Results for “VECTORS” — Page 11

NASA NTRS1990

Pacific-North American plate motion from very long baseline interferometry compared with motion inferred from magnetic anomalies, transform faults, and earthquake slip vectors

Geodetic VLBI measurements were used to test whether the Pacific-North American plate velocity averaged over several years of direct observation (1984-1987) equals that averaged over millions of years. It was also tested whether this velocity parallels the San Andreas fault, transform faults and earthquake slip vectors in the Gulf of California, and earthquake slip vectors along the Queen Charlotte fault, along the Alaskan peninsula, and along the Kamchatkan peninsula. The VLBI data provide an estimate of the direction of plate motion that is independent of estimates from fault azimuths and earthquake slip vectors. The Euler vector determined from VLBI was found to be nearly identical to the Euler vector of plate motion model NUVEL-1, which is based on the trends of transform faults, earthquake slip vectors, and spreading rates from marine magnetic anomalies that average motion since 3 Ma. The velocity between the Pacific and North American plates averaged over the past several years equals or nearly equals its velocity averaged over the past several million years, the difference along their boundary nowhere exceeding 4 + or - 7 mm/yr.

Argus, Donald F.↗

NASA NTRS1991

Design of thrust vectoring exhaust nozzles for real-time applications using neural networks

Thrust vectoring continues to be an important issue in military aircraft system designs. A recently developed concept of vectoring aircraft thrust makes use of flexible exhaust nozzles. Subtle modifications in the nozzle wall contours produce a non-uniform flow field containing a complex pattern of shock and expansion waves. The end result, due to the asymmetric velocity and pressure distributions, is vectored thrust. Specification of the nozzle contours required for a desired thrust vector angle (an inverse design problem) has been achieved with genetic algorithms. This approach is computationally intensive and prevents the nozzles from being designed in real-time, which is necessary for an operational aircraft system. An investigation was conducted into using genetic algorithms to train a neural network in an attempt to obtain, in real-time, two-dimensional nozzle contours. Results show that genetic algorithm trained neural networks provide a viable, real-time alternative for designing thrust vectoring nozzles contours. Thrust vector angles up to 20 deg were obtained within an average error of 0.0914 deg. The error surfaces encountered were highly degenerate and thus the robustness of genetic algorithms was well suited for minimizing global errors.

Prasanth, Ravi K.↗

NASA NTRS1992

Structure/load dependent vectors for linear structural dynamic analysis

The dynamic solution vectors yielded by the present structure/load dependent-vectors method for large-scale linear structural dynamic analyses involving complex loadings can be used as starting vectors, so that both structure and load characteristics are encompassed by the basis vectors. The method is shown to entail fewer vectors than current alternatives for a given level of accuracy, especially in the cases of structures that have external concentrated masses. Numerical results are presented which illustrate the advantages of this dependent-vectors method relative to other reduction methods.

Qin, Jiangning↗

NASA NTRS1992

Thrust vectoring characteristics of the F-18 high alpha research vehicle at angles of attack from 0 to 70 deg

An investigation was conducted to determine the multiaxis thrust-vectoring characteristics of the F-18 High Alpha Research Vehicle (HARV). A 0.10-scale model was modified with hardware to simulate the three-vane thrust vectoring system of the F-18/HARV. This investigation was conducted at Mach numbers ranging from 0.30 to 0.70, at angles of attack from 0 to 70 deg, and nozzle-pressure ratios from 2.0 to approximately 5.0. Results indicate that the thrust vectoring system of F-18/HARV can successfully generate multiaxis thrust vectoring. During vectoring, resultant thrust-vector angles were always less than the corresponding geometric vane deflection angle and were accompanied by large thrust losses.

Asbury, Scott C.↗

NASA NTRS1993

Rate determination from vector observations

Vector observations are a common class of attitude data provided by a wide variety of attitude sensors. Attitude determination from vector observations is a well-understood process and numerous algorithms such as the TRIAD algorithm exist. These algorithms require measurement of the line of site (LOS) vector to reference objects and knowledge of the LOS directions in some predetermined reference frame. Once attitude is determined, it is a simple matter to synthesize vehicle rate using some form of lead-lag filter, and then, use it for vehicle stabilization. Many situations arise, however, in which rate knowledge is required but knowledge of the nominal LOS directions are not available. This paper presents two methods for determining spacecraft angular rates from vector observations without a priori knowledge of the vector directions. The first approach uses an extended Kalman filter with a spacecraft dynamic model and a kinematic model representing the motion of the observed LOS vectors. The second approach uses a 'differential' TRIAD algorithm to compute the incremental direction cosine matrix, from which vehicle rate is then derived.

