Nozzle Erosion Reconstruction Model for Data Analysis in Rocket Engines and Correlation with Chamber Pressure

Graphite nozzles remain the dominant choice for small hybrid and solid rocket motors operating on laboratory and university budgets, owing to their low cost, ease of machining, and rapid turnaround during iterative design campaigns. These same programs, however, must contend with the fact that graphite erodes through coupled thermochemical and mechanical mechanisms when exposed to the oxidizing species generated by high-energy propellant combustion, and the resulting throat-area growth fundamentally alters the time histories of chamber pressure, thrust, and delivered specific impulse. This paper presents a nozzle-erosion reconstruction model that extracts the time-resolved throat area from coupled thrust and chamber-pressure measurements using the thrust coefficient relationship, scales the reconstructed area history against pre- and post-test throat measurements, identifies the onset and rate of erosion, and accounts for variable sensor lag between the thrust-stand and pressure-transducer signal chains. The model is exercised on two complementary sets of laboratory-scale GOX/ABS hybrid hot-fire data that together span roughly two orders of magnitude in total throat-area change and peak chamber pressures from 0.5 to 3.4 MPa: a controlled three-operating-point campaign conducted in support of the NASA Plume-Surface Interaction (PSI) program, and a set of higher-pressure firings from the laboratory development series in which the technique was matured. Reconstructed erosion-onset times, erosion rates, and total throat-diameter change are reported for each firing, the reconstruction accuracy is characterized as a function of erosion magnitude. A correlation of graphite erosion with chamber pressure is examined across the combined envelope. The results demonstrate the robustness of the reconstruction technique and provide a reusable framework for post-test reconstruction of transient nozzle geometry in rocket-engine ground testing.