The Physics of Tires

By Vince Ili 


In Part I of his Ultimate Guide to Suspension and Handling, Mike Kojima says that one of the biggest ways to improve a car's handling is to improve its tires.  I experienced this first-hand recently when I upgraded the wheels and tires on my Mustang.

But how do tires improve your car's handling and performance?  In order to discuss that, we need to talk about a little thing called “traction,” also known to us engineering geeks as friction.

What is Friction?

Friction is a force that resists the movement of two objects sliding along each other.  Put your hands together and rub them.  The resistance to them sliding along each other is friction.

Friction is a complicated thing, but fortunately, we can model it pretty well as a linear function:

F ≤  μ N

This says that the force of static friction (F) is less than or equal to the coefficient of friction (μ) multiplied by the normal force (N).  Friction's coefficient varies depending on the two objects that are rubbing against each other.  Ice has a low coefficient of friction, whereas rubber has a high one.

The normal force (in the case of tires and cars) is the pressure that the ground is exerting upwards to hold the tire up.  If the car is sitting still, it is simply equal to the weight of the car on that tire.  If the car is moving, weight transfer from cornering and acceleration will make the normal force increase or decrease.


Normal Force distributed on a tire

The Normal force is equal to the weight the object is exerting on the ground.  Remember that the force of the weight can change during acceleration and cornering because of weight transfer.


Now, why does that equation have a less-than-or-equal-to sign instead of an equals sign?  That's because we're talking about static friction right now, which occurs between two objects that currently aren't moving.  Static friction produces a force that resists movement up to a certain point.  Beyond that point, it can no longer prod ce any more resistance, and we begin to deal with dynamic friction.  Dynamic friction is always less than static friction, and that's why sliding tires are bad! 

To wrap your head around this, think about sliding a heavy box across the floor.  Have you noticed that it takes more force to get it moving than it does to keep it moving?  That's because dynamic friction is less than static friction.  You might be wondering how, exactly, a tire that is rolling along the ground is experiencing static friction (as opposed to dynamic).  Take a look at the next diagram.



Assume that this tire is rolling along the ground; it is not sliding.  At any given instant in time, the very top of the tire is rotating around the point on the very bottom of the tire that is touching the ground.  Because the tire is not sliding, we're dealing with static friction.

Ever wonder why anti-lock braking systems help you control a car better?  That's because when the wheels lock, the tires slide along the ground, creating dynamic friction instead of static.  ABS (or threshold braking) keeps the tires rotating and keeps static friction.


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Monday, July 18, 2011 9:06 PM
I never wanted a Mustang until the 2011 models came out. What a beautiful car, and a good write up too!
Tuesday, July 19, 2011 12:48 AM
How do you like the 555s? I've been starting the autocross my WRX and the tires I have had and loved, Michelin Pilot Sport A/S, are relatively low on grip and seem to be getting eaten quickly.
I, like you, need a tire to do both DD and autox.

Also, I'm jealous of your front suspension. With such high kingpin angle and low caster as WRXs have, my camber is way positive at that much steering angle.
Dusty Duster
Dusty Dusterlink
Tuesday, July 19, 2011 2:21 AM
I really like the NT555s, but remember that my previous tires were all-season radials. I definitely think they're a good balance of performance, practicality, and cost, though.
Tuesday, July 19, 2011 3:24 AM
Cool, thanks. I'm also on all seasons, definitely a performance oriented one but very much all season and not a grippy compound.

Everyone I autocross with says to just get Star Specs but I'd rather get something that lasts longer and I'm far from skilled enough to be competitive.

Mind if I message you in a few months to ask for an update?
Tuesday, July 19, 2011 3:39 AM
The one thing this article didn't mention is the reason dynamic friction is lower than static friction. It's because the coefficient of friction (mu) is lower in dynamic friction. The static frictional force grows until you reach a knee-point and then the frictional force drops to dynamic friction as mu changes over. Anywhoo, definitely makes you think twice about dive bombing into a blind hairpin on the street when you realize it only takes a little bit too much aggression to slip off the road.

