# Thread: Inertia of 29er vs 26er wheel

1. Originally Posted by meltingfeather
what you fail to understand is that 1) a 29er wheel "moves out" 1.5" relative to a 26" wheel, and 2) the distribution jtmartino is talking about is the fundamental nature of the shape, which is captured in the constant in the MoI equation (note that different shapes have different formulas, though all share the mr^2 term). in any case, if you calculate the MoI as I did, the constant controversy goes away and, as you can see based on the calculations I posted, there is still no energy or power effect.
the two wheels have different MoIs because the radius is different (1.5" different, if you need reminding), and the reason it doesn't affect acceleration (for the 1,894,274 time) is that the "moving out" of the tire and rim also slows the rotation of the wheel for a given speed.
good writtens!
Yeah, sorry about the 3in diff. My mistake

But seriously what is wrong with the calculations here?

2. Originally Posted by serious
But seriously what is wrong with the calculations here?
Nothing. It says exactly what we've been saying here all along.

In his equations, he chooses wheels of identical construction so mass scales with radius. He says:
But of course mass depends on radius. The mass of a cylinder is:
m = density 2 P r
Let's let the constant C be "density 2 P":
m = C r
So his conclusion is that only the mass of the wheel matters, just like we have been saying.

In the conclusions, he also says:

So this issue is finally settled, right? Unfortunately not. It takes this much energy to get the wheel up to speed, but once it's there, you only need to add more energy to make up for what has been lost to friction, and here the larger wheel wins.

Larger wheels have less rolling resistance...
Which is also what I have said all along.

Then he says:

A 200 pound (90.9 kg) bike/rider combination moving at 20 mph (8.94 m/s) has a kinetic energy of 3632 joules. Additionally you have rims/tires/tape/spokes that weigh around 800 grams, which at this speed (and 27inch wheels) will need about 15 joules per wheel (note that the cogs and freewheel add very little to the rotational inertia because though they are heavy, they have radiuses much smaller than the rim). So about 1 percent of the energy you expend while accelerating to 20 mph goes into the rotation of the wheels. A 13.5 inch wheel would give you roughly a half of a percent improvement in accelaration (actually even less, as these calculations ignore the energy you lost during acceleration to wind resistance and rolling resistance).
This is similar to the examples that have been presented here as well. Differences of less than 1%.

And finally:

I don't have good numbers right now on rolling resistance differences between different wheel sizes that are similarly inflated (email if you have good data), but my gut reaction is that you lose more in rolling resistance than you gain in accelaration.
Also true.

What he doesn't mention, odd considering his recumbent mindset, is that smaller wheels aren't always lighter. A 700c wheelset can be built lighter than many smaller wheelsets due to the availability of lighter rims and tires. We have been saying that here over and over again as well. He may not consider a wheel that large viable for his use, though.

3. Craigsj,

Right, but do you see how his first conclusion is what one would naturally make (see below)? Do you see why larger radius would be associated with larger mass by most people, even if radius does not play in the equation? But don't take this in the wrong way. I am not trying to justify my posts. Anyway, looking back at my posts, I was out of line with my language and I do apologize.

This means that for any given forward speed of the bicycle (v), the energy required just to get the wheel up to speed is greater for larger radius wheels. And this relationship is linear, e.g. a wheel that is 50% larger (in radius) will require 50% more energy to reach the same speed (note that this is only wheel rotation energy, not the much larger amount of energy needed to accelerate the bike and rider).

4. Originally Posted by serious
Craigsj,

Right, but do you see how his first conclusion is what one would naturally make (see below)? Do you see why larger radius would be associated with larger mass by most people, even if radius does not play in the equation? But don't take this in the wrong way. I am not trying to justify my posts. Anyway, looking back at my posts, I was out of line with my language and I do apologize.