Weiss, Jerold L.↗

NASA NTRS1993

Performance characteristics of a variable-area vane nozzle for vectoring an ASTOVL exhaust jet up to 45 deg

Many conceptual designs for advanced short-takeoff, vertical landing (ASTOVL) aircraft need exhaust nozzles that can vector the jet to provide forces and moments for controlling the aircraft's movement or attitude in flight near the ground. A type of nozzle that can both vector the jet and vary the jet flow area is called a vane nozzle. Basically, the nozzle consists of parallel, spaced-apart flow passages formed by pairs of vanes (vanesets) that can be rotated on axes perpendicular to the flow. Two important features of this type of nozzle are the abilities to vector the jet rearward up to 45 degrees and to produce less harsh pressure and velocity footprints during vertical landing than does an equivalent single jet. A one-third-scale model of a generic vane nozzle was tested with unheated air at the NASA Lewis Research Center's Powered Lift Facility. The model had three parallel flow passages. Each passage was formed by a vaneset consisting of a long and a short vane. The longer vanes controlled the jet vector angle, and the shorter controlled the flow area. Nozzle performance for three nominal flow areas (basic and plus or minus 21 percent of basic area), each at nominal jet vector angles from -20 deg (forward of vertical) to +45 deg (rearward of vertical) are presented. The tests were made with the nozzle mounted on a model tailpipe with a blind flange on the end to simulate a closed cruise nozzle, at tailpipe-to-ambient pressure ratios from 1.8 to 4.0. Also included are jet wake data, single-vaneset vector performance for long/short and equal-length vane designs, and pumping capability. The pumping capability arises from the subambient pressure developed in the cavities between the vanesets, which could be used to aspirate flow from a source such as the engine compartment. Some of the performance characteristics are compared with characteristics of a single-jet nozzle previously reported.

Mcardle, Jack G.↗

NASA NTRS1993

Performance characteristics of a variable-area vane nozzle for vectoring an ASTOVL exhaust jet up to 45 deg

Many conceptual designs for advanced short-takeoff, vertical landing (ASTOVL) aircraft need exhaust nozzles that can vector the jet to provide forces and moments for controlling the aircraft's movement or attitude in flight near the ground. A type of nozzle that can both vector the jet and vary the jet flow area is called a vane nozzle. Basically, the nozzle consists of parallel, spaced-apart flow passages formed by pairs of vanes (vanesets) that can be rotated on axes perpendicular to the flow. Two important features of this type of nozzle are the abilities to vector the jet rearward up to 45 degrees and to produce less harsh pressure and velocity footprints during vertical landing than does an equivalent single jet. A one-third-scale model of a generic vane nozzle was tested with unheated air at the NASA Lewis Research Center's Powered Lift Facility. The model had three parallel flow passages. Each passage was formed by a vaneset consisting of a long and a short vane. The longer vanes controlled the jet vector angle, and the shorter controlled the flow area. Nozzle performance for three nominal flow areas (basic and plus or minus 21 percent of basic area), each at nominal jet vector angles from -20 deg (forward of vertical) to +45 deg (rearward of vertical) are presented. The tests were made with the nozzle mounted on a model tailpipe with a blind flange on the end to simulate a closed cruise nozzle, at tailpipe-to-ambient pressure ratios from 1.8 to 4.0. Also included are jet wake data, single-vaneset vector performance for long/short and equal-length vane designs, and pumping capability. The pumping capability arises from the subambient pressure developed in the cavities between the vanesets, which could be used to aspirate flow from a source such as the engine compartment. Some of the performance characteristics are compared with characteristics of a single-jet nozzle previously reported.

Mcardle, Jack G.↗

NASA NTRS1993

Static internal performance of a single expansion ramp nozzle with multiaxis thrust vectoring capability

An investigation was conducted at static conditions in order to determine the internal performance characteristics of a multiaxis thrust vectoring single expansion ramp nozzle. Yaw vectoring was achieved by deflecting yaw flaps in the nozzle sidewall into the nozzle exhaust flow. In order to eliminate any physical interference between the variable angle yaw flap deflected into the exhaust flow and the nozzle upper ramp and lower flap which were deflected for pitch vectoring, the downstream corners of both the nozzle ramp and lower flap were cut off to allow for up to 30 deg of yaw vectoring. The effects of nozzle upper ramp and lower flap cutout, yaw flap hinge line location and hinge inclination angle, sidewall containment, geometric pitch vector angle, and geometric yaw vector angle were studied. This investigation was conducted in the static-test facility of the Langley 16-Foot Transonic Tunnel at nozzle pressure ratios up to 8.0.

