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Inertia of 29er vs 26er wheel

it's amazing how that tired ass, misinformed crap about inertia/rotating weight can still linger...
people who want to sound like they know what they're talking about but have no idea...

Originally Posted by Durga
Could you please explain?
I have... many times.
When it comes to acceleration and 26 vs. 29, all that matters is wheel mass. Talk of moment of inertia or the "flywheel effect" or leverage are all bogus.
Moment of Inertia is an abstract concept that is tossed around mostly by people who like to use big words. I'd bet the builder, while he might deserve respect, does not know what the formula for MoI is or how to measure it or what the value of it is for those wheels compared to others. If he did he wouldn't talk about it like he does. I'd also bet that he hasn't read any of the research that shows that even great changes in MoI do not have measurable impacts on performance.
The bottom line is that, like many other technical concepts, MoI is WAY overhyped and 99% of the times it is brought up it is irrelevant.

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Originally Posted by meltingfeather
I have... many times.
When it comes to acceleration and 26 vs. 29, all that matters is wheel mass. Talk of moment of inertia or the "flywheel effect" or leverage are all bogus.
Moment of Inertia is an abstract concept that is tossed around mostly by people who like to use big words. I'd bet the builder, while he might deserve respect, does not know what the formula for MoI is or how to measure it or what the value of it is for those wheels compared to others. If he did he wouldn't talk about it like he does. I'd also bet that he hasn't read any of the research that shows that even great changes in MoI do not have measurable impacts on performance.
The bottom line is that, like many other technical concepts, MoI is WAY overhyped and 99% of the times it is brought up it is irrelevant.
I'm not exactly sure what moment of inertia is, but the way the builder writes about inertia seems to make perfect sense. As we know, otherwise identical rims, tires, and spokes are always heavier in the 29er version. Therefore, unless using more advanced technology, 29er wheels will have greater inertia and slower acceleration compared to 26" wheels using the same components.
So I wouldn't disagree with the builder on either of his statements: 1) given the nature of a larger wheel with more material, 29ers are more accelerationally (made up) challenged 2) all things equal, a wheel with the lower inertia will accelerate better.
The builder never mentions moment of inertia, but his logic seems sound to me.

Originally Posted by Durga
As we know, otherwise identical rims, tires, and spokes are always heavier in the 29er version. Therefore, unless using more advanced technology, 29er wheels will have greater inertia and slower acceleration compared to 26" wheels using the same components.
So I wouldn't disagree with the builder on either of his statements: 1) given the nature of a larger wheel with more material, 29ers are more accelerationally (made up) challenged 2) all things equal, a wheel with the lower inertia will accelerate better.
The builder never mentions moment of inertia, but his logic seems sound to me.
Except you haven't considered the extent to which the differences matter.
In rough terms, wheels might make up 1/3 of the total inertia of the bike and the bike only 1/6  1/8 of the total inertia of the system. That means wheel inertia is maybe 45% of total inertia. A 29er wheel will be heavier with identical construction by roughly 10%, but that means 1/2% to the total system. It's of no consequence.
When you read the author say how critical it is to use ultralight spokes to reduce inertia, you know he's ignorant of the real issues.

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Originally Posted by craigsj
A 29er wheel will be heavier with identical construction by roughly 10%, but that means 1/2% to the total system. It's of no consequence.
I see your point. However, I think a 10% difference in wheel weight, centered mostly in the rim and tire, is definitely noticeable and significant. It's roughly the equivalent of going from a 600g to 500g tire. Plus, though you state the difference is only 1/2% of the total system, doesn't the fact that it's rotating mass bump that number up?
I guess what meltingfeather is really getting at is that the bump isn't as much as people often think. It's an interesting point. Fundamentally, the statements of the builder in question are sound (and make sense logically), but it would be interesting to find out just how much of a difference a change in rotational weight actually makes in energy expenditure compared to an identical change in static weight.

Originally Posted by Durga
I see your point. However, I think a 10% difference in wheel weight, centered mostly in the rim and tire, is definitely noticeable and significant. It's roughly the equivalent of going from a 600g to 500g tire. Plus, though you state the difference is only 1/2% of the total system, doesn't the fact that it's rotating mass bump that number up?
It is noticeable but not due to its contribution to overall inertia. Significant I'm not so sure.
I factored in the fact that it's rotating in my initial estimate of 1/3 of total inertia of the bike. Yes it does matter. The rim and tire matter twice as much as any other weight. Spokes are too light to really matter, nothing else on the bike is much different from anything else.
Originally Posted by Durga
I guess what meltingfeather is really getting at is that the bump isn't as much as people often think. It's an interesting point. Fundamentally, the statements of the builder in question are sound (and make sense logically), but it would be interesting to find out just how much of a difference a change in rotational weight actually makes in energy expenditure compared to an identical change in static weight.
Detailed calculations of that have been posted here before. They are pretty straightforward once you realize you don't have to worry about moments of inertia.

