TL;DR
Considering reasonable wheels: Wheel stiffness is more important than weight. A too light wheel, is not stable.
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Wired's physics are correct. However, neglect mechanical dynamics & handling.
Probably the biggest downside of light (& aero even more) wheels is: When your wheels are very light, they are prone to cross winds and "jump around" a lot due to their low inertia. And, well, you always have cross winds and bumpy roads, because only very few of us are track riders.
Considering the acceleration, you lose a lot of energy by "twisting" the wheel. That is: the hub starts to turn because the chain you pull with the crank arm in front is forcing it to do so. Then, all this tension is transferred to the spokes, rim and finally the tire. In that process most wheels lose a significant amount of energy by simply storing it via elastic torsion and releasing the energy without contributing to movement at all. As already said in another comment, we "pulse" the energy to the back wheel, as the maximum pulse comes due to our own biomechanics. And we have two pulses per revolution with a zero at almost vertical crank arm alignment!
Therefore you want to have stiff wheels! Which stands in stark contrast to light wheels.
The company Lightweight basically made its money by creating aerodynamic and very very stiff wheels for the weight they had. These wheels, however, are not maintainable any more & very expensive [2].
There are little papers, which have "done the math", as it is an interaction of many components and people tend to measure or, let's use a more "unscientific" word you used, "experience" the overall system answer, as in:
Gavin, H. (1996). "Bicycle-Wheel Spoke Patterns and Spoke Fatigue.",
J. Eng. Mech., 10.1061/(ASCE)0733-9399(1996)122:8(736), 736-742.
and/or by riding many different wheels and speaking to other cyclists, who happen to be engineers. Which happens more often than one thinks after reaching higher levels in the sport [1].
There is little money for that kind of research. TU Delft is the only university I know investing here. I'd be happy about anybody pointing me towards groups doing that, as I'll finish my Dr.-Ing. (as an engineering PhD is called here) in Germany this year.
Furthermore, jacquesm's comment nailed it: It's an aero compromise, as many (jackmott, thedufer, slashdotdash, etc...) already more or less said: Multiobjective Optimization at its best.
Ah good, that paper mentions Jim Papadopoulos. I did a small experiment with him back in '95 on perception of weight on the frame.
Looking at that paper, I've got a couple of comments:
1) I'm not clear where they're getting lateral forces when a bicycle is cornering, unless the rider is hanging off the side of the bike motorcycle style. (which is generally unnecessary as bikes have enough clearance to corner at ~45 degree lean angles).
2) It's unfortunate that they didn't instrument a trailing spoke as well, so that they could disentangle the torsional strains from the radial strains.
3) While the tangential/torsional strains are high, it's not clear what the loaded zone is there, nor how much energy is being stored in the wheel due to power pulses. I suppose I could pull out my old FEA model and port it to see.
Just out of curiosity, do you have any suggestions for stiff bicycle wheels? I've been looking for a sturdy wheelset for touring with a fairly heavy bike, but it's hard to navigate the offerings because they're all seemingly advertised based on lightness.
Drop me a mail (see my profile). I already feel guilty after mentioning Lightweight. However, they deserved it to be mentioned here, because it was a few idealistic guys revolutionizing wheel building in a garage start-up before they were bought a few years ago.
In my opinion, If you want durable wheels, the best way to go is wheels built by a _good_ wheel builder. That means properly tensioned (high), stress relieved (for fatigue life), and lubricated nipples (so you don't wind up the spokes). There are some places that will cater to tandems and touring bikes, but you have to be careful. I've seen a tandem specialty shop lace up a dedicated rear tandem hub to a lightweight mountain suspension front rim, with predictable results. Note that this is not a cheap option, as I think there's at least $150/wheel in parts here, as well as expert labor.
Parts wise, I'd look at something like:
* 36 hole hubs, either deore or ultegra level. 32 if you can't find 36. Not less than that. Some tandems go higher. This is more important on the rear wheel, where half (drive side) of the spokes are doing most of the work, because the other side's tension is so low.
* 3 cross, double butted spokes. It looks like the Dt Competitions are 2.0/1.7, which is a decent balance between elasticity and windup. 2.0/1.8 used to be my go-to choice, but that's hard to find now.
* Deepish section double eyelet rims, such as the Mavic Open Pro series. They should have closed section, not just a U for torsional rigidity.
* Grease the spoke threads and the nipple bearing surface.
* Tensioned just to the point of elastic instability in the rim, then backed off.
Reasoning:
* The key here is that you _never_ want a spoke to go slack under load. Once that happens, bad stuff happens with fatigue.
* 36 spokes puts either more spokes in the loaded zone.
* 3 cross lacing makes the spokes come in tangential to the hub, which reduces stresses on the spoke holes and prevents tearing of the hub.
* Double butted spokes allow the spoke to stretch more in initial tensioning for a given force on the spoke. As the rim deforms under load, the spoke will remain under tension to larger deformations.
* Eyelets make the nipples easier to turn in the rim, greasing even more so. Double eyelets also get support from second wall of the rim. I've had single eyelet rims (e.g. old MA series) fail where the inner wall of the rim pulled away from the braking surfaces.
