Does stiffness really matter on the bike?

Your description of power transfer is partially correct, Andrew, but what you don't allow for is energy lost in flexing the frame prior to being delivered to the cranks. As you push down on the crank arm and deliver power, it;s also being transfered into the frame through the crank arm and bottom bracket where it's lost. If the frame is very stiff, less of that energy is lost.

Considering how much flex I used to see around my BB on my old Orbea, I understand exactly what you're saying. 

Now, where does that energy go?  It doesn't just disappear, so unless it's being lost as sound or heat, the mechanical energy has to be transfered somewhere.  That's what I'm having a hard time understanding. 

The ground via the tires.

Well, frame flex is storing energy, just like a spring.   So you DO get most of it back.   Since no process is 100% efficient, you lose a little bit to heat.   (I'm guessing that the amount that your bike frame heats up during the process is much less than the amount of heat that gets carried away by conduction with the surrounding environment.¹)

Since the energy stored in a simple spring goes as the SQUARE of the distance of comression, a flexy frame is trying to store and release MUCH more energy than a stiff frame.  

If the process is 99% efficient, then a frame that moves 1 unit of measurement and stores 1 unit of energy will get .99 units of energy back.

If the frame moves 2 units of measurement, it will store 4 units of energy and you'll only get back 3.96 units of energy.

Your total energy lost is 4x higher in the "flexy" frame.   As the efficiency of the "frame spring" decreases, or the flexiness of the frame increases, your energy loss gets big quick.     (dang square in the equation!)


(yes, I used a simple model for a spring and simplified the concepts.   It's still mostly applicable, as far as I see it.)


1.  You can test this theory by:
      a.  Riding your bike 200 miles and then touch it.  If it's burning hot, your frame is gathering alot of heat.
      b.  If the above experiment fails, take your bike to deep space and ride it there.   If the bike is still not hot after touching it, it is losing more heat to black-body radiation than it is absorbing during pedaling.

I just don't think t?he energy lost ?a?s? ?h?e?a?t? from the efficiency of the spring ??c?a?n? ?b?e? ??a? ?m?e?a??s?u?r?a?b?l?e? ?a?m?o?u?n?t?.? ? ???????????????????????????????????????I? ?c?o?u?l?d? ?b?e? ?w?r?o?n?g? ?t?h?o?u?g?h?.? ?




Well, at least I won't have to worry about aerodynamics...

Generation of heat is not really the issue.  As long as the frame (or whatever components are being deformed -- the chain for example) are deformed within their elastic limits (before hysteresis kicks in, where the component 'remembers' the flex (partly) and the deformation (partly) 'holds' -- think of flexing a paper clip too far), the energy is not converted to heat.  (OK, these things are not perfect springs, but the degree to which they are not is negligible, I'd wager -- but I haven't done any calculations or anything).

The real issue is where the return of force is directed.  Is it directed into the drive train, or somewhere else?  I'm pretty sure that the answer is 'somewhere else' -- i.e., it is directed back into the rider's legs.  Now, if the rider were both a motor and a generator, so to speak, then great -- the force of the recoil of the deformed part would then be converted into energy that could be 'reused' by the rider.

And in fact, to a certain extent, the rider is a 'generator', because some of that recoil is stored (for example, in the rider's Achilles tendon, which itself acts like a kind of spring in this case, just as in running).  But the return is not perfect.  Some energy is lost.  Probably somebody has actually measured the difference in power that results in frames of different stiffness, but I don't know.

I can help out a little as an engineering student.

When modeling material a spring is often used to represent the stiffness. The element that is not so often used is the damper (dissipater of energy), because the influence is quite small. Non the less, it is still present. For those that have experience with riding on steel and aluminum the difference in comfort comes from the damping characteristic and not the stiffness. For those that like to know, steel has better damping.
So energy is not just lost through deflection but also damping of the frame. As was mentioned before the energy is not redirected to where you want because the whole frame deforms, not just the BB.
Heating happens due to the damping characteristic and is spread out through all of the frame. The surface is big enough to get rid of this heating without you knowing it.

Sidenote: perhaps you could measure a temperature difference at the BB when comparing outside riding and inside roller riding.

