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Slack variable to transform optimal control problem with scalar inequality constraint on state variables into unconstrained problem of higher dimension
Variable aspect ratio and variable sweep delta wing planforms for supersonic aircraft
Slack variable to transform optimal control problem with scalar inequality constraint on state variables into unconstrained problem
Variable dimension FORTRAN 4 version of the Automatic Synthesis Program (ASP) compensates for limitations within the program itself. Improvements are versatile programming language, convenient input/output format, new subprograms, variable dimensioning, and efficient storage.
A study was conducted to determine the flight characteristics and wing deployment transients for a variable geometry spacecraft concept having a hypersonic lift-to-drag ratio near 1.0, and employing fold-down wings. Unpowered flight conditions were considered throughout the study. The body of the spacecraft uses a trapezoidal cross section. The variable geometry wings, stowed in the sides of the vehicle, are deployed at transonic speeds.
Using only a one-dimensional subscripted variable, a FORTRAN computer subprogram was developed to linearly interpolate tabulated data of functions of four or less variables. The primary motivation was for faster computation.
The procedure to be followed in determining the thermal performance of a variable conductance heat pipe is documented. The nominal one-inch-diameter aluminum pipe is of a cold reservoir type whose overall length is nine feet. It has a capacity of 2 to 4 kW's equivalent to 8 to 16 kW-ft and an overall temperature control range of 50 to 95 F. Initial tests will be conducted with the pipe charged with ammonia to determine its capacity limits. Following introduction of the noncondensible gas (nitrogen), the variable conductance features of the pipe will be used.
An analytical model was developed to predict the performance characteristics of axisymmetric single-nozzle jet pumps with variable area mixing tubes. The primary flow may be subsonic or supersonic. The computer program uses integral techniques to calculate the velocity profiles and the wall static pressures that result from the mixing of the supersonic primary jet and the subsonic secondary flow. An experimental program was conducted to measure mixing tube wall static pressure variations, velocity profiles, and temperature profiles in a variable area mixing tube with a supersonic primary jet. Static pressure variations were measured at four different secondary flow rates. These test results were used to evaluate the analytical model. The analytical results compared well to the experimental data. Therefore, the analysis is believed to be ready for use to relate jet pump performance characteristics to mixing tube design.
The effort and results of a program to determine and study the critical process variables associated with the manufacture of aerospace, hermetically-sealed, nickel-cadmium cells are reported. During the period, the impregnation/polarization process variable study was brought to a close with the completion of a series of related experiments. The results of the experiments are summarized. During this period, a general characterization of cell separator materials was initiated. The major conclusions resulting from the characterization of materials are included.
A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.
Multispectral scanner data are potentially useful in a variety of remote sensing applications. Large-area surveys of earth resources carried out by automated recognition processing of these data are particularly important. However, the practical realization of such surveys is limited by a variability in the scanner signals that results in improper recognition of the data. This paper discusses ways by which some of this variability can be removed from the data by preprocessing with resultant improvements in recognition results.
Review of several variable-rate optical transmission schemes over an earth-to-space link which neutralize the effects of atmospheric turbulence. These adaptive laser communication systems exploit atmospheric reciprocity and the relatively long coherence time of the turbulence to monitor the time-varying state of the earth-to-space channel by using a satellite beacon and making appropriate measurements at the ground terminal. Optimal variable-rate strategy based on this channel-state information results is considerably improved performance in comparison with nonadaptive optical communication systems.
A relatively simple method is presented for including the effect of variable entropy at the boundary-layer edge in a heat transfer method developed previously. For each inviscid surface streamline an approximate shockwave shape is calculated using a modified form of Maslen's method for inviscid axisymmetric flows. The entropy for the streamline at the edge of the boundary layer is determined by equating the mass flux through the shock wave to that inside the boundary layer. Approximations used in this technique allow the heating rates along each inviscid surface streamline to be calculated independent of the other streamlines. The shock standoff distances computed by the present method are found to compare well with those computed by Maslen's asymmetric method. Heating rates are presented for blunted circular and elliptical cones and a typical space shuttle orbiter at angles of attack. Variable entropy effects are found to increase heating rates downstream of the nose significantly higher than those computed using normal-shock entropy, and turbulent heating rates increased more than laminar rates. Effects of Reynolds number and angles of attack are also shown.
Heat pipe technology pertinent to the design and application of self-controlled, variable conductance heat pipes for spacecraft thermal control is discussed. Investigations were conducted to: (1) provide additional confidence in existing design tools, (2) to generate new design tools, and (3) to develop superior variable conductance heat pipe designs. A computer program for designing and predicting the performance of the heat pipe systems was developed.
An investigation was made in the high Mach number test section of the Langley Unitary Plan wind tunnel on a variable-geometry high hypersonic performance spacecraft concept at Mach numbers from 2.30 to 4.63. The basic lifting body is designed for hypersonic lift-drag ratio near 3.0. The variable-geometry feature is a single-pivot two-position high wing which is deployed at subsonic speeds to improve vehicle landing characteristics. For the present investigation the wing was maintained in a stowed position, and the effects of horizontal stabilizer dihedral, elevon control effectiveness, and the addition of either a conventional single vertical tail or dorsal-fin-type vertical stabilizers on the longitudinal and lateral-directional stability and control characteristics were studied.
A method for solving a general class of three-dimensional boundary layer flows is developed. In the development, Levy-Lees variables are extended to three dimensions and equations are placed in these similarity variables. An implicit finite difference scheme which is stable for negative transverse velocities is used to solve these equations. The method developed is applied to obtain solutions for sharp and spherically blunted circular cones at angle of attack. Longitudinal and transverse distributions are presented for these cases. Good agreement is found with the results obtained by other numerical schemes and the experimental data of Tracy, for sharp circular cones at angle of attack. For spherically blunted cones at angle of attack, the results are in good agreement with axisymmetric sphere results up to the region where spherical symmetry holds.
The time-dependent, turbulent mean-flow, Reynolds stress, and heat flux equations in mass-averaged dependent variables are presented. These equations are given in conservative form for both generalized orthogonal and axisymmetric coordinates. For the case of small viscosity and thermal conductivity fluctuations, these equations are considerably simpler than the general Reynolds system of dependent variables for a compressible fluid and permit a more direct extension of low speed turbulence modeling to computer codes describing high speed turbulence fields.
An understanding of the principles which govern variable speed drive operation is discussed for successful drive application. The fundamental factors of torque, speed ratio, and power as they relate to drive selection are discussed. The basic types of variable speed drives, their operating characteristics and their applications are also presented.