[Scilab-users] Bicycle Dynamics

[Michael J. McCann]

Note my official Scilab address is via     mjmccann at ieee.org (IEEE in US)
but my email client uses my address     mjmccann at iee.org      (IEE now 
IET, in UK)

If you are interested in bicycle dynamics, stability and control you 
should look at the special edition of the IEEE Control Systems Magazine, 
October 2006, Volume 26 number 5, "Advances in Motorcycle Design and 
Control" There are hundreds of references going back to the late 1800s.  
Key authors in this journal were Alessandro Beghi and Ruggero Frezza, 
also David J. N. Limebeer and Robin S. Sharp. I happened  to keep a copy 
for personal interest, but I haven't worked in this field. It's all 
there, stability, wobble, weaving, shimmy, stabilization methods and 
geometry effects. On page 110 there's a picture of Albert Einstein 
turning a corner on a bicycle with his quote, "Life is like riding a 
bicycle. To keep your balance you must keep moving".

Thinking about the problem discussed here in Scilab/Xcos it seems to me 
that you are interested in the rotation about the contact line with the 
road, that the radius of gyration will be dominated by the height of the 
rider's  CG above the road unless it's a motor bike in which case the 
mass of the bike could well dominate the analysis and furthermore, since 
turning involves rotation about a vertical axis and at high speed, the 
wheels can have significant angular momentum (gyroscopic effect) you may 
have to consider the angular momentum in 3 space. Good luck.

Mike.
Dr. M.J. McCann,
MJMcCann Consulting
================
  On 14/05/2014 09:16, Dang, Christophe wrote:
>> it seems to me it should be
>> mg*l*cos(theta) - (mv^2/r)*l*sin(theta)
>> and not the contrary.
>>
>> Or?
> Or not.
> Sorry, you're right, I messed the axes up.
> A shame for someone writing "Mechanical calculation engineer" in his signature ;-)
>
> So, your calculation seems globally right.
>
> Now, your question "If anyone could confirm that the model seems to be realistic/ or correct" is not obvious:
> I ride my bike everyday to go to work, and if I have a pulse in the steering angle, I correct it with my balance...
>
> Not sure 'bout what I'm saying (and I wrote enough silly things yet), but once delta goes back to 0, r is back to infinity (straight movement),
> so what you should see is the biker falling.
>
> --
> Christophe Dang Ngoc Chan
> Mechanical calculation engineer
>
> ________________________________