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NASA NTRS2023

Relationship Between the Sub-Micron Fraction (SMF) and Fine-Mode Fraction (FMF) in the Context of AERONET Retrievals

The sub-micron (SM) aerosol optical depth (AOD) is an optical separation based on the fraction of particles below a specified cutoff radius of the particle size distribution (PSD) at a given particle radius. It is fundamentally different from spectrally separated FM (fine-mode) AOD. We present a simple (AOD-normalized) SM fraction versus FM fraction (SMF vs. FMF) linear equation that explains the well-recognized empirical result of SMF generally being greater than the FMF. The AERONET inversion (AERinv) products (combined inputs of spectral AOD and sky radiance) and the spectral deconvolution algorithm (SDA) products (input of AOD spectra) enable, respectively, an empirical SMF vs. FMF comparison at similar (columnar) remote sensing scales across a variety of aerosol types. SMF (AERinv-derived) vs. FMF (SDA-derived) behavior is primarily dependent on the relative truncated portion (ε c ) of the coarse-mode (CM) AOD associated with the cutoff portion of the CM PSD and, to a second order, the cutoff FM PSD and FM AOD (ε f ). The SMF vs. FMF equation largely explains the SMF vs. FMF behavior of the AERinv vs. SDA products as a function of PSD cutoff radius (“inflection point”) across an ensemble of AERONET sites and aerosol types (urban-industrial, biomass burning, dust, maritime and a mixed class of Arctic aerosols). The overarching dynamic was that the linear SMF vs. FMF relation pivots clockwise about the approximate (SMF, FMF) singularity of (1, 1) in a “linearly inverse” fashion (slope and intercept of approximately 1−ε c and ε c ) with increasing cutoff radius. SMF vs. FMF slopes and intercepts derived from AERinv and SDA retrievals confirmed the general domination of ε c over ε f in controlling that dynamic. A more general conclusion is the apparent confirmation that the optical impact of truncating modal (whole) PSD features can be detected by an SMF vs. FMF analysis.

Norman T. O'Neill↗

NASA NTRS2016

The Imaging X-Ray Polarimetry Explorer (IXPE)

The Imaging X-ray Polarimetry Explorer (IXPE) is an exciting international collaboration for a scientific mission that dramatically brings together the unique talents of the partners to expand observation space by simultaneously adding polarization measurements to the array of source properties currently measured (energy, time, and location). IXPE uniquely brings to the table polarimetric imaging. IXPE will thus open new dimensions for understanding how X-ray emission is produced in astrophysical objects, especially systems under extreme physical conditions-such as neutron stars and black holes. Polarization singularly probes physical anisotropies-ordered magnetic fields, aspheric matter distributions, or general relativistic coupling to black-hole spin-that are not otherwise measurable. Hence, IXPE complements all other investigations in high-energy astrophysics by adding important and relatively unexplored information to the parameter space for studying cosmic X-ray sources and processes, as well as for using extreme astrophysical environments as laboratories for fundamental physics.

X-ray astronomy x-ray polarimetry↗

NASA NTRSDate not supplied

Shape Approximation in Camera Fields of View for Parachute Visibility Applications

The ability to simulate camera line of sight and field of view is a powerful capability for flight mechanics simulations. This paper improves upon an existing camera visibility implementation that leverages geometry to estimate parachute visibility from a singular point by introducing a shape discretization method. The new method approximates a shape as a set of analytical points relative to a target marker within any number of camera fields of view. The method is developed in such a way to be generalized to a myriad of spacecraft applications. This effort focuses on an implementation to simulate parachute canopy visibility within the combined field of view of three cameras but additional applications are discussed. Monte Carlo analysis is used to assess the parachute canopy visibility example and demonstrate its improved performance over the previous method.

Evan Roelke↗

NASA NTRSDate not supplied

Shape Approximation in Camera Fields of View for Parachute Visibility Applications

Evan Roelke↗

NASA NTRS1978

Some recent theoretical and experimental developments in fracture mechanics

Recent theoretical and experimental developments in four distinct areas of fracture mechanics research are described. These are as follows: experimental comparisons of different nonlinear fracture toughness measures, including the nonlinear energy, R curve, COD and J integral methods; the singular elastic crack-tip stress and displacement equations and the validity of the proposition of their general adequacy as indicated, for example, by the biaxially loaded infinite sheet with a flat crack; the thermodynamic nature of surface energy induced by propagating cracks in relation to a general continuum thermodynamic description of brittle fracture; and analytical and experimental aspects of Mode II fracture, with experimental data for certain aluminum, steel and titanium alloys.

