Sorry for the long post. I spent a long time with my dad this morning talking over the question of whether moving-bottom bracket cyclists really can add power with their upper bodies. Short answer: yes. Here are my thoughts.
In a moving-bottom bracket (MBB) bicycle such as standard road bikes and the Cruzbike, movement of the bottom bracket (BB) by the upper body--given certain conditions-- can add torque useful for propelling the bike.
This seemed illogical at first glance. “Power is generated on a bike,” I thought, “by the rotation of the pedals around the BB."
My first thought was right. Mostly. A bike is moved forward by rotating the BB axle, which is connected to a chain, which connects to the axle of the drive wheel. The BB axle is rotated by generating torque using the crank (lever) arm. The pedal is placed at the farthest point along this lever arm, in order to generate the maximum torque (a measure of “turning force” according to Wikipedia). This rotational force is equal to the force applied on the lever arm multiplied by the distance between the point where the force is applied and the point of rotation. For example, if I applied 10 pounds of force on the end of a 1 foot wrench, I would be generating 10 ft/lbs of torque around the nut I wanted to unscrew.
Given these basic facts, it seems impossible to add power to a bicycle by moving the BB. One would be applying a force at the point of rotation. Given that the distance between the point where the force is applied and the point of rotation is zero, and that zero multiplied by any force is zero, we find that torque would always be zero around the BB if one moved only the BB.
Thus, as a way of adding power to the forward motion of a bike in the traditional way of increasing the torque around the BB, moving the BB is useless. However, that does not mean it is useless as a way to add torque, and thus power, to move the the bike forward.
One must simply look at a different point of rotation: the pedal. Assuming our legs during certain phases of the pedaling cycle have momentary stiffness and are attached to the pedal (the conditions I alluded to above), the pedal can be seen (momentarily) as a fixed point about which to rotate the BB.
Imagine a bike floating in mid-air. Now, freeze a pedal in its current position in space. Now, rotate the bike (and thus the BB) around that pedal. What I hope you will see--besides a churning vortex of human-powered transportation technology-- is the BB axle rotating around a lever arm (the crank) around the frozen pedal. What I also hope you will see, is that the drive wheel of the bike will spin; the rotation of the BB around the pedal has generated torque which can drive the bike chain and thus the drive wheel.
The difference from the traditional source of power on a bike, is that the point of rotation is the pedal, not the BB. Two different points of rotation, two different ways of generating useful power for the drive wheel.
This means that in an MBB bike, whether an upright or a Cruzbike, power can be generated using the upper body, but only if the legs hold some rigidity, allowing the BB to move relative to the the pedal and generate torque. Theoretically, someone with two peg legs could generate power on an MBB bike with only his upper body, as long as the pegs held the pedals in place relative to the BB.
Working through these thought-experiments has convinced me that, indeed, useful power can be added to MBB bicycles by using the upper body to rotate the BB relative to the pedals.