A digression on induced drag

Induced drag is commonly regarded as the undesired side effect of the lift generation in finite aspect ratio wings, which may lead to the erroneous conclusion that infinite wings and non-lifting finite wings are definitely induced drag free. In this work wing systems are investigated which, in spite of being non lifting, generate induced drag. The investigation includes corrugated wings with infinite and finite aspect ratios, the incompressible and the compressible subsonic ranges, steady and oscillatory motions. Also a non planar system is considered, namely the corrugated annular wing. The analysis is performed by means of classical linear analytical tools by extending Prandtl’s lifting line theory and reformulating it in term of a dipole line distribution instead of a vortex line. Several stimulating conclusions are found, apart from the evidence that non lifting wing systems exist, which are able to generate a large induced drag. The most interesting among these conclusions are: i) the induced drag has a maximum in correspondence of certain wavelengths of the wing corrugation (so that a ”worst wing system” can be identified); ii) the characteristic singular behaviour displayed by the linear compressible theories when transonic conditions are approached may be offset by the effect of the wing corrugation; iii)in the unsteady oscillatory case the induced drag may evolve to an induced propulsion depending on the phase relation between the instantaneous values of the lift and of the angle of attack.