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.
This is one of the most persistent and silly myths in cycling.
When biking at a steady speed, even when accounting for the fact that steady speed isn't entirely steady because humans pulse their power a bit, wheel weight is not worse than frame weight (the extra effort of each micro-acceleration is offset by the reduce slowdown between micro-accelerations and then some)
When climbing a mountain, wheel weight is not worse than frame weight
That is my spreadsheet, it is very very basic physics and it drives me crazy that people spew pseduo physics and comment on this "without taking the time to comapre the sizes of the effects"
take the time!
TLDNR; don't worry about wheel weight any more than frame weight. Addendum: don't worry about frame weight much either.
I'm no expert but I would say that wheels are closer to a ring. You're underestimating the moment of inertia of the wheels by a factor of about 2 by doing this. Might be well enough to throw off your conclusions. In fact if I read your spreadsheet correctly this would bring the rotational energy to about the same as the translation kinetic energy.
First three pedals are the only ones that count. All we ever, ever do is accelerate from a dead stop and cut people off at the 30ft line. I'm running front-specific rims front and rear to cut weight, and it's working.
This may not be applicable to cycling at large, but it's extremely important for BMX racing.
I think your spreadsheet makes several assumptions that are only true in theory.
As other have said, acceleration costs more energy. You don't get that back when braking.
More importantly, in practice, the road is not flat at all. There are small movements at every brick / stone that you cross, slightly rotating the bike forward and back. The momentum (MOI) multiplied with the weight of the bike for those those small movements is lost in energy. Weight at the ends of the bike (mostly the wheels) increases the momentum of the bike far more than weight in the center of the bike. I don't remember the exact energy formula, but think there is a power of 4 with the distance from the center in it...
I too have done the calculations, and with reasonable weight wheels it is totally trivial. Actually the weight of the bike itself is fairly trivial too unless you are a professional cyclist or regularly ride up mountains. The biggest difference it makes is how hard it is to pick the bike up.
Note that it is important if you have suspension though as you'll have a much smoother ride if the mass on the other side of the suspension from you is minimised. If the wheel is heavy the opposite and equal force will be felt when going over bumps.
The suspension reason isn't relevant to lightweight bicycles but important to keep in mind for other bikes.
I went for a bike fitting today and the guy that did the fitting was incredibly knowledgeable about all things bikes. He told me that due to the "physics" involved that wheels were 2 to 3 times heavier at speed. Turns out he was talking nonsense!
I wonder where this old wives tale about wheel weight comes from?
a 26inch wheel when spinning at 80 roations per minute (20km/h or 12mph) will have a Centripetal Acceleration of about 5g (G-Force) on the outermost spot. That does not make the wheel "heavier", but due to the gyroscopic effect and air resistance loose ever more energy, when spinning faster.
The article's conclusion isn't entirely correct. Mass on the wheels also affects braking (the reverse of acceleration), and handling (gyroscopes with less mass turn more easily). But otherwise, yeah, the standard line amongst racers is to upgrade your wheels before anything else (albeit racers do a lot more accelerating and braking that your average Sunday rider). Lighter wheels are like the SSDs of cycling: biggest bang-for-the-buck.
As a sidenote, the picture looks to be a late-1880s Columbia of some sort. Yup, same Columbia from whom you can buy a bicycle today (well, at least something bicycle-shaped; they haven't made good bicycles in over 100 years).
"Lighter wheels are like the SSDs of cycling: biggest bang-for-the-buck."
Completely wrong. Biggest bang for the buck is low CRR tires, then skinsuits, then, I don't know, maybe helmets. Then 100 other things, then light wheels.
Completely wrong. Biggest bang for the buck is low CRR tires, then skin suits,
Skin suits? Who let the triathletes in? :-) Horses for courses, I guess. For a crit, road race, and generally just riding around, I'll take a nice set of wheels before squeezing myself into a sausage casing.
Completely agreed. Tires a neglected by most cyclist. It is shocking how many people buy a nice bike and keep the stock tires, or worse, slap on conti gator-skins.
I haven't taken the time to compare the sizes of the effects, but it doesn't sit well that they blow past seemingly obvious ways extra wheel mass would go in the opposite direction. I see at least two places they do this:
Air Resistance:
> However, this force will produce a greater change in speed on the bike with less mass.
