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At least 991 records · Page 55

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NASA NTRS1972

The effect of multiple encounters on short period comet orbits

The observed orbital elements of short period comets are found to be consistent with the hypothesis of derivation from long period comets as long as two assumptions are made. First, the distribution of short period comets has been randomized by multiple encounters with Jupiter and second, the short period comets have lower velocities of encounter with Jupiter than is generally expected. Some 16% of the observed short period comets have lower encounter velocities than is allowed mathematically using Laplace's method. This may be due to double encounter processes with Jupiter and Saturn, or as a result of prolonged encounters. The distribution of unobservable short period comets can be inferred in part from the observed comets. Many have orbits between Jupiter and Saturn with somewhat higher inclinations than those with perihelions near the earth. Debris from those comets may form the major component of the zodiacal dust.

Lowrey, B. E.↗

NASA NTRS1972

A critical discussion of theories of flame spread across solid and liquid fuels.

Mathematical descriptions of flames spreading over liquid and solid fuels are obtained, using basic assumptions derived from observations or physical reasoning. A review of existing theories shows that they are incomplete in that they either treat an uncoupled problem of the condensed phase where the spreading rate and heat flux at the surface are given, or they merely determine the spreading rate in terms of a new vaguely defined eigenvalue. An important difference between the liquid and solid cases, due to convection, is pointed out, and it is shown that solid-fuel flame-spread theories which claim to apply to the liquid case, in reality do not apply to it. A mathematical formulation and a method of solution are presented for the phenomenon of flame spread over solid fuels with forward heat conduction in both the solid and the gas. The method uses an energy integral over the field to determine the spreading rate in terms of the basic properties of the fuel and air.

Sirignano, W. A.↗

NASA NTRS1973

The effect of multiple encounters on short-period comet orbits.

The observed orbital elements of short-period comets are found to be consistent with the hypothesis of derivation from long-period comets as long as two assumptions are made. First, the distribution of short-period comets has been randomized by multiple encounters with Jupiter and second, the short-period comets have low velocities of encounter with Jupiter. Some 16% of the observed short-period comets have lower encounter velocities than is allowed mathematically using Laplace's method. This may be due to double-encounter processes with Jupiter and Saturn. The distribution of unobservable short-period comets can be inferred in part from the observed comets. It is shown that there may be many short-period comets having orbits between Jupiter and Saturn with somewhat higher inclinations than those with perihelia near the earth.

Lowrey, B. E.↗

NASA NTRS1973

Synthesis of vibration dampers

A method which uses a mathematical accelerometer is proposed for determining the 3rd derivative of the displacement in shock absorbers.

Kamayev, V. A.↗

NASA NTRS1978

A simple method for designing structural models with closely spaced modes of vibration

A simple method for designing a mathematical model with closely spaced vibration modes is described. The design process begins with a reference model having specified geometry, continuous inertia and stiffness distributions, and degrees of freedom, all of which remain unchanged. Two natural frequencies of this model are then forced together by means of systematic perturbation of the model's discrete inertia and stiffness parameters. There is only one eigenvalue solution per design cycle, and the gradient vector is calculated directly from the resulting modal quantities. The minimization procedure employed is unconstrained. As applications, a cantilevered plane grid model with five degrees of freedom and a bending-torsion-oscillator with eleven degrees of freedom are treated.

Hallauer, W. L., Jr.↗

NASA NTRS1983

Aerothermal modeling, phase 1. Volume 1: Model assessment

Phase 1 was conducted as part of the overall NASA Hot Section Technology (HOST) Program. The purpose of this effort was to determine the predictive accuracy of and the deficiencies within the various analytical modules comprising the overall combustor aerothermal model used at General Electric, as well as to formulate recommendations for improvement where needed. This effort involved the assembly of a benchmark quality data base from selected available literature, and from General Electric engine and combustor component test data. This data base was supplemented with additional definitive data obtained from an experimental test program conducted as part of the Phase 1 effort. Using selections from this data base, assessment studies were conducted to evaluate the various modules. Assessment of the internal flow module was conducted using 2-D parabolic and ellipitic, as well as 3-D elliptic internal flow calculations of definitive test data selected from the assembled data base. The 2-D assessment provided methodical examination of the mathematical techniques and the physical submodules, while the 3-D assessment focused on usefulness as a design tool. Calculations of combustor linear metal temperatures, pressure loss performance, and airflow distribution were performed using aerothermal modules which were in general use for many years at General Electric. The results of these assessment provided for the identification of deficiencies within the modules. The deficiencies were addressed in some detail providing a foundation on which to formulate a prioritized list of recommendations for improvement.

