Forum Replies Created
June 17, 2013 at 5:27 pm #93941
Thanks for your insightful comments. It’s also nice to hear your perspective on the 1.6-watt magnitude. I admit that it seems to me that 1.6 watts gets lost in the noise of chain lube, jockey wheel bearings and tire rolling resistance. On the other hand, when you put 1.6 watts in terms of time and weight, it certainly seems more significant.
Thanks for clarifying your use of “heat.” It’s broad–all losses end up as heat, eventually–but I see what you mean. That said, consider out-of-plane bending of the crankarm (as when you stand on the pedal at BDC). When you unload the bottom pedal, the crank returns to its unloaded position without adding to forward propulsion and without literally heating the arm. (We agree that there’s a very small amount of hysteresis; I suspect some of the remaining losses are as low-frequency sound waves). That bending absolutely happens in a “real” pedal stroke, and that’s one component of the total strain energy that isn’t returned to the drivetrain.
But beyond these overly simplistic sub-cases, we’re just speculating. While I have some intuitive guesses about the subject, I don’t know the answer to the energy return question. Finding the answer would require either really well-controlled physical testing or, as you suggest, a more involved FEA model.
In order to properly address the power loss question with FEA, I would need highly detailed force data from a complete pedal revolution. You mentioned Metrigear, and it seems pretty likely that the Metrigear guys have those data. But if the boundary conditions (including force input and direction vs. time) are properly understood, such an analysis should give pretty good results. It would require a full transient solution with many load steps, but it’s doable. Sure, you could use a constant force input, but you’d still need to do a similarly involved analysis; why not go whole hog?
Your postscript hints at another point: carbon fiber cranks will certainly damp more power than aluminum ones, although how much more is unclear. Regardless of the degree of damping, there are situations to which a 700-gram aluminum crank would be much better suited than a 600-gram carbon crank. If I were facing off with Mark Cavendish in Tour de France field sprints–I can dream, can’t I?–I’d definitely want a stiff aluminum crank.
Thanks again for your thoughtful feedback.
JasonJune 14, 2013 at 11:40 pm #93907
Having read through the article and the above posts, I take the “upper bound” explanation applies to using an analysis of a beam with pure end moments instead of a closer approximation of a simple cantilever with an end point load (pedal). The difference between these two is fairly significant in determining stored energy.
Not quite. The pure moment condition is just one example of how to quantify the strain energy in a deformed body. If you click on the textbook link, you’ll see several other closed-form solutions, including one for torsional loading and another for axial loading. But none of these is very close to a crank under a pedaling load–even when you combine them–which is why one would use FEA. The FEA solution is much closer than even a linear combination (superposition) of all the applicable closed-form solutions.
A well-executed finite element solution can be very, very accurate. I’m not sure that this is the place to expound on how the finite element method works. But if you’re up to it, Google “FEA.” It’s very, very well understood. It’s inherently an approximation, but it can be an outstanding approximation. Correspondence between the FEA solution and the real world depends mostly on the analyst’s skill.
I used the phrase “upper bound” to explain why I assumed all strain energy was lost. The question of how much strain energy is returned to the drivetrain is kinematically murky and difficult to prove either way. I used strain energy to establish an upper limit to the amount of energy a crank can absorb.
While we can’t answer the question of drivetrain energy return, we can address whether the most flexible crank absorbs appreciably more energy than the stiffest crank: it does not.
Does that clarify things?
JasonJune 13, 2013 at 10:50 pm #93809
I’m the author of the strain energy section. (We’ve interacted before; I’m on the Weight Weenies forum as youngs_modulus). You’re right that I assumed that all strain energy was lost; I made that assumption because I wanted to find an upper bound for energy absorbed by loading the crank.
However, I did not assume that the strain energy was dissipated as heat. While some of the strain energy is certainly dissipated through hysteresis, I’m confident that it’s a fairly small percentage of the total. The remaining energy is dissipated when the crank springs back as it’s unloaded. The obvious question: how much of the returned energy is propulsive?
I intentionally left that question unanswered. Some of the energy that goes into bending the crank is dissipated in a non-propulsive manner; some of that energy may well help turn the crank. This question gets complicated when you consider that any propulsive spring-back gets reacted out through the legs.
These complications are why I didn’t attempt to answer the energy-return question. As I said before, I only wanted to find an upper bound for dissipation. It turns out that even if we assume all the energy is lost, the losses are still very small. We’re talking about ~1.6 watts’ difference* between the stiffest and most flexible cranks. In my opinion, it’s not worth worrying about. More to the point, it would be very hard to measure in the real world.
That said, if you can think of a way to measure propulsion from crank spring-back, I’m all ears!
* That’s 1.6 watts at 300 watts total output.
[Edit: specified total output for claimed power loss]
- This reply was modified 6 months ago by Jason Krantz.