# Frictional Force

1. May 26, 2004

### paul11273

I have a question regarding frictional force, and how it is related to a contact area.
Last week our professor mentioned that the frictional force between an object and a surface is independant of the surface area in contact.

If this is true, then why do vehicles in motorsports want to have wide tires to keep as much rubber on the ground as possible? According to the prof's statement, it shouldn't matter.

Can anyone explain the prof's statement? Or prove it wrong? Or introduce something that perhaps he left out?

Thanks.

2. May 26, 2004

### Simon666

3. May 26, 2004

### paul11273

Thanks for that link. But...I still don't quite get it. The link does state that there are exceptions to the general rule. However, how do you actually figure out those exceptions?

In an engineering application, how would you decide if it was worth it to add extra material to increase contact area in order to increase friction? Maybe the added material wouldn't matter. How would we know?

Any ideas?

4. May 26, 2004

### jamesrc

Friction is a very complicated phenomenon, so I don't have all the answers, but here's a little of what I know:

When you're considering something like Coulomb friction, the apparent macroscopic contact area is irrelevant. This is because the effective contact area is only a fraction of that. The effective contact area is determined by the roughness of the two surfaces on a microscopic level, where asperities are evident. Under a load, these asperities will deform (by Hooke's law), thus changing the effective contact area and, consequently changing the magnitude of the friction. So we see (more explicitly if you look at the equations, but nonetheless) that friction is independent of the apparent (macroscopic) contact area.

With tires, the model for friction changes, since the stretch of the tire tread affects things. Here is a site that talks about that a bit.

5. May 26, 2004

### Gokul43201

Staff Emeritus
We would know by trying. That's what experimentation is all about. If a theoretical understanding of a certain concept is lacking, you do experiments to see what different situations lead to. From those results, it may be possible to generate a theory.

However, the area of tribology (the study of friction, wear, etc.) is not new and has been extensively covered in the last three or four hundred years. In general, and to a fairly high degree of accuracy, the area independence (Amontons 2nd Law) is found to be true. So you need not spend time experimenting on that.

Now to answer your question about wider tires : The reason for wider tires is not that the increased contact area automatically leads to more friction (though there may be some effects that depend on the area indirectly). The design parameter that determines the coefficient of friction between the tires and the track is the something related to the molecular compressibility of the rubber. In other words, "the softer the rubber, the better the friction." However, when you use a softer rubber, you need to make the tires wide enough to give them strength. So, "the softer the tire, the wider it needs to be", to withstand design forces and moments.

Compare the two statements in quotes and you'll see why it looks like increasing the width (or contact area) gives you better friction.

Last edited: May 26, 2004
6. May 26, 2004

### turin

This may be the problem. I suggest to think of it as the most simplified approximation rather than a "general rule." The rule is certainly not general. Another example of this kind of misinterpretation that may help you put things into perspective is Hooke's Law for springs. Hooke's Law is not the "general rule," but it can serve you with an outstandingly accurate approximation for small perturbations. The general rule goes into reversible deformations (nonlinearity) and then eventually irreversible deformations (plasticity/hysteresis).

7. May 27, 2004

### paul11273

Gokul43201 -
I understand that a softer compound increases the friction coeffecient. So the primary reason for a fatter tire is to maintain structural integrity for a softer compound? The tire getting fatter is simply a necessity to allow the use of a softer compound. That makes sense.

Then it would follow that going to a wider tire of the same compound would not increase friction, right?

JamesRC,
So what you have said is that the contact patch we see is only a small part of the story. That what really counts is the contact at a microscopic level. That is why increased force causes more friction, slight deformations cause greater contact between "tiny grooves". That also ties into the softer compound tires. The softer it is, the more easily it can "fill in" the tiny grooves of the surface it rides on.
This microscopic contact area is what really matters? But then, wouldn't increasing the macroscopic area also cause the microscopic area to increase, probably my orders of magnitude higher, thus causing overall friction to increase?

8. May 27, 2004

### Gokul43201

Staff Emeritus
I'm certain that this is at least "mostly" correct.

But I've also come across arguments where your initial condition is a spinning tire, and the model that best works to describe the subsequent dynamics uses a probability factor. This probability factor has some weak dependence on the area of contact. But I think this only determines how long you are "likely" to keep spinning before you find traction.

9. May 27, 2004

### LURCH

One factor to take into consideration is the relative smoothness of the surfaces involved. If one surface is flexible (like tire rubber), increased contact area increases the probability that a certain point of potential contact will make actual contact at any given time.

