Results for “metric geometry” — Page 3

NASA NTRS1994

Models of pair annihilation in 1E 1740.7-2942 and the HEAO 1 A-4 annihilation source

We study possible models of two Galactic sources of transient pair annihilation radiation, 1E 1740.7-2942 and a source observed by High Energy Astronomy Observatory (HEAO) 1 A-4. We fit the observed spectral features by thermal annihilation spectra and find that the redshifts obtained by us are much larger than those obtained from fitting Caussian lines centered on 511 keV. This effect, which is due to the net blueshift (with respect to 511 keV) of the annihilation spectrum due to the thermal energies of pairs, puts strong constraints on models of sources. We consider those constraints first without considering the mechanism of positron production. From the shape of the observed spectra, we are able to rule out both spherical clouds and layers above cold matter as possible source geometries. The observed spectra are compatible with two source geometries: (1) a nearly face-on disk in the Kerr metric and (2) a jet close to a black hole. We consider, then, the origin of the pairs. Theories of both thermal and nonthermal pair equilibria predict that photon-pair production is unable to produce annihilation features that contain as much as half of the bolometric luminosity, which is observed. A possible solution to this problem is obscuration of a nonthermal source (in which pairs are produced by photon-photon collisions) and an outflow of pairs to an unobscured region. This makes annihilation in a jet the most likely model of the considered sources.

Maciolek-Niedzwiecki, Andrzej↗

NASA NTRS2014

Strain Gage Load Calibration of the Wing Interface Fittings for the Adaptive Compliant Trailing Edge Flap Flight Test

The safety-of-flight parameters for the Adaptive Compliant Trailing Edge (ACTE) flap experiment require that flap-to-wing interface loads be sensed and monitored in real time to ensure that the structural load limits of the wing are not exceeded. This paper discusses the strain gage load calibration testing and load equation derivation methodology for the ACTE interface fittings. Both the left and right wing flap interfaces were monitored; each contained four uniquely designed and instrumented flap interface fittings. The interface hardware design and instrumentation layout are discussed. Twenty-one applied test load cases were developed using the predicted in-flight loads. Pre-test predictions of strain gage responses were produced using finite element method models of the interface fittings. Predicted and measured test strains are presented. A load testing rig and three hydraulic jacks were used to apply combinations of shear, bending, and axial loads to the interface fittings. Hardware deflections under load were measured using photogrammetry and transducers. Due to deflections in the interface fitting hardware and test rig, finite element model techniques were used to calculate the reaction loads throughout the applied load range, taking into account the elastically-deformed geometry. The primary load equations were selected based on multiple calibration metrics. An independent set of validation cases was used to validate each derived equation. The 2-sigma residual errors for the shear loads were less than eight percent of the full-scale calibration load; the 2-sigma residual errors for the bending moment loads were less than three percent of the full-scale calibration load. The derived load equations for shear, bending, and axial loads are presented, with the calculated errors for both the calibration cases and the independent validation load cases.

Miller, Eric J.↗

NASA NTRS1995

Optically thin accretion disks in the Kerr metric

We calculate the structure of an effectively optically thin and geometrically thin accretion disk in the Kerr geometry, including electron-positron pairs. We show that the properties of the disk solutions are strongly dependent on the angular momentum of the central black hole. We find that close to a rapidly rotating hole there can be an appreciable pair density even for modest accretion rates. Pair critical accretion rates recently discovered in Newtonian disk models are also shown to be present in the general relativistic models, and we show that the geometrically thin disk approximations easily break down for rapidly rotating holes.

Bjornsson, G.↗

NASA NTRS2015

Quantifying Mapping Orbit Performance in the Vicinity of Primitive Bodies

Predicting and quantifying the capability of mapping orbits in the vicinity of primitive bodies is challenging given the complex orbit geometries that exist and the irregular shape of the bodies themselves. This paper employs various quantitative metrics to characterize the performance and relative effectiveness of various types of mapping orbits including terminator, quasi-terminator, hovering, pingpong, and conic-like trajectories. Metrics of interest include surface area coverage, lighting conditions, and the variety of viewing angles achieved. The metrics discussed in this investigation are intended to enable mission designers and project stakeholders to better characterize candidate mapping orbits during preliminary mission formulation activities.The goal of this investigation is to understand the trade space associated with carrying out remotesensing campaigns at small primitive bodies in the context of a robotic space mission. Specifically,this study seeks to understand the surface viewing geometries, ranges, etc. that are available fromseveral commonly proposed mapping orbits architectures.

