howardjd said:

I speak to my professors regularly about this. I've taken many lab courses and know how difficult it is to control a experiment and get worthwhile data, i've spent many weekends redoing and redoing labs to get good data. One problem I have is I do not have friends whom ride and could help me perform trials to get more data. I'm also injured and don't know how long it will be before I can ride enough to at least test. I'm pretty sure I am at least injured to the point competitive cycling is out of my future. I've been working on trying to develop a 3dimensional model predicting perpendicular motions of the bike as a result of applying force at the pedals which is off center line, and from producing forces across the seat and handle bars. The calculations would be pretty difficult and require tensors and Lagrange or Hamaltonian mechanics, right now I'm stuck on finding my equations of restraint. This model should help do determine how much the extra angular momentum of heavier bike wheels would reduce the small but visible side to side rocking motions that occur during riding. A high speed slow motion camera would be very helpful but I certainly don't have the money for that.Â

Frankly, I think you should first look to theory to find the appropriate equations and the relevant parameters. The theory will take you a long way. For instance, theory can show you in 3-space how a 3D wheel will respond to a given force. In four space, you can see how the wheel responds over time. You can then take those predicted responses and equations and see how they match up--via experimentation--with the real world. Unless physics gets turned on its head you'll find they should match up well assuming all independent variables have been accounted for. With respect to a wheel's angular momentum, MOI, and the rocking from side to side of a bike, you're going to have some parameters that are going to be real fuzzy and difficult to state explicitly, like how an individual's pedaling style influences the dynamics of interest, how a given rider's body influences said dynamics....... The human influence on the system will introduce all manner of uncertainty, hurdles, and headaches into your effort. IMHO, I'd break the problem down into manageable parts that can be tested with accuracy and precision and modeled in a straightforward way. Let's look at this in terms of a Hamiltonian: if you want to construct a Hamiltonian, the first thing you need to do is figure out the number of degrees of freedom of the system. You can try it head on and just attempt a single overarching Hamiltonian, but that might actually result in a serious cerebrovascular accident since there are, using a scientific term, shitloads of DOF. It's much easier to break things down into manageable segments: rear wheel dynamics; crank dynamics, front wheel dynamics...or however you need or want to break it down. There's a reason that particle physicists didn't start with writing an all encompassing Hamiltonian for the Standard Model of particle physics but instead assembled it out of parts. Have you see the thing?