Quote:
Originally Posted by jur
Regarding rolling resistance of small wheels, there are several aspects to consider:
1. The basic geometry consideration, that road bumps will slow a smaller wheel down more than a larger wheel, due to the fact that bumps have a bigger effect on a smaller wheel. Hence rolling resistance of an smaller, infinitely hard wheel is more.
2. But wheels are not infinitely hard, they are pneumatic. Road bike tires reach the optimum for typical road surfaces at about 110psi; anything more and the rolling resistance may actually increase because the tyre can no longer deform and smoothly roll over irregularities. So at this sort of pressure or slightly lower, the rolling resistance between the 2 sizes due to bumps become indistinguishable as the tyre effect dominates.
3. Due to the fact that a smaller wheel has a rounder contact patch compared to a bigger wheel, less of the tyre deforms, so resistance may actually be lower for the smaller wheel.
4. Put the smaller wheel on suspension, and bigger bumps begin to weigh in the small wheel's favour.
5. Aside from this, wind resistance dominates rolling resistance by a big margin.

It's my understanding that rolling resistance is, by definition, those loses entirely due to the weight of the vehicle flexing the tires and/or road. Inelastic collisions with bumps and road irregularities is a separate phenomenon that really has nothing to do with rolling per say. So while considerations #1, #2, and #4 may, in fact, increase the overall efficiency of movement by reducing the losses of inelastic collisions, it appears that they do so at the expense of greater rolling resistance. In particular it seems that for a material construction of given hysteresis a harder, high pressure tire must, by definition, have less rolling resistance because there is less flex to generate losses. I suspect that this is, in fact, Dr Moulton's idea behind having small high pressure tires on suspension: high pressure to reduce hysteresis due to rolling, small diameter to increase wheel stiffness at a given weight thereby reducing hysteresis due to rolling, and suspension to substitute inelastic collisions for controlled flex in a low hysteresis (also known as " elastic") material.
Point #3 is an interesting one which I've considered myself. Although one would think that, perhaps, a contact patch spanning fewer degrees of tire would imply less deformation and, thus, less rolling resistance. However, one must consider that since the contact patch is wider, each degree also flexes more. The wikipedia gives the equation, F=W*a/r, for the force of rolling resistance, which seems to clearly imply that for a wheel of equal stiffness and elasticity the wider contact patch does, indeed, have greater rolling resistance (although no derivation for the formula is given). However, it appears that locomotive train engineers along with Dr Moulton feel that the increased stiffness gained by using small diameter wheels more than compensates by reducing the coefficient of rolling friction, a.
I would love to hear Dr Moulton lecture on the topic because I doubt his autobiography will go into sufficient detail.
Last edited by itsajustme; 090908 at 09:36 AM.
