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Different semi-analytical reduced-order models for calculating the unsteady aerodynamic loads of subsonic slender wings are proposed. The lift-deficiency functions due to a unitary step change in the angle of attack and a unitary sharp-edged vertical gust are first obtained in the (reduced) time domain for both elliptical and rectangular wings of arbitrary aspect ratio, based on previous fundamental works available in the literature. Nonlinear optimisation is then employed to find their best analytical approximation as a series of exponential functions with optimal time constants and amplitudes, as intensively sought for efficient computations of the wing loads as well as aeroelastic stability analyses, especially in the context of aircraft’s preliminary multidisciplinary design and optimisation. When the gust penetration effect is also applied, the final curve fitting is performed in the (reduced) frequency domain, where the transfer function between flow perturbation and aerodynamic load is expressed as a series of rational functions with optimal poles and gains; the approximation of the corresponding indicial function is then still obtained as a series of exponential functions with optimal time constants and amplitudes in the (reduced) time domain via Laplace transform. The optimal parameters of the lift-deficiency functions are finally tabulated and analytically expressed as function of the wing’s aspect ratio, for each type of wing and flow perturbation. The obtained reduced-order models for unsteady aerodynamic loads are critically discussed and, due to their remarkable computational efficiency and theoretical insights, also suggested for suitable use in the preliminary multidisciplinary design and optimisation of flexible wings in the low-subsonic regime, characterised by attached incompressible flow.

SEMI-ANALYTICAL REDUCED-ORDER MODELS FOR THE UNSTEADY AERODYNAMIC LOADS OF SUBSONIC WINGS