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At least 739 records · Page 41

Effects of drift on the transport of cosmic rays. VI - A three-dimensional model including diffusion

The first results are presented from a series of computer simulations of the solar modulation of galactic cosmic rays using a full three-dimensional model which incorporates all known important effects on particle transport, particle drifts, convection with the solar wind, energy loss, and anisotropic diffusion. The model is time-independent in the coordinate frame rotating with the sun, so corotating effects can be studied. Modulation in an interplanetary magnetic field model is considered in which the current sheet separating the northern and southern solar hemispheres is warped and corotating with the sun. The amplitude of the warp is varied to simulate possible solar cycle variation of the magnetic field. Substantial effects due to the warp of the current sheet are found. Comparison of the model results with various data is presented. Among other things, it is shown that the intensity may decrease away from the current sheet for both signs of the magnetic field, as suggested by recent observations, and in contrast with inferences from earlier, more approximate calculations.

Kota, J.↗

Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization

Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. Here, we demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss–Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.

97 MATHEMATICS AND COMPUTING↗

Current Sheet Formation in a Conical Theta Pinch Faraday Accelerator with Radio-frequency Assisted Discharge

Data from an inductive conical theta pinch accelerator are presented to gain insight into the process of inductive current sheet formation in the presence of a preionized background gas produced by a steady-state RF-discharge. The presence of a preionized plasma has been previously shown to allow for current sheet formation at lower discharge voltages and energies than those found in other pulsed inductive accelerator concepts, leading to greater accelerator efficiencies at lower power levels. Time-resolved magnetic probe measurements are obtained for different background pressures and pulse energies to characterize the effects of these parameters on current sheet formation. Indices are defined that describe time-resolved current sheet characteristics, such as the total current owing in the current sheet, the time-integrated total current ('strength'), and current sheet velocity. It is found that for a given electric field strength, maximums in total current, strength, and velocity occur for one particular background pressure. At other pressures, these current sheet indices are considerably smaller. The trends observed in these indices are explained in terms of the principles behind Townsend breakdown that lead to a dependence on the ratio of the electric field to the background pressure. Time-integrated photographic data are also obtained at the same experimental conditions, and qualitatively they compare quite favorably with the time-resolved magnetic field data.

Polzin, Kurt A.↗

Regions of abnormally low proton temperature as signatures of ejecta: Solar cycle dependence and association with other ejecta signatures

Solar wind proton temperatures lower than expected for 'normal' solar wind expansion are a common signature of 'ejecta' (i.e. interplanetary coronal mass ejections). We have surveyed the OMNI solar wind data base for 1965-1991, and Helios data for 1974-1980, to identify regions of abnormally low temperatures. Their occurrence rate is clearly dependent on solar activity levels, in particular when the minority of events associated with encounters with the heliospheric plasma sheet are excluded. The analysis of the OMNI data may provide an indication of the rate of ejecta at the Earth, and hence of the CME rate, extending back to before spacecraft coronagraph observations became available in the early 1970's. We discuss the association of these solar wind structures with cosmic ray depressions bidirectional particle flows, and other ejecta signatures. Our impression is that no one ejecta signature provides a truly comprehensive indication of the presence of ejecta, but that abnormally low temperature depressions encompass most of the regions identified by these other individual signatures.

Richardson, I. G.↗

Ice sheet topography from retracked ERS-1 altimetry

An objective of the ERS-1 radar altimeter is to measure the surface topography of the polar ice sheets to a precision on the order of a meter. ERS-1 Waveform Altimeter Product (WAP) data was corrected for several processing errors. A range correction from the WAP waveforms, using the multiparameter retracking algorithm to account for range tracking limitations inherent to radar altimetry, was derived. From crossover analysis, the resulting precision is shown to be about 2.1 m in ocean mode and 2.2 m in ice mode. A topography map, produced with 23 days of corrected data, shows details of the western part of west Antarctic ice sheet and part of the Ross ice shelf including ice divides, ice stream boundaries, and ice shelf grounding lines.

