Rocket motors frequently implement carbon-based nozzle inserts to insulate the motor from the heat produced by combustion. Over time these inserts will erode due to oxidation at the surface wherein oxidizing species found in the combustion products react with the carbon to form carbon monoxide. It has been shown that the largest contributors/oxidants to erosion are H2O, CO2, and OH, due to their high concentrations within the exhaust products and the low activation energy needed to react with the carbon surface. As such, a clear understanding of the rate of oxidation, or erosion, is critical to rocket motor design. Previous research has modeled many of these characteristics, yet this has largely been limited to solid rocket motors with combustion chamber pressures greater than 6.9 MPa. Earlier studies have asserted that combustion chamber pressure has a linear effect on erosion rates, but it is unclear whether this linear assumption can be extrapolated to lower chamber pressures. This research lays the foundational work to explore the relationship between combustion chamber pressure and erosion rates at pressures below 6.89 MPa. Based on the numerical modeling and rocket motor test firings described in this study, preliminary findings indicate that this linear assumption may not hold at combustion chamber pressures below 3.4 MPa. Initial numerical modeling shows a non-linear increase in boundary layer thicknesses as combustion chamber pressures fall below 3.4 MPa. It is postulated that thicker boundary layer slows the diffusion of the oxidizing species to the surface thereby decreasing the rate of erosion. Thus, the modeled results suggest a non-linear relationship between nozzle erosion and pressure may be present at lower chamber pressures. Moreover, pure hydrocarbon fuels generate high fractions of key oxidizing species (H2O, CO2, and OH) in the product stream and the impact of these fuels on carbon nozzle erosion has remained largely unexplored. A hybrid rocket motor test stand (HRMTS) was developed to perform test fires of a HTPB-N2O hybrid motor at chamber pressures between 2.07 MPa and 4.83 MPa. Supplementary research was carried out that explored hybrid motor injectors and their effects of combustion instabilities. Major milestones included, implementation of a new semi-autonomous LabVIEW VI, creation of a MATLAB model that predicts motor performance, design and manufacture of a modular hybrid rocket motor, and the development of a secondary model that uses gathered test data to predict transient throat diameters. Furthermore, the predicted nozzle erosion was validated with the measured nozzle surface geometry pre and post-test fire through the utilization of a coordinate measuring machine (CMM). Initial results show that, despite the non-linear boundary layer growth, a linear relationship between combustion chamber pressure and nozzle erosion may still be true for chamber pressures below 6.89 MPa. Testing also illuminated correlations between combustion stability with injector pressure and nitrous oxide phase, for which, poor oxidizer vaporization and injector pressure dramatically decrease combustion stability and motor performance.