Why Do Wheels Roll More Efficiently Than Other Shapes?

[fog37]

TL;DR

Understand why a wheel works so well and does what it does so wheel

Hello,

The invention of the wheel changed the world. I imagine pulling a cart with square shaped wheels and how difficult and bumpy it would be.The wheel is essentially a circle, a polygon with infinite small sides while the square has only four sides. I guess that, at both end of the spectrum, the square would be the worst shape and the circle the best shape.

Without complicated force diagrams, is it hard to provide a high level explanation of why the wheel, with its circular shape, can roll and move and translate so easily compared to other shapes? I assume a force applied to the center of the shape. This force causes a torque that tries to rotate the shape itself. I guess the torque to rotate the wheel is always smaller than the torque required to rotate and translate other shapes...Is that somewhat correct?

Thank you for any insight.

 

[Baluncore]

I think the answer comes from the height change of the vehicle as the wheels turn.
A triangular wheel would be worse than a square wheel.
If the polygon wheels were out of time, it would throw the vehicle from side to side.
The timing would change when going around a corner.

 

[fog37]

Thank you Baluncore. I see your points.

Is there also some lever argument that makes the wheel better than other shapes? For a wheel, the ideal point of contact is simply a point that is at momentarily at rest (contact patch in real situations).

 

[Lnewqban]

... For a wheel, the ideal point of contact is simply a point that is at momentarily at rest (contact patch in real situations).

This tutorial is very good:
https://www.physicsforums.com/insights/explaining-rolling-motion/

What happens around the contact patch in real situations is very important.
For irregular surfaces (rocks) or deformable ones (sand), the bigger the diameter of the wheel, the better.
For flat solid surfaces, the lees deformation of the contact patch, the less energy is wasted.

Besides the lever effect against the area of dynamic friction (axis of the wheel), the capability of keeping the center of mass of the car more or less at a constant level, as mentioned in above post, is key in the success of the wheel.
Any other polygon rolling over a flat horizontal surface would create an up-down oscillation of the center of mass, with associated accelerations and forces and waste of energy.

There are some situations for which a round wheel is not ideal, like climbing stairs or the side of a rocky mountain.
Legs or wheels that mimic the profile tends to work more efficiently in those cases, based on the principle of a more linear trajectory of the center of mass of the object.

 

[fog37]

Really cool. Thanks Lnewqban. Let me process all of that.

 

[Lnewqban]

You are welcome.

https://en.m.wikipedia.org/wiki/Rolling_resistance

Please, read this article and come back with your conclusions.