Zwally, H. Jay↗

Failure prediction of thin beryllium sheets used in spacecraft structures

The primary objective of this study is to develop a method for prediction of failure of thin beryllium sheets that undergo complex states of stress. Major components of the research include experimental evaluation of strength parameters for cross-rolled beryllium sheet, application of the Tsai-Wu failure criterion to plate bending problems, development of a high order failure criterion, application of the new criterion to a variety of structures, and incorporation of both failure criteria into a finite element code. A Tsai-Wu failure model for SR-200 sheet material is developed from available tensile data, experiments carried out by NASA on two circular plates, and compression and off-axis experiments performed in this study. The failure surface obtained from the resulting criterion forms an ellipsoid. By supplementing experimental data used in the the two-dimensional criterion and modifying previously suggested failure criteria, a multi-dimensional failure surface is proposed for thin beryllium structures. The new criterion for orthotropic material is represented by a failure surface in six-dimensional stress space. In order to determine coefficients of the governing equation, a number of uniaxial, biaxial, and triaxial experiments are required. Details of these experiments and a complementary ultrasonic investigation are described in detail. Finally, validity of the criterion and newly determined mechanical properties is established through experiments on structures composed of SR200 sheet material. These experiments include a plate-plug arrangement under a complex state of stress and a series of plates with an out-of-plane central point load. Both criteria have been incorporated into a general purpose finite element analysis code. Numerical simulation incrementally applied loads to a structural component that is being designed and checks each nodal point in the model for exceedance of a failure criterion. If stresses at all locations do not exceed the failure criterion, the load is increased and the process is repeated. Failure results for the plate-plug and clamped plate tests are accurate to within 2 percent.

Roschke, Paul N.↗

PipeSight: A High-Performance Computing Platform for Pipeline Integrity Management

