• The space shuttle was used as a case study to access the interaction between max dynamic pressure and altitude due to the large amount of publicly available information about the spacecraft.

• To the right are the plotted results of a simple application of the rocket equation to the space shuttle main stage.

• In orange is a line of how maximum dynamic pressure of 33kpa varies with altitude and velocity. Which diverges at 40,000m to infinity as the air become too thin to act on the craft.

• At the optimum take off altitude of 17,000m max Q is never reached during any phase of flight. Thus allowing the rocket to operate with maximum thrust at all points in flight reducing the amount of overall time spent resisting earths gravity thus reducing gravitational losses and allowing for a more simplified first stage. 

In order to make this more practically applicable it was necessary to model the physics of the vehicle more acuratly and then  to fly the vehicle from multiple altitudes to determaine what real world efficencies might be aplicable. To this end a python program was developed to model the physics of the falcon 9. A  test of which was performed of various parabolic arcs to access which would be optimal for the rocket. However in doing so the method of parabolic arc may not be the most optimal way to fly the rocket and with a varying launch altitude the optimal flight trajectory is likely to similarly vary...

From the need to find an optimal way to fly the rocket to compare best case scenarios between altitudes a trajectory optimization tool was created using a genetic algorithm to generate the best possible velocity from the first stage of a falcon 9 with which we could compare with a launch of varying altitudes and initial velocities.