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There are claims often made that, eg, "An ounce of weight at the rims is like adding 7 ounces of frame weight." This is "common knowledge", but a few of us are skeptical, and our crude attempts at working out the math seem to support that skepticism.

So, let's assume a standard 700C bicycle tire, which has an outside radius of about 36cm, a bike weighing 90Kg with bike and rider, and a tire+tube+rim weighting 950g. With the simplifying assumption that all the wheel mass is at the outer diameter, how much effect does adding a gram of additional weight at the outer diameter have on acceleration, vs adding a gram of weight to the frame+rider?

I asked this question over in the physics Stack Exchange.

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up vote 7 down vote accepted

The answer I got was 2x -- adding one ounce (or gram) to the wheel at the outer diameter (ie, the tread) is equivalent, in terms of force/energy needed to accelerate, to adding twice that amount to the bike frame.

The answer was a bit involved and takes careful reading to fully understand, but the answer can also be explained with this thought experiment:

If you have a theoretical weightless wheel, fixed to a stationary axle (ie, not rolling on the ground), and you add a mass to its outer diameter, the energy needed to accelerate that added mass to some tangential velocity is the same as the energy that would be needed to accelerate the mass to the same linear velocity (ie, as if it were attached to a weightless bike frame).

But if our theoretical weightless wheel is not fixed on a stationary axle, but is instead attached to our theoretical weightless bike, we are accelerating the mass both tangentially AND linearly so we add the two energy requirements together, meaning it takes 2x the force to achieve the same acceleration and 2x the energy to accelerate to a given speed.

So the answer is 2x (and not 7x or 10x or whatever is often quoted).

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My favorite theoretical tangent is that the earth is just a big circle (it was proven round some time ago) and at any point you are just riding along a tangent... Since the tangent is FLAT... There are no hills when cycling :) => Just gravity. Thanks for sharing this. –  Glenn Gervais Dec 27 '11 at 3:42
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