Monday, April 30, 2012

Equipment - Wheel Inertia

I've always been a big believer in wheel inertia's effect on racing. I went against my thoughts and bought a heavier set of aero wheels (the HED Jets), thinking that if the pundits were right, they'd be better for me in the normal flat crits I do regularly. However I found that I had difficulties accelerating the heavier, more aero wheels. Eventually, against my "educated" thoughts, I used my non-aero clinchers. I immediately noticed a reduction in effort required to follow the group (a Tuesday night training series, normally driven by a few regular Cat 1s).

I proposed that weight does, in fact, have some significance in performance, but everyone (and I mean everyone) shot me down.

The problem is I can't prove it using any logic (math etc).

I think I found the answer.

Most aero pundits will point to the site, where they have a lot of interesting power/speed calculators. Using different wheels it's easy to see how their calculations show very little difference in distance covered given a certain power. Even using a pretty wide range of wheel weights (basically off their site), I couldn't come up with a significant difference between wheels in their calculators (like speed, given power, or power, given speed). I put in my own numbers for power, put in some wheel weights, and found that, wow, based on the math, I should race my TriSpokes all the time.

The reality is that "spin up", i.e. how fast a wheel spins up, makes a difference in acceleration. I find it exhilarating when I first ride the race wheels in March. My bike just leaps out from under me. I've measured pedal strokes required to get up to speed, sacrificing aero when dealing with multiple super hard accelerations. I'd be up to speed literally 2 or 3 pedal strokes before the others, soft pedaling while they finished ramping up to speed. I had some good results using the light wheels, and others using the aero ones.

(The races I have in mind were at the Tour of Michigan, where I could either run a TriSpoke or a 280g 28H box section wheel, the only two sets of race wheels I brought. Since the field was the same for each of the 8 races, the riders didn't vary much at all. Coincidentally my wheels were very similar to the wheels analyticcycling lists.)

Ultimately I raced most often with light, semi-aero wheels. My favorite wheels for many years were the Zipp 340s, as light as the Campy Record Crono 280g rims but a bit more aero. Later, after a few years of Spinergy Rev-X use (I wanted to support the company), and then some TriSpoke use (those early generation Zipps broke), I settled in on Reynolds DV46 tubulars. They happened to be very similar in profile to the Zipp 340s, were very light, and much more rigid than any other wheel I had in my quiver.

In 2010 I decided to try the wide aero wheels. The driving force was the Stinger 6 wheels. They were lighter than the DV46s and they were supposed to be significantly more aero. Light and aero, a win-win.

The wheels work great.

So I also got the HED Jet 6 front and Jet 9 rear, both aero wheels, both similar in profile to the Stingers. The Jet 6 front would be my training wheel so I would feel fluent on the Stinger 6s, and the Jet 9 I got because I figured aero trumps weight, and I wanted a really aero rear wheel.

(My wheel inventory philosophy is to get one very tall, very light rear wheel, and get two or three front wheels, one each of a shallow, kinda tall, and very tall. In the HED line up my ideal setup would be a Stinger 9 rear and the 4, 6, and 9 front. Now that they have a Stinger 7, I'd maybe go 7 rear, 4 and 7 front.)

When I got the Jets I was really psyched to use them in the Tuesday Night races. Slightly heavier, no dealing with wearing out tubulars, and more aero for the fast speeds I'd see in my only regular Cat 1-2-3 race (since the drivers at the races are basically Cat 1s).

To my dismay I found the Jets hard to accelerate. No matter what the math said on analyticcycling, I couldn't accelerate the wheels well, and I found myself getting tailed off quickly. When I used the lighter Stingers or, one night when I forgot the race wheels at home, the "non-aero" Bastognes (aka Ardennes), I found that I had a much easier time responding to the accelerations.

Something was wrong.

It wasn't me. I acknowledge that I explode regularly when I race, but I also know when it feels like something isn't right with my bike. The bike was fine but the Jet wheels were just a bit too heavy.

It had to be the math.

I examined the analyticcycling site a bit more in depth and I found something I think significant - the way they measure wheel inertia. They hang a wheel from a string (or similar non-stretch object) and measure the pendulum rate. The illustration shows the wheel being suspended from the tire area. This means the whole wheel acts as one unit. It does not allow differentiation between rim and hub. A 5 pound wheel with a 4 pound rim should swing in a similar fashion as a 5 pound wheel with a 1 pound rim. Hanging the wheel from the rim should (I think - remember, I failed physics, at least on paper) negate the weight distribution of the rim.

