I'm not trying to disprove anything. I agree with the theory. I'm saying that in the real world, and specifically the real world of leisure cycling as practiced by me and you, that the benefit of reducing rotating weight as opposed to any other weight is overstated.
In addition, the reduction in weight as practised by me and you in the context of mountain biking and often asked about on here, has a negligble effect on our performance.
I do agree that psychological factors associated with perceived performance benefits are important.

I said there will be force to lift the bike against gravity, and yes, this will be greater for heavier wheels due to their mass, however, the extra rotational inertia of the wheels does not affect the force needed to lift them. If it did, a spinning wheel (or anything else) would have to be heavier than a non spinning thing, which is not the case.

This would be fine if you were just trying to lift the bike over a fence but your trying to propel it forward as well as up by making the wheels go round in circles.

rs – he is right – the rotation of the mass can be ignored unless it is accelerating. going uphill at a steady speed nothing is accelerating

This would be fine if you were just trying to lift the bike over a fence but your trying to propel it forward as well as up by making the wheels go round in circles.

yes, but at constant speed, there is no acceleration, so inertia doesn't matter. It so happens that inertia and mass are directly proportional for non-rotating objects, and that rotational inertia is double that for objects where all the mass is concentrated at the same distance from the axis of rotation (like a wheel). When you lift something at constant speed, what matters is its mass, not its inertia.

I do agree that psychological factors associated with perceived performance benefits are important.

to which end it might be more useful to alter your beliefs creatively 🙂 For instance you could cultivate the belief that blue valve caps are faster.

Red bikes are faster – everyone knows that

Red bikes are faster – everyone knows that

I have a red rear hub and red nail varnish so I'm sorted 🙂

geek out here

http://www.math.usu.edu/~bryanb/math 2210/Rotational Inertia.doc

and here

http://www.analyticcycling.com/WheelsClimb_Page.html

Agreed, I'm quicker when I wear my new Raji gloves, and much quicker when I wear a cycling cap turned backwards instead of a helmet.

rs – he is right – the rotation of the mass can be ignored unless it is accelerating. going uphill at a steady speed nothing is accelerating

Well kind of…

When you're going up hill gravity is constantly pulling you down and your wheels are constantly wanting to decelerate. In order to overcome this deceleration you provide the acceleration force with your legs (at a constant speed these forces are balanced).
Unfortunately for us the inertia of the wheels is a contributing factor to what we are pedalling against. Thus at constant speed the rotating mass still has an effect on how much effort we have to put in.

EDIT: Also, if you think about it, the bike constantly accelerates and decelerates throught the pedal stroke. If yours doesn't you'll be given a new gold necklace in 2012.

Also, if you think about it, the bike constantly accelerates and decelerates throught the pedal stroke. If yours doesn't you'll be given a new gold necklace in 2012

Bingo. Out of the saddle on a big hill and roational inertia will make a difference.
Unless of cause your all roadies arguing the toss on a mountainbike forum

rs – your first link doesn't work and the second is starting from rest – so acceleration plays a part it is not steady state and there is no distinction between the effects due to rotating mass and static mass on the speed.

Thus at constant speed the rotating mass still has an effect on how much effort we have to put in.

Fixed that for you.

EDIT: Also, if you think about it, the bike constantly accelerates and decelerates throught the pedal stroke. If yours doesn't you'll be given a new gold necklace in 2012.

Yes, but these 'accelerations' are miniscule and are lessened by a heavier wheel….flywheel effect, remember?

The advantage of light bikes, and particularly light wheels, from a KE standpoint is that KE only comes into play when speed changes, and there are certainly two cases where lighter wheels should have an advantage: sprints, and corner jumps in a criterium.[13]

In a 250 m sprint from 36 to 47 km/h to (22 to 29 mph), a 90 kg bike/rider with 1.75 kg of rims/tires/spokes increases KE by 6,360 joules (6.4 kilocalories burned). Shaving 500 g from the rims/tires/spokes reduces this KE by 35 joules (1 kilocalorie = 1.163 watt-hour). The impact of this weight saving on speed or distance is rather difficult to calculate, and requires assumptions about rider power output and sprint distance. The Analytic Cycling web site allows this calculation, and gives a time/distance advantage of 0.16 s/188 cm for a sprinter who shaves 500 g off their wheels. If that weight went to make an aero wheel that was worth 0.03 mph (0.05 km/h) at 25 mph (40 km/h), the weight savings would be canceled by the aerodynamic advantage. For reference, the best aero bicycle wheels are worth about 0.4 mph (0.6 km/h) at 25, and so in this sprint would handily beat a set of wheels weighing 500 g less.

In a criterium race, a rider is often jumping out of every corner. If the rider has to brake entering each corner (no coasting to slow down), then the KE that is added in each jump is wasted as heat in braking. For a flat crit at 40 km/h, 1 km circuit, 4 corners per lap, 10 km/h speed loss at each corner, one hour duration, 80 kg rider/6.5 kg bike/1.75 kg rims/tires/spokes, there would be 160 corner jumps. This effort adds 387 kilocalories to the 1100 kilocalories required for the same ride at steady speed. Removing 500 g from the wheels, reduces the total body energy requirement by 4.4 kilocalories. If the extra 500 g in the wheels had resulted in a 0.3% reduction in aerodynamic drag factor (worth a 0.02 mph (0.03 km/h) speed increase at 25 mph), the caloric cost of the added weight effect would be canceled by the reduced work to overcome the wind.

