ticktockpedal

this has been talked about before, i've seen some links to cryptic german engineering tables, but..

what do you understand the impact of rotational (wheel) weight to be?

as i see it:

- heavier wheels need to be "wound-up" every time they accelerate, in addition to the net forward horizontal momentum gain.

- i have noticed a "gyroscopic" effect with heavier tires, where the spinning tire makes the entire bike more stable/more difficult to tilt off its axis. if you are pounding the bike out of the saddle up hill, is that additional inertia to bang back and forth?

- is there something about the weight at the outer-radius of the wheel needing to "reverse" all the way back to the rear every rotation? or is that just bunk?


anyone have a simple theory?

gerundium

all of you have seen newtons law, F = M*A

M = mass
F = the net force on the mass
A = acceleration.

for rotational systems a similar relationship holds.

M = I*a

M = the net torque on the system
a = the angular acceleration.
I = moment of inertia

For a wheel spinning up the mass is not as important as it's moment of inertia. more about that can be found here: Wiki but this contains mostly definitions and is hard to grasp without a solid mathematical base. for a simple approximation we can estimate the moment of inertia by considering it a combination of a thin circle (the rim) that rotates around it's center axis and a set of rods rotating around it's outer point. this ignores the hub, but that is not a problem because in the definition of the moment of inertia you multiply by the distance of a mass from the point of rotation squared. this means the hub has a very small impact on the total compared to the rim (due to large distance it is away from the center axis. This calculation is something i think is reasonable for a ballpark figure but i am not completely sure, a highly skilled mechanical engineer will probably weigh in to correct me if i am wrong. Civil engineering student myself so moving systems are a little rusty.

my approximation yields the following

I(rim) ~= m*r^2
m = mass
r = radius of the rim

I(spokes) ~= n*(1/3)*m*l^2
n = the number of spokes
m = mass of a single spoke
l = length of a single spoke
(this approximation assumes the end of the spoke to be in the center axis, which i will leave as is for simplicity sake)

I(hub) ~ 0
ignoring this for simplicity

I(total) = I(rim)+ I(spokes)+ I(hub) = n*(1/3)*m(spoke)*l^2 + m(rim)*r^2

you can try filling in this above relationship yourself if you know the mass of your rim and spoke seperately, and then you can compare between different wheels by comparing the approximation. Do note though that we have approximated the rim as a thin circle so for high rims like Zipp 404's for example this is incorrect and another more complicated approximation is in order and one that i can't come up with so easily (for those interested you would need to take the moment of inertia of a solid disk with the radius equal to the radius of the outer side of the ring and subtract a solid disk with the radius of the inner radius of the rim.)

Campag4life

A couple of things OP. Weight difference between hubs is very hard to feel. Because of the moment of inertia, the farther away from the axle centerline the more the added weight matters....but only for accelerating really.
I will tell you where it really matters...in the world of mountain biking. I own a 29er which have taken over the mtb scene but not without a fair outcry initially in particular because of moment of inertia mostly. Fat tired larger wheeled mountain bikes do not accelerate as quickly as a 26 inch bike...but they tend to hold their speed better and why they are starting to dominate mtb racing throughout the world although Europe has been slow to embrace 700c rim size mtbs.
Further...the wheel weight thing I believe for the amateur doesn't matter as much as wheel stiffness but if racing you want the lightest, stiffest wheelset you can find...and lightest tires without or without lightest tubes.

asgelle

Here https://www.biketechreview.com/review...el-performance With the full equation of motion in Appendix A here, https://www.biketechreview.com/images/appa.pdf

Pedaleur

Practically, it doesn't really matter.

That said...for the rim, it takes about twice as much energy to accelerate it than a comparable non-rotating mass. For spokes, significantly less than twice. For the hubs, you can consider them static.

So, let's say your rims weight 400g each. Ignoring the spokes, that means that instead of accelerating, say 80kg (bike + rider), it "feels like" accelerating 80.8kg, a difference of about 1%. Easily trumped by aerodynamics and many other factors.

For steady riding, including hill climbing, the energy difference is exactly zero**.

You also get energy back when you coast (so long as you don't brake).


**where 'exactly zero' is not quite zero when you consider very minor theoretical effects such as periodic pedaling. Long story.

kleinboogie

Maybe Newton was wrong or had a note in the margins that said it doesn't matter but somehow I doubt it. I notice the difference in wheel weights and rotational weight so yeah, it makes a difference. It helps to have enough wheelsets to compare. GL

Right Said Fred

Inertia works in both directions--it takes longer to get the heavier wheel up to speed, but it takes longer to slow it down once it's moving.

Minion1

True I misread the OP's question as being about intertia. Rotational weight does make a big difference.

embankmentlb

In my unscientific & possibly backward thinking a lighter wheel is always better. A heavy wheel may carry momentum that could be used efficiently like a flywheel if everything were constant. Nothing about road riding stays constant. Every minute change in speed, energy is robbed by the gyro effect. Moser used the momentum of big wheels to some success for the hour record, well, that & drugs....

achoo

Did you time yourself with different wheels? Under controlled conditions?

