Originally Posted by ShannonM

OK, so Robin Williams' First Law of Comedy has been fully honored in the thread, but I was completely serious and not trying to generate jokes.

When we pedal, there is some displacement of the centerline of the bottom bracket relative to the centerline of the bicycle. Obviously, making that displacement happen requires an input of force. The real question is, is that force lost, to any degree that matters? The answer to that question is, so far as anyone who's ever tried to measure it has been able to determine, no.

It turns out that things like frames, crankarms, stems, seatposts, handlebars, etc are very,very efficient springs. Which makes perfect sense... they're mostly made of metal, they have few if any moving parts, and there's not a damper anywhere to be found. Metals have vanishingly low internal losses, things that don't move don't generate friction, and there's not a part whose job it is to convert force into heat, so how can the pedalling force be lost? Where's it gonna go?

It's going to be returned into the system, because we're talking about undamped springs, and that's what springs do.

Where and when is it going top be returned to the system?

This is a more interesting question. Springs release their stored energy when the force compressing them (energy being put into the spring) is less than the force the spring is exerting on whatever is loading it.

Now think about pedal loads as a function of crankarm angle. They're increasing between roughly 1:30 and 4:30, peaking at the end of the downstroke. The rest of the circle, they're not very large at all, because almost nobody pulls up in the back half of the stroke, and even those who do don't do it very hard, so not much force is being applied.

But, wait... bicycles have two crankarms and pedals, because most bicyclists have two legs. That probably matters a lot, no? So, our right pedal is at 5:00 or so, the force on that pedal is falling very quickly, (it'll be almost zero by 7:00,)
the bottom bracket area and crankarm are at their maximum leftward deflection, and there's some energy stored in that deflection. What happens next? The left crankarm is at 11:30, and the force on it is just starting to increase from its minimum. So we have a double null in the force input by the rider... the legs aren't adding much energy into the system. So, the energy stored in the leftward deflection of the crank area becomes, for a brief, glorious moment, the largest force in the drivetrain. And what it wants to do is to drive the deflection to zero. And, since it's displaced to the left, that means moving things rightward. Which is exactly what the rider's left leg is going to start doing when the left foot gets to 1:30 and the left leg becomes the dominant factor in the system.

Basically, the bicycle returns almost all of the energy stored in its flex by the first pedal stroke on all subsequent pedal strokes, minus some very-small-but-not-zero amount that gets converted to heat because TANSTAAFL. In other words, your legs only pay the full cost of distorting the bicycle once. After the first stroke, the bicycle itself helps you to deflect it, so you don't have to.

And that's why stiffness is not a factor in bicycle performance.

--Shannon

PS: I'm pretty sure this is most of what Jan Heine and the BQ crew are talking about when they talk about "planing." They go farther than I'm comfortable with in saying that bicycle flex is a net positive for performance... although they do have some data to back that claim up, and they show their work. All I'm confident in saying is that it isn't a net negative.