@SteveKelepouris Are you saying that if I can't have perfection, then I should just abandon the whole idea?
Not at all, I still believe you are not getting Robert's point.
This image shows Robert's point:
You can fit different expressions to your experimental data. If you use polynomial expressions, the higher the order of the polynomial, the lower the fitting error (the higher the R value), but as the image shows, a lower error doesn't necessarily mean a more correct fit. In that image, if we were to estimate the value of the studied magnitude (vertical axis) at around a value of -4.5 for the parameter in the horizontal axis using the fitting curve (the line in blue), the estimated value would be very bad. If we used the linear fitting curve for that, the estimation would be much better.
How can one know if the fitting curve is correct? Plot the experimental data and the fitting curve on the same plot, and compare them.
Concerning the "exponential" expression that has been mentioned in several posts:
@Jean-YvesPochez as we know the exact formula from the firsts posts, we should use it instead of a polynomial approximation ...
@SteveKelepouris And we need to know C* which can ONLY be known through actual testing.
Maybe I am not getting all the intricacies that play a role here, and if that's the case I apologize for the noise. But, that "exponential" expression can be reduced to: Po=A*Kn^B where A is a constant, A=(a/alpha*rho*c)^(1/(1-n)) (all those are constants, right?), and B is another constant, B=1/(1-n). That is not an exponential, but a polynomial with a non integer exponent. You can fit your data, get A and B and you are done.
The data posted by Dennis (shown below) are best fitted by A=0.246785767 and B=1.473602726.
@Dennis H Steve,
However, that polynomial expression will not satisfactorily fit the experimental datasets corresponding to the fine ground KNSB and the KNDX, because of the shape of those curves (I haven't tried it, though). Interestingly, these are the two datasets you are having trouble with for the estimate of the pressure:
@SteveKelepouris KNSB fine gound: 1713.8 (not correct)
KNDX I get: -1658.4 (not correct)
I would recommend using a polynomial for those (or even for all of them, it wont make a difference), using the lowest polynomial degree that gives you a decent estimate (maybe those given by Dennis already do this). A polynomial with integer exponents, that is.