[python] Python stability

Hello all,

After seeing Juergen's great site and hearing from Dirk, I started doing some 
looking into the math of bike stability with the intent of building a Python. I 
bought some extra tubes I needed, so now on to design.

After some research, I programmed a small bit which gives the self-stable speed 
range (if any) of an idealized bike (fixed weight, ridden no-hands, thin 
"metal" wheels). The effect of real tires would depend on the pivot trail and 
angle, and I hope to do that at some point. For large trail, it is negligible. 
For small trail, the offset of the contact patch changes the effective steering 
angle as the bike leans. 

It appears, so far, that a few factors definitely allow a self-stable python. 
The most important is small-ish negative trail, no more than -4cm. A longer 
wheelbase, with rear mass CG more forward, a more horizontal pivot angle and 
several others can add stability. I'll try to compile it soon so others can try 
it out.
I noted that the "height" of the pivot is not the real factor, it is the angle 
and trail it creates. Actually, steeper angles -with the same trail- give a 
wider stable speed range. Think of the pivot moving up around the wheel until 
it approaches that of a Flevo. It appears that if the pivot was directly in 
front of one's crotch (!) it would add self-stability, but as it got higher up 
it would seem to make leg-steering awkward.
It does seem to be the large angle which gives the straightening "feel" users 
report, but it is the large negative trail which makes them unable to roll by 
themselves. With an angle of ~45deg. and ~4cm trail, a python should roll on 
its own around 4m/s.
Of course, inherently unstable bikes are ridable, it is just the amount of 
learning and attention required.

I'm still working on the script and understanding the meanings of the stability 
matrix equations, hopefully I'll be able to contribute something more concrete 
soon.
I want to use the seat from my old recumbent trike, which fit well, I just need 
to make up my mind about the final geometry. 

Cheers,
Ray Schumacher
http://rjs.org



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