Fun fact! Very few people believed that the Earth was, in fact, flat. The claim that "people believed in a flat earth" started as anti-Catholic propaganda by Protestants, and it spread further by a few historians in the 19th Century who wanted to split science and religion.

I'm with OP and Bacciagalupe on this, that I'd like to see some objective quantification regarding power transfer and frame stiffness.

I've performed a primitive experiment. Sitting in my chair, I took a length of steel and flexed it down forcefully against my leg. I repeated this procedure numerous times, each time allowing the steel to spring back to its original form. I also held it between my legs, flexing the steel alternately in both directions. I observed that it did involve an expenditure of metabolic energy, and that the energy was not transformed into movement of my chair. I concluded therefore, that there was indeed an energy loss.


On the other hand I've never noticed a perceptible flex in my trusty Nashbar frame, so it doesn't seem to be a burning issue. However, subjective impressions are mostly irrelevant.

Hopefully some smart college kids are reading this thread and choose it for a thesis.
It would be nice to compare old and new frames of varying materials to see how far along the industry has advanced - if at all.

General ramble, and maybe my physics is wrong, but:

I was always annoyed by the spring discussions of a frame, in the argument that it springs back and all force is restored. My annoyance was based on the fact that this is all forces normal (90 deg) to the force that matters. The only force that matters is that which is transferred down the chain, and therefore the force that is perpendicular and in the same plane to the crank radius. So frame movement seemed like wasted force.

I have changed my opinion, in that you put the same force into the frame, regardless of how much the frame deflects. If you break your pedalling forces into force vectors, they have everything to do with your body mechanics and the crank geometry, and little to do with the frame deflection. You put the same non-productive normal force into the frame whether it is noodley or not, and the only difference is how much it moves.

Now if that movement creates interference somewhere, you will lose productive power.

At least that is my current thought.

Jan Heine at Bicycle Quarterly has been talking about this for some time. This is just one page of his blog that sort of gets into it, but there is more. I, unfortunately, don't have the time to look it all up. http://janheine.wordpress.com/2013/0...ws-of-physics/ The comments are interesting too. His magazine also goes much deeper into a phenomenon that he calls "planing" and some reasons why some bikes are just easier to get moving than others.

http://janheine.wordpress.com/2011/0...ame-stiffness/

http://janheine.wordpress.com/2012/0...es-going-soft/

http://janheine.wordpress.com/2011/1...ame-stiffness/

This is from the last link. I think he is taking a fair look at the issue of frame stiffness related to performance. Worth a look.

Data or STFU. There's certainly no definitive answer to the benefits of increased stiffness from observation of real world race results. That is, riders on very stiff frames don't seem to win races much more frequently than riders on less stiff frames. This is in pretty stark contrast to racing a time trial with aerobars vs. "Merckx style" on normal drop handlebars.

There certainly are a myriad of possible mechanisms by which energy might be lost, but that's true in the stiff system as well. A stiff frame could exacerbate other sources of loss, such as flex in the wheels or tires. But we don't know, because the data is thin on the ground. And I for one am not impressed by speculation, especially speculation along the lines of how power loss due to frame flex is "obvious." The repeated discussion of frame stiffness over the years have made it pretty clear that the force vectors and movement of energy through a bicycle frame and drivetrain are, a: not at all simple, and b: not all that well understood by most of us, even the engineers who use their degrees as an excuse for simplistic thinking about complicated systems.

So rather than speculate and wave our hands about saying "well OF COURSE a stiffer frame puts more power on the road,", let's cut to the chase: HOW MUCH power is lost between the bottom bracket and the road due to frame flex? Specialized, Trek, etc. no doubt have the engineering expertise and data to provide a fairly precise answer, at least between, say, a Tarmac SL2 and SL4 or a Madone 7 vs. a Madone 5 or 6. But when people have asked for this data in the past, they have demurred. Why? One suspects it is because the answer is much less impressive, from a marketing standpoint, than "50% stiffer." Remember, these are companies that are happy to trumpet 5 watt gains from an aerodynamically-improved frame element. So it kind of leads one to suspect that any advantages due to greater frame are going to be far less, probably not even in the "marginal gains" range of the Sky team. Not 5 watts. Probably not 1 watt. And when you start throwing different cranks and other parts on the frames for the different builds and price points, that will surely muddy the waters still further. So any suggestion that a bicycle is faster than another because the frame is stiffer should be regarded with a great deal of suspicion. It's probably not true. And until someone provides some actual data to back it up, rather than handwaving and speculation, I simply don't buy it.

