Andrew Cooke | Contents | Latest | RSS | Twitter | Previous | Next

C[omp]ute

Welcome to my blog, which was once a mailing list of the same name and is still generated by mail. Please reply via the "comment" links.

Always interested in offers/projects/new ideas. Eclectic experience in fields like: numerical computing; Python web; Java enterprise; functional languages; GPGPU; SQL databases; etc. Based in Santiago, Chile; telecommute worldwide. CV; email.

Personal Projects

Lepl parser for Python.

Colorless Green.

Photography around Santiago.

SVG experiment.

Professional Portfolio

Calibration of seismometers.

Data access via web services.

Cache rewrite.

Extending OpenSSH.

C-ORM: docs, API.

Last 100 entries

[Link, Computing] Useful gcc flags; [Link] Voynich Manuscript Decoded; [Bike] Notes on Servicing Suspension Forks; [Links, Computing] Snap, Flatpack, Appimage; [Link, Computing] Oracle is leaving Java (to die); [Link, Politics] Cubans + Ultrasonics; [Book, Link] Laurent Binet; VirtualBox; [Book, Link] No One's Ways; [Link] The Biggest Problem For Cyclists Is Bad Driving; [Computing] Doxygen, Sphinx, Breathe; [Admin] Brokw Recent Permalinks; [Bike, Chile] Buying Bearings in Santiago; [Computing, Opensuse] Upgrading to 42.3; [Link, Physics] First Support for a Physics Theory of Life; [Link, Bike] Peruvian Frame Maker; [Link] Awesome Game Theory Tit-For-Tat Thing; [Food, Review] La Fabbrica - Good Italian Food In Santiago; [Link, Programming] MySQL UTF8 Broken; [Link, Books] Latin American Authors; [Link, Computing] Optimizatin Puzzle; [Link, Books, Politics] Orwell Prize; [Link] What the Hell Is Happening With Qatar?; [Link] Deep Learning + Virtual Tensor Machines; [Link] Scaled Composites: Largest Wingspan Ever; [Link] SCP Foundation; [Bike] Lessons From 2 Leading 2 Trailing; [Link] Veg Restaurants in Santiago; [Link] List of Contemporary Latin American Authors; [Bike] FTHR; [Link] Whoa - NSA Reduces Collection (of US Residents); [Link] Red Bull's Breitbart; [Link] Linux Threads; [Link] Punycode; [Link] Bull / Girl Statues on Wall Street; [Link] Beautiful Chair Video; Update: Lower Pressures; [Link] Neat Python Exceptions; [Link] Fix for Windows 10 to Avoid Ads; [Link] Attacks on ZRTP; [Link] UK Jazz Invasion; [Review] Cuba; [Link] Aricle on Gender Reversal of US Presidential Debate; {OpenSuse] Fix for Network Offline in Updater Applet; [Link] Parkinson's Related to Gut Flora; Farellones Bike Park; [Meta] Tags; Update: Second Ride; Schwalbe Thunder Burt 2.1 v Continental X-King 2.4; Mountain Biking in Santiago; Books on Ethics; Security Fail from Command Driven Interface; Everything Old is New Again; Interesting Take on Trump's Lies; Chutney v6; References on Entropy; Amusing "Alexa.." broadcast; The Shame of Chile's Education System; Playing mp4 gifs in Firefox on Opensuses Leap 42.2; Concurrency at Microsoft; Globalisation: Uk -> Chile; OpenSuse 42.2 and Synaptics Touch-Pads; Even; Cherry Jam; Lebanese Writer Amin Maalouf; C++ - it's the language of the future; Learning From Trump; Chinese Writer Hu Fayun; And; Apricot Jam; Also; Excellent Article on USA Politics; Oh Metafilter; Prejudice Against The Rurals; Also, Zizek; Trump; Why Trump Won; Doxygen + Latex on CentOS 6; SMASH - Solve 5 Biggest Problems in Physics; Good article on racism, brexit, and social divides; Grandaddy are back!; Consciousness From Max Entropy; Democrats; Harvard Will Fix Black Poverty; Modelling Bicycle Wheels; Amusing Polling Outlier; If Labour keeps telling working class people...; Populism and Choice; Books on Defeat; Enrique Ferrari - Argentine Author; Transcript of German Scientists on Learning of Hiroshima; Calvert Journal; Owen Jones on Twitter; Possible Japanese Authors; Complex American Literature; Chutney v5; Weird Componentized Virus; Interesting Argentinian Author - Antonio Di Benedetto; Useful Thread on MetaPhysics; RAND on fighting online anarchy (2001); NSA Hacked

© 2006-2017 Andrew Cooke (site) / post authors (content).

Modelling Bicycle Wheels

From: andrew cooke <andrew@...>

Date: Thu, 13 Oct 2016 10:50:46 -0300

I'm trying to do some simple (2D, simplified physics) modelling of
bicycle wheels.  Unfortunately, it's turning out to be harder than I
thought.

The immediate problem is that I am not able to find (efficiently and
reliably) the stable solution.  It seems that my equations for forces
and energy are correct, because occasionally a solution converges.
The difficulty is "numerical" in some sense.

I can think of three problems:

- Local forces

  I calculate the force at each "spoke hole" as the sum of three
  components - the spoke (in tension, connected to the fixed hub), and
  the two rim segments (in compression, spanning to adjacent holes).
  The simplified physics assumes a "hinge" at each hole.

  This sounds fairly reasonable (in particular, I have a Jobst quote
  somewhere supporting the hinge model), except that it assumes that
  the rim segment endpoints are in equilibrium.  In fact there may be
  net forces there (when not at equilibrium) which are "passed along"
  and also affect the hole under examination.

  I don't see any way to avoid this.  It's the ugly compromise one
  gets when finding a static solution to a system that would go
  through some dynamic evolution.  Ideally you would model the entire
  dynamics.  Instead, you iterate the static minimisation.  But some
  of the (GSL) minimisation routines I am using seem to handle this
  poorly.

- Local movement

  I describe the system as a collection of (x,y) coordinates of the
  holes (spoke end points).  So a simple physical action like
  contracting the rim inwards in response to spoke tension involves
  altering all the variables.

  I am not sure this is a problem for methods that use a matrix-based
  solution (since the solution can move multiple points), but it seems
  like it could seriously affect simplex minimisation.

  Instead, I could use some kind of Fourier scheme where zeroth order
  is a constant radial shift, etc etc.  The problem here is that it
  seems to make calculating derivatives much more expensive (although
  derivatives are not needed for simplex).

- Unstable collapse

  The hinge model assumes that the rim segments always have an
  internal (hub facing) angle less than 180 degrees.  If this is
  exceeded then the wheel becomes unstable and collapses.

  This may be a source of instabilities in the solution when an
  additional force is applied.  It would be useful to have some kind
  of minimisation that could easily detect this condition.

Given that I am currently stalled it seems like I have two options.  I
can implement the Fourier based approach (second above) or try to do
some kind of customized solution "by hand".

A hand-rolled approach could deal with item 1 above by using an
iterative alorithm (quasi-dynamic).  It could also handle the third
point if it used calculations tailored exactly to the configuration
used.

So I could calculate the approximate solution for each hole in
isolation as a pair of 1D roots (zero force perpendicular and parallel
to the chord from neighbouring holes).  This would be quick and allow
detection of the instability.  By moving the hole only a fraction of
the distance to the solution and then iterating the entire wheel I
would move towards a consistent solution.

Andrew

Comment on this post