Once a certain level of stiffness has been achieved, additional stiffness will not change the performance.

I believe the OP is also saying this about bicycles.

It wasn't really a request. I was trying to be nice.

I can make it all disappear if I want.

Or do I have to make it bold like this: MODERATORS NOTE, PLEASE DO NOT LOWER YOURSELF TO THE OBVIOUS SUGGESTIVE HUMOR.

OK, so Robin Williams' First Law of Comedy has been fully honored in the thread, but I was completely serious and not trying to generate jokes.

When we pedal, there is some displacement of the centerline of the bottom bracket relative to the centerline of the bicycle. Obviously, making that displacement happen requires an input of force. The real question is, is that force lost, to any degree that matters? The answer to that question is, so far as anyone who's ever tried to measure it has been able to determine, no.

It turns out that things like frames, crankarms, stems, seatposts, handlebars, etc are very,very efficient springs. Which makes perfect sense... they're mostly made of metal, they have few if any moving parts, and there's not a damper anywhere to be found. Metals have vanishingly low internal losses, things that don't move don't generate friction, and there's not a part whose job it is to convert force into heat, so how can the pedalling force be lost? Where's it gonna go?

It's going to be returned into the system, because we're talking about undamped springs, and that's what springs do.

Where and when is it going top be returned to the system?

This is a more interesting question. Springs release their stored energy when the force compressing them (energy being put into the spring) is less than the force the spring is exerting on whatever is loading it.

Now think about pedal loads as a function of crankarm angle. They're increasing between roughly 1:30 and 4:30, peaking at the end of the downstroke. The rest of the circle, they're not very large at all, because almost nobody pulls up in the back half of the stroke, and even those who do don't do it very hard, so not much force is being applied.

But, wait... bicycles have two crankarms and pedals, because most bicyclists have two legs. That probably matters a lot, no? So, our right pedal is at 5:00 or so, the force on that pedal is falling very quickly, (it'll be almost zero by 7:00,)
the bottom bracket area and crankarm are at their maximum leftward deflection, and there's some energy stored in that deflection. What happens next? The left crankarm is at 11:30, and the force on it is just starting to increase from its minimum. So we have a double null in the force input by the rider... the legs aren't adding much energy into the system. So, the energy stored in the leftward deflection of the crank area becomes, for a brief, glorious moment, the largest force in the drivetrain. And what it wants to do is to drive the deflection to zero. And, since it's displaced to the left, that means moving things rightward. Which is exactly what the rider's left leg is going to start doing when the left foot gets to 1:30 and the left leg becomes the dominant factor in the system.

Basically, the bicycle returns almost all of the energy stored in its flex by the first pedal stroke on all subsequent pedal strokes, minus some very-small-but-not-zero amount that gets converted to heat because TANSTAAFL. In other words, your legs only pay the full cost of distorting the bicycle once. After the first stroke, the bicycle itself helps you to deflect it, so you don't have to.

And that's why stiffness is not a factor in bicycle performance.

--Shannon

PS: I'm pretty sure this is most of what Jan Heine and the BQ crew are talking about when they talk about "planing." They go farther than I'm comfortable with in saying that bicycle flex is a net positive for performance... although they do have some data to back that claim up, and they show their work. All I'm confident in saying is that it isn't a net negative.

As with many things in the cycling world we tend to see small differences and represent them as life altering.

Yes, the only loss in energy with the frame flexing back and forth is from elastic hysteresis, which is very low for metals and carbon, compared to say an elastomer, where hysteresis can be quite significant.

It is a very small energy loss in absolute terms, never mind trying to compare the delta loss between two bike frames of slightly different stiffness. You would be pissing in the wind attempting to measure it!

There is a lot of BS talked about frame stiffness vs power transmission. At the end of the day if you put out 500W at the pedals, you will measure approximately 96-97% of that power at the rear hub due to drivetrain losses. So let’s say 480W at the rear hub. So how much of that 20W loss is likely due to frame flexing hysteresis? Let’s say for arguments sake it was as much as 5W. So if we then doubled the frame stiffness we might save 2.5W at a 500W output.

Frame stiffness is important, but not for raw power transmission. This idea of a stiffer frame transmitting more power to the wheel doesn’t really stack up with the physics.

I’m totally with you on the energy loss in frame flexing being negligible. But there is a LOT more to bicycle performance than mere power transmission. Stiffness affects handling characteristics profoundly and therefore bicycle performance as a whole.

Springy stuff does not dissipate energy. Squishy stuff does. Your bike is made of springy stuff. Your jiggling corpus, the air you are swimming in, and any oil you brought along to squeeze through some valves in a shock absorber are squishy. Stiffness changes the distance the springy parts flex and how fast. The squishy parts make the springy parts stop flexing.

