I've also included the ability for it to give you the TODR, LDR etc...etc..., was referring to those requiring Polynomials
Without knowing what you have done in the past, I can only speculate. However, if one (as I suspect you are doing) intends to represent the physical charts by a computer implementation, there are three basic ways to go about it (with the test for acceptability being the delta between model and AFM data set .. not much in the way of linear data in the AFM)
(a) first principles .. too hard to figure the empiricals to get adequate accuracy so one leaves this for the OEM .. as in the EFB etc implementations these days
(b) polynomial regressions. Generally, too difficult to run multivariate regressions and achieve adequate accuracy so the usual way is to run single regressions for the printed lines and then either run interpolations or on the fly regressions for between line points .. great fun .. been there ... done that for a number of AFM data sets with very high accuracy albeit with the attendant boring slave labour to make it all work OK .. especially if the data set has numerous discontinuities .. painful. I presume this is the way you played with the stuff ?
Big potential for getting the fingers burnt with extrapolation, though, depending on the order of the the equation and what antics it produces in the extrapolated region where one doesn't have data points to constrain the regression .. one can guard against this but, in general, a risky business.
(c) interpolations, commonly splines. Useful for small data sets but I always preferred setting up the regression analyses and go from there.
how do you know how the Aircraft will perform when above the 40degrees?
The main concern is hidden discontinuities in the engine data pack. If you have some other data for the higher OATs, then you probably are reasonably safe with extrapolation unless there be some (strange) significant differences at the takeoff rating. Without such comfort, extrapolating the engine data is, at best, risky business ..
it seems to be most of the information we have from our Manuals really came from someone jumping in the damned thing and taking it for a flight to figure out what will happen.
That would be most unusual as the aim is to end up with something which can be used to model performance. Common practice is to model the performance and then use FT to sample test the accuracy of the model. Often it then becomes an iterative exercise to end up with an acceptable final accuracy in the model .. which then goes into the AFM data set.
We do know how the aircraft will perform in the climb up to 50°C, both dual and single engine
That is a useful source of comfort, I suspect.
Why have a chart giving the climb data to 50, if 40 is the limit for take off?
A question of limitation, then, becomes a legal question, rather than an engineering concern ?