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NASA NTRS2002

Initialization of Formation Flying Using Primer Vector Theory

In this paper, we extend primer vector analysis to formation flying. Optimization of the classical rendezvous or free-time transfer problem between two orbits using primer vector theory has been extensively studied for one spacecraft. However, an increasing number of missions are now considering flying a set of spacecraft in close formation. Missions such as the Magnetospheric MultiScale (MMS) and Leonardo-BRDF (Bidirectional Reflectance Distribution Function) need to determine strategies to transfer each spacecraft from the common launch orbit to their respective operational orbit. In addition, all the spacecraft must synchronize their states so that they achieve the same desired formation geometry over each orbit. This periodicity requirement imposes constraints on the boundary conditions that can be used for the primer vector algorithm. In this work we explore the impact of the periodicity requirement in optimizing each spacecraft transfer trajectory using primer vector theory. We first present our adaptation of primer vector theory to formation flying. Using this method, we then compute the AV budget for each spacecraft subject to different formation endpoint constraints.

Mailhe, Laurie↗

NASA NTRS2003

Summary of Fluidic Thrust Vectoring Research Conducted at NASA Langley Research Center

Interest in low-observable aircraft and in lowering an aircraft's exhaust system weight sparked decades of research for fixed geometry exhaust nozzles. The desire for such integrated exhaust nozzles was the catalyst for new fluidic control techniques; including throat area control, expansion control, and thrust-vector angle control. This paper summarizes a variety of fluidic thrust vectoring concepts that have been tested both experimentally and computationally at NASA Langley Research Center. The nozzle concepts are divided into three categories according to the method used for fluidic thrust vectoring: the shock vector control method, the throat shifting method, and the counterflow method. This paper explains the thrust vectoring mechanism for each fluidic method, provides examples of configurations tested for each method, and discusses the advantages and disadvantages of each method.

Deere, Karen A.↗

NASA NTRS1999

Computational Investigation of Fluidic Counterflow Thrust Vectoring

A computational study of fluidic counterflow thrust vectoring has been conducted. Two-dimensional numerical simulations were run using the computational fluid dynamics code PAB3D with two-equation turbulence closure and linear Reynolds stress modeling. For validation, computational results were compared to experimental data obtained at the NASA Langley Jet Exit Test Facility. In general, computational results were in good agreement with experimental performance data, indicating that efficient thrust vectoring can be obtained with low secondary flow requirements (less than 1% of the primary flow). An examination of the computational flowfield has revealed new details about the generation of a countercurrent shear layer, its relation to secondary suction, and its role in thrust vectoring. In addition to providing new information about the physics of counterflow thrust vectoring, this work appears to be the first documented attempt to simulate the counterflow thrust vectoring problem using computational fluid dynamics.

Hunter, Craig A.↗

NASA NTRS1996

Spatial orientation of semicircular canals and afferent sensitivity vectors in pigeons

Rotational head motion in vertebrates is detected by the semicircular canal system, whose innervating primary afferent fibers carry information about movement in specific head planes. The semicircular canals have been qualitatively examined over a number of years, and the canal planes have been quantitatively characterized in several animal species. The present study first determined the geometric relationship between individual semicircular canals and between the canals and the stereotactic head planes in pigeons. Stereotactic measurements of multiple points along the circumference of the bony canals were taken, and the measured points fitted with a three-dimensional planar surface. Direction normals to the plane's surface were calculated and used to define angles between semicircular canal pairs. Because of the unusual shape of the anterior semicircular canals in pigeons, two planes, a major and a minor, were fitted to the canal's course. Calculated angle values for all canals indicated that the horizontal and posterior semicircular canals are nearly orthogonal, but the anterior canals have substantial deviations from orthogonality with other canal planes. Next, the responses of the afferent fibers that innervate each of the semicircular canals to 0.5 Hz sinusoidal rotation about an earth-vertical axis were obtained. The head orientation relative to the rotation axis was systematically varied so that directions of maximum sensitivity for each canal afferent could be determined. These sensitivity vectors were then compared with the canal plane direction normals. The afferents that innervated specific semicircular canals formed homogeneous clusters of sensitivity vectors in different head planes. The horizontal and posterior afferents had average sensitivity vectors that were largely co-incident with the innervated canal plane direction normals. Anterior canal afferents, however, appeared to synthesize contributions from the major and minor plane components of the bony canal structure to produce a resultant sensitivity vector that was positioned between the canal planes. Calculated angles between the average canal afferent sensitivity vectors revealed that direction orthogonality is preserved at the afferent signal level, even though deviations from canal plane orthogonality exist.

