A simplified lifting-surface theory that includes effects of compressibility and spanwise variation of section lift-curve slope is used to provide charts with which antisymmetric loading due to arbitrary antisymmetric angle of attack can be found for wings having symmetric plan forms with a constant spanwise sweep angle of the quarter-chord line. Consideration is given to the flexible wing in roll. Aerodynamic characteristics due to rolling, deflected ailerons, and sideslip of wings with dihedral are considered. Solutions are presented for straight-tapered wings for a range of swept plan forms.

From Summary :"Methods based on the linearized theory for supersonic flow were used to find the characteristics of two types of control surfaces on thin triangular wings. The first type, the constant-chord partial-span flap, was considered to extend either outboard from the center of the wing or inboard from the wing tip. The second type, the full-triangular-tip flap, was treated only for the case in which the Mach number component normal to the leading edge is supersonic. For each type, expressions were found for the lift, rolling-moment, pitching-moment, and hinge-moment characteristics."

"On the basis of linearized supersonic-flow theory, generalized equations were derived and calculations made for the lift and damping in roll of a limited series of thin sweptback tapered wings. Results are applicable to wings with streamwise tips and for a range of supersonic speeds for which the wing is wholly contained between the Mach cones springing from the wing apex and from the trailing edge of the root section. A further limitation is that the tip Mach lines may not intersect on the wing" (p. 395).

"Six numerical examples are presented for steady, two-dimensional, compressible, nonviscous flow in centrifugal compressors with thin straight blades, the center lines of which generate the surface of a right circular cone when rotated about the axis of the compressor. A seventh example is presented for incompressible flow. The solutions were obtained in a region of the compressors, including the impeller tip, that was considered to be unaffected by the diffuser vanes or by the impeller-inlet configuration" (p. 141).

"A general method of analysis is developed for two-dimensional, steady, compressible flow in stators or rotors of radial and mixed flow turbomachines with conic flow surfaces (surfaces of right circular cones generated by center line of flow passage in the axial-radial plane). The variables taken into account are: (1) tip speed of the rotor, (2) flow rate, (3) blade shape, (4) variation in passage height with radius, (5) number of blades, and (6) cone angle of the flow surface. Relaxation methods are used to solve the nonlinear differential equation for the stream function" (p. 1).

From Summary: "A series of publications on the source-distribution methods for evaluating the aerodynamics of thin wings at supersonic speeds is summarized, extended, and unified. Included in the first part are the deviations of: (a) the linearized partial-differential equation for unsteady flow at a substantially constant Mach number. b) The source-distribution solution for the perturbation-velocity potential that satisfies the boundary conditions of tangential flow at the surface and in the plane of the wing; and (c) the integral equation for determining the strength and the location of sources to describe the interaction effects (as represented by upwash) of the bottom and top wing surfaces through the region between the finite wing boundary and the foremost Mach wave. The second part deals with steady-state thin-wing problems. The third part of the report approximates the integral equation for unsteady upwash and includes a solution of approximate equation. Expressions are then derived to evaluate the load distributions for time-dependent finite-wing motions."