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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1943

On a new method for calculating the potential flow past a body of revolution

A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.

Kaplan, Carl↗
NASA NTRS1978

A new blade element method for calculating the performance of high and intermediate solidity axial flow fans

A method is presented to design and predict the performance of axial flow rotors operating in a duct. The same method is suitable for the design of ducted fans and open propellers. The unified method is based on the blade element approach and the vortex theory for determining the three dimensional effects, so that two dimensional airfoil data can be used for determining the resultant force on each blade element. Resolution of this force in the thrust and torque planes and integration allows the total performance of the rotor, fan or propeller to be predicted. Three different methods of analysis, one based on a momentum flow theory; another on the vortex theory of propellers; and a third based on the theory of ducted fans, agree and reduce cascade airfoil data to single line as a function of the loading and induced angle of attack at values of constant inflow angle. The theory applies for any solidity from .01 to over 1 and any blade section camber. The effects of the duct and blade number can be determined so that the procedure applies over the entire range from two blade open propellers, to ducted helicopter tail rotors, to axial flow compressors with or without guide vanes, and to wind tunnel drive fans.

Borst, H. V.↗
NASA NTRS1976

Numerical method to calculate the induced drag or optimum loading for arbitrary non-planar aircraft

A simple unified numerical method applicable to non-planar subsonic aircraft has been developed for calculating either the induced drag for an arbitrary loading or the optimum aircraft loading which results in minimum induced drag. The method utilizes a vortex lattice representation of the aircraft lifting surfaces coupled with the classic equations and theorems for computing and minimizing induced drag. Correlation of results from the numerical method with non-planar solutions obtained from other more complex theories indicates very good agreement. Comparison of the induced-drag computations using the numerical method with experimental data for planar and non-planar configurations was also very good.

Blackwell, J. A., Jr.↗
NASA NTRS1952

Method for calculating lift distributions for unswept wings with flaps or ailerons by use of nonlinear section lift data

A method is presented which allows the use of nonlinear section lift data in the calculation of the spanwise lift distribution of unswept wings with flaps or ailerons. This method is based upon lifting line theory and is an extension to the method described in NACA rep. 865. The mathematical treatment of the discontinuity in absolute angle of attack at the end of the flap or aileron involves the use of a correction factor which accounts for the inability of a limited trigonometric series to represent adequately the spanwise lift distribution. A treatment of the apparent discontinuity in maximum section lift coefficient is also described. Simplified computing forms containing detailed examples are given for both symmetrical and asymmetrical lift distributions. A few comparisons of calculated characteristics with those obtained experimentally are also presented.

Sivells, James C↗
NASA NTRS1952

An Impulse-Momentum Method for Calculating Landing-Gear Contact Conditions in Eccentric Landings

An impulse-momentum method for determining impact conditions for landing gears in eccentric landings is presented. The analysis is primarily concerned with the determination of contact velocities for impacts subsequent to initial touchdown in eccentric landings and with the determination of the effective mass acting on each landing gear. These parameters determine the energy-absorption requirements for the landing gear and, in conjunction with the particular characteristics of the landing gear, govern the magnitude of the ground loads. Changes in airplane angular and linear velocities and the magnitude of landing-gear vertical, drag, and side impulses resulting from a landing impact are determined by means of impulse-momentum relationships without the necessity for considering detailed force-time variations. The effective mass acting on each gear is also determined from the calculated landing-gear impulses. General equations applicable to any type of eccentric landing are written and solutions are obtained for the particular cases of an impact on one gear, a simultaneous impact on any two gears, and a symmetrical impact. In addition a solution is presented for a simplified two-degree-of-freedom system which allows rapid qualitative evaluation of the effects of certain principal parameters. The general analysis permits evaluation of the importance of such initial conditions at ground contact as vertical, horizontal, and side drift velocities, wing lift, roll and pitch angles, and rolling and pitching velocities, as well as the effects of such factors as landing gear location, airplane inertia, landing-gear length, energy-absorption efficiency, and wheel angular inertia on the severity of landing impacts. -A brief supplementary study which permits a limited evaluation of variable aerodynamic effects neglected in the analysis is presented in the appendix. Application of the analysis indicates that landing-gear impacts in eccentric landings can be appreciably more severe than impacts in symmetrical landings with the same sinking speed. The results also indicate the effects of landing-gear location, airplane inertia, initial wing lift, side drift velocity, attitude, and initial rolling velocity on the severity of both initial and subsequent landing-gear impacts. A comparison of the severity of impacts on auxiliary gears for tricycle and quadricycle configurations is also presented.

