Tire friction regarding contact area

[jgoff14]

So I was talking with my physics professor a while back about how friction force in a tire is independent of how much of the tire is in contact with the road. ie: Mu*(m*g) doesn't take into consideration the size of contact area and the friction is the same because essentially the weight (m*g) times friction coefficient (Mu) stays the same regardless of tire pressure. He was going to explain more to me but class ended at 9pm and it was 10pm so he told me to talk to him more about it next time. I forgot to but he was saying something about how tho the amount of friction force stays the same, the normal force changes, but we left off there... I was wondering why when airing down a tire you get better traction despite the lack of change in friction. It makes sense in a non physics/ common sense way that with more tire to grip and throw things it would be more likely to keep its traction but what is going on here from a physics point of view? Thanks all!

 

[rcgldr]

With a car of the same weight, the larger the contact patch area, the lower the load per unit area of the contact patch, which translates into somewhat higher grip, up to a point, due to something called tire load sensitivity, where the coefficient of friction decreases the with amount of load. There's a point where increasing contact patch area beyond some near optimal size has little additional effect.

http://en.wikipedia.org/wiki/Tire_load_sensitivity

 

[jgoff14]

Great job finding that. Wiki needs a little bit more help filling out a lot of their technical pages... come on physics forum, get on there and fix em up! ;)

 

[mp3car]

Another wikipedia page you might want to read is http://en.wikipedia.org/wiki/Rolling_resistance

Also, despite popular belief, if only replacing two tires, you should put them on the back, NOT the front... regardless of whether it's FWD, RWD or AWD...

A vehicle with two locked tires (or considerably less friction than the front) will "rotate" so the lower traction tires are in the front. Here is a demonstration of putting new in front vs. new in back...
http://www.michelinman.com/tire-care/tire-basics/

 

[Lsos]

I'm not sure the last statement really applies to most real-world situations. Nobody says "I need to change all my tires, but I will change only two". Usually it's only two that wear first, which in FWD would most likely be the fronts. If the fronts are bald and the rear are almost new, which quite often is the case, then obviously it doesn't make sense to replace the rears.

But I see your point that you don't want bald tires in the rear. Most everyday cars are designed so they don't rotate when turning or braking, but instead they tend to go straight. The brakes are usually set so that front tires lock up first, and the suspension so that the fronts slip first. However, if we allow the rear tires to get extremely worn, the car might indeed become "unstable" in some situations.

 

[xxChrisxx]

This old chestnut.

First thing you've got to realize is that coulomb friction applies only to fairly rigid materials. It doesn't fully describe how a flexible pneumatic tyre generates grip.

ie. F = mu*N doesn't really apply.
Tyres also use adhesion (which is why slicks generate more grip) and mechanical keying, which means they deform to take up the roughness of the road (imagine blu tak being pushed on a key) allowing a surface they can 'push off'.


The rest, about load sensitivity and rolling resistance has been talked about above.

 

[mp3car]

I apologize, I did not mean to say "new in front" b/c that obviously wouldn't have the "best" in the rear, which is what you want... so if you're only buying two, and assuming the fronts are the most worn, you'd move the backs to the front and put the new ones on the back...

Regarding cars being designed so they stay straight, I'm not sure, but I believe that is really only the case with stability assist systems. I have an '05 TL, and it has yaw sensors that can detect various types of skids/slides... such as the back coming around, and it can apply braking to individual wheels, along with letting off the throttle. I believe in most cases for stability assist, it applies braking only to the outer wheels if you're in a slide. It works very well from my experience. I also have an '05 MDX and the other day when we had about 6" of snow, the roads were nearly perfectly clear in areas surrounded by fields b/c the strong winds prevented the snow from settling on the roads. But just off to the side, there was snow. Since nobody was around, and the sides of the road were fields with no utility poles/ditches, I put the right side totally off the pavement in the snow (over grass) and laid on the brakes pretty hard with my hands just barely on the steering wheel... the car stayed perfectly straight... The other benefit of being able to apply brakes to individual wheels is so that if you're stuck and giving it gas... it senses the spinning wheel and applies braking to it so that the other wheel, the one with more traction, can get power. In the MDX's case, it is AWD with a 4WD "lock" that with the push of a button, can lock the rear differential and the front-to-rear... really this makes it more of a "3WD" b/c the front differential is still open. However, since it can apply brakes to whichever front wheel is spinning, I would say it's a "quasi-4WD" mode... but you can still get stuck if BOTH front wheels have very little or no traction b/c then it's just basically RWD...

xxChrisxx, very interesting point about the conventional formula not applying, i hadn't thought about that but i also think your point about deforming comes into play also...

As a complete aside, for anyone who buys performance tires - I just purchased what I feel are the best tires I've ever owned... Continental Extreme Contact DWS (dry/wet/snow). If you never get snow, then I think they have a summer variant that's just DW. No, I don't work for them! They also have what feels like zero harmonic issues (completely smooth at all speeds) and the installer said he's never had tires so naturally balanced, two of the wheels didn't require weights and the other two only required minimal... he also said looking down the side of the tires while on the balancer, he could see no warble (i.e. they were very "true").

 

[xxChrisxx]

xxChrisxx, very interesting point about the conventional formula not applying, i hadn't thought about that but i also think your point about deforming comes into play also...

It's something that most people don't think about, but once you've been told it becomes pretty obvious.

F= m*N is a linear relationship.
A tyres grip level vs load isn't.

We get this problem because of the way friction is taught in schools, tire examples are used to make it 'relevant to the world' rather than a box on a slope. As much as this keeps 15 year old boys interested it just opens a whole can of worms if they ever start to look at tire mechanics.

 

[Lsos]

With stability control systems it's obviously much easier to keep a car straight, as the computer adjusts to conditions on the fly. With older cars, they have to bias the brakes so that the fronts lock up first, and they set the suspension so that the fronts do most of the work...and therefore slip first. You lose performance, but it prevents families from spinning out the Ford Taurus on the way to church.

Of course, the more performance-oriented the car, the more "balanced" they make them, and as a result the driver needs to have some skill to drive them properly and not end up in a ditch.

First day I got my S2000, that's actually what almost happened. The transition from FWD to performance RWD wasn't so smooth and I had the car perpendicular to the road, on it's way to a ditch. Luckily, I played some Gran Turismo in my day and my reflexes were able to correct. Nevertheless, I went auto-crossing every weekend for the next few months.