ScienceIsCool said:
Oh yeah. And the efficiency is the same whether you're putting out 12 or 1200 Watts. The system is incredibly linear over a wide range of inputs.
John Swanson
www.bikephysics.com
From my calculations, the deflection of the frame is proportional to the force (hence torque) applied to the BB.
It is not proportional to power or wattage as power incorporates cadence.
Hence, for the
same power value, you can have differing force values on the pedals (with corresponding differing cadences) which
produce differing deflections and differing energy absorptions in the frame (proportional to the square of the deflection) and hence you can have DIFFERING EFFICIENCIES AT THE SAME POWER INPUTS.
Also by similar math, you can have the same absolute amount of energy energy lost at two different power inputs.
Also, the system appears to be a highly complex one, that involves multiple springlike deflections from multiple degrees of freedom (eg. torsional deflection of the frame, lateral deflection of the frame, vertical deflection of the frame, deflection of the crank, deflection of the chainring, deflection of the chain, deflection of the rear cassette, deflection of the hub/cassette, lateral deflection of the wheel, longitudinal deflection of the tire, lateral deflection of the tire). The amount of energy that the frame absorbs will be dependant on the interaction of all these points of "give" in the system. The determination of proportional energy absorptions (ie. losses - in the cases where the energy can't be retransferred back) would require, it seems, an iterative process of redistributing residuals and deflections throughout the system. It is enough though to realise that these various degrees of freedom influence/affect each other IMO.
It is also a factor that the crank torque is a varying quantity in the pedal stroke. If a significant portion of the high torque zone of the pedal stroke is taken up hypothetically stretching a very elastic chain, then force won't be absorbed in the frame until the chain deflection (stretch) reaches a point that it counteracts the force applied to the chain by the crank torque. The more deflection, the more that valuable displacement is lost in the high torque zone of the pedal stroke (around 3 o'clock), and hence less available to displace the frame. If springback occurs in the low torque zone of the stroke (in the case of the chain springing back) then it will interrupt the cadence rhythm.
Only when all paths of lesser resistance are loaded up, will the tire push on the road. The more give in the system, the less of the power arc of the stroke goes into propelling the bike. The system's components are interconnected by the fact that only after all lesser resistances are loaded up, will the frame deflect. Hence energy loss in the frame is dependant on energy losses (and elasticities) in the other degrees of freedom.