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NASA NTRS1979

Alternative signal processing techniques for a pulsed laser Doppler velocimeter system

The laser Doppler velocimeter system (LDV) being tested at NASA MSFC, Alabama, relies on a bank of classical filters for processing the returned lidar signal. Due to the complexity of this conventional filter system, alternative signal processing methods have been proposed for obtaining the Doppler spectrum. The fast Fourier transform (FFT) and the pulse-pair estimator are two techniques which appear to offer some advantages over the existing system. The work reported employs digital computer simulation to compare and evaluate these two processing methods for determining the first and second moments of the LDV velocity spectrum.

Calhoun, M. D.↗

NASA NTRS1979

Method for decomposing observed line shapes resulting from multiple causes - Application to plasma charge-exchange-neutral spectra

A method is given for decomposing the widths of observed spectral lines resulting from unresolved line splitting, additive kinetic processes of different types, instrumental broadening (slit function), Doppler broadening, etc. all superimposed. The second moments are used as measures of the various widths involved. The method is not applicable if dispersion type (Lorentz) broadening occurs. Application is made to plasma charge-exchange-neutral spectra of hydrogen, deuterium, and helium.

Patch, R. W.↗

NASA NTRS1977

Probing the solar wind with radio measurements of the second moment field

The dependence of spectral broadening on anisotropic electron-density irregularities and velocity fluctuations in the solar wind is investigated on the basis of results for a second moment mutual coherence function obtained by a parabolic-equation method. It is found that although anisotropic irregularities and wind-velocity fluctuations decrease the bandwidth of the spectrum relative to that for isotropic irregularities and no velocity fluctuations, the shape of the spectrum remains unchanged. Examination of the frequency dependence and shape of a computed angular spectrum indicates that the electron-density spectrum is consistent with a power law having a spectral index close to the value appropriate for the Kolmogorov spectrum. It is proposed that multiple-station observations of some total field be employed to measure the solar wind.

Woo, R.↗

NASA NTRS1972

The stability of motion of satellites with flexible appendages

The mathematical formulation associated with the problem of stability of motion of a satellite consisting of a main rigid body and three (or less) pairs of flexible rods is presented. The rods are capable of flexure in two orthogonal directions. Whereas the rotational motion of the body is described by generalized coordinates depending on time alone, the elastic displacements of the rods depend both on spatial position and time. Assuming no external torques, there exist motion integrals in the form of momentum integrals. These integrals can be regarded as constraint equations relating the system velocities, and used to reduce the number of variables describing the motion. The stability analysis has been carried out by means of an extension of the Liapunov direct method. Since the elastic vibrations result in energy dissipation, it is shown that the equilibrium position is asymptotically stable if the Hamiltonian is positive definite and unstable if it can take negative values in the neighborhood of the equilibrium. Determining the sign definiteness of the Hamiltonian is complicated by the fact that it contains spatial derivatives of the elastic displacements. Two methods are presented to cope with this problem. The first, the standard modal analysis in conjunction with series truncation, develops criteria in terms of infinite series associated with the natural modes and frequencies of the elastic rods. The second, the method of integral coordinates, yields closed-form stability criteria involving the system parameters, such as the body moments of inertia, the length and mass distribution of the rods, the lowest natural frequencies of the rods, and the satellite spin velocity.

Meirovitch, L.↗

NASA NTRS1924

The Influence of the Form of a Wooden Beam on Its Stiffness and Strength I : Deflection of Beams with Special Reference to Shear Deformations

The purpose of this investigation was to determine to what extent ordinary deflection formulas, which neglect shear deformations, are in error when applied to beams of various sections, and to develop reasonably accurate yet comparatively simple formulas which take into account such deformations. A great many tests were made to determine the amount of shear deformation for beams of various sections tested over many different spans. As the span over which the beam is tested is increased the error introduced by neglecting shear deformations becomes less, and the values obtained by substituting measured deflections in the ordinary formulas approach more nearly the modulus of elasticity in tension and compression. For short spans the error is considerable and increases rapidly as the span is reduced. Two formulas were developed for estimating the magnitude of shear deformations, both of which have been verified by tests. The first assumes the parabolic distribution of shear on a cross section of a beam and, starting with a differential volume, the distortion due to shear is determined by the ordinary methods of summarizing the work. The second assumes that the deflections due to shear in any two beams of the same length, height, and moment of inertia, which are similarly loaded, are proportional to the summations of the shear stresses on their respective vertical sections. Both formulas check experimental results very closely when the calculations are made with great refinement.

