Rotating mass, the math and the myth...

[Tompsk]

After reading many comments on rotating mass and what counts where I thought I'd do some sums (based on being an engineer and my A level maths studied many years ago). Having put the equations in a spreadsheet and making some reasonable(?) assumptions the results point to:

The effect of the rotating mass on a bike is less than 2% of the energy required to accelerate to a reasonable speed the masses involved (from 0mph up to 10 to 20mph).

The figures indicate the split is; 85% due to accelerating the riders mass, 13% accelerating the total mass of the bike and an additional 2% getting all the rotating bits up to speed. Note that this is independent of bearing friction and wind resistance which are not effected by the masses involved with all other things being equal.

Assumptions made: Rider 65kg, bike 10kg, 1/3 of 2kg wheels weight at the rim, weight of tyres (350g each) at rim + 25mm, shoes and pedals of 1kg total rotating at 60 rpm at radius of 170mm. I haven't calculated what the riders legs flapping up and down would add as I'm only looking at the rotating parts of the bike.

The equations are: linear energy = 1/2 m v^2, rotational energy = 1/2 m r w^2
(Where m is mass in kg, v is velocity in m/s, r is effective radius of rotating mass, w is angular velocity in radians per second)

The rotational energy one is interesting as it means having smaller wheels will not save rotational energy, e.g. with half diameter wheels the mass at the rim and radius are both halved but the angular velocity is doubled and being squared in the equation means it balances out. You will save on the 'linear' energy accelerating a smaller wheel of lower mass however.

My assumptions may be a bit off but they would have to be way off to change the 2% mentioned above by much unless my maths is wrong. Has anyone made calculations that differ much from the above? If you have some other assumptions I can quickly put them in the equation to see what effect that would have with my (slightly more than a) back of an envelope calculation

PS - I noticed I didn't take account of the tubes in the tyres (assumed 100g each) - this changes the percentage of the rotational energy to the total needed from 1.8% to 2.0%.

[Brucey]

I recently attended a lecture given by the technical director of British Cycling. He and his colleagues did a sensitivity analysis of all the things you could vary in the bike and rider. Mass (even rotating mass) came out as relatively unimportant, even in track events; there were about half a dozen other things that could be varied with expectation of greater benefit.

What is true is that rotating mass is more important than other forms of mass; adding 100g to the rim and tyre is differt to adding 100g to the bike frame or rider.

cheers

[Mr Evil]

There is an article from a few years back that did some calculations over a whole ride, showing that the effect of wheel mass is so small as to be inconsequential, and the difference of having that mass at the rim is even smaller.

Still, I'm sure people will persist in talking about the importance of rotating mass forevermore, as well as countless other myths.

[pwa]

Just to add a bit of complexity (you know you love it) I feel that the rotating mass of heavy footwear makes me tired on long rides. Heavy footwear can be hundreds of grams heavier than light footwear, and having to keep it rotating as you ride is a bit sapping. Or so it seems to me.

[[XAP]Bob]

I recently attended a lecture given by the technical director of British Cycling. He and his colleagues did a sensitivity analysis of all the things you could vary in the bike and rider. Mass (even rotating mass) came out as relatively unimportant, even in track events; there were about half a dozen other things that could be varied with expectation of greater benefit.

What is true is that rotating mass is more important than other forms of mass; adding 100g to the rim and tyre is differt to adding 100g to the bike frame or rider.

cheers

Yes - but what is interesting is that the size of the wheel has no effect on it's own (because the increased angular velocity perfectly cancels out the lower distance to the rim)
Obviously the size of the wheel does result in other changes...

[NATURAL ANKLING]

Hi,

Just to add a bit of complexity (you know you love it) I feel that the rotating mass of heavy footwear makes me tired on long rides. Heavy footwear can be hundreds of grams heavier than light footwear, and having to keep it rotating as you ride is a bit sapping. Or so it seems to me.

