Originally Posted by Pedaleur (Post 15868692)

We're getting down to needing to define how we're measuring work. If you're measuring work "at the pedal" then there are no non-productive forces, per se. Anything that causes a deflection will be returned to the system. Anything that doesn't cause a deflection won't do work.

Of course, if you measure work at the leg, then there is lots of wasted energy. Any force that is not tangential to the pedal motion will be "wasted": no work is being done at the pedal, but the leg is undergoing physiological loss.

Originally Posted by rpenmanparker (Post 15868676)

Energy or force, it is a vector quantity in this case. Once it goes in a straight line direction, it can never be converted to rotational motion. If you disagree, tell me how.

Originally Posted by rpenmanparker (Post 15868696)

Another thought. Here is the problem: even if the bike is a perfect spring, which it is not, the human leg is far from it. Reciprocal up and down motion can only become rotational if it returns to the leg. That's because the leg is the only machine that is driving the crank rotationally. Realistically, that is just not going to happen.

Originally Posted by Campag4life (Post 15868683)

I disagree with your thesis. If you are speaking of rocking the bike aka pendulous motion of crank axial center side to side...this is biomechanically more efficient to power the bike using the upper body as leverage. 'All' vectors of pedal force including all non-normal pedal force applied to crank arms translates to rotation energy of the crank which is co-planar to the rear drive wheel. There is no non-productive pedal force.

Originally Posted by Pedaleur (Post 15868731)

(Which is a nice way of saying I'm a helpless pedant...) ;-)

Originally Posted by Pedaleur (Post 15868715)

To be clear, energy is not a vector. Which is why the problem is easier that way. As noted in my other reply, it depends on what you consider your system.

If the system is the bicycle, then you "simply" draw a proper control volume and determine the energy flows.

From a force standpoint, the work done in flexing the frame (non-productive, in your terminology) is returned when the frame unwinds. I can't possibly draw out the vector solution -- it's way too complicated -- but conservation of energy says it must.

Again, if you include the leg in the control volume, there are lots of "wasted forces" because the leg expends energy without doing what we technically call work.

Originally Posted by rpenmanparker (Post 15868739)

How can that be true? There will always be a force vector component that rocks the BB instead of rotating the crank. The only way to avoid that would be for the force to be applied directly to rotating the spindle like by a motorized chuck instead of through the crank arms. That force must be wasted, period.

Originally Posted by Campag4life (Post 15868755)

The fact that the BB center rocks side to side is irrelevant. As I stated, this is the biomechanical reaction to the body during muscle contraction which is productive and not counter productive to powering the bicycle...as witnessed by every top sprinter in the planet when a bicycle is achieving maximum velocity. Pedal force rotates the crank arm normal to the BB center. There is no wasted pedal force other than competing pedal force between legs at different rotational intervals on the crank. An example of 'competing' pedal force would be track standing on a fixie. This occurs in very small intervals throughout a typical pedal stroke.

Originally Posted by rpenmanparker (Post 15868753)

Interesting, but here is the problem, as I think I have said elsewhere earlier: You can't put energy back into the leg muscles. Since the leg is the only driver of rotational motion, it stands to reason that you can't put the frame flex energy back anywhere that will drive the bike forward. I don't know where it goes, and I don't think it matters. It for sure doesn't go back into the legs in a usable form for propulsion. Hence, it is wasted.

Originally Posted by Bah Humbug (Post 15868789)

I agree. I also agree that frame stiffness affects little to nothing of the energy used to flex it - you spend the same amount of energy moving the BB shell less distance. Your energy is wasted (or stored, whichever) as soon as your leg pushes the BB shell sideways. How far it moves per unit energy is irrelevant.

Originally Posted by rpenmanparker (Post 15868809)

Yowza! I'm thinking for a flexy frame to slow down a rider, it would have to be so whippy as to disconcert the rider and cause him to not be able to pedal efficiently. I don't think we are talking about those kinds of bikes in this discussion.

