What determines optimal wheel size?

[SkepticJ]

As a lay person I've wondered this for a while.

Obviously heavy machinery that rolls on dirt and mud needs large tire/wheel diameters and widths to spread their weight out to an acceptable ground pressure, eventually having to switch over to cat tracks when larger wheels start to give negative returns.

But what about trains? They roll across the hardest, smoothest surfaces that anyone could reasonably wish for, but their wheels are still proportionally quite large. Why? Why are bicycle wheels so huge? At least for road bikes; for mountain bikes it makes more sense.

 

[huntoon]

Smaller wheels need higher RPMs to travel the same distance. Bigger wheels more easily travel at high speeds but at the sacrifice of torque.

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[Mech_Engineer]

Rolling resistance is proportional to 1/r of the wheel, so a large wheel has lower overall rolling resistance. Larger wheels also have lower angular velocity (RPM) at speed, making bearing selection easier. Still, I think rolling resistance is the biggest factor.

See here: http://www.engineeringtoolbox.com/rolling-friction-resistance-d_1303.html

 

[Pkruse]

Steel on steel rolling design is much different from pneumatic tires. It is more like roller bearing design. Care must be taken to make sure contact stresses are acceptable. Wheel diameter figures significantly in that set of tradeoffs.