroplaning. A full dry race tire is usually a slick.

Your original question would a car or bike navigate a 90 degree corner in 200 yards along side a painted white line. Watch this http://www.youtube.com/watch?v=VwB2ckjWdnE&feature=mfu_in_order&list=UL", a picture as they say is worth a thousand words. This is almost the scenario you describe in your post, You can see the car drifting and the bike at 45%+ degrees of lean, not slipping for the most part, as they come out of the corner the bikes superior power to weight ratio kicks in and the bike disappears.

If you want clinical accuracy I would guess that at least 30 factors would be involved, and with a little work I bet you could get most of them and learn a whole lot about your question in the process. Finally, watch this http://www.motogp.com/en/videos/2009/Hyper+Slow+Motion+at+Sachsenring" [Broken]. What you are watching is of a fast right left chicane being slowed down from very high speed, so the side load on the tires front and rear do not deform the tread as much.

Rhody...

P.S. If you want more examples, have a look at my thread over https://www.physicsforums.com/showthread.php?t=449857".
Oh, BTW Welcome to PF, I hope you feel welcome, stay and contribute to the collective, so to speak.

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Thanks Rhody. It was just a theoretical I was playing with. I'm more cyclist than moto-rider but it doesn't really matter, just playing with ideas and y'all have given me lots to think about. Plus I'm kinda fascinated by the physics involved in something as simple as turning a bicycle.

The main thing I wondered if someone were to remove as many contributing factors as possible (for simplicity's sake) if there was any practical advantage to leaning a round tire on a 2-wheeled vehicle vs a non-leaning 4-wheel platform.

If anyone wants to take the conversation further here's where my thoughts were stemming from -

WHAT IF - a car's 4-wheel platform could exist beneath a leaning passenger platform? The simplest way to imagine this is a moto atop a 4-wheel go-kart platform with some sort of parallelogram linkage to facilitate leaning. And if possible, some way to harness the gyroscopic forces (?) in the wheels such that by turning the handlebar it forces the moto into a lean. Something like that anyway.

Now take that idea a step further into a car's passenger compartment in place of the moto, so basically insert the parallelogram linkage between the passenger area & the wheel platform. The result being a car that automatically leans, so you get the stability of a car & the fun of carving turns on a moto.

Anyway, just a train of thought I had during a long drive thru a canyon, seemed like a cool idea.

That video was great, those guys have amazing precision in the lines they're able to hold. It looks like their overall road-holding abilities were very similar, all other things being equal.

Looked at your moto project, the cowling around the exhaust is freakin' beautiful, great lines. The rear swingarm is a work of art too. But that ATV with snow chains, man the trouble I could get in with that...

I've got a Suzuki SV650 in the back of the garage, almost never ride it & keep meaning to sell it, I'm just much better on things with pedals.

mender said:
If the tire pressure is the same for both bikes, the area of the contact patch will also be the same.
This is ignoring the fact that the tread surface on a tire isn't infinitely thin, and that the tread itself compresses and deforms under load, regardless of tire pressure, depending on construction and how "soft" the tire compound is.

To get the "wide tire" effect on motorcycle tires, the sidewalls have a larger radius than the centre - a parabolic shape as opposed to circular if you were to look at the tire from the back of the bike.
That varies from brand to brand in the case of sport bike tires. Some brands of tires use a nearly circular cross section, while others use the parabolic shape you mention.

rcgldr said:
That varies from brand to brand in the case of sport bike tires. Some brands of tires use a nearly circular cross section, while others use the parabolic shape you mention.
Some of the stock tires that Harley used on cruisers were absolutely crappy. When I wore out the front tire (Bridgestone) on my Fat Boy (Superglide with large tanks) I replaced it with a Continental Blitz. Very round, consistent-curvature tire that would hang on in a very hard turn. It was so large that I had to take out the fender-mounting bolts in order to get that wheel re-mounted on the front forks. Bikers would see my machine and say "Man!, what did you do? The bike looks so much better!" I'd never tell them, and I'd never tell them why I could run away from them on curvy roads. Some secrets are fun to keep. Skinny 19" wheels might look good from afar, but you can make the bikes a LOT more responsive with little effort.

seriously_tho said:
Looked at your moto project, the cowling around the exhaust is freakin' beautiful, great lines. The rear swingarm is a work of art too. But that ATV with snow chains, man the trouble I could get in with that...