This means that for any given forward speed of the bicycle (v), the energy required just to get the wheel up to speed is greater for larger radius wheels. And this relationship is linear, e.g. a wheel that is 50% larger (in radius) will require 50% more energy to reach the same speed (note that this is only wheel rotation energy, not the much larger amount of energy needed to accelerate the bike and rider).
Yes I do, and I have said this many times in the thread already. I would not say it as he did, though. I would say that the heavier wheel is requires more energy. While it is true that larger wheels are likely heavier, it is not always the case. There is no insight gained by continuing to insist that wheel radius itself is involved when it is simply mass.

As an example, many recumbents use small wheels and have to resort to relatively heavy construction due to availability of parts. They could be very light weight but aren't because ultralight rims and tires are simply not available. They are in larger sizes.

Here is the first page that showed up in my search of recumbent wheel weights. In every case these wheels are heavier than my road wheelset despite my bike have MTB disc wheels. The tires for these 20/26 recumbent wheels are vastly heavier than the ones I use as well. My road bike, despite its larger wheels, has less rotational inertia than most, if not all, 20/26 recumbent bikes. That's a fact simply because of real world limitations.

Of course, parts availability for 26ers and 29ers as similar in that regard at this point, so a weight weenie can always build a lighter 26er with current parts. That is rarely the issue though. The important thing is the weight, not the size, to the extent that it is important at all (which it really isn't).

5. Originally Posted by JeroenK
Well.. if you like to enter rolling resistance, be my guest! Be sure to base it on real world measurements, but I would not expect anything less from you
Now that I've had some time, I'll answer this again including rolling resistance.

I've attached four graphs. The first two represent the velocity, the second being a zoom of the last second of the test so the results can be seen better. The second two are distance.

The red and blue curves represent no rolling resistance. I added these to show that the results were consistent with the answer I provided earlier. The yellow graph is the 26er with rolling resistance factored in and the green is the 29er.

For rolling resistance, I chose 55W at 20kph. This may not be the lowest available, it's hard to tell, but it's representative of more an XC tire than an AM or DH one. For 29ers I chose a benefit of 10%. This is higher than it would be on pavement but wouldn't be unreasonable offroad IMO.

Notice that rolling resistance has a real impact and that the 29er is now faster than the 26er by an amount perhaps 3x greater than the difference with rolling resistance excluded. There is never a speed at which the 29er isn't at least as fast as the 26er, a surprising result. At the 20 second mark, the 29er is about 2m ahead AND rolling easier.

I modeled this using Sage, and online math system. Here is the source I used:

