Frame stiffness and efficiency

Since the other thread has become a trainwreck, let’s start anew.

I’m going to assume you’ve read the first 10 posts of that thread and not bothered with the next 50.

To me the interesting part of the discussion was where people started talking about possible mechanisms for energy return and the effect of hysteresis.

My two cents on this topic is that the width of the hysteresis loop (and thus the energy lost) is not the same for different materials nor for different speeds of loop. Metals have very low damping (loss factor of the order of 10^-4) while composites are higher (depending on matrix, fibre and layup but generally 10^-3 and up) so there is about ten times as much energy lost from a composite under flex.

I trace the trend towards stiffer bikes from when Gary Klein developed his large tube aluminium bikes about 40 years ago but it really got going when carbon took over the racing world. It may well be that this is a response to the higher damping of carbon composites: since the energy lost is so much greater, it makes sense to limit the excursion.

I also note that most references to bikes that appear to work with the rider (aka planing) are to metal bikes, specifically steel.


But the width of that hysteresis loop isn’t the whole story, right? Stiffer frames will flex less. Then there’s the question of whether or not restoring forces in the frame act in phase with a cyclist’s power cycle.

IMHO, I think the most important question is whether or not it even matters. I haven’t seen any data that quantifies energy lost due to said hysteresis, but my inclination is to think it’s not a lot and may be insignificant. Racing history is replete with racers who’ve won on noodly frames.

I think where frame stiffness does matter is in how a bike corners, descends, and maintains a line, but I’m happy to be proven wrong.

Perhaps the biggest effect that frame stiffness has on performance is a psychological one.


the frame stiffness thread is over there. matter of fact, I’m headed there right now.

I think you get the point although your reasoning is a bit different. The area (not width) of the hysteresis loop is detemined by frame stiffness and imput force.
Tel (total energy lost) = Al (area of loop) * Df (damping factor)*

In a noodly bike Al is high. If the materia of choice has a high Df you design around this by making a stiffer frame. That way Tel stays low.

This is of course important, but for now a different topic.

*Totally not the proper engineering terms.

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You’ve lost me here. Admittedly my engineering course was a long time ago but if I recall correctly the length of the curve corresponds to excursion along the stress / strain curve of the material on the load path and the width between the curves corresponds to the difference in strain on the return path.

Since stress is force times unit area and strain is length per unit length, the area inside the curve is the energy lost per unit volume.

The damping factor is the area inside the hysteresis curve divided by the area under the loading curve.

I think so too, the bike I mentioned in the other thread was intended to test this idea but yeah, that’s a topic for yet another thread

The wiki explains it probably better than I did.
Damping capacity - Wikipedia

It might actually be that I mixed some stuff up, was writing this in the train. Main point: energy loss through high damping factor can be mitigated by stiffer frame.

The wiki article explains it very badly so it is perhaps no wonder that you mixed this up.

Once you decode the article you will see that it confirms what I wrote. Your equation should read
total energy lost = damping factor * the area under the loading curve.

Since the damping factor is the ratio of the energy inside the loop to the energy under the loading curve, this is the same as saying that the energy lost is the area inside the loop.

I did address that in my first post but here’s a follow up thought: I cannot see that the difference in stiffness will ever make up for the difference in hysteresis.

Carbon composite has about ten times the damping factor of metals where the ratio of stiffnesses of the frames will be much less than that. Even if the area under the loading curve is halved for a carbon frame it is still losing five times as much energy.

Is your conclusion then that carbon frames can hardly be made comfortable unless you are willing to lose a lot of rider induced energy?

Or is it rather that you cannot make carbon chainstays compliant (for f.i. comfort reasons) without losing too much energy generated by the rider? And should comfort oriented compliance in carbon frames then be focussed on seat tube compliance?

But to get back to the chainstays: what about flex stays (something Cannondale promoted a lot)? A lot of race MTB’s use flex stays. Mainly because you have less pivot hardware, and thus less weight. Is the rider energy loss in such cases then more than offset by weight loss and increased grip to justify flex stays, you think?