Pavlak, Thomas A.↗

NASA NTRS2015

Quantifying Mapping Orbit Performance in the Vicinity of Primitive Bodies

Predicting and quantifying the capability of mapping orbits in the vicinity of primitive bodies is challenging given the complex orbit geometries that exist and the irregular shape of the bodies themselves. This paper employs various quantitative metrics to characterize the performance and relative effectiveness of various types of mapping orbits including terminator, quasi-terminator, hovering, ping pong, and conic-like trajectories. Metrics of interest include surface area coverage, lighting conditions, and the variety of viewing angles achieved. The metrics discussed in this investigation are intended to enable mission designers and project stakeholders to better characterize candidate mapping orbits during preliminary mission formulation activities. The goal of this investigation is to understand the trade space associated with carrying out remote sensing campaigns at small primitive bodies in the context of a robotic space mission. Specifically, this study seeks to understand the surface viewing geometries, ranges, etc. that are available from several commonly proposed mapping orbits architectures

Pavlak, Thomas A.↗

NASA NTRS1983

An orthogonal coordinate grid following the three-dimensional viscous flow over a concave surface

Swept wings designed for laminar flow control exhibit both centrifugal and crossflow instabilities which produce streamwise vortices that can lead to early transition from laminar to turbulent flow in the presence of Tollmien-Schlichting waves. This paper outlines an iterative algorithm for generation of an orthogonal, curvilinear, coordinate grid following the streamlines of the three-dimensional viscous flow over a swept, concave surface. The governing equations for the metric tensor are derived from the Riemann-Christoffel tensor for an Euclidian geometry. Unit vectors along streamline, normal and binormal directions are determined. The governing equations are not solved directly, but are employed only as compatibility equations. The scale factor for the streamline coordinate is obtained by an iterative integration scheme on a 200 x 100 x 5 grid, while the other two scale factors are determined from definitions. Sample results are obtained which indicate that the compatibility equation error decreases linearly with grid step size. Grids smaller than 200 x 100 x 5 are found to be inadequate to resolve the grid curvature.

Dagenhart, J. R↗

NASA NTRS2010

NASA Tech Briefs, December 2010

Topics include: Coherent Frequency Reference System for the NASA Deep Space Network; Diamond Heat-Spreader for Submillimeter-Wave Frequency Multipliers; 180-GHz I-Q Second Harmonic Resistive Mixer MMIC; Ultra-Low-Noise W-Band MMIC Detector Modules; 338-GHz Semiconductor Amplifier Module; Power Amplifier Module with 734-mW Continuous Wave Output Power; Multiple Differential-Amplifier MMICs Embedded in Waveguides; Rapid Corner Detection Using FPGAs; Special Component Designs for Differential-Amplifier MMICs; Multi-Stage System for Automatic Target Recognition; Single-Receiver GPS Phase Bias Resolution; Ultra-Wideband Angle-of-Arrival Tracking Systems; Update on Waveguide-Embedded Differential MMIC Amplifiers; Automation Framework for Flight Dynamics Products Generation; Product Operations Status Summary Metrics; Mars Terrain Generation; Application-Controlled Parallel Asynchronous Input/Output Utility; Planetary Image Geometry Library; Propulsion Design With Freeform Fabrication (PDFF); Economical Fabrication of Thick-Section Ceramic Matrix Composites; Process for Making a Noble Metal on Tin Oxide Catalyst; Stacked Corrugated Horn Rings; Refinements in an Mg/MgH2/H2O-Based Hydrogen Generator; Continuous/Batch Mg/MgH2/H2O-Based Hydrogen Generator; Strain System for the Motion Base Shuttle Mission Simulator; Ko Displacement Theory for Structural Shape Predictions; Pyrotechnic Actuator for Retracting Tubes Between MSL Subsystems; Surface-Enhanced X-Ray Fluorescence; Infrared Sensor on Unmanned Aircraft Transmits Time-Critical Wildfire Data; and Slopes To Prevent Trapping of Bubbles in Microfluidic Channels.

Source record↗

NASA NTRS1977

General relativity and satellite orbits - The motion of a test particle in the Schwarzschild metric

The motion of a satellite of negligible mass about a massive spherically symmetric object in a space of Schwarzschild geometry is calculated by using ordinary Newtonian methods for an inverse-square gravitational field acted upon by an inverse-cube disturbing function. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted in the Lagrange planetary equations. The equations can be integrated to calculate the displacement in position of the satellite due to the relativistic potential. For example, the Beacon Explorer C satellite is found to be displaced by about 17.4 cm after one revolution. For Mercury the advance of the perihelion is about 85 km after one orbit, and the maximum periodic displacement is about 13 km.

