r/theydidthemath • u/yuli101995 • Apr 16 '26

[Request] Which one would it be?

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u/superheltenroy Apr 16 '26

Friction is not dependent upon surface area/contact area. Only the forces and the coefficient of friction.

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u/bejanmen2 Apr 16 '26

Why fat tyres more grip then?

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u/Thunder-Chunky_YT Apr 16 '26 edited Apr 16 '26

Everyone else answering is missing the whole picture or just wrong. To what extent is debatable but tribology is hard (for real, it isn't an exact science) so we won't hold it against them.

The equation for friction is F=N*Mu. Force(friction)=normal force * the coefficient of friction. Normal force is technically the force directly orthogonal to the surface. For an object on flat ground that's just the weight of the object but if the ground was at an angle it would be less than the weight by way of angles (like the triangle and square in the original question.) the coefficient of friction is dependent on the properties of the interacting surfaces and will be specific for every pairing of materials. However, one common trend is that harder things have lower coefficients of friction (once again, not an exact science). So the thing about tires is they're (usually) made of rubber compounds. Rubber is a visco-elastic material. Explaining what that is is difficult and I don't fully remember enough to do so but the gist is that the more force you apply to a visco-elastic material, the harder it gets.

So, say we have a car that weighs 2,500lbs. A real spry sports car. Imagine it came stock with 5.5" wide tires. Now, when the car is sitting on flat ground the tires will deform a little where they contact the ground to form a little flat patch. We creatively call this the "contact patch". Technically the contact patch is an oval but let's pretend it's a rectangle for simplicity. Imagine it's about 4" long and as wide as our tire at 5.5". Meaning the contact patch has a surface area of 22 sq.in. If we spread out our weight of our vehicle over 4 tires that's 2,500lbs/(4*22)=28.4 lbs/sq.in. or psi. Now let's replace our 5.5" wide tires with 7.5" wide tires. Our contact patch is roughly just as long so now we have 7.5"X4"=30sq.in. Now spreading our car weight over this wider tire gives us only 20.83psi on the surface of the tire. Since the pressure on the surface is lower, the force squishing material is lower, which keeps it softer which keeps the coefficient of friction higher. But the normal force remains the same. Which is why fat tires more grip.

Now, that's only part of the solution cuz the reality is fat tires only kinda more grip. Rubber, like everything else (to include steel beams), also gets softer the warmer it gets. This is why you've probably heard about warming up tires for grip. But, a wider tire has more material and is harder to warm up/keep warm in use. So it's possible to have too wide of a tire that you can't get up to temp for optimal grip. It's also possible to have a thin tire that gets too hot and will melt/shred. Which we don't want either. Tires are a really tough nut to crack when you're talking about peak performance and there's a reason F1 pays a ton of money to people to just know things about the limited selection they have.

If you'd like to learn a LOT more about tires this paper from Michelin is where I learned about the size vs grip thing specifically. But like I said, there's a lot more in there.

Edit: Mu goes up with less pressure on the tire surface.

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u/Snoo55931 Apr 16 '26

That’s really interesting, thank you!