Effects of Longitudinal Elastic Camber on Slender Aircraft in Steady Symmetrical Flight

In 1957 the slender-delta type of configuration had been adopted in the U.K. as the most promising for a supersonic transport aircraft designed to cruise at about M = 2.0, and by 1959 one or two exploratory studies of the aeroelastic behaviour of such layouts had been made. Professor Etkin now suggested a mode of attack on the steady and quasi-steady aeroelastic problems, whereby such an aircraft would be regarded as a 'free-free' beam subject only to longitudinal bending, while aerodynamic loadings would be calculated in accordance with slender-wing theory. Under such conditions the mode of deformation corresponding to a particular steady or quasi-steady state is directly calculable by numerical solution of the appropriate differential equation, and the effects of aeroelasticity on the various trim, stability and manoeuvrability criteria are then readily computed. Following this suggestion, the first of the present authors developed the relevant mathematical theory in a general form, which permits some freedom of choice as to the method of calculating the aerodynamic loadings. Then, in collaboration with the second author, he embarked on a comprehensive programme of numerical applications (using a 'Mercury' digital computer) in which the influence of various parameters (planform, stiffness and mass distributions, etc.) on the aeroelastic characteristics was to be studied. The sensitivity of results to changes in the aerodynamic assumptions was also to be considered. By the end of 1962 a considerable volume of computations had been completed for one particular planform. Slender-wing theory had been used throughout for the calculation of aerodynamic loading due to elastic camber and the effects of varying stiffness and mass distributions had been investigated. At this stage, however, the impending transfer of the authors to other duties cast doubt upon the possibility of extending the work any further. Accordingly, the report which forms Part I of this R. & M. was written. This describes the method and presents the results of the calculations performed up to that time. Subsequently, the first author was able to carry the investigation a stage further by repeating the earlier calculations, using piston-theory aerodynamics instead of slender-wing theory for the computation of loading due to elastic camber. An extension to the theory of Part I, and appropriate modifications to computer programmes , made it possible also to calculate the effects of elastic camber on the longitudinal distributions of Replaces R. shear force and bending moment. This stage of the work was …