Tyre contact patch + friction physics discussions

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Tyre contact patch + friction physics discussions

Postby Malcolm » Thu Nov 24, 2005 2:12 pm

Now, I have been wondering about something for a couple of weeks now, and would like to see if any of you have anything intelligent to say about this.

Everyone knows that widers tyres = more grip....or does it?

Frictional force is found by the following formula

F = (mu) * N

where F = friction force
(mu) = coefficient of friction
N = normal reaction force (for our purposes, just assume this = weight force)

so what this means is that friction force is proportional to coefficient of friction between the two surfaces, and also proportional to weight force on the surfaces.

it's also worth pointing out that friction is a reactive force, ie this figure above is the maximum friction force a system can generate in reaction to an opposing force trying to accelerate the object, not a constant force.

Anyway, here's a simple thought experiement:
1. Take a block of steel, with a weight of 100 Newtons (that's about 10kg mass)
2. On the bottom of the steel block, affix a large piece of rubber
3. Place the block on smooth asphalt, rubber side down
4. Attach a rope to the steel block and pull with increasing force until it moves - let's say it takes X amount of force to move it.

Now, take an identical steel block, with rubber on the bottom, place it next to the other, and repeat the experiment. We now have twice the weight, 200N, and as you can obviously imagine, the force required to move them would be 2X

So what this all means, if you look at the formula from above:

F = (mu) * N
with our values from the first experiment, we have
X = (mu) * 100
so (mu) = X/100

from the second experiment we have
2X = (mu) * 200
or (mu) = 2X/100
which is the same as
(mu) = X/100

also from this relationship we can see that if we had 2 steel blocks of only 50N each, the force required to shift them would be half as much as 2X, so again we would have (mu) = X/100

so what this shows is that the coefficient of friction has not changed whatsoever, despite the fact that the contact patch has doubled from the first experiment to the second, and therefore the larger contact patch has not given us any increase in maximum available friction force....

so, does a wider tyre/larger contact patch really give you more available friction force?
(please don't answer this by saying you put bigger tyres on and got more grip, because that's not what I'm trying to establish)

Anyway, one reason I can think of for the apparent increase in traction when you increase tyre width, is that you're also increasing the mass moment of inertia for the wheel/tyre (basically the rotational equivalent of the linear value of mass), which means if you apply the same amount of torque to the wheel, the angular acceleration will be less because:
M = I * (alpha)
where M = moment (torque)
I = mass moment of inertia
(alpha) = angular acceleration

and btw M = I * (alpha) is the rotational equivalent of Newton's 2nd Law, F = m * a (force = mass * accelertion)



:D
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Postby RomanV » Thu Nov 24, 2005 2:57 pm

Well this is a very complicated topic, I would say complicated well past the limits of your equations.

There are so many more factors that affect tire performance, that I think real life testing/observation is the only way to establish this one way or the other.
As you have said yourself, 'in theory' usually means that the theory isnt comprehensive enough to take into account all of the variables that effect a real life outcome.

Things like sidewall flex and contact patch shape change noticably with wider/skinnier tires, as well as tire temperature, etc. and these influence a tires performance greatly.

Whenever I think about something like this, I always look to see what race cars do, as they've usually got the right idea.

Although a lot of race cars use very wide tires, I suspect this has a lot to do with tire longevity, as you have more surface area of tire to use up, meaning less frequent tire changes.

If your theory was correct, I doubt top fuel dragsters would run such wide tires, if they could save weight using skinnier tires with no disadvantage.
Tire longevity obviously isnt an issue for dragsters.
However I think that there are several good reasons why 'wide' tires arent used on street cars:

Extra cost.
tire temperature... (just a theory here) I would imagine that a wider tire dissipates heat better than a skinnier tire. (due to larger surface area) Which is good if you are caning it around, and your tire temps are getting undesirably high... But to keep the tire in the optimal temperature range on a shopping trolley/street car, skinnier tires are used.
(I dont know how much truth is in that, its just a thought)

Also greater frontal surface area = easier to aquaplane in the wet.
Not good for plain Jane whos going to pick her kids up from soccer.

Also more aerodynamic drag/lift is generated by the wider front face of the front tires... Dont know how much effect this has though.
Many newer cars have flaps in front of the front wheels, specifically to deflect air away from the face of the tire though, so I would imagine it is worth thinking about.

