Using a very simple drag model... I used the data from page 16 of
http://www.jmrconline.org/Drag_Coefficient_Prediction.pdf built a table of mach number and Cd and interpolated. (This is actual data from a 5" rocket, were building a 6" rocket so it seems reasonable)
One of the interesting results is this graph:
It shows peak altitude achieved (y axis in meters) piloted against the equivalent peak drag. The peak drag units here are equivalent velocity at sea level in m/sec. The peak is at 50500m and 303m/sec (165Kft and 677mph)
Another interesting result (from a slightly different run) I'm not using any real fancy integrator and the results vs time steps don't change much:
So this means for very crude integration steps you get reasonable results, thus allowing one to use the model for optimization seeking. Right now there are a number of limitations, the model assumes that the ISP does not change as the motor is throttled for peak drag limiting etc... so as I add more detail to the model it will be interesting to see what happens.