A class of dynamic sailplane winch-launch trajectory problems for maximum altitude is formulated. Numerical solutions are presented for representative values of maximum allowed lift coefficient and cable acceleration. The optimal trajectory is shown to consist of a climb-dive-climb sequence. An inequality constraint on cable retraction speed is also imposed and results in more realistic trajectories.

This Note proposes a restriction on possible solution procedures for thin-shock-layer theory. This restriction has been widely violated in solutions presented hitherto, although with negligible error apparently. Those cases are indicated where failure to apply the restriction leads to definite errors.

An alternative method of treating the boundary conditions for wing and body flow problems is developed and a detailed analysis for the flow around two-dimensional aerofoils is given. The basis of the method is the concept of an analytic continuation of the exterior flow to give a fictitious interior flow and a modified problem which can be solved using the ideas of thin-wing theory. The detailed analysis for flows described by the linear Prandtl-Glauert potential equation is given. The results obtained for several examples are satisfactory. The application of the theory to continuous and discontinuous transonic flows is outlined.

Evidence is presented to show that the universal law of the wall has a wider range of validity than the assumption l = ky, with k a universal constant. If an effective value of k is defined for the wall region its value is shown to vary between wide limits, and keff can be correlated with other parameters describing the flow in the wall region.

An approximate analysis of conditions at separation produced by turbulent boundary-layer/shock-wave interaction is presented for swept, cylindrically symmetric flows. An integral boundary-layer prediction method is used, incorporating Johnston crossflow profiles. The results indicate a marked reduction in pressure rise required to produce separation as sweep is increased. At low Reynolds numbers the skin friction at separation is inferred to be small, whereas at higher Reynolds numbers the presence of a vigorous streamwise flow may be detected. In the limiting case of zero sweep, or two-dimensional flow, predictions using the approximate analysis are shown to compare well with experimental results of pressure rise to separation.

The formulation of curved finite elements to represent a two-dimensional circular sandwich ring with honeycomb core and laminated faces is investigated. Assumed stress hybrid and equilibrium methods are found to be easier to employ in this case than the displacement approach. Using these methods, an element stiffness matrix is developed. The approximations of membrane faces and an infinite core normal stiffness are then used to develop simpler elements. Test cases show that these assumptions may become invalid, but that they are adequate for most practical cases where the core thickness to radius ratio and the face thickness to core thickness ratio are both low.

The numerical calculation of the subcritical, steady, three-dimensional, potential flow past a semi-infinite swept elliptic cylinder attached to a plane wall is described. The full equations of motion are written in terms of the velocity potential and the exact body-surface conditions are applied. The equations are expressed in coordinates defined by the body shape and further transformations are necessary to reduce the infinite domain to a finite working space and to concentrate the grid points in regions of greatest variation of potential. The resulting equations are solved using a finite-difference scheme. The Mach number distribution for a typical case is presented.