The wheel inertia table from that site ( Rotational Inertia) shows very little difference between wheel inertia measurements. This leads to the very close calculations of speed/power in the site's various calculators.

I found it hard to reconcile the site's calculators and my own experience.

I went as far as to contact the site but they politely brushed me off. Without any equations as suggestions I think I came off an an uneducated myth-chaser.

And I am, so I have no problem with that. I'm chasing the myth that, yes, weight does count. Aero is good but weight still matters.

Recently, when I clicked on an aero wheel ad (I find them absolutely irresistible), I found another site that had some interesting thoughts on the topic. 3T has some thoughts on aero and wheel weight. In it they calculate inertia a bit differently, by taking the mass and the radius.
(Page 4 of 5 has the inertia calculation)

3T's results show a dramatic difference in inertia just through a few spoke nipples (18 of them at 0.9g each, so 16.2g). Their numbers - if you move the spoke nipples from the rim to the hub, your inertia goes from 1.4 g m^2 to 0.008 g m^2.

That's huge.

If you used larger numbers, like a 100g difference in rim weight, the inertial differences would be even larger.

These numbers would reflect inertial differences between wheels more accurately. For example, if I used those 5 pound wheels as example, they'd come out like this:

5 pound wheel, 4 pound rim or hub, using 3T's dimensions for hub and rim radius (22mm and 294mm respectively).
Inertia = mass x radius^2

4 pound = 1816g
4 pound rim = 1816 x .294^2 = 156.97 g m^2
4 pound hub = 1816 x .022^2 = 0.87 g m^2

There is a tremendous difference in wheel inertia using this calculation. Using analyticcycling's methods I think there wouldn't be a lot of difference, if any. I have to admit that's speculation on my part because I haven't done the pendulum thing (or asked a physics person about results for my 5 pound wheel example), and the site doesn't detail the separate component weights of the wire wheel, i.e. the 32 spoke wheel.

I'll have to do some more research on this but this is the first time I made any kind of progress on this whole thing.

I knew there was a reason I was holding a sleeping Junior at 1 AM.


plantrob said...

Interesting how cyclists whose judgment I trust often have a very different experience with the effect of wheel weight than would be predicted by any mathematical analysis. There are certainly analyses out there (including this one at bike tech review that properly take rotational inertia into account - and still come up with a negligible effect on performance.

Marten said...

The Analytic Cycling calculator does calculate wheel inertia correctly. See the "parallel axis theorem" (Wikipedia has a page on it).

Also, the 3T calculations are only showing the difference of wheel inertia based on two spoke nipple configurations, not the total wheel inertia. The spoke nipples are only a small part of the total wheel inertia.

Aki said...

I'm a big fan of biketechreview - in fact I ask him stuff on a somewhat infrequent but persistent basis. I also trust his judgment when making calls on what counts and what doesn't count.

I'm also a huge fan of idea of cognitive dissonance. It can explain so many people's illogical thoughts.

And so here I am thinking stuff that, in the face of science, is illogical. I trust mathematics and physics, but if the experiment/measurement isn't set up properly, the results don't mean anything.

So I'm still convinced that there is something missing in the equations. If you gave me an option of a few different wheelsets, where I didn't know the weights, and asked me to accelerate them as hard as possible, it should be the case that all the wheels would accelerate at about the same rate initially, with the aero ones quickly overtaking the non-aero ones.

I actually did such an experiment with the most rudimentary of measuring devices (me and a cyclometer). I had basically the same tires on a slew of different wheels (Vittoria CX), and I went and did jumps (to "as fast as possible") for a couple hours, swapping wheels after a couple hard jumps. I even went back to previously tested wheels to see if my speed had dropped off.

I had a rough idea of weight (I was putting the wheels on/off the bike) but no real knowledge of actual weight.

What I found was that the lightest wheels accelerated much quicker, but most of them seemed to hit a wall at a certain speed. Since they happened to be less aero (like the Record Crono box rim) I attributed the aero wall to the rim's aerodynamics (correlation, I know, but it was all I had).

The fastest wheel was the TriSpoke, where I could go 6 mph faster at "as fast as possible". It also took a long time to get up to speed.