But the wheels act as (unsurprisingly) flywheels. Extra weight in the wheels adds both momentum and angular momentum, while frame mass adds only the former. This is exactly symmetric to their acceleration argument, so it's kind of shocking they skipped it.
Internal Friction
> More mass on a bike can increase the friction in the bearings—but again, this won’t matter where the mass is located.
As an extreme example, a massful wheel with a massless frame clearly has no bearing friction. I'm pretty sure wheel weight does not contribute to bearing friction.
Does anyone have any insight into why these matter less than the acceleration bit?
That seems like a very reasonable observation, and I would accept that as an answer if this were a discussion about road racing. However, the completely unqualified title (including the word "prove") implies something deeper. Road racing is never mentioned.
It's very common for bicycle enthusiasts to equate "better" with road racing. It's not just acceleration away from the group either. Almost all the effort you put into cycling at high speeds (say over 30 km/h) is overcoming wind resistance. You can save a huge portion of that effort by drafting behind someone. So in terms of saving effort (or making other people hurt) making and closing gaps is crucial.
But of course most people riding a bike are not racing. Even still acceleration is quite important. When you are on a relatively uniform gradient you can judge your power easily and make sure you don't go anaerobic. It's when you have to push hard to get over a small bump, or sprint ahead to get out of traffic, etc that you get into the red zone. Making those situations easier will make your whole ride easier.
But it is fair to point out that "good" bikes are really only "better" for certain situations. For example, my wife almost never travels faster than 20 km/h. Many of the things that are absolutely necessary on a "good" bike that is travelling at 40+ km/h make absolutely no difference for her. Lot's of people tootle around at 10-15 km/h. Any well maintained bicycle will be completely fine. In fact a "good" bicycle will be unsatisfactory because it will be hard to handle.
It's all about context. And in the context of talking about which bicycle is "better", the convention is to assume you are talking about road racing unless otherwise stated.
I have never ridden one (and I really want to ;-) ), but I've heard mixed reports on hills. You can push against the back of the seat, but you lose the advantage of using your weight on the pedals. Can anyone comment on what it's like for difficult hills? I have lots of gradients over 20% here and one of the hills I ride has a 30% section!
What BenFrantzDale said, plus: my old recumbent was front-wheel driven, but most of the weight was born by the rear-wheel.
So yes, I had problems on hills, because there was not enough weight on the driven wheel.
But mine was a very special kind of recumbent bikes, without a classic handlebar and instead steered with the feet. Most recumbents are driven on the rearwheel.
I have never ridden one either but weight on the pedals shouldn't matter. If you push down on a pedal as you extend your leg leaving your body at a constant height, that should be the same work as pushing just as hard over just as far against a seat. I'm sure there are subtleties – you can push more than your weight against a seat but a seat absorbs energy – but to first order it should be a wash.
I'm skeptical. When you're up out of the pedals and sprinting on a bike, you are transmitting an awful lot of energy. I don't quite see being able to push quite so hard when sat down.
One way of thinking about it is that work is force times distance, so if you aren't moving WRT the bike, and push just as far work goes by force. Assuming you don't have toe clips and so aren't pulling up with one foot while you push down with the other, then at most you can push down with your body weight. (You could push harder but that would leave your body accelerating up at the end of the stroke.)
You're thinking about it from a physics point of view, which is kind of abstract, and possibly not considering all the movement involved. I'm thinking about it from the point of sprinting for the finish line at a race last Sunday. I really don't think I could have brought the same force to bear while sitting down.
Also: modern bikes have clipless pedals, not toe clips.
Yes. For most people a good bike is a well maintained, comfortable bike with racks, fenders, chain guard and so on. For someone training for a triathlon a good bike is light, aggressive, a trillion gears etc.
I think hills are well covered - if you have to move the same amount of mass up either way, it doesn't much matter where said mass is on the bike.
Accelerating, as the article mentions, is the one place that their theory holds. My question was why that's considered more important than holding speed (which heavier wheels makes easier) or the extra bearing friction.
Last year I paid the $700 for custom made wheels. I fairly regularly go down short staircases (3 or 4 steps, or big curbs) and I used to blow through spokes like birthday cake candles.
No longer. Screw minimizing wheel weight. I want my bike to be an extension of myself. I want to be able to push it and for it to deliver. If I need to spend some extra joules on angular momentum, fine. My thighs need the workout anyway.
