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Educating the Debate – Part I

Starting with Dimensions, Weight and Strength

Words by Keith Scott.
October 7th, 2013

With three wheel sizes now here to stay, Banshee Bikes‘ designer and engineer Keith Scott wanted to dispel some myths about the different options. Be prepared for a lesson in basic physics, using real numbers and standardized comparisons…


educating-the-debate-large

You may have read certain online and printed marketing strategies which talk about wheel size with a significant bias towards one size. The size they promote will always be either the only size that the source company produces, or the size that they want to push. Intentional marketing spiels are often very misleading and can skew the purchaser’s judgement.

I feel it is my duty to set the record straight by writing a series of articles that kick off with this one, which addresses two key components of wheel size: weight and dimensions (and little bit of strength thrown in for good measure!). I plan to give unbiased information that you may find useful when deciding what size hoops you want your next purchase to be.

I can offer nonpartisan information (actual facts, rather than marketing blurb) as here at Banshee we offer all 3 mountain bike wheel sizes. We let the customer decide what they want rather than force it upon them, so have no reason to promote one over any other.

Every wheel size has its pros and cons, so picking the best wheel size for you really comes down to personal preference. The main things to consider when picking wheel size are your riding style, riding purpose (style or speed), the terrain you ride, and rider height, but there are also many other factors. I’ll try my best to cover the main ones.

So read on if you want some real numbers…

maxxis sizes

The following comparisons for this whole series are based on using Maxxis High Roller II 2.3″ tires on each wheel size with same rim width for all sizes.

Any comparison I do will be relative to 650b wheels since they are the middle wheel size and so it makes the % change figures clear and consistent.

Dimensions: (Outer tire dimensions taken from official Maxxis 3D files)

1

Straight away this table is likely to cause some confusion… because as you can see, none of the rims or tires match up to their name sake. You can find out why this is the case by reading from a master of bike knowledge, Sheldon Brown.

However, one point to notice is that while 650b is marketed as 27.5″, it is only 1″ larger diameter than 26″, and 1.5″ smaller than 29″, so it is significantly closer to 26″ than 29. The 650b tire (often marketed as the 27.5″) does not actually fall equally between the 26″ and the 29″ tires, so the characteristics of the 650b are far more similar to 26″ than 29″ wheels.

Weight

Static Weight

Obviously, tire and wheel build weights can vary significantly for all wheel sizes. So I’m sticking with 2.3″ wide High Roller II 3C/EXO/TR. For the wheels, I will use Stan’s ZTR Flow EX wheels for each size.

5

Static weight (the weight of an unrotating wheel) is often emphasized by marketing teams. But it only really matters when you lift the bike on and off a rack or carry it on your back. However, static weight does have an effect on the…

Moment of Inertia

Moment of inertia is resistance to angular velocity change about an axis of rotation. Basically, the higher the moment of inertia of a wheel the harder it is to accelerate (and decelerate). This is far more significant than static weight when riding a bike.

Moment of inertia is related to both radius and mass, as Moment of Inertia (I) = Mass x Radius². A low moment of inertia results in a fast accelerating wheel (easy to start spinning). The flip side of this is that a high moment of inertia is harder to decelerate (harder to stop spinning), and so the wheel will carry the speed better once rolling if all other factors are equal.

The below table shows approximate moments of inertia by using the BSD as the effective rotational radius for all wheel sizes.

4

What these numbers illustrate is that if you ride flowy trails that do not require lots of braking and accelerating back up to speed, then a larger wheel might be a better choice. However, if the trail demands regular braking and pedaling up to speed again then a smaller wheel might be better suited.

3

If using the same effective components, then as the wheel size increases the weight and inertia increase accordingly (as you would expect)… but because inertia increases at a rate that is proportional to the radius squared, it goes up more steeply than weight as the wheel size increases.

What does this really mean?

Lets take these numbers and do some simple calculations to look at how much kinetic energy is theoretically required (ignoring rolling resistance etc) to accelerate each pair of wheels up to 10m/s along a flat surface.

