A method is described whereby, at any point in an infinite parallel annulus, the approximate axial velocity due to a single row of high aspect ratio blades may be calculated from a knowledge of the conditions of flow adjacent to the blades. The method is based on the assumption of a simplified expression for the radial velocity, being the product of an unknown function of the radius and an exponential term independent of the radius containing an undetermined constant; the function and the undetermined constant are calculated by reference to the conditions of flow in the plane of the row considered. The flow due to any number of rows is then obtained by summing the radial velocity fields due to each row and obtaining the axial velocities by integration of the equation of continuity.

The solution of the problem with infinitely many rows is shown to have a simple form by virtue of the fact that the flow (provided that the velocities remain finite) settles down to a pattern which is periodic by one stage pitch.

It is assumed that pure anti-symmetric vibrations of an aircraft can exist, involving fuselage torsion but excluding fuselage bending. With this assumption, which in most cases is a reasonable approximation, the eigenvalue equations for anti-symmetric vibrations of a complete aircraft are derived in a very general form. The “lumped mass” approximation to the continuous mass distribution is used and sub-matrices are associated with properties of relatively simple branches of the system. The final eigenvalue equations are expressed in terms of these sub-matrices so that in a numerical application the physical system as such is considered only in relation to properties of the simple branches. It is assumed initially that the aircraft wing and tail have flexural axes of the conventional type, but the treatment is generalised to cover swept and cranked wing aircraft.