If you look at ferarris etc. where no costs are spared, I think you will find that they run fecking wide tires. :P

If you are thinking about stepping up from the 185's on the AW11, I reccomend it completely. :D
Go nuts, maybe get some 205s on there if you are daring. :lol:

Yeah, I know you dont run 185's, but I find factory 185's on a sports car rather amusing


Anyway, my thoughts on the matter are that the choice of tire width is more complicated than what you can describe with a simple formula, many other variables need to be taken into account. 8)
I also think that a lot of people incorrectly assume that the factory tire widths etc. are best, as factory setups often go 'middle of the road', geared towards the average buyer. The average buyer isnt necessarily someone who will cane it around all of the time, except in the case of ferraris etc, where they DO run wide tires. :)

So I think going to slightly wider than factory tires is a good thing from a performance point of view.
SW20s went from 205s to 225s or 235s on the rear for gen 2 (or 3?) onwards, to 'fix' the oversteer 'problem' :roll:

By providing more grip I would imagine. :P
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Postby Malcolm » Thu Nov 24, 2005 3:27 pm

well I'm not trying to say the basic examples I showed were what I feel represents what actually happens in reality, but rather trying to find how to expand the theory to account for contact patch.

I'm actually really just trying to analyse the effect of traction in straight line acceleration, not really cornering ATM.

I currently have 245s on the back of the aw11, and they definitely have a lot more grip than the 195's did! What I'm really trying to establish is, if all other factors are left the same, how does the tyre width or contact patch change the available friction force?

surface area definitely improves heat dissipation into the air, and having a larger contact patch means more heat can be transfered to the road surface.
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Postby fivebob » Thu Nov 24, 2005 3:43 pm

Racecar Engineering Mar/Apr 2005 wrote:ImageIt seems plainly obvious that wider tyres equals more traction but in reality it is far from this simple

ImageComplex processes of molecular bonding and mechanical interlock are at play when a tyre is in use and sliding results in a combination of both shearing and dragging processes

The wider the better?
Why are wide tyres better?
It has been recognised for about 40 years now that wide tyres provide more grip, at least when we are not limited by aquaplaning. One might suppose that this effect would be well understood by now, on a theoretical level as well as a practical one, yet the matter seems to be receiving a lot of attention from various authors lately. This seems to be due in part to the need for mathematical tyre models to be used in computer simulation.

On the face of it, one might wonder why there is any controversy about this at all, and also why it took people until the 1960s to try wide tyres. More tyre — more rubber on the road. More rubber on the road — more traction, right? Why wouldn’t this be obvious?

Essentially, there are two reasons it wasn’t obvious. First, according to Coulomb’s law for dry sliding friction, friction is independent of apparent contact area. It depends on the nature of the substances in contact and the normal (perpendicular) force. Second, a tyre’s contact patch area theoretically doesn’t vary with its width. If we widen the tread, the contact patch gets shorter, the area theoretically staying the same.

Let’s consider each of these notions. Coulomb’s law applies quite accurately to hard, dry, clean, smooth surfaces. However, a tyre tread is a soft, tough, sometimes tacky substance in contact with a hard, rough surface. When two hard, smooth surfaces are in contact, they actually touch only at a small percentage of their apparent or macroscopic contact area. Friction depends on molecular bonding in the small microscopic contact zones. As normal force increases, the microscopic contact area increases approximately proportionally, and consequently friction is directly proportional to normal force.

With rubber on pavement,however, there is not only the usual molecular bonding but also mechanical interlock between the asperities (high points) of the pavement and the compliant rubber. Sliding then involves a combination of shearing the rubber apart and dragging the asperities through it as the rubber reluctantly oozes around the asperities. The interface somewhat resembles a pair of meshing gears. With gears, when we increase the size and number of teeth in mesh, we increase the force required to shear off the teeth. It would be reasonable to expect a similar effect with the interlock between the tread and the pavement.

