Essentials of Supersonic Commercial Aircraft Conceptual Design

5Thin Wings in Two‐dimensional Flow

Airplane configurations optimized for achieving high aerodynamic efficiency in supersonic cruising flight typically feature a thin and slender wing with sharp trailing edges and a slender fuselage body with a smooth variation of the cross section area between the pointed nose and tail. In order to avoid unfavorable aerodynamic interactions, the arrangement of aircraft components is carefully optimized, and at small angles of attack such a configuration produces weak shock waves, thin boundary layers, and attached flows. An accurate method for computing the pressure distribution on a two‐dimensional airfoil is the shock‐expansion technique treated in Section 4.8. An alternative and widely used method is the linear theory for thin airfoils, which is applicable to two‐dimensional potential flow, and was first published in 1925 by the Swiss scientist J. Ackeret (1898–1981) [11]. This flow model replaces shock waves with Mach waves, disregarding variations in the local Mach number.

5.1 Small Perturbation Flow

Linear theory yields a good approximation of the pressure distribution at locations where flow separation is not dominant and can be used to compute the pressure distribution of thin airfoil sections at a small angle of attack in flows at transonic and low‐supersonic Mach numbers. For subsonic as well as supersonic flight at small angles of attack, the two‐dimensional flow in which a flying vehicle is immersed can be treated as predominantly ...