A Discrete-Vortex Method for Studying the Wing Rock of Delta Wings

Summary 1Introduction 1Symbols 3Mathematical Development 7Basic Assumptions 7Basic Flow Model 8General Description 8Complex Potential for Wing-Vortex System 9Coordinate and Velocity Transformations 10Solution Procedure 10Determination of Static Vortex Positions and Strengths at Zero Roll Angle 11Symmetric Boundary Conditions for Wing at Zero Roll Angle 11S-1 11S-2 11S-3 11Discussion of Symmetric Boundary Conditions 14Radial-Velocity Condition (S- 1) 14X-Axis Momentum Condition (S-2) 14Maximum Lateral Force Condition (S-3) 17Determination of Static Vortex Positions and Strengths at Nonzero Roll Angle 20Asymmetric Boundary Conditions for Wing at Nonzero Roll Angle 20AS- 1 20AS-2 20AS-3 21AS-4 21AS-5 21AS-6 22Discussion of Asymmetric Boundary Conditions 22Attached-Flow Streamline Conditions (AS-1 and AS-2) 22Constant Velocity-Potential Condition (AS-3) 22Radial-Velocity Conditions (AS-4 and AS-5) 26Momentum Condition (AS-6) 26Application of Nonzero Roll Boundary Conditions 26Determination of Dynamic Vortex Positions and Strengths 27Determination of Wing Rolling Moments 28Static Rolling Moments 28Moments Caused by Hysteretic Deflections of Vortices 29Attached-Flow Roll Damping 29Wing Rock Calculations 30Results and Discussion 31Static Vortex Positions and Strengths for Zero Roll Angle 31Static Vortex Positions and Strengths for Nonzero Roll Angle 34Wing Rock Time Histories 37Comparison of Calculated and Experimental Time Histories 37Comparison of Calculated and Experimental Hysteretic Deflections 40