Ok, so I have implemented the
Ok, so I have implemented the linearized bicycle stability equations used in the jbike6 matlab software on the open source sage mathematical software which I mentioned in my previous post.
This is going to be a bit too theoretical but nonetheless interesting. If you don't like maths, probably best to skip it. If you do like maths and/or are interested in what makes a bike be able to run stably without any steering input (no hands) have a look at the jbike6 website and especially the paper published in the proceedings of the Royal Society:
http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/*FinalBicyclePaperv45wAppendix.pdf
http://rspa.royalsocietypublishing.org/content/463/2084/1955
I have made a rough stab at capturing the vendetta's geometry and mass distributions to see what the software would spit out, and
Before going to the vendetta plot, the first plot below is the variation of the stability eigenvalues of a typical racing (DF) bike and rider combination, with velocity in meters per second along the bottom, and the eigenvalues on the y axis. This is all for small amplitude steering and lean motions, but the equations have been well benchmarked against full non-linear mechanics models and are good for showing trends in stability.
Notable points: The speed at which the yellow line starts is the speed at which oscillatory (weaving) behaviour starts to happen naturally. Below this speed, the bicycle will just fall over one way or the other (the pair of green lines which come together represent those "solutions" which can happen in a fast way (the upper line) or a slow way (the lower line). I'm not sure how there are two ways for a bike to topple over. Perhaps one way is with the steering towards the topple (which probably would go slower) and another way with the steer away from the topple. Anyway, after the two lines come together, but while the green line is still positive, it means that the weaving motions are amplified (growing) (the frequency of weaving is varying according to the yellow line/pi (or might be 2pi). So the bike is still unstable.
BUT, where the green line goes below zero (at about 5.4m/s for this bike model), the weaving dies away, and the bike will run stably without steering torques input. So, no-hands riding is then possible.
Above about 9m/s, where the red line becomes positive, this indicates instability for the case of "capsize" which is that the bike leans one way, the steering makes it then lean further and eventually the bike will go zooming around in a tightening circle and lay down. But this mode of instability is very slow growing and is no trouble for normal cyclists to counteract with either a steering input or a lean.
Now on to the vendetta curves (second graph). It looks very different. At this stage I have made a rough model by making a mass of 28kg in the form of two cylinders (i.e. legs!) which are fixed to the handlebars in the approximate geometry for where they are on a vendetta. Of course, on a real vendetta this isn't quite correct, since the end of the legs (feet) moves pretty much exactly as the handlebar/boom rotates, while further back along the legs there is less movement (and none at all at the hips). but at least it might give some indication of trends.
So what do the curves tell us? Well, see the yellow line now starts at about 11.5m/s (26mph). Perhaps this could be the instability that bumblief mentioned in his post above? Note that the low speed "topple" modes go all the way out to 11.5m/s - that is, active steering is required. (it's always possible to ride in unstable speed regions, as long as the controller (grey matter/muscles/senses) can react faster than the instability). Note there is an odd yellow loop at 2-3 m/s. Some sort of oscillating instability mode perhaps, but more likely a figment of the rough model.
Note also, the green line never crosses zero, so the bike is always unstable. Either the model is wrong, or when people ride a vendetta no hands they are still putting in sufficient (perhaps small) steering inputs with their feet. Since it isn't easy for most people to ride a V or silvio no hands, I'm guessing probably the latter.
If anyone wants to use the maths or help contribute to putting together a better model of the moments of inertia of a vendetta or silvio and rider, have a read of the paper and then have a look at the sage (open source, free, computer maths package) code
https://cloud.sagemath.com/projects/97da2c46-dec0-423e-b73e-a66455d08018/files/vendetta-linear-dynamics-eigenvalues.sagews