Hello Ray,
welcome to our list. I think you are member #50. Great to have some more mathematical brain power here. Dirk already made some nice calculation works.
The most important is smallish 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 have heard that NT bikes could be stable, if the trail is not too big and if there is enough weight on the front wheel. Maybe that corresponds to your idea.
So far we have the practical affirmation that a python with the usual dimensions is fairly rideable with 45 km/h on flat terrain and 50 km/h (14 m/s) coasting downhills. The latter requires more skill because the front wheel is not pulled but pushed. At low speed (< 10 km/h), the python is more stable than the flevo.
I noted that the "height" of the pivot is not the real factor, it is the angle and trail it creates.
Right.
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.
According to most people, the steering axis has to go through the middle between the two hip joints to minimize the pedalling/steering interferences. I wonder how the Tom Traylor like bikes are rideable.
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.
We are looking forward to your work.
In the next time I will build a scrap python which will undergo a lot of geometry and steering experiments. Some of them are: rubber pivot, four bar linkage pivot, shallow steering angles around 50 degrees and lesser negative trail. Will let you know.
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