Ah — good to connect real names with aliases. Your posts on Weight Weenies are certainly excellent.
It’s a funny difference in perspective: you say “only 1.6 watts” but I see “a whopping 1.6 watts”. That’s around 5 seconds up Old La Honda road, as much effect as 350 gram difference in crank mass.
By “heat” I am referring to conservation of energy. Assuming the leg can output the same power, aerobically limited, then power goes to either propulsion or to heat. The heat can be in the bicycle or in the human body. However, the leg sees a certain force-versus-position trajectory: one with an infinitely stiff crank, a slightly different one with a flexible crank. Assuming no power is lost in the bicycle itself, then it’s not obvious to me that the flexy-crank trajectory is going to yield more internal dissipation in the leg than the other. True, the crank may be pushing less against the leg during the upstroke, but this is balanced by the fact the leg is pushing less on the crank on the downstroke. Power transmitted to the crank would be reduced, but the aerobic system is worked less, and therefore the body is able to adjust and push harder. It spreads out the force pattern more over the distance of the pedal trajectory, perhaps, but the integral of force dot distance with respect to distance is constrained by the power.
Forget about the human leg: that’s hopelessly complex. I could assume the crank is hooked up to a lossless machine which is programmed to deliver a fixed amount of mechanical power to the crank such as the one Metrigear built to test the Vector. In that situation, the flex must be relieved either propulsively or via heat in the bicycle. I know in this situation my money’s on the vast majority of those 1.6 watts going into the drivetrain. It’s the obvious energy sink.
It would be interesting to see FEA of this.
P.S. There’s a general confusion (not from you, but in the subject as a whole) about the difference between elastic compliance and inelastic compliance. For example, if I put a thick insole in my shoe, it is easy to understand than when I compress it, then allow it to expand, I will get only a fraction of that energy back, and therefore it’s better to not use thick insoles. The insole will deform one way, then un-deform a different way, yielding hysteresis which results in heat generation. With highly springy materials like Al, and to a lesser extent carbon fiber which is more lossy, the direct hysteresis will be far less and so energy loss becomes more dependent on the nature of the load.