NASA Discipline Neuroscience↗

NASA NTRS2005

A Computational Study of a New Dual Throat Fluidic Thrust Vectoring Nozzle Concept

A computational investigation of a two-dimensional nozzle was completed to assess the use of fluidic injection to manipulate flow separation and cause thrust vectoring of the primary jet thrust. The nozzle was designed with a recessed cavity to enhance the throat shifting method of fluidic thrust vectoring. Several design cycles with the structured-grid, computational fluid dynamics code PAB3D and with experiments in the NASA Langley Research Center Jet Exit Test Facility have been completed to guide the nozzle design and analyze performance. This paper presents computational results on potential design improvements for best experimental configuration tested to date. Nozzle design variables included cavity divergence angle, cavity convergence angle and upstream throat height. Pulsed fluidic injection was also investigated for its ability to decrease mass flow requirements. Internal nozzle performance (wind-off conditions) and thrust vector angles were computed for several configurations over a range of nozzle pressure ratios from 2 to 7, with the fluidic injection flow rate equal to 3 percent of the primary flow rate. Computational results indicate that increasing cavity divergence angle beyond 10 is detrimental to thrust vectoring efficiency, while increasing cavity convergence angle from 20 to 30 improves thrust vectoring efficiency at nozzle pressure ratios greater than 2, albeit at the expense of discharge coefficient. Pulsed injection was no more efficient than steady injection for the Dual Throat Nozzle concept.

Deere, Karen A.↗

NASA NTRS2005

Attitude Control for an Aero-Vehicle Using Vector Thrusting and Variable Speed Control Moment Gyros

Stabilization of passively unstable thrust-levitated vehicles can require significant control inputs. Although thrust vectoring is a straightforward choice for realizing these inputs, this may lead to difficulties discussed in the paper. This paper examines supplementing thrust vectoring with Variable-Speed Control Moment Gyroscopes (VSCMGs). The paper describes how to allocate VSCMGs and the vectored thrust mechanism for attitude stabilization in frequency domain and also shows trade-off between vectored thrust and VSCMGs. Using an H2 control synthesis methodology in LMI optimization, a feedback control law is designed for a thrust-levitated research vehicle and is simulated with the full nonlinear model. It is demonstrated that VSCMGs can reduce the use of vectored thrust variation for stabilizing the hovering platform in the presence of strong wind gusts.

Shin, Jong-Yeob↗

NASA NTRS1989

Vector excitation speech or audio coder for transmission or storage

A vector excitation coder compresses vectors by using an optimum codebook designed off line, using an initial arbitrary codebook and a set of speech training vectors exploiting codevector sparsity (i.e., by making zero all but a selected number of samples of lowest amplitude in each of N codebook vectors). A fast-search method selects a number N.sub.c of good excitation vectors from the codebook, where N.sub.c is much smaller tha ORIGIN OF INVENTION The invention described herein was made in the performance of work under a NASA contract, and is subject to the provisions of Public Law 96-517 (35 USC 202) under which the inventors were granted a request to retain title.

Davidson, Grant↗

NASA NTRS2007

The Local Stellar Velocity Field via Vector Spherical Harmonics

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism. We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not corrected for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star. The Oort parameters determined by a straightforward least-squares adjustment in vector spherical harmonics are A=14.0 +/- 1.4, B=13.1 +/- 1.2, K=1.1 +/- 1.8, and C=2.9 +/- 1.4 km s(exp -1) kpc(exp -1). The physical meaning and the implications of these parameters are discussed in the framework of a general linear model of the velocity field. We find a few statistically significant higher degree harmonic terms that do not correspond to any parameters in the classical linear model. One of them, a third-degree electric harmonic, is tentatively explained as the response to a negative linear gradient of rotation velocity with distance from the Galactic plane, which we estimate at approximately -20 km s(exp -1) kpc(exp -1). A similar vertical gradient of rotation velocity has been detected for more distant stars representing the thick disk (z greater than 1 kpc), but here we surmise its existence in the thin disk at z less than 200 pc. The most unexpected and unexplained term within the Ogorodnikov-Milne model is the first-degree magnetic harmonic, representing a rigid rotation of the stellar field about the axis -Y pointing opposite to the direction of rotation. This harmonic comes out with a statistically robust coefficient of 6.2 +/- 0.9 km s(exp -1) kpc(exp -1) and is also present in the velocity field of more distant stars. The ensuing upward vertical motion of stars in the general direction of the Galactic center and the downward motion in the anticenter direction are opposite to the vector field expected from the stationary Galactic warp model.

