tomato coupe

I agree.

rpenmanparker 

Wrong. The other relationship that is important to know is K = f/d or force divided by displacement. So when K changes and force stays constant the displacement changes in the opposite direction. You can't put in the same force and the same energy and have different displacements. Energy varies as the square of displacement while force varies linearly with displacement (K not changing). And so on.

Bacciagalupe

Thanks for the clarification.

And to continue to be clear, I don't think anyone is saying that frame deflection is has zero loss -- I certainly am not. (E.g. I've been referring to "friction" rather than "damping.") The claim is that the losses are insignificant, or at least far smaller than typically assumed. As noted, that depends on points of comparison, and the context.

I do go farther than some, in that I assert that the certainty of that belief is unjustified, given the lack of empirical evidence. Or at least, people are taking what may be a reasonable assumption ("a traditional steel frame transfers less efficiently than a new CF frame") and applying it without justification and/or evidence to other situations ("therefore, this late-model bicycle that deflects at 70nm/deg at the BB is faster than this other late-model bicycle, which deflects at 60 nm/deg at the BB").

tomato coupe

Changing the spring constant directly changes the potential energy stored in the spring, assuming the same force is applied.

No one who has posted on the thread knows the values of the spring constant or the damping constant, so we don't know if the effect is significant. I think that's why the O.P. wants to see some data.

wphamilton

I think they're 50-100 hz sample rate, maybe too slow for the bottom bracket. Which is why I've been meaning to buy one for an arduino project ... yet, if all you want to know is the frequency and some data on the damping you might not need more than direction and magnitude.

wphamilton

The spring constant should be easy, no? Stand on it and see how much it bends.

tomato coupe

I think that your position is almost certainly correct for the "average" cyclist, but it may not hold for serious racers. The major difference between an average cyclist and a top pro is that the pro can produce a lot more power. Since the potential energy in a spring scales with the square of the applied force, the frame losses will also scale as the square of the applied force. Top sprinters may produce 3-4x more force at the pedals than an average cyclist, so frame losses could become significant for them. Given that pros are also interested in gaining every (tiny) advantage that they can, a stiff frame may mean a lot to them.

pallen

If the same force is applied, changing the spring constant changes the amount of deflection. Think about sitting on a car. When you sit on a Caddy with a cushy suspension, it will deflect a decent amount. Go sit on a sports car that has stiff spring (same force, you) and it will deflect less. Both will rebound and the energy stored will come back. The one that loses the most energy will be the one with the most dampening, not the one with the stiffest spring.

So, the question remains, how much dampening does a bicycle frame have? The spring part doesn't matter.

wphamilton

Higher spring constant means less deflection for given force means less energy going into bending the frame, so it does matter. Whatever amount doesn't "come back" is in proportion to the amount stored in the spring in the first place.

No offense pallen but maybe we need a sticky for that, or at least OP edit the original post and include a footnote.

waterrockets 

No, run some numbers through the equation E = 1/2(k)(x^2), try with k and x values of 100/100 and 200/50, respectively, to reflect doubling spring rate with the same force.

Yep.

Dozernaut

Hooke's Law may not apply to the carbon fiber used in bike frames.
https://link.springer.com/article/10....0366347#page-1
AKA Non-hookean
F=kx is an approximation.

I think the use strain energy would be of appropriate here.
The strain between the molecules will be released as heat and kinetic energy. Of the kinetic energy only some would be useful to propel the bike forward.

tomato coupe

Damping isn't everything - the spring constant still matters. An extremely stiff spring with high damping can still be less lossy than a soft spring with low damping. Very little potential energy may be stored in the stiff spring, so very little can be lost to damping. In the extreme case of an infinitely stiff spring, no energy can be lost to damping.

(Sorry, WPHamilton already explained this perfectly.)

pallen

Yes, in the real world that is correct. In the mathematical model the loss of the spring is modeled in the damper. It is an intrinsic part of material of the spring. Obviously we don't have shock absorbers in our road bikes.

pallen

I get that, but the argument here is about how much of the energy do you get back. For example, you store more energy in a soft spring, but you get 99.99% of it back vs storing a small amount of energy in a stiff spring and getting 99.99% back. The difference would be insignificant if there is not a lot of dampening in the system. If there is a lot of energy lost in "dampening", then the spring constant matters more. We still cant answer "significant" vs "insignificant" without actual numbers.

waterrockets 

I think the fact that we don't have actual numbers tells us that the numbers aren't big enough to worry about for most people. The frame manufacturers are showing x% increase in stiffness. If they were able to show numbers that said x% watt efficiency gain, then we'd have something. I don't think that with an SRM and a PowerTap in use on a 2014 CF race bike will show any loss differences with a 2013 CF race bike. The accuracy and precision are not high enough to detect the differences.

I think that if a rider is going for every possible advantage at any cost, then it makes sense to upgrade every year. For someone like me who just wants to have fun and win a few Cat 3 or Masters races every year, that can be accomplished on any reasonable race bike from the last 15 years.

pallen

I would guess that its not very significant, but I really have no idea. Maybe a stiff frame just feels good to some riders - I'm good with that.

rpenmanparker 

Not the square of the applied force, rather the square of the spring deflection.

tomato coupe

Either way ...

E = 1/2 * k * x * x

or

E = 1/2 * F * F * 1/k

rpenmanparker 

Yep.

Mark Kelly 

Data from Champoux's study of bicycle dynamics agrees with me rather than you: he has a damping factor of about 1.3% for the first bending mode: PDF here

tomato coupe

I haven't read the article. Does it say that hitting the frame with a hammer excites the first bending mode of the frame?

Bob Dopolina 

Incorrect. Twice.

Sean Kelly said that he was told his saddle was too low. His words, not mine.

A flexy fork means the bike will drift after the apex in high speed corners. The fork determines the tracking of the bicycle on high speed descents.

Mark Kelly 

You were talking about frame bending being heavily damped, I said I thought it wasn't. 1.3% is not heavily damped.

To relate this back to your original argument, you appeared to try to counter the rebound argument by saying that a softer frame would lose energy because it absorbed more energy when flexed and lost much of it on rebound because of heavy internal damping. I said I agreed with the first but not the second part of this argument.

I mentioned the hammer thing because the loss angle for metals is more or less constant with frequency, so the ringing is evidence that it isn't heavily damped. And because I like hitting frames with hammers.

Campag4life

Believe that is a good summary pallen.

Voodoo76

Note to self, don't let Mark "The Hammer" Kelly near my bike.