10. May 27, 2004

### krab

It's even worse than that. Going to wider tires without lowering tire pressure does not increase amount of rubber on road. Contact area is just weight divided by tire pressure.

Money spent on wider tires without going to softer, is wasted. In fact it has a negative impact in that it increases unsprung weight and rolling resistance. It can only help if the original tire is pushed so hard it frequently exceeds recommended temperature. Larger tires will run lower temp, other factors remaining constant.

11. Jun 5, 2004

### paul11273

What about going to a thinner tire in order to reduce rolling friction? Say on a bicycle. Is there any advantage, other than a weight savings, for a bike to use thinner tires?

12. Jun 5, 2004

### krab

Oh yes. The very most specialized racing bikes have the thinnest tires. The tradeoff is that the thinner the tire, the higher pressure is needed to keep it from bottoming on road irregularities. And of course the rider is subject to a lot of vibration.

13. Jun 10, 2004

### JohnDubYa

I have my own interpration of this effect, that relies on statistics. Since the coefficient of static friction is higher than kinetic friction, then the portion of the tire that remains in static contact with the surface dominates. A wider tire has a greater probably that a significant portion of the tire has not broken loose from the surface.

Heat kills tire traction. In general, you want your tires to run cool. At least that is my opinion on the matter.

14. Jun 10, 2004

### Gokul43201

Staff Emeritus
Oops ! There's better traction on a hot track. Pit crews prep new tires (keep them hot) before putting them on. The higher the temperature of the tire, the softer the rubber gets, and the better is the traction.

15. Jun 10, 2004

### paul11273

I definately agree that hot tires have better traction. I know this from my own experience with riding motorcycles.

However, I still am wrestling with the contact area/traction relationship.
Despite everyone's input on this question and my own googling, I have not come across anything that quantitatively explains this relationship. So far about the only thing I have to go on is $$F_{s}={\mu}_{s}N$$ which does not account for the surface area contact.

I thought this would have a fairly simple answer.

16. Jun 11, 2004

### JohnDubYa

The problem with hot tires is that its construction breaks down as the tire heats up. I once saw some data on this issue and the results were pretty convincing.

Heating up a tire before putting it on does little, as the tire cools down to its surroundings very quickly. For example, in water burnouts the tires get hot, but by the time the dragster gets the green the tires will have cooled down. Tires have huge surface area and lose heat to their surroundings very quickly.

But if you have any data that shows the relationship between tire temperature and traction, I would be willing to reconsider.

17. Jun 12, 2004

### paul11273

I definately agree that a tire will have a threshold where the rubber will begin to breakdown, resulting in adverse effects.
However, when people talk of the tire being "hot", they are reffering to the temperature it attains from running. A cold tire, at ambient air temperature, has noticeably less traction than once it has been running for a few minutes and has warmed up.
I do not have actual data for you, but I have experienced this difference myself. It is more noticeable on a spring or fall day when the air temp is 50-60 degress F vs. a summer day with 90-95 degree F temps.
I will search the web to see what I can come up with. I think that anyone who has ridden a motorcycle will agree with my own experience of "hot" vs. "cold" tires.

18. Jun 12, 2004

### JohnDubYa

RE: "I definately agree that a tire will have a threshold where the rubber will begin to breakdown, resulting in adverse effects."

The data I saw, however, showed an almost linear drop in traction with temperature, not a threshold.

I admit I was taken by surprise.

RE: "However, when people talk of the tire being "hot", they are reffering to the temperature it attains from running. A cold tire, at ambient air temperature, has noticeably less traction than once it has been running for a few minutes and has warmed up."

But this warming up may be just a relaxation of the rubber, similar to stretching exercises athletes perform before competition.

Maybe Goodyear or Hoosier has some data on the matter.

19. Jun 12, 2004

### kuengb

But new heat is produced while driving. The tyre is constantly deformed when it is rolling on the road (->inner friction), and there is of course a bit friction between tyre and road, depending on how you drive.

By the site below, formula one tyres run at 90-110 °C. I would say the connection between friction coeff. and temperature is not linear over far distances, each tyre compound has its optimal temperature. If you drive a winter tyre in summer you have less traction than with a summer tyre, although the first is then probably softer.

http://www.formula1.com/insight/technicalinfo/11/476.html [Broken]

Last edited by a moderator: May 1, 2017
20. Jun 12, 2004

### JohnDubYa

RE: "But new heat is produced while driving."

But that wasn't the issue I was describing.

RE: "I would say the connection between friction coeff. and temperature is not linear over far distances, each tyre compound has its optimal temperature."

Yes, I agree.