## Friday, September 3, 2010

### Cross-winds and trail and Bicycle Quarterly, part 3

Last two times, I discussed an article in Bicycle Quarterly which described how low-trail bikes should perform better in cross-winds. I showed that this is true for two effects from the sidewind, one that a bike leaning into a side-wind will tend to steer into the wind if it has positive trail, and the other that a sudden gust will cause a reaction force on the front wheel that will tend to rotate the wheel. Actually, these two effects are really the same, one the steady-state effect, the other a short-term effect. But what the article missed was that the sudden gust is also going to tend to blow the bike over in the direction of the wind, so an effect which causes the bike to suddenly steer away from the wind can compensate for this.

But there's another effect. Everyone knows that a deep-dish rim is often less stable than a shallow rim, or even that bladed spokes may be less stable than round ones. This is due to the direct force of the wind on the front wheel, although there are also contributions from the effects already discussed.

The key here is that the wind exerts force around the full perimeter of the wheel, which for simplification purposes might be considered axially symmetric. One can integrate force about the rim, but the simpler approach is to assume all the force is applied to the hub, which is the wheel's symmetry axis. So there will be an effective force on the hub proportional to the net force on the rim + spokes + hub + tire: the whole wheel.

Here's a diagram again of the hypothetical zero-trail Guru Photon:

Zero-trail bike

Indicated in the plot is a moment arm between the steering axis and the hub. Even with zero trail, there will be a torque applied to the wheel proportional to this distance, which is equal to the rake of the fork.

For a given head tube angle, rake decreases trail. So if you decrease trail by increasing rake, you increase the steering moment applied by the wind when it hits the wheel, even though you might be decreasing some of the effects previously described.

Back in the glory days of epic racing, long-rake forks were in style, presumably because the long curve smoothed out road vibrations:

Blog posts are always improved by a photo of Fausto Coppi

I don't think Fausto would want to clamp Zipp 1080's on that puppy.

Anyway, cross-winds aren't a simple matter, clearly. And I don't even address the lateral aerodynamic lift that deep carbon winds generate in cross-winds.