Yntema, Robert T↗
NASA NTRS1987

An evaluation of higher-order modal methods for calculating transient structural response

The present study evaluates a higher-order modal method proposed by Leung for transient structural analysis entitled the force-derivative method. This method repeatedly integrates by parts with respect to time the convolution-integral form of the structural response to produce successively better approximations to the contribution of the higher modes which are neglected in the modal summation. Comparisons are made of the force-derivative, the mode-displacement, and the mode-acceleration methods for several numerical example problems for various times, levels of damping, and forcing functions. The example problems include a tip-loaded cantilevered beam and a simply-supported multispan beam. The force-derivative method is shown to converge to an accurate solution in fewer modes than either the mode-displacement or the mode-acceleration methods. In addition, for problems in which there are a large number of closely-spaced frequencies whose mode shapes have a negligible contribution to the response, the force derivative method is very effective in representing the effect of the important, but otherwise neglected, higher modes.

Camarda, Charles J.↗
NASA NTRS1985

A comparison of finite-difference and finite-element methods for calculating free edge stresses in composites

It is pointed out that edge delamination is a serious failure mechanism for laminated composite materials. Various numerical methods have been utilized in attempts to calculate the interlaminar stress components which precede delamination in a laminate. There are, however, discrepancies regarding the results provided by different methods, taking into account a finite-difference procedure, a perturbation procedure, and finite element approaches. The present investigation has the objective to assess the capacity of a finite difference method to predict the character and magnitude of the interlaminar stress distributions near an interface corner. A second purpose of the investigation is to determine if predictions by finite element method in-plane, interlaminar stress components near an interface corner represent actual laminate behavior.

Bauld, N. R., Jr.↗
NASA NTRS1982

A vortex wake capturing method for potential flow calculations

A method is presented for modifying finite difference solutions of the potential equation to include the calculation of non-planar vortex wake features. The approach is an adaptation of Baker's 'cloud in cell' algorithm developed for the stream function-vorticity equations. The vortex wake is tracked in a Lagrangian frame of reference as a group of discrete vortex filaments. These are distributed to the Eulerian mesh system on which the velocity is calculated by a finite difference solution of the potential equation. An artificial viscosity introduced by the finite difference equations removes the singular nature of the vortex filaments. Computed examples are given for the two-dimensional time dependent roll-up of vortex wakes generated by wings with different spanwise loading distributions.

Murman, E. M.↗
NASA NTRS2001

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections: Electron-Hydrogen Elastic Scattering - Part 1

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

Bhatia, A. K.↗
NASA NTRS1954

Method for calculating the rolling and yawing moments due to rolling for unswept wings with or without flaps or ailerons by use of nonlinear section lift data

The methods of NACA reports 865 and 1090 have been applied to the calculation of the rolling-moment and yawing-moment coefficients due to rolling for unswept wings with or without flaps or ailerons. The methods are based on lifting-line theory and allow the use of nonlinear section lift data. The method presented in this report permits calculations to be made somewhat beyond maximum lift for wings having no twist or continuous twist and employing airfoil sections which do not display large discontinuities in the lift curves. Calculations can be made up to maximum lift for wings with discontinuous twist such as that produced by partial-span flaps or ailerons, or both. Two calculated examples are presented in simplified computing forms in order to illustrate the procedures involve.

