A good simple illustration of aerodynamic drag can be found here.
https://aerodyn.org/Drag/speed-drag.html
While the drag coefficient changes as a function of velocity, vehicle shape, length and surface roughness, the total drag always increases with the velocity provided you are comparing two vehicles at the same altitude (constant density).
The Total Drag Force is proportional to 1/2*rho*A*Cd*V^2, where rho is the atmospheric density, A is the cross-sectional area of the rocket, Cd is the drag coefficient and V^2 is the velocity squared. All other things being equal (density kept constant), the total drag forces at M=2 is 4x that @ M=1.
So despite rumors to the contrary, the sound barrier really isn't a barrier at all. A rocket will accelerate to a peak velocity where the drag forces equals the motor thrust. Breaking Mach isn't that complicated. All you need to break mach is a motor that burns long enough to accelerate the rocket with sufficient thrust to exceed the drag forces at Mach 1. (or Mach 2, 3 etc.)
Max Q is the peak dynamic pressure (in pounds per square inch)that occurs in a flight. Where it occurs depends on the rocket speed and altitude, but since most model and HP rockets don't really go that high for the atmospheric density to change significantly, for practical purposes, max Q occurs at the peak velocity which for many, but not all rockets, occurs at peak motor thrust.
If this is the case, the max Q (in pounds/square inch) can be simply calculated by dividing the peak motor thrust (in pounds) by the rocket's cross-sectional area (in square inches). (I'll leave it to the readers to do the mathematical proof.)
Furthermore, the peak thrust of the motor defines the aerodynamic structural loading on a rocket ascending vertically. If your motor develops 1 pound of peak thrust, the maximum structural load on the vehicle is 1 pound. If the motor develops 1000 pounds of peak thrust, the peak load on the vehicle is 1000 pounds. The peak loading on any one cross-section of the rocket (in PSI) is simply the peak thrust (in pounds) divided by the cross-sectional area (in square inches) of the member carrying the load. Provided all the structural components have a yield strength (in PSI) greater than this peak loading, the rocket will not shread. (Yes, it's really that simple.)
The only fly in the ointment is aerodynamic heating. Materials loose strength at high temperature and eventually fall apart, so there is a limit to how long and fast above Mach you can go at a given altitude before you have a themally induced material failurebut no model rockets and virtually all HP rockets don't have to worry about this.
Bob Krech
