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At least 1,423 records · Page 79

Some optical and kinetic properties of the nearby interstellar gas

A model for resonant scattering of sunlight by the nearby interstellar gas is developed which takes into account the modification of a Maxwell-Boltzmann velocity distribution by a central force. While the formalism applies to both hydrogen and helium, the latter is emphasized. Theoretical line profiles and integrated emission rates for helium are compared with those of approximate models and with existing observations. As a result of this analysis, an upward revision of the bulk flow velocity of interstellar helium relative to the solar system, previously deduced from He 584-A observations, is required. Velocities of 15-20 km/s, temperatures of the order of 5000-10,000 K, and densities of the order of 0.008-0.02 per cu cm are sufficient to explain the (helium) observations. However, higher-precision measurements are required in order to place more stringent limits on the gas parameters. Calculations of the flux of interstellar helium atoms impinging on earth's upper atmosphere show that the resulting impact ionization is small compared with terrestrial processes.

Meier, R. R.↗

Advances in dynamics and control of flexible spacecraft and space-based manipulations; Proceedings of the Symposium, ASME Winter Annual Meeting, Dallas, TX, Nov. 25-30, 1990

Consideration is given to control formulations for vibration suppression of an active structure in slewing motions, the use if distributed sensing in control of large flexible spacecraft, an improved shooting method for solving minimum-time maneuver problems, and nonlinear slew maneuver dynamics of large flexible spacecrafts. Attention is also given to initial experiments in trusterless locomotion control of a free-flying robot, dynamic analysis to evaluate viscoelastic passive damping augmentation for the Space Shuttle Remote Manipulator System, initial experiments in cooperative manipulation from a moving platform, and intelligent pipelined control architecture for remote robotic applications.

Joshi, Suresh M.↗

Use of networked workstations for parallel nonlinear structural dynamic simulations of rotating bladed-disk assemblies

The principal objective of this research is to investigate, develop and demonstrate coarse-grained, parallel-processing strategies for nonlinear dynamic simulations for rotating bladed-disk assemblies. The parallel -processing strategies addressed include numerical algorithms for parallel nonlinear solutions and techniques to effect load balancing among processors. The parallel environment employed is a distributed-memory, coarse-grained one consisting of networked workstations. A parallel explicit time integration method has been implemented for transient nonlinear solutions of rotationg bladed-disk assemblies. Automatic domain partitioning techniques have been investigated for load balancing among processors. Advanced computing environments, data structures and interactive computer graphics all contribute to an integrated parallel finite element analysis system to facilitate more efficient and powerful dynamic simulations.

Hsieh, Shang-Hsien↗

Flight Computer Design for the Space Technology 5 (ST-5) Mission

As part of NASA's New Millennium Program, the Space Technology 5 mission will validate a variety of technologies for nano-satellite and constellation mission applications. Included are: a miniaturized and low power X-band transponder, a constellation communication and navigation transceiver, a cold gas micro-thruster, two different variable emittance (thermal) controllers, flex cables for solar array power collection, autonomous groundbased constellation management tools, and a new CMOS ultra low-power, radiation-tolerant, +0.5 volt logic technology. The ST-5 focus is on small and low-power. A single-processor, multi-function flight computer will implement direct digital and analog interfaces to all of the other spacecraft subsystems and components. There will not be a distributed data system that uses a standardized serial bus such as MIL-STD-1553 or MIL-STD-1773. The flight software running on the single processor will be responsible for all real-time processing associated with: guidance, navigation and control, command and data handling (C&DH) including uplink/downlink, power switching and battery charge management, science data analysis and storage, intra-constellation communications, and housekeeping data collection and logging. As a nanosatellite trail-blazer for future constellations of up to 100 separate space vehicles, ST-5 will demonstrate a compact (single board), low power (5.5 watts) solution to the data acquisition, control, communications, processing and storage requirements that have traditionally required an entire network of separate circuit boards and/or avionics boxes. In addition to the New Millennium technologies, other major spacecraft subsystems include the power system electronics, a lithium-ion battery, triple-junction solar cell arrays, a science-grade magnetometer, a miniature spinning sun sensor, and a propulsion system.

