Tyres - Why is wide good?
Discussion
Sorry if this is off-topic, but I reckoned there must be clever people, and people who know about tyres, on this forum....
The boredom of unemployment got me doing an OU applied maths course. When I got to the unit on friction I got massively confused:
Frictional resistance is Coef-of-friction x pressure x contact area.
The area and the area part of pressure cancel, giving:
Friction is Coef-of-friction x force.
Note that the contact area makes no difference to the frictional resistance!
Now the bit that confuses me, is that this means that I might as well buy 145 tyres when I replace my 255's, because they're cheaper. (Though I don't think you get N rated 145's).
Can anyone explain why wide tyres work?
Simon
The boredom of unemployment got me doing an OU applied maths course. When I got to the unit on friction I got massively confused:
Frictional resistance is Coef-of-friction x pressure x contact area.
The area and the area part of pressure cancel, giving:
Friction is Coef-of-friction x force.
Note that the contact area makes no difference to the frictional resistance!
Now the bit that confuses me, is that this means that I might as well buy 145 tyres when I replace my 255's, because they're cheaper. (Though I don't think you get N rated 145's).
Can anyone explain why wide tyres work?
Simon
The trouble is, the frictional resistance for something with (now this next bit might be relevant) a constant coef of friction (mu) is independant of the contact patch.
with a bit of general approximation, an example for the outside loaded rear tyre on my 996 on hard cornering might be:
Contact patch on the rear wheel is about 100mm front-back x 255 wide x (say) 75% non grooved = about 20,000mm^2.
downwards force on that tyre is whatever it is, but let's say 40/60 fr/rr weight dist, and say 70/30 loaded/non-loaded dist, giving for kerb weight of about 1400Kg, a downward force on the tyre of about 5,000N.
That gives a contact patch pressure of about 0.25 N/mm^2
To work out a rough mu, and to keep the sums simple, pretend the cornering peaks at 1.0 lateral g, and that (to be consistent with the assumed weight dist) this tyre is doing 40% of the work of keeping the car from sliding.
The lateral force on this tyre is then 1 x 1,400 x 9.81 x 0.4 = about 5,500 KN.
This gives a mu close enough to 1 to pretend it is 1 for this discussion.
So, in this case, with 255 tyres, the max frictional resistance to opose lateral force on this wheel is:
mu x pressure x area
= 1 x 0.25 x 20,000
= 5000KN
Now, pretend the same car has 145 section tyres:
contact patch on the rear wheel is about 100mm front-back (for consistency) x 145 wide x (for consistency) 75% non grooved = about 10,875 mm^2.
Pressure = 0.46 N/mm^2
and so, in this case, with 145 tyres, the frictional resistance to opose lateral force on this wheel is:
mu x pressure x area
= 1 x 0.46 x 10,875
= 5000KN
So the maths says narrow tyres are as good as wide ones.
It all might be something to do with rubber having a higher mu at lower contact pressure - but I'd love to hear from someone who really can explain this...
In the meantime - next time I get pulled over for wild sliding I am going to claim mathematical research.
simon.
with a bit of general approximation, an example for the outside loaded rear tyre on my 996 on hard cornering might be:
Contact patch on the rear wheel is about 100mm front-back x 255 wide x (say) 75% non grooved = about 20,000mm^2.
downwards force on that tyre is whatever it is, but let's say 40/60 fr/rr weight dist, and say 70/30 loaded/non-loaded dist, giving for kerb weight of about 1400Kg, a downward force on the tyre of about 5,000N.
That gives a contact patch pressure of about 0.25 N/mm^2
To work out a rough mu, and to keep the sums simple, pretend the cornering peaks at 1.0 lateral g, and that (to be consistent with the assumed weight dist) this tyre is doing 40% of the work of keeping the car from sliding.
The lateral force on this tyre is then 1 x 1,400 x 9.81 x 0.4 = about 5,500 KN.
This gives a mu close enough to 1 to pretend it is 1 for this discussion.
So, in this case, with 255 tyres, the max frictional resistance to opose lateral force on this wheel is:
mu x pressure x area
= 1 x 0.25 x 20,000
= 5000KN
Now, pretend the same car has 145 section tyres:
contact patch on the rear wheel is about 100mm front-back (for consistency) x 145 wide x (for consistency) 75% non grooved = about 10,875 mm^2.
Pressure = 0.46 N/mm^2
and so, in this case, with 145 tyres, the frictional resistance to opose lateral force on this wheel is:
mu x pressure x area
= 1 x 0.46 x 10,875
= 5000KN
So the maths says narrow tyres are as good as wide ones.
