everyday life - Does the pressure inside a tire equal to its average ground pressure?

On one hand, I think they should be equal since the external force and internal force are equal in equilibrium. On the other hand, I don't see anything related between them, the inside pressure is hold by rubber strength, while ground pressure is equal to gravity, e.g a lightweight steel wheel can hold very high internal pressure but with low ground pressure

I have no idea, does the pressure inside the tire equal to ground pressure? Please explain it in detail

Answer

No, the pressure inside the tyre is slightly less than the pressure at the tyre/ground interface.

The pressure everywhere inside the tyre is the same - let's calls this $P_i$. If the area of the contact patch is $A$ then the air inside the tyre exerts a force on the ground of $F_i = P_iA$.

But the tyre itself has some elasticity. If you've ever handled a tyre that is off the wheel you'll know that it can support a considerable load even when uninflated (though obviously far less than the weight of a car). So the weight of the car deforms the tyre and this deformation of the tyre also creates an elastic force in a Hooke's law sort of way. Let's call this force $F_e$. Then the total force on the ground is:

$$ F_g = F_e + P_iA $$

and the pressure on the ground is:

$$ P_g = \frac{F_g}{A} = \frac{F_e}{A} + P_i $$

So the pressure at the tyre/ground contact is greater than the tyre pressure by $F_e/A$.

I think it would be very hard to predict the elastic force caused by the tyre deformation from first principles. I suspect the only way to get an idea of what $F_e$ is would be to measure it.