There were many inbetween wheels, RevX, 340s, 440s, and Ventos (the 16 spoke sister to the aluminum rim aero 12 spoke Shamal).

I even had a clincher RevX, but I don't remember anything significant about it.

I'm convinced and unable to prove that if someone got calculations for acceleration from lower speeds to higher speeds (typical response to attacks, like 25 mph to 35-40 mph), jumps out of corners (25 to 30 mph), etc.

I also think a rider's inefficiencies (pedal stroke flaws) doesn't get reflected in mathematical equations. I'm no electric motor, when I do a spin scan there are large differences between my down/up stroke and the rest of the pedal circle. I can smooth it out consciously but it's not how I ride.

Ultimately if weight really didn't matter we wouldn't have light wheels, we'd just have super aero wheels. Everyone would be running a 1200g rear disk wheel, if nothing else. For most conditions a 1000g tall front wheel would be great.

But neither you nor I nor virtually anyone else runs those wheels. It's not cost (a rear disk isn't that expensive compared to a 808 or 1080 etc), it's not ridiculousness (they run them on the track, but then again they hit some ridiculous top speeds regularly, and the fixed gear forces a smooth pedal stroke), it's because of something else. Cognitive dissonance? Maybe.

I'm still convinced that inertia matters. I just can't prove it. Until I run my Jet 6/9 combo and roll across the finishline with the others (I never have), I'll remain convinced that using the lighter Stingers or the Bastognes helps (and not only have I rolled across the finish with those wheels, I've placed 1st, 2nd, 3rd on them).

Aki said...

I mean no offense to you PR - the math supports your statement, and trust me, I'm a math type of guy.

I'm chasing a myth (I even say it in the post) and I'm trying to get thoughts and ideas along this idea, even if they disprove my thoughts.

plantrob said...

No offense taken in the least :-). Regarding your experiment - it's important to realize that the cyclometer is an instrument that emphasizes wheel inertia: the only thing you're accelerating is the wheel. The point of the full-bike calculations is that the contribution of the wheel to the effective mass being accelerated (even taking into account rotational inertia) is small compared to that of the total rider-plus-bike package. You take rider+bike out of the equation on the cyclometer, so I'm not surprised you find a more pronounced effect of wheel weight.

Marten said...

Aki, here is a qualitative description of how the pendulum test can differentiate wheel rotational inertia. The equations are ok.

When the wheel is swinging back and forth in the pendulum, it is actually doing two distinct motions, the back and forth swing along the arc, as well as rotating cw and ccw. The total movement is a sum of these two movements. Each movement is affected by a different type of inertia, linear for the first, rotational for the second. The total inertia is the sum of both of these. Because the linear inertia is just the mass, it is easy to separate out the contribution from rotational inertia.

I was convinced that rotational inertia must be very important, especially for a flat crit, with hard accelerations, and lots of pack drafting to minimize the aero advantage. Given a choice between a 1900g "aero" wheelset, and a 1500g non-aero wheelset, I'd take the 1500g any day.

However, even with the worst case scenario that I could come up with, the heavy aero wheel still ends up ahead. My specific situation was an 18-25 mph acceleration in 3 seconds. It is easy to calculate how much extra energy it takes to accelerate the extra rotating mass, and compare that to the energy savings over that same duration from the aero wheels. Even neglecting any aero savings from the rear wheel, the heavy rear wheels still end up ahead.

JR said...

I have been meaning to ask you, what size are your chain stays? I'd imagine that makes a difference in your "feel" of wheel inertia. And I agree with your analysis by the way.

Aki said...

PR - I don't know if I was clear but I was sprinting on the bike, so it was me, the bike, and the whatever wheels I had stuck on the bike for those laps. Yes, the difference would be just the wheels, at least I hope so. Purely unscientific in the sense that I didn't have control over much else (wind etc).

M - I'll have to look at this page a bit closer. I don't understand at first glance but I appreciate the explanation/link on the theory behind the method of measurement.

As far as the difference in inertia, I understand that - and if moving 16 grams inward 27 cm makes a huge difference, then having a lighter rim (versus a heavier one) should also make a difference.

I may be chasing an illusion, but my perception (taking into account an understand that I may "need/desire" to see a difference, which, honestly, would be easier if there was no weight effect - I could get rid of a lot of my light wheels and buy less expensive heavy aero wheels).

plantrob said...