The Phase I feasibility study completed as part of this project has led to a number of innovative technologies being developed and has laid the foundation for a successful Phase II effort to commercialize a platform for managing the integrity of pipelines for the damage mechanisms of the new, hybrid-energy based economy. To ground the development efforts and direction of the project, an extensive market research and customer discovery effort was undertaken early in Phase I. Through this effort, a number of pipeline owners and operators were interviewed, and the following key findings were discovered about the pipeline industry: • Small pipeline operators do not have the central engineering groups necessary to perform their own independent analysis of inspection data, but instead rely on summarized tally sheets provided to them by inspection service providers. • The time it takes to go from an inspection to a completed engineering assessment, even for small segments of pipeline, can take anywhere from 30-120 days. During this delay, critical threats can (and have been known to) cause failures. • Uncertainty is often not accounted for in the assessment of pipeline integrity. The tally sheets provided by third-party service providers are almost always deterministic in nature, identifying threats that present a concern only to the current (not the future) integrity of the pipeline. • It is uncommon to apply the latest technologies to perform advanced assessments of damaged pipelines. There is a desire to use more advanced analysis capabilities to assess threats. Many pipeline operators indicated that they would often excavate a pipeline to perform an inspection and find that the damage was not as bad as they anticipated, thus using limited resources unnecessarily. Companies are not consistent in their use of inspection data to determine corrosion rates, and those that do only calculate deterministic corrosion rates. • The industry has prominently relied on time-based inspections but has recently started to transition to risk-based inspections. However, there appears to be no uniform guidance on how to do so while properly accounting for all sources of uncertainty. • Companies are not storing inspection data in a manner that allows for the ready determination of temporal trends. • Predictive maintenance principles and practices are beginning to be used by early adopters • Some pipelines are being re-purposed to transport different process fluids than they were designed for, e.g., H 2 and CO 2 rich process streams to serve the new hybrid-energy based economy, which are presenting new integrity concerns for the existing pipeline network that crisscrosses the United States. As a result of these discoveries, we were able to target the development efforts in Phase I to best serve the needs of the industry. In Phase I, we developed a way to correlate multiple large-scale scans of the pipeline to determine a probabilistic corrosion rate that accounts for all sources of error and uncertainty in the inspection process. This probabilistic corrosion rate can be used to predict the future thickness distribution of the pipe wall. We demonstrate how this analysis may be performed in an analytical fashion and has been implemented in such a manner that it can be readily distributed using GPU computing through integration of the Kokkos programming model. We also make a very novel extension of the analytical corrosion rate model to Bayesian Networks (an explainable AI technique) that can account for non-parametric distributions of corrosion rates. With the predictions made above for the probabilistic corrosion rate and corresponding future distribution of the pipe wall thickness, we can assess the integrity of the pipeline through the use of a probabilistic engineering assessment. We developed a novel screening data analysis approach that can rapidly identify ‘hotspots’ (local thin areas) where the integrity of the pipeline is a concern. Once more, we implemented this screening approach in C++ to leverage GPU computing via the Kokkos programming model. After the critical hotspots are identified, we developed a program that can automatically generate an advanced finite element model of the damaged regions. Since the number of damaged regions that require advanced analysis can number in the thousands, we integrated an open-source container-native workflow engine for orchestrating parallel jobs on the cloud. Initially, these advanced numerical models were only designed to account for loading due to internal pressure. However, in a slight pivot from the initial Phase I proposal, we developed a complete pipe stress analysis program (called Simflex) which can simulate the complete pipeline and its response to thermal expansion, pressure, thermal bowing, weight, wind, earthquake, support displacement, support friction and external forces. This pipe stress analysis program was written generically, to handle any piping system, but contains the features needed to model long pipelines (i.e., it incorporates a model for soil mechanics and can account for the nonlinear boundary conditions necessary to simulate long underground pipelines). This pipe stress analysis program can simulate any segment of the pipeline (simple or complex) under any set of conditions and loads, to determine the supplemental loads (axial forces and bending moments) at the location of damage. This enables the most accurate state of stress to be accounted for in the pipeline, which can prove critical when evaluating the integrity of a damaged region. In the process of developing the technologies to perform the integrity assessment of the pipeline, we also extended one of the industry standard approaches for performing the assessment of local thin areas that extend more in the circumferential direction than the longitudinal direction of the pipeline. This approach was presented to the API 579-1/AS ME FFS-1 steering committee in November 2021 for consideration in the next edition of the industry standard for Fitness-For-Service (expected to be released in 2023). To help pipeline operators make decisions with the results on any integrity assessment, we developed a new approach to the life-cycle management of pipelines which uses a Bayesian Decision Network. The network is designed to help pipeline operators plan and prioritize inspection activities and ultimately make smarter, more cost-effective decisions. The Bayesian approach accounts for all sources of uncertainty and carries them through to the final optimal decisions, providing a probabilistic framework for optimizing inspection intervals. The proof-of-concept networks developed in the feasibility study are complete, verified, and are focused on a subset of the pipeline. To expand this novel approach to the scale necessary for an entire network of pipelines in Phase II, we will leverage the DOE-funded Bengi solver for industrial-scale decision making with Bayesian Networks [22]. Once implemented, we will be able to provide the pipeline industry with a much-needed tool for optimal inspection planning using truly explainable artificial intelligence (XAI). To handle all of these advanced capabilities into a cloud-based platform, the architecture of the Equity Engineering Cloud (EEC) was extended to include Argo Workflows, a framework capable of distributing and managing a massive number of jobs that consume their own resources, such that thousands of serial finite element simulations can be run in parallel. As part of this substantial undertaking, we also integrated Argo Continuous Delivery (CD) into the EEC, to aid with the rapid prototyping and iterations that will be imperative to the success of the PipeSight platform’s Agile development process in Phase II. As part of the pipe stress analysis program, we also developed a custom visualizer that leverages the DOE-funded VTK visualization library. We added custom contouring capabilities and a means for interacting visually with both the inputs and outputs of the pipe stress analysis program. We also developed routines for automating the post-processing of the finite element simulations to determine if any failure criteria are met and to visualize the deformations, stresses and strains in ParaView using the exodus II file format (a subset of netCDF).