Capone, Francis J.↗

NASA NTRS1994

Modeling the two-point correlation of the vector stream function

A new model for the two-point vector stream function correlation has been developed using tensor invariant arguments and evaluated by the comparison of model predictions with DNS data for incompressible homogeneous turbulent shear flow. This two-point vector stream function model correlation can then be used to calculate the two-point velocity correlation function and other quantities useful in turbulence modeling. The model assumes that the two-point vector stream function correlation can be written in terms of the separation vector and a new tensor function that depends only on the magnitude of the separation vector. The model has a single free model coefficient, which has been chosen by comparison with the DNS data. The relative error of the model predictions of the two-point vector stream function correlation is only a few percent for a broad range of the model coefficient. Predictions of the derivatives of this correlation, which are of interest in turbulence modeling, may not be this accurate.

Oberlack, M.↗

NASA NTRS1995

Internal performance characteristics of thrust-vectored axisymmetric ejector nozzles

A series of thrust-vectored axisymmetric ejector nozzles were designed and experimentally tested for internal performance and pumping characteristics at the Langley research center. This study indicated that discontinuities in the performance occurred at low primary nozzle pressure ratios and that these discontinuities were mitigated by decreasing expansion area ratio. The addition of secondary flow increased the performance of the nozzles. The mid-to-high range of secondary flow provided the most overall improvements, and the greatest improvements were seen for the largest ejector area ratio. Thrust vectoring the ejector nozzles caused a reduction in performance and discharge coefficient. With or without secondary flow, the vectored ejector nozzles produced thrust vector angles that were equivalent to or greater than the geometric turning angle. With or without secondary flow, spacing ratio (ejector passage symmetry) had little effect on performance (gross thrust ratio), discharge coefficient, or thrust vector angle. For the unvectored ejectors, a small amount of secondary flow was sufficient to reduce the pressure levels on the shroud to provide cooling, but for the vectored ejector nozzles, a larger amount of secondary air was required to reduce the pressure levels to provide cooling.

Lamb, Milton↗

NASA NTRS1994

A new technique for the measurement of surface shear stress vectors using liquid crystal coatings

Research has recently shown that liquid crystal coating (LCC) color-change response to shear depends on both shear stress magnitude and direction. Additional research was thus conducted to extend the LCC method from a flow-visualization tool to a surface shear stress vector measurement technique. A shear-sensitive LCC was applied to a planar test surface and illuminated by white light from the normal direction. A fiber optic probe was used to capture light scattered by the LCC from a point on the centerline of a turbulent, tangential-jet flow. Both the relative shear stress magnitude and the relative in-plane view angle between the sensor and the centerline shear vector were systematically varied. A spectrophotometer was used to obtain scattered-light spectra which were used to quantify the LCC color (dominant wavelength) as a function of shear stress magnitude and direction. At any fixed shear stress magnitude, the minimum dominant wavelength was measured when the shear vector was aligned with and directed away from the observer; changes in the relative in-plane view angle to either side of this vector/observer aligned position resulted in symmetric Gaussian increases in measured dominant wavelength. Based on these results, a vector measurement methodology, involving multiple oblique-view observations of the test surface, was formulated. Under present test conditions, the measurement resolution of this technique was found to be +/- 1 deg for vector orientations and +/- 5% for vector magnitudes. An approach t o extend the present methodology to full-surface applications is proposed.

Reda, Daniel C.↗

NASA NTRS1996

SSM/I and ECMWF Wind Vector Comparison

Wentz was the first to convincingly show that satellite microwave radiometers have the potential to measure the oceanic wind vector. The most compelling evidence for this conclusion was the monthly wind vector maps derived solely from a statistical analysis of Special Sensor Microwave Imager (SSM/I) observations. In a qualitative sense, these maps clearly showed the general circulation over the world's oceans. In this report we take a closer look at the SSM/I monthly wind vector maps and compare them to European Center for Medium-Range Weather Forecasts (ECMWF) wind fields. This investigation leads both to an empirical comparison of SSM/I calculated wind vectors with ECMWF wind vectors, and to an examination of possible reasons that the SSM/I calculated wind vector direction would be inherently more reliable at some locations than others.

