# Impact of rim weight on energy output when biking uphill

For a real world problem, I've been puzzling over the trend to go after very light-weight rims for bicycles. My BS in physics hasn't provided me with solid answers. I am a bit rusty.

I have found a feeling of increased stability when running heavier rims and attributed this to an increase in momentum. That said, many fellow riders have said I am having to expend considerably more energy to keep these heavy rims moving forward, esp. when going up a hill.

Most of the information I have found on the relationship between momentum and energy refers to relativity and small particles. Please help me out here.

Thank you,
Katie

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mgb_phys
Homework Helper
I can't see that it would make much difference, a few 100g extra on a bike+rider weight of 80kg. Compared to aerodynamic effects I don't think the gyroscope effects of a bike wheel is significant.

Andy Resnick
Heavier rims will give a better sense of stability, but that's due to rotational properties of the wheel- concentrating the mass near the outer edge will increase the moment of inertia over a disc of uniform density. But then you have more mass to lug up against gravity, and more mass to accelerate in the face of loss- from traction, aerodynamics, etc.

rcgldr
Homework Helper
If all the mass were at the rim, the effective increase in inertia is double that of the mass of the rim, but this only affects acceleration and deceleration. At constant speed, the increase is just a matter of the mass of the rim.

mgb_phys
Homework Helper
Rotational energy stored = 0.5 I w^2 and for a hoop I = mr^2/2
At 50km/h a 700mm wheel is rotating at around 6 rev/s or 44rad/s.

So an extra 100g in the rim would store an extra = 0.5 * (0.1 * 0.35^2)/2 * 44^2 = 6J

Unless I've made a mistake somewhere, completely negligible.

uart
If all the mass were at the rim, the effective increase in inertia is double that of the mass of the rim, but this only affects acceleration and deceleration. At constant speed, the increase is just a matter of the mass of the rim.

Yes that's exactly the situation. So racing cyclists want to have their rims/tires as light as possible because weight there has a two times effect on the overall inertia of a rolling bike, and they of course want to be able to react as fast as possible in a sprint or chase-down.

As for going up hills it's not inertia but just gravity coming into play so the effect is only one times. That is, it makes absolutely no difference whether the extra weight is on your tires/rims or in your drink bottle or around your waist, wherever it is it will impede your climbing just the same.

A brief comment that uphill the inertia also matters since you are constantly accelerating the wheels to maintain a constant speed.

Also, the trade off in this is how much flex you get in the wheel, consider the spokes as shock absorbers and the wheel a suspension system when they get light. What happens is a strong rider will deform the wheel enough to lose some momentum during the high-torque portion of the stroke, this is very noticable to heavy riders so they normally will choose a deeper profile and more spokes or a composite wheel with more strength to counteract it.