initial comments Franke Riess SuhrFrom: bikengr@netnet.net
Sent: Saturday, October 15, 2005 6:46 PM
To: Andy Ruina
Cc: Schwab, A.L.
Subject: initial comments Franke Riess Suhr

This refers to AN ADVANCED MODEL OF BICYCLE DYNAMICS 
G. Franke, W. Suhr, F. Riess 
Eur. J. Physics 11 (1990)  116-121 

Here are some initial comments, Andy you can certainly put them on the website. 
I hope and expect these can be modified and extended. Maybe even the authors can 
rebut or clear up. 

Section 2 the analysis of bicycle geometry is a lovely piece of work. Now I have 
made my own exhaustive evaluation of the spherical trigonometry of the leaned 
steered bicycle, I can see that they neatly anticipated many of my calculations 
in a reasonably clean way. I did not confirm equations in detail, but the 
methods are fine. 

The authors end up with a numerical (not analytical) solution for frame pitch 
angles based on rearframe lean and the steer angle. I didn't understand how this 
is implemented. 

What is not entirely clear is what fundamental triad they use in analysis. Looks 
like a co-ordinate system that leans and yaws with the rear frame, but has one 
axis parallel to the ground. The authors are not clear about where the origin 
is, so the checking of details in the next section is quickly awash in 
uncertainty. 

Section 3 Dynamics 

My problems begin in this section. As noted above, lack of explicit definition, 
or explicit examples, makes it hard to interpret some notation. The matrix D has 
to do with motion relative to the fundamental triad, while A has to do with lean 
and yaw of that triad. I can't dispute what I can't follow. 

But bring your attention to what follows eq (14). "Only the most important 
angular momenta are taken into account, those of the rear and front wheel (in 
hub direction) and of the steering system:" 

It looks like (15) and (16) exhibit spin angular momenta of the wheels. But the 
wording seems to imply that tip angular momentum, of the wheels themselves 
[necessary in a gyroscope to exhibit the wobbles of free precessions] and of the 
rider [who has a very significant mass-center moment of inertia tensor] has been 
neglected? 

In other words, for the linear problem, the model is something like point masses 
plus gyrostats? Note that angular momentum vector [though unstated I assume 
giving moment of momentum about an axis through each body's mass center] is 
given exactly along certain vectors, which are not even rotation axes -- this 
suggests an inertia tensor of the form NN, namely a uniaxial tensor, which is 
intolerable as an approximation for any real inertia. [Can not be exhibited by 
any body.] 

My further suspicion about this modelling is that it ignores any pitch angular 
momentum of the frames -- irrelevant for linear theory but not necessarily for 
nonlinear. 




Transferring my attention to the angular momentum balance equation (19) I have 
additional bafflement. (Andy you might know enough about 'rates with respect to 
frames' to decode their formalism.) The time rate of change of mass center 
angular momentum L is used (for both wheels and the front assembly), then there 
is a term relating to rates of linear momentum an offset from some origin. 
[Typo, the equation should have a dot over the p] 

Andy, apart from this typo, is the equation a correct one, when L is defined 
correctly? 

My current hypothesis is, the dynamic analysis is flawed by 1. simplification to 
point masses and      2. inconsistent neglect of certain terms in the moment of 
momentum of the bodies. 

Few specific numbers are avaiable for the bicycle they model, except the 
wheelbase, trail, and rider mass. 

I vaguely remember some pre-publication discussion with the authors, which they 
kindly acknowledge. The upshot was, they could not get agreement with JBike5, 
but I don't recall their data, nor do I have highest confidence in the 
programming of JBike5 at that time. 

JMP