When I was researching bikes last fall I ultimately settled on a 29er, which refers to the tire size. Instead of a traditional 26 inch wheel, a 29er has a 29 inch wheel. The idea is lower rolling resistance, better traction, and a ton of other benefits. The bigger wheels seem to be the trend of the future with mountain bikes.
There is a lot of differing opinions on the internet about the tire size, ranging from people hating 29ers to people who never ride a 26 inch wheel bike after changing. The one big argument against larger wheels is slower acceleration and heavier weight. The wheels weigh more due to the bigger size and more material, and with the larger diameter and resulting higher moment of inertia, it will take more energy to spin a 29er wheel up to speed. My initial reaction was the effect is probably minimal, but I never got around to calculating the difference until today.
The following is a comparison of energy required for acceleration of a 26 vs 29er bike based on calculations only. For the analysis, specifications from manufacturers are used. Both bikes will use Bontrager Rythm Elite Tubeless Disc wheels at 1,835g and 1,955g for the smaller and larger size respectively. Bontrager Jones ACX Aramid Clincher 2.2 width tires are used, with a weight of 520g and 650g respectively. Tubes are assumed to weigh 200g for each size tire. I am assuming the wheel has of its weight at the ISO bead seat diameter of 559 and 622 mm for the two different wheel sizes. This is not completely accurate, but I am not going to mathematically integrate the individual wheel parts to account for density gradients and variable geometry. The moment of inertia calculation should be within 10% using my approximation, and the comparison between the two bikes should be nearly identical with less than one percent error based on using the same assumption for both.
The wheels are on a bike frame that weighs 8,000g for both tire sizes. The total weight of the wheels with tubes and tires is 3,275 and 3,655 for the 26 inch and 29 inch wheels respectively. The total bike weight is therefore 11,275g (24.8 lbs) and 11,655g (25.6 lbs) with the bigger wheel bike being heavier. The moment of inertia of the wheels is 0.256 and 0.354 kg-meters squared. The small change in diameter is squared, which makes the seemingly small change in diameter have a large affect on the moment of inertia.
Now for the results. Lets assume both bikes start from a stop and accelerate to 8 meters per second (17.9 mph) on flat ground. The calculation is only for energy to bring the bike up to speed, and does not consider rolling resistance or other losses. It will take 436 Joules to bring the bike up to speed for the 26" wheels versus 457 Joules for the 29" wheels for an increase of about 4.9%. 29ers are claimed to have decreased rolling resistance. Assuming both tires have the same coefficient of rolling friction since they are using the same tire, the 29er should have a 10% lower rolling resistance due to the larger wheel diameter, which more than makes up for the losses due to weight and tire diameter.
This analysis isn't quite complete. In the calculation, a common error was made as I ignored the weight of the rider. Bicyclists, bicycle magazines, and other sources always talk about bike weight without including the rider effect on the performance. If one bike weighs 24 lbs and another weighs 25 lbs, the simple calculation would be one bike is 4% lighter than the other. If you include a 175 lb rider, the difference in weight of the complete bike and rider together is only 0.5%. Only considering bicycle weight exaggerates the performance enhancement.
If I recalculate the results again assuming a 155 lb rider (me) the difference is even smaller than before. The total energy required to bring the bike and rider to 8 meters per second velocity is 2,690 Joules for the 26" bike versus 2,711 Joules for a 29er bike, or about 0.8%. The rolling friction difference is for the most part not affected by rider weight. There will still be a 10% benefit of lower rolling resistance with the bigger wheels, therefore the losses from a heavier and larger diameter wheeled bike should be completely outweighed by lower rolling resistance.
If you are going to drag race the two bikes in real life, the 29er should win if both riders weigh the same, have the same energy output, and both bikes are built from similar quality components. The difference between the two is very small. The weight argument is certainly not valid.
NOTE: The calculations above do include the effect of rotating mass, which is the reason why I had to calculate the moment of inertia of the wheels. The larger diameter wheels spin slower, so the amount of energy required to spin the wheels only up to speed is only about 12% different. The amount of energy required to accelerate the wheels up to rotational speed is only about 17% of the total energy to accelerate the whole bike (ignoring rider). The majority of the energy to accelerate the bike is due to bike mass.
UPDATE 3/23/08: In response to a comment, I was asked to recalculate the numbers based on slightly heavier tubes for the 29er. A 29er wheel is about 11% bigger in circumference, so I am going to calculate the tube to have an 11% higher mass, or 222g versus 200g for the 26er. The results change by 2 Joules, or 459 Joules to accelerate the bike and wheels up to speed, or about 5.4% more than a 26er (versus 4.9% with the same mass tubes analysis). The rider and bike combined will require 0.87% more energy to accelerate than a 26er with the heavier tubes, with a roughly 10% lower rolling resistance.
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17 comments:
Well done - I think
I am not too math minded
but - I think the rotating wheel mass increase affects rider efficiency to a detriment
how would you calculate this?
once the mass is in motion (rider/bike) the wheel/tire rotating mass has the most affect on efficiency / consumption of rider energy
Also - 29er tubes I think weigh about 80 to 100g more than 26er tubes.
can you do some re-calculations or clarify for my short bus brain?
thanks
I updated the calculations, see above.
You would need a very heavy tube to make a 29er slower than a 26er. The wheels do have the most affect on energy use once up to speed, but that is where the 29ers really outperform the 26er due to lower rolling resistance! The biggest 29er disadvantage you will see is during acceleration, and that is why my calculations are based on acceleration and not constant speed riding. The wheel mass has very little affect on constant speed energy consumption since there is no acceleration of the wheel. The only affect it would have is slightly higher rolling resistance due to increased mass if the tires were the same size, which is completely negated by the larger diameter lower rolling resistance wheels.
