Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “data validation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15

Space Shuttle Plume Simulation Effect on Aerodynamics

Technology for simulating plumes in wind tunnel tests was not adequate to provide the required confidence in test data where plume induced aerodynamic effects might be significant. A broad research program was undertaken to correct the deficiency. Four tasks within the program are reported. Three of these tasks involve conducting experiments, related to three different aspects of the plume simulation problem: (1) base pressures; (2) lateral jet pressures; and (3) plume parameters. The fourth task involves collecting all of the base pressure test data generated during the program. Base pressures were measured on a classic cone ogive cylinder body as affected by the coaxial, high temperature exhaust plumes of a variety of solid propellant rockets. Valid data were obtained at supersonic freestream conditions but not at transonic. Pressure data related to lateral (separation) jets at M infinity = 4.5, for multiple clustered nozzles canted to the freestream and operating at high dynamic pressure ratios. All program goals were met although the model hardware was found to be large relative to the wind tunnel size so that operation was limited for some nozzle configurations.

Hair, L. M.↗

Active Learning with Rationales for Identifying Operationally Significant Anomalies in Aviation

A major focus of the commercial aviation community is discovery of unknown safety events in flight operations data. Data-driven unsupervised anomaly detection methods are better at capturing unknown safety events compared to rule-based methods which only look for known violations. However, not all statistical anomalies that are discovered by these unsupervised anomaly detection methods are operationally significant (e.g., represent a safety concern). Subject Matter Experts (SMEs) have to spend significant time reviewing these statistical anomalies individually to identify a few operationally significant ones. In this paper we propose an active learning algorithm that incorporates SME feedback in the form of rationales to build a classifier that can distinguish between uninteresting and operationally significant anomalies. Experimental evaluation on real aviation data shows that our approach improves detection of operationally significant events by as much as 75% compared to the state-of-the-art. The learnt classifier also generalizes well to additional validation data sets.

anomaly detection↗

Altimetry for the Future: Building on 25 Years of Progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the ‘‘Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion.

Saleh Abdalla↗

Quantifying Interannual Variability of the UTLS Ozone Using Assimilation of Satellite Data

An accurate representation of spatial and temporal variability of the Upper Troposphere Lower Stratosphere (UTLS) ozone is essential for understanding both the tropospheric ozone budget and ozone s contribution to radiative forcing. The complex, dynamically driven structure of trace gas fields in the UTLS presents a challenge to data-based and modelling studies. Small features are not fully resolved in data from limb-sounding instruments such as the Microwave Limb Sounder on EOS-Aura (the EOS-MLS), but are captured in assimilation of those data as vertical structure is added from the assimilated meteorology. This will be demonstrated using a multi-year assimilation of EOS-MLS observations in the Goddard Earth Observing System, Version 5 (GEOS-5) data assimilation system. The results demonstrate the realism of the seasonal and year to year variability of laminar structures in the mid-latitudinal ozone field between years 2005-2007, for which independent validation data are available from the HIRDLS instrument. The analysis is done in the context of the underlying large scale dynamics. The lifetimes of most research instruments are too short for them to be used throughout the duration of long-term (at least 3 decades) reanalyses. For example, the EOS-MLS instrument has operated since mid-2004 until present. By contrast, Solar Backscatter Ultra Violet (SBUV) measurements provide continuous data since late 1978, but their vertical resolution is insufficient to represent the profile shape in the UTLS. Assimilation of these SBUV/2 observations in the GEOS-5 data assimilation system has hitherto not captured a realistic ozone structure in the UTLS, even though transport studies using GEOS-5 wind fields do show such structures. We show that careful construction of the background error covariance structure in GEOS-5 can lead to more realistic UTLS ozone fields when assimilating SBUV/2 observations. The reasoning behind this will be discussed, emphasizing the need to retain the sharp gradient of ozone concentrations across the tropopause. We analyze the UTLS ozone distributions in multi-year SBUV/2 assimilation experiments, comparing the results against the independent HIRDLSdataset and, for a longer period, with the MLS assimilation and discuss the consequences for tropospheric ozone and radiative forcing.

