Think about the front tires on a drag race car, they are very thin just like bicycle tires specifically to reduce rolling resistance. The reason cars need wide drive tires is because the extreme amount of power needs traction however just like a wide tire robs speed on a bicycle it robs speed in a car, the difference is the car has to have them for traction and the bicycle doesn’t. TLDR the cars engine makes waaaay more power than a human and cars are waaay faster so it needs bigger drive tires
The fastest motorbikes actually has very thick tires.
The fastest drag race cars have thick rear tires to have as much traction as possible while accelerating.
F1 race cars have thick tires all around for maximum traction on cornering.
The fastest bicycle (powered by pedals) benefit from a thinner profile as it would have less drag. A bicycle (with its rider) is much lighter and doesn’t travel at speeds where its inertia would overcome its grip on corners. The torque from pedaling isn’t enough to overcome the traction either.
In a hypothetical world where all wheels have maximum grip/traction, they would be better to be as thin as its load-bearing capacity can take to have the least amount of drag as possible.
Technically, for both cars and bicycles the fastest have thin tyres. The reason being thin tyres have less rolling friction, and this higher speeds can be achieved.
Take a look at the wheels of the world record beating cars like Thrust SSC or Bloodhound. They are very thin like a bicycle.
The fast cars you are thinking of are fast production cars, racing cars etc. These cars are not only built for top speed, but good acceleration. This requires a large contact area between the tyre and the road, as others have mentioned, to stop the tyre slipping under acceleration.
Top fuel dragsters produce about 100000x more power than a human. The challenge is how to lay that much power down without skidding. Hence the big tires. They also have no gearbox; they rely on tire deformation to generate traction and change the final drive ratio as the car accelerate. That eats up some power, but they have power to spare.
Because humans are so wimpy, bikes need skinny tires to cut wind and rolling resistance. You see the odd fat-bike, and the fat wheels help with flotation, but that’s about it.
Bicycles are limited to the power of the rider, so to make them faster you reduce resistance by using narrower, high pressure tyres and making it more aerodynamic.
Fast cars have plenty of power, and are limited in how fast they can (safely) drive by how much grip they have – put 1000hp in a car on tiny tyres and it can drive fast, but will wheelspin when accelerating and skid when braking or cornering. Fat tyres give more contact area with the ground which improves grip.
The tire choice depends on what you want to do with it. If you have low acceleration and don’t take many corners (and are able to lean into corners) you don’t need very wide tires, so you go for the lightest.
If all you do is accelerate, brake, turn into a corner, accelerate again, take a high speed corner etc you want all the grip you can get so you go for wide tires.
This is combined in drag racing, the rear wheels are the ones that transfer the power of the engine to the road surface and ‘push’ you off. The front wheels are not used for acceleration ~~and braking~~ so they are very thin.
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