Thursday, November 20, 2014

Are fat wheels heavy?

I think most smart bike people will acknowledge that fat tires have superior traction and flotation on sketchy surfaces, in winter conditions, etc. But the tradeoff is that they're so heavy and slow!

Thirteen years ago, the University of Minnesota decided to grant me a master's degree in geophysics, and I figure it's finally time to apply that credential to some useful purpose. So why not start by measuring something. Here's a 120tpi Dillinger 26x4" on the scale:
The scale reads 1352 g with packaging included. Add in a Q-tubes 26x2.4-2.7 superlight tube and a standard Marge Lite rim, and we have a tire/rim mass of approximately 2.28 kg.

For comparison, consider a more "typical" winter bike wheel. A Schwalbe Marathon Winter 29x2.0 studded tire is listed at 1265g. On a typical 520g rim with a typical 220g tube, this typical winter wheel weighs in at just over 2.00 kg.

But the acceleration of a wheel with an applied torque is not quite as simple as a basic mass comparison. We also have to consider the size of the wheel, since mass farther from the center of rotation is harder to accelerate. The important physical quantity here is moment of inertia. The lower this number, the faster the wheel accelerates under a given torque. Most cyclists prefer a lower value for moment of inertia, though having a higher value increases rolling momentum, which is desirable sometimes. If I assume that the effective radial center of momentum of each wheel is in the center of the tire (halfway between the rim bead seat and the outer tread of the tire), the 29" wheel has an effective radius of approximately 0.340 m. The fat tire 26" wheel has an effective radius of approximately 0.330 m.  The formula for moment of inertia is I = m x r x r. So square the radius and multiply by the mass. For the fat tire 26" wheel, the value of I is 0.24 kgm^2. For the 29" wheel the value is 0.23 kgm^2. These are about double that of a typical high-performance road racing wheel.

I consider these two inertia values to be effectively the same, given the simplifying approximations I made. But the fat tire is widely regarded (by armchair experts) as heavy and slow, while almost nobody thinks to comment on how heavy and slow a typical 700C/29" winter wheel is.

Note that I'm assuming that the mass of a hub and spokes don't contribute to the inertia calculation. Assuming the same hub mass, the 26" wheel has a slight advantage because the spokes are shorter and lighter. But the more important mass is further out on the wheel. That's why I just consider the mass of the rim, tire, and tube. Also, I'm not considering the effect of tire rolling resistance or aerodynamics. My general sense is that a high-quality fat tire inflated to an appropriate pressure has lower rolling resistance than a Schwalbe Marathon Winter, but the skinnier tire has lower aerodynamic drag.

2 comments:

Leslie said...

Dude! I didn't realize your MS was in geophysics!

My MS is in engineering geology, then I'd dome some PhD work in Appalachian tectonics.

And, Jan Heine's PhD was in geomorphology and paleoclimates...

Johnny said...

^ Same thoughts as Leslie. I'm a Hydrologist with a BS in Geology and MS in Hydrogeology. Nice to know another earth nerd!