Generally speaking but don't forget you've got a hooks law thing going on. .half K xsquared. But two questions, is distance in your equation only the flex of the frame, or a displacement of the point of contact? Two different things, and why are you holding force as a constant and not say, some function of power? There are a lot of potential differences between the two situations. The direction of the force vector relative to the frame is one. I don't think this problem simplifies that easily - I think that simplifying assumptions in this case may introduce error ranges that swamp the results.

Priceless. :roflmao: :roflmao:

I don't think the recovery crowd is realizing that the spring-like return of energy is not re-entering the system in such a way as to power the bicycle. The "bucket" experiment is a farce. When the force on the spring is relieved in real life, the crank is no longer in position to receive the energy return in a way that turns it forward. Pressure on one side of the BB for example isn't relieved until the crank on that side is "past 6:00". At that point the upward motion of the BB is not pushing the crank forward relative to the pedals but backward. No damn good. I think the losses may be small, and want to some data to show that, but I surely don't think they are small because energy is recovered.

Except (in theory) it is. When the spring returns, it pushes the leg up a small amount, which reduces the amount of force required to lift the leg on the upstroke, which means more force in the pedaling mechanism winds up going to the drivetrain.

And yet again, actual evidence is required in order to figure out what is actually going on.

Follow my reasoning. The BB is at one end of a torque arm, and the pedal is at the other. When the BB rises while the pedal is past 6:00, it actually causes the pedal to have further to move. Relative to the BB the pedal goes down or backwards. The leg is not attached to the bottom bracket but to the pedal which is at the other end of the arm. Yes, need data. We still agree on that.

No, it causes the BB to push back, which pushes the rising leg up.


And the leg is getting pushed up. The returned energy is not going directly to the drivetrain, it is saving your leg a small amount of energy during the pedal stroke. It's an indirect benefit, but a benefit nonetheless.

Here's a much more detailed explication of the theory. http://www.bikethink.com/bicycle-frame-efficiency/

I understand your opinion, but I don't get it. The freewheeling effect makes the leg essentially disconnected from the BB. The BB goes up, but 170-180mm away at the other end of the crank, the foot has no impetus to rise in response. The freewheel just turns backwards instead (in a relative sense), and that involves almost no force. Of course if the foot is coming around, the freewheel doesn't really turn backward, but in a relative sense that is what is happening. I've seen the article you referenced, but the foot is not on the spring as in the discussion! It is at the other end of the crank arm. That is the whole difference. That is why the energy doesn't go back into the leg or the drive train in a way to produce forward motion of the bike. Diagram it. Foot/pedal at 9:00. BB at the center of the clock face but depressed a little. Now bring the BB back up to the center of the circle. If the connection between the pedal, crank and BB spindle were rigid, the foot would rise along with the BB. But the crank can travel backwards with almost no force applied. So the foot doesn't rise. Does anybody see this?

Here is another thing to consider, another viewpoint. Supposing the vertical down force (and deflection of the BB) is completely unloaded at the instant the crank passes 6:00. At that point the crank is a rigid member in the vertical direction and the instantaneous rise of the BB would, indeed be accompanied by an instantaneous rise of the pedal and consequently the leg. BUT at that point the majority of the pedaling force is tangent to the bottom of the crank circle and the effective motion of the foot is rearward. So the rise in the leg has no effect on the force needed to turn the crank. Of course non of this is so simple. But I think a detailed examination of the motions and forces would show that whenever the BB "spring" is unloading and rising, it is because the direction of motion of the foot and pedal is becoming more horizontal. The more vertical load released by the BB, the less the leg can use it.

Just a few more posts to make it to 9 pages. I am so, so proud of y'all....

The stiffness that bike frame manufacturers are trying to maximize is the LATERAL stiffness, not the vertical stiffness.

The Roubiax/Domane bikes have low vertical stiffness thanks to lossy dampers in the seat stays. If vertical stiffness mattered those bikes would be staggering slow. They aren't.