Wargan, K.↗

Optimal Estimation Framework for Ocean Color Atmospheric Correction and Pixel-level Uncertainty Quantification

Ocean color remote sensing requires compensation for atmospheric scattering and absorption (aerosol, Rayleigh, and trace gases), referred to as atmospheric correction (AC). AC allows inference of parameters such as spectrally resolved remote sensing reflectance ( R rs )(λ) ; sr 1 ) at the ocean surface from the top-of-atmosphere reflectance. Often, the uncertainty of this process is not fully explored. Bayesian inference techniques provide a simultaneous AC and uncertainty assessment via a full posterior distribution of the relevant variables, given the prior distribution of those variables and the radiative transfer (RT) likelihood function. Given uncertainties in the algorithm inputs, the Bayesian framework enables better constraints on the AC process by using the complete spectral information compared to traditional approaches that use only a subset of bands for AC. This paper investigates a Bayesian inference research method (Optimal Estimation, OE) for ocean color AC by simultaneously retrieving atmospheric and ocean properties using all visible and near-infrared spectral bands. The OE algorithm analytically approximates the posterior distribution of parameters based on normality assumptions and provides a potentially viable operational algorithm with a reduced computational expense. We developed a Neural Network (NN) RT forward model look-up-table-based emulator to increase algorithm efficiency further and thus speed up the likelihood computations. We then applied the OE algorithm to synthetic data and observations from the MODerate resolution Imaging Spectroradiometer (MODIS) on NASA’s Aqua spacecraft. We compared the R rs )(λ) retrieval and its uncertainty estimates from the OE method with in-situ validation data from the SeaWiFS Bio-optical Archive and Storage System (SeaBASS) and Aerosol Robotic Network Ocean Color (AERONET-OC) datasets. The OE algorithm improved R rs )(λ) estimates relative to the NASA standard operational algorithm by improving all statistical metrics at 443, 555, and 667 nm. Unphysical negative R rs )(λ) , which often appear in complex water conditions, was reduced by a factor of 3. The OE-derived pixel-level R rs )(λ) uncertainty estimates were also assessed relative to in-situ data and were shown to have skill.

Atmospheric correction↗

Comparison Between Predicted and Experimentally Measured Flow Fields at the Exit of the SSME HPFTP Impeller

Validation of CFD codes is a critical first step in the process of developing CFD design capability. The MSFC Pump Technology Team has recognized the importance of validation and has thus funded several experimental programs designed to obtain CFD quality validation data. The first data set to become available is for the SSME High Pressure Fuel Turbopump Impeller. LDV Data was taken at the impeller inlet (to obtain a reliable inlet boundary condition) and three radial positions at the impeller discharge. Our CFD code, TASCflow, is used within the Propulsion and Commercial Pump industry as a tool for pump design. The objective of this work, therefore, is to further validate TASCflow for application in pump design. TASCflow was used to predict flow at the impeller discharge for flowrates of 80, 100 and 115 percent of design flow. Comparison to data has been made with encouraging results.

Bache, George↗

From LIMS to OMPS-LP: Limb Ozone Observations for Future Reanalyses

High vertical resolution and accuracy of ozone data from satellite-borne limb sounders has made them an invaluable tool in scientific studies of the middle and upper atmosphere. However, it was not until recently that these measurements were successfully incorporated in atmospheric reanalyses: of the major multidecadal reanalyses only ECMWF's (European Centre for Medium-Range Weather Forecasts') ERA (ECMWF Re-Analysis)-Interim/ERA5 and NASA's MERRA-2 (Modern-Era Retrospective Analysis for Research and Applications-2) use limb ozone data. Validation and comparison studies have demonstrated that the addition of observations from the Microwave Limb Sounder (MLS) on EOS (Earth Observing System) Aura greatly improved the quality of ozone fields in MERRA-2 making these assimilated data sets useful for scientific research. In this presentation, we will show the results of test experiments assimilating retrieved ozone from the Limb Infrared Monitor of the Stratosphere (LIMS, 1978/1979) and Ozone Mapping Profiler Suite Limb Profiler (OMPS-LP, 2012 to present). Our approach builds on the established assimilation methodology used for MLS in MERRA-2 and, in the case of OMPS-LP, extends the excellent record of MLS ozone assimilation into the post-EOS era in Earth observations. We will show case studies, discuss comparisons of the new experiments with MERRA-2, strategies for bias correction and the potential for combined assimilation of multiple limb ozone data types in future reanalyses for studies of multidecadal stratospheric ozone changes including trends.