Kenworthy, M. J.↗

NASA NTRS1985

Generation of Surface Coordinates by Elliptic Partial Differential Equations

The problem of generating spatial coordinates by numerical methods through carefully selected mathematical models is of current interest both in mechanics and physics. The problem of generation of a desired system of coordinates in a given surface was considered, which essentially is an effort directed to the problem of grid generation in a two-dimensional non-Euclidean space. The mathematical model selected for this purpose is based on the formulae of Gauss for a surface. The proposed equations can be used to generate a new coordinate system from the data of an already given coordinate system in a surface. If the coefficients of the first and second fundamental forms have been given, then the proposed equations can be used to generate a surface satisfying the given data (surface fitting). The proposed equations can also be used to generate surfaces in the space between two arbitrary given surfaces, thus providing 3D grids in an Euclidean space.

Warsi, Z. U. A.↗

NASA NTRS1985

Statement of contamination problem

Space station contamination information is given. There are five major areas in which there are task requirements: (1) potential contaminants need to be identified, i.e., both the sources and types of contaminants, (2) the scope and magnitude of contaminant effects need to be determined, i.e., toxicological effects, microbacteriological effects and impurities, (3) mathematical models for predictive methods need to be developed. (4) state-of-the-art and advanced technologies for monitoring contaminants and for methods of decontamination need to be identified, and (5) automated monitoring and control systems need to be designed.

Hoffler, W.↗

NASA NTRS1986

Numerical study of combustion processes in afterburners

Mathematical models and numerical methods are presented for computer modeling of aeroengine afterburners. A computer code GEMCHIP is described briefly. The algorithms SIMPLER, for gas flow predictions, and DROPLET, for droplet flow calculations, are incorporated in this code. The block correction technique is adopted to facilitate convergence. The method of handling irregular shapes of combustors and flameholders is described. The predicted results for a low-bypass-ratio turbofan afterburner in the cases of gaseous combustion and multiphase spray combustion are provided and analyzed, and engineering guides for afterburner optimization are presented.

Zhou, Xiaoqing↗

NASA NTRS1986

Three-dimensional vibrations of twisted cantilevered parallelepipeds

A large number of references dealing with the vibrations of twisted, cantilevered beams and plates exist in the literature. These works show considerable disagreement concerning the effect of twist angle upon frequencies. The present work is the first three-dimensional study of the problem. Displacement components are assumed in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. The Ritz method is then applied. Accurate frequencies are calculated for twisted thick plates and are compared with ones obtained recently by others using beam, shell, and finite element theory.

Leissa, A.↗

NASA NTRS1988

Monte Carlo particle-trajectory models for neutral cometary gases. I - Models and equations. II - The spatial morphology of the Lyman-alpha coma

The mathematical derivations of various methods employed in the Monte Carlo particle-trajectory model (MCPTM) are presented, and the application of the MCPTM to the calculation of the photochemical heating of the inner coma through the partial thermalization of cometary hydrogen atoms produced by the photodissociation of water is discussed. This model is then used to explain the observed morphology of the spatially extended Ly-alpha comas of comets. The rocket and Skylab images of the Ly-alpha coma of Comet Kohoutek are examined.

