I didn't perform an experiment. I used the known values of stiffness and computed the theoretical losses. But yes, you made one of my points for me. The losses are generally too small to be measured...

This is how I calculated the losses:

- Assume the stiffness values (expressed as k = N/mm) represent a linear, spring relationship. And it should because there are no non-linear elements.

- The energy stored in a spring (and subsequently lost) is equal to 0.5kx^2 where x is the displacement.

- The amount of displacement can be estimated from F = kx and P = Tw, where P is power, T is torque, and w is the rotational speed of the cranks.

- For a given power output and cadence, you can figure the average torque on the crank.

- Assuming the instantaneous peak torque is ~ 4 times average (that's generous) and using a force diagram, you can calculate the force that goes into bending the frame (i.e., pushing on our model of a spring)

- This force gives you the energy stored in the spring as described above: 0.5kx^2 and all that.

- This energy loss happens twice every rotation of the cranks, which happens 2cadence/60 seconds.

- Therefore, the power lost is equal to Energyx30/cadence Watts.

- Divide that by the original power input and there's your efficiency.

I found that using this model, which should be accurate by way better than an order of magnitude, the efficiency of a bike frame is ~99.95%. That might change by ~0.025% depending on whether you have a super stiff or super flexible frame.

John Swanson

www.bikephysics.com