Just because it feels different doesn't mean it's slower.

zzzwillzzz

+1
feel is a terrible indicator and is meaningless w/o data

Jazzy Hands

I am assuming you are talking about moment of inertia.
If you have two wheels of same weight, but one is a disk (relatively equal weight distribution) while the other has most of the weight in the rim, the later will have a greater moment of inertia.
Basically, this means that it is easier to get the 1st wheel spinning. However, the it is easier to keep the 2nd wheel spinning (but it takes more energy to begin spinning).
This is noticeable at stoplights. If you have the first, it is easier to accelerate from a stop, but it is easier to maintain your speed on the 2nd.

kleinboogie

I'm not really into the science, I'll leave that to the academicians. For me, time and speed are only relevant in regards to power for which I have hours and hours of video with my Garmin overlay in varying situations to tell me what happened. Boring for most, educational for me. Cheers

garciawork

Most interesting thread I have read in a while. Thanks math geeks! I have always understood physics pretty well (in theory) but the actual math always screws me up...

urbanknight

Psht. The more expensive a wheelset is, the faster it feels to me. That's solid evidence right there.

kf9yr

As I look at the original post I see 3 statements

1. I agree a heavier wheel with more weight on the rim is harder to "wind up" as there is a higher moment of inertia. This also works in reverse when you're braking. I have a 1200g set of carbon wheels that I can absolutely feel accellerating easier from stoplights than my much heavier Ultegra wheelset. This wouldn't make much of a difference in a TT but when you need to accellerate and decelerate or climb a lot I don't see how it can't make an improvement, especially on a long ride.

2. More weight at the outside of the wheel would of course make more of a gyroscopic effect but it would be felt more on a downhill as the rotational speed of the wheels is much slower on the uphill than on the downhill. I would go with the lighter wheels for climbing as I wouldn't have to pedal the extra weight up the hill.

3. If the weight around the circumference of the rim wasn't very close to equal you would have quite a scare on a fast descent. There isn't any weight redistribution going on or the wheels would feel like they were trying to buck you off at 40 mph.

If there wasn't a discernable, measurable difference with lighter wheels the pros wouldn't all be riding on them during their races.

Campag4life

I think the point about diminishing return when it comes to wheel weight and this encompasses what some average amateurs spend on carbon wheels...is we ain't pros. Pros care about tenths of a second. The fat guy riding a Cervelo with $2K carbon wheelset shouldn't and will be passed by the fit senior on a CAAD10 every time with 2000g Al wheels.
Should the goal be to find a 'lightish' wheelset that is decently stiff? Of course but...a hundred grams of wheel weight for another $500-700 is a waste of money for the amateur. Truth about carbon wheels is most buy them more for the looks than the performance...yes they perform well as they should but so does a 1500 gram Al wheelset for $1K less.

Matt Gaunt

Very interestng thread, thanks for this everyone.

My own experience is this: yes, rotational mass is noticeable, particularly at the traffic lights. Once up to speed, I think the effect is much less appreciable, though YMMV.

The whole climbing / deep carbon wheel offerings debate will continue but Campag4life had it right for me when he said most buy carbon for looks, rather than performance.

lazerzxr

I ride Fulcrum racing zeros (about 1500g) and Shimano R500 (about 2kg i think) They are $000 apart. The fulcrums are stiffer, look better and have not broken any spokes. Weight.....I cant really tell.

I stayed away from carbon as I do a lot of descending and want my brakes as good as they can be

spock

At one time I had a steel chrome wheel in the back that I got off of ebay for pretty cheap when my Ukai 27' wheel went bad. I was riding it for about a month before spokes started popping because of a bad build...

But, it was great to ride with.

Definitely harder to accelerate, but once it starts spinning it spins forever and it was easy to keep the momentum and a joy as far as pedal stroke goes. That thing just went going.. Don't really know how to explain it.

JSS

If you are a professional racer competing against your peers where a few seconds can be the difference between first and fourth place factors like lighter wheel sets and aerodynamics make a difference, otherwise the fancy gear is only good for staring down other riders in the parking lot before the ride:: for me owning the parking lot is worth it......

MadFiber Wheel Set 1082 grams

asgelle

If I'm an amateur racer competing against my peers where a few seconds can be the difference between first and fourth place, do the factors like lighter wheel sets and aerodynamics stop making a difference? Why?

urbanknight

Just because you can't measure it doesn't mean it isn't there. Did Cavendish reach the finish line first because he was stronger or because his wheels were more aerodynamic and lightweight? The answer is somewhere in the middle, isn't it?

JSS

Good point, the stakes may be different, but bragging rights are the same............

paulfeng

+1

As a physicist, I approve of this message.

I reminded myself the other week of how this rotational dynamics works and convinced myself to stop obsessing over the idea of a lighter wheelset. The money is better spend elsewhere for me.