Another good all season tire is the Pirelli P4. Great treadwear, deep tread for snow and water, and decently handling for dry weather. It's also relatively cheap for an 80,000 mile tire. Braking leaves a little to be desired, but otherwise it's a great tire. My 240SX runs nothing but Nittos, they make the best tires for small cars. I use Neo Gens which would be good for a DD like a Civic that sees occasional track use. When I wear them out I want to switch to NT-05s and go up at least 3 sizes (205 tires are way too skinny for 240s).
Tuesday, July 19, 2011 4:28 AM
My next set (on new wheels) is going to be Yokohama S.drives (300TW). My current set has been a set of General Altimax HPs (440TW). Not a bad cheap all season, though I have slid a couple times in the rain during panic stops. Really more driver error than anything but I blame the weather, it's sunny all year, summer hits and then suddenly every road has 1/2in+ of water for a week and I don't remember how hard I'm supposed to push the brake to avoid lock ups because it's been 10-11 months since I've had any practice at it. When I got my car it had Michelin Symmetrys (600tw?) and those were terrible in the rain or dry, my grandfather chirped them without even trying. That was when the car was bone stock, I even still had traction control (AC compressor)!
Dusty Duster
Dusty Dusterlink
Tuesday, July 19, 2011 4:29 AM

Yes, feel free to message me. You can also check out my car's build thread in the forums:

Tuesday, July 19, 2011 5:15 AM
Yup, tires are absolutely crucial for going fast. Race teams that make the wrong choice in tire compound get left behind. Pretty much the ultimate auto-x tire right now is the Hankook RS3. They also make for one of the fastest track day tires. The Yokohama AD08s are right up there with them for track days. Star Specs are pretty fast for auto-x and track days, but I hate their feel; I had low confidence in them causing me to go slower. I love the Bridgestone Potenza RE-11s for an all-around kick-ass anywhere tire. It's a little slower than the RS3s and AD08s, but makes up for it in overall street use with regards to ride quality and tread life.

In one step down, you have the Potenza S04s that just came out which trade ultimate grip for tread life. Continential tires in the high performance street tire catagory have also been getting excellent reviews. Michelin always makes good stuff, but very pricey and not really any better performance wise in my opinion.
Tuesday, July 19, 2011 6:11 AM
@ six cylinders-- I have the Yokohama S-Drives (on base model 17's) on my G35 Coupe, and the difference in grip from the stock All-Season Goodyear RS-A's is amazing. They are awesome for autocross and in the rain! These tires changed the entire character of the car, and the @ the limit performance is really predictable. You wont be disappointed!
Dusty Duster
Dusty Dusterlink
Tuesday, July 19, 2011 6:21 AM
Yup, I always "knew" tires made a big difference, but I didn't really know how big of a difference until writing this article.
Tuesday, July 19, 2011 6:44 AM
Continental sketches me out a LOT.

The ExtremeContact DW/DWS have a lot of good press, and a lot of bad reviews on forums. Apparently they have really soft sidewalls which results in a comfortable tire but not great responses and big problems with going out-of-round, even just overnight.
Since for more than half of the year I'm at college where my car sits for up to a week inbetween drives, that's not good and I'd rather have traction and responsiveness and traction for autocross than comfort.

I'm liking the suggestions / comments on tires though. As above, I currently have stock size (205/50R17) Michelin Pilot Sport All Seasons on my WRX, and love them as an everyday tire but they're not up to autocrossing. They're (I think) a 500tw tire. Compared to stock they are smoother, quieter, have noticeably better dry grip, and
I know more negative camber will make them work better, but for now their shoulders are wearing really badly. One autocross school early in the summer where an instructor was having me be really aggressive (I felt I was overdriving car, tire, and myself) contributed to that a lot but still I'm disappointed with how much autocross disintegrates them.

Everyone I autocross with / have asked so far has just said "Star Specs!!!!!!!1" But also that they may only last one season... bad for my budget.

Something like the RE-11 - Nitto 555 - S.drive sounds up my alley, good grip but making concessions to treadwear.
Dusty Duster
Dusty Dusterlink
Tuesday, July 19, 2011 6:55 AM
Nitto also makes the NT05, which is similar to the '555, but with 200 treadwear and correspondingly better dry grip. Wet traction is about the same, at least according to their website.

But I've also heard some guys say "Nitto tires are for people who don't want to be competitive." I think it depends on personal preference, after a point.
Tuesday, July 19, 2011 7:01 AM
Definitely seems like a preference thing.

I'd like to have a longer lasting tire, though, than an NT05 or Star Spec (which are also 200).
The Conti ExtremeContact DW seemed to have great traction and review with a 340 tread grade, but looks to me to have a lot of way-too-sounding press reviews and many complaints on forums, etc.

Anyway, my Pilot Sports have a good amount of tread left but are just wearing alarmingly quick and don't have as much grip as I'd like even as a developing novice, so something to keep looking at over the next few months and not tonight.
Tuesday, July 19, 2011 8:28 AM
This i a good review of the basic physics involved. I look forward to a more advanced part II!