Another place where light wheels are claimed to have great advantage is in climbing. Though one may hear expressions such as "these wheels were worth 1-2 mph", etc. The formula for power suggests that 1 lb saved is worth 0.06 mph (0.1 km/h) on a 7% grade, and even a 4 lb saving is worth only 0.25 mph (0.4 km/h) for a light rider. So, where is the big savings in wheel weight reduction coming from? One argument is that there is no such improvement; that it is "placebo effect". But it has been proposed that the speed variation with each pedal stroke when riding up a hill explains such an advantage. However the energy of speed variation is conserved; during the power phase of pedaling the bike speeds up slightly, which stores KE, and in the "dead spot" at the top of the pedal stroke the bike slows down, which recovers that KE. Thus increased rotating mass may slightly reduce speed variations, but it does not add energy requirement beyond that of the same non-rotating mass.

Lighter bikes are easier to get up hills, but the cost of "rotating mass" is only an issue during a rapid acceleration, and it is small even then.

Nicked from Wikipedia…
http://en.wikipedia.org/wiki/Bicycle_performance

and your wheels are constantly wanting to decelerate

confused thinking. Force is required to lift the wheels (and every other part of the bike and rider), and this is a static gravitational matter unrelated to inertia.

Just because calulated energy input might be say 1% greater or lesser doesn't necessarily equate to 1% faster or slower results, it won't be a linear scale, especially when performing at or close to your limits.

Classic STW threaad this one – nearly as good as Wobbly wheels for folk arguing black is white and totally getting the wrong end of the stick.

How come SFB and I are on the same side and right? Most unusual 🙂

not sure what everyone else has said, probably something about not accelerating when going at a steady speed.
.
friction is slowing your wheels down which you have to overcome by accelerating them, therefore you're always having to accelerate them unless those friction forces are overcome by gravity which they won't be if you're going uphill
.
that's what I reckon

How come SFB and I are on the same side and right?

Newton sorted this out over 300 years ago, it's not exactly cutting edge 🙂

bakes – holding them at steady speed is not accelerating – Doh!

friction is slowing your wheels down which you have to overcome by accelerating them, therefore you're always having to acclerate them unless those friction forces are overcome by gravity which they won't be if you're going uphill

uh, if you're going at constant speed then, by definition, there is no deceleration! Yes, you have to overcome friction and gravity, neither of which are related to rotational inertia.

If your are trying to climb a "rough" hill (and on a bike thatcan be pretty much anything that's not smooth tarmac you will naturally try to maintain a steady pace (especially with a group)as your wheel overcomes every little lump and bump you have to input a little more power to spin the wheel back up to speed (There will be some degree of flywheel effect but the losses, especially at low speed will be quite substantial) A lighter wheel will feel easier to pedal especially if you pushing quite hard, but I reckon it comes down to rolling resistance (friction) more than anything.

it's impossible to hold them at steady speed though, especially on a mountain bike
especially with all the bumps, rocks, cracks, roots constantly slowing you down, even in small amounts, they are constant and will add up
.
EDIT: what oliver said

by definition

definition means nothing

just imagining the speed i could go if I was always accelerating 😆

Bakes – but a heavy wheel with more rotational inertia will be less prone to slowing over bumps…………..

hmmm, true TJ, good point
I'm not wrong though

it's impossible to hold them at steady speed though, especially on a mountain bike
especially with all the bumps, rocks, cracks, roots constantly slowing you down, even in small amounts, they are constant and will add up

no, they average out 🙂

definition means nothing

rghly kdlbcp er wbcvbbe rtmq eppt! (definition-free language)

just imagining the speed i could go if I was always accelerating

That would be the same speed as you can go, spun out, in your fastest gear, or faster, if gravity assisted.

The corrected perspective is – imagine how fast I could go if I wasn't constantly being subjected to forces that cause deceleration.

When you're going up hill gravity is constantly pulling you down and your wheels are constantly wanting to decelerate.

Yeah, but if your wheels are heavy they will have more inertia and resist deceleration more than light wheels.

On the steady climb described there will not be a difference, but when it comes to interesting MTB stuff; slowing, speeding up, switchbacks, swoopiness, the agility of lighter wheels will become apparent.

the agility of lighter wheels will become apparent.

or perhaps the skittishness ?

"just imagining the speed i could go if I was always accelerating"

That would be the same speed as you can go, spun out, in your fastest gear, or faster, if gravity assisted.

it goes without saying that to be always accelerating you'd need some other source of motive power than pedalling, and I imagine avoiding obstacles will become harder as you approach the speed of light…

yes but as I approach the speed of light I would also become close to infinite mass & everything would have to get out of my way or get crushed in my path 😈