Combi, Michael R.↗

NASA NTRS1990

Applications of different design methodologies in navigation systems and development at JPL

The NASA/JPL deep space navigation system consists of a complex array of measurement systems, data processing systems, and support facilities, with components located both on the ground and on-board interplanetary spacecraft. From its beginings nearly 30 years ago, this system has steadily evolved and grown to meet the demands for ever-increasing navigation accuracy placed on it by a succession of unmanned planetary missions. Principal characteristics of this system are its capabilities and great complexity. Three examples in the design and development of interplanetary space navigation systems are examined in order to make a brief assessment of the usefulness of three basic design theories, known as normative, rational, and heuristic. Evaluation of the examples indicates that a heuristic approach, coupled with rational-based mathematical and computational analysis methods, is used most often in problems such as orbit determination strategy development and mission navigation system design, while normative methods have seen only limited use is such applications as the development of large software systems and in the design of certain operational navigation subsystems.

Thurman, S. W.↗

NASA NTRS1991

Determination of alloy content from plume spectral measurements

The mathematical derivation for a method to determine the identities and amounts of alloys present in a flame where numerous alloys may be present is described. This method is applicable if the total number of elemental species from all alloys that may be in the flame is greater than or equal to the total number of alloys. Arranging the atomic spectral line emission equations for the elemental species as a series of simultaneous equations enables solution for identity and amount of the alloy present in the flame. This technique is intended for identification and quantification of alloy content in the plume of a rocket engine. Spectroscopic measurements reveal the atomic species entrained in the plume. Identification of eroding alloys may lead to the identification of the eroding component.

Madzsar, George C.↗

NASA NTRS1991

Determination of alloy content from plume spectral measurements

The mathematical derivation for a method to determine the identities and amounts of alloys present in a flame where numerous alloys may be present is described. This method is applicable if the total number of elemental species from all alloys that may be in the flame is greater than or equal to the total number of alloys. Arranging the atomic spectral line emission equations for the elemental species as a series of simultaneous equations enables solution for identify and amount of the alloy present in the flame. This technique is intended for identification and quantification of alloy content in the plume of a rocket engine. Spectroscopic measurements reveal the atomic species entrained in the plume. Identification of eroding alloys may lead to the identification of the eroding component.

Madzsar, George C.↗

NASA NTRS1989

Space biology initiative program definition review. Trade study 3: Hardware miniaturization versus cost

The optimum hardware miniaturization level with the lowest cost impact for space biology hardware was determined. Space biology hardware and/or components/subassemblies/assemblies which are the most likely candidates for application of miniaturization are to be defined and relative cost impacts of such miniaturization are to be analyzed. A mathematical or statistical analysis method with the capability to support development of parametric cost analysis impacts for levels of production design miniaturization are provided.

Jackson, L. Neal↗

NASA NTRS1922

Utilization conditions of different types of airplanes

This report presents examples of different methods of comparing aircraft mathematically. In the example given a biplane and monoplane are compared as to what speed one type of airplane is better at than another.

AIRPLANES - CONSTRUCTION↗

NASA NTRS1994

More About The Enhanced Projection-And-Assembly Method

Report discusses enhanced projection-and-assembly (EP&A) method and its application to Galileo spacecraft. EP&A method and its predecessor, projection-and-assembly (P&A) method, described in "Enhanced Method of Reduction of Mathematical Models" (NPO-18402), and "Two-Stage Reduction of Dynamical Models" (NPO-18723).

Lee, Allen Y.↗

NASA NTRS1993

Computer program for analysis of high speed, single row, angular contact, spherical roller bearing, SASHBEAN. Volume 2: Mathematical formulation and analysis

Spherical roller bearings have typically been used in applications with speeds limited to about 5000 rpm and loads limited for operation at less than about 0.25 million DN. However, spherical roller bearings are now being designed for high load and high speed applications including aerospace applications. A computer program, SASHBEAN, was developed to provide an analytical tool to design, analyze, and predict the performance of high speed, single row, angular contact (including zero contact angle), spherical roller bearings. The material presented is the mathematical formulation and analytical methods used to develop computer program SASHBEAN. For a given set of operating conditions, the program calculates the bearings ring deflections (axial and radial), roller deflections, contact areas stresses, depth and magnitude of maximum shear stresses, axial thrust, rolling element and cage rotational speeds, lubrication parameters, fatigue lives, and rates of heat generation. Centrifugal forces and gyroscopic moments are fully considered. The program is also capable of performing steady-state and time-transient thermal analyses of the bearing system.

Aggarwal, Arun K.↗