Speer, David↗

Sensitivity of Photolysis Frequencies and Key Tropospheric Oxidants in a Global Model to Cloud Vertical Distributions and Optical Properties

Clouds affect tropospheric photochemistry through modification of solar radiation that determines photolysis frequencies. As a follow-up study to our recent assessment of the radiative effects of clouds on tropospheric chemistry, this paper presents an analysis of the sensitivity of such effects to cloud vertical distributions and optical properties (cloud optical depths (CODs) and cloud single scattering albedo), in a global 3-D chemical transport model (GEOS-Chem). GEOS-Chem was driven with a series of meteorological archives (GEOS1- STRAT, GEOS-3 and GEOS-4) generated by the NASA Goddard Earth Observing System data assimilation system. Clouds in GEOS1-STRAT and GEOS-3 have more similar vertical distributions (with substantially smaller CODs in GEOS1-STRAT) while those in GEOS-4 are optically much thinner in the tropical upper troposphere. We find that the radiative impact of clouds on global photolysis frequencies and hydroxyl radical (OH) is more sensitive to the vertical distribution of clouds than to the magnitude of column CODs. With random vertical overlap for clouds, the model calculated changes in global mean OH (J(O1D), J(NO2)) due to the radiative effects of clouds in June are about 0.0% (0.4%, 0.9%), 0.8% (1.7%, 3.1%), and 7.3% (4.1%, 6.0%), for GEOS1-STRAT, GEOS-3 and GEOS-4, respectively; the geographic distributions of these quantities show much larger changes, with maximum decrease in OH concentrations of approx.15-35% near the midlatitude surface. The much larger global impact of clouds in GEOS-4 reflects the fact that more solar radiation is able to penetrate through the optically thin upper-tropospheric clouds, increasing backscattering from low-level clouds. Model simulations with each of the three cloud distributions all show that the change in the global burden of ozone due to clouds is less than 5%. Model perturbation experiments with GEOS-3, where the magnitude of 3-D CODs are progressively varied from -100% to 100%, predict only modest changes (<5%) in global mean OH concentrations. J(O1D), J(NO2) and OH3 concentrations show the strongest sensitivity for small CODs and become insensitive at large CODs due to saturation effects. Caution should be exercised not to use in photochemical models a value for cloud single scattering albedo lower than about 0.999 in order to be consistent with the current knowledge of cloud absorption at the ultraviolet wavelengths.

Liu, Hongyu↗

NASA Tech Briefs, June 2010

Topics covered include: Situational Awareness from a Low-Cost Camera System; Data Acquisition System for Multi-Frequency Radar Flight Operations Preparation; Mercury Toolset for Spatiotemporal Metadata; Social Tagging of Mission Data; Integrating Radar Image Data with Google Maps; Demonstration of a Submillimeter-Wave HEMT Oscillator Module at 330 GHz; Flexible Peripheral Component Interconnect Input/Output Card; Interface Supports Lightweight Subsystem Routing for Flight Applications; MMIC Amplifiers and Wafer Probes for 350 to 500 GHz; Public Risk Assessment Program; Particle Swarm Optimization Toolbox; Telescience Support Center Data System Software; Update on PISCES; Ground and Space Radar Volume Matching and Comparison Software; Web-Based Interface for Command and Control of Network Sensors; Orbit Determination Toolbox; Distributed Observer Network; Computer-Automated Evolution of Spacecraft X-Band Antennas; Practical Loop-Shaping Design of Feedback Control Systems; Fully Printed High-Frequency Phased-Array Antenna on Flexible Substrate; Formula for the Removal and Remediation of Polychlorinated Biphenyls in Painted Structures; Integrated Solar Concentrator and Shielded Radiator; Water Membrane Evaporator; Modeling of Failure for Analysis of Triaxial Braided Carbon Fiber Composites; Catalyst for Carbon Monoxide Oxidation; Titanium Hydroxide - a Volatile Species at High Temperature; Selective Functionalization of Carbon Nanotubes: Part II; Steerable Hopping Six-Legged Robot; Launchable and Retrievable Tetherobot; Hybrid Heat Exchangers; Orbital Winch for High-Strength, Space-Survivable Tethers; Parameterized Linear Longitudinal Airship Model; and Physics of Life: A Model for Non-Newtonian Properties of Living Systems.

