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The suggestion is to use F=PA to measure the car weight, where P is the tire pressure, A is the area the tires in contact with the ground, and F is the unknown: the weight of the car (measured in terms of gravitational force).

I don't think this works. To see why, suppose we make the tires out of a very stiff material. We control the pressure P, but changing the pressure will not change the surface area A. Therefore, by changing P we can set F to whatever we want, which shows that we are not actually measuring the weight of the car. The basic issue here is that the air pressure is not the only thing that is supporting the car.

I don't know how important the stiffness effect is for real tires, but I suspect they are sufficiently stiff that it matters a lot.

I think he nixes your case at the start, when he goes through the sanity check thinking about the flat tire. Also, I think your rigid body case use the walls of the tires to apply force to the care, not the force from the pressure to keep the car static, which is why it fails.

I agree that higher tire pressure results in smaller surface area, but it's not clear to me that the tire itself does not support the car, skewing the result. So I'm not convinced this sanity check is sufficient. For example, as another commenter mentioned, run-flat tires can support the car on stiffness alone.

I agree, the sanity check is not sufficient. It confirms the concept that as pressure decreases, area increases, but is not sufficient to confirm a linear relationship. In the limit, the area clearly does not become infinite when pressure drops to 0.

For the case you suggested above, this is essentially how run-flat tires work. Of course, the sidewall of the tire isn't as stiff as the support ring, but they do provide some support.

He mentions the flat tire, but he ignores the fact the pressure of a flat tire is 0, leading his measuring method concludes that the weight of the car = F = PA = 0A = 0. His measuring method flunks his sanity check, but he never notices.

Let P_m be the pressure recommended by the manufacturer. A better sanity test would be to fill the tires to .75P_m, then to 1.5P_m, and see if the area in contact with the ground has shrunk in half.

With a completely flat tire, the rubber sandwiched under the rim will transfer weight directly from the rim to the floor, so the pressure equation won't apply.

> I don't know how important the stiffness effect is for real tires, but I suspect they are sufficiently stiff that it matters a lot.

It's odd, because as I was reading your comment, I was thinking the exact opposite. I am considering the force it takes to squish a flat tire. A person can squish a (regular car's) flat tire with his/her hands.

My gut-check tells me that the stiffness of each tire can lift less than 10kg/20lbs... multiplied by 4, that still is not a huge contributor to the overall weight.

It’s certainly possible my intuition is wrong. Run-flat tires can support the whole car, but it is possible this support only kicks in at very low pressure.

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