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 are the best functions to fit to the measured
coordinates? In selected cases, a straight line would be valid, but most often not. After all, the functions are typically solution to differential equations…

What functions are reasonable to adapt to the measured data?

Simple polynomial have the advantage that all measurements are used to fit one set of parameters. However, they are also well-known to produce oscillations between measured points. On the other hand, interpolating cubic polynomials have less oscillation problems but are… interpolating, so the measurement errors are not smoothed out. Furthermore, I have estimates of the measurement uncertainty of each point, so I would like to use that for fitting a global function.

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 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 in fact our legal document. The left panel shows OAT and pressure altitude, middle panel is take off mass, and rightmost panel shows wind.

Thanks

[![enter image description here](https://i.stack.imgur.com/J6ToI.jpg)](https://i.stack.imgur.com/J6ToI.jpg)