Source record↗

Advanced Turboprop Transport Aircraft Modeling for the Electrified Powertrain Flight Demonstration Project

The objective of this study is to establish models for state of the art, representative regional non-electrified turboprop configurations in the 19 to 50 passenger capability range and assess performance impacts from advanced aircraft technologies. Two of these models will serve as reference baseline configurations for comparison to electrified aircraft propulsion (EAP) demonstrator concepts for the Electrified Powertrain Flight Demonstration (EPFD) project. The other two non-electrified configurations will primarily assess the impacts of advanced technologies on fuel consumption and CO₂ emissions. This paper details an aircraft synthesis and performance analysis approach using the General Aviation Synthesis Program (GASP) which is used to establish baseline performance capabilities, calibrate airplane and engine models using published manufacturer data and conduct technology sensitivity studies. Advanced technologies are selected from the categories of propulsion, aerodynamics, and flight systems. A GASP-Monte Carlo simulation framework for uncertainty propagation is used to obtain performance distributions of the expected fuel burn, weight reduction and CO₂ emissions reductions from advanced aircraft technologies. Significant fuel burn savings from application of aerodynamics and propulsion technologies was observed.

Dahlia D.V. Pham↗

Application of boundary integral method to elastoplastic analysis of V-notched beams

The boundary integral equation method was applied in the solution of the plane elastoplastic problems. The use of this method was illustrated by obtaining stress and strain distributions for a number of specimens with a single edge notch and subjected to pure bending. The boundary integral equation method reduced the nonhomogeneous biharmonic equation to two coupled Fredholm-type integral equations. These integral equations were replaced by a system of simultaneous algebraic equations and solved numerically in conjunction with the method of successive elastic solutions.

Rzasnicki, W.↗

Preliminary Analysis of Acoustic Measurements from the NASA-Gulfstream Airframe Noise Flight Test

The NASA-Gulfstream joint Airframe Noise Flight Test program was conducted at the NASA Wallops Flight Facility during October, 2006. The primary objective of the AFN flight test was to acquire baseline airframe noise data on a regional jet class of transport in order to determine noise source strengths and distributions for model validation. To accomplish this task, two measuring systems were used: a ground-based microphone array and individual microphones. Acoustic data for a Gulfstream G550 aircraft were acquired over the course of ten days. Over twenty-four test conditions were flown. The test matrix was designed to provide an acoustic characterization of both the full aircraft and individual airframe components and included cruise to landing configurations. Noise sources were isolated by selectively deploying individual components (flaps, main landing gear, nose gear, spoilers, etc.) and altering the airspeed, glide path, and engine settings. The AFN flight test program confirmed that the airframe is a major contributor to the noise from regional jets during landing operations. Sound pressure levels from the individual microphones on the ground revealed the flap system to be the dominant airframe noise source for the G550 aircraft. The corresponding array beamform maps showed that most of the radiated sound from the flaps originates from the side edges. Using velocity to the sixth power and Strouhal scaling of the sound pressure spectra obtained at different speeds failed to collapse the data into a single spectrum. The best data collapse was obtained when the frequencies were left unscaled.

Khorrami, Mehdi R.↗

Inter-computer communication architecture for a mixed redundancy distributed system

The triply redundant intercomputer network for the Advanced Information Processing System (AIPS), an architecture developed to serve as the core avionics system for a broad range of aerospace vehicles, is discussed. The AIPS intercomputer network provides a high-speed, Byzantine-fault-resilient communication service between processing sites, even in the presence of arbitrary failures of simplex and duplex processing sites on the IC network. The IC network contention poll has evolved from the Laning Poll. An analysis of the failure modes and effects and a simulation of the AIPS contention poll, demonstrate the robustness of the system.

Lala, Jaynarayan H.↗

Development and analysis of SCR requirements tables for system scenarios

We describe the use of scenarios to develop and refine requirement tables for parts of the Earth Observing System Data and Information System (EOSDIS). The National Aeronautics and Space Administration (NASA) is developing EOSDIS as part of its Mission-To-Planet-Earth (MTPE) project to accept instrument/platform observation requests from end-user scientists, schedule and perform requested observations of the Earth from space, collect and process the observed data, and distribute data to scientists and archives. Current requirements for the system are managed with tools that allow developers to trace the relationships between requirements and other development artifacts, including other requirements. In addition, the user community (e.g., earth and atmospheric scientists), in conjunction with NASA, has generated scenarios describing the actions of EOSDIS subsystems in response to user requests and other system activities. As part of a research effort in verification and validation techniques, this paper describes our efforts to develop requirements tables from these scenarios for the EOSDIS Core System (ECS). The tables specify event-driven mode transitions based on techniques developed by the Naval Research Lab's (NRL) Software Cost Reduction (SCR) project. The SCR approach has proven effective in specifying requirements for large systems in an unambiguous, terse format that enhance identification of incomplete and inconsistent requirements. We describe development of SCR tables from user scenarios and identify the strengths and weaknesses of our approach in contrast to the requirements tracing approach. We also evaluate the capabilities of both approach to respond to the volatility of requirements in large, complex systems.