Newlin, J A↗

NASA NTRS1973

Statistical turbulence theory and turbulence phenomenology

The application of deductive turbulence theory for validity determination of turbulence phenomenology at the level of second-order, single-point moments is considered. Particular emphasis is placed on the phenomenological formula relating the dissipation to the turbulence energy and the Rotta-type formula for the return to isotropy. Methods which deal directly with most or all the scales of motion explicitly are reviewed briefly. The statistical theory of turbulence is presented as an expansion about randomness. Two concepts are involved: (1) a modeling of the turbulence as nearly multipoint Gaussian, and (2) a simultaneous introduction of a generalized eddy viscosity operator.

Herring, J. R.↗

NASA NTRS1977

An optimal Space Shuttle ascent trajectory for the first orbital flight test

An optimal solution of the ascent trajectory of the Space Shuttle for the first orbital flight test is presented; the optimization is a minimum propellant, four-control problem in yaw angle, roll angle, pitch angle and vacuum thrust of each Space Shuttle main engine. Piecewise linear segments with juncture points treated as parameters are employed to model the controls. Equations of motion for a three-dimensional flight with pitch plane moment balance about an oblate are integrated numerically with a fourth-order Runge-Kutta method; two- and one-dimensional cubic spline function curve fits of aerodynamic coefficients are used during the first and second stages, respectively. The constraint minimization problem is solved with the Davidon-Fletcher-Powell function method.

Johnson, I. L., Jr.↗

NASA NTRS1974

Analysis of strip antennas in the presence of a dielectric inhomogeneity

Moment method solutions are considered for treating the problem of wire antennas in the presence of an arbitrary dielectric inhomogeneity. In the first method, the current on the wire and the electric field intensity in the inhomogeneity are treated as independent unknowns, while in the second and third methods they are treated as dependent unknowns. The third method is applied to the problem of strip antennas in an electrically thin dielectric slab. Numerical results are presented, and are in good agreement with measurements and previous calculations.

Newman, E. H.↗

NASA NTRS1974

Ion and electron temperatures in the SUMMA mirror device by emission spectroscopy

Ion and electron temperatures, and ion drift were measured in a superconducting magnetic mirror apparatus by observing the Doppler-broadened charge-exchange component of the 667.8 and 587.6 nanometer He lines in He plasma, and the H sub alpha and H sub beta lines in H2 plasma. The second moment of the line profiles was used as the parameter for determining ion temperature. Corrections for magnetic splitting, fine structure, monochromator slit function, and variation in charge-exchange cross section with energy are included. Electron temperatures were measured by the line ratio method for the corona model, and correlations of ion and electron temperatures with plasma parameters are presented.

Patch, R. W.↗

NASA NTRS1975

Saturation effects associated with sound propagation in a turbulent medium

A theoretical analysis of the acoustic wave field radiated by a time-harmonic point source in a homogeneous, isotropic turbulent medium is presented. The smoothing method is used to study the incoherent, or randomly fluctuating, component of the wave field. The analysis considers the effect on the wave of the velocity fluctuations, as well as the index-of-refraction fluctuations, of the medium. An approximate expression for the second moment of the incoherent wave is obtained for the case in which the wavelenght is much less than the minimum correlation length of the medium. This expression shows that the fluctuations of the wave increase initially in proportion to the propagation distance, but that at larger distances they tend to a limiting, or saturation, value. These results agree with observations of waves propagating in real media. It is also found that the mean square of the total (i.e., coherent plus incoherent) acoustic pressure is unaffected by the randomness of the medium.

Wenzel, A. R.↗

NASA NTRS1957

A second-order shock-expansion method applicable to bodies of revolution near zero lift

A second-order shock-expansion method applicable to bodies of revolution is developed by the use of the predictions of the generalized shock-expansion method in combination with characteristics theory. Equations defining the zero-lift pressure distributions and the normal-force and pitching-moment derivatives are derived. Comparisons with experimental results show that the method is applicable at values of the similarity parameter, the ratio of free-stream Mach number to nose fineness ratio, from about 0.4 to 2.

Source record↗

NASA NTRS1976

Stability derivatives for bodies of revolution at subsonic speeds

The paper considers a rigid pointed body of revolution in a steady uniform subsonic flow. The body performs harmonic small-amplitude pitching oscillations around its zero angle of attack position. The body is assumed to be smooth and sufficiently slender so that the small perturbation concept can be applied. The basis of the method used, following Revell (1960), is the relation of a body-fixed perturbation potential to the general velocity potential. Normal force distributions as well as total force and moment coefficients are calculated for parabolic spindles and the numerical results show good agreement between Revell's second-order slender body theory and the present theory for the static stability derivatives of the parabolic spindles.

