how does using smaller tyres on a car improve it’s range/fuel efficiency?

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From my theoretical understanding shouldn’t larger tyres give you more range? My reasoning being that larger tyres = more distance travelled in a single rotation.

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Larger tires travel more distance over a single rotation but they require more force to turn. In a perfect world with no friction it equals out. Larger tires also have more rotational inertia so you need to put more energy into them to start them spinning and to slow down and are physically larger which increases air resistance

Smaller tires = less energy loss to friction. Same reason why trains are super efficient – very narrow wheels that only make contact with the rail, thus you need much less energy to drive them.

Rule of thumb: The smaller the contact surface, the lower the friction.

Thinner and smaller tires have less friction with the road surface thus less loss of energy to heat. Pumping up your tires over the recommended pressure level would do the same (but potentially cause a rapture) because the tire gets less deformed while rotating.

BUT VERY IMPORTANT: less contact surface and less friction also causes a longer braking distance! Because it’s the friction of the road to the tire that is stopping you from sliding! So I don’t recommend switching your tires to smaller, thinner ones or pumping them up over the recommended pressure level!

Think about how much footprint ( “patch”) a tire has on the ground. If that footprint is more, there will be more friction loss. But with too little friction you lose traction.

Here’s an ELI15 . Not great but passable:

http://ffden-2.phys.uaf.edu/211_fall2013.web.dir/connor_mattson/physics.html

In addition to the other good explanations regarding tire width, and rotating mass there might be confusion about tire diameter and people miscalculating their range when they change tires. If you swap your stock tires for a smaller diameter tire your odometer will not know that a shorter distance was travelled each revolution, so your odometer will falsely show a greater range than you really achieved, leading to perceived efficiency gains that aren’t really there.