Callahan, John R.↗

Planetary Protection Bioburden Analysis Program

This program is a Microsoft Access program that performed statistical analysis of the colony counts from assays performed on the Mars Science Laboratory (MSL) spacecraft to determine the bioburden density, 3-sigma biodensity, and the total bioburdens required for the MSL prelaunch reports. It also contains numerous tools that report the data in various ways to simplify the reports required. The program performs all the calculations directly in the MS Access program. Prior to this development, the data was exported to large Excel files that had to be cut and pasted to provide the desired results. The program contains a main menu and a number of submenus. Analyses can be performed by using either all the assays, or only the accountable assays that will be used in the final analysis. There are three options on the first menu: either calculate using (1) the old MER (Mars Exploration Rover) statistics, (2) the MSL statistics for all the assays, or This software implements penetration limit equations for common micrometeoroid and orbital debris (MMOD) shield configurations, windows, and thermal protection systems. Allowable MMOD risk is formulated in terms of the probability of penetration (PNP) of the spacecraft pressure hull. For calculating the risk, spacecraft geometry models, mission profiles, debris environment models, and penetration limit equations for installed shielding configurations are required. Risk assessment software such as NASA's BUMPERII is used to calculate mission PNP; however, they are unsuitable for use in shield design and preliminary analysis studies. The software defines a single equation for the design and performance evaluation of common MMOD shielding configurations, windows, and thermal protection systems, along with a description of their validity range and guidelines for their application. Recommendations are based on preliminary reviews of fundamental assumptions, and accuracy in predicting experimental impact test results. The software is programmed in Visual Basic for Applications for installation as a simple add-in for Microsoft Excel. The user is directed to a graphical user interface (GUI) that requires user inputs and provides solutions directly in Microsoft Excel workbooks. This work was done by Shannon Ryan of the USRA Lunar and Planetary Institute for Johnson Space Center. Further information is contained in a TSP (see page 1). MSC- 24582-1 Micrometeoroid and Orbital Debris (MMOD) Shield Ballistic Limit Analysis Program Lyndon B. Johnson Space Center, Houston, Texas Commercially, because it is so generic, Enigma can be used for almost any project that requires engineering visualization, model building, or animation. Models in Enigma can be exported to many other formats for use in other applications as well. Educationally, Enigma is being used to allow university students to visualize robotic algorithms in a simulation mode before using them with actual hardware. This work was done by David Shores and Sharon P. Goza of Johnson Space Center; Cheyenne McKeegan, Rick Easley, Janet Way, and Shonn Everett of MEI Technologies; Mark Manning of PTI; and Mark Guerra, Ray Kraesig, and William Leu of Tietronix Software, Inc. For further information, contact the JSC Innovation Partnerships Office at (281) 483-3809. MSC-24211-1 Spitzer Telemetry Processing System NASA's Jet Propulsion Laboratory, Pasadena, California The Spitzer Telemetry Processing System (SirtfTlmProc) was designed to address objectives of JPL's Multi-mission Image Processing Lab (MIPL) in processing spacecraft telemetry and distributing the resulting data to the science community. To minimize costs and maximize operability, the software design focused on automated error recovery, performance, and information management. The system processes telemetry from the Spitzer spacecraft and delivers Level 0 products to the Spitzer Science Center. SirtfTlmProc is a unique system with automated error notification and recovery, with a real-time continuous service that can go quiescent after periods of inactivity. The software can process 2 GB of telemetry and deliver Level 0 science products to the end user in four hours. It provides analysis tools so the operator can manage the system and troubleshoot problems. It automates telemetry processing in order to reduce staffing costs. This work was done by Alice Stanboli, Elmain M. Martinez, and James M. McAuley of Caltech for NASA's Jet Propulsion Laboratory. For more information, contact iaoffice @jpl.nasa.gov. This software is available for commercial licensing. Please contact Dan Broderick at Daniel.F. Broderick@jpl.nasa.gov. Refer to NPO-47803. NASA Tech Briefs, September 2013 29 This rapid response computer program predicts Orbiter Wing Leading Edge (WLE) damage caused by ice or foam impact during a Space Shuttle launch (Program "IMPACT2"). The program was developed after the Columbia accident in order to assess quickly WLE damage due to ice, foam, or metal impact (if any) during a Shuttle launch. IMPACT2 simulates an impact event in a few minutes for foam impactors, and in seconds for ice and metal impactors. The damage criterion is derived from results obtained from one sophisticated commercial program, which requires hours to carry out simulations of the same impact events. The program was designed to run much faster than the commercial program with prediction of projectile threshold velocities within 10 to 15% of commercial-program values. The mathematical model involves coupling of Orbiter wing normal modes of vibration to nonlinear or linear springmass models. IMPACT2 solves nonlinear or linear impact problems using classical normal modes of vibration of a target, and nonlinear/ linear time-domain equations for the projectile. Impact loads and stresses developed in the target are computed as functions of time. This model is novel because of its speed of execution. A typical model of foam, or other projectile characterized by material nonlinearities, impacting an RCC panel is executed in minutes instead of hours needed by the commercial programs. Target damage due to impact can be assessed quickly, provided that target vibration modes and allowable stress are known. This work was done by Robert Clark, Jr., Paul Cotter, and Constantine Michalopoulos of The Boeing Company for Johnson Space Center. For further information, contact the JSC Innovation Partnerships Office at (281) 483-3809. MSC-24988-1 Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2) Lyndon B. Johnson Space Center, Houston, Texas (3) the MSL statistics for only the accountable assays. Other options on the main menu include a data editing form and utility programs that produce various reports requested by the microbiologists and the project, and tools to generate the groupings for the final analyses. The analyses can be carried out in three ways: Each assay can be treated separately, the assays can be collectively treated for the whole zone as a group, or the assays can be collected in groups designated by the JPL Planetary Protection Manager. The latter approach was used to generate the final report because assays on the same equipment or similar equipment can be assumed to have been exposed to the same environment and cleaning. Thus, the statistics are improved by having a larger population, thereby reducing the standard deviation by the square root of N. For each method mentioned above, three reports are available. The first is a detailed report including all the data. This version was very useful in verifying the calculations. The second is a brief report that is similar to the full detailed report, but does not print out the data. The third is a grand total and summary report in which each assay requires only one line. For the first and second reports, most of the calculations are performed in the report section itself. For the third, all the calculations are performed directly in the query bound to the report. All the numerical results were verified by comparing them with Excel templates, then exporting the data from the Planetary Protection Analysis program to Excel.

