[python] Re: Stability Theory

Hi Jürgen,

>Thanks a lot for the metric version.

You're welcome. Thanks for the bike idea!

>How to get:
>   - front mass height

Hand (and all others) assume a "no-hands" rider, so the front mass is the 
center of their fork/tire/bags etc mass. It is complicated by having the mass 
of the python rider's legs normally attached. It should be a measure of the 
mass that turns with the front, as best as you can estimate.

>   - front mass to pivot

As above. I assume that it is fairly far forward; maybe looking at side photos 
is best.

>   - front wheel moment of inertia

The value of 50 in/lbs**2 was for a narrow street wheel, so adjust accordingly. 
It is almost entirely a function of rim and tire weight/mass.

>   - front mass inertia factor
>   - inertial angle of front mass from horizontal

There are uncertain in my mind. The factor I use is a multiplier for the "base" 
moment factors of various authors. Remember, they assumed an upright rider. The 
factors are probably right, but the rear angle is probably not. The angle is 
the angle of the strongest moment, from vertical, ~60deg for an upright rider's 
mass.

>and the same for the rear.
>How can one mesure the position of CG?

You can use scales under the tire(s) to find the for-aft distribution. Most men 
have a CG around their hips as well. The question is, how much "belongs" to the 
rear vs. the front? Only  the leg mass that moves much with steering (feet, 
calves, little thigh) counts as front mass. So the upper thighs should be 
counted as rear mass.

>Does the calculation include the self-centering
>effect, which I consider important for the low
>speed stability?

Yes, it paraphrases the code at the end of Hand's 200 page paper. I was testing 
a comment made in another last night; adding a spring to the pivot changes a 
specific pair of the equations only, so I added the optional spring's +/- K 
value. It seems from the results that using a "normal" spring, like a rubber 
bushing, has an effect which depends on wheelbase and pivot angle. It can 
increase or decrease stability depending on the other factors. A negative, 
de-centering, spring can also go either way, but the effect is also that it can 
offset some of the python's natural centering force, which can sometimes be too 
strong. So, if you have an existing bike, either type of spring might help, 
depending.
I'll post this version later this week. I'm trying to figure out how to work a 
damper into the equations, and maybe a proxy for wide tires' steering effects.

Cheers,
Ray 

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