I'm not trying to come down too hard on you here: you're right that energy losses to deformation aren't worth worrying about because they're so low.
So....no power is "lost" if it is so small that it is insignificant and unmeasureable (by any cycling power meter).
(I happen to be a thermodynamicist and using common language on a cycling forum, not impressing people with vacuous theoretical subtleties. Yes, I am acutely aware that flexing actually does dissipate a miniscule amount of energy. I depend on that phenomenon every day in my job.
Hey; awesome! I didn't mean to patronize you, but I also couldn't have guessed what you do for a living. (I still can't, quite...is your last name "Carnot" by any chance?)
"Vacuous" is an interesting way to describe theoretical subtleties. Maybe you mean to say that the losses are so small as to be of no concern? If so, we totally agree on that point.
If you weren't losing any energy to flex to begin with, how can you get anything back with tuned flex?
"Mechanical Impedance". Look it up.
Hey, you caught me! I was using common language on a cycling forum. Why so testy?
As far as I can tell, we fundamentally agree with each other, so I don't get the snark. Henry Kissinger once (supposedly) observed that the arguments in academia get so vicious because the stakes are so low. These are pretty low stakes.
It is not that you are "getting it back", it is that it is transferred more efficiently.
These are the same thing. If there are no losses, then efficiency is already at 100%. A golf club with stiffness "tuned" the wrong way isn't 100% efficient, at least not the way I'm using the term.
Here again, it is only VERY theoretical, and that's why I only mentioned it in passing, it is about as useful as worrying about how much your losing through flexing.
Here again, we agree. And I understand that when you mentioned driving the bike/rider system at resonance, you were only saying, "hey, it's possible," rather than trying to argue that it's happening and measurable. And that's fine, but you just sneered at "vacuous theoretical subtleties," so I'm not sure why this is different.
Besides, your initial post said that no energy is lost to "flex". If that's true, there is no hysteresis and no mechanical impedance. So my question still stands: if there's no mechanical impedance, what would it mean to reduce (via "tuned flex") what's already zero?
For mechanical impedance to matter, the bike/rider system would have to have a mode near 1.67 Hz to be excited by the forcing frequency (the rider's pedaling). A cadence of 100 RPM works out to about 1.67 Hz. What part of a bike/rider system do you think has a mode near 1.67 Hz?
Again, I realize that you don't genuinely think this is happening. But Jan Heine sure does, which is why I went out of my way to discuss it.
The point of all this is that "No, you are not losing any power through crank or frame flex. It might bother you, but you are not actually losing any power."
Yep; we basically agree. You are
losing a small-but-nontrivial amount of power, but there's nothing you can do about it. There's not a measurable amount of difference in power absorption between, say, two different cranks. (Or, if there is, no one has yet measured it).
The crank "unwinds" as you go through the rest of your pedal stroke, but there's no obvious way for that unwinding to be converted to forward motion.
Simply resist it, by keep force on the pedal. Force (resisting) *velocity = power, just exactly the same as when you are deliberately stepping down on the pedal. (Admittedly, AGAIN, it is a miniscule amount. But very real. )
Well, there are three problems with that:
- Pedal float and foot/shoe compliance makes it impossible to resist the small torsional unwinding of the crank near BDC.
- There are many strains that, even when resisted, don't get turned into forward motion. For example, at BDC, it doesn't matter how hard you push down--you're not going to move the bike forward. You're bending the crank and the pedal spindle when you push down, but even when they spring back, they don't create forward motion.
- The biggest problem is that resisting the spring is physiologically the same thing as pedaling harder. Resisting the spring force does no work in the physical sense, but it requires muscular effort. A rider's muscular effort is stored as strain energy within the crank, and then the rider must exert additional effort to resist the "spring-back" of the crank. Yes, energy is stored, but the spring needs something to push against in order to turn the stored energy into forward motion. The only spring-resisting force comes from the rider's legs. So the rider can recover the stored energy, but must exert more energy to do so. On balance, it's a losing proposition.
I'm not saying that none of the energy stored in the spring gets turned into forward motion; I'm just saying that it's not clear how much of it, if any, gets returned without further effort/calories from the rider.
I had never heard of Heine's "planing" so I went out and read some stuff, an I think it is at least plausible that it would have a much greater effect on power out put than any "dissipation" in the materials.
Heine is trained as a paleoclimatologist, but his command of mechanics is about as good as my understanding of paleoclimatology. He hypothesizes that riders produce more measureable power on a flexible bike than they do on a slightly stiffer one. He claims to have found that a rider on a more-flexible bike produced 12% more power
than on a slightly stiffer bike. In the words of Wolfgang Pauli, Heine isn't right; he's not even wrong. His "experiment" doesn't test his hypothesis and he won't publish his data.
If a flexible frame were 12% more efficient than a stiffer frame, I promise you that the engineers at Cervelo, Trek and other manufacturers would bend over backwards to equip their teams with bendy frames. 12% more watts is an enormous (and imaginary) advantage. In reality, pedaling inputs are well below any relevant natural frequencies. It's not that flexible bikes are inefficient; they're just not more or less efficient to pedal than stiff bikes.
Even more damning is that his "planing" theory predicts that bicycle efficiency should be exquisitely sensitive to cadence, and it's not. If his flexible, more efficient frame is resonating ("planing") at the rider's chosen cadence, then the stiffer bike would resonate at a higher cadence. You and I agree, Rick, that bicycles are high-Q systems
, so the "planing" response should exist over a narrow cadence range, maybe 10 RPM. In other words, if Heine's bike "planes" best at 100 RPM, it should be drastically less efficient below 95 RPM and above 105 RPM. But Heine has a strange aversion to testable hypotheses, so he hasn't addressed this. And if the peak efficiency range is broader than this, there's necessarily a lot of damping/energy dissipation happening, but we just agreed that wasn't the case.
(I'm not kidding about this aversion. He has rejected the Chung method for his rolling resistance tests, even though it's objectively much better than his own poorly-designed experiment. If he knew what he was doing, he'd be excited about getting better data with an improved experiment).