Beaudet, Robert A.↗

Three-Axis Distributed Fiber Optic Strain Measurement in 3D Woven Composite Structures

Recent advancements in composite materials technologies have broken further from traditional designs and require advanced instrumentation and analysis capabilities. Success or failure is highly dependent on design analysis and manufacturing processes. By monitoring smart structures throughout manufacturing and service life, residual and operational stresses can be assessed and structural integrity maintained. Composite smart structures can be manufactured by integrating fiber optic sensors into existing composite materials processes such as ply layup, filament winding and three-dimensional weaving. In this work optical fiber was integrated into 3D woven composite parts at a commercial woven products manufacturing facility. The fiber was then used to monitor the structures during a VARTM manufacturing process, and subsequent static and dynamic testing. Low cost telecommunications-grade optical fiber acts as the sensor using a high resolution commercial Optical Frequency Domain Reflectometer (OFDR) system providing distributed strain measurement at spatial resolutions as low as 2mm. Strain measurements using the optical fiber sensors are correlated to resistive strain gage measurements during static structural loading. Keywords: fiber optic, distributed strain sensing, Rayleigh scatter, optical frequency domain reflectometry

Castellucci, Matt↗

Jupiter Systems Data Analysis Program Galileo Multi-Spectral Analysis of the Galilean Satellites

