Step Response of Unsteady Aerodynamics Acting on Plane Swept Wing in Incompressible Flow for Finite State Modeling

Abstract

This paper considers approximating unsteady aerodynamic forces acting on a plane swept wing in the time domain. Time responses of the aerodynamic forces caused by a step movement of a wing in incompressible flow are calculated by using the time domain vortex element method. It was found that transient characteristics of the step responses associated with a certain generalized aerodynamic force can be represented by one decreasing function regardless of wing motions. By approximating each decreasing function with a set of exponential functions and by calculating apparent mass coefficients and steady state forces, a mathematical model for the aerodynamic forces in the form of 1st-order linear time-invariant differential equations (the state equations) is obtained. The accuracy and the applicability of the method have been confirmed through the comparison between the approximated aerodynamic forces and the unsteady forces calculated directly in the time domain or measured experimentally.