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NASA NTRS1988

Performance and lifetime assessment of MPD arc thruster technology

A summary of performance and lifetime characteristics of pulsed and steady-state magnetoplasmadynamic (MPD) thrusters is presented. The technical focus is on cargo vehicle propulsion for exploration-class missions to the Moon and Mars. Relatively high MPD thruster efficiencies of 0.43 and 0.69 have been reported at about 5000 s specific impulse using hydrogen and lithium, respectively. Efficiencies of 0.10 to 0.35 in the 1000 to 4500 s specific impulse range have been obtained with other propellants (e.g., Ar, NH3, N2). Thermal efficiency data in excess of 0.80 at MW power levels using pulsed thrusters indicate the potential of high MPD thruster performance. Extended tests of pulsed and steady-state MPD thrusters yield total impulses at least two to three orders of magnitude below that necessary for cargo vehicle propulsion. Performance tests and diagnostics for life-limiting mechanisms of megawatt-class thrusters will require high fidelity test stands which handle in excess of 10 kA and a vacuum facility whose operational pressure is less than 3 x 10 to the -4 torr.

Sovey, James S.↗

NASA NTRS1988

Performance and lifetime assessment of MPD arc thruster technology

Sovey, James S.↗

NASA NTRS2016

The Geoscience Spaceborne Imaging Spectroscopy Technical Committees Calibration and Validation Workshop

Calibration is the process of quantitatively defining a system's responses to known, controlled signal inputs, and validation is the process of assessing, by independent means, the quality of the data products derived from those system outputs [1]. Similar to other Earth observation (EO) sensors, the calibration and validation of spaceborne imaging spectroscopy sensors is a fundamental underpinning activity. Calibration and validation determine the quality and integrity of the data provided by spaceborne imaging spectroscopy sensors and have enormous downstream impacts on the accuracy and reliability of products generated from these sensors. At least five imaging spectroscopy satellites are planned to be launched within the next five years, with the two most advanced scheduled to be launched in the next two years [2]. The launch of these sensors requires the establishment of suitable, standardized, and harmonized calibration and validation strategies to ensure that high-quality data are acquired and comparable between these sensor systems. Such activities are extremely important for the community of imaging spectroscopy users. Recognizing the need to focus on this underpinning topic, the Geoscience Spaceborne Imaging Spectroscopy (previously, the International Spaceborne Imaging Spectroscopy) Technical Committee launched a calibration and validation initiative at the 2013 International Geoscience and Remote Sensing Symposium (IGARSS) in Melbourne, Australia, and a post-conference activity of a vicarious calibration field trip at Lake Lefroy in Western Australia.

Ong, Cindy↗

NASA NTRS1976

Preliminary assessment of systems for deriving liquid and gaseous fuels from waste or grown organics

The overall feasibility of the chemical conversion of waste or grown organic matter to fuel is examined from the technical, economic, and social viewpoints. The energy contribution from a system that uses waste and grown organic feedstocks is estimated as 4 to 12 percent of our current energy consumption. Estimates of today's market prices for these fuels are included. Economic and social issues are as important as technology in determining the feasibility of such a proposal. An orderly program of development and demonstration is recommended to provide reliable data for an assessment of the viability of the proposal.

Graham, R. W.↗

NASA NTRS2007

Engineering and Safety Partnership Enhances Safety of the Space Shuttle Program (SSP)

Project Management must use the risk assessment documents (RADs) as tools to support their decision making process. Therefore, these documents have to be initiated, developed, and evolved parallel to the life of the project. Technical preparation and safety compliance of these documents require a great deal of resources. Updating these documents after-the-fact not only requires substantial increase in resources - Project Cost -, but this task is also not useful and perhaps an unnecessary expense. Hazard Reports (HRs), Failure Modes and Effects Analysis (FMEAs), Critical Item Lists (CILs), Risk Management process are, among others, within this category. A positive action resulting from a strong partnership between interested parties is one way to get these documents and related processes and requirements, released and updated in useful time. The Space Shuttle Program (SSP) at the Marshall Space Flight Center has implemented a process which is having positive results and gaining acceptance within the Agency. A hybrid Panel, with equal interest and responsibilities for the two larger organizations, Safety and Engineering, is the focal point of this process. Called the Marshall Safety and Engineering Review Panel (MSERP), its charter (Space Shuttle Program Directive 110 F, April 15, 2005), and its Operating Control Plan emphasizes the technical and safety responsibilities over the program risk documents: HRs; FMEA/CILs; Engineering Changes; anomalies/problem resolutions and corrective action implementations, and trend analysis. The MSERP has undertaken its responsibilities with objectivity, assertiveness, dedication, has operated with focus, and has shown significant results and promising perspectives. The MSERP has been deeply involved in propulsion systems and integration, real time technical issues and other relevant reviews, since its conception. These activities have transformed the propulsion MSERP in a truly participative and value added panel, making a difference for the safety of the Space Shuttle Vehicle, its crew, and personnel. Because of the MSERP's valuable contribution to the assessment of safety risk for the SSP, this paper also proposes an enhanced Panel concept that takes this successful partnership concept to a higher level of 'true partnership'. The proposed panel is aimed to be responsible for the review and assessment of all risk relative to Safety for new and future aerospace and related programs.

