So no, deflated spherical wheels is not a good idea :/
From that fact, you are saying that "obviously" the deformation of a cylinder (with some diameter/width ratio) filled with gaz at a certain pressure against a flat surface will lead to a higher surface than a sphere with the same pressure?
It's not obvious at all. Give me math+physics proof or GTFO.
A perfect cylinder has a line of contact with the road: the width of the wheel. A perfect sphere has a point of contact.
Obviously you wouldn't see perfect eithers when talking about real-world tire implementations, but the perfect examples here are indicative of cylinders having more surface area with higher air pressure, whereas higher air pressure is the preferred state due to wheel wear and tear and handling issues that occur at low pressures.
Not to mention cylindrical wheels inherently resist lateral motion, have lower unsprung weights/volumes, and don't have the unnecessary engineering struggles of turning a spherical object into a pneumatic device.
I'm all for trying new things and testing wacky designs, but lots of people have looked at spherical wheels over the past few decades (Goodyear's implementation is a personal favorite[1]) and concluded they're pretty much just good looking, rather than an improvement in engineering over current wheels.
Given how good they look though, I'd love for someone to find a way to make them actually work.
And both have an area of zero. And the area is what matters here.
> but the perfect examples here are indicative of cylinders having more surface area with higher air pressure
This is not true. It's physically impossible. (What you have done is the geometrical equivalent of dividing by zero to prove 1 = 2.)
Weight of car / Contact patch / number of wheels = PSI + strength of sidewall.
And the pressure on the ground must exactly equal the pressure in the tire adjusted for the size of the area of ground contact.
Do you see how for any given PSI (including the strength of the sidewall) the contact patch is an exact figure? The forces must all be equal, it's a basic law of physics.
There are certainly engineering issues, I'm not arguing about that. But the size of contact patch is not one of them. Put the same PSI in a cylindrical or spherical tire (neglecting the PSI contribution of the rubber) and the contact patch will have an identical size.
Typically wheels are made of metal wires and are stiff - so they don't like large contact areas because it means lots of flex. But it doesn't have to be that way. You can make a material that doesn't care about flex - if would be harder to make obviously, but it's not an impossible obstacle.
Instead of wasting our time with ridiculous demands maybe just GTFOutside and look at some real tires.
Weight of car / Contact patch / number of wheels = PSI + strength of sidewall.
PSI literally means: Pounds per square inch. Pounds of car per square inch of contact patch.
> a spherical tire will have to deform more than an equivalent cylindrical tire
This is true.
> With current materials this means you'll have to run it at a lower inflation pressure
This is not true. Yes, the strength of the rubber plays a part (adding to the effective PSI), but not a large effect unless you are almost flat.
If you keep the PSI at normal levels the contact patch will be exactly the same size as it is now, and the tire will deform on the bottom. So just design it to be extra flexible.