what about crank arm flex? and wheel flex? those could be parts of the flex equation also.

Wheel flex definitely. I've got a set of ksyrium elite's that just haven't been "right" since a guy stuck a foot in them during a crit last year, and they now flex quite a bit and I lose a lot of power. I had a set of custom wheels built up for myself for Christmas and the difference is night and day.

The only way you lose power to wheel flex is if they flex into the brake pads. Torque flex from pedaling action will result in no loss at all -- well I guess it would in the CF-spoked wheels, but it's going to be so small that it's not even worth the pixels it takes to mention it.

Crankarm, seatpost, and handle bar flex are all also going to return any flex to the system. No losses.

Faster in an actual race? I would think so because of cornering. Also, wouldn't flexing metal parts (rims/frame) lose at least SOME energy due to heat? There is some friction there, even if it's negligible.

Think of it this way.

If you had to lift a weight using a pulley system twice, once with a super strong chain, the second time with a flexible peice of nylon, you will have a harder time lifting it with the nylon because you "wasting" energy on stretching the nylon.

So yes, stiffer frames are faster. Assuming all things equal you will probably gain a tiny amount of performance. Not noticeable of course.

Next topic.

Waterrockets -- you don't find this to be a satisfactory non-equation-laden response?

I sure don't.

Your analogy was definately not worth bumping a one and a half month old thread. Once the nylon is stretched, the effect should be the same on pulling(it won't continue stretching as you pull). Your analogy would be better if you said there is a weight you are pulling in opposite directions with your hands. Additionally, when a frame flexes in one direction, as it returns it should "give back" to the other direction. Either way these analogies do nothing to prove the topic.

The only time anyone can say "next topic" is when they've built exact same dimensional bikes with greatly varied stiffness qualities and power testing is done at actual riding speeds and conditions.

My thought is we would find stiffness numbers moot.

Any test of anything vs. hr will have too many variables to mean anything unless the frame flex is sapping like 10% of your power.

This only works if the pedal is forward, right? A pedal at 6 oclock will still flex the frame, (but not flex the chain or BB (torsionally) or the crank arm (in the line of the cranks)). When you release it, it won't spin the back wheel. Maybe most of that forward motion is tension on the chain, BB, crank arm and some vertical flexing of the frame? I dunno.

Along these lines, I've heard it said (maybe by you?) that the flex will transfer back into the drivetrain if the frame returns to the '0' position before the flexing pedal reaches 6 0clock. Is this true? Has anyone seen video that would confirm that the frame rebounds by this time (or confirmed it with some other technique)?

Boy, if someone would invent some type of theoretical boundary around the frame... and calculate the work in and work out...

Let me think... let me think...

How did this get bumped?

Hahaha. Maybe if the rider is sweating we can use a Mollier chart.

I gotta start looking at the dates before I start replying to posts.

And if you were a mechanical engineer of genius, one of the worlds greatest bike designers, or an idiot savant who could run a Finite Element Analysis in your head, this would might something.

But you're not, so it doesn't.

Finite Element Analysis says that you're wrong -

https://www.bikethink.com/Frameflex.htm

Keith Bontrager's famous rant on frame flex says that you're wrong (look it up on the Internet Wayback machine - Trek had it pulled when they bought Bontrager) and so does David Kirk, who while not of Bontrager's legendary ability still seems to be pretty competent: https://www.kirkframeworks.com/Flex.htm

Well, yes: as previously stated, reality is not limited by what you think. Mr FEA says that your model is too simplistic.

no no no no no no no no no

heh. The zombie thread.

Lets stop reviving old threads. It's getting old... ha

Hi

Did this test ever materialize, waterrockets? What is the latest on this subject?

As I'm racing an old 531 steel frame now, I do not notice the frame being a limiting factor. It's stiff enough. I've raced carbon and alu and I enjoy steel more. Wondering if I should build the alu Cannondale frame that I have up on the wall but this thread reminded me of the crazy stiffness, I'm going to ride steel at least the rest of the year.

I think frame stiffness is waaay overrated. I know stiff frames feel faster accelerating but that's mostly all it is, a feeling.

I know but I just went through the whole thread and there was no conclusion on the subject! I want a conclusion!

I, for one, think this topic is fascinating. I'm starting to think that neither thesis totally correct or incorrect.

I.

If you follow the back trail through this thread (brings back memories, it does), you'll see mention of the "bucket test", which is basically a test where you put a pedal at 3 o'clock, put a bucket upside down underneath the pedal but not touching. If you stand on that pedal with the brakes engaged, you'll find the pedal will now deflect enough to touch the top of the bucket, and if you release the brakes at this point, you'll find the bike moves forward. A second version of this test is proposed in this thread where you place the pedals at 6 o'clock. Now if you stand on the pedal with the brakes engaged, and release the brakes, you don't get any movement. So, at the 3 o'clock crankarm position, deflecting the pedals results in energy releasing into the drivetrain. At 6 o'clock, it doesn't.

II.

Call a line connecting both hubs of the bike the "x axis", and a line vertical from the bottom bracket the "z axis". I think we can all agree that pedaling forces are primarily downward vectors along the z axis (pulling the pedal leads to almost nothing), and the bottom bracket is most susceptible to flex if the force applied to it is primarily in the downward direction, producing a twist in the bottom bracket around the x axis. One can see this easily on a trainer with a flexy frame.