6

The above table shows the following:

-Rotational kinetic energy (energy of a stationary spinning wheel with external velocity of 10m/s).
-Center of Mass (CoM) kinetic energy (energy of static mass traveling at 10m/s).
-Total kinetic energy (adding together rotational and center of mass values).

The kinetic energy contained in each wheelset rolling at 10m/s is then compared to that of the 650b wheel value.

What this shows is that these 26″ wheels require 4.87% less energy to accelerate up to 10M/s than 650b, and that 29″ wheels require 6.71% more energy than 650b.

On the flip side, once traveling at 10m/s each wheel requires the same amount of energy to come to a complete stop… so if we consider rolling and wind resistance forces equal for all wheel sizes, then the 29″ wheel will continue to roll 6.71% further than the 650b wheel which rolls 4.87% further than the 26″ wheel. This is due to the 29er wheels having the most momentum for any given speed.

Strength

A factor that is strangely often overlooked by marketing teams is that of the strength and stiffness of the wheel. I find this particularly strange as wheels cost a lot of money, and are subject to a lot of abuse, and personally the lifespan of a wheel is a significant factor to me when choosing what set to invest in.

If comparing like to like wheel builds (same rims, hubs etc), smaller wheels will always inherently be stronger than larger wheels. This is due to wider gaps between spoke eyelets and poorer spoke triangulation etc. So strength to weight ratio is something that will always be won by smaller wheels.

It is however easy enough to compensate for this by getting stronger and stiffer wheels, but they do generally either weigh, or cost more. So something has to give.

It doesn’t stop there….

Weight, dimensions and strength are obviously very important factors to take into account when considering what wheel size to choose. But… there are other factors too! And if this mini-blast of physics chat hasn’t put you off too much, stay tuned for future articles about topics where bigger wheels have the advantage.


There’s no longer a question as to whether we’ll have three wheel sizes in mountain biking, so it’s nice to have some comparative data to help understand the options…

  • Dirk

    I actually though Giant did a pretty good job of this with their latest ad campaign. Funny that they refer to it as “27.5 Technology” though.
    http://www.giant-bicycles.com/en-us/technology/tech27-5/94/

    Interesting stuff there about contact patch and angle of attack.

  • builttoride

    If you hadn’t noticed, Giant’s marketing spiel is HIGHLY bias towards 650b as that is what they are moving to. This is one of the reasons I am writting an this series.

    For example:

    Look at the phrasing:
    ’27.5-inch wheels are only 5 percent heavier than 26-inch. By comparison, 29-inch wheels are 11 percent heavier than 26-inch.’

    Rewritten [remove ONLY] and add it at the back and change the comparison

    27.5-inch wheels are 5 percent heavier than 26-inch. By comparison, 29-inch wheels are are only 6 percent heavier than 27.5-inch.

    The satistics are being manipulated to make one size look most favourable… in reality there is no perfect size as they are all on sliding scales of pro’s and cons.

    Also, a lot of their claims are simply not accurate, and I will be going on to things like attack angle, tire pressure, contact patch etc in the rest of the series to correct the numbers.

    Although yeah, giant have made it look prettier than I am and that sells! haha

  • Dirk

    Cool. Look forward to seeing some actual math.

  • Jerry-Rig

    There’s also the fun/playful factor. I know some people who are selling their 650b’s due to that.

  • jrcd

    Great work! Looking forward to the rest of it.

    I’d love to see some additional articles on different aspects of mountain biking analyzed from a physics perspective!

  • morgman

    Hey all, I’ve just updated the article with a new section about kinetic energy, under the header “What does this really mean?”

  • buzzes

    I love this…..thank your for sharing an educated OPINION which is yours and qualified and not bent by marketumb!