The stiffness in question is the left/right motion of the BB. This motion generate zero useful work, but it also doesn't consume a whole lot of energy. Consider this, you push hard on the right pedal, the BB moves left, but then when you push the left pedal, you're counter-acting the motion. Really what you're looking at is a driven-mass-spring system. As long as you don't hit some oscillation condition, you essential wind up with a small amount stored in the BB "spring". A stiffer spring reduces the stored energy, so it helps. The trick is that the losses start to get insignificant compared to drivetrain losses, and so beyond a certain point, stiffer doesn't really matter.

I read the website. Not impressed. He does static FEA to quantify the stress and strain, which is all well and good, then he asserts the conclusion without relying on data at all. He does got a cool animation of a simplified system.

I think the BB motion is more complex than that. It isn't purely vertical or lateral but rather a rocking motion from the alternating stresses on the two sides of the crank/BB spindle. The BB doesn't move left and right, but rather down on the left and up on the right, then vice-versa.

Sorry, but since you're at this thing. What is your thoughts about Calfee's new Manta?

Your reasoning is based on the assumption that any potential return of energy from the frame 'spring' happens after the pedal reaches the bottom of its travel (i.e. 'past 6:00'). But that's not the case. Let's consider the forces when the rider starts a pedal stroke with the right pedal. As the pedal goes past the center position the rider's foot starts to push down on it resulting in the primary action of turning the crank but also losing some energy by twisting the bottom bracket area of the frame toward the left (i.e. during this part of the pedal stroke the pedal moves a bit farther for a given rotation of the crank than it would if the frame were perfectly rigid). As the pedal motion continues the downward pedal force increases, probably reaching a maximum around the 3 o'clock position, so the bottom bracket also reaches its maximum deflection to the left at that point. Now the downward force on the pedal starts to diminish so the bottom bracket starts to spring back. This spring back has the effect that as the rider's right foot goes down farther in the pedal stroke the crank actually turns a little more than it would otherwise, so at least some of the crank motion lost earlier is now recovered. By the time the pedal reaches the bottom of the rotation (6 o'clock) the rider is no longer pushing harder with his right foot than with his left and the bottom bracket has returned to the neutral position - all of the spring motion has now been restored.

If the frame acts as a perfect spring then all the energy that went into deflecting the bottom bracket to the left that happened between the 12 and 3 o'clock pedal positions would be recovered between the 3 and 6 o'clock positions. But if some of the energy gets coverted to heating up the metal of the frame then there will be some energy loss compared to a perfectly rigid frame.

Its effectively the same as a Roubiax/Domane.

I think it will be quite different from those two, even though Craig mentioned those bikes in the context of flex/suspension bikes.
But this bike will even more so, be affected (when you pedal,... powerloss?) due to the suspension.

1) Why on Earth would you make that assumption?
2) It doesn't really change anything.

What you're missing is that when the BB deforms, it also tilts; i.e. the leg drops a little more. Pushing the BB back essentially lifts up the BB slightly, which in turn lifts the leg and/or shortens the distance of the upstroke.

It doesn't matter that the direction of travel of the BB is not a forward motion, nor is there any such claim. Again, what happens is as the spring action kicks in, the leg is lifted. Otherwise, you would have to use slightly more energy from the action of pedaling to lift your leg. It's an indirect benefit.

As I follow these discussions I get the feeling something is wrong. For instance, isn't the upstroke distance relative to the rotation axis twice the crank length regardless of what happens to the bottom bracket? In a non-accelerating reference frame fixed to the bottom bracket (just moving up or down) your foot wouldn't see a difference regardless of the speed. On the other hand if the bottom bracket is accelerating up during your upstroke (lifting your leg) it would make your leg feel heavier, not lighter.

The frame spring relaxes when the pressure eases, generally somewhere on the downstroke. Perpendicular pressure that is - if you're tilting the bike sprinting it changes the picture. So is the theory that all of the energy is returned on the upstroke or the downstroke? How have we ruled out that the energy isn't returned as increased in muscular tension in the leg? And if so, might there be a pre-load benefit as is sometimes the case in athletics?

As I get older I am more loathe to put a pen and pencil to this kind of question, but I think writing out some equations is going to be the only way to get anywhere. Or maybe a computer simulation. Why don't you young-uns with some time get rigorous with it, let's see some solid work.

