R. L. Carmichael

PAN AIR - A higher order panel method for predicting subsonic or supersonic linear potential flows about arbitrary configurations

PAN AIR is a computer program for predicting subsonic or supersonic linear potential flow about arbitrary configurations. It uses linear source and quadratic doublet strength distributions. These higher-order distributions have been implemented in a manner that greatly reduces the numerical stability problems that have plagued earlier attempts to make surface paneling methods work successfully for supersonic flow. PAN AIRs problem-solving capability, numerical approach, modeling features, and program architecture are described. Numerical results are presented for a variety of geometries at supersonic Mach numbers.

ALGORITHM FOR CALCULATING COORDINATES OF CAMBERED NACA AIRFOILS AT SPECIFIED CHORD LOCATIONS

The equations for the NACA 4-digit and 4-digitmodified sections are in algebraic form and easily incorporated into various geometrical procedures that define a vehicle and any necessary flow field grid. The 6-series and 6A-series airfoils are more complex because they are developed by conformal mapping procedures. Even though there are computer programs available (refs 1-3) that can produce a large table of points on the surface of the airfoil, there is a frequently expressed desire for an algorithm that will calculate the upper and lower ordinates and slopes of a cambered airfoil at a specified chord location that requires no interpolation on the part of the user. The purpose of this paper is to present such an algorithm and describe subroutines that may be used for these calculations. A public domain computer program incorporating these procedures has been written and may be downloaded from the author’s web site. This program is modular, allowing its internal procedures to be used in other programs.

Three-dimensional canard-wing shape optimization in aircraft cruise and maneuver environments

This paper demonstrates a numerical technique for canard-wing shape optimization at two operating conditions. For purposes of simplicity, a mean surface wing paneling code is employed for the aerodynamic calculations. The optimization procedures are based on the method of feasible directions. The shape functions for describing the thickness, camber, and twist are based on polynomial representations. The primary design requirements imposed restrictions on the canard and wing volumes and on the lift coefficients at the operating conditions. Results indicate that significant improvements in minimum drag and lift-to-drag ratio are possible with reasonable aircraft geometries. Calculations were done for supersonic speeds with Mach numbers ranging from 1 to 6. Planforms were mainly of a delta shape with aspect ratio of 1.

SGP: a simple graphics package

This paper presents a simple scheme for manipulating graphical information. The basic idea is to generate a user-readable, and therefore editable, file of device-independent picture descriptions. This file would typically be created by a set of FORTRAN-callable subroutines, each having a specific function (draw a vector, draw an axis, write text), but could be created in more direct ways by a user sufficiently familiar with the file structure. Once such a file has been created and perhaps examined and edited, a postprocessor may be selected to translate the file into the device-dependent instructions necessary to produce a picture on a specific device. If the file is saved, a different postprocessor could obviously be used later to generate the same picture on another device.

Canard-Wing Shape Optimization with Aerodynamic Requirements

THIS paper demonstrates a numerical technique for canard-wing shape optimization at two operating conditions. For purposes of simplicity, a mean surface wing paneling code1 is employed for the aerodynamic calculations. The optimization procedures2 are based on the method of feasible directions. The shape functions for describing thickness, camber, and twist are based on polynomial representations. The primary design requirements imposed restrictions on the canard and wing volumes and on the lift coefficients at the operating conditions. Results indicate that significant improvements in minimum drag and lift-to-drag ratio are possible with reasonable aircraft geometries. Calculations were done for supersonic speeds with Mach numbers ranging from 1 to 6. Planforms were mainly of a delta shape with aspect ratio of 1, with the canard and wing in the same plane. Contents The shape functions for the thickness,3 and camber, and twist4 were each expressed as a ten-term polynomial function of the Cartesian coordinates defined in the canard-wing plane. The coefficients of these polynomials had the status of optimization variables. Volumes of the wing and canard are constrained to specified values and correspond to the volumes of the base configuration in which both the canard and wing have 5% parabolic sections. The study initially explored minimizing wave drag through wing-canard shaping by calculating the optimum thickness distribution with zero camber and twist. The results are shown in Fig. 1 for two canard sizes as well as for a wing-along case. Wave drag reductions of up to 50%, relative to the base configuration with constant thickness ratio airfoils, are feasible while still meeting canard-wing internal volume limits. The improvements in drag become more pronounced at high Mach numbers. The optimum shapes were found to be similar to those reported by Strand 3 for the wing-alone case, indicating that the presence of the canard does not introduce significant perturbations in the shape functions. The second study explored the reduction in drag due to lift through optimization of the camber and twist of the lifting surface with zero thickness (Fig. 2). Again, results are shown for two canard sizes as well as for a wing-alone case. The configurations with subsonic leading edges show drag reductions of up to 36% by use of optimum camber and twist of the lifting surface. The potential for improvement tends to diminish with increasing Mach number in contrast with the results for the optimization of thickness. Figure 3 shows, in terms of LID, the data of Fig. 2 and includes a simple flat