The Aerospike nozzle and cowl design was derived from the work done by Che-Ching Lee and Donald D. Thompson in “FORTRAN PROGRAM FOR PLUG NOZZLE DESIGN”, specifically the information regarding internal-external expansion plug nozzles. The design methodology behind using this Technical Memorandum for The Aerospike Project’s design was a combination of utilizing the statements and explanations found within the paper as well as utilizing the FORTRAN IV code provided. The Fortran code was first meticulously translated into MATLAB which was then followed by deconstructing many of the equations that were used into their simpler base equations in order to both better understand the process of the system and replace calculated ideal theoretical values with values determined through simulations. 

 

The code makes the assumptions that the internal expansion occurs as a Prandtl-Meyer expansion wave, the external expansion occurs as a Prandtl-Meyer expansion wave about the lip of the cowl, inviscid flow, isentropic flow, one-dimensional flow, axisymmetric flow, ideal gas, constant specific heat ratio, and flow properties on the first of the right-running wave are equal to those on the last left-running wave. Given the combustion chamber pressure and temperature, specific heat ratio, universal gas constant, specific gas constant, molecular weight, radius of internal circular arc contour, estimated Mach number at the end of the internal expansion, the number of internal contour points and external contour points, the angle between plug axis and Prandtl-Meyer expansion wave at the throat, and the exit radius which results in the nondimensionalized two-dimensional coordinates of the spike and cowl contour, the dimensionalized two-dimensional coordinates of the spike and cowl contour, pressure ratio at each point on the spike contour, temperature ratio at each point on the spike contour, cumulative vacuum thrust coefficient cumulative specific impulse by mass, cumulative vacuum specific impulse, and thrust.