Recently there has been renewed interest in the concept of an all-wing aircraft as a means of producing cheap air transport over relatively short distances. It is natural that with the large amount of information on slender wings now available an all-wing aircraft based on a sharp-edged slender planform should be considered for this role. One of the difficulties immediately faced in developing this concept is that since the aircraft must carry a large number of passengers it is necessary that as much of the wing area as possible should be deep enough to provide for a large passenger cabin. Thus the wing will be very thick over a large part of its area. If this condition is not met, then the aircraft has too much wing area and hence too high a structure weight. Typically one may think of an aircraft with a delta wing of aspect ratio 2 and with a wing thickness of from 15% to 20% of the root chord over as much of the wing area as possible. At first sight thickness of this order eliminates the main advantage of slender wings since the effect of thickness is usually to reduce the strength of the leading-edge vortices and hence the non-linear lift. Thus the incidence for a given lift is increased above that for a thin wing. This in turn means that the lift-to-drag ratio may be smaller.