The Mission

So this blog is a public way of sharing the effort on solving a math problem in an online, collaborative way.  I pick the problem and do the main work defining the solution path. I will incorporate ideas and help from the readers.  I have no idea how a reader might find this place, but if you do, feel free to contribute.  You may email long contributions if they involve detailed derivations or calculations or may use the comment feature to contribute ideas, corrections, encouragement, or ridicule to the blog entry.  I will incorporate the changes into a single consistent blog entry.

The first problem is a mathematical model of a bicycle wheel.  I want to relate deflection in a wheel with the number of turns of the spoke nipples to bring the wheel into true.  The solution is organized in a way to help anyone who happens by to get started understanding and contributing to the problem.   I plan to have posts labeled as the following.  I will update them as work progresses.  The posts will go by the same name with a new date for each time the section is modified.

1. Background
1. General structural analysis
1. Euler Bernoulli Equation
2. 3D strain equation
2. Bicycle wheel modeling
3. Finite element solutions
4. Modal solutions
2. Nomenclature
3. Assumptions
4. Method of solution
1. General equations for rim
1. What I am trying to figure out right now
2. The derivation so far
2. Boundary conditions
3. General equation for spoke
1. Geometric transformations from Cartesian to polar
2. Hooke's law
3. Nipples and j-bends. Estimates of magnitude of error for neglecting
4. Spoke to spoke contact. Estimates of magnitude of error for neglecting 
4. Axial equations
5. Radial Equations
6. Hooke's law for bending
7. Dimensionless equations
8. Modal method vs finite element
9. Integration of strain equations to yield a solution in form of a Green's function
5. Data
1. Radial and axial bending moments for rim
2. Elastic constant for spoke
3. Radius of the equivalent, one-dimensional rim
4. Axle width. Inner and outer spoke offsets
5. Spoke positions Effect of rim joint
6. Measuring directly vs fitting the data with regression analysis.
6. Experimental system
1. Test wheel
2. Truing stand
1. Dial indicators for measuring deflection
3. Tension meter for measuring spoke tension
4. Measurement methods and data logging
5. Measurement accuracy estimates 
6. Data from test rim