Tarun Antony

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

Started July 7, 2023

Abstract or project description

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 will look into is taken from this website (Wayne.C.Gramlich, DESIGN EQUATIONS, https://gramlich.net/projects/rocket/eqns.html#nozzle, 1996) .Despite the older publication date, proven by this paper, it still is an effective tool to calculate the said engine hardware geometries. This paper will prove the method by first calculating the nozzle throat, and exit areas for a hypothetical cold gas thruster. After these calculations, the nozzle would be realized for said simple cold gas thruster, where after firing, pressure sensors in various sections of the thruster would measure the firing(s) and after a display of the data in the form of graphs, the algebraically derived predictions will be compared to the data, proving the method. A practical demonstration was chosen as physical evidence is oftentimes the best proof. After this point, the second use for the process (hot gas thrusters) will be addressed. Calculations for a simulated rocket nozzle will be completed to finish off the exploration. A final point to be put forward in this abstract is that this paper is not only proof, but also a secondary explanation of the method, including units for each variable.