I will probably do a few more posts comparing hill climbing ability and constant speed riding when I get time...
Hi...
This makes total sense to me, thanks...
Given that I am 215 lbs it would make even more sense to go with the 29er correct?
I test road a 26er and a 29er today and without any math or data I felt mush more resistance trying to get the 29er moving... which is as to be expected but your analysis seems to indicate that the extra energy required to accelerate would be recaptured by maintaining a higher speed with less force... is this correct?
I don't see any reason to buy a 26er; a 29er is superior in almost every way.
You probably think the 29er is slower just because people tell you that is what to expect and it is more of a perception issue. An extra kilogram of bike weight is negligible. Buy a good bike and you will be happy, no matter what the wheel size. The 29er has less rolling resistance, so once you are up to speed you are significantly reducing the amount of energy you are using to roll down the trail. Improved traction with a 29er is always good. I'm amazed how it digs in and powers up steep hills with loose dirt.
Where did you get the 10 % less rolling resistance figure for a 29er wheel? Did you consider the different shape of the contact patch and reactions involved when integrating over the contact patch?
The 10% savings is calculated...and yes.
Mass moment of inertia is irrelevant because the different sized wheel rolls at a proportionately different speed. The velocity of the wheel with respect to the ground is always the same at the contact patch, it is always zero. The sole difference in inertia between the wheels is due to weight. It seems no one understands that, even those who claim to be able to do an "engineering analysis".
Your assumption of weight centered at 85% of diameter is wrong. It varies somewhat but it is about 70-75%. It is also irrelevant as it doesn't really vary with wheel size and I've already explained why moment of inertia doesn't matter. Doing the rudimentary calculations to determine this would be the least someone can do if they claim to be doing an "engineering analysis". I have done this for a variety of wheels and it never changes more than a couple percent.
Add 75% of the weight difference in the wieght of the wheels to the overall weight difference and that's the total difference in momentum. Rolling resistance matters more, though I see no "engineering analysis" that justifies your 10% claim.
The inherent difference in weight (mass) due to the increased circumference is about 11% for a 29" rim/tire. The rotational inertia of a hoop (similar to wheel/tire) = (mass)x(radius)squared. This results in the 29er having roughly a 36% greater rotational inertia. However, this applies only to the difference in the rim/tire of the 26" and 29er.
Overall, this gives the 29er about a 1/2% disadvantage in acceleration. With all the other advantages (particularly if you're a large rider), it's pretty insignificant overall.
Tim K
The wheel is usually at 0 velocity at the contact patch (but not always...), but the rest of your comment regarding the speed of the wheel is invalid. This model takes into account getting the wheel up to speed. Based on your assumption, it would take 0 energy to get a wheel mounted in a truing stand up to X velocity at the tire surface, which is clearly incorrect. It clearly requires energy to make a wheel spin.
The roughly 10% output of the model is calculated based on contact patch, diameter, etc.
the one thing you have left out is that 26ers are much more nimble (dealing with tight technical stuff), which really is a huge part of mountain biking. just a thought. but having owned both types of bikes (and loving them each for what they are), 26ers definitely are easier to rip tight courses on. Be it a "subjective analysis", it is pretty consistent amongst riders.
All well and good, except that the 10% less rolling resistance for the 29er seems to have been plucked out of nowhere. May i ask what the physics behind this is?
Also, there will be a ~10% increase in aerodynamic drag from the wheel, albeit negligible at low speeds, but quite possibly greater than the rolling resistance figures at 8m/s+.
Can't you actually test those values in some kind of wheel test facility? like they do brake tests with car and truck tires?
Having ridden both bikes, I have a few perceptions I'd like to add and get some comments on, if you would.
Changing from a 26er to a 29er (while not the only variable change when changing bikes), I definitely felt that my 29er kept more inertia. For example, when I rode through a short gully, I wouldn't have to work much to get over the far lip on the 29er, where it'd take a few petals on the 26er. It sounds like your analysis would be that this is due to rolling resistance rather than MOI?
Also, on a biking trip with a friend on a full suspension frame, he really out-climbed me on a long climb. Of course fitness and gearing play into the mix, but I really expected the loss of his energy through the suspension would be quite evident after a few miles. I was the one falling behind, and wondered if it was related to the increased wheel size. Perhaps my vanity got the best of me?
Last one - after leaving Colorado and moving to the East Coast, I found that the 29ers don't seem quite as nimble on the tighter trails with more trees. I was definitely not in practice, nor familiar with the trails, but just thought you might weigh in analytically.
Thanks!
One last confirmation - yes, 10% rolling resistance reduction is calculated based on the relation between rolling resistance and tire diameter. I am assuming the identical tire brand, model, and tread pattern for a truly equal comparison.
All of this comparison really comes down to the rider. If you use the capability of the 29er, you will have better traction and you can exploit that traction through higher lean angles in corners (faster speed) to counteract any penalties by cornering. I haven't found the corning to be a problem. I have friends on a 26er who can't corner as fast as my 29er due to skill and experience. Go ride and you will be faster, simple as that.
I continuously rode at the limit of my 26er with washouts in corners way too frequently. All of my 29ers have a cornering traction limit that is much harder to exceed.
To Tim: I have found that my full suspension 29er is faster up hills than my 29er hardail even though it is heavier (and I don't lock out the suspension). The reason is I can stay seated and keep pedaling even if I am hitting constant bumps, tree roots, rocks, etc. where I would otherwise have to get out of the saddle. More time pedaling means less time coasting and decreasing speed. Normalized data (fitness level, weather, riding group) from the same uphill between different bikes always shows the full suspension is faster.
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