Science!

I think the human factor of getting the response immediately is significant in the racing/marginal gains world. A stiff frame will be an advantage in a race where tactical acceleration is in play (i.e. not a time trial).

My only thought to add to the pile is Sean Kelly didn't seem to be hampered on his old twist -o -flex Vitus. I thought mine was down right scary in a sprint. My second worst bike I had the builder "Make it as stiff as possible". I was a big guy (165 lbs) at the time. It was fun to ride for about an hour on a smooth crit course. An hour on a bumpy road was more than plenty and I just wanted off. So my final answer is yes and no. Horses for courses.

We may need more.

Since you know so much about this, maybe you can tell us the time required for the bottom bracket to naturally return to it's unstressed position and the damping time for side-to-side motion of a bottom bracket. In other words, what are the resonant frequency and Q factors for side-to-side motion of a typical bottom bracket?

Looking up stuff to copy and paste.

I know someone who had his students do a survey of the resonant frequency of bike frames. They never found one that had a resonance less than 10Hz. They don't resonate much at all when fully assembled. Putting the wheels in eliminates the lower resonant frequencies. The motion is dominated by the static loading, not any kind of vibration phenomenon. I have never quite understood how the deflection of the bb would store energy that would be dissipated by moving the chain in a productive way. But then again, it probably can't take that much energy to get it into the deflected position in the first place. So you can't expect to get anything out of it.

I have seen a slow motion video of fork deflection when someone did a bunny hop. It was scary as all get out. I think the fork did a couple of heavily damped cycles and then stopped.

I think the main thing that changed as frames got stiffer was less problems with chains rubbing on front derailleurs.

I don't know, and I'm not aware of any measurements that have been done.

Intuitively, I'd think that the ~3 Hz input from the rider's legs would dominate, but I don't know if that's true. I can't imagine how it would matter... how is the frequency domain behavior of the frame supposed to generate significant losses that would vary directly with frame stiffness?

With apologies to the guys at Singer Porsche, everything does not matter.

--Shannon

Give us an estimate then.

Around 500 Hz for a 1" diameter thin-walled tube around 22-24" long, according to the people who make wind chimes. Q would be quite narrow, or tubular bells couldn't work.

As this is almost 200 times the pedaling frequency, it would seem to be irrelevant to the discussion.

Why do you think it matters?

--Shannon

An empty tube is a horrible model for the side-to-side motion of a bottom bracket. Not even close.

Sorry, I thought you were asking about the steel itself. Mea Culpa, my bad, whatever.

And you still haven't answered the question of why this number that you're demanding is relevant to the question at hand. Do you think there is some frequency domain mechanism at work that would make "flex wastes energy" a true statement? Like, what... phase cancellation? Resonant heating, like a 3 Hz microwave? Harmonic distortion in the rider's 5th chakra?

In other words, do you actually have a point to make at all?

--Shannon

You made a broad statement about frame losses that directly involve the side-to-side motion of the bottom bracket. If you can't even provide rough estimates for the parameters that determine the motion of the bottom bracket, you have no hope of describing the dynamics of the bike+rider system.

The poster also isn’t introducing something novel

The soft aluminium Duralinox fork actually suited the punishing parcours of Paris-Roubaix and the whippiness of the main triangle may have even complemented Kelly’s smooth pedalling style: he won races on the Vitus 979 right up until his second and final Milan-San Remo victory in 1992.

https://www.cyclingweekly.com/news/l...tus-979-194179

If I need a bit more suspension, I can just put 5 psi less in the tires, it seems like the most logical place to have, well, flex.

The power losses may be negligible, but you just couldn't argue in favour of "more frame flex".In the modern days of CF goodness you can have a nice, stiff bike which is also light and aero (and good looking to boot), and which feels really solid when you're descending at speed.

See post 13

Stiffness Does Not Matter

I love it when people use principles of physics and engineering .... without any experimental data.

Great that you have studied science .... might I suggest that we review Bacon's scientific method? Until you have done experiments and observed the outcomes, and checked whether your results support your hypothesis .... this is all just, to use the precise scientific term, "used food."

Some interesting comments so far. Some not so. One thing I know for certain from personal experience, frame flex is overplayed as a way to sell. Two guys in the local race circuit that were amazingly fast and won crits all the time, along with mountain bike races, were on Sling Shots. If any of you have ridden one of these creatures it is at first scary, but when your body and mind acclimate to it, all is well. These flexible fliers performed quite well under the legs of two seriously powerful riders and never seemed to hinder their performance.
Eventually they took their Sling Shots to national level races and found another level of talent out there, but they still faired well considering they had zero altitude living in their lives. Flat landers that rode frames designed to flex an inch or more laterally as well as vertically. It worked for them!