jano wrote:What about you put pen on paper and show us some of your calculations about how vertical or lateral flex of a bike frame magically becomes forward movement of a bike? Then we talk again. Until then I stay by my conclusion, based on what I learned as an engineer, and that is that part of the energy that produces flex in the frame is returned and will be absorbed by the rider who is the only part of the bike/rider whole that has a dynamic adaptive function, unless you ride one of those Time Aktiv frames with a mass damper built into the fork.
You need to attempt to do some calculations so you can understand why there is nothing there. The spring in the system just changes the force and response curve slightly. When it is springing back, the rider is still applying motive force to the system.
jano wrote:Alternatively you could can save yourself a lot of time and just do an empiric test by replacing your cranks with a straight tube, stand on it and induce flex into the frame by shifting your weight from left to right and back. Let us know the longitudinal speed you achieved by doing this.
Your simplified example unfortunately doesn't model what is happening. No need to simplify. Our "bar" is a crank that's attached to a chain drive. When force is applied to make the cranks go around, the frame absorbs some of that energy by moving away from the force. When the force declines, the frame returns it by moving back to where it was.
If it helps you could simplify it by looking just at the crank and assume a sinusoidal tangential force is applied to it, and flexes like a spring. The frame is doing the same thing, it's just more complicated.
formerly rruff...