Rubincam, D. P.↗

NASA NTRSDate not supplied

Experimental and Numerical Investigation of the NASA High Efficiency Centrifugal Compressor Vaned Stage Geometry and Aerodynamic Performance

Since its inception in the early 2010s, the NASA High Efficiency Centrifugal Compressor (HECC) has been enigmatic for the propulsion research community: experimental data and numerical simulations of the stage have generally not aligned in their quantifications of performance metrics. Typically, the fault for these disagreements is assigned to the numerical simulations as the simulations are models, and models are inherently incomplete representations of the experiment. This “incompleteness” may manifest in assumptions regarding roughness or heat transfer, simplifications of the flow path (i.e., neglecting bleed flows), or the oft-scapegoated turbulence model. In the case of HECC, recent work showed unexpected discrepancies between the intended impeller geometry defined in the design report (termed Design-Intent) and the manufactured impeller used in the experimental campaigns (termed As-Manufactured). That work used numerical simulations to establish that the geometric differences between the Design-Intent and As-Manufactured impellers were significant enough to result in drastically different performance predictions for the HECC vaneless diffuser configuration. The Design-Intent impeller simulations over predicted the performance relative to the experiment, whereas the As-Manufactured simulations better represented the experimental data, both in terms of one-dimensional performance metrics and spanwise flow profiles. This effort expands on that work by examining in detail the geometry and aerodynamic performance of the HECC vaned diffuser configuration. Further differences between the Design-Intent and As-Manufactured geometries have been discovered in the vaned diffuser and exit guide vanes, and these differences are documented herein. The summations of the geometric differences for all of the components were used to create two numerical models of HECC vaned diffuser configuration: the Design-Intent simulations which are generated from the original geometry definitions given in the design report and the As-Manufactured simulations which are the best available representation of the manufactured compressor hardware used in the experimental test campaigns. In congruence with the earlier vaneless diffuser work, the numerical predictions of the Design-Intent choked mass flow rate, total pressure ratio, and efficiency were notably greater than that of the As-Manufactured simulations. To increase confidence in the experimental dataset, measurements from a recent test campaign conducted in 2024 are used to validate the original experimental data acquired from 2012 to 2014 with good repeatability overall, especially considering the passage of time and differences in the data acquisition systems between the test campaigns. Both numerical simulations were then extensively evaluated against the experimental data. The As-Manufactured simulations provided better estimates of the stage performance than the Design-Intent cases in terms of most performance metrics. Nonetheless, more detailed results still show opportunities for improvement. Despite a more accurate representation of the physical hardware, characterization of the impeller work input remains a challenge even for rigorously developed numerical models.

vaned diffuser↗

NASA NTRSDate not supplied

Experimental and Numerical Investigation of the NASA High Efficiency Centrifugal Compressor Vaned Stage Geometry and Aerodynamic Performance

Since its inception in the early 2010s, the NASA High Efficiency Centrifugal Compressor (HECC) has been enigmatic for the propulsion research community: experimental data and numerical simulations of the stage have generally not aligned in their quantifications of performance metrics. Typically, the fault for these disagreements is assigned to the numerical simulations as the simulations are models, and models are inherently incomplete representations of the experiment. This “incompleteness” may manifest in assumptions regarding roughness or heat transfer, simplifications of the flow path (i.e., neglecting bleed flows), or the oft-scapegoated turbulence model. In the case of HECC, recent work showed unexpected discrepancies between the intended impeller geometry defined in the design report (termed Design-Intent) and the manufactured impeller used in the experimental campaigns (termed As-Manufactured). That work used numerical simulations to establish that the geometric differences between the Design-Intent and As-Manufactured impellers were significant enough to result in drastically different performance predictions for the HECC vaneless diffuser configuration. The Design-Intent impeller simulations over predicted the performance relative to the experiment, whereas the As-Manufactured simulations better represented the experimental data, both in terms of one-dimensional performance metrics and spanwise flow profiles. This effort expands on that work by examining in detail the geometry and aerodynamic performance of the HECC vaned diffuser configuration. Further differences between the Design-Intent and As-Manufactured geometries have been discovered in the vaned diffuser and exit guide vanes, and these differences are documented herein. The summations of the geometric differences for all of the components were used to create two numerical models of HECC vaned diffuser configuration: the Design-Intent simulations which are generated from the original geometry definitions given in the design report and the As-Manufactured simulations which are the best available representation of the manufactured compressor hardware used in the experimental test campaigns. In congruence with the earlier vaneless diffuser work, the numerical predictions of the Design-Intent choked mass flow rate, total pressure ratio, and efficiency were notably greater than that of the As-Manufactured simulations. To increase confidence in the experimental dataset, measurements from a recent test campaign conducted in 2024 are used to validate the original experimental data acquired from 2012 to 2014 with good repeatability overall, especially considering the passage of time and differences in the data acquisition systems between the test campaigns. Both numerical simulations were then extensively evaluated against the experimental data. The As-Manufactured simulations provided better estimates of the stage performance than the Design-Intent cases in terms of most performance metrics. Nonetheless, more detailed results still show opportunities for improvement. Despite a more accurate representation of the physical hardware, characterization of the impeller work input remains a challenge even for rigorously developed numerical models.

