I have these curves,
From this curve I can determine the life of a prop shaft due to gyroscopic forces at different yaw angles and certain speeds. I performed curve fitting on data points to get accurate high order polynomials for this interval of yaw angles. The polynomials are as follows,
y_150 = @(x) 22*((x-23)/4.9)^4 - 48*((x-23)/4.9)^3 + 27*((x-23)/4.9)^2 - 37*((x-23)/4.9) + 40;
y_200 = @(x) 11*((x-19)/4.8)^4 - 48*((x-19)/4.8)^3 + 73*((x-19)/4.8)^2 - 72*((x-19)/4.8) + 48;
y_212 = @(x) 23*((x-19)/4.8)^4 - 43*((x-19)/4.8)^3 + 22*((x-19)/4.8)^2 - 40*((x-19)/4.8) + 41;
But what about at 180 knots? Or 205 knots? Can I do some sort of 3 dimensional interpolation to account for different speeds? Since it is not considered good enough to use the closest speed value.
I would appreciate ANY ideas or comments on this problem.
Part of the problem is you don't have estimates for the quality of the individual fits. All your curves go asymptotic, so the constant terms are likely to have large uncertainties.
The first thing I'd do is re-run the fits but cut off the data at, say, 16 or 18 degrees to avoid the asymptotic region.
Next, the zero-point values for 200 and 212 are almost certainly not identical -- your fitting coefficients look suspiciously to have been rounded to integers, which is not a good idea. If you can re-calcuate, then at least you will have three points on a curve for each Yaw angle, which makes sensible fitting along the Lifetime axis more likely to occur.