Wargan, K.↗

Analysis of Shockwave Radiation Data in Nitrogen

Data from a pure nitrogen test series in the Electric Arc Shock Tube Facility were previously reported for velocities spanning 6-12 km/s at a free-stream pressure of 0.2 Torr. This test series provides validation data for a range of physical phenomena to investigate, including vibrational relaxation, molecular radiation, nitrogen dissociation and ionization, and atomic radiation and ionization. This paper details analysis of data obtained at a nominal velocity of 10.3 km/s. The spectra are analyzed to extract temperatures and the densities of excited states as a function of position behind the shock. The effect of different methods for calculating state populations and ionization processes is assessed, as is a rigorous assessment of the atomic line lists, with both missing and extra lines identified.

Nitrogen↗

Kepler Planet Detection Metrics: Per-Target Flux-Level Transit Injection Tests of TPS for Data Release 25

Quantifying the ability of a transiting planet survey to recover transit signals has commonly been accomplished through Monte-Carlo injection of transit signals into the observed data and subsequent running of the signal search algorithm (Gilliland et al., 2000; Weldrake et al., 2005; Burke et al., 2006). In order to characterize the performance of the Kepler pipeline (Twicken et al., 2016; Jenkins et al., 2017) on a sample of over 200,000 stars, two complementary injection and recovery tests are utilized:1. Injection of a single transit signal per target into the image or pixel-level data, hereafter referred to as pixel-level transit injection (PLTI), with subsequent processing through the Photometric Analysis (PA), Presearch Data Conditioning (PDC), Transiting Planet Search (TPS), and Data Validation (DV) modules of the Kepler pipeline. The PLTI quantification of the Kepler pipeline's completeness has been described previously by Christiansen et al. (2015, 2016); the completeness of the final SOC 9.3 Kepler pipeline acting on the Data Release 25 (DR25) light curves is described by Christiansen (2017).2. Injection of multiple transit signals per target into the normalized flux time series data with a subsequent transit search using a stream-lined version of the Transiting Planet Search (TPS) module. This test, hereafter referred to as flux-level transit injection (FLTI), is the subject of this document. By running a heavily modified version of TPS, FLTI is able to perform many injections on selected targets and determine in some detail which injected signals are recoverable. Significant numerical efficiency gains are enabled by precomputing the data conditioning steps at the onset of TPS and limiting the search parameter space (i.e., orbital period, transit duration, and ephemeris zero-point) to a small region around each injected transit signal.The PLTI test has the advantage that it follows transit signals through all processing steps of the Kepler pipeline, and the recovered signals can be further classified as planet candidates or false positives in the exact same manner as detections from the nominal (i.e., observed) pipeline run (Twicken et al., 2016, Thompson et al., in preparation). To date, the PLTI test has been the standard means of measuring pipeline completeness averaged over large samples of targets (Christiansen et al., 2015, 2016; Christiansen, 2017). However, since the PLTI test uses only one injection per target, it does not elucidate individual-target variations in pipeline completeness due to differences in stellar properties or astrophysical variability. Thus, we developed the FLTI test to provide a numerically efficient way to fully map individual targets and explore the performance of the pipeline in greater detail. The FLTI tests thereby allow a thorough validation of the pipeline completeness models (such as window function (Burke and Catanzarite, 2017a), detection efficiency (Burke Catanzarite, 2017b), etc.) across the spectrum of Kepler targets (i.e., various astrophysical phenomena and differences in instrumental noise). Tests during development of the FLTI capability revealed that there are significant target-to-target variations in the detection efficiency.

