First derivatives of flow quantities behind two-dimensional, nonuniform supersonic flow over a convex corner

A method of determining spatial derivatives of flow quantities behind an expansion fan as a function of the curvature of the streamline behind the fan is developed. Taylor series expansions of flow quantities within the fan are used and boundary conditions satisfied to the first and second order so that the curvature of the characteristics in the fan may be determined. A system of linear equations for the spatial derivatives is then developed. An application of the method to shock coalescence including asymmetric effects is described

Spatial derivatives of flow quantities behind curved shocks of all strengths

Explicit formulas in terms of shock curvature are developed for spatial derivatives of flow quantities behind a curved shock for two-dimensional inviscid steady flow. Factors which yield the equations indeterminate as the shock strength approaches 0 have been cancelled analytically so that formulas are valid for shocks of any strength. An application for the method is shown in the solution of shock coalescence when nonaxisymmetric effects are felt through derivatives in the circumferential direction. The solution of this problem requires flow derivatives behind the shock in both the axial and radial direction

Limitations on wind-tunnel pressure signature extrapolation

Analysis of some recent experimental sonic boom data has revived the hypothesis that there is a closeness limit to the near-field separation distance from which measured wind tunnel pressure signatures can be extrapolated to the ground as though generated by a supersonic-cruise aircraft. Geometric acoustic theory is used to derive an estimate of this distance and the sample data is used to provide a preliminary indication of practical separation distance values

Validation of a pair of computer codes for estimation and optimization of subsonic aerodynamic performance of simple hinged-flap systems for thin swept wings

Extensive correlations of computer code results with experimental data are employed to illustrate the use of linearized theory attached flow methods for the estimation and optimization of the aerodynamic performance of simple hinged flap systems. Use of attached flow methods is based on the premise that high levels of aerodynamic efficiency require a flow that is as nearly attached as circumstances permit. A variety of swept wing configurations are considered ranging from fighters to supersonic transports, all with leading- and trailing-edge flaps for enhancement of subsonic aerodynamic efficiency. The results indicate that linearized theory attached flow computer code methods provide a rational basis for the estimation and optimization of flap system aerodynamic performance at subsonic speeds. The analysis also indicates that vortex flap design is not an opposing approach but is closely related to attached flow design concepts. The successful vortex flap design actually suppresses the formation of detached vortices to produce a small vortex which is restricted almost entirely to the leading edge flap itself

Wind-tunnel investigation of the validity of a sonic-boom-minimization concept

The Langley unitary plan unitary plan wind tunnel was used to determine the validity of a sonic-boom-minimization theory. Five models - two reference and three low-boom constrained - were tested at design Mach numbers of 1.5 and 2.7. Results show that the pressure signatures generated by the low-boom models had significantly lower overpressure levels than those produced by the reference models and that small changes in the Mach number and/or the lift caused relatively small changes in the signature shape and overpressure level. Boundary-layer effects were found in the signature shape and overpressure level. Boundary-layer effects were found to be sizable on the low-boom models, and when viscous corrections were included in the analysis, improved agreement between the predicted and the measured signatures was noted. Since this agreement was better at Mach 1.5 than at Mach 2.7, it was concluded that the minimization method was definitely valid at Mach 1.5 and was probably valid at Mach 2.7, with further work needed to resolve the uncertainty

Current research in sonic-boom minimization

A review is given of several questions as yet unanswered in the area of sonic-boom research. Efforts, both here at Langley and elsewhere, in the area of minimization, human response, design techniques and in developing higher order propagation methods are discussed. In addition, a wind-tunnel test program being conducted to assess the validity of minimization methods based on a forward spike in the F-function is described

Minimization of sonic-boom parameters in real and isothermal atmospheres

The procedure for sonic-boom minimization introduced by Seebass and George for an isothermal atmosphere was converted for use in the real atmosphere by means of the appropriate equations for sonic-boom pressure signature advance, ray-tube area, and acoustic impedance. Results of calculations using both atmospheres indicate that except for low Mach numbers or high altitudes, the isothermal atmosphere with a scale height of 7620 m (25 000 ft) gives a reasonable estimate of the values of overpressure, impulse, and characteristic overpressure obtained by using the real atmosphere. The results also show that for aircraft design studies, propagation of a known F-function, or minimization studies at low supersonic Mach numbers, the isothermal approximation is not adequate

Charts for determining potential minimum sonic-boom overpressures for supersonic cruise aircraft

Charts which give an estimation of minimum achievable sonic-boom levels for supersonic cruise aircraft are presented. A minimization method based on modified linear theory was analyzed. Results show several combinations of Mach number, altitude, and aircraft length and weight. Overpressure and impulse values are given for two types of sonic boom signatures for each of these conditions: (1) a flat top or minimum overpressure signature which has a pressure plateau behind the initial shock, and (2) a minimum shock signature which allows a pressure rise after the initial shock. Results are given for the effects of nose shape

An analysis of shock coalescence including three-dimensional effects with application to sonic boom extrapolation

A method for analyzing shock coalescence which includes three dimensional effects was developed. The method is based on an extension of the axisymmetric solution, with asymmetric effects introduced through an additional set of governing equations, derived by taking the second circumferential derivative of the standard shock equations in the plane of symmetry. The coalescence method is consistent with and has been combined with a nonlinear sonic boom extrapolation program which is based on the method of characteristics. The extrapolation program, is able to extrapolate pressure signatures which include embedded shocks from an initial data line in the plane of symmetry at approximately one body length from the axis of the aircraft to the ground. The axisymmetric shock coalescence solution, the asymmetric shock coalescence solution, the method of incorporating these solutions into the extrapolation program, and the methods used to determine spatial derivatives needed in the coalescence solution are described. Results of the method are shown for a body of revolution at a small, positive angle of attack