Search NASA⌕ Search

SEARCH · Search NASA

Results for “Radiation Environment”

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.

511 records
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Accelerating SNP Development with Radiation Source Approximations for Far-Field Environment Modeling

The successful development and deployment of space nuclear power and propulsion technology requires a high-fidelity, efficient means of modeling ex-core radiation fields. Monte Carlo particle transport codes provide enable the highest level of fidelity in radiation field modeling but are inefficient for modeling ex-core radiation without modification. This paper details the development of an approach to ex-core radiation field modeling that maintains the fidelity of a Monte Carlo transport approach without sacrificing computational efficiency. This approach is based on recent improvements to an existing Monte Carlo transport acceleration technique known as surface source banking. As the transport of many particles is required to ensure adequate uncertainty in far field transport, analytical reconstruction techniques are employed to represent surface source banks as sampleable series of distributions in particle phase from which an arbitrarily large number of particles can be generated and simulated. All steps of this approach are incorporated into an AMA model to test both the underlying mathematics of the analytical source reconstruction process, as well as the relevance of the technique as a whole towards SNP applications. These tests demonstrated that this approach is capable of accelerating far-field radiation modeling in SNP-relevant scenarios by factors of at least nine over purely eigenvalue-based scenarios without significantly sacrificing simulation accuracy.

Surface Source Banking↗
NASA NTRS1987

Radiation hardening design of nuclear powered spacecraft

The design and operation of space systems utilizing nuclear fueled power systems must consider the radiation environment from the earliest stages of their design. A range of nuclear systems are being considered for present and future satellite systems capable of supplying tens of kilowatts to multimegawatt and generating a corresponding range of radiation environments. The effects of these radiations on electronics and materials can be minimized by implementing early design considerations which maximize the design efficiency and minimize the impact on system mass. Space systems design considerations for the radiation environment must include all sources in addition to the self induced gamma ray and neutron radiation. These include the orbital dependent environment from the high energy electron and protons encountered in natural space. The system trades which the designer must consider in the development of space platforms which utilize nuclear reactor power supplies are discussed.

R E Schmidt↗
NASA NTRS1965

Symposium on Thermal Radiation of Solids

The Symposium was intended to provide for presentation and discussion of significant developments in the theory of thermal radiation of solids and in our understanding of the important effects of surfaces and interfaces and of surface imperfections on this radiation, of the effects of the space environment on radiation properties, and of the application of this information to the thermal designer's problems. Presentation of data as such-for example, absorptances and emittances of various types of coatings-was not considered a primary purpose of the Symposium; nevertheless, as the reader will observe, an appreciable amount of significant data of this type is contained in some of the papers. Developments in measurement techniques were also not considered basic to the main theme, especially since it was the theme of the preceding Symposium. However, because the subject remains of continuing concern, one session was devoted to it. These Proceedings contain all the papers presented orally at the Symposium together with the discussions that followed them, and, in addition, nine papers that were accepted for publication only. Each paper was reviewed by the session chairman and by the editor, and any apparent technical discrepancies were called to the attention of the author for clarification. As a further aid to the reader, the editor has tried to achieve some degree of uniformity in organization and format of the papers—at least to the extent permitted by the subject matter, and he has also striven for clarity and readability of the text. In this task he has had not only the cooperation of the authors but also extensive help from the Langley Technical Editing Section, the Langley Library (where most of the cited references were checked), and the NASA Headquarters Technical Publications Branch.

Solids↗
NASA NTRS1973

Terrestrial Environment (Climatic) Criteria Guidelines for Use in Aerospace Vehicle Development, 1973 Revision

