I've been working on a design for a sounding rocket that can go to the Karman line, that I want to make my senior capstone project next year. As a part of this process, I am making a program to estimate the maximum altitude attained by the rocket and its going pretty well.
However, the current estimation I have is still a huuuuuge over estimation because it does not consider the effects of trans and supersonic flight on the coefficient of drag, which I imagine will have a dramatic impact on this code's output (notice the max velocity is 6800 ft/s...)
I was able to find this image relating atlas Cd to mach number here:
How can I make a curve similar to this for our project? The rocket body is going to be a (ogive or parabolic probably) cone with a long cylindrical body and fins. I estimate that the Cd will be about .2-.25 at low speed flight.
How can I go about making a curve like this? How do I know at what mach number the pressure will be highest for my design? Should I change nose-cone shape to reduce drag at sonic speed? Are there any resources to guide me in the right direction here? Any advice would be greatly appreciated. We have access to a pretty slow wind tunnel and fluid dynamics software if that can help us any.