Wheel size facts Part 2.... Rollover factors.

Here is some more independant wheel info to help you decide which wheel size is for you. I will be taking the same dimensions as discussed in Part 1 to perform these calculations. These theoretical calculations do NOT take into account tire deformation... which I will talk a bit about later. This week, get ready to deal with everyone's school subject fav - some trigonometry! So belt up, and let's rollover some wheel-based maths (oh dear....!)

'Rollover':

You'll almost definitely have heard 29er riders saying just how much better their bikes roll over obstacles on the trail. "I carried so much more speed through that rough section!", or something similar. This is probably the key reason that riders and manfacturers give for having a bigger wheel size... But what does this mean, and just how much better do they perform this action?

The diagram below (Fig. 1) shows the height of a square-edge obstacle, and the angle of attack vis-à-vis the wheel:

Fig. 1

When a wheel makes contact with a square-edge obstacle (for example, the curb of a pavement - that's British speak for 'sidewalk'), the angle of attack = the angle of the tangent of the wheel at point of contact with the square edge obsticle and the horizontal as shown above.

Fig. 2

Fig. 2 how each wheel size's angle of attack varies with obstacle height across a range of square-edge obstacle heights. Of course these values are all perfect and theoretical (not taking into account tire deformation, tire pressure or bike lean angles etc.)

The angle of attack itself doesn't really tell you much without applying basic trigonometrical functions to to break it down into horizontal and vertical force vectors. In a simplified form without friction or deformation, if a wheel runs into a vertical obstacle higher than the axle height, it will stop you instantly (horizontal force / vertical force = infinity). Conversely, if an obstacle has zero height it will not slow you down at all (horizontal force / vertical force = 0). On Fig. 3, you can see how the force vector varies as obstacle height increases for each wheel size (the higher the Tan (Angle of Attack), the more it will slow you down):

Fig. 3

Fig. 4 shows how the force vectors vary as a % relative to the 650b wheel. A positive number represents a higher horizontal resistance (effectively, this means it slows you down more). So, you can see that 26" wheels will slow down more than 650b wheels which in turn will slow down more than 29".

This graph clearly shows that the relative efficiency is not consistent across all obstacle heights. The larger the obstacle, the larger the effect the wheel size will have. So it is impossible to say that one wheel is x% more efficient over square-edged hits than any other size without saying the size of obstacle, tire size, and tire pressure etc etc.

Fig. 4

It should also be said that not only are big wheels more efficient at rolling over square-edge hits, but they also result in a smoother ride. This is because, for any given speed, the larger the diameter of the wheel the longer it is in contact with the obstacle (i.e. it hits it sooner and leaves it later). Therefore it has longer to react to the obstacle. Plus, the bigger the wheel the less of it is going to drop into holes (think braking bumps), hence 29ers feel like they smooth the trail out.

Once again I want to make it very clear that these numbers are based on wheels that do not deform at all, and that are rolling over perfectly square-edged obstacles, which is obviously not realistic. So let's have a quick look at some real world factors that significantly complicate the situation.

Tire deformation helps to absorb the impact of hitting a square-edge obsticle. This not only reduces the shock that is transferred to the frame and rider, but also makes the wheel roll more efficiently over an obstacle by effectively reducing the angle of attack when it absorbs it. The more the tire absorbs the obstacle the better, so actually lower pressure tires roll over obstacles like this more efficiently (unless you get a snake bite!).

Tire size is an important factor... for example you could realistically have a larger outside diameter running a very high volume tire on 26" wheels than a small volume tire on a 650b wheel. In this situation the 26" wheel would roll over things better than 650b, so tire height should be considered if analysing options.

We have indeed confirmed that big wheels roll over obstacles better than small wheels, and help maintain momentum as a result. But frame geometry and axle path also play a factor if the frame has suspension, as the suspension can help absorption of obstacles and make the bike roll over them better. The slacker the head angle or more rearward the axle path, the better a bike will roll over an obstacle if all other factors are equal.

Plus there is one very very significant factor that none of these numbers take into account...We can bunny hop over things! This is why you should never listen to arguments taken from automotive industry as the car can't be thrown around independently of the driver.


If this second installment of wheel physics hasn't boggled you even more than the first part, the third blog post will tackle contact area and grip. Woop!

Wheel size facts Part 1.... Dimensions, Weight and Strength.

You may have read certain online and printed marketing strategies which talk about wheelsize 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 blog posts 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 wheelsize 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... 
 

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 constant.

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


      
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.

Static weight (the weight of an un-rotating wheel) is often emphasised 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. 



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.

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.

The above table shows the following:

-Rotational kinetic energy (energy of a stationary spinning wheels 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 blog posts about topics where bigger wheels have the advantage.