In theory, the rolling resistance of wheels decreases as the diameter of the wheel increases. This is on the assumption that all other factors are equal: the tyres are of identical cross-section and carcase construction, with equal internal air pressures and equal external applied loads, rolling at low speeds in still air where no significant aerodynamic effects apply, on smooth hard road surfaces, with the wheels on hubs with insignificant bearing friction.
Yet it is clear from observation and testing that, under some circumstances, some smaller diameter bicycle wheels can roll as easily, or even more easily, than some larger diameter wheels. This does not mean that the theory is wrong – merely that one or more of the “other factors” is not equal. The easiest factor for the average rider to control is tyre pressure. It’s a fair assumption, confirmed by everyday observation, that most cyclists ride on tyres that are at sub-optimal pressures. So, pumping up the tyres of a small-wheeler to the maximum recommended by the tyre manufacturer may well be enough to allow it to roll more easily than many other cycles with larger wheels. Choosing a small diameter tyre with a supple carcase will also help. At racing speeds, wheel aerodynamics and unsprung mass of the whole bicycle and rider ensemble can also enter into the equation and may, for example, favour a well-designed small-wheeler with suspension.
Between 1998 and 2002, British engineer John Lafford carried out rolling resistance tests on various tyres, ranging in tyre bead seat diameter from 305 mm to 622 mm (i.e. nominal wheel diameters of 16-inch to 28-inch). The manufacturers and product types, cross-sections, tread patterns, state of wear and tyre pressures all varied quite considerably. His full data may be found here: http://www.legslarry.beerdrinkers.co.uk/tech/JL.htm
Below is a chart generated directly from John Lafford’s data using Microsoft Excel. The vertical axis shows the various tyres tested, ranked by bead seat diameter – biggest at the top and smallest at the bottom. The horizontal axis shows rolling resistance – the less the better. The straight, backward-sloping, black line is a computer-generated trend line which reflects the general truth of the theory that rolling resistance decreases with tyre diameter. But it is immediately apparent that the rolling resistance of any particular tyre diameter may vary considerably, confirming the variance due to those “other factors” that may not be equal in reality. Hence we find some of the smaller tyres under certain conditions have actual rolling resistances lower than some of the larger tyres.