It may not be apparent at first glance, but Bike Friday actually uses two different wheels on the bikes. While they are not easily interchangable (i.e. you can’t put the smaller one on a bike built for the larger one and you can’t switch tires/rims/tubes), they are both referred to as twenty inch wheels in the bike industry. The confusion comes in how they’re measured and the 20″ designation uses a pretty shoddy, non-universal system.
In any case, the question often comes up as to why we offer more than one size wheel since the smaller of the two offers complete versatility as far as tire widths. They also seem to climb a little bit better. Though there are other factors, the primary factor we offer the larger one is that empirically we have found that the larger wheel actually tends to be faster for the performance oriented.
And now at long last, I finally bring you the actual physics explanation from my old physics professor, Tim Jenkins:
The reason the smaller wheel is better at climbing is due to torque. Draw a sketch of two wheels, one large and one small, on an incline. Draw a downward force acting on the axle of the wheel (this is a normal force that depends on the weight of the bicycle and the rider and the geometry of the bike but should be nearly the same for both wheels). Draw a line from the axle to the point of contact between the wheel and the incline. The torque we are interested in is the torque due to the downward force about the point of contact. Note that the perpendicular distance between the line of the force and the point of contact is less for the smaller wheel, so the torque is less for the smaller wheel. This torque must be overcome for the bike to climb.
The smaller wheel being harder on the level is also due to torque, in this case the torque due to friction between the tire and the road (this is the force that propels the bike forward). In this case the force is perpendicular to the line of the force and the lever arm equals the radius of the wheel so the larger wheel has a larger torque (draw the sketch to see this).