Yes, your physics are wrong. The bicycle frame and drivetrain, as a spring system, is more complicated than you imagine and doesn't work the way you think it does. It's extremely easy to demonstrate that loading a frame perpendicularly to the chain and then releasing it will transfer that energy into the drivetrain. The question is not where the energy that moves the bottom bracket sideways goes, but how much of it returns to the drivetrain versus how much is lost to hysteresis.

Taking your thought approach to its conclusion... work is the integral of force over distance, so you could say that you're wasting more energy if you apply an equal force in a non-productive direction, but it moves farther.

C'mon. Road race wins is hardly a metric for determining anything about bike performance.

Simplifying the problem is not the same as simplistic thinking. In fact, being able to properly simplify the problem is what makes a good engineer a good engineer.** Simplistic thinking is saying that because the frame acts as a spring, all the flex energy is returned. By simplifying the problem, Brian has demonstrated that reasoning to be incorrect.

Now, the magnitude of the effect is open for investigation (cervelo seems to claim up to a few percent), but the difference is physically plausible.

--

**Or as a colleague puts it: "A good engineer doesn't solve problems, he or she just reduces them to another set of problems that are of no concern."

Reckon that insulating the frame and recording its temperature would clear that up?

Relatively simple experiment.

Crank power meter + Hub power meter. Compare the ratio between crank vs hub (which should equal the drivetrain loss).

Now use two bikes, one with a standard carbon frame. The second bike with an intentionally flexy frame. You want to make sure both frames have minimal damping components. Comparing the drivetrain loss under real riding conditions would give you a sense for how much it really matters.

All I know is women like stiffness over speed, I must comply! :thumb:

Yes. I don't need to examine them personally, but I need for them to exist and for someone to have verified them. In fact, people have known the earth is round for thousands of years, there are lots of different ways to know it's true. It's pretty well established, about as close as you can get to having been proven.

Frame stiffness = more power transfer isn't in the same boat at all. People say it a lot. But people say all kinds of things, and they're not all true. So it being something you hear a lot isn't the same thing as their being maps and calculations, not by a long shot. Keep in mind this idea about stiffness being the same as performance is something we hear a lot from companies that want us to buy expensive frames from them.

You could rephrase your question and ask if you believe everything you hear. But that wouldn't be very helpful.

Yes, providing your crank turning mechanism acts like a real rider. For example a chuck turning a BB spindle wouldn't be a valid test as there would be no out of plane forces.

The fact that the big boys don't publish what they know is very suspicious.

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.

Robert...can you define what you mean by pedal force in 'non-productive directions' ?

You posited a "non-productive direction" without any real basis.

It's _much_ easier to think of the problem in terms of energy. The energy in a deformed frame has to go somewhere: the road, the leg, or heat. Heat is probably small compared to the other two. If the leg were akin to a spring (or more precisely, a perfect machine), then the energy wouldn't be lost and "eventually" make it to the road. Worrying about vectors and torques and such just complicates the analysis.

Yes, you would need to build up a full bike with a real rider. The advantage of crank power meter and hub power meter is that you can correct for increases in rider power, and address the real source of loss. The only other thing to correct for is to ensure the cyclist uses the same gear combinations on each bike, so that drivetrain losses are equivalent.

Of course. The only productive pedal force is in rotating the crank. The alternating rocking force due to the pedals and crank arm being connected to the BB by a torque arm (spindle) can never propel the bicycle forward. It is non-productive. Even if returned to the "system", it will never be rotating the crank. Interestingly, one way to "stiffen" the system is to place the cranks closer to the center of the BB. What is that called, smaller Q-factor? But the force that is not purely rotational will never move the bike forward. It doesn't matter how much or little the frame responds to it (flexible or stiff, respectively), the force is the same. It is only the deflection which changes in response to the flex mod of the system in the direction this non-productive force is being applied, not the actual amount of the wasted force. Looked at this way, I am tempted to conclude that teaching riders best pedaling form is much more important than frame stiffness in achieving ultimate speed. Isn't this what used to be taught?

Agreed.

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.

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.

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.

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.