The frame will store energy much in the way of a spring. Force causes a proportional deflection. Energy is force integrated over a distance, meaning that energy is stored proportional the square of the deflection. Peak energy is stored at peak deflection, and as the force is reduced, the energy will reduce faster. For example, if you reduced the force causing the deflection by 1/2, the deflection will reduce by 1/2, and the energy stored will be reduced to 1/4 of the initial. This means, for all practical purposes, most of the energy transfer in and out of the frame will occur very close to the peak force. Most of the energy will be stored as the force is reaching its peak, and most of the energy will be released just after the force has reached its peak.

I think we can also safely assume that damping in the frame is minimal (the frame doesn't appreciably heat up as you ride), and because there is a very large mass attached to this spring (your body), the frequency of the system will simply be the forcing frequency (your pedaling rpm).

III.

We have two boundary conditions, pedal at 3 o'clock (energy returned to drivetrain) and pedal at 6 o'clock (energy not returned to drivetrain). I think it is safe to assume that there is a continuity between these two points. For example, if the bucket test were done with the pedals at a position halfway between the 3 and 6 o'clock positions, half the energy would be returned to the drivetrain, half will not (in a static system, the energy remains stored; in a dynamic system, the energy goes into raising the mass of the foot/leg/body - since this occurs on the downstroke, the energy is simply lost).

To me, this strongly indicates that for a person with a pedal stroke where max force is applied at the 3 o'clock pedal position, frame flex matters not at all. Energy is returned to the system as soon as it is diverted. The model for this would be moderate to hard steady efforts, seated in the saddle; like a time trial or steady climb.

If, on the other hand, the maximum force is applied near or at the 6 o'clock position, the frame would divert that energy away from the drivetrain and put it into raising the body's gravitational center. The model for this would be pedaling from a standing position or a standing sprint. Depending on how much a person weighs, gearing, and her pedal stroke, the maximum force could well be at the bottom of the pedal stroke. In this case, a flexy frame diverts power from the drivetrain and doesn't give it back. Incidentally, because the CG of the body is raised by the energy release, it makes the bike feel "springy" or "whippy", like you are bouncing on a spring, which lends steel bikes their unique feel.

The conclusion then, is flexy frames demand a smooth pedal stroke where maximum force is applied at or near the 3 o'clock pedal position and will work just fine for most riders. Most of cycling is done seated and at steady effort and a flexible frame does not penalize this. Flexy frames do, however, penalize anything done out of the saddle and where the maximum force is closer to the 6 o'clock position, which means it penalizes riders when they are search for absolute power regardless of efficiency. This makes a flexible frame bad for sport competition.

Stiff frames avoid this power diversion altogether, which is why the sport bike market moves in this direction.

TL;DR: Whether or not the system returns energy to the drivetrain depends on where the peak force is applied in the pedal stroke. if peak force is at the 3 o'clock pedal position (seated, steady pedaling), energy is returned; if peak force is at the 6 o'clock position (standing or choppy pedaling), energy is not returned.

Energy can be stored in the flex or in the potential energy of lift the riders CG higher. The question is whether this stored energy is later returned usefully or dissopated through other mechanisms (damping being one possibility). You can bounce up and down in place on your legs or on a pogo stick and expend a lot of energy without going anywhere. Similarly you can expend a lot of energy accomplishing no useful work lifting weights at the gym or by flexing the springs in a Bowflex. With flex in a bike, some of the stored energy may be returned usefully but some is certainly lost.

In Engineering we accept that a spring when used within its elastic range is 100% efficient. Elastic range means we do not disturb the atomic bonds and there is no permanent deformation. The force to compress a spring is linear to its change in length, meaning all the work as energy going into the spring is stored. It follows that when the force is removed from the spring, it returns all the energy stored as it decompresses.

A frame that deflects due to lack of stiffness, essentially behaves exactly the same as a spring.

In practice, if a cyclist is exerting maximum force on the pedal at say 3 o'clock, the frame will absorb some of that work (energy) as it flexes, it will be lost to going through the chain to the back wheel. As the pedal stroke progresses though, at say somewhere between 5 and 9' O clock, the frame will lose its deflection and return to it's normal unstressed position. When that happens, it returns the work, or energy into the drive train.

Another way to look at this is that even the stiffest frame on the market flexes, even if that flex is only a thousandth of an inch. It means all we have done, is increased the spring rate to a much stiffer spring, but it will still absorb and release the same energy.

The fact that a spring is 100% efficient means there is no energy loss.

There are practical limits though, on one of my old classic noodles, the back wheel loses traction from side to side under a full power sprint, which means energy is lost.

Riding with a flat tire as posted above is different, as we are increasing rolling resistance exponentially and turning it into heat absorbed by the tire. Big energy loss.

In short, fatter tubes save weight by producing the same strength with less material. I can remember way back never getting more than two seasons on a steel frame, before it cracks, somewhere. Do some research and see some folks with their light weight Trek's complaining about cracks. It is the strength that is important.

This is the standard answer but the model it's based on may be too simple to be useful. Or correct in practice.

Return flex from some directions could be transferred to muscle flex for instance. Wasted work.