Progress was made on this project at the University of Colorado, particularly concerning analysis of data of the galilean moons Io and Europa. The goal of the Io portion of this study is to incorporate Near Infrared Mapping Spectrometer (NIMS) measured sulfur dioxide (SO2) frost amounts into models used with Ultraviolet spectrometer (UVS) spectra, in order to better constrain SO2 gas amounts determined by the UVS. The overall goal of this portion of the study is to better understand the thickness and distribution of Io's SO2 atmosphere. The goal of the analysis of the Europa data is to better understand the source of the UV absorption feature centered near 280 rim which has been noted in disk-integrated spectra primarily on the trailing hemisphere. The NIMS data indicate asymmetric water ice bands on Europa, particularly over the trailing hemisphere, and especially concentrated in the visibly dark regions associated with chaotic terrain and lines. The UPS data, the first-ever disk-resolved UV spectra of Europa, shown that the UV absorber is likely concentrated in regions where the NIMS data show asymmetric water ice bands. The material that produces both spectral features is likely the same, and we use data from both wavelength regions to better understand this material, and whether it is endogenically or exogenically produced. This work is still in progress at JPL.

Hendrix, Amanda↗

Evaluation of NASA's MERRA Precipitation Product in Reproducing the Observed Trend and Distribution of Extreme Precipitation Events in the United States

This study evaluates the performance of NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA) precipitation product in reproducing the trend and distribution of extreme precipitation events. Utilizing the extreme value theory, time-invariant and time-variant extreme value distributions are developed to model the trends and changes in the patterns of extreme precipitation events over the contiguous United States during 1979-2010. The Climate Prediction Center (CPC) U.S.Unified gridded observation data are used as the observational dataset. The CPC analysis shows that the eastern and western parts of the United States are experiencing positive and negative trends in annual maxima, respectively. The continental-scale patterns of change found in MERRA seem to reasonably mirror the observed patterns of change found in CPC. This is not previously expected, given the difficulty in constraining precipitation in reanalysis products. MERRA tends to overestimate the frequency at which the 99th percentile of precipitation is exceeded because this threshold tends to be lower in MERRA, making it easier to be exceeded. This feature is dominant during the summer months. MERRA tends to reproduce spatial patterns of the scale and location parameters of the generalized extreme value and generalized Pareto distributions. However, MERRA underestimates these parameters, particularly over the Gulf Coast states, leading to lower magnitudes in extreme precipitation events. Two issues in MERRA are identified: 1) MERRA shows a spurious negative trend in Nebraska and Kansas, which is most likely related to the changes in the satellite observing system over time that has apparently affected the water cycle in the central United States, and 2) the patterns of positive trend over the Gulf Coast states and along the East Coast seem to be correlated with the tropical cyclones in these regions. The analysis of the trends in the seasonal precipitation extremes indicates that the hurricane and winter seasons are contributing the most to these trend patterns in the southeastern United States. In addition, the increasing annual trend simulated by MERRA in the Gulf Coast region is due to an incorrect trend in winter precipitation extremes.

MERRA↗

Some economic benefits of a synchronous earth observatory satellite

An analysis was made of the economic benefits which might be derived from reduced forecasting errors made possible by data obtained from a synchronous satellite system which can collect earth observation and meteorological data continuously and on demand. User costs directly associated with achieving benefits are included. In the analysis, benefits were evaluated which might be obtained as a result of improved thunderstorm forecasting, frost warning, and grain harvest forecasting capabilities. The anticipated system capabilities were used to arrive at realistic estimates of system performance on which to base the benefit analysis. Emphasis was placed on the benefits which result from system forecasting accuracies. Benefits from improved thunderstorm forecasts are indicated for the construction, air transportation, and agricultural industries. The effects of improved frost warning capability on the citrus crop are determined. The benefits from improved grain forecasting capability are evaluated in terms of both U.S. benefits resulting from domestic grain distribution and U.S. benefits from international grain distribution.

Battacharyya, R. K.↗

Radar altimeter mean return wave forms from near-normal-incidence ocean surface scattering

For a nearly Gaussian transmitted pulse shape scattered from a nearly Gaussian distributed sea surface, a small argument series expansion of one term lead to a several term power series expression for the mean return waveform. Specific expressions are given for the first four terms. These results, which require less computer time than numerical convolution, are useful for data analysis from current or past radar altimeters and for design studies of future systems. Several representative results are presented for an idealized Seasat-1 radar altimeter.

Hayne, G. S.↗