Do you know how to construct a contour graph? Its a way of plotting more than 2 dimensions on one graph without actually having to draw more than 2 dimensions. The downside is you have to hold your main variable constant for the graph, so it takes multiple graphs to cover multiple values of your main variable.
I see these a lot, in school. I'm taking mechanical engineering, and these pop up all the time, especially in fluid mechanics. These graphs take a lot of data, and a lot of work to produce though, so it would be quite a commitment to formulate them. I can't see them being all that accurate anyway, since there are more variables at work that you had listed. For instance no two staves of the same wood are identical, so even if you had two bows with the same dimensions and wood there would still be a relatively large margin of error.
You would need to include in the model all the dimensions of the bow including all angles of reflex/deflex and taper angles, you would need to quantify the grade of the wood to account for differences between two staves of the same species, and then there is the problem of accounting for defects like knots which you may have had to work around. And even after all this it may not be applicable to the so-called character bows.
All this being said, you probably could generate a model that could roughly predict what you want, but it would be rough estimations at best.