DR25↗

NASA Scientific Data Purchase Project: From Collection to User

NASA's Scientific Data Purchase (SDP) project is currently a $70 million operation managed by the Earth Science Applications Directorate at Stennis Space Center. The SDP project was developed in 1997 to purchase scientific data from commercial sources for distribution to NASA Earth science researchers. Our current data holdings include 8TB of remote sensing imagery consisting of 18 products from 4 companies. Our anticipated data volume is 60 TB by 2004, and we will be receiving new data products from several additional companies. Our current system capacity is 24 TB, expandable to 89 TB. Operations include tasking of new data collections, archive ordering, shipment verification, data validation, distribution, metrics, finances, customer feedback, and technical support. The program has been included in the Stennis Space Center Commercial Remote Sensing ISO 9001 registration since its inception. Our operational system includes automatic quality control checks on data received (with MatLab analysis); internally developed, custom Web-based interfaces that tie into commercial-off-the-shelf software; and an integrated relational database that links and tracks all data through operations. We've distributed nearly 1500 datasets, and almost 18,000 data files have been downloaded from our public web site; on a 10-point scale, our customer satisfaction index is 8.32 at a 23% response level. More information about the SDP is available on our Web site.

Nicholson, Lamar↗

NOAA-20 VIIRS Thermal Emissive Bands On-Orbit Performance

The VIIRS (Visible Infrared Imaging Radiometer Suite) instrument onboard the NOAA-20 satellite (launched on November 18, 2017) started to collect Earth-view data after its nadir door opened on December 13, 2017. Seven of the VIIRS bands, I4-5 and M12-16 are thermal emissive bands (TEBs), covering a spectral range from 3.6 to 12.5 meters. They began collecting valid data after the cold focal plane assembly (CFPA) cooled down to its nominal operating temperature on January 6, 2018. This paper will present the performance of each TEB, including calibration coefficients, noise equivalent differential temperature (NEdT), on-orbit calibration coefficient estimates from scheduled onboard blackbody warm-up and cool-down (WUCD) data, as well as related telemetry temperatures. Several methods are tested and compared in the WUCD data analysis for estimating the calibration coefficients. Based on the preliminary results, the NEdT of each band is well below the design specification and very close to that of the VIIRS onboard the Suomi National Polar-orbiting Partnership (SNPP) satellite. The detector gains appear stable for bands on the short- and mid-wave infrared CFPA, whereas the detector gains have larger than expected degradation for bands on the long-wave infrared CFPA during the early mission. All TEB-related telemetry temperatures are stable. The on-orbit performance of NOAA-20 VIIRS TEB is compared with VIIRS onboard the SNPP.

Thermal Emissive Bands (TEB)↗

Combined Retrievals of Boreal Forest Fire Aerosol Properties with a Polarimeter and Lidar

Absorbing aerosols play an important, but uncertain, role in the global climate. Much of this uncertainty is due to a lack of adequate aerosol measurements. While great strides have been made in observational capability in the previous years and decades, it has become increasingly apparent that this development must continue. Scanning polarimeters have been designed to help resolve this issue by making accurate, multi-spectral, multi-angle polarized observations. This work involves the use of the Research Scanning Polarimeter (RSP). The RSP was designed as the airborne prototype for the Aerosol Polarimetery Sensor (APS), which was due to be launched as part of the (ultimately failed) NASA Glory mission. Field observations with the RSP, however, have established that simultaneous retrievals of aerosol absorption and vertical distribution over bright land surfaces are quite uncertain. We test a merger of RSP and High Spectral Resolution Lidar (HSRL) data with observations of boreal forest fire smoke, collected during the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS). During ARCTAS, the RSP and HSRL instruments were mounted on the same aircraft, and validation data were provided by instruments on an aircraft flying a coordinated flight pattern. We found that the lidar data did indeed improve aerosol retrievals using an optimal estimation method, although not primarily because of the constraints imposed on the aerosol vertical distribution. The more useful piece of information from the HSRL was the total column aerosol optical depth, which was used to select the initial value (optimization starting point) of the aerosol number concentration. When ground based sun photometer network climatologies of number concentration were used as an initial value, we found that roughly half of the retrievals had unrealistic sizes and imaginary indices, even though the retrieved spectral optical depths agreed within uncertainties to independent observations. The convergence to an unrealistic local minimum by the optimal estimator is related to the relatively low sensitivity to particles smaller than 0.1 ( m) at large optical thicknesses. Thus, optimization algorithms used for operational aerosol retrievals of the fine mode size distribution, when the total optical depth is large, will require initial values generated from table look-ups that exclude unrealistic size/complex index mixtures. External constraints from lidar on initial values used in the optimal estimation methods will also be valuable in reducing the likelihood of obtaining spurious retrievals.

