Sunday, October 21, 2007

Steering Geometry

In spite of the fact that the modern bicycle has been around for considerably over a century and even the recumbent bicycle for over 80 years, understanding bicycle steering is a persistently difficult problem in dynamics.

Contrary to popular belief, gyroscopic forces play only a minimal role in determining 2 wheel vehicle stability. Check out this site for a whole bunch of interesting experiments with counter spinning wheels and interesting steering geometries.

Another bit of required reading is David Jones' classic treatise on bicycle stability in which he attempts to build unridable bikes.

For this subject and just about everything else related to bicycle technology, check out Bicycling Science.

Finally for a good, relatively concise writeup on the dynamics of 2 wheel vehicles , check out this wikipedia article.

Boiling down the above, there are really 3 variables that we can vary with our design.
The combination of the above give us:
The difference between mechanical trail and trail seems subtle, and in fact it is, but Jim Papadopoulos makes the case in bicycling science that MT is a more relevant measurement of how the bike actually handles. It represents the lever arm through which the perpendicular component of the vertical support force acts. In other words it is the lever length that forces the wheel to turn in the direction of a turn when you lean the bike. It's also interesting to note that two bicycles which have the same T may have a very different MT due to differences in head tube angle.

Having said all that, increasing T and MT all other things being equal will cause the bike to be more stable. Stability is a bit of a loaded term since it is usually used in the above mentioned documentations to discuss the ridabilty of a bicycle hands-free. For my purposes however I'm considering a more subjective view. A "stable" bike is one that feels like it is "on rails" and wants to hold it's line. An unstable bike is one that is lively feeling and handles quickly. The best handling bikes are compromises between the two. It would be easy to make a bike so stable that it was practically impossible to knock over once at speed. Unfortunately it would also be so stable that swerving to avoid that car or pothole would be equally impossible.

For my particular design I'm starting with an existing fork. It's a kinesis 650C Aluminum Tri fork. It's light, good quality, and fits the 559 wheel size adequately with either long reach brakes or some creativity. I measured the rake on this fork to be 34.54mm, and it's axle to crown length is 340.36mm. I'm also decided on using 559 rims with 25mm tires for the purposes of this design. If I ever want to use wider tires (for touring for example) I'll need to make a new fork anyway since this one won't clear wide tires. At that point I'll simply optimize it's rake for the new wheel size.

Since I have 2 of my variables fixed already by deciding on a fork and a wheel size, I need only to decide on head tube angle. The first thing I did on my drawing was to draw in the fork rake by drawing a circle with radius 34.54 centered on the front axle. Then for the heck of it I drew in case where the headtube was simply perpendicular to the maintube. This is the maroon line. This gives me a headtube angle of about 71.3, T of 68.61 and MT of 65. These T and MT numbers are very high. The highest MT listed in a table of common values in Bicycling Science (Table 8.1, p274 of Third ed) is 58.5, and the highest T's are 76.2 and 69.8, but both are found on track bikes. This does however put it close to the Bacchetta Aero, which is obviously a successful design.

I am still uncomfortable with the very high MT and T numbers so I decided to see what I would get if I fixed the trail at 60mm. This is a good common number for a stable touring (or similar) bike. This is the blue line. I get a HTA of 72.8 and a MT of 57.32. These are still on the stable end of normal, but they are much more inline with what is out there in the upright world. This also puts my trail nicely between the 70's of the Aero and the 50mm of the Volae Team.

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