Transforming Aerodynamic Datasets into Parametric Equations for use in Multidisciplinary Design Optimization

This paper presents a method of transforming aerodynamic datasets generated in Aerodynamic Preliminary Analysis System (APAS) into parametric equations which may subsequently be used in a multidisciplinary design optimization (MDO) environment for analyzing aerospace vehicles. APAS is an analysis code which allows the user to create a simple geometric model of a vehicle and then calculate the aerodynamic force coefficients of lift, drag, and pitching moment over a wide range of flight conditions. As such, APAS is a very useful tool for conceptual level vehicle designs since it allows the force coefficients for a given design to be calculated relatively quickly and easily. However, APAS suffers from an outdated user interface and, because it is tedious to generate a new dataset during each design iteration, it is quite difficult to integrate into an MDO framework. Hence the desire for a method of transforming the APAS output into a more usable form. The approach taken and described in this paper involves the use of regression analysis techniques and response surface methodology to accomplish the data transformation with two goals in mind. The first goal was to develop a parametric model for calculating the aerodynamic coefficients for a single unique geometry. The second goal was to extend this model to capture the effects of changes in vehicle geometry. This paper presents the results and gives the model developed for analyzing a sample vehicle for both cases. NOMENCLATURE APAS Aerodynamic Preliminary Analysis System AR wing aspect ratio Cd coefficient of drag Cdo coefficient of drag at zero lift Cl coefficient of lift Clo coefficient of lift at zero angle of attack Cm coefficient of pitching moment HABP Hypersonic Arbitrary Body Program K parameter relating Cd to Cl M Mach number MDO multidisciplinary design optimization POST Program to Optimize Simulated Trajectories S lift slope parameter UDP Unified Distributed Panel α angle of attack (degrees) Λ wing leading edge sweep angle (degrees) INTRODUCTION Aerodynamic Preliminary Analysis System (APAS) is an industry-standard tool for calculating aerodynamic force coefficients for use in the conceptual design of aerospace vehicles. This tool, developed by NASA and Rockwell International for use in the design of the Space Shuttle, is useful for aerodynamic analysis, but due to it’s highly interactive nature, it does not lend itself well to an iterative or optimized overall vehicle design process. Aerodynamic analysis of a vehicle using APAS first requires the user to define a geometric model of † Graduate Research Assistant, School of Aerospace Engineering, Student member AIAA. * Assistant Professor, School of Aerospace Engineering, Senior member AIAA. Copyright © 1998 by Jeffery M. Scott and John R. Olds. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.