The Proof and Process of Calculating the Geometries for a Rocket Nozzle

Abstract

There are many methods to calculate rocket nozzle geometries from reliable sources like NASA, with a necessary proficiency of precalculus/calculus. For most situations, it works, however for those who are only proficient in math to the degree of algebra, there is a lack of solutions. The method that this paper uses takes an expansion ratio equation from [1]. Despite the older publication date, proven by this paper, it still is an effective tool to calculate the said engine hardware geometries. This paper proves the method by first calculating the nozzle throat, and exit areas for a hypothetical cold gas thruster. After these calculations, a physical testing unit is built where after firing, a pressure gauge in the thrust chamber measures the firing(s) performance. After a display of the data in the form of graphs, the algebraically derived predictions will be compared to the data, thereby proving the method. A practical demonstration was chosen to provide sound evidence for the viability of the method. In summary, this paper is not only proof, but also a secondary explanation of the method for designing a rocket nozzle and proof of the viability of a 3D printed nozzle under low pressure.