Downhill bikes weight 40 pounds, BMX's have 36 spoke wheels for 20" rims, etc.. for good reason: they are built to be good at what they do. You want to go race faster, you get light wheels, with medium to deep section rims.
How much do you weigh? I (used to) regularly drop off of stuff a foot or two and I never had any problems. My bike wheels can't have come close to that price. (I did need to move to downhill tubes as those kept getting pinches).
I weigh 165 pounds / 75 kg and I do this on a fairly large roadbike (I'm 6'1.5" / 187 cm). Are you slightly overfilling your tires? Say 90 PSI if the wheels are marked for 80? I found that really helps. But I do still get pinches fairly regularly.
Yeah, I'm kinda crazy with the thing. I've been considering trying out some stuff at the BMX park in Toronto really early in the morning so I don't get laughed at.
Tall guy who used to bmx here. Never broke a spoke but munted a few few wheels and one set of bearings. I dearly wish for a bmx scaled up by something like 1.3x or 1.5x. My neck has never recovered from the stupid head-tilted-up pose that bike forced me into. Loved the bike though!
How tall are you? We've got all kinds of stuff for tall people. Check out 24" BMX bikes (aka cruisers) - a cruiser with a long frame and 7" or 8" bars would probably suit you well.
Road bike nerds have known this for a while. If you ride a lot you will immediately feel the acceleration difference in a wheelset that totals around 1450g front and rear with hubs, spokes, nipples and rims (example: White Industries road hubs, Sapim CX-Ray spokes, medium profile high quality aluminum rim) vs the same spoke count "cheap" wheelset that might weigh 1800g.
That is all before you get into the category of exotic and expensive deep profile CF rim wheelsets that cost $1500+/pair...
Interestingly we have a guy at work who had a leg amputated. The shock absorber is by RockShox, and looks the same as the rear suspension on mountain bikes.
Fun story: My daily commuter is a ~50lbs cargo bike. The bike shop dude was trying to upsell me on some featherweight rims for my 26x2 tires. Concerns about mass were left behind a long time ago...
ya zips are spendy (but very nice). I am more of Flo fan for me $900 for a pair.. plenty aero.. fairly heavy.. but I can lose 1 pound from my belly for less than the $3000 nicer wheels would cost me to lose a pound.
Did you measure the acceleration difference that 350g/1800g makes? Say time 0-30 km/h with each set of wheels? (or perhaps better yet 5-30, to avoid starting from a stand-still). Because it sounds absurd that such a small change could be "immediately felt" - assuming bike+rider weighs on the order of 100 kgs.
> You will have double the increase in energy by adding mass to the wheel.
Is this always true regardless of wheel radius? At first I was thinking it has to depend on radius, but then thought about how the ground contact point has a zero velocity, and the exact other side of the wheel is always double the velocity of the bike frame relative to the ground, regardless of wheel radius. I'm not sure if this is a reasonable intuition. Maybe it makes sense that a gram added to the rim is always double the difference in effort that a gram added to the axle or frame or rider is.
Yes, the kinetic energy of a uniform ring on the outside of the wheel is exactly double of the kinetic energy of an equal mass elsewhere on the vehicle. You can prove this by integrating around the circle; the key is that the ratio of the velocity of a point on the ring to the velocity of the vehicle depends solely on the angle. (The point in contact with the ground isn't moving, while the point at the top of the tire is moving at 2v.)
Note that this applies only to the outside of the wheel; there is a cost to weight closer to the centre of the wheel, but not as much. (Also, things get weird with non-rotationally-uniform wheels, but people tend to avoid those for other reasons.)
It's discussed in terms of inertia and momentum, but these quantities are the useful quantities when discussing rotation about an axis.
Speaking loosly, applying a force perpendicular to the radius of a rotating body changes its angular velocity, which is a factor of momentum. The moment of inertia determines in part how large the torque on the mass is for a given force about the center.
To get a constant horizontal speed, a small-radius wheel must turn faster than a large-radius wheel. For a constant turn rate & rim mass, a small-radius wheel will have less energy than a large-radius one. I suspect (given the article's statement doesn't depend on the wheel radius) that these precisely cancel, but I haven't done the math to prove it.
>Well for adult bikes you are pretty much fixed at 700C. If making a bike pedaled contraption not so much.
