Tire physics

[bjhines]

Good Article......

 

WHY ARE WIDE TIRES BETTER?

 

It has been recognized for about 40 years now that wide tires provide more grip, at least when we are not limited by aquaplaning. One might suppose that this effect would be 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 tire models to be used in computer simulation. I have encountered the question at least twice in the past month, once in a seminar presented by Paul Haney, based on his recent book about tires, and once in Paul Van Valkenburgh’s November Racecar Engineering column. The issue has also come up in my work as an advisor to the UNC Charlotte Formula SAE team.

 

On the face of it, one might wonder why there is any controversy about this, and also why it took people until the 1960’s to try wide tires. More tire, 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 instead on the nature of the substances in contact, the normal (perpendicular) force, and nothing else. Second, a tire’s contact patch area theoretically doesn’t vary with its width anyway. If we widen the tread, the contact patch just gets shorter, and the area theoretically stays the same.

 

Let’s consider each of these notions. Coulomb’s law applies quite accurately to hard, dry, clean, smooth surfaces. However, a tire 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 tire 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; where friction force is almost directly proportional to normal force. Above this range, the tire 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 for a ways, 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 evidently not enough to keep the coefficient of friction constant.

 

The contact patch growth is interesting in itself, and a bit counter-intuitive. A tire can be considered a flexible bladder, inflated to some known pressure, and supporting a load. If such a bladder is extremely limp when uninflated, like a toy balloon, and we inflate it, place it on a smooth, flat 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 tire approximates this behavior, then it follows that the contact patch area depends only on the

load or normal force and the inflation pressure. If we make the tire 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 tire gives an advantage focuses on reasons we might expect a wider tire to yield greater lateral force than a narrower one, assuming similar construction and identical pressure, tread compound, and load.

 

One theory, advanced by the late Chuck Hallum and evidently picked up by Paul Van Valkenburgh in his recent column, is that a tire 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 tire 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 tires are also known to reach peak force at smaller slip angles. Therefore, a wider tire 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 tires give more grip even when stone cold.

 

There is little doubt that they do. If you have a street car with four identical tires, and you replace the rear tires and wheels with ones an inch wider, using the same make and model of tire, with no other changes, the handling balance will shift markedly toward understeer. You will see this effect at all times, from the first turn in a journey 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 tire makes more efficient use of its contact patch, even if the contact patch isn’t larger.

 

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

 

First of all, the degree to which tires follow the A = Fn/P rule varies considerably. A very flexible tire, at moderate load, may have a contact patch as large as 97% of theoretical. A fairly stiff tire may be well below 80%. We are all aware of run-flat tires currently being sold, which will hold up a Corvette with no inflation pressure at all. As P approaches zero, Fn/P approaches infinity. If A does not approach infinity, and the tire 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 tires, with run-flats being an unrepresentative extreme. Yet I have seen dramatic differences in carcass rigidity in different makes of racing tires intended for the same application. The Formula SAE car run by the University of North Carolina Charlotte uses 10” wheels. Hoosier and Goodyear both make 6” nominal-width tires for the application. The stiffnesses of these tires differ dramatically. The Hoosiers are much more flexible than the Goodyears. The Goodyears are so stiff that they will support the front of the car (without driver), with little visible deflection, when completely deflated – run-flat racing tires! How closely do these tires approximate A = Fn/P in this load range? Not very closely at all.

 

My point here is that tire 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 tires differing only in width do have the same contact patch area at the same inflation pressure and load, or even that tires of the same size do.

 

Anyway, if it is approximately true that A = Fn/P, it follows that a wide tire will have greater vertical stiffness, or tire 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 tire spring rate, a wide tire needs a lower inflation pressure. Consequently, if we compare wide and narrow tires at similar static deflection or tire 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 tire wider, not only does vertical stiffness increase for a given inflation pressure, so does the tension in the carcass due to inflation pressure. A tire 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 the “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 preload, the tire acts stiffer laterally. This effect can easily be seen in bicycle tires. A fat bicycle tire will feel harder to the thumb than a skinny one, at any given pressure. If we try to inflate a mountain bike tire to the pressure we’d use in a narrow road racing tire, the tire will expand its bead off the rim and blow out. So when we compare narrow and wide tires 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 tire runs, they also influence how fast it wears. Therefore, assuming good camber control, a wide tire should last longer than a narrow one, with similar tread compound. The astute reader will see where I’m headed with this. If we need to run a given number of laps or miles on a set of tires, then with wider tires we can trade away some of the inherent longevity advantage, and run a softer compound.

