[python] Re: Stability Theory

At 05:31 PM 2/16/2005 +0100, you wrote:

>>Trail and angle really define the bike, I don't think BB-seat length would be 
>>much influence. It would only slightly decrease the distance from the front 
>>mass to the pivot axis.
>
>Then we could just prolong the wheelbase! 

Hi Dirk,

Maybe...
I actually got a nice compiled version of my program going this evening: 
http://rjs.org/Python/wxFrameGeometry.zip
Also a CSV file of some results for a selection of geometry ranges from a first 
DOS version:
http://rjs.org/Python/result.csv
and of course, things turn out to be not as simple as I'd like.
(I apologize in advance for not using metric, the largest part of the papers I 
read used US measure. If it is useful, I can easily add a metric display 
option.)
 
There is a lot of inter-relation among the variables, and many zones of 
stability in the 17-dimensional input space. Also, keep in mind that much of 
this code is based on other's theoretical math, and that there are a few 
important simplifications in the model: a bike built similar to a standard 
upright, the wheels are thin blades, and the pivot has no friction or 
elasticity. So, the results should only be viewed as trends for the variables - 
it works OK for the "standard" bikes.
I hope to grasp the math better some time soon; for instance, the rider's mass 
has inertial moments in two dimensions for both front and rear and I'm not sure 
how to correctly change the angle for a recumbent vs. the upright. There is a 
lot to this stuff - some people have done doctoral theses and not fully solved 
it - ex.:
http://tam.cornell.edu/~ruina/hplab/downloads/Bicycle_papers/Hand_Thesis.PDF 
(200 pages,12.5 Meg, PDF) 

Apparently, the main effect of high speed instability is runaway oscillation, 
so the recumbent person's body would act like a damper, and other pivot dampers 
would help, at the possible expense of low speeds. With more playing around, 
some good trends might emerge.

If the code works for you (I hope, I tested on WinME and 2000) let me know. You 
might need http://rjs.org/Python/OLEAUT32.DLL 
The plot/calcs will execute after you let up on a scroll bar, or click "Plot".
Mouse over the boxes for a short description.

I hope it's illustrative; I don't feel that I "know" the "best" geometry yet. 
If others can verify that the stability range (if any) of their flevo or python 
matches this theory (or not!) the algorithms could be adjusted for low racers, 
if needed.

Cheers,
Ray

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