The title of this paper may be said to cover almost the whole field of the immediate endeavours of those who are concerned with the design and technical development of military aeroplanes, and especially of fighters. The term transonic is not precise, but may be defined conveniently as applying to those speeds of flight, in the region of the speed of sound, when all the customary aerodynamic design rules cease to operate. Theoretically, therefore, transonic flight consists entirely of problems.