With increasing normal force, this interlock gets deeper, as the asperities are pushed further into the rubber. However, we might reasonably expect that at least beyond a certain point, the asperities are pushed into the rubber to pretty nearly their full depth, and further increase in normal force does not proportionately increase the mechanical interlock. With greater macroscopic contact area, it should take a greater normal force to reach this region of diminishing return. A tyre typically does show characteristics that would match this hypothesis. It will often have a range of loadings where its coefficient of friction is almost constant and where friction force is almost directly proportional to normal force. Above this range, the tyre exhibits much greater load sensitivity of the coefficient of friction. The curve of friction force as a function of normal force goes up almost as a straight line, then begins to droop at an increasing rate. Of course, the contact patch does not remain the same macroscopic size as load increases. It grows as we add load. Nevertheless, this contact patch growth is not enough to keep the coefficient of friction constant.

The contact patch growth is interesting in itself, and a bit counter- intuitive. A tyre can be considered a flexible bladder, inflated to some known pressure, and supporting a load. If such a bladder is extremely limp when deflated — like a toy balloon — and we inflate it, place it on a smooth, fiat surface and press down on it with a known force, the area of contact with the surface is equal to the normal force divided by the pressure A = Fn/P

If a tyre approximates this behaviour, then it follows that the contact patch area depends only on the load or normal force and the inflation pressure. If we make the tyre wider, then at any given load and pressure the contact patch doesn’t get bigger, it just gets wider and shorter. Accordingly, much discussion of the reasons a wide tyre gives an advantage focuses on reasons we might expect a wider tyre to yield greater lateral force than a narrower one, assuming similar construction and identical pressure, tread compound and load.

One theory is that a tyre is primarily limited by thermodynamics. It generates drag when running at a slip angle. The drag times the speed equals a power consumption, or rate of energy flow. This energy is converted into heat. For the system to be in equilibrium, the heat must be dissipated as fast as it is generated. Even short of the point of true equilibrium, the tread compound needs to be kept below a temperature where it softens to the point of being greasy rather than tacky. If the contact patch is shorter, that means that each square inch of tread surface spends less time getting heated and more time getting cooled.

Also, when a tyre is operating near its lateral force limit, the front portion of the contact patch is ‘stuck’ to the road and the rear portion is a ‘slip zone’ in which the tread moves across the pavement in a series of slip-and-grip cycles. The slip zone grows as we approach the point of breakaway. Beyond the point of breakaway, the entire contact patch is slip zone. The slip zone generates less force and more heat than the adhering zone. A shorter, wider contact patch is thought to have a larger adhering zone and a smaller slip zone at a given slip angle, and wider tyres are also known to reach peak force at smaller slip angles. Therefore, a wider tyre is not only better able to manage heat, but also generates less heat at a given lateral force. This all makes sense, but it fails to explain why wide tyres give more grip even when stone cold.

There is little doubt that they do. If you have a street car with four identical tyres, and you replace the rear tyres and wheels with ones an inch wider, using the same make and model of tyre, with no other changes, the handling balance will shift markedly toward understeer. You will see this effect at all times, from the first turn to the last — surely this effect is not coming from heat management? Paul Haney explains this by the larger adhering zone theory described above. The tyre makes more efficient use of its contact patch, even if the contact patch isn’t actually larger.

As much sense as the above theories make, they ignore some real world effects that have a bearing on the situation.

ImageA classic example of the ‘bigger is better’ tyre theory the hugely successful Lotus 72

First of all, the degree to which tyres follow the A = Fn/P rule varies considerably.A very flexible tyre, at moderate load, may have a contact patch as large as 97 per cent of theoretical, whereas a fairly stiff tyre may be well below 8o percent.

We are all aware of run-flat tyres currently being sold, which will hold up a car with no inflation pressure at all. As A = Fn/P approaches infinity. If A does not approach infinity, and the tyre does not go flat, the contact patch area as a percentage of theoretically predicted area approaches zero.

One might suppose that the effect of carcass stiffness would be significant mainly in street tyres, with run-fiats being an unrepresentative extreme. Yet I have seen dramatic differences in carcass rigidity in different makes of racing tyres intended for the same application. The Formula SAF car run by the University of North Carolina Charlotte uses 10in wheels. Hoosier and Goodyear both make 6in nominal-width tyres for the application. The stiffnesses of these tyres differ dramatically, with the Hoosiers being much more flexible than the Goodyears. The Goodyears are so stiff that they will support the front of the car (without the weight of the driver) with little visible deflection, even when completely deflated — run-flat racing tyres! So how closely do these tyres approximate A = Fn/P in this load range? Not very closely at all.

