Küssner's Function in the Sharp Edged Gust Problem-A Correction

Semi-Analytical Reduced-Order Models for the Unsteady Aerodynamic Loads of Subsonic Wings

“…B may be obtained by fitting the exact curves [20][21][22][23][24][25], as the result of a nonlinear constrained optimisation problem [70] where the approximation error is minimised in a root mean square sense [96] in both cases. It is important to stress that Kussner's lift-deficiency function is also the airfoil circulation corresponding to Wagner's lift-deficiency function [93][94][95].…”

“…Assuming incompressible potential flow [19], Wagner and Kussner derived the lift-deficiency functions due to a unitary step change in the angle of attack [20] and a unitary sharp-edged vertical gust [21][22] for a thin flat airfoil in the (reduced) time domain, respectively, while Theodorsen [23] and Sears [24][25] solved the same problems in the (reduced) frequency domain. Based on these very fundamental twodimensional studies [26][27][28], the lift-deficiency functions due to a unitary step change in the angle of attack and a unitary sharp-edged vertical gust [29] have been investigated for thin flat wings of various shapes [30][31][32][33][34][35][36][37][38], including elliptical [39][40], rectangular [41] swept trapezoidal [42] and delta wings [43], for which panel-based methods are particularly useful [44][45][46][47].…”

Semi-Analytical Reduced-Order Models for the Aeroelastic Behavior of Subsonic Flexible Wings via Generalised Plate and Beam Formulations

“…For two-dimensional unsteady incompressible potential flow, Theodorsen and Sears [26][27][28] lift-deficiency functions account for the inflow [19] generated by the travelling wake of a flat aerofoil due an harmonic oscillation and a sinusoidal gust, respectively; the relative indicialadmittance functions for the circulatory lift build-up due to a unit step in the angle of attack and a unit sharp-edge gust are then given by Wagner and Kussner [23][24][25], respectively.…”

“…Coherently assuming an ideal elliptical loading due to a suitable distribution of elementary vortex loops, the wing's lift-deficiency coefficient D L C 3 and circulation D w 3 from a unit step in the angle of attack are written along with the tips-induced downwash w V as [20]: are the lift-deficiency coefficient and related circulation given by Wagner and Kussner functions for a two-dimensional flat aerofoil (which account for the inflow generated by the travelling wake), respectively [23][24][25]:…”

“…Modified strip theory (MST) is adopted for the aerodynamic load [15][16], tuned strip theory (TST) being readily resumed for comparison and completeness [17][18]. Peters' in-flow theory is adopted for calculating the two-dimensional unsteady airload around each morphing wing section [19], where approximate lift-deficiency functions [20][21][22] for both a unit step-change in the angle of attack and a unit sharp-edged gust are employed in place of classic Theodorsen/Wagner's and Sears/Kussner's functions [23][24][25][26][27][28], respectively. Both plate-like and beam-like linear models are considered for the structural dynamics, within a unified formulation [29][30].…”