Knobelspiesse, K.↗

Analytical Redundancy Using Kalman Filters for Rocket Engine Sensor Validation

The use of sensor redundancy is crucial in aerospace systems to maintain safe, reliable operation. While hardware redundancy is more common in application, analytical redundancy can provide a viable alternative in systems where the installation of multiple redundant sensors is not viable. To this end, the use of Kalman filters to analytically validate sensor measurements within rocket engines was explored. First, a dynamic model of the RS 25 engine, a derivative of the Space Shuttle Main Engine (SSME), was reduced to a subset of relations, focused around the main combustion chamber pressure. These relations were used within the Kalman filter algorithm to generate an estimate of sensor measurements to be compared with true measurements for data validation purposes. By using a bank of Kalman filters, the residuals between the estimated and true measurements were used to detect and isolate sensor faults. Through fault simulations, the sensor validation performance of this Kalman filter bank design was compared to a hardware redundancy check. Sensor bias and drift faults of various magnitudes were injected into nominal RS 25 engine test data. Results for both approaches show comparable fault detection with most bias faults found nearly instantaneously by both algorithms. Drift fault detection results show certain cases where one algorithm is faster than the other. The key advantage of the Kalman filter algorithm is shown in fault isolation performance where it can isolate faults between two redundant sensors while the hardware redundancy comparisons cannot.

sensors↗

Onboard autonomy on the Three Corner Sat mission

In 2003, the student-built three satellite constellation Three Corner Sat (3CS) Mission will demonstrate onboard autonomy including: science data validation and prioritization, mission re-planning, and robust execution. Future observations will be planned onboard based on the quality of aquired science, available memory and power, and anticipated downlinks. These capabilities will allow 3CS to aquire additional science data if resources are available and to return only the highest quality science data.

Planning scheduling autonomy↗

Blunt-Body Entry Vehicle Aerothermodynamics: Transition and Turbulence on the CEV and MSL Configurations

Recent, current, and planned NASA missions that employ blunt-body entry vehicles pose aerothermodynamic problems that challenge the state-of-the art of experimental and computational methods. The issues of boundary-layer transition and turbulent heating on the heat shield have become important in the designs of both the Mars Science Laboratory and Crew Exploration Vehicle. While considerable experience in these general areas exists, that experience is mainly derived from simple geometries; e.g. sharp-cones and flat-plates, or from lifting bodies such as the Space Shuttle Orbiter. For blunt-body vehicles, application of existing data, correlations, and comparisons is questionable because an all, or mostly, subsonic flow field is produced behind the bow shock, as compared to the supersonic (or even hypersonic) flow of other configurations. Because of the need for design and validation data for projects such as MSL and CEV, many new experimental studies have been conducted in the last decade to obtain detailed boundary-layer transition and turbulent heating data on this class of vehicle. In this paper, details of several of the test programs are reviewed. The laminar and turbulent data from these various test are shown to correlate in terms of edge-based Stanton and Reynolds number functions. Correlations are developed from the data for transition onset and turbulent heating augmentation as functions of momentum thickness Reynolds number. These correlation can be employed as engineering-level design and analysis tools.