Wentz, Frank J.↗

NASA NTRS1997

Improvements in Block-Krylov Ritz Vectors and the Boundary Flexibility Method of Component Synthesis

A method of dynamic substructuring is presented which utilizes a set of static Ritz vectors as a replacement for normal eigenvectors in component mode synthesis. This set of Ritz vectors is generated in a recurrence relationship, proposed by Wilson, which has the form of a block-Krylov subspace. The initial seed to the recurrence algorithm is based upon the boundary flexibility vectors of the component. Improvements have been made in the formulation of the initial seed to the Krylov sequence, through the use of block-filtering. A method to shift the Krylov sequence to create Ritz vectors that will represent the dynamic behavior of the component at target frequencies, the target frequency being determined by the applied forcing functions, has been developed. A method to terminate the Krylov sequence has also been developed. Various orthonormalization schemes have been developed and evaluated, including the Cholesky/QR method. Several auxiliary theorems and proofs which illustrate issues in component mode synthesis and loss of orthogonality in the Krylov sequence have also been presented. The resulting methodology is applicable to both fixed and free- interface boundary components, and results in a general component model appropriate for any type of dynamic analysis. The accuracy is found to be comparable to that of component synthesis based upon normal modes, using fewer generalized coordinates. In addition, the block-Krylov recurrence algorithm is a series of static solutions and so requires significantly less computation than solving the normal eigenspace problem. The requirement for less vectors to form the component, coupled with the lower computational expense of calculating these Ritz vectors, combine to create a method more efficient than traditional component mode synthesis.

Carney, Kelly Scott↗

NASA NTRS1997

Multi-Axis Fluidic Thrust Vectoring of a Supersonic Jet Using Counterflow

The most common techniques currently used to efficiently vector supersonic jets require external flaps and or pivoting devices. Fluidic thrust vectoring using counterflow eliminates the need for such complex hardware. Thus, the promise of decreases in both weight and drag as well as increased maneuverability makes this technique an attractive alternative. This technique has been successfully employed to achieve single axis fluidic thrust vectoring of a Mach 2 rectangular jet. To better compete with contemporary systems the current study extends this technique to multi-axis thrust vectoring of a Mach 2 diamond-shaped jet by applying counterflow to one of its four sides. To evaluate the performance of this technique the Planar Laser Scattering (PLS) technique is used to show the continuous vectoring of the diamond jet up to 20 degrees. Also, cross-stream PLS images are acquired to show the vectoring can be achieved off all four surfaces of the diamond jet.

Barber, Edward L.↗

NASA NTRS1998

Attitude Determination Using Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.

Markley, F. Landis↗

NASA NTRS1999

Attitude Determination Using Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.

Markley, F. Landis↗

NASA NTRS1994

Implementation and Assessment of Advanced Analog Vector-Matrix Processor

This paper discusses the design and implementation of an analog optical vecto-rmatrix coprocessor with a throughput of 128 Mops for a personal computer. Vector matrix calculations are inherently parallel, providing a promising domain for the use of optical calculators. However, to date, digital optical systems have proven too cumbersome to replace electronics, and analog processors have not demonstrated sufficient accuracy in large scale systems. The goal of the work described in this paper is to demonstrate a viable optical coprocessor for linear operations. The analog optical processor presented has been integrated with a personal computer to provide full functionality and is the first demonstration of an optical linear algebra processor with a throughput greater than 100 Mops. The optical vector matrix processor consists of a laser diode source, an acoustooptical modulator array to input the vector information, a liquid crystal spatial light modulator to input the matrix information, an avalanche photodiode array to read out the result vector of the vector matrix multiplication, as well as transport optics and the electronics necessary to drive the optical modulators and interface to the computer. The intent of this research is to provide a low cost, highly energy efficient coprocessor for linear operations. Measurements of the analog accuracy of the processor performing 128 Mops are presented along with an assessment of the implications for future systems. A range of noise sources, including cross-talk, source amplitude fluctuations, shot noise at the detector, and non-linearities of the optoelectronic components are measured and compared to determine the most significant source of error. The possibilities for reducing these sources of error are discussed. Also, the total error is compared with that expected from a statistical analysis of the individual components and their relation to the vector-matrix operation. The sufficiency of the measured accuracy of the processor is compared with that required for a range of typical problems. Calculations resolving alloy concentrations from spectral plume data of rocket engines are implemented on the optical processor, demonstrating its sufficiency for this problem. We also show how this technology can be easily extended to a 100 x 100 10 MHz (200 Cops) processor.

Gary, Charles K.↗

NASA NTRS2001

Fast Quaternion Attitude Estimation from Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. Existing closed-form attitude estimates based on Wahba's optimality criterion for two arbitrarily weighted observations are somewhat slow to evaluate. This paper presents two new fast quaternion attitude estimation algorithms using two vector observations, one optimal and one suboptimal. The suboptimal method gives the same estimate as the TRIAD algorithm, at reduced computational cost. Simulations show that the TRIAD estimate is almost as accurate as the optimal estimate in representative test scenarios.

Markley, F. Landis↗