centrifugal compressor↗

NASA NTRS2022

A Survey of Mathematical Structures for Lunar Networks

To sustain the current and increasing accessibility of space, a scalable communications infrastructure (i.e. the Solar System Internet, SSI) is necessary. The goal of this paper is to begin the discovery of the fundamental underlying mathematical structure of space networks to help the research community harness these structures for algorithm development and optimization. To ensure the applicability of the research, the approaches are considered through the lens of simulated scenarios inspired by the Artemis Back-to-the-Moon mission set for 2024. We note that any approach to an SSI must fit under the umbrella of Delay Tolerant Networking (DTN), due to celestial mobility, high link latencies, high variance in link latencies, disconnections, lack of end-to-end paths, and so on. These difficulties are exacerbated by the fact that the underlying structure of a space network is a time-evolving network and may experience multiple discontinuities in its topology. In this paper we propose several novel approaches to a mathematical foundation for Delay Tolerant Networking Theory that fall outside the traditional scope of temporal network theory. These techniques include methods from Topological Data Analysis, Dynamic Graph Analysis, Applied Algebraic Geometry, Probability Theory, and Game Theory. Some of these methods include tools adapted to the study of dynamic metric spaces, such as zigzag persistent homology and their higher parameter analogs. We find that several of these methods target desired engineering outcomes such as discovery and automatic sub-netting. While each approach is theoretical, they are also algorithmic in nature and offer immediate practical applications. The paper concludes with comparisons of the various methods along with suggestions for future work.

Delay tolerant networking↗

NASA NTRSDate not supplied

Virtual Fit Assessment: Validation using Historical Spacesuit Fit Data

Virtual fit tests using 3D body scans have provided a cost-effective means to predictively assess spacesuit fit for the current and future astronaut population. However, fit is a complex issue influenced by physical interferences, subjective preference, and many other factors. Fit can substantially differ between the type of hardware, environmental conditions, and tasks being performed. Namely, fit changes across different contexts, such as 3D printed mockup evaluations, pressurized one-g suited test events, neutral buoyancy and other training events, and flight extravehicular activities (EVA). These challenges make it difficult to validate virtual fit frameworks to physical suit sizing. This study proposes a new method of validation using the wealth of historically archived suit fit data. Physically Assessed Fit (PAF) data was assessed from astronauts and test volunteers who wore the legacy Extravehicular Mobility Unit (EMU). The data was collected during the past decades at NASA and considered to be most reliable and dependable. Each participant was 3D scanned for body shape and spacesuit-critical dimensions were measured per NASA guidelines. The participants’ size preference for hard upper torso (HUT) assembly was retrieved from their pressurized suit fit check records. Fit assessments were also updated after one-g EVA training, neutral buoyancy training, and EVA flights. Virtually Assessed Fit (VAF) was done by overlaying the CAD model of a HUT with the 3D body scans of the PAF participants. Each body scan was iteratively adjusted for the position inside the HUT to minimize the suit-to-body contact interference while satisfying a set of prescribed requirements. Then the residual contact area, depth, and volume were quantified as VAF metrics. This process was repeated for the different HUT sizes, including medium, large, and extra-large. Statistical modeling is currently in progress and will be presented at the conference. A statistical classifier will be developed to predict a fit probability for different HUT sizes as a function of the corresponding person’s VAF metrics. The HUT size with the highest fit probability will constitute the most likely size selection for the person, and the prediction will be compared against the corresponding PAF data. The participant data will be randomly pre-grouped into either a model development or validation subset. While the model development subset will be used to build the probability model, the validation subset will be used to assess the model accuracy. Also, the locations and magnitudes of suit-body-contacts will be estimated from VAF. This information can identify the critical suit geometry and body shape features that influence suit fit. The variations found in PAF size selections by subjects with similar VAF metrics will allow for investigations into subjective preferences, for example, tight versus loose fit. Overall, this study is expected to provide a structured validation of a virtual suit fit framework, which has not been possible in the past. The outcome can also provide useful insights and potential limitations for interpreting virtual fit tests for future spacesuit designs and population accommodation.

