INVESTIGATION OF ATMOSPHERIC DENSITY VARIATION ON MODEL ROCKET PERFORMANCE

Atmospheric density is the environmental parameter to which small-scale rocket altitude performance is most sensitive, yet it is routinely treated as a fixed constant in amateur and educational practice. This paper presents a combined analytical, numerical and literature-based investigation of how variation in air density affects model and high-power rocket flight. A closed-form expression for the coast-phase apogee sensitivity to density is derived and shown to be bounded between zero, in the ballistic limit, and negative unity, in the drag-limited limit, with the governing parameter being the ratio of burnout velocity to terminal velocity. The four physical drivers of density variation — temperature, barometric pressure, water-vapor content and traversed altitude — are quantified separately using the CIPM moist-air formulation, which shows that humidity alone accounts for up to 2.8 % of density at 40 °C and is of the same order as errors practitioners routinely attempt to correct. A three-degree-of-freedom trajectory model with Mach- and Reynolds-dependent drag is integrated for a representative 54 mm high-power vehicle across three measured atmospheric states. A 15.3 % reduction in launch-site density, corresponding to a density altitude of 1692 m, increases predicted apogee by 7.1 %, peak velocity by 1.0 % and coast-phase duration by 4.9 %. The analysis further establishes an asymmetry that is widely misunderstood: static margin is density-invariant, because density cancels from the centre-of-pressure computation, whereas the pitch natural frequency and aerodynamic damping both scale with density and are therefore degraded in low-density conditions. Recommendations for offset-ISA anchoring and Monte Carlo uncertainty propagation in predictive rocketry are given.