Duarte, Alberto↗

DOE OSTI2020

SECARB-USA: Data Quality Methodology

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Southeast Regional CO 2 Utilization and Storage Acceleration Partnership (SECARB-USA): Data Quality Methodology (4.2.1)

SECARB-USA Deliverable 4.2.1 utilizes the outputs from the Needs Assessment (Subtask 2.1) to develop a data quality methodology. Many types of data are needed to evaluate a site for technical and financial viability. Several inventories of data types have been produced (for example NETL, 2010). The objective here is to organize the data types so that the needs met are specified. From this cross index (Table 1 in the Appendix), it will be possible in future tasks to (1) determine, on a site-specific basis, how much of each data type is required at each stage of a project to meet the need, and conversely (2) to further specify and define the data collection methods applied such that the data are tailored to fit that need. Derivative tables can then be developed to semi-quantitively evaluate the extent to which need is critical for early go/no decision points, or if it is more important than average, requiring faster or larger capitalization and spend to meet the need. In an additional step, the current availability of data for a site can be semi-quantitively assessed. From the table of data criticality and the table of data availability, site-specific cost for meeting the data needs can be determined, and allow a pre-permit spend estimated for a portfolio of projects. All of the data needs to evaluate a site are somewhat interconnected. We used criterion (2) above to determine if the data collection design would have to be modified to meet the need; if this was commonly true a linkage was shown. The application of this cross index to sites in the subsequent tasks will demonstrate that the demand for data types varies site-to-site and project-to-project. Examples of factors to be considered are the complexity of the geology, the injection goals such as rate and duration of the injection, and the types of risk and risk tolerance of key stakeholders. In future tasks the team will compare the demand for data with existing data availability. This will, in turn, determine when data needs to be acquired to support project development. For example, in a project area with complex structure, 3-D seismic data may be needed earlier and more urgently than in an area with simple rock body geometries. In some locations, a 3-D seismic survey has already been collected and can be purchased. In other locations the project developer will need to collect these data. For another example, a project near an urban area or near to a park may generate earlier and more substantive public concern than a site that is developed in mined lands. A calculation using the derivative from table 1 will show the different investment needs. Project cost will vary corresponding to data criticality and data availability.

42 ENGINEERING↗

NASA NTRS2017

Relevance of the American Statistical Society's Warning on P-Values for Conjunction Assessment

On March 7, 2016, the American Statistical Association (ASA) issued an online editorial paper on the "context, process, and purpose of p-values." According to the paper, "the statement articulates in non-technical terms a few select principles that could improve the conductor interpretation of quantitative science, according to widespread consensus in the statistical community." This "consensus" statement was accompanied by 21 "commentaries" expressing a diversity of opinions among the panel of experts ASA convened. In the present work, we express our view that the ASA p-value warning has relevance to the space object Conjunction Assessment (CA) community.

p-values↗

DOE OSTI2023

Impact of Thermal Scattering Law on Similarity Assessment in Light-Water or Polyethylene-Moderated Systems