24 POWER TRANSMISSION AND DISTRIBUTION↗

A new method for recognizing quadric surfaces from range data and its application to telerobotics and automation

The problem of recognizing and positioning of objects in three-dimensional space is important for robotics and navigation applications. In recent years, digital range data, also referred to as range images or depth maps, have been available for the analysis of three-dimensional objects owing to the development of several active range finding techniques. The distinct advantage of range images is the explicitness of the surface information available. Many industrial and navigational robotics tasks will be more easily accomplished if such explicit information can be efficiently interpreted. In this research, a new technique based on analytic geometry for the recognition and description of three-dimensional quadric surfaces from range images is presented. Beginning with the explicit representation of quadrics, a set of ten coefficients are determined for various three-dimensional surfaces. For each quadric surface, a unique set of two-dimensional curves which serve as a feature set is obtained from the various angles at which the object is intersected with a plane. Based on a discriminant method, each of the curves is classified as a parabola, circle, ellipse, hyperbola, or a line. Each quadric surface is shown to be uniquely characterized by a set of these two-dimensional curves, thus allowing discrimination from the others. Before the recognition process can be implemented, the range data have to undergo a set of pre-processing operations, thereby making it more presentable to classification algorithms. One such pre-processing step is to study the effect of median filtering on raw range images. Utilizing a variety of surface curvature techniques, reliable sets of image data that approximate the shape of a quadric surface are determined. Since the initial orientation of the surfaces is unknown, a new technique is developed wherein all the rotation parameters are determined and subsequently eliminated. This approach enables us to position the quadric surfaces in a desired coordinate system. Experiments were conducted on raw range images of spheres, cylinders, and cones. Experiments were also performed on simulated data for surfaces such as hyperboloids of one and two sheets, elliptical and hyperbolic paraboloids, elliptical and hyperbolic cylinders, ellipsoids and the quadric cones. Both the real and simulated data yielded excellent results. Our approach is found to be more accurate and computationally inexpensive as compared to traditional approaches, such as the three-dimensional discriminant approach which involves evaluation of the rank of a matrix. Finally, we have proposed one other new approach, which involves the formulation of a mapping between the explicit and implicit forms of representing quadric surfaces. This approach, when fully realized, will yield a three-dimensional discriminant, which will recognize quadric surfaces based upon their component surfaces patches. This approach is faster than prior approaches and at the same time is invariant to pose and orientation of the surfaces in three-dimensional space.

Alvertos, Nicolas↗

The Ice, Cloud, and Land Elevation Satellite-2 Mission: A Global Geolocated Photon Product Derived from the Advanced Topographic Laser Altimeter System

The Ice, Cloud, and land Elevation Satellite – 2 (ICESat-2) observatory was launched on 15 September 2018 to measure ice sheet and glacier elevation change, sea ice freeboard, and enable the determination of the heights of Earth’s forests. ICESat-2’s laser altimeter, the Advanced Topographic Laser Altimeter System (ATLAS) uses green (532 nm) laser light and single-photon sensitive detection to measure time of flight and subsequently surface height along each of its six beams. In this paper, we describe the major components of ATLAS, including the transmitter, the receiver and the components of the timing system. We present the major components of the ICESat-2 observatory, including the Global Positioning System, star trackers and inertial measurement unit. The ICESat-2 Level 1B data product (ATL02) provides the precise photon round-trip time of flight, among other data. The ICESat-2 Level 2A data product (ATL03) combines the photon times of flight with the observatory position and attitude to determine the geodetic location (i.e. the latitude, longitude and height) of the ground bounce point of photons detected by ATLAS. The ATL03 data product is used by higher-level (Level 3A) surface-specific data products to determine glacier and ice sheet height, sea ice freeboard, vegetation canopy height, ocean surface topography, and inland water body height.

ICESat-2↗

Instabilities connected with neutral sheets in the solar wind

A preliminary study is presented of two sets of data obtained by HEOS 1 and OGO 5 in the solar wind, which reveal the internal structure of two neutral sheets and their two-dimensional structure. HEOS 1 observations of the effects of the tearing mode instability in one of the sheets are described, including complicated structures connected with the sector boundary, sharp increases and decreases in the magnetic field intensity, and the presence of closed loops. HEOS 1 and OGO 5 observations of large oscillations due to plasma pressure imbalances are discussed, and it is concluded that an interchange instability may have been observed.

