Modeling the rolling 65-degree delta wing with critical state encounters

Abstract

An aerodynamic model is developed for the rolling moment on a 65-degree delta wing for rolling motions about the longitudinal body-axis inclined to the flow at 30 degrees. Modeling is complicated by the presence of discontinuities in the static data, either in their value or their slope, called critical states. These critical states are associated with changes in the static flow topology, such as vortex breakdown crossing the trailing edge of the delta wing. The time scales of the flow field response to changes in roll angle vary across critical states, and lengthy transient effects often persist long after a critical state has been crossed. Modeling the rolling moment is further complicated by multiple time scales within a single flow field topology. Both a short time scale inversely proportional to the convection speed and a time scale that is an order of magnitude longer due to the lags in the vortex breakdown locations contribute to the rolling moment response. The aerodynamic model is developed in the Laplace domain and presented in state-space form. Comparisons to experimental data show that the model predicts the rolling moment for motions with multiple critical state crossings for which a locally-linear method fails. Nomenclature b = wingspan, ft C[ b o d y a x i s r o l l i n g m o m e n t , nondimensionalized with respect to qSb (A positive rolling moment tends to force the starboard wing down.) C[ = predicted rolling moment C[. = partial derivative of rolling moment v coefficient with respect to nondimensional roll rate err' = normalized least-squares error Aerospace Engineer, former graduate student in Stanford University Department of Aeronautics and Astronautics, Member AIAA This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. J k 1 s S t t' ur CO x