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The hinged tire

Bend tires and save milage with them
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Low rolling friction requires small contact patches among other things. High braking efficiency requires large contact patches. This is a way we can get more of each when needed.

This tire would have a kind of hinge built into the tire, a very stiff bit of rubber. Under normal weight for the car it would not flex. But a braking car puts far more weight on the front wheels. Under this condition the hinge, which would go all the way around the tire in the middle, would be forced to stretch. The tire would expand horizontally. Thereby the contact patch would be significantly expanded but only on the front wheels during braking. So the wheels with the most opportunity for grip would have more grip right when it's needed but otherwise rolling friction would not be increased.

Voice, Nov 17 2020

Centrifugal-center Tire
[xaviergisz, Nov 17 2020]

Airless tyre https://www.google....Aw&biw=1280&bih=672
Stretching widthways seems to be strongly fought against. [wjt, Nov 21 2020]

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       sp tyre
xenzag, Nov 17 2020
  

       Perhaps we could work it the other way. With some added mass in the middle of the tread, "centrifugal force" could more severely render the tire contact patch smaller by stretching out the diameter of the center beads. Then as the car slowed down for a curve or somesuch, the rolling diameter of the tire could shrink down again to allow more contact area.
RayfordSteele, Nov 17 2020
  

       Wait a minute, I thought this was strictly a forum for unhinged ideas.
AusCan531, Nov 18 2020
  

       It's possible (but expensive and heavy) to have a self inflating tire system. What if such a system overinflates the tires when it senses good conditions (normal highway travel). It could be equipped with a large valve to quickly reduce the tire pressure in the event of maneuvering or braking that would benefit from softer tires. Maybe the increased fuel efficiency could pay back the cost of the system. I would worry about such a system malfunctioning and would also worry about handling while the air is being let out, but I think the normally recommended tire pressure is a compromise considering handling, tire wear, and tire heating, so reducing the pressure below what is currently considered normal during emergency braking may actually increase safety as well.
scad mientist, Nov 18 2020
  

       Since a softer tyre has higher rolling resistance, you could (almost) not need brakes at all; just gradually (faster or slower, depending on need) reduce the tyre pressure and let the rolling resistance be the brake. Obviously it would need a tyre designed to handle it (maybe foam-filled or partially "air-less", but with an airtight outer layer?).
neutrinos_shadow, Nov 18 2020
  

       Might be an idea for those complete airless tyres, which rely on material flex and has spaces for hinging and extra material placement. It's seems a couple of orders higher in force vectoring calculations, though.
wjt, Nov 21 2020
  
      
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