interpolation-empirical formula
 

hi.. I am very much confused for quite some time. Somebody please help me. I have a particular problem of shock wave diffraction from a tube end. After the shock wave is exited from the tube end, I calculated the locations of the shock wave with respect to time. I have the X-T relation as a third degree polynomial for a particular Mach number of shock wave diffracting at the tube end [t=f(x)]. So for various Mach numbers I have different functions for t and x, (third degree polynomials). I just want to make an empirical formula with these three parameters M, t and x, so that for any Mach number,I will be able to find out the x-t relationship as a third degree polynomial. I have been trying for last few days..but not reaching anywhere..somebody please give some hints on how to do that...

thanks Grig