Theoretically, the tyre size does not change grip as Amontons 2nd law states that friction force remains the same. The tyre size is really about matching width to the amount of energy being transferred to the ground, i.e. narrower tyres will run hotter.
Before I get shot down in flames, there are many other factors but the principle that a wider tyre will provide more grip is not necessarily the case unless you have the power to keep them warm.
I would say that the author of that comment is both right and wrong. The reasons why is far from obvious. I'm not an expert in any way but I do enjoy reading up on subjects that interest me. Race car rubber is one of them! But please take it for what it is.
Contact patch
Contrary to common belief the contact patch is not bigger with wider tyres, with the same internal pressure. The contact patch is calculated with area=load/pressure. With wider tyres the contact patch is obviously wider than with a narrow tire, but the area is the same.
Amontons 2nd law is tempting to use here, but rubber's friction is not that simple. Rubber generates friction in three different ways: adhesion, deformation, and wear. The generated friction force is not linear and very complicated.
Slip angle
Slip angle is what generates grip, or to be more precise - lateral force. When a race car is cornering, the slip angle is the difference in what direction the tyres are pointing and the direction the car is heading. A race car generates maximum lateral force around 7-11 degrees of slip.
The term "slip angle" is a bit missleading, as with small slip angles there is no slip in the contact patch. In fact, it is the elastic nature of rubber that does the work here.
Lateral deformation in the contact patch
This is where the magic begins. The lateral force is generated by the tyres resistance to deflection. The deflection is not the same along the contact patch, but is built up gradually, non-linear.
So what is your point??
That wider tires do provide higher levels of lateral grip, because the wider contact patch leaves more room for the tyre to resist deflection. And resistance for deflection = force.
And heat?
More grip = more energy = heat. Too much of it means overheating, to little means cold tires. Wider tyres get warmer (not cooler) than narrow tires, because they generate more lateral force! They also cool faster than narrow tyres, because they have a larger surface area. And that is what makes it problematic.
Conclusion
Wider tyres = more grip in the corners. If you don't utilize the higher level of grip, they'll cool too much on the straights and they'll be outside of optimal temperature range.
Source and recommended reading:
The racing & high-performance tire - Paul Haney
When I wrote this post I sent an email to Paul to confirm a few thoughts. He wrote back to me within an hour - respect!
Wow! That a pretty cool response to a 5 minute post on PH. I'm really not a tyre expert, just really relating what I've learnt over the years.
ReplyDeleteMy response would be that you need to qualify you argument 'That wider tires do provide higher levels of lateral grip, because the wider contact patch leaves more room for the tyre to resist deflection' with 'for any given slip angle'
(For simplicity lets also assume the same arguments apply to slip rates resulting from acceleration and braking.)
Now if this is true then the narrower tyre requires a greater slip angle (slip rate) to match the same force as the wider tyre. So, the greater flexing and smaller mass of the narrower tyre will heat it up more readily than a larger tyre for a given force. Of course the narrower tyre will exceed the optimum angle (or slip rate) before the wider one. That's when you need to go for wider tyres. My point was that, for a 140 BHP Caterham, a narrower tyre may work better as the main reason for a wider tyre is to allow a margin for higher traction forces of the higher BHP cars (circle of grip etc.),rather than the cornering forces.
There's also the higher un-spung weight and higher rolling resistance to consider.
An interesting subject!
Cheers,
David
Thank you for your comment!
ReplyDeleteNot sure I understand you correctly, but an increased slip angle does not mean higher lateral force on a narrow tyre. When the optimum slip angle/rate is achieved the generated force will decline if the slip is increased.
A bit beside the point but when I wrote that post I learned something new - a tyre's surface temperature is very short lived and very little of it transfers into the tyre's inside, because of the very high insulation properties of rubber and the effective cooling from the wind.
That means that excessive sliding and weaving doesn't make much good for heating up the tyres. The best way would be braking and accelerating as that makes the side walls flex which is much more effective.
So your conclusion is right, a light car can't keep the heat up in wide tyres. And as you write, un-sprung weight and rolling resistance is also to consider.
What puzzles me, is that if my conclusions are right, wider tyres would _decrease_ the longitudinal forces, and could be _less_ suitable for high hp cars! That is very counter-intuitive. On the other hand they have more engine power to heat the tyres up on the straights, and top-fuel dragsters do have very narrow tyres.
Great to have someone to interested in thechnical detail to chat to :).
ReplyDeleteThinking this through further it can be simplified to the following points: The energy used to heat the tyres can only come from one source - the kinetic energy in the system i.e. from what engine has put in.
Lower powered cars put less energy in and therefore using a narrower rear tyre can be beneficial to maintaining tyre temperature (potential grip) and obtaining a reasonable slip angle from the available power (balance of the car).
Quote: [Not sure I understand you correctly, but an increased slip angle does not mean higher lateral force on a narrow tyre. When the optimum slip angle/rate is achieved the generated force will decline if the slip is increased.]
What I was trying to suggest was that it is harder to achieve optimum slip angle on a wider tyre because they are harder to keep warm. Running a narrower makes it easier to achieve the designed loads and temperature and therefore giving the optimum slip angle and grip – which potentially could be more than a wider cold tyre.
As an aside, your analysis above does not state what happens when the slip angle is exceeded and the tyre starts to slide. In this case the grip levels are similar for all widths. What is important is that tyre temperature is allowed to reach optimum so that maximum slip angle can be obtained which will generate the maximum force before grip breaks down.
Quote [What puzzles me, is that if my conclusions are right, wider tyres would _decrease_ the longitudinal forces, and could be _less_ suitable for high hp cars! That is very counter-intuitive. On the other hand they have more engine power to heat the tyres up on the straights, and top-fuel dragsters do have very narrow tyres]
ReplyDeleteYou are right: Caterham can produce around 1.3G lateral but only about 1.1 longitudinal. That doesn’t matter too much as the most powerful cars can only accelerate at about 0.5g and under braking there is a massive weight transfer which compensates
I wrote another question to Paul Haney regarding longitudinal grip.
ReplyDelete------
"Braking and acceleration increase with CP area and tread grip. Managing load transfer is the key. I'm not sure the tread width matters except when camber gain removes load from the inside of the CP. That gets worse with wider tread. As I said, tire choices are seldom rational."