Formisano, V.↗

Towards three-body unitarity in D{sup +}{yields}K{sup -}{pi}{sup +}{pi}{sup +}

We assess the importance of final state interactions in D{sup +}{yields}K{sup -}{pi}{sup +}{pi}{sup +}, stressing the consistency between two- and three-body interactions. The basic building block in the calculation is a K{pi} amplitude based on unitarized chiral perturbation theory and with parameters determined by a fit to elastic LASS data. Its analytic extension to the second sheet allows the determination of two poles, associated with the {kappa} and the K{sup *}(1430), and a representation of the amplitude based on them is constructed. The problem of unitarity in the three-body system is formulated in terms of an integral equation, inspired in the Faddeev formalism, which implements a convolution between the weak vertex and the final state hadronic interaction. Three different topologies are considered for the former and, subsequently, the decay amplitude is expressed as a perturbation series. Each term in this series is systematically related to the previous one and a resummation was performed. Remaining effects owing to single and double rescattering processes were then added and results compared to FOCUS data. We found that proper three-body effects are important at threshold and fade away rapidly at higher energies. Our model, based on a vector-weak vertex, can describe qualitative features of the modulus of the decay amplitude and agrees well with its phase in the elastic region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Using PEACE Data from the four CLUSTER Spacecraft to Measure Compressibility, Vorticity, and the Taylor Microscale in the Magnetosheath and Plasma Sheet

We present determinations of compressibility and vorticity in the magnetosheath and plasma sheet using moments from the four PEACE thermal electron instruments on CLUSTER. The methodology used assumes a linear variation of the moments throughout the volume defined by the four satellites, which allows spatially independent estimates of the divergence, curl, and gradient. Once the vorticity has been computed, it is possible to estimate directly the Taylor microscale. We have shown previously that the technique works well in the solar wind. Because the background flow speed in the magnetosheath and plasma sheet is usually less than the Alfven speed, the Taylor frozen-in-flow approximation cannot be used. Consequently, this four spacecraft approach is the only viable method for obtaining the wave number properties of the ambient fluctuations. Our results using electron velocity moments will be compared with previous work using magnetometer data from the FGM experiment on Cluster.

Goldstein, Melvyn L.↗

Electron Pitch-Angle Distribution in Pressure Balance Structures Measured by Ulysses/SWOOPS

Pressure balance structures (PBSs) are a common feature in the high-latitude solar wind near solar minimum. From previous studies, PBSs are believed to be remnants of coronal plumes. Yamauchi et al [2002] investigated the magnetic structures of the PBSs, applying a minimum variance analysis to Ulysses/Magnetometer data. They found that PBSs contain structures like current sheets or plasmoids, and suggested that PBSs are associated with network activity such as magnetic reconnection in the photosphere at the base of polar plumes. We have investigated energetic electron data from Ulysses/SWOOPS to see whether bi-directional electron flow exists and we have found evidence supporting the earlier conclusions. We find that 45 ot of 53 PBSs show local bi-directional or isotopic electron flux or flux associated with current-sheet structure. Only five events show the pitch-angle distribution expected for Alfvenic fluctuations. We conclude that PBSs do contain magnetic structures such as current sheets or plasmoids that are expected as a result of network activity at the base of polar plumes.

Yamauchi, Yohei↗

Microwave Breakdown of Air Initiated by an Electromagnetic Vibrator Placed on a Dielectric Surface

The feasibility of air breakdown initiation by a quasi-optical subcritical-field microwave beam has been studied experimentally. Breakdown has been initiated by a linear electromagnetic vibrator, which was placed in a traveling electromagnetic wave (i) on the surface of a dielectric sheet that faces wavevector k of the wave, (ii) on the opposite surface of the sheet, and (iii) near the sheet. Fields induced at the ends of the vibrator have been calculated theoretically for all arrangements. Numerical estimates and experimental data have shown that when a vibrator is placed on a dielectric surface, electrical breakdown of air may be initiated in a much deeper subcritical field of the microwave beam than when it is placed in the field of a traveling microwave.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Bending Stiffness of Multiwall Sandwich

