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Various methods are presented and assessed for approximating the aerodynamic forces so that the State Space formulation and off-the-imaginary axis analysis are retained. The advantages of retaining these features are considerable, not only in simplifying the flutter analysis, but especially for more advanced applications such as optimal design of active control in which the flutter is merely a constraint to the optimization problem.
A nonlinear boundary value problem governing the subsonic flow in a single, extended, blade passage region of a high-deflection, two dimensional, oscillating cascade is derived. The blades are assumed to be undergoing identical harmonic motions of small amplitude with constant phase angle between the motion of adjacent blades. An asymptotic perturbation approach is used to determine the velocity potential. This formulation can be used in the numerical determination of unsteady potential and thus the unsteady aerodynamic force and moment under various combinations of cascade and flow parameters.
A nonlinear perturbation theory is formulated for the solution of the multicomponent equations of energy, mass, and momentum conservation in the atmosphere. The theory is three-dimensional and includes the effects of heat conduction and advection, viscosity, ion drag, and diffusion. The theory is described as a superposition of mathematical modes obtained by expanding the physical quantities into vector and spherical harmonics. The coupling between the various modes, both linear and nonlinear, is included. The theory provides a basis for the treatment of the thermosphere and its interaction with the lower atmosphere, where 'mode coupling' is most important. As an example, a comparison is presented between one-dimensional and three-dimensional calculations of the fundamental mode of the diurnal component in the thermosphere. Coupling between the lowest modes is considered to describe the physical conditions of the lower thermosphere where inertia and Coriolis forces become dominant over the ion-drag and viscous forces. In this region, the latitude structures of the temperature, wind field, and diffusively controlled oxygen are shown to change significantly.
A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.
Contact-impact problems involving finite deformation axisymmetric membranes are solved by the finite element method with explicit time integration. The formulation of the membrane element and the contact constraint conditions are discussed. The hyperelastic, compressible Blatz and Ko material is used to model the material properties of the membrane. Two example problems are presented.
Consumables models required for the mission planning and scheduling function are formulated. The relation of the models to prelaunch, onboard, ground support, and postmission functions for the space transportation systems is established. Analytical models consisting of an orbiter planning processor with consumables data base is developed. A method of recognizing potential constraint violations in both the planning and flight operations functions, and a flight data file storage/retrieval of information over an extended period which interfaces with a flight operations processor for monitoring of the actual flights is presented.
Routine determination of inviscid subsonic flow fields about wing-body-tail configurations employing a Green's function approach for numerical solution of the perturbation velocity potential equation is successfully extended into the high subsonic subcritical flow regime and into the shock-free supersonic flow regime. A modified Green's function formulation, valid throughout a range of Mach numbers including transonic, that takes an explicit accounting of the intrinsic nonlinearity in the parent governing partial differential equations is developed. Some considerations pertinent to flow field predictions in the transonic flow regime are discussed.
Predictions of wear on contemporary copper-based brake material sliding against 17-22 AS grade steel, wear testing equipment, formulation of wear, and test results are discussed. An initial investigation of worn surfaces of the brake material and a mating steel rotor was carried out. A wear model proposed suggests initiation of cracks at a hard particle inclusion site in the surface layer of the brake material; crack propagation allows particles to be removed by intersection of cracks. Mutual relations between sliding variables, load, time, hardness, and surface temperature are studied. Empirical formulas are exhibited.
The problem of calculating the steady-state free-electron energy distribution in a hydrogen gas is considered in order to study departures of that distribution from a Maxwellian at sufficiently low degrees of ionization. A model kinetic equation is formulated and solved analytically for the one-particle electron distribution function in a steady-state partially ionized hydrogen gas, and it is shown that the formal solution can be accurately approximated by using the WKB method. The solutions obtained indicate that the high-energy tail of the distribution is susceptible to distortion by imbalanced inelastic collisions for ionization fractions not exceeding about 0.1 and that such departures from a Maxwellian can lead to significant changes in the collisional excitation and ionization rates of ground-state hydrogen atoms. Expressions for the electron-hydrogen collision rates are derived which explicitly display their dependence on the hydrogen departure coefficients. The results are applied in order to compare self-consistent predictions with those based on the a priori assumption of a Maxwellian distribution for models of the thermal ionization equilibrium of hydrogen in the optically thin limit, spectral-line formation by a gas consisting of two-level atoms, and radiative transfer in finite slabs by a gas of four-level hydrogen atoms.