A collaborative effort between Pacific Northwest National Laboratory (PNNL) and Oak Ridge National Laboratory (ORNL) is underway to provide a technical basis and methodology for the criticality safety community to use the sum of fractions (SoF) method for generating limits for mixtures of “selected actinide nuclides” included in the ANSI/ANS 8.15 standard. The PNNL scope in this project is to define a range of mixtures of 233 U, 235 U, and 239 Pu moderated with either light water or polyethylene and to examine the critical masses for these mixtures. The ORNL scope is primarily to provide validation support for these studies. More complete discussion of the project and its validation aspects will be presented at the upcoming International Conference on Nuclear Criticality Safety (ICNC) this Fall in Sendai, Japan. Clear differences in benchmark similarity to application systems as assessed by the integral parameter ck are noted in the validation studies performed as part of this project as a function of moderator. The c k value is a correlation coefficient that represents that amount of shared uncertainty in k eff due to cross sections between two systems. Individual nuclide-reaction contributions between the two systems can be simply summed to arrive at the total c k value. Specifically, the c k values for light-water–moderated solution experiments are higher for a water-moderated application than for a polyethylene-moderated application. This result is neither totally unexpected nor surprising, but the magnitude of the difference was difficult to anticipate. The TSUNAMI sequence, in the SCALE 6.2.4 code package developed by ORNL, was used to generate eigenvalues and reactivity effects with perturbation-theory based approach through sensitivity coefficients for all nuclides in the system with all reactions and energy groups. The TSUNAMI-Indices and Parameters (IP) sequence then uses the sensitivity data generated through TSUNAMI to generate relational parameters (i.e., c k ) to determine the degree of similarity between systems. One detail of the SCALE material and data implementation must be discussed at this point. Several thermal scattering laws (TSLs) are available for 1 H. SCALE uses a different nuclide ID number for each TSL; essentially, each version of 1 H is treated as a unique nuclide. For example, 1 H bound in water ( 1 H-H2O) is assigned the nuclide ID 1001, whereas 1 H bound in polyethylene (h-poly) is assigned the nuclide ID 9001001. The same cross section data are used for all reactions in 1 H, regardless of TSL, except for scattering below the TSL cutoff energy. TSUNAMI-IP treats different nuclide IDs as different nuclides; thus, no uncertainty is shared between 1 H-H2O and h-poly, despite much of the same data, including covariance data, being used for both nuclides. This presents a question: how much of the difference in assessed similarity between water- and polyethylene-moderated systems is due to the moderators, and how much is caused by the treatment of 1 H-H2O and h poly with cross section and covariance data. The extended edits generated by TSUANMI-IP allow for an investigation of this issue specifically, as well as a demonstration of the general techniques available within TSUNAMI to understand the results of the similarity assessment. This paper presents and analyzes the similarity assessment of both water- and polyethylene-moderated systems for a single benchmark: PST-002-001.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Gasification of Coal and Biomass: The Route to Net-Negative-Carbon Power and Hydrogen