meltingfeather: When it comes to acceleration and 26 vs. 29, all that matters is wheel mass. Talk of moment of inertia or the "flywheel effect" or leverage are all bogus.
The stuff about the spokes is a bit of bogus, but moment of inertia is very real and it relates directly to rotational mass (mostly rim and tire/tubes). Just like mass affects momentum, rotational mass affects moment of inertia. And the greater the rotational mass the more rotational force will be required to change its rotational rate. Also the further out the object's mass is, the more rotational inertia the object has, and the more rotational force (torque) is required to change its rotation rate.
I am sure you feel the difference between 2100g wheels with 825g rubber and 1550g wheels with 500g rubber. In fact the difference is huge, although we are talking about 1/3 lighter set of wheels.
My rides:
Lynskey Ti Pro29 SL singlespeed
KHS Team 29
SWorks Roubaix SL3 Dura Ace
Pake French 75 track

Originally Posted by serious
meltingfeather: When it comes to acceleration and 26 vs. 29, all that matters is wheel mass. Talk of moment of inertia or the "flywheel effect" or leverage are all bogus.
The stuff about the spokes is a bit of bogus, but moment of inertia is very real and it relates directly to rotational mass (mostly rim and tire/tubes). Just like mass affects momentum, rotational mass affects moment of inertia. And the greater the rotational mass the more rotational force will be required to change its rotational rate. Also the further out the object's mass is, the more rotational inertia the object has, and the more rotational force (torque) is required to change its rotation rate.
And how do you think any of this affected his component choice?
I understand what MoI is and how it relates here, which is why I made the comments I did. The fact is, he built a light wheelset for a weight weenie bike. Spicing the explanation up with technical terms is just blowing smoke and I call it like I see it. I guarantee you he didn't consider or even look at MoI in quantitative terms in spec'ing the wheelset, he just picked the lightest components he could.
At the end of the day, what I said about wheel mass, diameter, and acceleration is still a fact of life. A 29er wheel and a 26" wheel of the same mass will not accelerate any differently in terms of actual effort. Discussion of perceived effort is something entirely different and, incidentally, a topic on which MoI has exactly zero bearing. There is no special consideration of MoI that a 29er wheel needs vs. 26".
Originally Posted by serious
I am sure you feel the difference between 2100g wheels with 825g rubber and 1550g wheels with 500g rubber. In fact the difference is huge, although we are talking about 1/3 lighter set of wheels.
huh?
Last edited by meltingfeather; 04242012 at 03:16 PM.

mtbr member
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It's been 25 years since I did this kind of stuff, but hey, someone here might have some fun with this.
I'd say for theoretical purposes, a wheel is close to a ring torus, at very least to see the relative differences in moment of inertia:
Torus  from Wolfram MathWorld
Have fun!!!!!
I guess I could see how the "moment of inertia" might influence acceleration (overcoming the resistance the mass presents to a change), but I'm in the whole "more rotating mass tracks better on my fully rigid rig" camp, more specifically, blissfully ignorant and using the size of my smile as my gauge of what works for me

Meltingfeather: A 29er wheel and a 26" wheel of the same mass will not accelerate any differently in terms of actual effort
Wrong! The difference in effort is similar to 2 less teeth on a sprocket. As I said, the farther the mass is from the center, the harder it is to accelerate.
My rides:
Lynskey Ti Pro29 SL singlespeed
KHS Team 29
SWorks Roubaix SL3 Dura Ace
Pake French 75 track

Originally Posted by serious
Meltingfeather: A 29er wheel and a 26" wheel of the same mass will not accelerate any differently in terms of actual effort
Wrong! The difference in effort is similar to 2 less teeth on a sprocket. As I said, the farther the mass is from the center, the harder it is to accelerate.
So you don't understand the rolling wheel OR how gearing works?
What you said about moment of inertia is true, but what you don't realize is that moment of inertia doesn't matter in a rolling wheel. While increasing the wheel radius does increase the moment of inertia, it decreases angular velocity at the same time. Those simultaneous changes cancel each other out, leaving only the change in mass. Furthermore, only the mass in the rim and tire matter.
As for your gearing comment, you obviously just made that up but "2 teeth" isn't a change in gearing. You are missing a denominator.

