No, it just means the energy is absorbed over a smaller distance, but it’s the same amount of energy. The stiffness affects the degree of deflection, but not the force input to cause that deflection.

Hypothetically, you could measure power at the pedals and power at the rear wheel.

If the same power meters, cranks, rear wheel c,hain and derailleur are used, and the same BB is used, the difference should be the same if the bikes are equally efficient regardless of stiffness.

The only confounding factor which would have to be controlled would be the BB shell tolerances and alignment.

It's the same amount of energy being exerted on it, but I don't think that means the same amount of energy is stored. If I exert 5w with my foot against a brick wall, the brick wall doesn't deflect at all. By your logic, that means the 5w is being stored in an infinitely small amount of space.on the wall. What I think is actually happening is the 5w is being dissipated into reshaping my foot.

Isn't resistance by definition the opposition of the flow of energy? If the stiffer bike is more resistant, then it is actually less energy that is being transferred to it.

We’re not talking about an infinitely stiff bike, however. There is still deflection, just less. And even so, physics sez force vectors must be balanced.

And even in your brick wall example, the force is reshaping your foot. It’s not magically pushing 90° down the wall. On a magical infinitely stiff bike, the lateral force is mashing rider A’s foot in the shoe, not pulling the chain.

And with that I’m done on the topic.

1. The displacement of a spring is proportional to the force applied to the spring. The potential energy stored in the spring scales with the square of the displacement, and therefore the square of the force. A soft spring will therefore store more potential energy than a stiff spring when an equal force is applied.
2. All real springs are damped, so some energy is lost when a spring is compressed and then allowed to relax. Given two springs, one stiff and one soft, with equal losses, the soft spring will lose more energy than the stiff spring when subject to the same forces.

No, it is NOT the same amount of energy. I think you may be confusing force and energy. Just because it takes the same force does not mean it takes the same energy.

The amount of energy a spring absorbs and stores is a function of the force applied to it over the distance that it compresses. That is also the amount of energy that the spring releases.

So the more flexible frame does absorb more energy when it bends, but it also releases that same amount of energy when it straightens out again.

The underlying debate about whether stiffness effects efficiency has to do with whether the released energy of the spring (the bike frame) is

a) significant enough to worry about
and
b) going into driving the bike forwards or being used up in some other (less useful) way.

EDIT: the post above mine (Tomato Coupe) details this very well. Also, the part about real springs having some damping is true and worth noting, though I think in the case of a steel spring (steel bike frame) this is probably negligible for the current discussion.

One does not apply energy to a pedal or a brick wall, one applies a force.

The problem is that you can't just think of the frame by itself, you have to look at the bike + rider system. When you add a soft doughy* rider to a bike, you introduce new avenues for energy loss.

* Sorry, no offense intended.

Here.

The implication being that when a frame flexes such that a rider's full energy is split between forward motion and downward flex, that upon un-flexing the frame returns that energy directly into forward motion. I suspect a spring could achieve this, aside from heat loss, as it's force is in-line with both compression and return. But a frame's flex would have to be spot-on equivalent and in-line, and occur at a time when the rider could actually use it, for the return, in order to recover that energy in the form of the forward motion that was previously lost. Wouldn't it?

No.

No. For the same applied forces, a stiffer spring in the middle of a power train tends to absorb less energy than a flexier spring. This is because work is force integrated over distance, and a flexier spring deflects farther for a given force.

Just trying to surmise this thread is a visual...



John

Nailed it.

I am unclear what you mean by "in line". But whatever vectors are relevant to the forces that the spring releases would be the same involved when it is compressed. I think that is a bit of a red herring, here.

As far as the timing, that would be part of the question I pose at the end of my post (the part that you did not quote).

Yep, that's the whole issue. The energy that goes into flexing the frame has to be returned at the right time and in a way that generates forward motion. Unfortunately, the mechanism by which that returned energy can generate forward motion involves the riders legs, and this introduces losses to the system. (Legs make terrible springs.)

Well, since the entire lightweight bicycle doesn't weigh very much then why not suspend the rider on the frame instead of suspending the rider and frame on the wheels ? In the first case the entire bicycle would be un-sprung weight while in the second case only the wheels and suspension would be un-sprung weight. But again the bicycle doesn't weigh very much against the total weight of bicycle and rider.

The problems would seem to be that a seat suspension would hinder pedaling while sitting in the seat. But then if there were only a handlebar suspension that would tend to pitch the rider's weight forward. If there were both a seat suspension and a handlebar suspension the rider would move more vertically. Of course there is a Specialized 20mm handlebar springing and dampening.

Now one bicycle developer has a seat compliance system that moves the seat mostly front and rear and not as much up and down. I suppose that the development has our attention. Well, it's the Cannondale Kingpin system that should be considered. They call it a suspension while I call it a seat-compliance-system. But another system is the Trek rear IsoSpeed. Then the Trek front IsoSpeed is a front-to-rear movement of the handlebars !

My solution is a stiff frame with a deflecting fork and deflecting seat post. Of course my sport is not long-range rides but short downhill courses like a paved sports-car track but relative to the 40 MPH speed of the bicycle.

Or maybe we should test the Cannondale Kingpin rear system with the Specialized Future Shock front system ?

Now we all know that a wheel suspension at the rear of a bicycle does reduce pedaling effectiveness.

Seems simple enough to me .... the motion of the crank translates the motion of the foot into motion of the chain and ultimately, the rear wheel, which propels the bike forward. Anything in the system which transfers energy anywhere not alo0ng the perfect (circular) path of the crank, wastes propulsive energy.

Think about a bike with really loose bottom bracket bearings, or cranks which weren't tight to the spindle---no one would be trying to convince anyone else that those things in some way returned energy to the bike because "ya know, conservation of energy." If the whole frame flexes at the bottom bracket, same effect---some of the potential propulsive energy goes in different directions. When the frames snaps back (or is pushed back by the other crank) it is still lateral, not longitudinal motion, and this does Not help propel the bike.

it's going Sideways, people. Unless you want your bike to go sideways , any sideways motion is wasted, since "wasted" in this case means "not propelling the bike forward."

The only way the bike could be acting as a spring and propelling itself forward with energy from deflection would be if the bottom bracket twisted longitudinally under load---but that would imply a fixed or high-friction crank bearing.

Think about it .... if your wheel shakes from side to side really badly, are you going to claim that its okay, because the energy lost will be returned and help propel the bike forward.?

For maximum efficiency, everything has to stay in the plane in which it is meant to operate. Every angular flax is a waste of energy. Y'all are engineers with degrees and all that ....

Ask the race-car engineer: Is frame flax a good thing? Does it make the car go faster? No ... eventually it breaks drivetrains because all those drivetrain parts are designed to work in very specific relative orientations. The forces involved with automobile engines are so large that transmissions will explode, gears will strip, cranks will snap .... the forces involved with cycling are so puny that realy almost nothing happens ... which I think was the OP's point, he just said it badly.

The answer is to buy lighter weight bottle cages, to compensate.

Oh, and wax you chain, shave your legs, and run disc brakes.

Dammit, Jim, I'm a lawyer, not a physicist!

I have a bone to pick with you.

John

I'm so confused by this issue and all the conflicting opinions on it (which generally all have to be better informed than mine) that I've decided that the best approach is to ask the bikes. They're not talking.

Look man, you can listen to the bikes but you can't hear them. There's a difference man. Just because you're listening to them doesn't mean you're hearing them.

I'm hearing them, it's just not talking.

And I can't for the life of me understand why anyone would pay money for those buzzy hubs. Talk about things I wish I couldn't hear!