Right on the money. Second law of thermodynamics. Best way to mitigate power loss is minimize frame displacement aka elastic strain to begin with ergo a stiffer frame. Flex portends energy loss. No such thing as 100% efficient restitution.

To me the no data comment...sorry Robert...is misguided. There is also the conflation of vertical and lateral stiffness. There is obviously a relationship between the two. This came up in a recent discussion about the SL4 Roubaix which is said to have the same vertical stiffness of the SL3 but has greater lateral stiffness. As a result the SL4 Roubaix takes big hits harder than the SL3...but the SL4 feels more lively aka there is more direct power transfer...Specialized made the rear triangle stiffer. When the SL3 Tarmac came out..pros loved the bike but if any criticism was levied...it was the bike felt too stiff. So, Specialized worked their technical magic again with the Tarmac SL4 and softened vertical flex and made the bike even stiffer laterally.

Robert, if there is middle ground on this issue between you and me, I believe we both agree about diminishing return. I side with Giant's thesis that past a given point, more stiffness doesn't matter...at least for the average weekend warrior. In fact, it may make the bike less livable. But here is the point. Stiffness is rider specific. Indeed bike stiffness doesn't change frame to frame for a given model...or much due to production variation...but rider strength can vary a lot. A guy like Boonen can flex an uber stiff frame in a sprint where a top amateur can't get it to flex .1mm. So the rider matters. Robert, you are a light guy and likely not a power house. So indeed your Ti frame maybe plenty stiff for guys like you and me and if we don't flex it much during full effort therefore a stiffer frame doesn't manifest more speed...diminishing return. And of course the unquantifiable metric in the equation of stiffness is comfort. This is hard to put a no. to. Robert where is the data on comfort?...lol...and yet most believe a Roubaix with more laid out angles and friendlier flex is more comfortable than a Venge.

As to why manufacturer's don't post data...I have to laugh as an engineer developing products for over two decades. Average public would only misinterpret the data and use it as the wrong reason to buy a given frame...or a discriminator to discard a given frame. Force/displacement? What layperson understands this correlation relative to their particular power output? None I know of. Most that ride bikes don't know their max power output. Also frame stiffness can't be measured by the public to verify. Either can the metric called 'comfort'. Further, manufacturers would lie about stiffness nos. as a basis to sell more product..competitive advantage like some do about weight...and the same reason many makers resist even publishing weight nos. But would stiffness nos. really sell more product? An argument could be made that many would shy away from an uber stiff frame because of fear it would be bone jarring. And then there is product diversity. Posting metrics would expose just how similar frame models are. Take my bike...a Roubaix SL3 Pro...best bike I have ever owned or ridden...for 'me'. Compare this to the top of line SL3 Sworks. Same carbon mold. On more tick of flex mod for the carbon used...11R versus 10R...allowing for slightly less carbon..reducing gram weight by less than a handful. Most believe the $1K price difference for undetectable performance advantage to be fool's gold. Publishing stiffness nos. would expose the truth aka myth that a Sworks bike is worth $1K more.

Lastly...the status quo argument. Why do manufacturers make custom stiff frames for 2000w riders like Thor and Boonen...and incur this tremendous cost. Because frame deflection is much greater with these riders under full power. It has obviously been exposed in testing that 2000w guys which are a freak of nature need a stiffer frame to reduce flex. Also...status quo is a 'work in progress'. What has happened over the last 20 years in bike frames? The status quo has morphed. It has changed into a new paradigm aka status quo toward stiffer. Why? Technology continues to evolve. It has obviously been demonstrated by countless testing of pro teams, riders and engineers that more stiffness manifests more efficient energy transfer. Technology has allowed the absolute lightest stiffest frames to be produced with tremendous yield strength and fatigue life which permit exploitation of both low weight and high stiffness. Twenty years ago this combination wasn't possible with the technology of that time period.

To me there is a sweet spot relative to frame stiffness btw. I don't race bikes for a living. But I want a stiff bike I know gives me an advantage when competing with my friends. I don't want to ride a century on a Foil or a Venge for example. These frame feel too stiff to me...not unlike the calls for change when the Tarmac SL3 came out...to soften its vertical flex a bit...which Specialized engineers responded with.