Code:
```var ('t')

ma=81.7
mb=82.3
tb=0
te=20
p(t)=600
p6(t)=600-10*vc
p9(t)=600-9*vd
va(t)=sqrt(2 * p(t) * t / ma)
vb(t)=sqrt(2 * p(t) * t / mb)
vc(t)=sqrt(2 * p6(t) * t / ma)
vd(t)=sqrt(2 * p9(t) * t / mb)
sa(t)=va * t / 2
sb(t)=vb * t / 2
sc(t)=vc * t / 2
sd(t)=vd * t / 2

pa=plot(va,(tb,te),rgbcolor=('red'));
pb=plot(vb,(tb,te),rgbcolor=('blue'));
pc=plot(vc,(tb,te),rgbcolor=('yellow'));
pd=plot(vd,(tb,te),rgbcolor=('green'));
p=pa+pb+pc+pd;
p.show()

pa=plot(sa,(tb,te),rgbcolor=('red'));
pb=plot(sb,(tb,te),rgbcolor=('blue'));
pc=plot(sc,(tb,te),rgbcolor=('yellow'));
pd=plot(sd,(tb,te),rgbcolor=('green'));
p=pa+pb+pc+pd;
p.show();```

6. Who cares. Go out and ride.

7. Sweet negative rep because you didn't like my comment??? LOL

8. Originally Posted by meltingfeather
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.
Are there any academic research papers which have looked at this by hooking up two bikes with wheels/tires of identical mass but one a 29" and one a 26"? I would be interested to see the force required for each to get them from say 0-30 kph and then repeating the experiment with wheels that have the same weight/radius ratio. Does this even matter or is it automatic, as it seems from the equations you are using, that the extra mass increases the force needed not the size EEE of the wheel? I know this is an old thread but as an analytical guy I can't get enough of it. I always thought it was tougher to climb with a 29" wheel than a 26" wheel. I guess I could try to find a 26" Wheelset that weighs the same as my 29" set and see which is tougher to push.

Edit: with identical gearing, say like a SS setup?

9. Originally Posted by ChewynMe
Are there any academic research papers which have looked at this by hooking up two bikes with wheels/tires of identical mass but one a 29" and one a 26"? I would be interested to see the force required for each to get them from say 0-30 kph and then repeating the experiment with wheels that have the same weight/radius ratio. Does this even matter or is it automatic, as it seems from the equations you are using, that the extra mass increases the force needed not the size EEE of the wheel? I know this is an old thread but as an analytical guy I can't get enough of it. I always thought it was tougher to climb with a 29" wheel than a 26" wheel. I guess I could try to find a 26" Wheelset that weighs the same as my 29" set and see which is tougher to push.

Edit: with identical gearing, say like a SS setup?
"Academic research papers" aren't the type of medium that speaks to detractors on this issue. All of the facts have been laid out in both mathematical and colloquial terms, and there's no real basis for disputing them on merit, so if one refuses to accept the facts, there's no reasoning or even a point to discussion.
Second, you don't need a study to flesh this issue out. First principles arguments are clear, and all that would happen is that people who don't believe the results would say that the study is not relevant to riders on trails for (fill in your) reason.
That said, I'd love to see a study if you find one.

10. So, taking a slightly less rigorous approach: - who feels that their 29er is harder work than their 26er?

I selected Arch Ex rims for my 29er as I felt that the flexier nature of the larger wheel might require a bit more strengh than my 355 rims on my 26er. In theory that disadvantages my 29er twice over compared with my 26er. My 26er is certainly a fabulous bike, but I do seem to prefer my 29er. I guess the harder to accelarate thing is counterbalanced by the conservation of momentum thing. Go Figure!

11. Originally Posted by Tea@Dimbola
So, taking a slightly less rigorous approach: - who feels that their 29er is harder work than their 26er?
My 29er are definitely less work, but my only 26" bike is my Big Dummy, which I use for hauling cargo (lumber, groceries, beer, the dog etc.)

12. Mass distribution (density) of the rim & tire related to the distance (lentht of path).

If you cut 29" and 26" rims&tires and lay it next to each other. You get two spaghettis. Longer and shorter.
there is some mass distribution related to for example 1cm of the lenght of each spaghetti.
Lets assume this distribution is the same. I see no reason why the density or tire or rim should be different for 29" vs 26" wheel

for example both wheels travel 1000cm of distance
for 29" you are moving more rotating mass - this is the reason it should need more energy in kJ to travel 1000cm?
but the 29" spins slower - therefore it should need less energy in kJ to travel 1000cm?
Which prevails?

Sorry I red just to page 8. this thread is really 150%

13. There are some basic, entry level 36ers available. I guess one may want to build a comparably designed 26er with parts of similar quality.
26 rim is 559mm and 36 rim is 787mm so every one would see the difference clearly.

14. I am now any wiser. Was expecting some math evidence.
What do you think meltingfeather?

15. Originally Posted by Cowan
I am now any wiser. Was expecting some math evidence.
What do you think meltingfeather?
I think it's covered exhaustively in the thread.

16. I am confused. Thought you explained MoI?
Maybe I did not read carefully.

17. Maybe could you gather all the facts and math evidence from your contributions and paste it into one post? Possibly I am not the only one who would appreciate this. It is going to make this thread much more useful.

18. Originally Posted by ChewynMe