Ah, yes, I misinterpreted your post - I was picturing a stationary setup (not sure why). Please ignore (and feel free to remove) my previous comment.

Aki said...

JR - On my test bike (back in the day) I had 40.5 cm stays. On my current bike (Tsunami) I have 39 cm stays. I used the Jets on the original Tsunami frame setup, 40.5 cm stays. That same frame now has ~39 cm stays on it now also (I just received it back and still have to build it up etc).

M - thanks for the detailed explanation. For some reason your comments are hitting my email later than the others, so I'm answering your posts out of order.

I should point out that I don't doubt the aero wheel's benefits. I'm just at a loss to explain what happened to me in 2010-2011 when I ran heavy but aero wheels and got annihilated, but when I ran light or aero (or both) I could hold my own.

Marten said...

Aki, I think that your open attitude to this is great, that's the best way to learn. Much of it really does seem counter intuitive, because weight is something that we can feel so much more directly. We can easily heft two bikes, one in each arm to compare weights, but isn't as easy to compare aerodynamic savings.

Not sure if this link will work in the comments, but it includes a similar discussion about this comparison (and a link to one of your posts). I may try and clean it up, to make the process, and results more clear.

Aki said...

PR - now that I incorporated a reply to your post I'll just leave your disclaimer post up :)

M - Thanks for the comment on attitude, and thanks for the more detailed explanations. I seem to get beaten down pretty hard whenever I propose this whole concept. For me, though, it's hard to argue against getting dropped vs hanging in and placing. Problem is that I'm not very "learned" in this area and so I'm going primarily on my observations. I try to be impartial but that doesn't mean anything without numbers backing me up.

Aki said...

M - I got a chance to look at the link. It's funny, someone referenced one of my posts as a "weight is important" thing. Immediately someone responded that the numbers prove that I'm wrong and that he'd take the math/science every day of the week and twice on Sundays.

I have no qualm with their opinions but my experiences seem to defy the numbers.

I'll have to contact the biketech guy because he's good at telling me I'm mistaken. Since he's raced with me and watched me race he relates his explanations to stuff I can relate to.

WMdeR said...

Dear Aki,

Rotational inertia does matter when accelerating.

If you work out the math, then the old saw about doubling rotating weight is about right for rims and tires. Hubs are effectively not rotating weight, so all those light-ish wheelsets that get light by using 215g hubs and Ti cassettes aren't buying you the relief you seek. I = MR^2, so changes to the mass as far from the center of rotation as possible provide the most benefit.

Wheelsets with 220g tubulars, 290g rims, aluminum nipples, and as few light-gauge spokes as are reliable for your purposes are light where it matters (for acceleration).

Top speed is limited by aerodynamic drag on the flats, but sprints aren't won by everyone winding out to top speed and hanging out there to see who has the highest top speed.

You can measure the rotational inertia of any object about some arbitrary point, then transform that measured rotational inertia about the point you measured it to the center of mass using the parallel axis theorem.

What Analytic Cycling is doing is determining the moment of inertia about the nail from which you hang the string and wheel using the period of oscillation of the resulting pendulum, then applying the Parallel axis theorem. You could get the same answer by applying I=Sum(MR^2) if you knew the radius of each element about the center of rotation and the mass of each element.

I'd check their units, too. They're not measuring things in grams--they're looking at kilograms-m^2 (SI units).

By the way, if you weigh 68kg, your bike weighs 7Kg, and you switch your 28g spoke nipples from the rim bed to the hub, you've saved roughly whatever those nipples weighed.

So, for a given linear acceleration a, the relative difference would be ('roundabouts--it would be exact if the mass of the nipples were at the road contact surface) twice the mass of the nipples divided by the total mass of you and your machine. Given a 75Kg total mass and 28g nipples, you'd have 0.00075 difference, or 0.08% change in the required force to accelerate the bike at a given rate.

Now, drop 5kg off of the rider, and and that's almost 7% easier to accelerate.

Alternatively, lets say you got rid of half of the rotating mass of your wheels.

In acceleration, you'd save about 2Kg (half of a two kilogram wheelset, including tires etc, times two) out of the 75Kg total mass, or 2.7%.

That would probably be worth chasing if you're winning races based on how quickly you can get from 25mph to 40mph.