Liebowitz, H.↗

NASA NTRS1980

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface. Part 1: Analysis

The basic crack problem which is essential for the study of subcritical crack propagation and fracture of layered structural materials is considered. Because of the apparent analytical difficulties, the problem is idealized as one of plane strain or plane stress. An additional simplifying assumption is made by restricting the formulation of the problem to crack geometries and loading conditions which have a plane of symmetry perpendicular to the interface. The general problem is formulated in terms of a coupled system of four integral equations. For each relevant crack configuration of practical interest, the singular behavior of the solution near and at the ends and points of intersection of the cracks is investigated and the related characteristic equations are obtained. The edge crack terminating at and crossing the interface, the T-shaped crack consisting of a broken layer and a delamination crack, the cross-shaped crack which consists of a delamination crack intersecting a crack which is perpendicular to the interface, and a delamination crack initiating from a stress-free boundary of the bonded layers are some of the practical crack geometries considered.

Lu, M. C.↗

NASA NTRS1983

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface. I Analysis. II - Solution and results

The basic crack problem which is essential for the study of subcritical crack propagation and fracture of layered structural materials is considered. Because of the apparent analytical difficulties, the problem is idealized as one of plane strain or plane stress. An additional simplifying assumption is made by restricting the formulation of the problem to crack geometries and loading conditions which have a plane of symmetry perpendicular to the interface. The general problem is formulated in terms of a coupled systems of four integral equations. For each relevant crack configuration of practical interest, the singular behavior of the solution near and at the ends and points of intersection of the cracks is investigated and the related characteristic equations are obtained. The edge crack terminating at and crossing the interface, the T-shaped crack consisting of a broken layer and a delamination crack, the cross-shaped crack which consists of a delamination crack intersecting a crack which is perpendicular to the interface, and a delamination crack initiating from a stress-free boundary of the bonded layers are some of the practical crack geometries considered. Previously announced in STAR as N80-18428 and N80-18429

Lu, M.-C.↗

NASA NTRS2018

Green's Function Applicable to Turbofan Exhaust Noise in Jets with an External Center-Body

The problem of propagation of sound across the shear layer in a turbofan jet exhaust with an external center-body is discussed. The wave equation of interest is compressible Rayleigh equation. Two forms of the equation are considered, and the Green's function solutions subject to appropriate surface conditions on the center-body and flight condition in the ambient are presented. Directivity studied in a heated exhaust at temperature ratio of 2.0 and Mach number 0.90 indicate that a rigid center-body tends to increase the sound propagation at forward angles relative to an exhaust without a center-body, while application of suitable surface liner may significantly reduce this enhancement. A general form of the far-field solution to the propagation equation in a parallel flow under supersonic conditions and in the neighborhood of the shear layer singularity is also discussed.

Noise↗

NASA NTRS1972

Lifting-surface theory for calculating the loading induced on a wing by a flap

A method is described for using lifting-surface theory to obtain the pressure distribution on a wing with a trailing-edge flap or control surface. The loading has a logarithmic singularity at the flap edges, which may be determined directly by the method of matched asymptotic expansions. Expressions are given for the singular flap loading for various flap hinge line and side edge geometries, both for steady and unsteady flap deflection. The regular part of the flap loading must be obtained by inverting the lifting-surface-theory integral equation relating the pressure and the downwash on the wing: procedures are described to accomplish this for a general wing and flap geometry. The method is applied to several example wings, and the results are compared with experimental data. Theory and test correlate well.

Johnson, W. A.↗

NASA NTRS2009

Magnetopause Reconnection Impact Parameters from Multiple Spacecraft Magnetic Field Measurements

We present a novel technique that exploits multiple spacecraft data to determine the impact parameters of the most general form of magnetic reconnection at the magnetopause. The method consists of a superposed epoch of multiple spacecraft magnetometer measurements that yields the instantaneous magnetic spatial gradients near a magnetopause reconnection site. The gradients establish the instantaneous positions of the spacecraft relative to the reconnection site. The analysis is well suited to evaluating the spatial scales of singular field line reconnection, which is characterized by a two-dimensional x-type topology adjacent and perpendicular to a reconnecting singular field line. Application of the method to Cluster data known to lie in the vicinity of a northward IMF reconnection site establishes a field topology consistent with singular field line reconnection and a normal magnetic field component of 20 nT. The corresponding current structure consists of a 130 km sheet possibly embedding a thinner. bifurcated sheet.

