but the chuck-it works, in part, by capturing energy from a longer duration than the forward part of the throw. momentum from the backwards part of the arm movement flexes the arm back, and then the spring action of the arm wanting to return to it's unflexed position is added to the forward momentum when you move your arm forward. tape the ball in and keep going back and forth, and the springiness of the thing is no longer helping you. in fact, the ball is actually moving slightly LESS than it would be with a rigid arm because the energy storage and return of flexing the thing is surely not 100% efficient. similarly, cycling is a constant activity, so it's not like for every "throw/ride" you're adding another 20 or 30% of stored up kinetic energy. when would such energy be input into the frame? and if there was a "inputting energy into the frame" cycle, would it not be more efficient to simply transfer that energy through the chain, into the rear wheel, and turn the wheel?

it's quite believable that past a certain amount of power the frame will flex on each downstroke. getting the energy used to flex the frame back would be nice, but not as nice as it not happening in the first place. if the argument is that somehow the frame flexing forces the rider to do MORE work which then gets converted to forward motion, well, that's really irrelevant because now you're asking more of the cardiovascular system, and again, it has to be more efficient to just turn the cranks faster/harder.

what i could easily believe is that IF a frame is noodly, there are good and bad types of noodly, in which some return the energy badly and others return it goodly. i'm 6'2 and can pretty easily put down 1000w for a very short duration or 500w for a longer one, and my very light bike doesn't seem particularly noodly. it's very, very hard to imagine that even 5% of those 1000w are going into flexing the few ounces of carbon fiber in the area in question.