Theoretical pressure distributions on nonlifting circular-arc airfoils in two-dimensional flows with high subsonic free-stream velocity are found by determining approximate solutions, through an iteration process, of an integral equation for transonic flow proposed by Oswatitsch. The integral equation stems directly from the smalldisturbance theory for transonic flow. This method of analysis pos¬sesses the advantage of remaining in the physical, rather than the hodograph, variables and can be applied to airfoils having curved surfaces. After discussion of the derivation of the integral equation and qualitative aspects of the solution, results of calculations carried out for circular-arc airfoils in flows with free-stream Mach numbers up to unity are described. These results indicate most of the principal phenomena observed in experimental studies. At subcritical Mach numbers, the pressure distribution is symmetrical about the midchord position and the drag is zero. The magnitude of the pressure coefficient is found to increase more rapidly with increasing Mach number than the Prandtl-Glauert rule would indicate. When the critical Mach number is exceeded, compression shocks occur, the fore-and-aft symmetry of the pressure distribution is lost, and the airfoil experiences a drag force. As the Mach number is increased further, the shock wave becomes of greater intensity and moves rearward along the chord, thereby producing a rapid increase in the magnitude of the pressure drag coefficient. At Mach numbers close to unity, the variation of the pressure, local Mach number, and drag conforms, within the limitations of transonic small perturbation theory, to the known trends associated with the Mach number freeze. Some comparisons with experimental results are also included.nThe solutions are obtained using an iteration process which differs from the classical methods in that the quadratic nature of the integral equation is recognized. If the iteration calculations are started using the linear-theory solution, it is shown that the retention of the quad-ratic feature has the interesting effect of forbidding shock-free super-critical second-order solutions. In order to obtain solutions for supercritical Mach numbers, it is necessary to start the iteration cal-culations with a velocity or pressure distribution which contains a compression shock. When this is done, it is found that the iteration procedure converges to a definite result.
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