Martina, Albert P↗
NASA NTRS1981

A vortex-lattice method for calculating longitudinal dynamic stability derivatives of oscillating delta wings

A nonsteady vortex-lattice method is introduced for predicting the dynamic stability derivatives of a delta wing undergoing an oscillatory motion. The analysis is applied to several types of small oscillations in pitch. The angle of attack varied between + or - 1 deg, with the mean held at 0 deg when the flow was assumed to be attached and between + or - 1 deg and the mean held at 15 deg when both leading-edge separation and wake roll-up were included. The computed results for damping in pitch are compared with several other methods and with experiments, and are found to be consistent and in good agreement.

Levin, D.↗
NASA NTRS1988

A multi-element vortex lattice method for calculating the geometry and effects of a helicopter rotor wake in forward flight

A method is described for the analysis of the unsteady, incompressible potential flow associated with a helicopter rotor and it's wake in forward flight. This method is particularly useful in low advance ratio flight due to the major contribution, in the near field, of the deformed wake. The rotor geometry is prescribed and the unsteady wake geometry is computed from the local flow perturbation velocities. The wake is modeled as a full vortex lattice. The rotor geometry is arbitrary and several rotor blades can be represented. The unsteady airloads on the rotor blades are computed in the presence of the deformed rotor wake by a time-stepping technique. Solution for the load distribution on the blade surfaces is found by prescribing boundary conditions in a reference system which rotates with the blade tips. Transformation tensors are used to describe the contribution of the wake in the inertial system to the rotor in the rotating reference system. The effects of blade cyclic pitch variation are computed using a rotation tensor. The deformation of the wake is computed in the inertial frame. The wake is started impulsively from rest, allowing a natural convection of the wake with time.

Berry, John D.↗
NASA NTRS1989

'Nose method' of calculating critical cooling rates for glass formation

The use of the so-called 'nose method' for computing critical cooling rates for glass formation is examined and compared with other methods, presenting data for the glass-forming systems SiO2, GeO2, and P2O5. It is shown that, for homogeneous crystallization, the nose-method will give an overestimate of Rc, a conclusion which was drawn after assessing the enfluence of a range of values for the parameters which control crystal growth and nucleation. The paper also proposes an alternative simple procedure (termed the 'cutoff method') for computing critical cooling rates from T-T-T diagrams, which was shown in the SiO2 and GeO2 systems to be superior to the nose method.

Weinberg, Michael C.↗
NASA NTRS1994

A method of calculating the safe fatigue life of compact, highly-stressed components

This paper describes a method which has been developed for estimating the safe fatigue life of compact, highly-stressed and inaccessible components for aeroplanes and helicopters of the Royal Air Force. It is explained why the Design Requirements for British Military Aircraft do not favor the use of a damage-tolerance approach in these circumstances.

Cardick, Arthur W.↗
NASA NTRS1991

Method for calculating and observing microwave absorption by a sphere in a single mode rectangular cavity

A new theory of microwave absorption by a lossy dielectric sphere in a single mode rectangular cavity has been recently developed. The absorption was treated in the framework of an electromagnetic scattering problem. That theory is summarized here and calculated results that bear on optimizing the processing of materials are illustrated. Methods for observing power absorption and other results predicted by the scattering model are discussed. Cavity perturbation theory provides a bridge between theoretical calculations and experimental observations, and a special problem that arises when an established version of cavity perturbation theory is applied to spheres is identified, analyzed, and resolved. The direct problem of predicting shifts in frequency and Q from model calculations is discussed for a sphere in a cavity when the sphere's complex dielectric constant is known. Also, the inverse problem of determining the complex dielectric constants from measured values of those shifts is considered. The small sphere limit, where an electrostatic or quasistatic model is valid, is treated in detail, and planned work on parallel problems for larger spheres is described.

Jackson, H. W.↗
NASA NTRS1953

Method for calculating the rolling and yawing moments due to rolling for unswept wings with or without flaps or ailerons by use of nonlinear section lift data

The methods of NACA Reports 865 and 1090 have been applied to the calculation of the rolling- and yawing-moment coefficients due to rolling for unswept wings with or without flaps or ailerons. The methods allow the use of nonlinear section lift data together with lifting-line theory. Two calculated examples are presented in simplified computing forms in order to illustrate the procedures involved.

CONTROLS - COMPLETE WINGS↗