In the above post, I wanted to refer to the Domane when talking about seat tube compliance. But look at what Specialized has now done to the Diverge: 2023 Specialized Diverge STR review: Absurdly comfy, but also heavy and pricey - CyclingTips

My conclusion is that hysteretic losses are not likely to be important: if they were, carbon frames would lose more energy than metal ones in all reasonable values of stiffness.

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Well, if the frame is so stiff that there is no deflection, there will of course not be any energy loss.

It is only recently that compliance is seen as something useful. Before that happened the race was on to make things 200% stiffer with each generation.

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I think you mentioned it on the original thread before it derailed. People are confused with the “losses” and run comparisons with pole-vault that you bend and restore energy… if you are able to bend it (then the "if too stiff…). This comparison is wrong cause in the pole case, you accumulate energy in the same plane you want to be pushed. On a bike the flex is latera,l on a perpendicular plane to the one we want energy to be used. in other words, I could flex a frame purely left to right all day long and release this “stored-energy” and the bike won’t move an inch, but I did spend muscular energy to store it.
In summary the frame stiffness it’s not a matter of loss inside the metal/carbon but how it interacts from the biomechanics of the pedaling gesture.

This article and video demonstrate that the lateral flex is not independent of the drivetrain though: Frame Flex - GCN Tech – The Bicycle Academy

The best way to introduce flex into the system is pneumatic tires.

The second best is making it vertically compliant (but not torsionally or laterally) which you can do with carbon but can’t really do with metals. So, seatpost which can flex up and down, CF handlebars which can flex a bit for the front end.

In places where road maintainence isn’t a dirty word, a 25mm tire at a reasonable pressure and a reasonably engineered CF frame is pretty comfortable. I have a modern steel gravel / cross bike and it’s a pretty stiff ride, too.

Sure, take it on gravel or cobbles and you want more suspension (hence the diverge and other attempts), but even on light gravel a CF road race bike with wider tires is absolutely workable, as we saw in the championships which were admittedly light on the terrain tackled.

I’ve ridden a Specialized Ruby with the front suspension and while it’s superfluous for most riding, on the <1% of messed up surfaces it works well without robbing the rider of measurable power.


The example in the video is a clear illustration of largely missing the point. The fact that a frame builder misses it, bothers me.
From a mechanical standpoint what they did is not at all how the pedal stroke works. They release the lateral deformation when the pedal is still in the 3 o’clock position. We create the lateral deformation during the downstroke and it’s released at the end, when the pedals gets closer to the vertical and has no real contribution to forward movement.
From an efficiency point of view, you want the frame not to store energy during the most efficient part of the cycle, when the pedal is between 1:30 and 4:30, (that is also where you tilt your bike left and right when out of the saddle and accentuate the lateral flex).

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I don’t have a mechanical engineering background, just trying to understand things and have more questions.

Deflection would be proportional to torque, right? If peak torque is at 3 o clock, as soon as pedal stroke continues and torque drops, would deflection begin to return to normal and return energy to the drivetrain? It doesn’t get all saved up and released at once, it would get progressively returned as torque drops off through the stroke?

You are right, the energy is not released at once but released when the force drops, that happen to be coupled with the lower efficiency pedaling phase. The energy is stored 90deg (left-right) away from the one used to propel you (up-down to make it simple), so not very efficient (then the erroneous comparisons on vault-poles or trampolines that I read about in another thread where the energy is stored in the direction you want to go).

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But it’s not really a pure left/right deflection, is it? Everything is twisting during deflection and untwisting when torque starts to drop off.

It’d be fun test to have power meters in both the hub and the crank/pedals and compare the curves for the total work. If energy is all lost the shape of the curve would be the same with some loss in the hub. If returned, the shape would be different but area under the curve the same. Curious how the effect may be different for differences in pedal style and intensity (e.g., Z2 vs sprint).