Brian said...

The math is right on the website; I would question its accuracy. You are subtracting two large numbers (surely the rotational inertial around the penduluum axis dwarfs the rotational inertia of the wheel itself given the extreme difference in radius of rotation) to get a small number. Very small inaccuracies in the large number will result in very large errors in the resulting calculation.

A better test would be to place a known weight (say, 1lb) on the rim, and using the axle of the wheel as the pendulum axis, do the same calculation. At least this way the numbers being subtracted are the same order of magnitude as the result.

Danny said...

My issue with the Analytic Cycling tool (I'm guessing you're talking about the "Criterium Corner" case) is that: it's asking the wrong question; and it fails to take into account the non-linear response of the human body (burn too many matches and you get dropped!).

It's asking the wrong question, because the determinant of crit performance (from my limited 2 seasons worth of racing!) is holding onto wheels without killing yourself - it's not the steady state power output to maintain a fixed position to the wheel in front that really counts (and this is where aero helps), it's the speed with which you close gaps and the power spike you require to achieve that. The big bit of missing math is the drafting effect with respect to distance behind the wheel in front. My subjective feeling is that lighter wheels ultimately lead to lower power spikes in this situation, thus few matches burnt. I'm sure there's also a (real) psychological effect. If you feel like your bike is lively, it's easier mentally to turn it on, rather than that feeling of dread you get when a large gap opens and you know you're going to have to kill yourself to close it ;-)

Sean said...

Brian has a good point here. I was also suspicious. However, I ran through his computations and although he made some errors on significant figures, they are not severe. He claims numbers like 0.0885 but really should say 0.089 +- 0.001. At this level of accuracy I would say that it should be possible to differentiate the wheels.

It would seem that the "point mass" inertia dwarfs the rotational inertia in the pendulum equation, but this depends on the length of the pendulum. As r_0 gets large, it doesn't matter much. But I noticed that he chose 1.7m pendulum length, which is appropriate for a wheel that's approx 0.7m.

In other words I was also suspicious about the difference between large numbers, but it appears that he has used enough precision is his measurements to mitigate this. Example, for the 2nd entry in the table, I obtain:

I_c = 4.1775 - 4.0862 = 0.0913, but due to sig figs, this is really 0.091.

So I think his numbers are credible. This is a really small effect. However, as Will notes, it's small but significant. For the numbers given, I get about a 2% effect depending on one's weight. So if you take weight out of rotation it's basically the same as taking that much weight off the bike entirely.

Main point? I think fitness and leg strength and rider weight still dominate. But I don't doubt that you notice the difference pretty easily.

Anonymous said...

I look forward to your additional physics "research" and hope that you will post your results in a future entry.

The reality is that "spin up", i.e. how fast a wheel spins up, makes a difference in acceleration.

Yes but the reality also is that this is a negligible factor in bicycle racing. In my opinion, it's irresponsible to hype lighter-weight wheels on the basis of this "spin-up" concept which has already been widely discredited. "Spin-up" is wishful thinking by the "Fred" cyclist to justify why they dropped so much money on a wheelset.

Aki said...

Sorry for the big pause in notes as I was pretty sick the last few days.

Will, Brian, Danny, Sean - I appreciate your thoughts on this. I never thought of the effect of measuring a large quantity then using that to determine a small delta, and the implications for error there. I also realized that I am, at least while under the influence of Nyquil, completely unable to do any math beyond simple addition and such.

Someone suggested a cool experiment that I'd like to do if I have both time and the legs to execute. It's simply in its design; I'll probably try to use either a race or races (depending on if I'm fortunate enough to flat in a race with a free lap rule, or if I can sit out a lap and rejoin with a different wheel). If I had two identical wheels that would be best (one weighted, one not) but since I don't I'll have to just go by SRM readings using significantly different weight wheels (I'm thinking in the 500-700g range). If the races don't work out I may do some sprints on my sprint loop, changing wheels frequently to mix up the wheel weights. Either way it involves some time on the bike, some additional purchases, and trying to control some variables. Since I didn't have time to ride once in a week's time this could be hard. But I'll try and do it sooner than later.

Anon - Although I appreciate the note on your hopes for my future experiments on spin up, your derogatory statement doesn't help your case any. It's okay to direct flak at yourself (so, for example, you could identify yourself as a "Fred") but not at others.