Hollis, Brian R.↗

Near-Global Variability of Stratospheric Water Vapor Observed by SAGE III/ISS

The Stratospheric Aerosol and Gas Experiment III instrument on the International Space Station (SAGE III/ISS) has been making high quality solar occultation measurements of stratospheric water vapor since June 2017. Here we evaluate the large-scale geophysical variability of the SAGE III/ISS water vapor measurements for the first 3 years of observations (2017–2020) as part of data validation for retrieval version 5.1 (v5.1). Detailed comparisons of SAGE III/ISS v5.1 with the Aura Microwave Limb Sounder (MLS) version 5 retrievals show overall excellent agreement in terms of seasonal mean structure and large-scale variability. SAGE III/ISS data capture the well-known seasonal variations in water vapor including the vertically propagating “tape recorder” in the tropics and lower stratospheric maxima linked to the NH summer monsoons. The high vertical resolution (∼2 km) measurements from SAGE III/ISS demonstrate contributions of the monsoons to the wet phase of “tape recorder” during the Northern Hemisphere (NH) summer. Interannual variations over the short data record are also consistent between SAGE III/ISS and MLS in the stratosphere between 16 and 30 km. We furthermore evaluate large-scale variations in relative humidity (RH) derived from the high vertical resolution SAGE III/ISS water vapor measurements, highlighting the detailed seasonal behavior and links to thermal structure near the tropical tropopause. Spatial distributions of RH at the cold point tropopause (CPT) show a close link between high RH and the minimum CPT temperature in both the NH winter and summer, consistent with temperature control of water vapor near the tropopause.

water vapor↗

Comparing Spray Characteristics from Reynolds Averaged Navier-Stokes (RANS) National Combustion Code (NCC) Calculations Against Experimental Data for a Turbulent Reacting Flow

Developing physics-based tools to aid in reducing harmful combustion emissions, like Nitrogen Oxides (NOx), Carbon Monoxide (CO), Unburnt Hydrocarbons (UHC s), and Sulfur Dioxides (SOx), is an important goal of aeronautics research at NASA. As part of that effort, NASA Glenn Research Center is performing a detailed assessment and validation of an in-house combustion CFD code known as the National Combustion Code (NCC) for turbulent reacting flows. To assess the current capabilities of NCC for simulating turbulent reacting flows with liquid jet fuel injection, a set of Single Swirler Lean Direct Injection (LDI) experiments performed at the University of Cincinnati was chosen as an initial validation data set. This Jet-A/air combustion experiment operates at a lean equivalence ratio of 0.75 at atmospheric pressure and has a 4 percent static pressure drop across the swirler. Detailed comparisons of NCC predictions for gas temperature and gaseous emissions (CO and NOx) against this experiment are considered in a previous work. The current paper is focused on detailed comparisons of the spray characteristics (radial profiles of drop size distribution and at several radial rakes) from NCC simulations against the experimental data. Comparisons against experimental data show that the use of the correlation for primary spray break-up implemented by Raju in the NCC produces most realistic results, but this result needs to be improved. Given the single or ten step chemical kinetics models, use of a spray size correlation gives similar, acceptable results

Iannetti, Anthony C.↗

Mutual coupling effects in antenna arrays, volume 1

Mutual coupling between rectangular apertures in a finite antenna array, in an infinite ground plane, is analyzed using the vector potential approach. The method of moments is used to solve the equations that result from setting the tangential magnetic fields across each aperture equal. The approximation uses a set of vector potential model functions to solve for equivalent magnetic currents. A computer program was written to carry out this analysis and the resulting currents were used to determine the co- and cross-polarized far zone radiation patterns. Numerical results for various arrays using several modes in the approximation are presented. Results for one and two aperture arrays are compared against published data to check on the agreement of this model with previous work. Computer derived results are also compared against experimental results to test the accuracy of the model. These tests of the accuracy of the program showed that it yields valid data.

Collin, R. E.↗