For racing/road bikes, maybe. You're leaving out the 26" wheel adult bikes (which over time has encompassed 5 different rim diameters[1]) and 24" wheel bikes that are targeted at youth, but smaller adults sometimes prefer (well, those that have been give the option).
My bike pedaled contraption is a rear suspension compact long wheelbase recumbent with two real 20" (406mm rim) tires and they're spectacular.
I feel like less and less bikes are going for 26s. It used to be that the smallest bike or so from each manufacturer used 650C, then everything else used 700C. Seems like most manufactures just went to 700C for all adult bikes over the last few years...
Aerodynamics trumps weight for cyclists, even for wheels.
"In summary, wheels account for almost 10% of the total power required to race your bike and the dominant factor in wheel performance is aerodynamics. Wheel mass is a second order effect (nearly 10 times less significant) and wheel inertia is a third order effect (nearly 100 times less significant)."
Considering time trial or the last meters of a sprint, I completely agree.
Riding in a bunch, race or the city. Not so much. In Crits (80 laps times 4 corners at least) or a city ride you don't move fast most of the time, but bike handle, accelerate & brake most of the time.
This is pretty standard stuff in automobile land. Unsprung weight (includes slightly more stuff than this, but same basics) is known to have a disproportionate effect relative to, say, the driver gaining a couple lbs. People don't talk about it as much as other performance factors, but this is why magnesium wheels have existed for upper end cars for a while, and carbon-fiber more recently.
On the flip side, this is also exactly the same reason why flywheels outside of automobile land, when used as energy storage devices, are hugely massive.
Or to take the alternate view, if you want to get fit, get a heavy wheel. I'm having a super strong one built right now, and extra weight is fine by me.
Or take another alternate view: if you want to have a lighter bike and you don't want to pay for it, lose body weight instead. Then you'll be both lighter and fitter. Only once you've lost as much body weight as you can reasonably lose does investing heavily in a lighter bike make sense!
Naturally this doesn't, of course, diminish the fact that lighter wheels give you more bang-for-the-buck than lighter anything-else, due to the physics described in the article. But if the difference between heavy, cheap wheels and light, expensive ones is a few hundred grams and a few thousand dollars, losing a pound of body fat is likely a better bet.
Or those trendy fat tire bikes. Yes, they are great on sand and snow, but pointless and even counterproductive on the asphalt where I am seeing them more lately.
Increase in unsprung weight is also bad for suspension[1] and handling[2].
Here's something they don't mention in the article: the location of the mass in the wheel has a direct relationship to torque. The same mass located in the hub will take less torque to move than if the mass were located in the rim. So acceleration could in part be improved merely by relocating mass in the wheel. (But that's just wheel acceleration torque; you'll still need to do the same amount of work to move the same total mass of the bike at the same speed)
Also, for the same weight tire rubber, wider tires would create increased friction and slow the tire down more.
I'd be curious to see the math on 29 inch mtb wheels vs other sizes. Of course there are other things in play there like the ability to roll over obstacles (29ers do this well) and maneuver in tight spaces (not quite so good).
The same conclusions about mass hurting acceleration also occur with the car, but the relative masses are so different, it's mostly irrelevant (cars are a lot heavier than bike frames).
The main difference comes with the ability of a lighter wheel to be able to fully track the road, and not leave it on a bounce. This gives better traction. (But somewhat greater vibration in the cabin.)
Unsprung mass is more about the effectiveness of suspension in keeping the wheel on the road. This is about rotating mass and the fact that you have to 'speed up the wheel twice', once in translation and once in rotation, and so rotating mass stores more kinetic energy than non-rotating mass.
Taken to the extreme, what is going to move faster, a thin strip of steel on 6 logs, or 6 logs on a thin strip of steel with, say cartwheels wheels under that?
I think "unsprung weight" is a different idea, at least in bike racing. Unsprung weight represents the weight not supported by suspension. In road racing, the suspension is the rider, so the entire bike is unsprung weight.
Not quite. This is a direct relation to "rotating mass", which does include tires and rims but also includes stuff like driveshafts, which are made of shockingly thin tubes of steel or carbon fiber for this reason.
Unsprung mass is relevant to vehicles with suspensions (including mountain bikes). The inertia of the vehicle is set against the inertia of the wheel when it's being pressed back down on the backside of a bump.
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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].
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[1]: http://www.uci.ch/road/ucievents/continentalcircuits/
[2]: http://lightweight.info/us/en