Search NASA⌕ Search

SEARCH · Search NASA

Results for “FORMULAS - STRUTS - EULER”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

Formulas for propellers in yaw and charts of the side-force derivative

General formulas are given for propellers for the rate of change of side-force coefficient with angle of yaw and for the rate of change of pitching-moment coefficient with angle of yaw. Charts of the side-force derivative are given for two propellers of different plan form. The charts cover solidities of two to six blades and single and dual rotation. The blade angle ranges from 15 degrees or 20 degrees to 60 degrees.

Ribner, Herbert S↗

Methods and formulas for calculating the strength of plate and shell constructions as used in airplane design

This report is a compilation of previously published articles on formulas and methods of calculation for the determination of the strength and stability of plate and shell construction as employed in airplane design. In particular, it treats the problem of isotropic, orthotopic, and stiffened rectangular plates, thin curved panels, and circular cylinders under various loading conditions. The purpose of appending the pertinent literature references following the subjects discussed was to facilitate a comprehensive study of the treated problems.

Heck, O S↗

Exponential Formulae and Effective Operations

One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).

Mielnik, Bogdan↗

Formulas Pertinent to the Calculation of Flow-Field Effects at Supersonic Speeds Due to Wing Thickness

Expressions based on linearized supersonic-flow theory are derived for the perturbation velocity potential in space due to wing thickness for rectangular wings with biconvex airfoil sections and for arrow, delta, and quadrilateral wings with wedge-type airfoil sections. The complete range of supersonic speeds is considered subject to a minor aspect-ratio-Mach number restriction for the rectangular plan form and to the condition that the trailing edge is supersonic for the sweptback wings. The formulas presented can be utilized in determining the induced-flow characteristics at any point in the field and are readily adaptable for either numerical computation or analytical determination of any velocity components desired.

Margolis, Kenneth↗

A Study of Supersonic Surface Sources: The Ffowcs Williams-Hawkings Equation and the Kirchhoff Formula

In this paper we address the mathematical problem of noise generation from high speed moving surfaces. The problem we are solving is the linear wave equation with sources on a moving surface. The Ffowcs Williams-Hawkings (FW-H) equation as well as the govern- ing equation for deriving the Kirchhoff formula for moving surfaces are both this type of partial differential equation. We give a new exact solution of this problem here in closed form which is valid for subsonic and supersonic motion of the surface but it is particularly suitable for supersonically moving surfaces. This new solution is the simplest of all high speed formulations of Langley and is denoted formulation 4 following the tradition of numbering of our major results for the prediction of the noise of rotating blades. We show that for a smooth surface moving at supersonic speed, our solution has only removable singularities. Thus it can be used for numerical work.

Farassat, F.↗

Flight Performance Handbook for Orbital Operations: Orbital Mechanics and Astrodynamics Formulae, Theorems, Techniques, and Applications

This handbook provides parametric data useful both to the space vehicle designer and mission analyst. It provides numerical and analytical relationships between missions and gross vehicle characteristics as a function of performance parameters. The effects of missile constraints and gross guidance limitations plus operational constraints such as launch site location, tracking net location, orbit visibility and mission on trajectory and orbit design parameters are exhibited. The influence of state-of- the-art applications of solar power as compared to future applications of nuclear power on orbit design parameters, such as eclipse time, are among the parameters included in the study. The principal aim, however, is in providing the analyst with useful parametric design information to cover the general area of earth satellite missions in the region of near-earth to cislunar space and beyond and from injection to atmospheric entry and controlled descent. The chapters are organized around the central idea of orbital operations in the 1961-1969 era with emphasis on parametric flight mechanics studies for ascent phase and parking orbits, transfer maneuvers, rendezvous maneuver, operational orbit considerations, and operational orbit control. The results are based almost entirely on the principles of flight and celestial mechanics. Numerous practical examples have been worked out in detail. This is especially important where it has been difficult or impossible to represent all possible variations of the parameters. The handbook contains analytical formulae and sufficient textual material to permit their proper use. The analytic methods consist of both exact and rapid, approximate methods. Scores of tables, working graphs and illustrations amplify the mathematical models which, together with important facts and data, cover the engineering and scientific applications of orbital mechanics. Each of the five major chapters are arranged to provide a rapid review of an entire astrodynamic subject. By the use of compact graphical and tabular presentation the full scope of the material is made available in an easy-to-use style. Throughout the volume the analyst is shown, by means of suitable introductions, notes, authoritative examples, and cross-references the vital interrelation of the various orbital mechanics topics in the general field of earth satellites and satellite rendezvous. The handbook is designed to give the analyst rapid, reliable access to the mathematics of orbital mechanics needed for virtually any working requirements.

