Mathematical functions in performance diagrams
I don't know if this is the right forum, so mods feel free to delete my question if it doesn't fit.
I have taken upon myself to digitise some scanned old performance diagrams, e.g. roll distance as function of mass and OAT, TAS as function of power setting, etc. The obvious goal is to allow the computations to be performed in a computer instead of on paper (that is: almost never). I have written some tools to do measurements of the line intersections in the documents, so consider that problem solved. However, what functions should I fit to the measured coordinates? In select cases, a straight line is valid, but most often not. After all, the functions are typically solution to differential equations...
Could you advise me as to what functions are reasonable to adapt to the measured data? I would like to avoid fitting simple polynomials since they may produce oscillations between measured points. I would also like to avoid interpolating cubic splines, since they...interpolate my measured points, and the measurements are of varying quality. Ideally, I would like a closed-formula for each type of curve, but I know that might be a tall order. My goal is to automate the computations, so the required precision is in the order of what you would produce with a pen and a ruler.
So, what do you suggest I do? My background is in computing science, but the physics behind these curves is beyond me. Any suggestions will be greatly appreciated.
As an example I attach the "roll distance as a function of OAT, mass, and wind" for our PA-28-161. The image shows the actual document from our POH. I apologise for the Swedish labels, but this is after all our legal document. Left panel shows OAT and pressure altitude, middle
panel is take off mass, and rightmost panel shows wind.