Wheel Design and Structural Analysis Program

The use of the analytical wheel model for evaluating structural properties of a wheel design is an obvious application that may have more uses than the truing algorithm.

The goal of this application  is to evaluate stiffness in various directions, buckling spoke tension, maximum and minimum tension in the spokes, and maximum deflection under normal and limiting case loads.  The wheel can be analyzed with different combinations of tension, spoke diameters, spoke lacing patterns, hubs, and rims.  The wheel is an interconnected structure in which all components and loads affect one another.  Human intuition about the structural mechanics fails us in figuring out how one change will affect the wheel as a whole.  The resulting myth and false information about what different designs achieve for the rider leads to poor designs.  This tool allows some quantitative measures of wheel's properties.  Exploration of the parameter space replaces intuition with real science.

Some changes have to be made to add the capability for external loading to the wheel.  We have added point loads representing externally applied radial, axial and azimuthal loads.  Combinations of these loads can simulate virtually any riding condition.  The radial load represents the vertical load of the wheel against the road.  The axial load is a side load from turning or rocking the wheel.  Azimuthal load is the load from pedaling or braking.  The model assumes mechanical equilibrium and computes the reaction loads for the externally applied loads.

We have designed the calculation so that a number of values can be entered for a parameter or load so that the outputs may be plotted as a function of the range of inputs.

In its present form, the code exists as a Matlab program.  I have not uploaded it to the Mathworks because I still hope to commercialize it.  Proposals on creating an app are welcome.

Will the real Thomas Wilson Please Stand Up

I googled Thomas Wilson bicycle wheel.  Interestingly, I personally was not on the first, second, or third page.  I did find a Thomas Wilson who is a service manager at a cyling shop, a storyteller who wrote about his 6 year old learning to ride a bicycle and his brother 20 months younger who duplicated the feat almost immediately.  I found that Thomas Wilson was in Back to the Future as the redoubtable, Biff Tannen.  I have long know about Tom Wilson and Tom Wilson Jr. , father and son, who have drawn the cartoon Ziggy, for 45 years.  Tom, Tommy or Thomas Wilson has played several times in the NFL, NHL , MLB, and  professionally for the Australian national team.

There are innumerable Dr. Thomas Wilson’s.  You could be treated multiple times for every conceivable ailment all by one or another Dr. Wilson.

There are professors, lawyers, and all sorts of other professionals who appear when googling the name.

Thomas Wilson, it is like not having a name at all.

Hasty Post on Modeling Equations

My last post on Introduction to Introduction to the Model Derivation and Overview of Equations was a bit hasty.  After finding a way to link documents that actually transferred the equations, I was eager to try it.  However, there are still some problems with the linked document.  The equation numbers have been stripped so there are gaps in the text where the reference is given and there are no numbers attached to any equation.  The other problem is that I was actually in the midst of an update on this version to add external load.  I had not gotten very far but the incomplete editing would probably be confusing.  The equations are difficult enough to understand without the inconsistencies inflicted by the author.

Please give me your forbearance.  I will update the document as I have time over then next few days. In the meantime, some comments from readers would be appreciated.

Introduction to the Model Derivation and Overview of Equations

In this linked document, the overall layout of modeling equations is described.  The matrix form of each equation is given.  Detailed derivations of the matrix elements will be given in subsequent posts.

It appears that the equation numbers generated by Mathtype are not recognized by Googledocs and are not given.  This may make the document unusable. Please advise if you cannot follow the text because of this problem.

Overview of Matrix Structure of Wheel Model

Background on Bicycle Wheel Modeling and Wheel Truing

In this post, I have uploaded my background section from my derivation of the truing algorithm.  Please comment if the link works for you and you can read the document.

Background on the Bicycle Wheel Model and Truing Algorithm

Reintroduction

In the linked document below, I have updated the introduction to the bicycle wheel.  This post is a small experiment.  If it works, I will publish my wheel derivation in sections.  Let me know in the comments if you are able to go to the link and read the document.  There are a couple of equation objects that are almost correctly formatted.  The only problem is that the symbol appears above the line rather than on the line as intended.  

Introduction

Maybe the bicycle wheel truing algorithm will go public after all.

It is Christmas and I am trying my best to give the bicycle wheel truing algorithm away.  The bicycle wheel is in moving toward a release for free use.  Actually, there is already a release, albeit one suitable for a limited audience.  I made contact with some cyclists who also happen to work for Mathworks.  I translated my algorithm from Scilab to Matlab and uploaded two cases to the Mathworks File Exchange to facilitate the work with Mathworks folks.  It is my sincere hope that this collaboration with Mathworks will result in something for the bicycling community.  But, since the algorithm is on the Mathworks File Exchange server which is up in the public domain, if you are a Matlab programmer and have a copy of Matlab on you computer and want to get really deep into coding to see how this great idea works, you can go here

https://www.mathworks.com/matlabcentral/fileexchange/60333-modeling-verification-and-truing-example-for-bicycle-wheel

and here

https://www.mathworks.com/matlabcentral/fileexchange/60333-modeling-verification-and-truing-example-for-bicycle-wheel

For the rest of the world, the plan at the moment is to develop a graphical user interface that calls the Matlab routines as royalty-free, compiled functions.  The graphical user interface should make it accessible to an average person who knows how to use a browser.  I am currently working on a version that embeds the truing algorithm in an Excel spreadsheet.  A user would be able to download the spreadsheet and true his wheel.

I am also adding features to check the design of the submitted wheel.  I will calculate the spoke tension under limiting load conditions so that the maximum and minimum tension are calculated.  The maximum should be compared to the yield stress of the spoke and the load limit of the rim at the spoke seat.  The minimum is compared to zero tension.  Zero tension means the spoke is slack and not supporting the rim.  I will also calculate the spoke tension for buckling, deflection at maximum load, and other parameters that are useful in wheel design.  This project is still challenging and fun.  I hope to engage others in pursuing the many ideas the spring from the development.

I am giving away my part of the bicycle wheel truing work.  That is great and to all of you who download and use the algorithm, you are welcome.  It still is not totally free because you still need wheel truing gear.  [Disclaimer, I get nothing from the equipment suppliers from whom you purchase your wheel truing gear.]  This is what you will need.  You will need a wheel truing stand with dial indicators for the radial and lateral displacement measurements and a tension meter.  I think digital indicators make the job infinitely easier than mechanical indicators.   I personally have been keeping Park Tool Company (http://www.parktool.com) afloat for the past couple of years with my many purchases.  Among them, I have a Park 2.2 truing stand and the dial indicator accessory TS 2DI.  I also have one of every type of spoke wrench Park Tool sells.  I replaced the mechanical indicators in the TS 2DI with iGaging digital units.  It was a one for one swap.  Igaging is a great place to get innovative digital measuring tools, www.igaging.com.   I am waiting for the multiplexed wireless indicators to be available from iGaging for this application, http://www.igaging.com/page26.html.  All three measurements use an indicator device so potentially the truing operation could avoid transferring readings manually from the indicator to the computer.   You can use any spoke tension measurement that you prefer.  I have a Park TM-1 and I also have Douglas Pepelko's most excellent app for measuring tension with an iPhone.  You can get his app from the iTunes store:

https://itunes.apple.com/us/app/spoke-tension-gauge/id518870820?mt=8

I crave a WheelFanatyk tension meter but am holding out for a tool that interfaces wirelessly with the bicycle wheel algorithm.  http://www.wheelfanatyk.com/store/digital-tension-gauge/  I hope wheelfanatyk will adopt the iGaging indicators with wireless communication to make my truing system really computerized.