Bradley A. Steinfeldt’s research while affiliated with Georgia Institute of Technology and other places

Analytic equations for the aerodynamic force and moment coefficients of simple geometries in rarefied hypersonic flow.

Aerodynamic forces and moments are significant perturbations on low-Earth-orbiting objects, second in magnitude to the nonspherical gravity field. Traditionally, the aerodynamic perturbations are calculated using a direct simulation Monte Carlo method. Under certain assumptions, these forces and moments can be described analytically via free-molecular flow theory. Using symbolic manipulation techniques, exact expressions for the free-molecular aerodynamics of analytic shapes can be derived. In this investigation, analytic expressions for the aerodynamic force and moment coefficients of primitive and composite parametric surfaces are derived, then validated against industry-standard direct simulation Monte Carlo techniques. A framework for the rapid and accurate calculation of free-molecular aerodynamics of composite geometries based on superposition is described. This framework is applied to axisymmetric composite geometries. Results within 6% of direct simulation Monte Carlo calculations are obtained in 0.05% of the time. The analytic aerodynamics models enable rapid trajectory and uncertainty propagation for low-Earth-orbiting objects. A case study on aerodynamic perturbations of a low-Earth-orbit nanosatellite is included to demonstrate application of these analytic models. The case study shows that these derived analytical free-molecular aerodynamics produce results that are applicable to inclusion in rapid trajectory propagation tools for orbit prediction and conceptual mission design.

The extensibility of a linear rapid robust design methodology is examined. This analysis is approached from a computational cost and accuracy perspective. The sensitivity of the solution's computational cost is examined by analysing effects such as the number of design variables, nonlinearity of the CAs, and nonlinearity of the response in addition to several potential complexity metrics. Relative to traditional robust design methods, the linear rapid robust design methodology scaled better with the size of the problem and had performance that exceeded the traditional techniques examined. The accuracy of applying a method with linear fundamentals to nonlinear problems was examined. It is observed that if the magnitude of nonlinearity is less than 1000 times that of the nominal linear response, the error associated with applying successive linearization will result in errors in the response less than 10% compared to the full nonlinear error.

The goal of this investigation is to understand the sizing and performance of supersonic inflatable aerodynamic decelerators for Earth-based sounding rocket applications. The recovery system under examination is composed of a supersonic inflatable aerodynamic decelerator and a guided parafoil system to achieve sub-100 m miss distances. Three supersonic inflatable aerodynamic decelerator configurations (tension cone, attached isotensoid, and trailing isotensoid) are examined using the metrics of decelerator mass, aerodynamic performance, and vehicle integration. In terms of aerodynamic performance, the tension cone is the preferred choice for the sizes investigated. The attached isotensoid was shown to be the most mass efficient decelerator, whereas the trailing isotensoid was found to be the more ideal decelerator for vehicle integration.Athree-degree-of-freedom trajectory simulation is used in conjunction with Monte Carlo uncertainty analysis to assess the landed accuracy capability of the proposed architectures. In 95% of the cases examined, the drag-modulated inflatable aerodynamic decelerator provides arrivals within the 10 km parafoil capability region, meeting the sub-100 m landed recovery goals. In 76% of the cases examined, the dragmodulated inflatable aerodynamic decelerator arrives within 5 km of this target zone. Copyright © 2014 by the American Institute of Aeronautics and Astronautics, Inc.

A probabilistic treatment of the Pareto chart can provide benefits to the fields of quality control, sensitivity analysis, and conceptual design. The probabilistic Pareto chart can inform a decision-maker about the relative significance of distributed factors and highlight anomalies in a dataset. This investigation provides a framework for creating a probabilistic Pareto chart, as well as examples to enable a discussion of the information provided by both the deterministic and probabilistic Pareto charts. The applications presented in this investigation demonstrate the probabilistic Pareto chart’s ability to highlight anomalous trends and to determine the significance of variables in non-linear functions. © 2015, American Institute of Aeronautics and Astronautics Inc. All Rights Reserved.

Viewing the multidisciplinary design problem as a dynamical system a number of tools from the established field of dynamical system theory became available to the multidisciplinary design community. This work demonstrates the applicability of applying the Kalman filter in a manner similar to linear covariance analysis to the multidisciplinary design problem to obtain robustness characteristics. In addition to robustness characteristics, the estimation theory is shown to be applicable to design decomposition. Following theoretical development, two example problems demonstrate the applicability of applying dynamical system theory. For a linear, two contributing analysis problem showed the mean was able to be estimated with an error less than 0.08% and a matrix norm bounded the variance to less than 37.8% relative to analytic propagation. This error is shown to be a function of the geometry of the matrix two-norm and reduces as the problem dimensionality increases. The use of estimation theory is also shown to be applicable for nonlinear designs through a two-bar truss problem through successive linearization.

This paper presents an assessment of a supersonic inflatable aerodynamic decelerator for use on a sounding rocket payload bus structure for a high-altitude sample return mission. Three decelerator configurations, the tension cone, attached isotensoid, and the trailing isotensoid, were examined on the metrics of decelerator mass, aerodynamic performance, and vehicle integration. The mass calculated for diameters ranging from approximately 0.5 to 1.1 m with a baseline dimater 0.9 m is shown to be similar between each configuration. However, the attached isotensoid configuration is shown to be the least mass solution. Greater than 50% drag performance degradation results when the attachment point recessed from the forebody of the bus structure. Using multiattribute decision making techniques, the trailing isotensoid, is identified to be the most advantageous decelerator optionfor use in this application.

Fast, high-fidelity trajectory propagation of objects in near-Earth orbits is a key capability for space situational awareness and mitigating probability of collisions on orbit. This high-fidelity analysis requires accurate aerodynamics prediction for objects in the free-molecular regime of flight, but most tools for aerodynamic prediction for this regime either are found using assumptions or are computationally intensive. Symbolic manipulation software can be used to analytically integrate expressions for pressure and shear pressure coefficients, as derived by Regan and Anandakrishnan, acting on a general body in free-molecular regime to derive aerodynamic force and moment expressions. The analytical aerodynamics prediction method is described and relations have been developed for the sphere, cylinder, panel, and rectangular prism. The NASA-developed Direct Simulation Monte Carlo Analysis Code is used to validate the analytical expressions and it is shown that expressions are accurate within 0.38%. These generalized analytic expressions in terms of angle of attack, sideslip angle, freestream conditions, wall temperature, and accommodation coefficients allow near-instantaneous computation of the rarefied aerodynamics and enables space situation awareness analysis.

This work examines the extensibility of a linear rapid robust design methodology enabled by viewing the multidisciplinary design optimization problem as a dynamical system to nonlinear problems. This analysis is approached from a computational and accuracy perspectives. The sensitivity of the solution's computational cost is examined by analyzing effects such as the number of design variables, nonlinearity of the CAs, and nonlinearity in addition to several potential complexity metrics. Relative to traditional robust design methods, the linear rapid robust design methodology scaled better with the size of the problem and had performance that exceeded the traditional techniques examined. The accuracy of applying a method with linear fundamentals to nonlinear problems was examined. It is observed that if the magnitude of nonlinearity is less than 1,000 times that of the nominal linear response, the error associated with applying successive linearization will result in 1σ errors in the response less than 10% compared to the full nonlinear error.