One promising process that is a candidate for meeting the goals of the US Department of Energy’s 21st Century Power Plant initiative is to gasify a mixture of coal and biomass to yield a syngas, which can have CO2 removed and then be used to produce hydrogen as well as an off-gas that can be used to flexibly produce power. This concept would overall be carbon net-negative and readily meet the 21st Century Power Plant initiative targets of smaller scale MW generation, high ramp rates and turndown, feedstock flexibility, and high efficiency—at a reasonable cost. Moreover, adding the large-scale production of “ultra-green” hydrogen yields a system tailored for the coming hydrogen economy, providing long-term energy storage and an attractive co-product for sale. The objective of the work being led by the Electric Power Research Institute, Inc. (EPRI), with support by Bechtel Corporation (Bechtel), Gas Technology Institute (GTI), Hamilton Mauer International, Inc. (HMI), Nebraska Public Power District (NPPD), NexantECA, Inc. (Nexant), and Wärtsilä, is to perform a front-end design and engineering (FEED) study on an oxygen-blown gasification system coupled with water-gas shift, pre-combustion CO2 capture, and pressure-swing adsorption working off a coal/biomass mix to yield high-purity hydrogen and a fuel off-gas that can generate power. Several designs are being considered that will be capable of producing 50 MW net from a flexible generator, over 8500 kg/hr of hydrogen, and net-negative CO2 emissions, at an efficiency of 50% net HHV. The plant would be hosted at an NPPD site, where opportunities for enhanced oil recovery and sequestration have been investigated and the need for low-carbon power and hydrogen is imminent. The principal biomass to be used is corn stover—prevalent in Nebraska where the plant will be located—mixed with Powder River Basin (PRB) coal, necessitating a gasifier that can use this feedstock and be flexible to allow other types. Waste plastics will also be reviewed for use. Two oxygen-blown gasifiers have been identified as candidates that have done testing with biomass including corn stover: the GTI gasifier—a high-pressure, fluidized-bed type—and HMI’s, a lower pressure moving-bed type. Both have relative advantages that are being investigated in the Phase I design study, with a resultant down select of one system for which the FEED will be performed in Phase II. The technical tasks for the proposed project are: • Design Development: Completion of design activities necessary to provide inputs for the FEED study. Multiple design cases will be assessed with the selection of the optimal one for the FEED. • Investment Case Preparation: Development of the draft investment case for the proposed process with business cases performed for the proposed host site and two other locations. • Host Site Selection: Evaluation of the two potential host sites within NPPD’s portfolio to select the preferred candidate based on technical, economic, and environmental considerations. • Environmental Information Volume (EIV) Development: Completion of the EIV for the host site. • FEED Study: Completion of a FEED study based on the design selected in Phase I. A Greenhouse Gas Life Cycle Analysis will also be performed for the process. • Update Investment Case: Finalization of the investment case based on findings from the FEED. The advantages of the proposed project are significant. Having an engaged U.S. power utility willing to provide a host site that will produce energy from coal plus a deep and experienced team is critical; the process meets all the goals of DOE’s 21st Century Power Plant initiative at an estimated total plant cost of ~$880M and a production cost of hydrogen of ~$2/kg-H2 while producing net-negative carbon power. If developed, this process has real commercial potential in the United States—supported by EPRI’s initial review of the considerable interest from selected U.S. utilities—and elsewhere around the globe. The process has fewer environmental hurdles compared to other concepts, lowering regulatory and protest risks—providing a pathway to preserving the viability of a critical indigenous energy source by transforming its use to match a changing world. This presentation will outline the motivation for the effort, summarize project plans, work completed to date, results of the Design Development task, and detailed work scope for the remainder of the project.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2024

Gamma-Ray and Cosmic Ray Muon Modalities for Cargo Inspection

Screening and inspection of cargo containers are two essential methods to nondestructively examine the contents of shipment. These methods enable the detection of illicit transportation of unauthorized materials such as nuclear and radioactive materials, explosives, drugs, and so on, typically at borders or secure facilities. Although high-energy X-ray transmission is a standard system and is widely used for cargo inspection, the inherent challenges of high false-positive rates and high attenuation factors necessitate the development of complementary techniques that can increase the detection efficiency and accuracy in large and dense materials. Gamma-rays, which possess higher penetration characteristics because of their high energy, offer an alternative nonintrusive modality for cargo scanning. They represent a promising inspection method when compared to X-rays for three reasons: (1) improved ability to detect nuclear and radioactive materials, (2) higher inspection throughput rates, and (3) lower false-positive rates. Currently, there are two main gamma-ray inspection techniques, active and passive interrogation. Active interrogation can be further grouped into (1) gamma-ray transmission imaging and (2) neutron-induced gamma-ray emission detection. Gamma-ray transmission imaging utilizes differences in material densities for mapping the shipment contents and detecting anomalies. It is analogous to the X-ray transmission method; however, the high-energy photons make it more difficult to shield against, which enables more efficient performance in large and dense material inspection. Neutron-induced gamma-ray emission inspection is designed for the detection of nuclear and radioactive material because those materials emit characteristic gamma-rays when they are activated by neutron absorption. On the other hand, passive interrogation techniques rely on high-efficiency detectors to detect radiation emitted from hidden special nuclear or other radioactive materials. Similar to passive interrogation, cosmic ray muon monitoring and imaging are relatively new techniques that do not require external radioactive sources. These techniques have received attention as a potential next-generation radiographic probe to identify illicit transportation of nuclear and radioactive materials in cargo containers. Cosmic ray muons have unique features, (1) much higher energies than X-rays or gamma-rays (on the order of 10−1—104 GeV), (2) enhanced penetration capability, and (3) natural occurrence, thereby eliminating the need for induced radiation sources. These features enable cosmic ray muons to be utilized for detection of special nuclear materials in high-background-noise environments. By analyzing incoming and outgoing muon trajectories, scattering angles, and energies, it has been shown that it would be possible to locate hidden and well-shielded materials in cargo containers via three-dimensional muon tomography images or signal analysis. Gamma-rays, cosmic ray muons, and other nonintrusive cargo inspection modalities are complementary to each other, allowing them to address various cargo inspection conditions (i.e., scanning time, cost, radiation exposure level, and types of target materials). This chapter presents a detailed review of the theoretical fundamentals and technical principles behind the current gamma-ray and cosmic ray muon modalities for cargo inspection. Additionally, critical assessments and suggestions for the future directions to advance the use of gamma and muon modalities are discussed.

