Originally Posted by
Maelochs
Seems simple enough to me .... the motion of the crank translates the motion of the foot into motion of the chain and ultimately, the rear wheel, which propels the bike forward. Anything in the system which transfers energy anywhere not alo0ng the perfect (circular) path of the crank, wastes propulsive energy.
Think about a bike with really loose bottom bracket bearings, or cranks which weren't tight to the spindle---no one would be trying to convince anyone else that those things in some way returned energy to the bike because "ya know, conservation of energy." If the whole frame flexes at the bottom bracket, same effect---some of the potential propulsive energy goes in different directions. When the frames snaps back (or is pushed back by the other crank) it is still lateral, not longitudinal motion, and this does Not help propel the bike.
it's going Sideways, people. Unless you want your bike to go sideways , any sideways motion is wasted, since "wasted" in this case means "not propelling the bike forward."
The only way the bike could be acting as a spring and propelling itself forward with energy from deflection would be if the bottom bracket twisted longitudinally under load---but that would imply a fixed or high-friction crank bearing.
Think about it .... if your wheel shakes from side to side really badly, are you going to claim that its okay, because the energy lost will be returned and help propel the bike forward.?
For maximum efficiency, everything has to stay in the plane in which it is meant to operate. Every angular flax is a waste of energy. Y'all are engineers with degrees and all that ....
I believe your understanding of how the spring (bike frame) is storing and releasing energy is a little off, and the highlighted statement may go to the root of it.
What "direction" the frame appears to be flexing is a red herring. Here is is what is going on:
When you apply force and power through the cranks, the cranks exert a force on the bb shell (and the frame). The frame needs to match that force, otherwise the cranks would not redirect the force of the pedals to the chain. With an infinitely stiff frame, the force would be matched completely with no deflection thus no energy goes into bending the frame. With a real world frame, it deflects until the force is matched. It takes energy to do this, thus you temporarily lose this energy to the spring (frame). The less stiff the frame, the more it needs to deflect to match the force, and the more energy is diverted/stored in the frame.
Now consider what forces on the cranks are causing the crank to exert a force on the frame. 1- The force pushing on the crank arm, and 2- the force of the chain pulling straight back on the top of the chain ring.
When that stored energy is released, it is going to do so in the exact opposite direction (vector). Thus, unbending force of the frame will act on the crank in the exact opposite vector as when the crank deflected the frame, and the crank in turn directs this force in an opposite vector to the to the chain (pulling pulling forward.... thus the drive force) and back into the crank arm (force against you pedaling).
I believe the key as to whether you waste energy (and how much) has to do with how much of that energy goes through the chain and how much back through the cranks (
*see caveat below). And honestly, this is where I get a little fuzzy

(Perhaps someone else can pick up here) .I believe is has a lot to do with the timing of your pedal stroke in relation the the frequency/timing of the spring - and I am pretty sure that is what the concept of "planing" is all about.
BTW, the example above is just one of the many ways that a frame may be flexing and storing/releasing energy. Here is another: The force on the chain causes tension on the chain that is trying to pull the chainring and cog closer together. Since the chainring and cog are both off-center of the frame, they can get closer to each other by bending the frame between the BB and rear axle. Thus, there is always some bending force on most frames when you pedal. A really stiff frame bends minimally, thus diverting/storing little energy. A more flexible one bends more, thus storing more energy. This is a perfect example of the direction of the frame deflection being misleading. The frame may be bending to the side, but the forces acting on it are along the chain line. And along the chain-line is where this frame/spring is going to return this force (and energy).
*There are also loses due to damping, but that is a different subject. And for metal springs, it is minimal.