Self Centering Effect

On the python mailing list there has been a lot of talk about the self centering effect of the python. When you sit on your python you can feel the python straitening up. The seat position is lowest when the bike is straight. When you turn the seat goes up.

I do not know if this is very relevant to the stability of the bicycle, but it does effect how the bicycle feels. It certainly does not feel like a flevo.

The subject about stability is very complicated, and goes way over my head. But it is very fun to delv into this subject. Do some archeology and plundering on my attic, excavating precious formulas from the textbooks I find there.

If your serious about bicycles physics, following link might help: http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/overview_papers_and_links.htm. Or another http://ist-socrates.berkeley.edu/~fajans/Teaching/bicycles.html.

One critical note on bicycle dynamics: it's very fine, but it does its calculations while abstracting the human away. The bike may be unstable, but that doesn't mean that you are going to slam your head against the tarmac. You riding on that bicycle form a strong feedback loop, which can make the whole (the bike plus yourself) a stable entity.

Everybody who tried drinking and cycling will agree that it is not the bike that is keeping the person from falling into a ditch.

The real question to answer is how much instability can we take before getting into trouble. This obviously depends on the ability of the rider. And the python like the flevo take a long time to learn.

Here are some graphs showing the effect of steering on the seat height. The negative trail, combined with a pivot angle make the seat go up and down. Where the pivot is located along the pivot axis does not matter at all. This is especially important for the 20 inch python, where there is trouble with ground clearance.

Simular calculations where made by Juergen", but where not put in any glossy graphs. His results and mine more or less are the same but not exactly.

Following settings were used ---trying to emulate Jürgens bike):

wheel radius315mm
wheel base radius1300mm
seat height300mm

(The height of the seat is the height of the intersection of the pivot axis with the seat).

I used octave (similar to matlab but freeware) to calculate the graphs. Here are the programs: flevo2.m and flevo_base.m

Seat height versus turning angle

The first graph shows the self centering effect best. The pivot is at an angle of 55 degrees. The graph measures the seat height in relation to the turning angle. When the trail is positive the seat will get lower (up to a certain point then it rises again. may be the formulas have a bug still).

Seat height versus trail

The following graphs show the seat height when the steering angle is turned 20 degrees (the 20degrees is just choosen randomly).

The graph below depicts how the seat height changes when the trail is changed. This picture shows that the negative trail has a positive effect on the self centering capabilities of the python. The greater the negative trail, the better.

It also shows that the changes are actually quite low (maximally 5mm when turning 20degrees). According to users of the bike, it is noticable.

Seat height versus pivot angle

The third graph is a variation of the first. This time the angle of the pivot is changed continuously for a few values of trail. Here it is even clearer to see that a flevo (positive trail) has not the centering effect as a python has.

It also shows a maximal self centering effect around 55degrees, with trail having only a little influence. When going below that angle the centering capability drops again.