An Experiment in Frame Geometry

My utility bike is a 1974 Schwinn Sports Tourer. It has a straight gauge chromo frame with fillet-brazed joints. The frame design could have come out of the Rivendell catalog: low bottom bracket, moderately long chain stays, and 73 degree head and seat tubes.

I bought it off Ebay in 2003 or so. I converted it to a 7-speed internal hub and added fenders and lights and other utilitarian stuff. It has averaged more than 1500 miles per year since then, commuting to work and running errands.

The bike has a few faults. One is that a 35mm tire is a tight fit laterally in the fork – the sides of the tires tend to rub on the fender and/or fork blades if everything is not set just so.

The second fault is that it rides harshly over bumps, even with 35 mm tires. I would ascribe this to the relatively stout straight-gauge tubing used in the frame. My sportier bike,  with steeper angles, shorter chain stays, and narrower tires but built with standard-gauge butted tubing, is much more forgiving. It is unclear from the information out there whether the Schwinn fork is chromo, but the rear triangle is reportedly plain carbon steel.

And the third problem is that the bike cannot be ridden no-hands at any speed because of a serious shimmy.  This shimmy damps out even with light hand contact on the bars, but it is a significant annoyance.

My theory (at least I have not found anybody who states it exactly this way) is that shimmy in bikes, at least in many cases, is a harmonic phenomenon something like a torsion pendulum, with the trail of the fork, which tends to make the bike go in a straight line, acting as the spring. In a torsion pendulum, the frequency of oscillation is determined by the stiffness of the torsion spring and the moment of inertia of the system.

Bikes are a little more complex than the simple torsion pendulum example, because there are two mass/moment of inertia systems influencing the oscillation. The first is the obvious one: front wheel, tire, any luggage on the front — everything that pivots around the steering axis. The second mass and moment of inertia system is not so obvious. Because the head tube moves side to side as the as the fork is turned, all of the mass of the bike that does not pivot around the steering axis pivots instead around the contact point of the rear tire. This means that the frame, rider, rear luggage, back wheel, and any other paraphernalia influence any oscillation, with mass closer to the front of the bike or extending behind the back wheel (and thus farther from the pivot point) having greater moment than weight directly over the back wheel.

In this conceptual model, shimmy occurs when the front (pivoting around the steering axis) moment of inertia/trail system has a similar natural frequency of oscillation as the back (pivoting around the rear tire contact point) moment of inertia/trail system. Since these two systems are so different, it may also be that oscillation will occur when harmonics are similar.

I don’t know a definitive way to test this theory, but if it is a good model, changing weight distribution should affect a shimmy, as should changing fork trail without changing weight distribution. I have had experiences when changing weight distribution seemed to cause or eliminate shimmy, though other times the shimmy seemed to be insensitive to changes. The Schwinn does not have racks or baskets on the front, so I can’t change loads there, but the shimmy does not respond much to a wide range of loads on the back. I have tried added damping by adjusting the headset too tight with no change. The shimmy persists with tires from 28mm to 35mm and different front hubs.

I decided what I needed was a new fork. The fork crown would be wide enough that there would be no problem with the 35mm tires. The blades would be mid-weight chromo to see if the over-bumps-ride ride would improve over the unknown material of the original fork. And I would try a low-trail design, as championed by Jan Heine of Bicycle Quarterly (here, for example).

Here are the results.

Problem 1: Solved. There is now plenty of clearance.

Problem 2: With the new fork, the bike rides only marginally better over bumps (based on subjective observation), even with the greater offset. Maybe a fork built with lighter fork blades would have enough more give to make a difference, but I think that would be inappropriate for a bike that gets this much abuse. Then again, maybe I will try it someday just to see how much difference it does make. Anyway, the bike got a new sprung Brooks saddle to handle some of the jarring, but that does not help my hands.

Problem 3: The finished fork results in about 25mm of trail, which is at the low end of accepted practice. Somewhat to my surprise, the handling did not change all that much. It feels quick and maneuverable at low speeds and it feels a little twitchy at downhill speeds, but it still in the range of what I would call normal.

The bike now has much less tendency to shimmy – reducing the trail seems to have worked in that regard. If the above theory is correct, increasing the trail should have also worked.

And for a bonus, I discovered that brazed-on centerpulls do indeed have a nice solid feel. But this mounting did not make enough difference in braking to make up for the trouble of making the mounting studs.

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