This is a calculation of the chordwise lift distribution, total lift, and moment on a two-dimensional wing striking a sharp-edged gust a t supersonic speed. A direct solution is established by considering a distribution of sources in a fluid at rest. An alternate method using Busemann's conical flow is also shown to be applicable. The time history of the total lift and mid-chord moment is discussed. I t is shown tha t the total lift increases with time and reaches a maximum that corresponds to the steadystate phase of the flow. The mid-chord moment goes through a maximum independent of the Mach Number if the latter value is larger than 4/7r, while this maximum can become infinite for a range of Mach Numbers between 4/TT and 1. (1) INTRODUCTION CONSIDERABLE ATTENTION has been given lately to nonstationary flow problems of wings flying at supersonic speeds. Most of the work, however, has been concerned with the aerodynamic forces on an oscillating airfoil from the standpoint of flutter analysis. The problem of the wing hitting a sharp-edged gust is of a different nature and turns out to be actually much simpler than the oscillating airfoil problems. It is shown in section 2 that it may be treated by a distribution of sources of a simple type along the chord and that the pressure distribution may be derived by elementary methods. The procedure does not introduce a moving fluid but considers a fluid at rest in which nonstationary sources are distributed in a layer of variable extent. This point of view, which is closer to acoustics than to aerodynamics, is somewhat novel and seems to present advantages of simplicity and closeness to physical reality in certain categories of problems. The pressure distribution derived by this method is applied to the calculation of the time history of lift and moment on the wing in section 3. Particular attention is given to the value of the mid-chord moment;.-which starts from zero, rises to a maximum,,and goes back to zero. The value of this maximum and related 4ata is evaluated in section 4. These results are of particular interest to the designer. The derivation of the pressure as given in section 1 is only one of the methods that may be used in this problem. As an independent check and as an illustration of the application of Busemann's method of conical flow to a nonstationary problem, an alternate derivation is given for the pressure distribution in section 4. Received August 15, 1948. * Member of Cornell Aeronautical Laboratory consulting staff. Also Professor of Applied Physical Sciences, Brown University. In a paper by Schwarz procedures used in oscillating airfoil theory are extended to the problem of a wing striking a sharp-edged gust at supersonic speed. Results for an oscillating down-wash lead to the gust problem by a Fourier integral representation. This method constitutes a considerable detour and introduces intermediate results of a transcendental nature which are actually not needed and are more complicated than the result. I t may be verified that the expression derived in the present paper for the pressure distribution is equivalent to that derived by Schwarz. He does not, however, discuss the physical aspects of the problem or derive expressions for lift and moment. (2) DERIVATION OF THE PRESSURE DISTRIBUTION The wing of chord / enters a uniform gust of upward velocity i/0 at the supersonic velocity V (Fig. 1). The velocity component normal to the wing must remain zero, and this condition is equivalent to the generation of a velocity normal to the wing which cancels the gust velocity (Fig. 2). This may also be considered as a reflection of the gust on the wing. Because the velocity is supersonic, the pressure distribution on. one side does not influence the pressure on the other, and therefore we need only consider the bottom side. The pressure distribution on top will be the same except for a reversal of sign. For the same reason the pressure distribution is not influenced by the trailing edge, and
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