The theoretical fundamentals and mathematical definitions for calculations involved with dual polarized radio links are given. Detailed derivations and results are discussed for several formulations applied to a general dual polarized radio link.
The Kirchhoff integral formulation is evaluated for its effectiveness in quantitatively predicting the sound radiated from an oscillating airfoil whose chord length is comparable with the acoustic wavelength. A rigid airfoil section was oscillated at samll amplitude in a medium at rest to produce the sound field. Simultaneous amplitude and phase measurements were made of surface pressure and surface velocity distributions and the acoustic free field. Measured surface pressure and motion are used in applying the theory, and airfoil thickness and contour are taken into account. The result was that the theory overpredicted the sound pressure level by 2 to 5, depending on direction. Differences are also noted in the sound field phase behavior.
A recursively formulated, first-order, semianalytic artificial satellite theory, based on the generalized method of averaging is presented in two volumes. Volume I comprehensively discusses the theory of the generalized method of averaging applied to the artificial satellite problem. Volume II presents the explicit development in the nonsingular equinoctial elements of the first-order average equations of motion. The recursive algorithms used to evaluate the first-order averaged equations of motion are also presented in Volume II. This semianalytic theory is, in principle, valid for a term of arbitrary degree in the expansion of the third-body disturbing function (nonresonant cases only) and for a term of arbitrary degree and order in the expansion of the nonspherical gravitational potential function.
The Eikonal equation of geometrical optics and a weak scattering wave-optical formulation are separately used to calculate first- and second-order effects of turbulence on radio propagation through an atmosphere with uniformly varying average refractive index combined with a random component due to turbulence. The extent to which perturbations in bending angle and Doppler frequency affects atmospheric profiles of temperature and pressure derived from Doppler measurements is considered. The determination of the power spectra of turbulence effects, the contribution of different terms, and the use of the spectra for studying planetary atmospheres are discussed.
A definition of the level C requirements for onboard maneuver targeting software is provided. Included are revisions of the level C software requirements delineated in JSC IN 78-FM-27, Proximity Operations Software; Level C Requirements, dated May 1978. The software supports the terminal phase midcourse (TPM) maneuver, braking and close-in operations as well as supporting computation of the rendezvous corrective combination maneuver (NCC), and the terminal phase initiation (TPI). Specific formulation is contained here for the orbit targeting specialist function including the processing logic, linkage, and data base definitions for all modules. The crew interface with the software is through the keyboard and the ORBIT-TGT display.
Procedures are given for formulating, blending, and applying MS-74 white thermal-control coating and CC-1 primer to spacecraft structures. Improved ultraviolet stability, higher emittance and low absorptivity, and enhanced adhesion characteristics result from the revised procedures.
Lumped volume dynamic equations are derived using an energy state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.
A class of simple climate models including those of the Budyko-Sellers type are formulated from a variational principle. A functional is constructed for the zonally averaged mean annual temperature field such that extrema of the functional occur when the climate satisfies the usual energy-balance equation. Local minima of the functional correspond to stable solutions while saddle points correspond to unstable solutions. The technique can be used to construct approximate solutions from trial functions and to carry out finite-amplitude stability analyses. A spectral example is given in explicit detail.
The consistent formulation of the governing nonlinear equations of motion for a coupled rotor/support system is presented. Rotor/support coupling is clearly documented by enforcing dynamic equilibrium between the rotor and the moving flexible support. The nonlinear periodic coefficient equations of motion are applicable to both coupled rotor/fuselage aeroelastic problems of helicopters in hover or forward flight and coupled rotor/tower dynamics of a large horizontal axis wind turbine (HAWT). Finally, the equations of motion are used to study the influence of flexible supports and nonlinear terms on rotor aeroelastic stability and response of a large two-bladed HAWT.