 

Okay, summing up, what does a wider tire get us?

1. It runs cooler, and/or

2. it makes more efficient use of its contact patch by having a greater percentage adhering, and/or

3. it can run at lower inflation pressure and therefore actually have a larger contact patch, and/or

4. it can have greater lateral stiffness at a given pressure and therefore keep its tread planted better, and/or

5. 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 blend and balance them, and get a tire 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?

[Dtsnlvrs]

 

Well it sounds good anyway, and I will only add that if you wanna know what it is like to drive a 350whp 240Z...take a bone stock 240Z to Italy and drive on their marble substrated roads...damn they are slick

[Guest Mike]

Post #41 is a good read. I suspect statement #3 of "summing up" in that post is causing some of the confusion. Probably all of us inflate larger tires to less PSI than smaller ones because this increases rubber-to-pavement contact area.

[rudypoochris]

Nice. That is a really interesting write up!

[thehelix112]

Maybe its the academic in me, but I feel obligated to cite that article in #41 as from Mark Ortiz at The Performance Tech Forum/Board

 

Damn good read btw.

 

Dave

[dr_hunt]

The maximum traction is at insipient slip, just before actually slipping. F=mu(s)*F(normal). There is mu static, mu insipient, and mu dynamic. There is a specific range of mu for asphalt dry and wet. Take a hotwheels car, tape the rear tires to the top of the car so they don't turn or rotate, slide it down a slide in the playground with the car facing forward. Guess what happens? The rear swaps ends with the front. mu dynamic is alot less than mu static or mu insipient. It's a fact! It's not rocket science, pretty simple really. If you want to get alot more technical then rubber compound comes into play, but still rather simple. As for rolling resistance, think of mountain bike vs. road bike tires, the tire pressure, contact patch, etc., still pretty simple. Narrow tires have less rolling resistance since they are less flexible, they have the same normal force. Land speed cars are geared alot different than anything else, they do the flying mile, not standing start and they are not applying loads of torque to the tires.

[Pop N Wood]

The maximum traction is at insipient slip, just before actually slipping. F=mu(s)*F(normal). There is mu static, mu insipient, and mu dynamic. There is a specific range of mu for asphalt dry and wet. Take a hotwheels car, tape the rear tires to the top of the car so they don't turn or rotate, slide it down a slide in the playground with the car facing forward. Guess what happens? The rear swaps ends with the front. mu dynamic is alot less than mu static or mu insipient. It's a fact! It's not rocket science, pretty simple really. If you want to get alot more technical then rubber compound comes into play, but still rather simple. As for rolling resistance, think of mountain bike vs. road bike tires, the tire pressure, contact patch, etc., still pretty simple. Narrow tires have less rolling resistance since they are less flexible, they have the same normal force. Land speed cars are geared alot different than anything else, they do the flying mile, not standing start and they are not applying loads of torque to the tires.

 

But where would you put the #9 resistors on a hot wheel car?

 

I am not building a race car. Do you think #3 or #4 resistors would be enough for my street car?

[dr_hunt]

But where would you put the #9 resistors on a hot wheel car?

 

I am not building a race car. Do you think #3 or #4 resistors would be enough for my street car?

 

Even for a street car I'd go #9 resistors. Nothing says performance like the #9. Wow all the gearheads when you show them what you have under the hood!

[Guest Mike]

POP... #9 resistors are used to tune static attraction. Nothing but #9 will work. It's a MAGIC number!!!

[Guest Mike]

Dammit Doc... You beat me to it!!

[HeatRaveR]

If tires lose grip when they get hot, then why to Indy car racers wiggle the steering wheel while awaiting the checkered flag and why to drag racers do burn-outs?

 

Race tires perform best when warm (basically their heat range is shifted higher), so they do that wiggling/burning out to warm them up quicker.

[johnc]

Mostly the weaving is done to clean off the tires. When you have to slow down under caution and drive on the non-racing line the tires pick up a lot of marbles. Weaving back and forth, hard, cleans the junk off.

[Guest Mike]

Hmm.. well I've learned something new... again. I always heard it was to heat up the rubber.