Rigid body You and your friends are shopping for new tires for your car. Since g

Question

Rigid body

You and your friends are shopping for new tires for your car. Since gas costs $3.00/gal, you want to purchase tires that will save you money on the cost of fuel. Friend 1 says, "You should buy the big diameter tires because you can cover more distance for each turn of the tire, thus save you money on gas." Friend 2 says, "I disagree, the larger tire has more moment of inertia and will requrie more rotational energy to turn, thus you save more money on gas by buying the smaller diameter tire." Use a sketch, reasoning, calculations and assess which friend is correct.

Explanation / Answer

Friend 2

With wheel diameter increases come a decrease in sidewall size in order to maintain the same overall tire+wheel combo size. It’s important to stay as close to the stock tire+wheel combo size as the overall wheel size affects gearing.
Smaller wheels improve acceleration at the expense of top end, and taller wheels decrease acceleration while theoretically increasing top speed (though in practice top speed is limited by power and drag long before tire size. Increasing tire size usually also hurts top end acceleration and top speed as it decreases the engine’s ability to overcome the air drag holding the car back). There will also be changes in your speedometer reading in most cars with different sized wheels.
In any case, making the overall wheel/tire combo taller or shorter will again affect suspension geometry. You can change it a small amount without any real adverse effects but try to stay as close as possible when choosing a new size.
The big “gotcha” with sidewall size is that the smaller the sidewall, the less protection your probably expensive rims will have from the inevitable pothole or road debris. You can run lower profile tires with stronger wheels, but in general the stronger the wheel, the heavier it is as well.

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