craigsj,
I am an engineer and I know exactly what I am talking about. First, forget about a rolling wheel, it is an accelerating wheel we worry about, ok? Changing the size of the wheel (from 26 to 29 in) is similar to changing the size of the sprocket (decreasing by about 2 teeth), from a gearing ratio. How difficult is that to understand?
So if you ride 32:16 on 26er, you will be 32:18 on 29er, to keep the effort similar in terms of acceleration. Unfortunately, if all materials are the same (rim, tube, tire), there will be more of it on a 29er wheel (there is more diameter to cover), hence the additional weight, and that will be felt in acceleration, but can be addressed by additional changes in gearing ratios.
My rides:
Lynskey Ti Pro29 SL singlespeed
KHS Team 29
SWorks Roubaix SL3 Dura Ace
Pake French 75 track

Originally Posted by serious
craigsj,
I am an engineer and I know exactly what I am talking about. First, forget about a rolling wheel, it is an accelerating wheel we worry about, ok?
No, not OK. A bicycle wheel rolls always. There is never a reason to "forget" about that so as to come to the wrong conclusions.
Originally Posted by serious
Changing the size of the wheel (from 26 to 29 in) is similar to changing the size of the sprocket (decreasing by about 2 teeth), from a gearing ratio. How difficult is that to understand?
It's easy to understand, just irrational. You yourself just listed a numerator and a denominator for wheel size (29" and 26") yet not for the change in sprocket size. How difficult is that to understand?
Originally Posted by serious
So if you ride 32:16 on 26er, you will be 32:18 on 29er, to keep the effort similar in terms of acceleration.
You have now changed the subject. The subject was wheel inertia, now it's the effect of wheel size on gearing. Yes, a 29er changes gearing over a 26er by roughly 10%. That has nothing to do with wheel mass, moments of inertia, or acceleration.
Originally Posted by serious
Unfortunately, if all materials are the same (rim, tube, tire), there will be more of it on a 29er wheel (there is more diameter to cover), hence the additional weight, and that will be felt in acceleration, but can be addressed by additional changes in gearing ratios.
Yes, that has been recognized from the very beginning. It is only the extra mass of the wheel that matters, not the diameter. That's what MF said that you took exception to. It is also of very little consequence and would not be appropriate to "address" it with gearing, much less with an incomplete representation of gearing.

Originally Posted by serious
craigsj,
I am an engineer and I know exactly what I am talking about. First, forget about a rolling wheel, it is an accelerating wheel we worry about, ok? Changing the size of the wheel (from 26 to 29 in) is similar to changing the size of the sprocket (decreasing by about 2 teeth), from a gearing ratio. How difficult is that to understand?
So if you ride 32:16 on 26er, you will be 32:18 on 29er, to keep the effort similar in terms of acceleration. Unfortunately, if all materials are the same (rim, tube, tire), there will be more of it on a 29er wheel (there is more diameter to cover), hence the additional weight, and that will be felt in acceleration, but can be addressed by additional changes in gearing ratios.
So you've changed the topic, and I said nothing about gearing previously, but you agree that, given the same gearing and wheel mass, a 29er will not require additional effort?
Since you're an engineer and know what you are talking about, forgive me if it sounds odd for me to tell you that effort (energy, work, etc.) and gearing are not one and the same as you state. Gearing affects the distribution of force and time (small force + long time or large force + short time), not the effort (work done).

I did not change the topic. I am trying to relate wheel size changes to gearing changes for those that still do not understand that diamater (just like rotational weight) make a difference. And I am relating gearing to torque, because acceleration is the real issue (but craigsj still needs to learn that fact of life ).
Also you said: "but you agree that, given the same gearing and wheel mass, a 29er will not require additional effort?" It has to be "gear inches" that has to be the same not just gearing. But I am certain this is what you are getting at, right?
My rides:
Lynskey Ti Pro29 SL singlespeed
KHS Team 29
SWorks Roubaix SL3 Dura Ace
Pake French 75 track

Originally Posted by serious
I did not change the topic. I am trying to relate wheel size changes to gearing changes for those that still do not understand that diamater (just like rotational weight) make a difference. And I am relating gearing to torque, because acceleration is the real issue (but craigsj still needs to learn that fact of life ).
you absolutely did change the topic. read your first post. nothing about gearing... all about inertia and mass and greater torque to change rotation rate. incidentally, you did not in that "explanation" acknowledge the critical point that radius affects rotation rate in such a way as to remove radius alltogether from the energy requirement calculation (my whole point).
Originally Posted by serious
Also you said: "but you agree that, given the same gearing and wheel mass, a 29er will not require additional effort?" It has to be "gear inches" that has to be the same not just gearing. But I am certain this is what you are getting at, right?
you are being pedantic, but at least you understand what I'm saying.
you still didn't answer the question...
and you still seem to be equating gearing (gear inches or whatever you want to call it) with effort. are you telling me it takes less effort (energy) to climb a hill if you do it in a lower gear?