Liu, D. D.↗

NASA NTRS1977

The signature of parallel electric fields in a collisionless plasma

The presence of a parallel electric field in the magnetosphere should be apparent through its effect on particles. An analysis is made of particle trajectories in phase space for a steady state collisionless plasma. The analysis utilizes the concepts of distribution function, total energy, and magnetic moment because all three quantities are conserved in a steady state situation in the absence of collisions. Two methods are presented for using particle data to gain information on the potential distribution. The first method involves the use of measurements of both ion and electron distribution functions and invokes the principle of quasi-neutrality. The second method involves the observation of discontinuities in velocity space which can be interpreted in terms of the effect of the electric field on the apparent loss or source cone.

Whipple, E. C., Jr.↗

NASA NTRS1972

Strongly coupled stress waves in heterogeneous plates.

Consideration of coupled stress waves generated by an impulsive load applied at one end of a semiinfinite plate. For the field equations governing the one-dimensional coupled waves a hyperbolic system of equations is obtained in which a strong coupling in the second derivatives exists. The method of characteristics described by Chou and Mortimer (1967) is extended to cover the case of strong coupling, and a study is made of the transient stress waves in a semiinfinite plate subjected to an initial step input. Coupled discontinuity fronts are found to propagate at different velocities. The normal plate stress and the bending moment at different time regimes are illustrated by graphs.

Wang, A. S. D.↗

NASA NTRS1917

Report on Behavior of Aeroplanes in Gusts

Part 1 presents the results of a wind tunnel test of a biplane model with an 18 inch span. The lift, drift, and pitching moment were measured for a series of angles of incidence corresponding to the maximum possible changes of flight attitude. Only the discussion of symmetrical or longitudinal changes is given. From the observed rate of variation of the forces and pitching moment, it was possible to calculate the derivatives needed in the complete theory of longitudinal stability in still air. The damping of the pitching oscillation was also determined experimentally. Part 2 presents a theoretical method for determining the effects of gusts on aeroplanes in the following cases: (1) head-on gusts rising from 0 to j feet per second with various degrees of sharpness, (2) up gusts of the same type, (3) rotary gusts of the same type, (4) rear gusts and down gusts are included by merely changing the sign of j.

Hunsaker, J C↗

NASA NTRS1923

General theory of thin wing sections

This report contains a new, simple method of calculating the air forces to which thin wings are subjected at small angles of attack, if their curvature is not too great. Two simple integrals are the result. They contain only the coordinates of the wing section. The first integral gives the angle of attack at which the lift of the wing is zero, the second integral gives the moment experienced by the wing when its angle is zero. The two constants thus obtained are sufficient to determine the lift and moment for any other angle of attack. This with the theory of the aerodynamical induction, and with our empirical knowledge of the drag due to friction, the results are valuable for actual wings also. A particular result obtained is the calculation of the elevator effect. (author)

Munk, Max M↗

NASA NTRS1931

Metal-truss wing spars

The purpose of the study was to develop improvements in the current methods for the calculation of the loads in members of metal truss wing spars which are subjected to combined bending and compression. The theory developed here has two important practical applications. One is the calculation of the effective moment of inertia of a truss spar from the geometry of the spar and the loads to which the spar is to be subjected. The second is the determination of the most economical location of metal for stiffening a truss spar which has too much deflection.

Swickard, Andrew E↗

NASA NTRS1923

General biplane theory

This report deals with the air forces on biplane cellule. The first part of the report deals with the two-dimensional problem neglecting viscosity. The variation of the section, chord, gap, stagger, and decalage are investigated, a great number of examples are calculated, and all numerical results are given in tables. For the biplane without stagger it is found that the loss of lift in consequence of the mutual influence of the two wing sections is only half as much if the lift is produced by the curvature of the section as it is when the lift is produced by the inclination of the chord to the direction of motion. The second part deals with the influence of the lateral dimensions. It is found that the loss of lift due to induction is almost unchanged, whether the biplane is staggered or not. In the third part conclusions from previous investigations are drawn, viscosity and experimental experience are brought in, and the method is simplified for practical application. Simple formulas give the drag, lift, and moment. In order to make use of the simple formulas more convenient, tables for the dynamical pressure, induced drag, and angle of attack are added so that practically no computation is needed for the application of the results.

Munk, Max M↗