A procedure for computing surface wave trajectories on an inhomogeneous surface

Equations are derived for computing surface waves on smooth surfaces, including surfaces with a nonuniform wave speed. The prior literature dealt primarily with the theoretical development with little consideration given to computational methods, and examples were limited to waves on surfaces of simple analytic description, such as cones, spheres, and cylinders. The computational procedure presented is a relatively general method. Sample calculations illustrate the procedure for a class of practical shapes of the type that include aerodynamic and hydrodynamic surfaces. Equations are also included for computing the spreading of rays into a surrounding medium that will support waves

Diffracted and head waves associated with waves on nonseparable surfaces

A theory is presented for computing waves radiated from waves on a smooth surface. With the assumption that attention of the surface wave is due only to radiation and not to dissipation in the surface material, the radiation coefficient is derived in terms of the attenuation factor. The excitation coefficient is determined by the reciprocity condition. Formulas for the shape and the spreading of the radiated wave are derived, and some sample calculations are presented. An investigation of resonant phase matching for nonseparable surfaces is presented with a sample calculation. A discussion of how such calculations might be related to resonant frequencies of nonseparable thin shell structures is included. A description is given of nonseparable surfaces that can be modeled in the vector that facilitates use of the appropriate formulas of differential geometry

A method for designing blended wing-body configurations for low wave drag

A procedure for tailoring a blended wing-body configuration to reduce its computed wave drag is described. The method utilizes an iterative algorithm within the framework of first-order linear theory. Four computed examples are included. In each case, the zero-lift wave drag was reduced without an increase in the drag due to lift

Trajectory fitting in function space with application to analytic modeling of surfaces

A theory for representing a parameter-dependent function as a function trajectory is described. Additionally, a theory for determining a piecewise analytic fit to the trajectory is described. An example is given that illustrates the application of the theory to generating a smooth surface through a discrete set of input cross-section shapes. A simple procedure for smoothing in the parameter direction is discussed, and a computed example is given. Application of the theory to aerodynamic surface modeling is demonstrated by applying it to a blended wing-fuselage surface

A simplified approach to axisymmetric dual-reflector antenna design

A procedure is described for designing dual reflector antennas. The analysis is developed by taking each reflector to be the envelope of its tangent planes. Rather than specifying the phase distribution in the emitted beam, the slopes of the emitted rays were specified. Thus, both the output wave shape and angular distribution of intensity can be specified. Computed examples include variations from both Cassegrain and Gregorian systems, permitting deviation from uniform source distributions and from parallel beam property of conventional systems

On minimizing the number of calculations in design-by-analysis codes

A method is presented for aerodynamic design for a specified pressure distribution, using analysis codes only. The method requires a very conservative number of analysis runs, and therefore is appropriate when the analysis code is a large code in terms of storage and/or running time. Three model problems illustrate some capabilities and limitations of the method

A performance index approach to aerodynamic design with the use of analysis codes only

A method is described for designing an aerodynamic configuration for a specified performance vector, based on results from several similar, but not identical, trial configurations, each defined by a geometry parameter vector. The theory shows the method effective provided that: (1) the results for the trial configuration provide sufficient variation so that a linear combination of them approximates the specified performance; and (2) the difference between the performance vectors (including the specifed performance) are sufficiently small that the linearity assumption of sensitivity analysis applies to the differences. A computed example describes the design of a high supersonic Mach number missile wing body configuration based on results from a set of four trial configurations

Automatic computation of wing-fuselage intersection lines and fillet inserts with fixed-area constraint

Procedures for automatic computation of wing-fuselage juncture geometry are described. These procedures begin with a geometry in wave-drag format. First, an intersection line is computed by extrapolating the wing to the fuselage. Then two types of filleting procedures are described, both of which utilize a combination of analytical and numerical techniques appropriate for automatic calculation. An analytical technique for estimating the added volume due to the fillet is derived, and an iterative procedure for revising the fuselage to compensate for this additional volume is given. Sample results are included in graphical form

Fuselage design for a specified Mach-sliced area distribution

A procedure for designing a fuselage having a prescribed effective area distribution computed from -90 deg Mach slices is described. This type of calculation is an essential tool in designing a complete configuration with an effective area distribution that corresponds to a desired sonic boom signature shape. Sample calculations are given for M=2 and M=3 designs. The examples include fuselages constrained to have circular cross sections and fuselages having cross sections of arbitrary shape. It is found that, for a prescribed effective area distribution having sharp variations, the iterative procedure converges to a smoothed approximation to the prescribed distribution. For a smooth prescribed area distribution, the solution is not unique