Originally Posted by serious
I did not change the topic. I am trying to relate wheel size changes to gearing changes for those that still do not understand that diamater (just like rotational weight) make a difference. And I am relating gearing to torque, because acceleration is the real issue (but craigsj still needs to learn that fact of life ).
If you are now going to claim you were arguing gearing differences all along, then you have utterly failed to understand even the slightest bit of the conversation that occurred before you. Don't tell someone he's wrong when, first off, he is not and, second, you haven't bothered to understand what he is talking about.
You know, if you shift up to your big chainring your wheel gets harder to "accelerate" as well. How does what spoke you choose change that?

Here is an MTBR thread where this is discussed at length. Both MF and I participated.
Here is a repost of comment #118 made by smilinsteve. I chose it since neither MF or I wrote it:
"Yeah I was hung up on this for a while, so I’ll explain it. Starting from the link you posted, the energy of a wheel rolling down a ramp is equal to is rotational plus translational energies:
E(trans)=½mv²
E(rot)=½Iω²
As craig pointed out, it does take more energy to spin a larger wheel to a certain rotational velocity, but the larger wheel spins more slowly for a given translational velocity. So the extra energy to spin it is canceled by the less angular velocity it needs.
Mathematically, Melting Feather showed the equation that the total energy of a rolling wheel is dependent on the mass and the translational velocity, not the radius. He didn’t derive this formula though, so I’ll do that now.
Put some energy into a wheel to make it roll and that energy is converted to translation and rotation:
E = ½mv² + ½Iω²
I’m going to use moment of inertia I = mr², as for a hoop or hollow cylinder
And ω= angular velocity (rad/sec), which is related to translational velocity for a rolling wheel (not slipping) by ω= V/r (1 rotation = 2pi radians and circumference =2pi*r)
Substituting:
E= ½mv² + ½mr²ω²
E= ½mv² + ½mr²( v²/ r²)
Notice the r²’s cancel out in the second term and you are left with
E=mv²
So, you can see the energy it takes to get a wheel up to certain translational velocity depends on its mass. More mass more energy. Higher velocity, more energy. The size of the wheel doesn’t matter assuming the distribution of the mass of the wheel stays the same ( a different distribution of mass would change the moment of intertia formula and therefore the result)."

Originally Posted by meltingfeather
you still didn't answer the question...
and you still seem to be equating gearing (gear inches or whatever you want to call it) with effort. are you telling me it takes less effort (energy) to climb a hill if you do it in a lower gear?
Less Torque! As in the force required to accelerate a wheel.
My rides:
Lynskey Ti Pro29 SL singlespeed
KHS Team 29
SWorks Roubaix SL3 Dura Ace
Pake French 75 track

craigsj,
This supports my statement! Especially the last sentence, since mass distribution is certainly different on a larger wheel. Too funny.
Last edited by serious; 04252012 at 11:32 AM.
My rides:
Lynskey Ti Pro29 SL singlespeed
KHS Team 29
SWorks Roubaix SL3 Dura Ace
Pake French 75 track

Originally Posted by serious
Less Torque! As in the force required to accelerate a wheel.
less torque over a longer period (due to lower velocity) = the same amount of work (effort)
you are starting to throw red herrings and confuse the topic. i think i've explained in very plain terms what i mean, so i'll leave you to your antics.

So all else being equal, how is a 29 inch wheel/tire assembly going to ever have less mass than an equivalent 26 inch wheel/tire?

Thank you tl1, that is the point of this sentence: The size of the wheel doesn’t matter assuming the distribution of the mass of the wheel stays the same
As you indicate the mass distribution is certainly not the same.
My rides:
Lynskey Ti Pro29 SL singlespeed
KHS Team 29
SWorks Roubaix SL3 Dura Ace
Pake French 75 track

Originally Posted by tl1
So all else being equal, how is a 29 inch wheel/tire assembly going to ever have less mass than an equivalent 26 inch wheel/tire?
what do you mean by, "all else equal?"
either the mass is equal or the rim and tire specs are equal... they are mutually exclusive.
i think it's pretty obvious that the same spec wheel in 29er will weigh more than the 26" version... i forget when humans typically learn that, but it's in the single digits, age wise, I think.
my point is that talk of moment of inertia and "flywheel effect" is irrelevant.
my goal is to help dispel the myth that 29er wheels are somehow harder to accelerate due to diameter. mass is all that matters.
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