Why does tire friction depend on tire width (contrary to F ≤ μ N)? Does this also explain why grip does not increase quite linearly with normal force? (I believe this phenomenon explains why light cars are so fast and why sway bars can effect car balance.) What effect does temperature play on grip - IE when should I use tire warmers and when should I spray my tire down with water? Perhaps a explanation of tire construction and sidewall stiffness would help clarify steering feel. What happens to a tire on the edge of static friction - why do some tires offer better feedback or more noise before they start sliding? How do drifters choose tires? How do they keep them from popping the bead? I know the more smoke I see on a drift the quicker my rubber is being worn away. Do I really need to replace my tire when I have only 3/32 of tread left and its mid summer in San Diego? If I just started exposing the cord can I drive home from autocross or will I die on the freeway?

Clearly I have some answers but many more questions. I know MotoIQ has the answers we want! There is certainly some advanced tribology here, but the application specific experience should be enough. I haven't spent enough time on the track to know....
Dusty Duster
Dusty Dusterlink
Tuesday, July 19, 2011 9:15 AM
The coefficient of friction depends on a lot of things, not just the material. It also depends on the shape of the two objects. So wider tires would have a higher coefficient of friction because there is more surface area. (An interesting side note is that the coefficient of friction between rubber and concrete is higher than one. In other words, it requires more than the weight of the car to get the vehicle to slide on its tires!)

Remember, the linear function I showed you is an approximation. It isn't really a linear function; but in a lot of instances it's close to a linear function. For instance, street tires are designed to start sliding gradually. Many R-compounds let go all at once. That means a street tire would not be linear near the end of its grip.

Heat generally makes rubber softer, which would increase its coefficient of friction to a certain point. But if it gets too hot, it can become slick. So there is a curve for grip versus temperature.
Tuesday, July 19, 2011 12:11 PM
Actually, a wider tire DOES NOT have a higher coefficient of friction. Coefficient of friction is set between two materiels, IE the COF between steel and ice is a number, and the COF between rubber and asphalt is another number.

Say you put a 225 tire on the front right of your Mustang and a 275 on the front left. The area of the contact patch will be the same (assuming constant tire pressures), but the shape will be different. the wider tire, however, will have a wider but shorter contact patch and the skinnier tire will have a longer, thinner contact patch.

So the next piece of the puzzle has to do with integrating over different areas (I don't remember the math =D), but what comes out is the fact that for a given loading, two widths of tire will produce the same amount of traction but the wider tire will have more lateral traction and the skinnier tire will have more longitudinal traction.
Dusty Duster
Dusty Dusterlink
Tuesday, July 19, 2011 4:37 PM
@NBruno. Wrong. Coefficient of friction is a SYSTEM attribute, not a material one. Read the article on Wikipedia if you don't believe me.
Dusty Duster
Dusty Dusterlink
Tuesday, July 19, 2011 4:41 PM
In other words, yes, you integrate to find the coefficient of friction FOR THE SYSTEM you are working with in order to generate the linear function I listed in the article. You could say a BASE coefficient of friction exists between two materials, irrespective of a given system defining their interaction. But whenever you write the one equation to define the interactions of two objects in a system, you would use a single coefficient of friction that exists FOR THOSE TWO OBJECTS. That coefficient of friction would vary based only on the materials, but on the shape and size of the objects.
Tuesday, July 19, 2011 5:02 PM
I'm not saying COF is a materiel property. But for a given condition, contact area has nothing to do with COF. That's all I'm saying.
Tuesday, July 19, 2011 8:21 PM
In theory, Coefficient of Friction is absolutely a material property.

But tires are affected by a lot more than friction alone:
-There are adhesion forces between the tire and asphalt, especially on softer performance-oriented tires
-The tire actually squeezes into the pavement some, creating a mechanical connection and requiring the tire to deform before it will slide
-The tire itself is flexing in many directions while this is going on.
These, especially the second one, describes some of tire behavior, especially the way that tires actually generate maximum grip when they are sliding a little bit.
And why more rubber generates more grip.

For practical purposes, a 'system mu' can be created, which as NBruno explained will actually be a two-dimensional value, and then with the system mu things can, as Dusty Duster said, be much more easily modeled with the linear equation.

I wouldn't say either NBruno or Dusty Duster are wrong; they're both right in their own way. Regardless, tires are really complicated.
Wednesday, July 20, 2011 3:58 AM
If two tires are identical in every way except for the tire width, wouldn't you simply be modifying the shape and size of the friction circle? Every piece of tread that is contained in the contact patch has a very small part of the overall normal force pressing down on it and therefore has a given frictional force. Making the tire wider gives you more points of cotnact. Mu hasn't changed because the tire is the same, and the normal is the same (ignoring the fact that the wider tire IS a bit heavier). But because there are more points of contact, the tire has more overall grip. The maximum frictional force of the infintessimal parts of the tire has not changed, but because there are more points the grip of the tire overall HAS increased.