Bae, Junghyun↗

DOE OSTI2025

Exploring the Potential of Rainwater Harvesting for Cooling Towers: A Systematic Review and Regional Feasibility Assessment

Water scarcity has driven interest in rainwater harvesting, especially for U.S. industries like power and manufacturing, which dedicate a large percentage of their water needs to cooling towers. This paper provides a comprehensive systematic review of studies on the use of rainwater in cooling tower applications, along with an assessment of the regional feasibility of integrating RWH in U.S. manufacturing cooling towers. The systematic review examines the technical, economic, environmental, and policy feasibility of utilizing harvested rainwater, and the regional feasibility analysis evaluates the practical implementation of RWH in manufacturing cooling towers, considering factors such as regional RWH potential, water costs, state policies, and the industrial water use of manufacturing facilities per state. This study supports the hypothesis that RWH for cooling towers is technically feasible, economically viable, and environmentally beneficial. Harvested rainwater is naturally less conductive and soft, and rainwater reuse minimizes the ecological footprint. Supportive state policies, regional RWH potential, and rising water costs across the U.S. are important variables that may impact RWH adoption. The review highlights rooftop RWH as the most studied method and notes that implementing RWH requires infrastructure changes and filtration techniques. While initial investment costs may be high, operational and maintenance costs are low, making RWHS economically feasible over time. Regions with higher water costs and supportive policies are more likely to benefit from RWH adoption. The study provides a foundation for understanding the potential for using RWH in industrial cooling towers.

Cooling towers↗

DOE OSTI2022

Supply Chain Sustainability Analysis of Renewable Hydrocarbon Fuels via Indirect Liquefaction, Hydrothermal Liquefaction, Combined Algal Processing, and Biochemical Conversion: Update of the 2021 State-of-Technology Cases

The Department of Energy’s (DOE) Bioenergy Technologies Office (BETO) aims to develop and deploy technologies to transform renewable biomass resources into commercially viable, high-performance biofuels, bioproducts, and biopower through public and private partnerships. BETO and its national laboratory teams conduct in-depth techno-economic assessments (TEA) of biomass feedstock supply and logistics and conversion technologies to produce biofuels. There are two general types of TEAs: A design case outlines a target case (future projection) for a particular biofuel pathway. It informs R&D priorities by identifying areas in need of improvement, tracks sustainability impact of R&D, and provides goals and benchmarks against which technology progress is assessed. A state of technology (SOT) analysis assesses progress within and across relevant technology areas based on actual results at current experimental scales relative to technical targets and cost goals from design cases, and includes technical, economic, and environmental criteria as available.

09 BIOMASS FUELS↗

DOE OSTI2022

Supply Chain Sustainability Analysis of Renewable Hydrocarbon Fuels via Indirect Liquefaction, Hydrothermal Liquefaction, Combined Algal Processing, and Biochemical Conversion: Update of the 2021 State-of-Technology Cases

09 BIOMASS FUELS↗

DOE OSTI2025

Recycling Disassembled Automotive Plastic Components for New Vehicle Components: Enabling the Automotive Circular Economy

As the automotive industry increasingly relies on plastic components to meet fuel efficiency and emissions targets, the challenge of managing end-of-life vehicle (ELV) plastics continues to grow. Currently, more than 80% of ELV plastics in the U.S. are landfilled due to limited economic incentives and technical barriers to recycling. This study examines a mechanical recycling pathway for thermoplastic components disassembled from ELVs and assesses their usability for reintegration into new vehicle parts. Four representative materials were chosen based on material labels embedded in recovered parts and aligned with their virgin industrial equivalents: polypropylene (PP), 10% talc-filled PP (PP-T10), 20% talc-filled PP (PP-T20), and a 20% glass-/mineral-filled polyamide (PA6 + GF7 + MF13). The materials underwent shredding, drying, and injection molding before being characterized by particle size analysis, density measurement, thermal analysis (TGA, DSC), mechanical testing, and heat deflection temperature (HDT) evaluation. The results in this work indicated that minor differences in crystallinity were observed and small differences between model materials and ELV materials could have contributed to these changes. Mechanical testing revealed that neat polypropylene suffered a 15–20% reduction in stiffness and tensile strength, but talc-filled polypropylene and glass/mineral-filled nylon retained >90% of their modulus, strength, and heat deflection temperature values relative to virgin controls. Differences between virgin and ELV materials could have been attributed to use life degradation, contamination during use life, or even chemical/processing differences in model materials and ELV materials. However, these findings suggest that mechanically recycled, disassembled ELV plastics can retain sufficient structural performance to support circularity efforts in the automotive sector.