* Grease the spoke threads and nipples. You want the nipples to turn on the spoke threads, not seize up and torque up the spoke like a spring. If you first ride a new wheel and hear it pinging, that's the spokes unspringing and unscrewing. Likewise, a good builder will always back off the tension a bit till there's no torque in the spoke.
* All other things equal, a wheel with twice the tension on the spokes will hold twice the load before you unload the bottom spokes, and have a much better fatigue resistance. So, take the tension as high as possible.
FWIW, nearly all that advice agrees with "The Bicycle Wheel" by Jobst Brandt, with the exception of rim selection. Rim selection though is tricky these days, as most wheels are now sold as a unit rather than parts.
Yes, when accelerating, wheel mass is worse
than frame weight, but only a tiny amount.
and Wired's physics are correct in the case of accelerating a wheel to the steady state of a spinning wheel.
Edit:
To expand on this a bit: This "tiny amount" is a lot when you are among people close to your performance. And I'm talking about stiffness vs. weight. Stiffness is just so much more important, because the sum of these infinitesimal losses is just huge:
Modern riders rpm: 100 which equals to 200 energy pulses per minute, because each leg has a rest phase and a full force phase per revolution.
In a 4h race: 240 * 200 which are 48000 pulses. Now imagine you have a super light but not very stiff wheel (because it's light, you know)... that's a lot of lost energy.
Stiffness & Damping are closely related, as the book title above already implies. A part of the energy is lost in heat and structural changes. And another part is basically unused as it's unused by design:
Imagine the following experiment. You need to push a box using many impulses over a specific length. At the side of the box is a plate, which you are punching, which is attached to a spring which itself is attached to the box.
Now, let's go the extreme. Your impulses are so short and weak, that the spring absorbs most of it and the box hardly moves. The energy quantum you transferred via impulse, was used up by the spring and the spring released it by its own = Lost by design.
Now, let's get your impulses bigger and longer. You'll move the box better. And now let's gradually fixate or, say, stiffen the spring. Each hit moves the box directly.
That's stiffness.
You hit the pedal and you experience how the bike just instantly starts to accelerate your body forward. Which a very stiff wheelset and bike would do. Now get on a fully. Thick tires, springs everywhere. Hit the pedal. You'll feel like cycling under water.
It should be possible to put limits on the lost energy of individual components, and in doing so, quantify the range of the problem.
e.g.: For now, let's assume that the wheel is a torsional spring, we're putting a force of 1000N (~100kg*g) at the rim, (roughly 300NM torque) and it deflects 1 degree. The energy that goes into the elastic deformation of a torsional spring is k(theta)^/2, t=k(theta), so energy = t(theta)/2. Plugging the numbers, you get 2.5 joules.
Now, 1000N is a lot of force, and you're only likely to have that level of force with a heavy rider in a very low gear. (i.e., your tires have a coefficient of friction around 1, so that's implying 100kg on the back tire just to prevent wheelspin) But 2.5 joules starts to sound like it _might_ be measurable, and maybe look at the numbers a little more closely to see if they're reasonable.
I'm only a fairly decent rider, but even then that's only about 1% of my 5 minute output, (if you assume 1 power stroke per second).
Side note: Rumors were that the big LA had 20min+ values above 7.5, which is pure alien. The 5min test is hell, because one stresses _all_ energy systems in the human body to their maximum effort. So you ride in pain after something like 30 secs till the finish, which feels eternal.
The 20min test is more easy compared to that, as it is very close to your general endurance. Thus, a top rider these days would rip his legs & mind out, when climbing besides the former LA.
Well, my 5 minute number is how long it takes me to climb a steepish local hill, when I'm doing a few reps. So it's imprecise, and there's like one significant figure. 250-300 watts is my guess. And half as fast as cat3? Yeah, I could see that.
My point still is, it's possible to calculate the upper limit on losses from wheel flex under power load, and I'd assert that they are small enough to not matter. And what's more, the effect of torsional spring type flex goes down (at a constant power output) as speed goes up.
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TL;DR Considering reasonable wheels: Wheel stiffness is more important than weight. A too light wheel, is not stable.
---
Wired's physics are correct. However, neglect mechanical dynamics & handling.
Probably the biggest downside of light (& aero even more) wheels is: When your wheels are very light, they are prone to cross winds and "jump around" a lot due to their low inertia. And, well, you always have cross winds and bumpy roads, because only very few of us are track riders.
Considering the acceleration, you lose a lot of energy by "twisting" the wheel. That is: the hub starts to turn because the chain you pull with the crank arm in front is forcing it to do so. Then, all this tension is transferred to the spokes, rim and finally the tire. In that process most wheels lose a significant amount of energy by simply storing it via elastic torsion and releasing the energy without contributing to movement at all. As already said in another comment, we "pulse" the energy to the back wheel, as the maximum pulse comes due to our own biomechanics. And we have two pulses per revolution with a zero at almost vertical crank arm alignment!
Therefore you want to have stiff wheels! Which stands in stark contrast to light wheels.
The company Lightweight basically made its money by creating aerodynamic and very very stiff wheels for the weight they had. These wheels, however, are not maintainable any more & very expensive [2].
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[1]: http://www.uci.ch/road/ucievents/continentalcircuits/
[2]: http://lightweight.info/us/en