It all might be something to do with rubber having a higher mu at lower contact pressure - but I'd love to hear from someone who really can explain this...
In the meantime - next time I get pulled over for wild sliding I am going to claim mathematical research.
simon.
with reference to the comment from James:
the bit about 1 g was just to come up with some sort value for mu, which I assumed would be constant for rubber of a certain compound.
I can almost go along with your argument that wider tyres allow softer compound, and it is the softer compound that provides a highe mu, and more grip, but I am a bit doubtful that the same brand and designation tyre has a range of compounds for different widths.
Still confused. Think I'll 'ask goodwin'.
simon
the bit about 1 g was just to come up with some sort value for mu, which I assumed would be constant for rubber of a certain compound.
I can almost go along with your argument that wider tyres allow softer compound, and it is the softer compound that provides a highe mu, and more grip, but I am a bit doubtful that the same brand and designation tyre has a range of compounds for different widths.
Still confused. Think I'll 'ask goodwin'.
simon
911newbie said:
In fact friction isn;t quite as simple as student text books make it out to be.
A little surfing found plenty to support this.
Found a very interesting and math rich set of articles at www.pelicanparts.com/techarticles/physics_racing/
part 22 has loads of equations for slip angle, which probably explain everything, but it will take me a while to understand it.
Interestingly - this article is hosted by Pelican Parts - seemingly a Porsche part outfit.
The Toyo link was interesting, but whilst stated that larger contact patch = more grip, didn't go anywhere to explain it.
Did find ads for a book:
THE RACING & HIGH-PERFORMANCE TIRE
Using the Tires to Tune for Grip and Balance
by Paul Haney
Chapter 6, Tire Behavior, explains how a tire produces lateral force and turns a car. An interview with Jim Hall tells the story of tire development leading to wider treads. Learn the real reason why wide tires produce more grip.
Myth 1: The classic equation for friction is Cf = Ff/Fvert. Contact area doesn't matter. Wrong!
The truth is rubber generates friction force in at least three ways, the major components of friction being adhesion, momentary molecular bonding, and deformation, mechanical keying.
Will buy this, read and try and understand.
Now I'm worried that other things aren't as simple as student text books say.
In fact, the Earth is tetrahedral, but the jump from the flat earth model was too much, and it was much easier to pretend it's round.
simon
Having read and, I believe, understood Paul Haney’s excellent book I now feel up to commenting on the excellent post from greenv8s.
The big mistake I had been making was to assume that there was some truth in that oft quoted motoring journalists line about ‘more rubber on the road’ when talking about cars with wide tyres.
Contact patch area is a function of vertical load on the wheel and the tyre internal pressure – the tyre deforms to achieve this area (pressure x area = force). The tyre construction is such that the tread width is essentially fixed, so the deformation manifests itself as lengthening or shortening the contact patch length.
Thought that greenv8s explanation of slip angle and effect of contact patch length was great. The book helped take me through this a bit more slowly.
After understanding this, my next question was why doesn’t increasing pressure in the tyre further improve grip, since more pressure = less contact patch area = shorter contact patch = better grip?
The answer is to do with the fact that more rubber on the road does help grip – this is due to the hysteresis properties of rubber. As rubber expands to fill a depression in the road (or a gap between aspersions), it takes some (small) time to do so. When a tyre is sliding (and due to the slip angle, the rear most portion of the contact patch slides at even low cornering forces), this means that the upward rise of the depression to which the tyre is moving has more rubber acting on it that does the upwards rise on the other side. This allows a pressure differential in the lateral plane, providing frictional resistance over and above that offered by simple friction. (Pictures would help here).
Now, as the tyre vertical load increases, the rubber is forced more fully, and more quickly into the depressions, overcoming the hysteresis and reacting on both sides of the upward rise from the depression more evenly – giving less pressure differential and less grip.
Hence, low tyre pressure is better for grip from deformation and hysteresis.
Tuning the pressure is about balancing the contact patch length (which is better as pressure goes up), and the contact patch pressure (which is better as tyre pressure goes down). Of course – high pressure gives harsh ride, and low pressure increases tyre deflection, which increases heat (promoting wear and potentially catastrophic failure), reduces responsiveness, and is less fuel efficient (like I care?), and these factors are also considered when optimising tyre pressure. In fact, track work with road tyres creates so much heat that the tyres become severely damaged (as I know from SCCA autotesting with Hertz rentals in the US, sorry Hertz). Even though the optimum grip is achieved at low pressures (because the hysteresis element is significant), use of road tyres on the track is better at highish pressures (40PSI+), for this reason. In fact, the best way to increase grip (without going into suspension or aerodynamic changes) is to widen the tyre – this gives a shorter contact patch for the same inflation pressure.