I can see how the damping that occurs at the molecular level can result in a loss of energy.  As you said, this loss would be spread out and would therefore dissipate quickly.  Measuring how much energy this accounts for would be pretty difficult though. 

That makes a lot of sense.  I was trying to visualize the flexing of a BB and since most of the energy is returned on the bounce back, I was trying to figure out where it was returning to.  Probably not into the drive train, as you said.  Having that return to the riders body makes a lot of sense. 

Assuming the flex is caused by downward force - you mashing the pedal - then when the frame rebounds, energy will get returned mostly where you can't benefit from it: upward.

I just had to state that the Subject line of this post is waaaaaaaay too funny to me.

I think it's more of a side to side thing.  The downward force is getting transfered to the drivetrain, since the frame material allows for flex but not stretch.  The side to side is where the frame flexes and energy is lost.  I'm just trying to get a good idea of where that energy gets lost to, if at all. 

I had to reword it 4-5 times to come up with one that I thought wouldn't draw those types of responses...

It's not just the loss of energy being transferred to the road, it's when the bounce-back occurs. When you push down on the pedal, you want the energy transferred to the road as soon as possible, not stored in the frame/chain/crank/etc. until it gets released by letting up on the pedal (which means much of the energy is being transferred back into the pedal/crank as pressure is released instead of ever making it to the road).

In addition, flex has to be counteracted at some point. As the frame twists, it needs to be counteracted somewhere - like with the handlebars and/or seat. The more 'springy' it is, the more effort it takes to counteract and the more unpredictable the effort will be.

It gets transferred back into the pedal as the pressure is released, never making it to the road. Like bouncing on a bad trampoline. A very small, uncomfortable one.

If you're smashing the frame downward with the left foot, then it's going to rebound when you're pressing down with your right foot.   This essentially causes the BB to move upward in relation to your foot.   Unless it all happens when the feet are at the very top/bottom of the pedal stroke, then all the energy returned from the frame is going to be reclaimed as tension in your tendons/muscles or into rotational movement of the crank.   (assuming the "downward" motion is parallel to the planes described by the circular motion of the pedals. )

It gets really complex because the BB doesn't just move DOWN, it moves SIDEWAYS too.   Torsional forces like that can get pretty complex.

Here's a video of the flexing that can occur:  http://www.youtube.com/watch?v=nEYJfQpq_oQ

"stiffness" needs a modifier.   "Does frame stiffness really matter on the bike?"

The example I was gonna use. If you turned the anology to running, and really exaggerated it, compare running on concrete, to running on a trampoline. 

I thought of that one, but the stiffness of other components come into play as well.  (i.e. crank)

Taka a heavy duty mtb with front and rear suspension, a powermeter on the pedals and one on the rear hub and you have a great energy loss testing bike. Change stiffness and damping and document the loss of energy between the pedals and rear hub.
This should give a good relation between stiffness and energy loss and damping and energy loss.

Although I have very little biking experience I would say designing your stiffness for comfort and allignment of your drivetrain is more important than stiffness for energy preservation (don't exaggerate is statement into 'sloppy BBs are fine as long as I don't feel the putholes in the road').

Why do you feel this way?  My feeling is that minimizing power losses would be paramount.  If it's an extra 5-10W, that can make a huge difference. 

small point.  It doesn't stop at the pedal, it gets transferred all the way back into your leg.


I suppose if you modeled the whole system as a series of springs:  legs->pedals->cranks->frame..... every piece of the model has the ability to store and release energy, and each one comes with a cost(efficiency) for doing so.    If you can minimize the amount of energy that is able to be stored/released in each piece, you can maximize power transfer to the road.

The other point about how much energy you're using to counteract all of the flexing to keep the bike going in a straight line is a good one.   If you look at the video of the trainer that I posted, the back tire is moving pretty significantly.   That means that the rear tire path down the road is going to be more like a sinewave than a straight line.   The closer to straight you can get, the less distance you have to travel.

I believe I've heard bike marketing (or Bikesnob making fun of bike marketing) mentioning things like:  "laterally stiff but vertically compliant"

If you can make a bike that is vertically compliant...  it is more comfortable to ride (eases the feel of the potholes)

If you can make a bike that is laterally stiff... the BB doesn't swing from side to side and  take he chainstays and rear wheel with it.