Are there any academic research papers which have looked at this by hooking up two bikes with wheels/tires of identical mass but one a 29" and one a 26"? I would be interested to see the force required for each to get them from say 0-30 kph and then repeating the experiment with wheels that have the same weight/radius ratio. Does this even matter or is it automatic, as it seems from the equations you are using, that the extra mass increases the force needed not the size EEE of the wheel? I know this is an old thread but as an analytical guy I can't get enough of it. I always thought it was tougher to climb with a 29" wheel than a 26" wheel. I guess I could try to find a 26" Wheelset that weighs the same as my 29" set and see which is tougher to push.

Edit: with identical gearing, say like a SS setup?
If you truly wish to make scientific comparisons, (taking the rider out of the equation) you should first understand what you are looking for. What variables offer an improvement. (or are a handicap)
It's already been discussed to death, and force isn't what you should be looking at. It's power, expressed in watts.
You also can't compare different diameter wheels with the same gearing. You need to compare them with the same "gear inches", ( or "rollout") since the gears and wheel size are multiplied together at the ground. Even the difference between taller and shorter tires affect the amount of distance travelled, (rollout) and the power required. This has all been discussed already as well. If the wheel mass is equal, (and the bike mass) and the gear inches are equal, ther is no increase in power needed to propel a larger 29er bike.

After all things being said, I myself haven't found any significant advantage to 29er wheels after spending all season switching back and forth between the two wheel sizes.
My riding is unaffected using either wheel size, and is more affected by my physical condition on that day. Some days its just easier for me to flow through certain sections of trail, or climb/descend better regardless of the wheel size I'm riding.

I'm strictly a XC rider, not very tall, and ride only lightweight hardtail bikes, so that has some influence on my preferences as well. I know taller riders seem to prefer the taller wheels, and that makes sense, since the wheels seem more proportional on a tall bike.

I do have to say that the 29er wheels I use are heavier than the 26er wheels, and it doesn't really affect my performance, or change my riding style. The single biggest reason my performance changes other than physical ability, is how well my bike is shifting, and how well I can time my shifts.

Seems like the wheel size is just more of a rider preference thing, and everyone is looking to convince others, that the size they prefer is best.
(and I really don't get the reason for 650b wheels, but I know they will eventually replace the 26er as the standard wheel size in the future.)

19. Why make scientific comparisons and why remove the rider? This is a bicycle, and without a rider it has no moment of diddly squat.
And as for equal planes. How long has it been since 29 and 26 shared geos or drives? And are you gonna have the Honda robot ride it to test your math? Cause if not, the rider MUST be taken into account.
Modern materials, geometries and training make this entire thread bogus...... Just sayin'

20. Originally Posted by curtboroff
Why make scientific comparisons and why remove the rider? This is a bicycle, and without a rider it has no moment of diddly squat.
And as for equal planes. How long has it been since 29 and 26 shared geos or drives? And are you gonna have the Honda robot ride it to test your math? Cause if not, the rider MUST be taken into account.
Modern materials, geometries and training make this entire thread bogus...... Just sayin'
I can agree with that.

21. Ok, let me rephrase.
According to your exact math. Does riding 29" bike require more or less kJ. Riders fatigue and efficiency is all what concerns me.

I am going to ride 1000miles adventure race (for the third time) am I gonna be losing or gaining from 29"? hard terrain 10km/h
Thanks

Taking into consideration all what has been said: same conditions, "same" hardware, adjusted gearing, geometry, better rolling resistance, higher weight of the wheels etc..

22. Originally Posted by Cowan
Ok, let me rephrase.
According to your exact math. Does riding 29" bike require more or less kJ.
I don't want to get too deep back into this thread, but your question is a bit OT. This thread is about inertia of wheels, not overall energy of riding a bike. You should start a new thread with that topic and get a good healthy discussion going over there - it will definitely be more useful than adding to this one, which is lengthy and meandering.

23. Originally Posted by Cowan
Ok, let me rephrase.
According to your exact math. Does riding 29" bike require more or less kJ. Riders fatigue and efficiency is all what concerns me.
The bottom line is that this question is oversimplistic and therefore has no meaningful answer. The answer is and will always be, "it depends."
In order to gain any kind of confidence in measurements which yield objective comparison, the circumstances would need to be controlled to the point that posters like so many in this and any other technical discussion thread dismiss the results as irrelevant to a rider on a trail.
Your question attempts to bridge two worlds by seeking the most simple, boiled down answer (more or less energy) to an infinitely complicated problem.

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