The hysteresis effect also explains why slicks work – saying that the contact patch area is a function of the tyre pressure is true for the tread carcass area on the inside of the tyre. The tread carcass is stiff enough to mean that grooves in the tread create increased contact pressure at the rubber to road interface, reducing hysteresis effect and reducing grip.
This has been a fantastically interesting diversion from doing any maths for a couple of weeks, and now I’m getting a bit behind, but I feel that it was worth it to understand one of the great mysteries of (my) life.
I did ‘ask Goodwin’ before the post from greenv8s, and it will be very interesting to see if he comes up with the same answer – since to do so would be to admit that every time motoring journo’s come out with that ‘more rubber on the road..’ line, they are demonstrating complete ignorance of their subject
Regarding the last post from ChrisW – the OD of the tyre isn’t really significant in determining contact patch length, the construction of the tyre means the tread width is pretty much fixed, and the tread carcass deflects to give whatever area is required to support the vertical load.
Shame this, as I’d love to convince myself my 17”s had more ultimate grip than 18”s.
Simon
The big mistake I had been making was to assume that there was some truth in that oft quoted motoring journalists line about ‘more rubber on the road’ when talking about cars with wide tyres.
Contact patch area is a function of vertical load on the wheel and the tyre internal pressure – the tyre deforms to achieve this area (pressure x area = force). The tyre construction is such that the tread width is essentially fixed, so the deformation manifests itself as lengthening or shortening the contact patch length.
Thought that greenv8s explanation of slip angle and effect of contact patch length was great. The book helped take me through this a bit more slowly.
After understanding this, my next question was why doesn’t increasing pressure in the tyre further improve grip, since more pressure = less contact patch area = shorter contact patch = better grip?
The answer is to do with the fact that more rubber on the road does help grip – this is due to the hysteresis properties of rubber. As rubber expands to fill a depression in the road (or a gap between aspersions), it takes some (small) time to do so. When a tyre is sliding (and due to the slip angle, the rear most portion of the contact patch slides at even low cornering forces), this means that the upward rise of the depression to which the tyre is moving has more rubber acting on it that does the upwards rise on the other side. This allows a pressure differential in the lateral plane, providing frictional resistance over and above that offered by simple friction. (Pictures would help here).
Now, as the tyre vertical load increases, the rubber is forced more fully, and more quickly into the depressions, overcoming the hysteresis and reacting on both sides of the upward rise from the depression more evenly – giving less pressure differential and less grip.
Hence, low tyre pressure is better for grip from deformation and hysteresis.
Tuning the pressure is about balancing the contact patch length (which is better as pressure goes up), and the contact patch pressure (which is better as tyre pressure goes down). Of course – high pressure gives harsh ride, and low pressure increases tyre deflection, which increases heat (promoting wear and potentially catastrophic failure), reduces responsiveness, and is less fuel efficient (like I care?), and these factors are also considered when optimising tyre pressure. In fact, track work with road tyres creates so much heat that the tyres become severely damaged (as I know from SCCA autotesting with Hertz rentals in the US, sorry Hertz). Even though the optimum grip is achieved at low pressures (because the hysteresis element is significant), use of road tyres on the track is better at highish pressures (40PSI+), for this reason. In fact, the best way to increase grip (without going into suspension or aerodynamic changes) is to widen the tyre – this gives a shorter contact patch for the same inflation pressure.
The hysteresis effect also explains why slicks work – saying that the contact patch area is a function of the tyre pressure is true for the tread carcass area on the inside of the tyre. The tread carcass is stiff enough to mean that grooves in the tread create increased contact pressure at the rubber to road interface, reducing hysteresis effect and reducing grip.
This has been a fantastically interesting diversion from doing any maths for a couple of weeks, and now I’m getting a bit behind, but I feel that it was worth it to understand one of the great mysteries of (my) life.
I did ‘ask Goodwin’ before the post from greenv8s, and it will be very interesting to see if he comes up with the same answer – since to do so would be to admit that every time motoring journo’s come out with that ‘more rubber on the road..’ line, they are demonstrating complete ignorance of their subject
Regarding the last post from ChrisW – the OD of the tyre isn’t really significant in determining contact patch length, the construction of the tyre means the tread width is pretty much fixed, and the tread carcass deflects to give whatever area is required to support the vertical load.
Shame this, as I’d love to convince myself my 17”s had more ultimate grip than 18”s.
Simon
Gassing Station | Porsche General | Top of Page | What's New | My Stuff