The same is also said of walking boots.
I suffered from unstable ankles, still do, I did not learn of this till later in life after dozens of sprained ankles
My current walking boots which were described as mountain walking boots are heavy BUT because of their construction they almost totally eliminate any lateral twist, meaning that you can walk laterally along a slope but it feels like you are on flat land, to the point of I found it impossible to sprain my ankles with these boots, alas they are now too old and the sole has unstitched, modern walking boots have changed so much but no longer offer that level of support.
Remove lateral support in walking boots when on unpathed moorland etc and your feet suffer early fatigue.
I found a NOS pair of boots like my old ones for my partner but I am still looking.

I admit in the case of cycling you don't need heavy footwear or more support unless some of your journey cycling will be on foot on unpathed land.

What you are saying is similar to carrying load on back, putting twice the load on the bike would be less tiring for sure.

[cycleruk]

With the reference to shoes, would not the weight of one shoe balance out the weight of the other when talking about rotational mass.?
Yes the shoes weight will be additional to the whole so a light pair will be beneficial overall.

[Tompsk]

"With the reference to shoes, would not the weight of one shoe balance out the weight of the other when talking about rotational mass.?
Yes the shoes weight will be additional to the whole so a light pair will be beneficial overall."

No - you would still have to speed up the pair. However, they are balanced - a bit like adding 2 lead weights on opposite sides of a wheel.

[reohn2]

It's my understanding that a wheel with heavier periphery will spin longer due to it's flywheel effect and so will accelerate slower but once up to cruising speed will be easier to keep moving,and when going slower such climbing the heavier wheel will take more energy to keep moving at the same speed as a lighter wheel.
The bigger the tyre and rim the heavier the wheel in relation to a narrow tyre and correspondingly narrow rim which is lighter.
How much that matters depends on speed,no?
So if I'm happy to climb slower than though cruise at a similar speed to a lightweight wheeled bike this should be OK,no?

[Tompsk]

I recently attended a lecture given by the technical director of British Cycling. He and his colleagues did a sensitivity analysis of all the things you could vary in the bike and rider. Mass (even rotating mass) came out as relatively unimportant, even in track events; there were about half a dozen other things that could be varied with expectation of greater benefit.

What is true is that rotating mass is more important than other forms of mass; adding 100g to the rim and tyre is differt to adding 100g to the bike frame or rider.

cheers

Rotating mass IS double the effect of non-rotating - however it is 2x (not allot) = (not allot). e.g. my calculations show +100g on the outside of the wheel increases the energy needed to accelerate by 0.26%, 100g on a non-rotating part adds 0.13% to the energy needed. This is important if you are sprinting the final 250m of a grand tour or track event sprint when 10cm can mean winning or loosing - however probably slightly less important to most others?

[Tompsk]

It's my understanding that a wheel with heavier periphery will spin longer due to it's flywheel effect and so will accelerate slower but once up to cruising speed will be easier to keep moving,and when going slower such climbing the heavier wheel will take more energy to keep moving at the same speed as a lighter wheel.
The bigger the tyre and rim the heavier the wheel in relation to a narrow tyre and correspondingly narrow rim which is lighter.
How much that matters depends on speed,no?
So if I'm happy to climb slower than though cruise at a similar speed to a lightweight wheeled bike this should be OK,no?

If the speed does not change it does not take more energy to keep a rotating object going - however, having heavy anything makes it harder to go up hills! But if it is rotating or not makes no difference.

[NATURAL ANKLING]

Hi,

With the reference to shoes, would not the weight of one shoe balance out the weight of the other when talking about rotational mass.?
Yes the shoes weight will be additional to the whole so a light pair will be beneficial overall.

Aren't the feet accelerating and retarding so mass here would have a dampening/ dragging effect ?, no advantage in heavy shoes for cycling unless its for dual purpose.

Edited - When cycling at constant speed

[Keezx]

It's all calculated and discussed before all over the world, nothing new.
Having 2 rims at 100+ gr/per rim equals having an extra waterbottle with 0,4 l water.
For most people not noticable in performance.
What IS noticable , is a light front wheel which feels more "agile" and that's what most people confuse with easy spinning up etc.

[NATURAL ANKLING]

Hi,
Steering geometry and tyre profile will also affect the way the bike steers and feels.................

[Keezx]

Yes, and another 50 things, but what's the relevance with the subject?