automotive recycling↗

NASA NTRS1978

The Ten-Ecosystem Study - Landsat ADP mapping of forest and rangeland in the United States

The Ten-Ecosystem Study was designed to assess the maximum information content of Landsat data and its utility for large area classification using a uniform technical approach on the 10 generalized forest and rangeland ecosystems of the United States. Conclusions on the feasibility of using Landsat remote sensing automatic data processing methods, selecting the best seasons, analyzing costs and the effects of site complexity, miscellaneous analysis, problems, and recommendations were derived from 2 years of study, the project being three-fourths completed.

Kan, E. P.↗

NASA NTRS1991

Direct broadcast satellite-radio market, legal, regulatory, and business considerations

A Direct Broadcast Satellite-Radio (DBS-R) System offers the prospect of delivering high quality audio broadcasts to large audiences at costs lower than or comparable to those incurred using the current means of broadcasting. The maturation of mobile communications technologies, and advances in microelectronics and digital signal processing now make it possible to bring this technology to the marketplace. Heightened consumer interest in improved audio quality coupled with the technological and economic feasibility of meeting this demand via DBS-R make it opportune to start planning for implementation of DBS-R Systems. NASA-Lewis and the Voice of America as part of their on-going efforts to improve the quality of international audio broadcasts, have undertaken a number of tasks to more clearly define the technical, marketing, organizational, legal, and regulatory issues underlying implementation of DBS-R Systems. The results and an assessment is presented of the business considerations underlying the construction, launch, and operation of DBS-R Systems.

Sood, Des R.↗

NASA NTRS1994

Progress in modeling atmospheric propagation of sonic booms

The improved simulation of sonic boom propagation through the real atmosphere requires greater understanding of how the transient acoustic pulses popularly termed sonic booms are affected by humidity and turbulence. A realistic atmosphere is invariably somewhat turbulent, and may be characterized by an ambient fluid velocity v and sound speed c that vary from point to point. The absolute humidity will also vary from point to point, although possibly not as irregularly. What is ideally desired is a relatively simple scheme for predicting the probable spreads in key sonic boom signature parameters. Such parameters could be peak amplitudes, rise times, or gross quantities obtainable by signal processing that correlate well with annoyance or damage potential. The practical desire for the prediction scheme is that it require a relatively small amount of knowledge, possibly of a statistical nature, concerning the atmosphere along, the propagation path from the aircraft to the ground. The impact of such a scheme, if developed, implemented, and verified, would be that it would give the persons who make planning decisions a tool for assessing the magnitude of environmental problems that might result from any given overflight or sequence of overflights. The technical approach that has been followed by the author and some of his colleagues is to formulate a hierarchy of simple approximate models based on fundamental physical principles and then to test these models against existing data. For propagation of sonic booms and of other types of acoustic pulses in nonturbulent model atmospheres, there exists a basic overall theoretical model that has evolved as an outgrowth of geometrical acoustics. This theoretical model depicts the sound as propagating within ray tubes in a manner analogous to sound in a waveguide of slowly varying cross-section. Propagation along the ray tube is quasi-one-dimensional, and a wave equation for unidirectional wave propagation is used. A nonlinear term is added to this equation to account for nonlinear steepening, and the formulation has been carried through to allow for spatially varying sound speed, ambient density, and ambient wind velocities. The model intrinsically neglects diffraction, so it cannot take into account what has previously been mentioned in the literature as possibly important mechanisms for turbulence-related distortion. The model as originally developed could predict an idealized N-waveform which often agrees with data in terms of peak amplitude and overall positive phase duration. It is possible, moreover, to develop simple methods based on the physics of relaxation processes for incorporating molecular relaxation into the quasi-one-dimensional model of nonlinear propagation along ray tubes.

Pierce, Allan D.↗