  • skiitsbetter

    Cool. I’m a new engineer and I’ve done some similar calc’s myself after seeing that Giant PR.
    -I was getting pretty even energies at a given speed. The larger wheels rotate slower, this cancels out the increased MoI?
    -the advantages in moments of inertia in different wheel sizes goes away if you use heavier tires!
    I did some calculations about contact patch and angle of attack as well. I think angle of attack comes into play when people talk about how much more fun 26 is because you can “feel” the trail better.
    Wheel durability is something that I feel is not being addressed. For the casual rider concerned about fun and not STRAVA or race times, it might be nice to have a wheel that you don’t have to true as often…

  • john-b

    The kinetic energy calculations are for just the moving wheels themselves, in isolation, if I understood correctly. To understand the impact on the rider (that is, what the rider might actually notice), would it be better to look at the delta in kinetic energy for the entire system (that is, including the rider and the rest of the bike)?

    If we assume a 180 lb rider on a bike which weighs about 26 lbs not counting the wheels (206 lbs / 2.2 = about 94 kg), then the kinetic energy of the rest of the system is 0.5 * 94 kg * (10 m/s)^2 = 4700 J.

    26: Ek = 4700 + 694 = 5394 J (-0.7% change from 27.5)
    27.5: Ek = 4700 + 730 = 5430 J
    29: Ek = 4700 + 779 = 5479 J (+0.9% change from 27.5)

    Another way to look at it is that 36 J delta between 26″ and 27.5″ wheels at 10 m/s is the Ek for a mass of 0.72 kg, or 1.6 lbs. So if you put a 750 mL water bottle on your bike, you would notice that about as much as the difference in the wheel change for accelerating and decelerating, based on the kinetic energy view of things. This is not taking into account the angle of attack or any other factor.

    I am an electrical guy, not mechanical, so if I messed something up in the math please feel free to slag me mercilessly.

  • ReductiMat

    This is great!

  • burnbern

    Can’t wait for more! I love actual numbers…

  • Gravityfreak

    Really really enjoyed this thanks Keith. Looking fwd to the next installment!

  • Kevin_m31

    Actual numbers with assumptions listed, holy cow batman I thought this was the bike industry. Random numbers and unsubstantiated %gains are all I’ve ever wanted.

    A few thoughts I would put forth. The static weight may not mean much towards rolling, but if your trying to flick the bike around and such you will feel it. It’s also weight at the extremes of the bike which means you need to use more force to move it around then say if it were in the middle of the bike. You can also apply the “unsprung mass” buzz term as well. Another factor for decreased strength with bigger wheels is that you have a larger leaver for a taco-rifec time.

    Good stuff though guys!

  • gwh

    Nice work!
    I suppose one could put some numbers to “flickability” by analysing the force input at the crank arm and handlebars to change the direction of the angular velocity in a set time frame. How much harder is it to table a 29er than a 26 on a 4ft high jump at 30km/h? Physics has the answer!

  • builttoride

    John b: I was just choosing to keep this article purely to wheel size, but you are correct that there are soo many other things to consider, and that wheels are just a small part of things. Since this article seems to have gone down pretty well (I wasn’t sure anyone would actually read it), I may go on and write many more than look at all dfferent aspects of riding physics to put things in perspective.

    Kevin: Actually the ‘flickability’ most the time has a lot more to do with gyroscopic affect than static weight if turning wheels or whiping bike out etc are considered. http://www.youtube.com/watch?v=NeXIV-wMVUk this segment of a lecture shows how the front wheel being turned helps you do big moto whips. Since gyroscopic factors are governed by both moment of inertia, and rotational speed, static mass will become a smaller factor the faster you are traveling unless it is a purely vertical ‘flick’ lke a bunny hop.

    gwh: you are right… go for it and let us know what you calculate!

  • john-b

    That would be great Keith! I have always wanted to see this type of analysis. Look forward to your future articles.

  • Johnny Laroux

    Great article. I look forward to further updates!

    It’s so nice to see an article like this about the dreaded wheel size debate where the standard comment is “29ers suck” or “29ers are gay” like is so common on another popular bike forum, who’s name shall not be mentioned. This kind of unbiased information that isn’t based on marketing, or someones perceived idea that 27.5 and 29″ bikes even though they have never ridden one, is very refreshing. Keep it coming!

