26 vs 29er Mountain Bikes - an Engineering Analysis

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.

Hot Air

The following joke was in the Summer 2007 issue of The Bent (publication of Tau Beta Pi engineering honor society):

Realizing he was lost, a balloonist dropped down to ask directions. "Excuse me, but I'm a little off course" he shouted. "I promisted to meet a friend an hour ago, I don't know where I am."
A woman hollered back: "You're in a hot air balloon hovering approximately 30 feet above the ground. You're at exactly 40 degrees, 22minutes, and 21 seconds North latitude and 70 degrees, 30 minutes, and 33 seconds West longitude."
"Amazing," the balloonist replied. "You must be an engineer!"
"I am," she replied, "How did you know?"
"Well," answered the balloonist, "everything you told me is technically correct, but I can't use your information. I'm still lost and you haven't been much help at all. If anything, you've delayed my trip."
The woman thought for a moment, then replied: "You must be in management."
"I am," replied the balloonist, "but how did you know?"
"Well," said the woman, "you don't know where you are or where you're going. You've risen to your position due to a large quantity of hot air. You made a promise that you have no idea how to keep, and you expect people beneath you to solve your problems."
"In fact," she said, "you're in exactly the same position you were before we met, but somehow it's now my fault."

This joke hits on several good points, and I'm sure that is why it was included in this issue. Maybe engineers do need to work on communicating with others in management, but is that the only issue?

Many companies have a shortsighted goal of raising the shareholder value without looking at the long term effects. My last internship was a great example of such a situation. Several pieces of equipment were installed based on low bids without looking at the lifecycle cost. What was purchased and installed definitely had a lower purchase cost, but the price the company payed for the low end equipment was an additional several thousand dollars a month in operating costs. In addition, the low cost supplier was located in a different state. Just getting the supplier in the door of the facility for repair is incredibly costly when mileage, wages while traveling, expenses, and a hotel are figured into the labor cost. Compare this to a local distributor with a better product, saving thousands a month in operating cost for just a slightly higher capital cost, with a full inventory of replacement parts 20 minutes away. Money was not saved going with the lowest bid. Any savings was gone in just a few months of operation.

In other examples, management has held back research and development trying to save costs. For one turbine manufacturer, management would not pay for a $32,000 casting for testing purposes, stating that a lower cost alternative would need to be found. Six months later, the part is purchased for $31,500. $500 was saved, but the company lost six months in the race to get a patent and beat other manufacturers to the next generation of turbomachinery. Was money saved this time? When a single unit of the turbine manufacturer's equipment would sell for millions of dollars, $500 is nothing. When the lead competitor beats the company to the technology and market share is lost, that $500 would seem like a stupid amount to worry about.

What is the answer? Spending frivolously is certainly not; costs should be kept to a minimum whenever possible. Instead, if one option costs more, ask why. There is probably a reason, and the extra cost may or may not be beneficial. Look to the long term when investing in technology and ask the technical experts on the subject (engineers) to determine the best course of action.