My point here is that tyre stiffness — vertically, laterally, and otherwise, is not purely a function of inflation pressure, so it is a bit risky to try to infer contact patch size from pressure and load. Therefore, we don’t necessarily know that two tyres differing only in width will have the same contact patch area at the same inflation pressure and load, or even that tyres of the same size do. Anyway, if it is approximately true that A = Fn/P , it follows that a wide tyre will have greater vertical stiffness, or tyre spring rate, than a narrow one, at any given inflation pressure. It will also have a smaller static deflection at a given load, which is why the contact patch is shorter. The flip side of this is that for a given static deflection, or tyre spring rate, a wide tyre needs a lower inflation pressure. Consequently, if we compare wide and narrow tyres at similar static deflection, or tyre spring rate, rather than similar pressure, they will have similar length contact patches and the wider one really will have more rubber on the road, just as we would intuitively suppose from looking at them.

As we make a tyre wider, not only does vertical stiffness increase for a given inflation pressure, so does the tension in the carcass due to inflation pressure. A tyre is a form of pressure vessel. We may think of it as a roughly cylindrical tank, bent into a circle to form a donut or torus. Borrowing from the terminology of pressure vessel design, we may speak of ‘hoop stress’in the walls the tensile stress analogous to the load on a barrel hoop. For a given inflation pressure, the hoop stress is directly proportional to the cross-sectional circumference, or mean cross-sectional diameter. When the carcass is under a higher pre-load, the tyre acts stiffer laterally. This effect can easily be seen in bicycle tyres. A fat bicycle tyre will feel harder to the thumb than a skinny one, at any given pressure. If we try to inflate a mountain bike tyre to the pressure we’d use in a narrow road racing tyre, the tyre will expand its bead off the rim and blow out. So when we compare narrow and wide tyres at equal inflation pressures, the wider one will be stiffer laterally as well as vertically, and it will achieve this at no penalty in contact patch size.

Finally, there is the question of tread wear. As we have noted, if the contact patch is longer, it has a larger slipping zone near the limit of adhesion, and it also spends a greater portion of each revolution in contact with the road. Not only do these factors influence how hot the tyre runs, but also how fast it wears. Therefore, assuming good camber control, a wide tyre should last longer than a narrow one, with similar tread compound.

The astute reader will see where I’m headed. If we need to run a given number of laps or miles on a set of tyres, then with wider tyres we can trade some of the inherent longevity advantage, and run a softer compound. Okay, summing up, what does a wider tyre get us?
  • It runs cooler, and/or
  • it makes more efficient use of its contact patch by having a greater percentage adhering, and/or
  • it can run at lower inflation pressure and therefore actually have a larger contact patch, and/or
  • it can have greater lateral stiffness at a given pressure and therefore keep its tread planted better, and or it can use a softer, stickier, faster-wearing compound without penalty in longevity.
Note that most of these effects in turn play off against each other. We can only blend and balance them, and get a tyre that is somewhat cooler running, has a somewhat lower operating pressure and somewhat larger contact patch, has somewhat greater lateral stiffness, and survives long enough with a somewhat stickier compound, all at the same time. That would explain an improvement in grip, wouldn’t it?

ImageIn theory, a wide tyre with a similar tread compound should last longer than a narrow one, allowing teams to use a softer compound. However, driving style can affect this drastically..
Last edited by fivebob on Fri Nov 25, 2005 11:40 am, edited 3 times in total.
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Postby Malcolm » Thu Nov 24, 2005 4:02 pm

Image racecar engineering rocks Image


thanks fivebob :) that explains everything
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Postby vvega » Thu Nov 24, 2005 9:41 pm

I call FAQ :D

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Postby pidge » Thu Nov 24, 2005 9:43 pm

Make this a Sticky! :lol:
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Postby RomanV » Fri Nov 25, 2005 12:51 am

FAQ worthy, definitely. 8)

This question comes up quite often, its good to have something definitive on the subject. 8)
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Postby method » Fri Nov 25, 2005 12:56 am

That was a good read, i had always assumed it was something to do with how the tyres "bite" the asphalt rather than just pure friction.
Thanks :D
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Postby fivebob » Fri Nov 25, 2005 1:24 pm

All_Fours wrote:Image racecar engineering rocks Image

Indeed it does, and it doesn't date that quickly either. I still refer to some of the first issues I bought over 10 years ago.

