Extension of the continuous time unsteady vortex lattice method for arbitrary motion, control surface deflection and induced drag calculation

In this paper a continuous time state space aerodynamic model is extended for accepting arbitrary motion, control surface deflection and gust velocities as inputs. Equations for formulating the inner state equation are outlined first followed by the numerical description of the boundary condition. The force calculation is presented using an unsteady form of the Kutta-Joukowski theorem enabling the method of unsteady induced drag prediction. Methods for linearization are presented. The resulting model inputs are motion, control surface deflection and gust velocities and accelerations while the system outputs are panel forces. To validate the modeling approach, comparisons to analytical methods are carried out for various oscillatory motions. Besides integrated coefficients for vertical force, drag, pitching moment and hingemoment, comparisons for unsteady pressure distributions are carried out. The comparisons indicate good agreement for a large range of reduced frequencies. The influence of wake truncation distance and discretization is discussed. Because of its time-domain formulation, the model is especially suitable for efficient aerodynamic loads analysis within aeroelastic modeling, analysis and optimization frameworks for preliminary aircraft design.