Ambrosio, Alphonso↗

Test of a General Formula for Black Hole Gravitational Wave Kicks

Although the gravitational wave kick velocity in the orbital plane of coalescing black holes has been understood for some time, apparently conflicting formulae have been proposed for the dominant outof- plane kick, each a good fit to different data sets. This is important to resolve because it is only the out-of-plane kicks that can reach more than 500 km s-l and can thus eject merged remnants from galaxies. Using a different ansatz for the out-of-plane kick, we show that we can fit almost all existing data to better than 5%. This is good enough for any astrophysical calculation and shows that the previous apparent conflict was only because the two data sets explored different aspects of the kick parameter space.

van Meter, James R.↗

Evaluation of AMSOIL® -ANT PGW Coolant Formula Change and Super Space AMSOIL Development

AMSOIL ® Propylene Glycol Water (PGW), is the baselined internal thermal control fluid for multiple manned spacecraft including Gateway (HALO, IHAB, and ALM modules) and Orion. The use of AMSOIL-ANT PGW was originally validated through extensive NASA/Collins materials-compatibility testing (circa 2008–2015). However, in late 2019, AMSOIL implemented an unannounced change in its PG inhibitor package. Because of this reformulation, concerns around materials compatibility arose. Therefore, NASA initiated corrosion rate and coolant stability testing in 2024. Results showed that the reformulated AMSOIL PG produced substantially elevated corrosion rates in aluminum alloys (about two times when compared to the original AMSOIL PG formula) accompanied by visible surface degradation. Coolant stability testing indicated accelerated propylene-glycol breakdown as well, with glycolate levels about nine times higher than the original formulation. Based on these findings, NASA Materials & Processes and Thermal Control Systems groups have baselined the use of the original PGW chemistry for all spacecraft use. In response, AMSOIL produced a reformulated variant, “Super Space AMSOIL” (ANT-SSA), compliant with MPCV 70156.This paper documents the reformulation testing completed, details on the formulation change, and the development of Super Space AMSOIL.

Woody Beringer↗

Evaluation of AMSOIL ® -ANT PGW Coolant Formula Change and Super Space AMSOIL ® Development

AMSOIL ® Propylene Glycol Water (PGW), is the baselined internal thermal control fluid for multiple manned spacecraft including Gateway (HALO, IHAB, and ALM modules) and Orion. The use of AMSOIL-ANT PGW was originally validated through extensive NASA/Collins materials-compatibility testing (circa 2008–2015). However, in late 2019, AMSOIL implemented an unannounced change in its PG inhibitor package. Because of this reformulation, concerns around materials compatibility arose. Therefore, NASA initiated corrosion rate and coolant stability testing in 2024. Results showed that the reformulated AMSOIL PG produced substantially elevated corrosion rates in aluminum alloys (about two times when compared to the original AMSOIL PG formula) accompanied by visible surface degradation. Coolant stability testing indicated accelerated propylene-glycol breakdown as well, with glycolate levels about nine times higher than the original formulation. Based on these findings, NASA Materials & Processes and Thermal Control Systems groups have baselined the use of the original PGW chemistry for all spacecraft use. In response, AMSOIL produced a reformulated variant, “Super Space AMSOIL” (ANT-SSA), compliant with MPCV 70156.This paper documents the reformulation testing completed, details on the formulation change, and the development of Super Space AMSOIL.

David Brockett↗

Wind tunnel tests of correction formula for wings of large span

The theory (wing experiments in an artificial air stream are subject to error, due to the fact that the wing is not situated in an unlimited body of air) by means of which the given drag correction was obtained, was based on various assumptions (e.g., elliptical distribution of lift) which do not always hold true. For this reason it was desirable to test the equation for the additional drag in regard to its reliability and range of application.

WINGS - WIND TUNNEL TESTS↗

A few more mechanical-flight formulas without the aid of polar diagrams

The reliability of the assumption of a parabolic shape of the polar curve is investigated and found satisfactory for all practical purposes. It is further shown that the aerodynamically best possible or "ideal" airplane is produced on this assumption. Lastly, detailed suggestions are given on the possibilities of application of this method of calculation. It especially simplifies the design and evaluation of structural changes and the determination of the limits of technical possibilities. The present report deals only with the relations of the airfoils. The mutual action of the airfoils, engine and propeller will be treated in a subsequent report.

FORMULAS - PERFORMANCE↗