Let the air popper cool down ...

There's a lot of flexing going on in the thread at the moment.

Thanks. I tell my kids that even a lousy guy like me can have a reasonable career if the bar for "reasonable" is set low enough.

Ha! I was referring to myself -- since I'm a social scientist.

Me too.

But I tell the students that almost all of the really interesting statistical procedures developed since WWII have been developed to address problems in the non-experimental fields. Almost all of the statistical procedures used in physics, or chemistry, or engineering, are pretty much similar to what Fisher and Jerzy Neyman (hallowed be his name) were doing in the 1930's. I work in the social sciences exactly because the data are crappier, we use observational rather than experimental data, and there's so much noise that we have to filter out to get to the signal. (As a not-so-aside, that's pretty much how I came up my approach to measuring aero and rolling drag -- I'm so used to crappy data in my regular day job that when I applied normal crappy data techniques to the relatively clean data from bicycle sensors the results turned out pretty well. It's also why a lot of engineers and physicists were pretty skeptical when I said I had done this. They think social scientists aren't real scientists and said, "that can't work because if it did, we would do it that way."). Linear regression was originally developed to investigate a social science problem; so was stochastic branching processes, which later was used by physicists to model nuclear fissioning and, um, the atomic bomb. Those were originally social science methods, taken over by the "hard" sciences. I'm very popular at parties.

Yeah, I was joking. (Mostly.) Of course, hypothesis formulation and testing is pretty similar across the sciences (social and physical), and I've found that a well-trained researcher can recognize good methods in a variety of fields.

As far as the math is concerned, my field coined its own term for some of the most commonly-used statistical methods...But as I always told students: once you understand regression analysis, you understand how most cause-effect relationships are tested.

All right. Here is my criticism of the concept. In order to store energy, movement is required. A bike frame - even a noodly one - is stiff. Now that we have a bowyer in the conversation, imagine a bike frame strung like a bow. How far could you pull it back? How far would the arrow go? Not far, because the bike frame cannot store very much energy, because it's stiff. A spring that barely moves is storing barely any energy. When you pedal a bike you are putting in a force similar in magnitude to pulling a bowstring. This is enough to sometimes bend some bikes enough the wheel rubs the brake pad. That's like a millimeter, or a fraction of a degree. A bow, which is actually flexible and does return a lot of energy, lets the arrow slide about two feet. A spring moves in proportion to the force and stores energy in proportion to the movement squared. A spring that is 2x stiffer stores a quarter of the energy for the same force. A bike frame that is 100x stiffer than the bow stores 0.001% of the energy. It's just not enough to change the resistance profile enough to account for a 4% much less 12%.

Here's an experiment many roadies could pull off. Put the front wheel in a trainer and nose it up against a wall. Put the pedal at the first click over 3 o'clock. Prop a ruler up on the back side of the pedal and set up your phone to film the ruler. Stand on the pedal. Your full weight is as much torque as you will ever give it. Each 1/8th inch of movement of the crank is one degree that it could be "giving back"

You've got the right idea, but some details are wrong. The displacement of a spring is equal to the applied force divided by the spring constant. The energy stored in the spring is equal to 1/2 times the spring constant times the displacement squared, which is 1/2 times the applied force squared divided by the spring constant. So, if you double the spring constant the spring will store half the energy if the force remains the same.

F = k * x –––> x = F / k

E = 1/2 * k * x * x –––> E = 1/2 * F * F / k

The focus on the amount of energy seems to be why this bothers people. So let's put it this way - if you push down on the crank hard enough to shorten the chainstay length by (let's say) 1mm during the highest torque portion, you will get that full 1mm back when torque drops sufficiently for the stays to unwind. Not 0.8mm, not 2mm - a full 1mm. And we know it is 1mm because all this happens within the frame's range of elastic deformation and frames don't change shape over time. In other words, no spring set occurs.

What did the rider lose by the frame flexing? 1mm of road at the moment of peak torque. What did the rider get back? 1mm of road distributed over several moments after peak torque.

Why might the rider want to move that 1mm from the moment it should have been expressed to where it actually happened? Because that means the peak momentary torque was lower, and the rider didn't have to contend with that wall. Instead peak torque is buffered by momentarily lowering the gearing by putting the chain's output somewhere other than the road.


That's all that's happening. So the math is Loss of Energy from Flex In + Loss of Energy from Flex Out - Savings of Energy in Rider From Not having to Overcome Peak Torque = Net gain/loss of energy. And since we are dealing with materials that make good springs, the first two losses are very low.

Not much grant money in that……

Certainly his tires exhibit planing, don’t they?

Actually, no. But, what do I know -- I don't have a PhD in geology.

Another fantastic fact filled post from the master of the drive by.

What floors me is that you like to pretend your posts have any content.

Sorry, but I'm no longer willing to invest the time that would be required to point out all the mistakes in your theory of planing. Maybe there is another physicist on the forum that is willing to take on the task.

That's why I work in industry.

What do you mean "no longer"???? You have NEVER pointed out anything, unless you think "Um, no." is an argument. Do you actually think denial is a valid counter to anything, ever? Do you just feel a sense of belonging or something by posting vacuous nothingburgers to whatever thread you happen to have a non-opinion about?

I addressed several of your misconceptions early in the thread.

Like this gem, where you once again say "nope", by way of naming my posts and saying that you disagree. But you never demonstrate how, you just appeal to the implication that other things are at work that YOU CAN'T NAME.

This is not information:
"That's wrong."
"It's different than what you said."
"I disagree."
"That's not right."
"It's complicated."

If you want to pretend to argue about something, propose what you think is actually happening and why that invalidates what someone else has said. But you don't, can't and have never done that.

Maybe I'm giving you too much credit for being deceptive or lazy, but I guess it is possible that you justs don't understand the difference between simple denial and making a counterargument.

Context is important:

Very incorrect.

Yes, this shows that you can say "it's complicated" more than once without offering any sort of counter explanation about where that flex could possibly be going or how it is released, even though we know it is produced via chain tension and chain tension never drops to zero.

It's complicated.
It's complicated.
It's complicated.
It's complicated.
It's complicated.
It's complicated.
It's complicated.


It's not, unless you simply don't have the ability to picture how any of this works, including some sort of imaginary 'complication' you can't describe.

What is the physical reason a bicycle frame cannot be modeled as a simple spring (one that obeys a 1-D simple harmonic oscillator equation at small displacements)?

Because its motions are not restricted to 1 dimension.

OK, a 2-D SHO (which can be transformed into a 1-D by rotation).