Originally Posted by Bah Humbug (Post 15868823)

Uh, did I say it affected the rider? Or were you just emphatically agreeing?

Originally Posted by Campag4life (Post 15868683)

I disagree with your thesis. If you are speaking of rocking the bike aka pendulous motion of crank axial center side to side...this is biomechanically more efficient to power the bike using the upper body as leverage. 'All' vectors of pedal force including all non-normal pedal force applied to crank arms translates to rotation energy of the crank which is co-planar to the rear drive wheel. There is no non-productive pedal force.

Originally Posted by wphamilton (Post 15868844)

Except perhaps that which produces flex in the frame. Which is the question, isn't it?

Originally Posted by rpenmanparker (Post 15868860)

Well played! That is what I was trying to emphasize to C4L just not so succinctly. If you admit the BB is rocking (just one example, unfortunately), how can you say energy is not being wasted? The BB isn't a perpetual motion machine. And its rocking isn't ever going to translate into forward motion of the bike. QED

Originally Posted by rpenmanparker (Post 15868584)

Whether the frame is stiff or flexible, the rider will exert the same amount of force in non-productive directions. A stiff frame will move a little in response to these forces, a flexible frame will move a lot. But the wasted force will be the same, just with two different magnitude results in frame flexing. Once the force is exerted in non-productive directions, it doesn't matter whether it is recovered or not, it never gets channeled in a productive direction. It may be easier to pedal a stiff frame because it is not moving all over the place, but I doubt that a certain amount of pedaling force exerted by a human rider, i.e. not perfectly directed in circular motion, will make any difference on the two types of frames. The fact that the crank arms necessarily push the BB from side to side (as the are not centered on the BB, of course) is paramount. Force pushing the BB from side to side is the same whether the frame is flexy or stiff. It is just the amount of movement (strain) in response to the force (stress) that is different.

Originally Posted by laserfj (Post 15868880)

Correct.

I wonder if the increased flex would lead to more inefficiencies (ie larger % of force being non-productive).

Other than that, you have successfully answered the question. Now the question is how much more arguing will still follow...

Originally Posted by laserfj (Post 15868880)

I wonder if the increased flex would lead to more inefficiencies (ie larger % of force being non-productive).

Originally Posted by laserfj (Post 15868880)

I wonder if the increased flex would lead to more inefficiencies (ie larger % of force being non-productive).

Originally Posted by rpenmanparker (Post 15868899)

That's what I was discussing in another reply. The flex would have to be so extreme, it seems to me, that it interfered with the rider's ability to pedal efficiently. That level of flex is not characteristic of any modern racing bike. Heck, if Sean Kelly could sprint on a Vitus noodle, I don't suppose that level of flex even exists.

Originally Posted by rpenmanparker (Post 15868753)

Interesting, but here is the problem, as I think I have said elsewhere earlier: You can't put energy back into the leg muscles. Since the leg is the only driver of rotational motion, it stands to reason that you can't put the frame flex energy back anywhere that will drive the bike forward. I don't know where it goes, and I don't think it matters. It for sure doesn't go back into the legs in a usable form for propulsion. Hence, it is wasted.

Originally Posted by Pedaleur (Post 15868692)

Of course, if you measure work at the leg, then there is lots of wasted energy. Any force that is not tangential to the pedal motion will be "wasted": no work is being done at the pedal, but the leg is undergoing physiological loss.

Originally Posted by Bah Humbug (Post 15868873)

And more to the point, I can put the bike on the trainer, grab the rear brakes, stand on the pedals, and rock them back and forth. Pretty sure that's not putting anything into the trainer unit (chain not moving), but I'd get tired eventually. Wasted energy. Same amount on a flexy steel bike vs a carbon wunderbike, if I rock the pedals equally hard. Still not doing anything useful.

Originally Posted by Pedaleur (Post 15868907)

...