By a slight modification to den Hartog’s classical theory of harmonically forced vibration off resonance it is shown that, with such distorted forcing wave forms as might be encountered in the stalling or choking flutter of an aerofoil in cascade, the influence of damping on the amplitude of motion can still be assessed with considerable accuracy by the assumption of an equivalent harmonic excitation. The result is valid for any amount of Coulomb damping at which motion is significant in the presence of any “ velocity ” damping coefficient up to that defined by a logarithmic decrement of about 1-3, the formal conclusion of the argument being stated in Section 4.

For many conventional aircraft, the thickness of the wing and fuselage can be represented approximately by source distributions in the plane of the wing and on the axis of the fuselage. Such aircraft may be considered as having essentially planar thickness distributions. However, missiles with cruciform wings, biplane arrangements, “ ring ” wings and so on, require non-planar source distributions to represent the wing and fuselage thickness. For this reason, the term “ spatial thickness distribution ” is used.

To simplify the investigation of spatial thickness distributions, a singularity representing an element of volume is introduced. It is shown that the optimum distribution of such elements in a prescribed space gives rise to a minimum wave drag value consistent with that obtained for a Sears- Haack optimum body of revolution.

Ward’s slender-body theory is extended to derive first approximations to the external forces on slender bodies of general cross section with discontinuous profile slope. Two classes of body are considered: bodies whose profile (typified by the local radius) is continuous between the nose and base, and certain bodies whose profile is discontinuous, such as bodies with annular or side air intakes and wing-bodies on which the wing has an unswept leading edge. (Where air intakes are concerned, it is assumed that they are sharp-edged and that there is no “ spillage ” of the internal flow).

The following conclusions apply to the former class of bodies. The variation of drag with Mach number is found to depend only on the discontinuities in the longitudinal rate of change of the cross-sectional area, and is thus independent of cross-sectional shape. The drag itself is unchanged if the direction of the flow is reversed. The expressions for lift and moment assume the same forms as for smooth pointed bodies, the lift depending only on conditions at the base of the body.

The general theory is applied to winged bodies of revolution with an unswept wing leading edge: the results bear a marked resemblance to those obtained by Ward. The results for wings alone are seen to be applicable, with one modification, to subsonic as well as to supersonic speeds.

A formula is derived for the buckling in compression of an orthotropic sandwich panel, with all edges simply-supported. Two special types of symmetrical sandwiches, that of a sandwich having zero core flexural stiffnesses and of a corrugated core sandwich, are considered, and curves giving the critical buckling end load per inch are presented. An approximate theory is also given for the bending of sandwich panels under the action of an axial compressive load and a uniform lateral pressure. Curves are presented giving the maximum bending moments in a corrugated core sandwich panel.

A generalised conical flow theory is used to deduce an integral equation relating the velocity potential on a delta wing (with subsonic leading edges) to the given downwash distribution over the wing. The complete solution of this integral equation is derived. This complete solution is composed of two parts, one being symmetric and the other anti-symmetric with respect to the span wise co-ordinate; each part represents a velocity potential. For example, if y is the spanwise co-ordinate and x is measured in the free stream direction, then a downwash of the form w= - α11 Ux|y| is symmetric and will give rise to a symmetric potential, whereas w= - α11 Ux|y| sgn y is anti-symmetric and gives rise to an anti-symmetric potential. The velocity potentials of such flows are given in the form of Tables for all downwashes up to and including homogenous cubics in the spanwise and streamwise co-ordinates. Table III gives similar formulae in the limiting case when the leading edges become transonic; these are compared with results given elsewhere and serve as a check on the results of Tables I and II.