Tables for Supersonic Flow Around Right Circular Cones at Small Angle of Attack

Abstract

The solution of supersonic flow fields by the method of characteristics requires that starting conditions be known. Ferri, in reference 1, developed a method-of-characteristics solution for axially symmetric bodies of revolution at small angles of attack. With computing machinery that is now available, this has become a feasible method for computing the aerodynamic characteristics of bodies near zero angle of attack. For sharp-nosed bodies of revolution, the required starting line may be obtained by computing the flow field about a cone at a small angle of attack. This calculation is readily performed using Stone's theory in reference 2. Some solutions of this theory are available in reference 3. However, the manner in which these results are presented, namely in a wind-fixed coordinate system, makes their use somewhat cumbersome. Additionally, as pointed out in reference 4, the flow component perpendicular to the meridian planes was computed incorrectly. The results contained herein have been computed in the same basic manner as those of reference 3 with the correct velocity normal to the meridian planes. Also, all results have been transferred into the body-fixed coordinate system. Therefore, the values tabulated herein may be used, in conjunction with the respective zero-angle-of-attack results of reference 5, as starting conditions for the method-of-characteristics solution of the flow field about axially symmetric bodies of revolution at small angles of attack. As in the zero-angle-of-attack case (ref. 5) the present results have been computed using the ideal gas value of 1.4 for the ratio of the specific heats of air. Solutions are given for cone angles from 2.5 deg to 30 deg in increments of 2.5 deg. For each cone angle, results were computed for a constant series of free-stream Mach numbers from 1.5 to 20. In addition, a solution was computed which yielded the minimum free-stream Mach number for a completely supersonic conical flow field. For cone angles of 27.5 deg and 30 deg, this minimum free-stream Mach number was above 1.5. Consequently, solutions at this Mach number were not computed for these two cone angles