Cyclist33
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- Warrington
Depending on how you model the wheel,
If you model it as a hollow disc then that would be correct, but the hub and spokes account for probably half of the weight. So more accurate to model it is a solid disc rather than a hollow one.
So it would be I=1/2M*R^2 So the change of inertia by a bigger wheel will be even less.
Looked on wiggle and picked 2 pricier wheels, that seemed identical other than size.
http://www.wiggle.co.uk/sram-rise-60-29er-rear-mtb-wheel/
http://www.wiggle.co.uk/sram-rise-60-mtb-rear-wheel/
It only gives the weight as a wheel set, so lets assume that front and rear are equal and half the weights.
29er rear is 710g
26 is 665
Without tyres, 29 radius is 0.3683m
26 is 0.3302
Inertia for the 29 is 0.048 kg m^2
and for the 26 0.036 kg m^2
So while the numbers may seem small, it's actually just over a 30% increase of inertia PER WHEEL, and not a difference I would call negligible.
BUT,
Inertia of the wheels is relevant to acceleration, deceleration, and turning. That all acts independently of momentum.
Though the momentum p = mv
Lets assume a 10kg bike without wheels, and a 70kg rider. And, a speed of just over 12mph to give an easy 5.5m/s
For the 26 you have a total weight of 81.33kg with momentum of 447.32 kg m/s
For the 29 a total weight of 81.42kg and momentum of 447.81 kg m/s
So about 0.1% difference in momentum by changing. So, in some situations it will like to have an effect. Changing direction is unlikely to be any different between the 2 wheel sizes.
Climbing hills? Climbing a steep hill at just under 8mph or 3.5 m/s?
26 is 284.66 kg m/s
29 is 284.97 kg m/s
A difference of less than 0.05% so sticking 29s on going up a hill isn't going to slow you down much.
A quick descent at 20mph ish or 8.5m/s?
26 is 691.31 kg m/s vs
29 at 692.07 kg m/s
A difference of 0.1% again.
So it seems what you gain downhill is similar or equal to what you would lose going uphill. The difference in acceleration between them would be negligible. The idea that the wheels spin up easier is flawed in that the wheel is independent of the bicycle. Stick it on a spindle and sure it will spin up and slow down quicker, but having to transmit that motion into the whole bicycle the 29" wheel isn't likely to have a massive effect.
They shown some considerable differences, but with such a small study, as he said it's statistically negligible. There are too many factors that could have accounted for the difference, course familiarity for one, more familiar with the course later on in the day when the 29" wheel was used? They didn't say in what order each run was done in? Course changes, becoming cleaner and faster throughout the day? It happens in all forms of gravel racing too.
Did they change the gearing between the different wheels? As the larger wheels will roll faster for the same gearing and cadence. A true test should have made sure that the gearing of the bike was adjusted for each wheel size.
The angle of attack works out around 2degrees ish less for the 29" wheel (I really can't be bothered typing out the differentiation, much easier on paper)
So there is an advantage for 29" wheels there, though it only works out to be an advantage of around 15mm or so. Hitting something 115mm on a 29" wheel is roughly the same as hitting something 100mm on a 26" wheel. Again, I don't think that is enough to cause a massive difference in speed, especially with suspension systems too.
It honestly doesn't seem to have any significant advantage, other than a psychological one, as with anything involving human performance. If you think you're quicker with it, you most likely will be.
Careful now - you demonstrated a point logically from scientific principles - now you will be villified as if a crackpot who thinks the world is (roughly) spherical.