I don't think anyone has argued that there's no energy loss - the questions are how much, and how much if any is recovered, and what are the bio-mechanical implications?

Most people will agree that to some point lateral stiffness is preferable, but that doesn't really answer the questions beyond a marketing perspective. You mentioned that it's rider specific. There's a sweet spot for your preference. I think you must be correct, and yet I wonder how much of the rider-specific preference is based on perception without necessarily a quantifiable gain.

Yeah, hate to admit it, but for pedaling perfect circles, you are mostly right. There is still the complication of the twist in the crank arm when it is at positions between 12:00 and 6:00. Because of that the down force on the BB may not exactly maximize at 3:00. And the whole other situation of imperfect pedaling. I suspect the common force "circle" looks nothing like tangent at every point on the circle. I bet most folks push almost purely forward to 3:00 and then nearly purely down to 6:00. I suspect the components in the horizontal and vertical directions don't look much like sine waves at all. Then there is the situation of out-of-the-saddle sprinting with the whole body weight bouncing up and down which is kind of what I was thinking of when I said the down force maximized at 6:00. But setting all that aside, you are right for the perfectly angular force situation. Whether the returning "springs" help at all, I just don't know. Thanks for setting me straight.

I don't think I've set anyone straight, just venting my confusion. As you say, it's more complicated than that.

For what it's worth, my intuition is that internal friction/heat losses due to the spring action will turn out to be insignificant, and that only a fraction of the power used to deform the frame laterally can be subsequently utilized to propel the bike forward, but that the losses in a moderately stiff frame will turn out to be objectively inconsequential.

C4L, thanks for the extensive analysis. I don't disagree with much of what you wrote. For the world we live in (is that status quo?) what you say is largely correct. Here is the difference between us: I just want to know because I am curious about those things. It doesn't matter to me (at this point) how it will translate into new products or whatever. I just would like to know. The numbers mean a lot to me for shaping my understanding of the world. I am not saying the pros are wrong about needing stiffer frames, just that I would like to know exactly how right they are. I suppose I am still generating research ideas like when gainfully employed. I'm used to being able to go to the lab and answer a question. Just frustrated about that no longer being the case, I suppose.

RIDE magazine did old school/new school bike comparison several years ago using powermeters on several models of 80's steel race bikes and new carbon bikes.

As I expected, adjusted for weight it took more watts for the older more flexible frames and wheels to climb the same course (by a fairly big percentage). It was also worth noting that the average descent took a LOT more time. Sprinting was impacted. They didn't start breaking it down into components, because they really didn't need to. So yes, there's data out there.

There's plenty of data out there about aerodynamics and drag.

Any decent engineer can explain energy transfer and any physics student knows energy in cannot equal energy out. Flex uses energy. So does drag. The End.

What gets missed is the human component and how fatigue affects watts over duration. That's also a given for anybody with a rudimentary understanding of physiology...more fatigue, less watts.

Horses for courses. No one is going to ride RAAM on a Fuji SST and track sprinters aren't going to win much on a Litespeed Ghisallo.

Unless you're racing or doing a lot of high speed cornering, or are a fat ass, stiffness isn't a big concern.

If marketing BS gets your panties in a giant bunch you should leave civilization as we know it and become a hermit in some forest, because marketing pervades everything down to the makeup people's wives put on and the Rogaine most of the 41 uses.

Cool. I enjoy sharing perspective with others here with a scientific background.
Was just providing my opinion on why the data isn't available to the public...part marketing I believe and also intellectual property as mentioned.

We can have a whole another conversation about data and even the philosophical construct of 'perception'. Take words. What we use to communicate. They are but an imperfect metaphor for describing reality which is the truth...which you use as a metaphor for data. But data isn't the truth. Because data is an imperfect analog of reality. Yes it is used and to some degree with consequence...but there is test set up and measurement error and also the indices or metrics of measurement itself. Much of data taken is immaterial or not relevant or can be recorded incorrectly and lastly and most importantly, vastly misunderstood by the public to linkage with their experience.