An analytical and experimental study was carried out to understand the extensional and flexural behavior of multiwall sandwich, a metallic insulation composed of alternate layers of flat and dimpled foil. The multiwall sandwich was structurally analyzed by using several simplifying assumptions combined with a finite element analysis. The simplifying assumptions made in this analysis were evaluated by bending and tensile tests. Test results validate the assumption that flat sheets in compression do not significantly contribute to the flexural stiffness of multiwall sandwich for the multiwall geometry tested. However, calculations show that thicker flat sheets may contribute significantly to bending stiffness and cannot be ignored. Results of this analytical approach compare well with test data; both show that the extensional stiffness of the dimpled sheet in he 0 deg direction is about 30 percent of that for a flat sheet, and that in the 45 deg direction, it is about 10 percent. The analytical and experimental multiwall bending stiffness showed good agreement for the particular geometry tested.

Blosser, M. L.↗

Compressing Aviation Data in XML Format

Design, operations and maintenance activities in aviation involve analysis of variety of aviation data. This data is typically in disparate formats making it difficult to use with different software packages. Use of a self-describing and extensible standard called XML provides a solution to this interoperability problem. XML provides a standardized language for describing the contents of an information stream, performing the same kind of definitional role for Web content as a database schema performs for relational databases. XML data can be easily customized for display using Extensible Style Sheets (XSL). While self-describing nature of XML makes it easy to reuse, it also increases the size of data significantly. Therefore, transfemng a dataset in XML form can decrease throughput and increase data transfer time significantly. It also increases storage requirements significantly. A natural solution to the problem is to compress the data using suitable algorithm and transfer it in the compressed form. We found that XML-specific compressors such as Xmill and XMLPPM generally outperform traditional compressors. However, optimal use of Xmill requires of discovery of optimal options to use while running Xmill. This, in turn, depends on the nature of data used. Manual disc0ver.y of optimal setting can require an engineer to experiment for weeks. We have devised an XML compression advisory tool that can analyze sample data files and recommend what compression tool would work the best for this data and what are the optimal settings to be used with a XML compression tool.

Patel, Hemil↗

NASA-ISRO Synthetic Aperture Radar (NISAR) Mission

NISAR is a multi-disciplinary Earth-observing radar mission that makes global measurements of land surface changes that will greatly improve Earth system models. NISAR data will clarify spatially and temporally complex phenomena, including ecosystem disturbances, ice sheet collapse, and natural hazards including earthquakes, tsunamis, volcanoes, and landslides. It provides societally relevant data that will enable better protection of life and property. The mission, a NASA-ISRO partnership, uses two fully polarimetric SARs, one at L-band (L-SAR) and one at S-band (S-SAR), in exact repeating orbits every 12 days that allows interferometric combination of data on repeated passes. NASA provides the L SAR; a shared deployable reflector; an engineering payload that supports mission-specific data handling, navigation and communication functions; science observation planning and L SAR data processing. ISRO provides the S-SAR, spacecraft, launch vehicle, satellite operations, and S-SAR data processing. The mission will be launched from the Satish Dhawan Space Centre, Sriharikota, India. Mission development has addressed many unique challenges and incorporates many “firsts” for a jointly-developed free-flyer radar science mission.

Sarma, C V H S↗

An investigation of oblique hypervelocity impact

This report describes the results of an investigation of phenomena associated with the oblique hypervelocity impact of spherical projectiles on multi-sheet aluminum structures. A model to be employed in the design of meteoroid and space debris protection systems for space structures is developed. The model consists of equations relating crater and perforation damage of a multi-sheet structure to parameters such as projectile size, impact velocity, and trajectory obliquity. The equations are obtained through a regression analysis of oblique hypervelocity impact test data. This data shows that the response of a multi-sheet structure to oblique impact is significantly different from its response to normal hypervelocity impact. It was found that obliquely incident projectiles produce ricochet debris that can severely damage panels or instrumentation located on the exterior of a space structure. Obliquity effects of high-speed impact must, therefore, be considered in the design of any structure exposed to the hazardous meteoroid and space debris environment.

Schonberg, William P.↗