    I’m 6’4″, and recently bought a Trance X29 after going through a slew of 26″ trail and All Mountain bikes. For my size and riding style, it is the first bike that I have actually felt fit me. To me, it feels right. Sure it’s got it’s negative aspects, but so do the other wheel sizes. I think what it comes down to is the right balance of pros vs. cons for each individual rider. I would never tell someone they shouldn’t ride a certain wheel size based on my own opinions or experiences. My son also rides a 29er for trails, and hucks it and jumps stuff that the nay-sayers will tell you it can’t do, but he has a skill set that allows him to ride any bike well.

    That being said…I still love my 26″ DH bike, as it is the right tool for the job. In the end, I still say its the rider…not the bike.

  • DaveB

    Thanks Keith, for posting this, it is really good stuff. I appreciate the elevation of intelligence in the discussion.

    John b- a good point, and nice addition to the discussion.

  • Vikb

    Just to muddy the waters. I run a big 2.4″ Conti Trail King [essentially a 2.5" tire] on my 26er to get a bigger out diameter and the improved roll over through tech. When I get my next FS bike it will likely be a 650B or possibly a 29er. In either case I won’t put a massive 2.4″ tire on my bike because the wheel will be bigger and my wheel weight and inertia won’t be bigger.

    Just something to consider….you won’t necessarily just use the same width tire as you change wheel sizes.

    Thanks for taking the time to write the article!

  • craigsj

    Keith has failed to take into account that the larger wheels rotate slower to obtain 10m/s so his rotational KE numbers are wrong. It’s of no consequence anyway as the differences are tiny compared to the overall KE of the system as john-b pointed out already. The percentage differences in weight and KE will be the same assuming constant distribution of mass.

    • jimshapiro

      Actually, he did take into account the different angular velocities of the wheels. I did my own calculation of both the rotational (1/2 * I * omega^2) and translational (1/2 * m * v^2) energies of all three wheel sizes and my numbers are in agreement with Keith’s.

      • craigsj

        Great, show your work then.

        When you sum the rotational and translational kinetic energies of a rolling wheel, you get E = m * v ^ 2. Why? Because omega = v / r. Larger wheels roll slower and the radius terms in the rotational equation cancel out. See here: http://en.wikipedia.org/wiki/Bicycle_performance

        I’m eager to see how your numbers agree with his in light of the fact that his cannot possibly be right.

      • craigsj

        Going through Keith’s data:

        First, he didn’t use identical wheel builds but biased the data in favor of 650B. Using identical wheel builds to 3 digits, the wheel weights should be 3830, 3990, and 4130 grams. This ignores that fact that the tubes could be the same. The relative weights are -4% and +3.5%, already different.

        Next, Keith botched the effective rotational radius numbers completely. He used rim diameter for wheel radius! I used 0.328, 0.340, and 0.358 meters. I also dropped the hub and spoke weight since they contribute so little to rotational inertia, yield moments of inertia of .326, .369, and .427 Km * m^2, hugely different from Keith’s erroneous numbers. The percentage change is -11.7 and +15.7 compared to Keith’s -11.9 and +18.9. Notice how Keith’s numbers are biased against 29 and in favor of 650B? Not that it matters since moment of inertia is irrelevant…

        Last, physics tells us that rotational and translational kinetic energy of a rolling wheel must be the same yet Keith’s are wildly different. Now we know why, he botched the moment of inertia estimate by a factor of 3.7x! His total Ek numbers should be 383, 399, and 413 Joules, not 694, 730, and 779 J. The difference is -4% and +3.5%, same as the wheel weight. Why? Because radius doesn’t matter.

        I didn’t bother to see how Keith arrived his flawed answer so perhaps he did adjust for angular velocity but just did it wrong. I’m curious, Jim, did you make the same mistakes Keith made?