The equations defining compressible flow are sufficiently complicated to preclude general analysis, but, in particular cases, can often be simplified and manipulated into a form amenable to solution. Problems connected with aircraft have, in the past, usually fallen into this category, where the non-linear equations can be simplified to a linear form and reasonably accurate solutions deduced. At hypersonic speeds, however, the more usual assumptions become invalid, no reasonable simplification can be made, and, except in certain specialised cases, no solutions can be deduced. Hence the problem of deriving the flow pattern around some specified shape becomes, in general, insoluble. The simple caret wing was proposed seven years ago by Nonweiler to avoid such difficulty. His elegant idea was to reverse the normal process of deducing the flow field round a given body shape, and instead to deduce body shapes that would generate specific, simple, flow patterns. From known flow fields lifting bodies may be obtained, by replacing .streamlines with solid surfaces, and the caret wing is one example. Nonweiler’s original notion has sin:e been extended by a number of people.