If you mean that a smaller circumference wheel will always be slower with the same power input, my understanding is that this is incorrect and that, if anything, the reverse is true, particularly at high speeds on smooth surfaces.

The reasons I believe that, all else being equal, the small tire is faster are:

• The frontal area of the tire and rim is smaller in the same proportion as the reduction in circumference (or outer diameter) of the tire.
• The frontal area of the spokes is smaller to a greater degree than the reduction in circumference (or outer diameter) of the tire. The primary reason for this is that as the wheel size reduces, spoke length reduces faster because the amount of the diameter occupied by hub, rim, and tire remains the same. There is a secondary smaller effect stemming from a slightly lower velocity at the outer tip of the spoke where the peak velocity is highest and thus matters the most (square law effect). A third potential reduction in drag is that the greater strength of the smaller rim makes it feasible to use fewer spokes.

As far as velocities are concerned, regardless of the wheel size.

• Where the rubber meets the road, its velocity is zero (unless the tire is skidding)
• The axle of the wheel moves forward at the speed of the bike. (for example 20 mph)
• The top of the tire moves forward at twice the speed of the bike (40 mph in this example)