Galaxy↗

NASA NTRS2009

Progressive Classification Using Support Vector Machines

An algorithm for progressive classification of data, analogous to progressive rendering of images, makes it possible to compromise between speed and accuracy. This algorithm uses support vector machines (SVMs) to classify data. An SVM is a machine learning algorithm that builds a mathematical model of the desired classification concept by identifying the critical data points, called support vectors. Coarse approximations to the concept require only a few support vectors, while precise, highly accurate models require far more support vectors. Once the model has been constructed, the SVM can be applied to new observations. The cost of classifying a new observation is proportional to the number of support vectors in the model. When computational resources are limited, an SVM of the appropriate complexity can be produced. However, if the constraints are not known when the model is constructed, or if they can change over time, a method for adaptively responding to the current resource constraints is required. This capability is particularly relevant for spacecraft (or any other real-time systems) that perform onboard data analysis. The new algorithm enables the fast, interactive application of an SVM classifier to a new set of data. The classification process achieved by this algorithm is characterized as progressive because a coarse approximation to the true classification is generated rapidly and thereafter iteratively refined. The algorithm uses two SVMs: (1) a fast, approximate one and (2) slow, highly accurate one. New data are initially classified by the fast SVM, producing a baseline approximate classification. For each classified data point, the algorithm calculates a confidence index that indicates the likelihood that it was classified correctly in the first pass. Next, the data points are sorted by their confidence indices and progressively reclassified by the slower, more accurate SVM, starting with the items most likely to be incorrectly classified. The user can halt this reclassification process at any point, thereby obtaining the best possible result for a given amount of computation time. Alternatively, the results can be displayed as they are generated, providing the user with real-time feedback about the current accuracy of classification.

Wagstaff, Kiri↗

NASA NTRS2003

Vector-Ordering Filter Procedure for Data Reduction

The vector-ordering filter (VOF) technique involves a procedure for sampling a large population of data vectors to select a subset of data vectors that fully characterize the state space of the large population. The VOF technique enables a large reduction of the volume of data that must be handled in the automated monitoring system and method discussed in the two immediately preceding articles. In so doing, the VOF technique enables the development of data-driven mathematical models of a monitored asset from sets of data that would otherwise exceed the memory capacities of conventional engineering computers. Data-driven mathematical models have been shown to offer high fidelity for purposes of control and monitoring of assets. In practice, a collection of asset-operating observations is acquired with the intention that the collection contain observations characteristic of the full dynamic range of operation of the asset. Often, such a collection contains an extremely large number of observations, many of which are redundant. The VOF technique fills the need for a means to extract, from the original collection of observational data, a reduced data matrix that excludes redundant data while maintaining the full statistical character and dynamic range of the original data. The reduced data matrix can then be used as the input data for development of a mathematical model of the monitored asset, or as training data for a neural-network substitute for an explicit mathematical model of the asset. Alternatively, the reduced data matrix can, itself, be used directly as a mathematical model of the monitored asset, as is commonly done in multivariate state-estimation techniques. The original data are collected from the asset over a range of operating states and are put in matrix form. Each column vector in the original data matrix represents the signal values acquired at a particular operational state of the asset. Thus, the number of columns of the original data matrix equals the number of observed states and the number of rows in this matrix equals the number of signals acquired at each observation. In the VOF technique, one extracts the reduced data matrix from the original data matrix through the selection of a representative subset of the column (state) vectors.

Bickford, Randall L.↗

NASA NTRS2012

MISR 17.6 KM Gridded Cloud Motion Vectors: Overview and Assessment

The MISR (Multi-angle Imaging SpectroRadiometer) instrument on the Terra satellite has been retrieving cloud motion vectors (CMVs) globally and almost continuously since early in 2000. In February 2012 the new MISR Level 2 Cloud product was publicly released, providing cloud motion vectors at 17.6 km resolution with improved accuracy and roughly threefold increased coverage relative to the 70.4 km resolution vectors of the current MISR Level 2 Stereo product (which remains available). MISR retrieves both horizontal cloud motion and height from the apparent displacement due to parallax and movement of cloud features across three visible channel (670nm) camera views over a span of 200 seconds. The retrieval has comparable accuracy to operational atmospheric motion vectors from other current sensors, but holds the additional advantage of global coverage and finer precision height retrieval that is insensitive to radiometric calibration. The MISR mission is expected to continue operation for many more years, possibly until 2019, and Level 2 Cloud has the possibility of being produced with a sensing-to-availability lag of 5 hours. This report compares MISR CMV with collocated motion vectors from arctic rawinsonde sites, and from the GOES and MODISTerra instruments. CMV at heights below 3 km exhibit the smallest differences, as small as 3.3 m/s for MISR and GOES. Clouds above 3 km exhibit larger differences, as large as 8.9 m/s for MISR and MODIS. Typical differences are on the order of 6 m/s.