Wendel, Deirdre E.↗

NASA NTRS1984

The crack-inclusion interaction problem

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

Xue-Hui, L.↗

NASA NTRS1986

The crack-inclusion interaction problem

Liu, X.-H.↗

NASA NTRS1991

A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities

A Fourier-Chebyshev pseudospectral method for solving steady 3D Navier-Stokes equations in cylindrical cavities is presented and discussed. The general method is pseudo-unsteady and uses a semi-implicit finite difference scheme for the time discretization. The generalized ADI (Alternating Direction Implicit) procedure is then applied to reduce the problem to a successive solution of one-dimensional problems. The spatial approximation uses a Fourier-Galerkin approximation in the periodic direction and a Chebyshev-collocation approximation in the other directions. Difficulties related to the pressure are surmounted by using the artifical compressibility method. A suitable variable change was chosen to avoid the problem of singularity at the axis generated by cylindrical coordinates. The method is first tested on an advection-diffusion equation and then on the Navier-Stokes equations. Finally, the method is illustrated by a convection problem of a differentially heated fluid.

Pulicani, J. P.↗

NASA NTRS1994

Hypersonic vehicle model and control law development using H(infinity) and micron synthesis

The control system design for a Single Stage To Orbit (SSTO) air breathing vehicle will be central to a successful mission because a precise ascent trajectory will preserve narrow payload margins. The air breathing propulsion system requires the vehicle to fly roughly halfway around the Earth through atmospheric turbulence. The turbulence, the high sensitivity of the propulsion system to inlet flow conditions, the relatively large uncertainty of the parameters characterizing the vehicle, and continuous acceleration make the problem especially challenging. Adequate stability margins must be provided without sacrificing payload mass since payload margins are critical. Therefore, a multivariable control theory capable of explicitly including both uncertainty and performance is needed. The H(infinity) controller in general provides good robustness but can result in conservative solutions for practical problems involving structured uncertainty. Structured singular value mu framework for analysis and synthesis is potentially much less conservative and hence more appropriate for problems with tight margins. An SSTO control system requires: highly accurate tracking of velocity and altitude commands while limiting angle-of-attack oscillations, minimized control power usage, and a stabilized vehicle when atmospheric turbulence and system uncertainty are present. The controller designs using H(infinity) and mu-synthesis procedures were compared. An integrated flight/propulsion dynamic mathematical model of a conical accelerator vehicle was linearized as the vehicle accelerated through Mach 8. Vehicle acceleration through the selected flight condition gives rise to parametric variation that was modeled as a structured uncertainty. The mu-analysis approach was used in the frequency domain to conduct controller analysis and was confirmed by time history plots. Results demonstrate the inherent advantages of the mu framework for this class of problems.

Gregory, Irene M.↗

NASA NTRS1963

ORBITAL ELEMENT EQUATIONS FOR OPTIMUM LOW THRUST TRAJECTORIES

The three dimensional optimum trajectory relations developed by Messrs J. G. Cox and W. A. Shaw in Reference I, are transformed into- a form that appears more amenable to low thrust trajectory calculations. Orbital element coordinates, commonly used in Celestial Mechanics, are employed due to their slow variation in low thrust applications. Combinations of these elements and a generalized eccentric anomaly are utilized in arranging the resulting equations- in a form which does not contain circular singularities.

Spacecraft Guidance↗

NASA NTRS1992

An evaluation of training effectiveness of an intelligent tutoring system

The study evaluated the training effectiveness of an intelligent tutoring system (ITS) for the Remote Manipulator System (RMS). The study examined how well individuals learn the training content and skills from the RMS ITS and to what extent the content and skills learned using the ITS transfer to RMS task performance in the SES, a high fidelity simulator. Three astronauts completed 8 2-hour ITS sessions addressing movement in three coordinate systems, grapple, ungrapple, berth, and unberth procedures, and singularities and reach limits. Their performance was also observed in an SES training session. Performance data were collected using multiple measures: ITS task performance, transfer performance on the SES, a conceptual knowledge test, an opinion survey completed by astronauts, and comments and observations from astronauts and trainers. Results indicated the RMS ITS to be moderately effective and provided evidence of the efficacy of ITS's, in general. Comments and suggestions are provided relating to how the ITS could be improved and to enable decision makers to judge the effectiveness of the RMS ITS.

Johnson, Debra Steele↗

NASA NTRS2005

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs such as thrust. The engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends upon knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined which accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

Litt, Jonathan S.↗

NASA NTRS2007

An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation

A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs, such as thrust. The engine's performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends on knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined that accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.

Litt, Jonathan S.↗