What is the truth behind bike weight? Does it really help THAT much?

alienator

Simple: from the first and second order analysis of forces in bike/rider system. From the complete lack of data making any correlation whatsoever between bike stiffness and improved performance.

Math. Science. Look 'em up, and give 'em a try. People actually use it in the real world.

TheDarkLord

You know, your condescending attitude is really disgusting at times. What is even worse is how a scientist like you twists statistics or the lack of it to suit your own argument in totally non-scientific ways. Do you really publish papers with such twisted interpretations? Or are you a theorist?

Crankyfeet

So lack of data on the effect of stiffness = alienator having an opinion on the effect of stiffness.

Interesting logic for he who decries having an opinion when there is no data to support it...

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ScienceIsCool

I didn't perform an experiment. I used the known values of stiffness and computed the theoretical losses. But yes, you made one of my points for me. The losses are generally too small to be measured...

This is how I calculated the losses:

- Assume the stiffness values (expressed as k = N/mm) represent a linear, spring relationship. And it should because there are no non-linear elements.
- The energy stored in a spring (and subsequently lost) is equal to 0.5kx^2 where x is the displacement.
- The amount of displacement can be estimated from F = kx and P = Tw, where P is power, T is torque, and w is the rotational speed of the cranks.
- For a given power output and cadence, you can figure the average torque on the crank.
- Assuming the instantaneous peak torque is ~ 4 times average (that's generous) and using a force diagram, you can calculate the force that goes into bending the frame (i.e., pushing on our model of a spring)
- This force gives you the energy stored in the spring as described above: 0.5kx^2 and all that.
- This energy loss happens twice every rotation of the cranks, which happens 2cadence/60 seconds.
- Therefore, the power lost is equal to Energyx30/cadence Watts.
- Divide that by the original power input and there's your efficiency.

I found that using this model, which should be accurate by way better than an order of magnitude, the efficiency of a bike frame is ~99.95%. That might change by ~0.025% depending on whether you have a super stiff or super flexible frame.

John Swanson
www.bikephysics.com

TheDarkLord

Maybe alienator is just confused with what inferences can or cannot be drawn from "lack of data". Case in point - there is no data showing that string theory is right. Hence, string theory should be wrong. Right, alienator?

ScienceIsCool

Oh yeah. And the efficiency is the same whether you're putting out 12 or 1200 Watts. The system is incredibly linear over a wide range of inputs.

John Swanson
www.bikephysics.com

TheDarkLord

I would include a damping term though, as there is bound to be some energy that will be absobed by the bike frame. The damping term could dominate the losses in the system; but I wouldn't be surprised if any loss is very small.

Yojimbo_

I'm not pretending to understand string theory; however, I believe there are 6 different theories, all requiring many more dimensions than the four we live with.

They can't all be right.

TheDarkLord

I don't know anything much about it either, and I have heard some talks where some string theories could be united in a more general framework (like M-theory), but it was just an analogy (maybe a poor one) to show that the lack of data by itself should not be the basis for some conclusions.

ScienceIsCool

Nah. You don't really need a damping term because you don't care *where* the losses are. It's enough to know that any energy you put into this spring system is lost. Besides, the only effect a damping mechanism would have is to improve the overall efficiency...

John Swanson
www.bikephysics.com

Crankyfeet

Sorry I haven't had time to really go through your model. But how do you determine the separate values for "k" and "x"? F= kx is different from the energy equation which needs to square the "x" value?

And how is your model able to determine the difference between a "noodly" frame and a very stiff frame. I can't see where the frame properties are accounted for in your model?

I need more time to go through and understand your model though. Thanks in any case, John, for your explanation.

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TheDarkLord

Fair point. Although I admit I don't visualise the system well enough to really follow your calculations.

ScienceIsCool

I know that this was a quick summary and perhaps not the easiest to "digest". But hopefully I can answer your questions. The value of k comes directly from published data on frame stiffness. To be honest, I can't remember where I got my numbers, but I think it was from the famous "Tour" testing.

I then use k with the estimated F (from the Torque, power, cadence, and force diagrams) to calculate x. x = F/k

From there, I can calculate the energy loss: E = 0.5kx^2

And with a few more sums, I get the overall efficiency. I'll try to find my old, longwinded posts on the subject. If I can't find them, maybe I'll write them all out again. But don't hold your breath, I've been busy lately and I'm feeling lazy.

John Swanson
www.bikephysics.com

TheDarkLord

Maybe you can make a document (with a scan/image of the force diagram) and put it on your website?