Han Kim↗

NASA NTRS2010

A Computational Framework to Control Verification and Robustness Analysis

This paper presents a methodology for evaluating the robustness of a controller based on its ability to satisfy the design requirements. The framework proposed is generic since it allows for high-fidelity models, arbitrary control structures and arbitrary functional dependencies between the requirements and the uncertain parameters. The cornerstone of this contribution is the ability to bound the region of the uncertain parameter space where the degradation in closed-loop performance remains acceptable. The size of this bounding set, whose geometry can be prescribed according to deterministic or probabilistic uncertainty models, is a measure of robustness. The robustness metrics proposed herein are the parametric safety margin, the reliability index, the failure probability and upper bounds to this probability. The performance observed at the control verification setting, where the assumptions and approximations used for control design may no longer hold, will fully determine the proposed control assessment.

Crespo, Luis G.↗

NASA NTRS2015

Evaluating Performance of UAS Detect-And-Avoid System Using a Fast-Time Simulation Tool

Most unmanned aircraft systems will be required to be equipped with a Detect-and-Avoid (DAA) system. The surveillance performance of the DAA system to detect and track intruder aircraft will depend on the encounter geometries that unmanned aircraft are expected to have with other aircraft in the airspace. The performance of DAA alerting and avoidance system is also dependent on the timeliness of alerting for UAS pilots to give a sufficient time to determine and command a resolution maneuver to avoid well clear separation violations. This presentation introduces general background of UAS DAA systems and concept of well clear separation standard to satisfy see and avoid regulations. The presentation shows the several UAS mission profiles and analysis of the encounter geometries that were simulated using historical VFR traffic data and some proposed UAS missions. This presentation introduces several potential metrics for evaluating the performance of a DAA system and shows the results that measured through fast-time simulation with traffic scenarios that include NAS-wide VFR manned aircraft and IFR UAS flights. At the end, some research areas will be briefly discussed.

UAS↗

NASA NTRSDate not supplied

Flying Qualities Analysis and Piloted Simulation Testing of a Lift+Cruise Vehicle with Propulsion Failures in Hover and Low-Speed Conditions

The recent emergence of electric-Vertical Take-Off and Landing (eVTOL) vehicles for Urban Air Mobility (UAM) applications has resulted in a wide variety of configurations with unique stability and control characteristics. NASA is currently conducting research to develop conceptual design tools to accelerate public acceptance of these vehicles which includes requirements for safety during failure scenarios. This paper summarizes progress toward a toolbox for predicting flying qualities of eVTOL vehicles during critical propulsion failures that could impact the allowable design of the vehicle geometry or control system. Key topics include unique vulnerabilities of eVTOL/multirotor vehicles to propulsion failures, relevant flying qualities design metrics, and simulation modeling requirements for assessing flying qualities degradation due to failures. Results of a piloted simulation study conducted in the NASA Ames Vertical Motion Simulator (VMS) are presented. The VMS experiment was designed to assess and validate key handling qualities and safety design metrics for propulsion failures. These results show the correlation between control system design requirements and the degradation in handling qualities for various propulsion failures.

George Altamirano↗

NASA NTRS1966

Rotating masses and their effect on inertial frames.

Rotating masses effect on inertial frames, analyzing stress energy tensor and Schwarzschild geometry

INERTIAL FORCE↗

NASA NTRS2008

Parallel Anisotropic Tetrahedral Adaptation

An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domain-decomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.

Park, Michael A.↗

NASA NTRS2017

An Alternative Time Metric to Modified Tau for Unmanned Aircraft System Detect And Avoid

A new horizontal time metric, Time to Protected Zone, is proposed for use in the Detect and Avoid (DAA) Systems equipped by unmanned aircraft systems (UAS). This time metric has three advantages over the currently adopted time metric, modified tau: it corresponds to a physical event, it is linear with time, and it can be directly used to prioritize intruding aircraft. The protected zone defines an area around the UAS that can be a function of each intruding aircraft's surveillance measurement errors. Even with its advantages, the Time to Protected Zone depends explicitly on encounter geometry and may be more sensitive to surveillance sensor errors than modified tau. To quantify its sensitivity, simulation of 972 encounters using realistic sensor models and a proprietary fusion tracker is performed. Two sensitivity metrics, the probability of time reversal and the average absolute time error, are computed for both the Time to Protected Zone and modified tau. Results show that the sensitivity of the Time to Protected Zone is comparable to that of modified tau if the dimensions of the protected zone are adequately defined.

alert↗