I've got a Suzuki SV650 in the back of the garage, almost never ride it & keep meaning to sell it, I'm just much better on things with pedals.

seriously,

Thanks, the cowling cover is carbon fiber made by Taylor racing, I have a carbon fiber rear fender on it now as well. The swing arm weighs 22 lbs and the whole bike with fuel 445 lbs.

I like your thinking approach, outside the box. You may or may not have heard about the late John Britten, and may enjoy this Kiwi's http://www.youtube.com/watch?v=QM_aNwaodd4". He was another original thinker, and an extremely focused and hard worker. He left us far to soon at age 45 from the spread of skin cancer. He would have done may more great things I am sure had he lived.

Rhody...

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seriously_tho said:
WHAT IF - a car's 4-wheel platform could exist beneath a leaning passenger platform? The simplest way to imagine this is a moto atop a 4-wheel go-kart platform with some sort of parallelogram linkage to facilitate leaning.

You might like to Google for some "tilting high speed train" designs. The issues are not quite the same as for a car, but the basic idea is to go round curves in the track at much higher speeds than the track was originally designed for.

seriously_tho said:
what if - a car's 4-wheel platform could exist beneath a leaning passenger platform?
The issue with that is ground clearance, in order to lean a wide platform, you'd have to raise the center of mass, which increase the differential in tire load, which reduces grip because of the tire load senstivity I mentioned earlier. There have been some "skinny" 3 wheel and 4 wheel platform that lean, with the passengers front and back as opposed to side by side, mostly novelties and not effective in terms of improved cornering speeds.

I've no doubt there'd be challenges to overcome, well beyond my abilities.

What if the suspension articulated relative to the turns, leaning the wheels in a 4-wheel platform parallel to the passenger area? What if the outside of the passenger area lifted rather than the inside lowering into the turn?

I think if the wheels leaned with the vehicle it would eliminate any reduced traction as a result of raised center of mass or tire load differential. (I may have botched some terms in there)

It's easier to balance a broomstick on end in your hand than a pencil. So maybe a taller leaning vehicle isn't a bad thing.

Bottom line tho, it doesn't sound like the leaning vehicle vs the flat has any mechanical cornering advantages other than thrill. And if that 1.3g figure mentioned is accurate there's plenty of thrill in there.

rcgldr said:
This is ignoring the fact that the tread surface on a tire isn't infinitely thin, and that the tread itself compresses and deforms under load, regardless of tire pressure, depending on construction and how "soft" the tire compound is.

That varies from brand to brand in the case of sport bike tires. Some brands of tires use a nearly circular cross section, while others use the parabolic shape you mention.
Yes. Tires are quite complex but one must start somewhere. I was supplying the foundation; we can fill in the details as needed.

This video shows you how an ametuer driver can get their hands on a powerful car and win the race. No way in hell she would've done that on the bike being an ametuer. A better biker has a tougher time aroudn the same track

Lamborghini Gallardo vs. Ducati 999

Mosler MT900 Photon vs. Ducati 999

Suzuki GSXR1000 vs Westerfield XTR4

its all about contact area...TIRES..Tires ... tires

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Both videos have been deleted...

I rec'd a newsletter from DIYaudio.com today, the writing hits right at the core of what makes us tinkerers tick. It may resonate for y'all too. A true pleasure to read:

So, let's get on with the real fun things, clearing off the workbench, lining up the tools, putting away the parts scattered everywhere from the last project, and searching the internet for more bargain parts. Then that smell of solder flux as construction begins. All the stuff we love to do, and few seem to understand - except for our friends here.

Taking away a car's downforce is a bit unrealistic, you might as well limit a motorcycle from leaning. And if you want a video try this one. It is a race between a very good motorcycle and a so-so sports car.
The bike loses. That is because the car does have better cornering. The bike out accelerates the car, so you could have a different result for a different track.