@uberthin-How a tire lets go and gives feedback is dependent on a lot of things, including sidewall stiffness, tire construction, material properties, etc. I don't know exactly what contributes the most, but I'd say tire construction and sidewall stiffness. Mike can better explain why drifters choose tires. As for not popping the bead, the bead is a steel ring and as an ex-tire changer they are very stiff. A sliding tire does not really shock the bead and side as much as you would expect. When a car crashes, that's when you usually see the beads pop. The shock on the tire is enough to blow the bead. As for wear, by the time you have worn off the sipes or small small grooves in a tire, you should be replacing them. The rubber underneath is harder and heat cycled and will provide less grip than it was new (this is why old tires lose grip despite having more tread). As for the belts, it depends. If the belts are still laminated to the tire carcass, then you can drive hom (just watch the potholes). If the belts are starting to separate from the rest of the tire you should put on the spare. A delaminating tire can be extremely dangerous. A blown tire with no tread is also incredibly difficult to replace and tire shops will charge you more to remove a shredded tire. I've had to do these before it really sucks.
Wednesday, July 20, 2011 2:59 PM
Very informative!
I find myself rereading the article over and over.
Thursday, July 21, 2011 1:09 AM
Doesn't the coefficient of friction decrease with load? I always thought that was the justification for bigger tires.
Thursday, July 21, 2011 2:57 AM
The conversation you guys are having reminds me of a couple posts I made about friction between two materials. They were posts mainly on clutches, but the same applies for tires and I even get into tires a good bit toward the end.

Physics 101: The Normal Force and Physics 101: Friction Basics

Physics 501: Advanced Friction

Physics 701: Friction Between Non-solid Surfaces

bigBcraig actually hit on the basics more or less 4 posts up.
Thursday, July 21, 2011 3:25 AM
@Daewoo of Death- Yes, since frictional force is equal to load. Normal force doesn't change, so mu does change. It is generally linear until the max static mu, then it drops and becomes constant under kinetic (dynamic) friction.
Dusty Duster
Dusty Dusterlink
Thursday, July 21, 2011 6:17 AM
Beaters is right. Friction is not a linear (or even continuous) function. Portions of friction's effect on a system can be modeled linearly, which is what I pointed out in the article.

The coefficient of friction is a material property that when used in context of a system (such as I was using it in the article) becomes a system property.
Friday, July 22, 2011 11:58 PM
Another question I thought of. If coefficient of friction is always higher in static than dynamic situations, why do drag racers shoot for 18% slip?

Saturday, July 23, 2011 4:07 AM
As one of my prior posts, has to do that tires operate on much more than traditional friction alone. Tires (particularly soft racing rubber) have some adhesive properties; and deforms a bit 'into' the road, forming a mechanical connection on which to transfer force. Think of trying to slide your hands against eathother, and then trying again with one of your hands' fingertips curled over the top of the other hand. The tire makes thousands of little finger-holds on the pavement, unless its slipping too quickly to deform and 'catch' some.

These relationships vary by tire, and end up describing how some tires transition smoothly between grip and slip, versus how some 'let go' much more aggressively.

And I really don't understand all of the forces at work or all of the science behind the reaction. But that's my practical / simplified understanding.
Saturday, July 23, 2011 4:12 AM
Actually, read BenFanner's links a couple posts up. Having just opened them, they're fantastic and describe a pretty good amount of what I could not articulate.

It doesn't really go into slip much but might still help you imagine what i was saying.
Dusty Duster
Dusty Dusterlink
Monday, July 25, 2011 12:43 AM
Watch an extreme slow-motion video of drag slicks deforming during launch. You'll see what Craig is talking about.
Wednesday, July 27, 2011 2:46 PM
I don't mean to be a dick but - you can't go outside the friction/traction circle. Sliding or doing burnouts just means you've fallen off the outer edge and come back closer to the center of the circle.

If sliding meant you were outside the circle it would be faster!

Dusty Duster
Dusty Dusterlink
Saturday, August 06, 2011 3:00 PM
No offense, but what you posted makes absolutely zero sense. How could you "fall off the edge and come back closer to the center"? You can't. If you're sliding, you are operating under dynamic friction. (The traction circle is a tool for visualizing the limits of a tire's static friction.)

And how would being outside the circle make you faster? Again, that is completely nonsensical.
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