For another take on the subject from Paul Haney's book "The Racing & High-Performance Tire" see http://www.insideracingtechnology.com/tirebkexerpt1.htm
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Postby method » Fri Nov 25, 2005 1:52 pm

Where are these books purchased from?

Sounds pretty damn interesting.
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Postby crnkin » Sat Nov 26, 2005 6:52 pm

fivebob wrote:
Racecar Engineering Mar/Apr 2005 wrote:Second, a tyre’s contact patch area theoretically doesn’t vary with its width. If we widen the tread, the contact patch gets shorter, the area theoretically staying the same.


8O

right....
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Postby fivebob » Sat Nov 26, 2005 7:03 pm

crnkin wrote:
fivebob wrote:
Racecar Engineering Mar/Apr 2005 wrote:Second, a tyre’s contact patch area theoretically doesn’t vary with its width. If we widen the tread, the contact patch gets shorter, the area theoretically staying the same.


8O

right....

Your point being??????
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Postby vvega » Sat Nov 26, 2005 11:28 pm

as you widen a tyre width wise the longnatudal area will decrease
ao the contact patch grows wider and thinner

its quite a well known fact


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Postby method » Sat Nov 26, 2005 11:33 pm

Unless you decrease the tyre pressure as you increase the width to keep the same length of contact area :lol:
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Postby crnkin » Sun Nov 27, 2005 1:14 pm

hang on hang on

Im thinking of width being 265- 285 sorta things.

Is he meaning width as in 17 inch, 18 inch? cos then yeah i fully understand but the word here is used out of cotext with the way he has used width throughout the article... ???
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Postby vvega » Sun Nov 27, 2005 8:57 pm

thats not width that diameter

width as in 255 vrs 275

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Postby crnkin » Wed Nov 30, 2005 7:15 pm

soooooooooooooo 155 width vs a 300 width tyre in same siametre, with same tyre pressures, same sidewall flex, same car, 155 has more contact area than the 300, so therefore if weight is the same and compound is the same, 155 hold more lateral g forces than a 300. huh?

HAVE I GONE NUTTY! cos if i havent then you guys have! explain?
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Postby fivebob » Wed Nov 30, 2005 7:44 pm

crnkin wrote:soooooooooooooo 155 width vs a 300 width tyre in same siametre, with same tyre pressures, same sidewall flex, same car, 155 has more contact area than the 300, so therefore if weight is the same and compound is the same, 155 hold more lateral g forces than a 300. huh?

HAVE I GONE NUTTY! cos if i havent then you guys have! explain?

I can't speak for your sanity, but it seems your reading comprehension is lacking. Perhaps this summary will make it clearer :wink:

Second, a tyre’s contact patch area theoretically doesn’t vary with its width. If we widen the tread, the contact patch gets shorter, the area theoretically staying the same.


A shorter, wider contact patch is thought to have a larger adhering zone and a smaller slip zone at a given slip angle


If the contact patch is shorter, that means that each square inch of tread surface spends less time getting heated and more time getting cooled.


The tyre makes more efficient use of its contact patch, even if the contact patch isn’t actually larger.


Consequently, if we compare wide and narrow tyres at similar static deflection, or tyre spring rate, rather than similar pressure, they will have similar length contact patches and the wider one really will have more rubber on the road

So when we compare narrow and wide tyres at equal inflation pressures, the wider one will be stiffer laterally as well as vertically, and it will achieve this at no penalty in contact patch size.

  • it makes more efficient use of its contact patch by having a greater percentage adhering, and/or
  • it can run at lower inflation pressure and therefore actually have a larger contact patch, and/or
  • it can have greater lateral stiffness at a given pressure and therefore keep its tread planted better, and or it can use a softer, stickier, faster-wearing compound without penalty in longevity.
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Postby crnkin » Wed Nov 30, 2005 8:07 pm

hmmmmmmmmmmmmmmmmmmmmm......

Soooooooooooooo even if i cant understand why the contact patch stays the same, i do (now) understand why the grip etc is better- to a degree i question this though, although the writer himself acknowledges many variables...

Explain how the width influences the contact patch? Thats got me stuck
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