Comparison of Pre- and Post-Flight Estimations of Pitch Damping Coefficients for Unguided Entry Vehicles
Introduction: Pre-flight predictions of pitch damping coefficient (𝐶!!+𝐶!"̇)curves are used in entry simulations to determine flight readiness and if any dynamic remediation strategies are required. Accurate characterization of these pitch damping coefficient curves is crucial for mission success. Historically, pre-flight estimations of these curves are derived experimentally either via ballistic range testing or with 1-degree-of-freedom (DOF) free-or forced-oscillation wind tunnel testing. Methodology:With post-flight best-estimated trajectories, a fitting procedure as described in Karlgaard, et. al. [1] is used to compare pre-and post-flight pitch damping coefficients. This technique relies on an assumed analytical form of the trajectory, a limited 3-DOF representation described in Schoenenbergerand Queen [2], which results in anEuler-Cauchy solution form.This solution assumes constant density,thus limited amplitude multi-peak windows of the trajectory are considered to populate the pitch damping-amplitudes pace. Fig. 1 shows preliminary estimations of the pitch damping coefficients estimated using the post-flight best estimated trajectoryfor MER B, using a3-amplitude-peak window. Important to note is that the Euler-Cauchy solution also assumes planar motion, thus coning or 𝛽contribution is not included. Further,the estimated post-flight pitch damping approximations and the pre-flight predictions shown are effective representations of pitch damping, or the integrated effect of the pitch damping coefficient over one pitch cycle at the corresponding cycle’s peak amplitude. Effective pitch damping coefficient curves provide more intuitive insights about where the vehicle is stable and permits readily processed comparisons between data-sets. It is important to note that most pitch damping curves, such as those reported in aerodatabases and utilized in flight mechanics trajectory simulations, are represented in instantaneous angle-of-attack space distinct from what is presented in Fig 1. The extracted post-flight pitch damping coefficient points show a wide range of values across a narrow band of amplitudes (Fig.1a), albeit centered on the published pre-flight approximation. This also applies to the prediction as a function of Mach in Fig1b, where the post-flight scatter points are centered around the pre-flight predictions, but the pre-flight predictions notably lack data aboveMach 5.Further tuning of the technique, such as changing the number of peaks considered in each stencil, resolving density in higher resolution, and employing more accurate fitting procedures (beyond scipy.curve_fit()), will be performed. PosterFocus:This study will apply this reconstruction method to the as-flown trajectories for the following unguided entry vehicles: MER A, MER B, IRVE3, Phoenix, Insight, Pathfinder, and SIAD. The pitch damping coefficient will be derived from these trajectories and compared with the pre-flight predictions. Comparing across different missions, entry environments, and vehicle geometries can inform where our pre-flight testing methodologies accurately capture the flight dynamics. Results will provide valuable insight into the accuracy of pre-flight predicted pitch damping curves. Beyond that, this method can shed light on how accurate these curves need to be, which can inform uncertainty ranges applied to pre-flight curves for other missions.