why don't cars have bigger wheels/tyres?
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Answer it!
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The strength of anything is based on its cross surface area. For the wheels to support the weight of a car + say 4 or 5 people in it, it has to be strong in the first place. In terms of the laws of scaling, if you scale something up by a factor of say 2, its weight increases by 4 times whereas its strength only increases by 2. This can be seen in an ant and elephant comparison, whereby the ant can carry a few times its own weight while the elephant can't.
The next thing would be the effort required to spin the wheel. if you had gigantic wheels on your bicycle, say 2 meters long, it will be harder to even get it moving. This is due to Torque, which we see in everyday life like your door handles. The longer your handle, the easier it is to push it down and open the door, however, imagine you're the door. the longer the handle is, the harder it is to resist being opened. Thus cars need engines which are as strong as those you can find in sports cars just to keep the car going, which is inefficient.
Hope this helps and i'm just explaining in the POV of physics =D
The thing is, all the different aspects have to be taken into account. Bigger wheels would have some advantages, but they would be outweighed by the disadvantages.
First of all, it's a matter of material mass/strength. Take a stick that is 3 feet long and try to break it over your knee. Assuming you didn't pick a really strong stick, you should be able to do it pretty easily. Now take a stick the same diameter but only 1 foot long. Trying to break that will be much harder because you won't have the same leverage. It's the same with metal--if you have a larger diameter wheel, you face the flex and strain that comes from bending over a much larger distance. The only answer to this would be to put more material to support that strain, and that gives you two more disadvantages.
You would need to spend more to use that much more material, and that means cars would cost more to make and, therefore, to buy. The other problem is that more weight means more fuel consumption for acceleration. So while you may get better handling, you would use a horrible amount of fuel while in traffic or driving in a city.
There are steps being taken to address some of the things you've mentioned, though. For example, it is possible to get wheels that are wider (for increased grip) made from lighter materials, but they are more expensive (you generally have to buy them afterward, not with the car. Also, there are rims that have thinner tires now as well. This helps because it reduces weight (strength per weight of rubber is much less than metal), and less flexibility gives a more direct feel on the road (or so I hear, I've never driven on those tires).
I do agree that some new vehicles, especially electrics, have wheels so small they do look a bit ridiculous. But especially with the capacity of electric vehicles to run for any length of time, weight is a premium because less weight = more carrying distance per charge. Aesthetically, I think that an 18-20 inch (45.7-50.8 cm) is generally ideal for a normal passenger car, but even then, there are times when those wouldn't work very well either.
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