What is the effect of adding weight to a wheel vs adding it to the frame?

Question

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.

Answer 1

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).

Answer 2

The reason why people talk about the effects of adding weight to the wheels vs. frame is not acceleration (the 2x result from Daniel R. Hicks answer is correct for this, btw.) but rather suspension: Unsuspended weight needs to follow every unevenness in the road faithfully, and that costs energy. Suspended weight does not need to follow each root/stone/pothole and burns less energy accordingly. For cars with their excellent suspensions, this is easily a 7x difference.

Bikes, however, have very little suspension. The main sources of suspension are the tire itself and the rider themself. The tire usually does a good job at evening out the small high frequency unevenesses which would otherwise have a significant potential of draining energy (depending on tire pressure, of course - this is the reason why a too high pressure can actually increase rolling resistance). The vast amount of the larger, low frequency disturbances (pot holes, uneven paver blocks, roots, etc.) transmits through the frame to be absorbed by the rider.

However, spokes also play a part in suspension, so a gram at the rim does indeed drain more energy than a gram at the frame. But this is a small effect, much smaller than 2x I'd wager.

Things change drastically when you add suspension to your bike: The suspension exists to stop pot holes and such from transmitting through to the frame, bringing the energy drain factor up to near the values for cars.

Answer 3

So, it is well known in physics that a solid disc (weight evenly distributed) beats a hoop (weight evenly distributed on the periphery) and a sphere (weight distributed evenly) beats both a disc and a hoop when rolled down a plane using nothing but gravity. It all comes down to the weights distance from the axis. At the beginning it takes more energy to move a specific weight or when going up hill. But if a flywheel is used that is potential energy and the heavier the flywheel the more energy will be stored in the rotation. But like a Yoyo it's not a 100% return. It will however help you up the next hill if a constant rotation speed is maintained until needed. Have you ever coasted down one hill and didn't have to pedal again until about halfway up the next? Ya, that's it. If you are 120lbs and your bike is 10lbs plus you add a 60lb flywheel and you can get the flywheel up to say 1,000 rpms it will probably carry you up a pretty big hill. Let's get that guy Colin from YouTube to build a contraption to figure this out. (He built mag shoes to walk on the ceiling)