MISR (Multi-angle Imaging SpectroRadiometer)↗

NASA NTRS2019

Creating Data-Driven Vector Visualizations of Satellite Orbit Tracks Using NASA GIBS and Worldview

NASA Earth Observing System (EOS) currently operates dozens of remote sensing satellites, many of which can be viewed directly in NASA’s open-source Worldview application. Much of this satellite imagery can be viewed in near-real time as it is processed and served by NASA’s Global Imagery Browse Service (GIBS). To better educate users on the time and location of imagery, GIBS serves orbit track specific layers for each satellite. Worldview has historically served these layers as raster images but recent updates have enabled the application to now serve these layers using vector tiles. With the release of Worldview v3.0, orbit track layers can be displayed using mapbox vector tiles (MVT). This visualization format allows users to not only view and change the color of orbit track layers, as they could do previously with rasters, but also inspect individual vector points and filter layers by specific parameters such as time. The data contained within a MVT is further enhanced in Worldview with the combination of a JSON description file served from GIBS used to describe the MVT data. This presentation will provide an overview of the process of consuming orbit track vector tiles and data files from GIBS using a pipeline to configure, build and ultimately display the orbit tracks in Worldview. Furthermore, the presentation aims to describe how others can leverage our open-source code to display and enhance vector layers in their own applications.

Rice, Zachary↗

NASA NTRS1973

Aerodynamic characteristics of a vectored-thrust V/STOL fighter in the transition speed range

A wind-tunnel investigation was conducted with a vectored-thrust V/STOL fighter configuration. The model was equipped with two nacelle-mounted vectored-thrust jet simulators and one lift-jet simulator. The vectored-thrust jet could be tested at two alternate longitudinal positions and three nozzle deflection angles. The vectored-thrust configuration with the rear nozzles showed an increase in lift and a decrease in pitching moment when compared with the forward nozzles. The rear nozzles also improve stall characteristics.

Mineck, R. E.↗

NASA NTRS1974

Solid rocket thrust vector control

Thrust vector control systems that superimpose a side force on the motor thrust, steering being achieved by the side force causing a moment about the vehicle center of gravity are described. A brief review of thrust vector control systems is presented, and two systems, flexible joint and liquid injection, are treated in detail. Treatment of the flexible-joint thrust vector control system is limited to the design of the flexible joint and its insulation against hot motor gases. Treatment of the liquid injection thrust vector control system is limited to discussion of the injectant, valves, piping, storage tanks, and pressurization system; no evaluation is presented of the nozzle except for (1) the effect of the injectant and erosion at the injection port and (2) the effect of injection on pressure distribution within the nozzle.

Source record↗

NASA NTRS1976

A vector autopilot system

Current technology has evolved low cost, highly reliable solid state vector magnetometers with excellent angular resolution. This paper discusses the role of a three-axis magnetometer as a new instrument for aircraft attitude determination. Using flight data acquired by an instrumented aircraft, attitude is calculated using the earth's magnetic field vector and compared to measured attitudes. The magnetic field alone is not adequate to resolve all attitude variations and the need for a second reference angle or vector is discussed. A system combining the functions of heading determination and attitude measurement is presented to show that both functions can be implemented with essentially the same component count required to measure heading alone. It is concluded that with the correlation achieved in calculated and measured attitude there is a potential application of vector magnetometry in attitude measurement systems.

Pietila, R.↗

NASA NTRS1977

Symbolic computer vector analysis

A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.

Stoutemyer, D. R.↗

NASA NTRS1979

Flux vector splitting of the inviscid equations with application to finite difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Steger, J. L.↗

NASA NTRS1978

Analysis of dissection algorithms for vector computers

Recently two dissection algorithms (one-way and incomplete nested dissection) have been developed for solving the sparse positive definite linear systems arising from n by n grid problems. Concurrently, vector computers (such as the CDC STAR-100 and TI ASC) have been developed for large scientific applications. An analysis of the use of dissection algorithms on vector computers dictates that vectors of maximum length be utilized thereby implying little or no dissection; on the other hand, minimizing operation counts suggest that considerable dissection be performed. In this paper we discuss the resolution of this conflict by minimizing the total time required by vectorized versions of the two algorithms.

George, A.↗