This document provides guidelines on probable climatic extremes and probabilities-of-occurrence of terrestrial environment data specifically applicable for NASA space vehicles and associated equipment development. The geographic areas encompassed are The Eastern Test Range (Cape Kennedy, Florida); Huntsville, Alabama; New Orleans, Louisiana; The Space and Missile Test Center (Vandenberg AFB California); Sacramento, California; Wallops Test Range (Wallops Island, Virginia); White Sands Missile Range, New Mexico; and intermediate transportation areas. In addition, sections have been included to provide information on the general distribution of natural environment extremes in the United States (excluding Alaska and Hawaii), cloud cover, and some worldwide climatic extremes. Although all these areas are covered, the major emphasis is given to the Kennedy Space Center launch area and Vandenburg Air Force Base due to importance in NASA's future large space vehicle programs. This document presents the latest available information on probable climatic extremes, and supersedes information presented in TM X-64589. The information in this document is recommended for employment in the development of space vehicles and associated equipment design and operational criteria, unless otherwise stated in contract work specifications.

cloud cover↗
NASA NTRS2026

A Study of Space Environment Effect on Highly Thermally Conductive Hybrid Carbon Fiber Polymer Composites

A set of novel highly thermally conductive hybrid carbon fiber (CF) polymer composites has been developed for lightweight thermal radiator applications in space missions. This study investigates the effects of the space environment on these materials following exposure in low-Earth orbit (LEO) during the Materials International Space Station Experiment (MISSE)-17 flight mission, where samples experienced 159 days of combined atomic oxygen (AO), ultraviolet (UV) radiation, high vacuum, space radiation and thermal cycling. Post-flight characterization included weight loss, surface morphology, thermo-optical properties, molecular structures, glass transition temperature, thermal degradation and thermal conductivity analyses. The pyrolytic graphite sheet (PGS) samples exhibited negligible weight loss, stable thermo-optical property, and only minor oxidation signature on the exposed surface. Although AO erosion of the epoxy polymer matrix was evident, carbon nanotube (CNT)-infused PGS/CF epoxy composites retained high thermal emissivity and preserved their high thermal conductivities. These results demonstrate that the novel highly thermally conductive hybrid CF composites possess strong environmental resilience and are promising candidates for lightweight thermal radiators and thermal management components in future space exploration missions.

Space Environment↗
NASA NTRSDate not supplied

Lunar Surface Crater Thermal Effects on Lander Radiator Performance

Lunar surface craters smaller than the spatial resolution of surface meshes used in typical Lunar surface thermal models (10 to 60 meters per pixel) may impact the accuracy of thermal model extrema predictions. The goal of this study is to investigate the thermal sensitivity of representative lander systems with realistic thermal surface orientations in bare and cratered terrain environments at relevant Artemis mission locations. This thermal analysis task investigates the impact of lunar surface craters on lander radiator performance by comparing heat rejection capability results between bare and cratered terrain environments. This study examines external body-mounted lander radiator thermal performance across varying lander heights (5.5m, 20m, 50m) and radiator orientations (horizontal, 45º tilted, and vertical) at two representative Artemis mission latitudes (-89.5ºS and -82.5ºS), spanning from the Shackleton Connecting Ridge to Mons Mouton Plateau.

Lunar Surface↗
NASA NTRS2025

Radiation-Resistant Ti/BN Coatings: Insights From 171 Days Exposure to Space Radiation and Atomic Oxygen in Low Orbit

Atmospheric Plasma Spray (APS) and Vacuum Plasma Spray (VPS) techniques were used to develop Ti/2 vol.% hBN coatings, for extreme space environments and tested aboard the International Space Station as part of the MISSE-17 (Materials International Space Station Experiments) program. The coatings were exposed to atomic oxygen, space radiation, and low-orbit thermal cycling. VPS coatings showed a 56% increase in microhardness, a 26% rise in elastic modulus, minimal porosity and crack density changes compared to APS coatings. The change in mechanical properties is attributed to the formation of TiO, TiO₂ and TiN from nitrogen retention, alongside radiation-induced dislocations, which enhanced surface hardening. The oxidation of titanium led to the formation of TiO and TiO₂, while boron nitride was retained and underwent transmutation in VPS coatings. XPS and EDS analyses confirmed the enhanced space-environment resistance of VPS coatings, making them ideal for long-term spacecraft protection in lunar and Martian conditions.

Abhijith Kunneparambil Sukumaran↗
NASA NTRS2026

Thermal Considerations for 2039 Opposition Class Nuclear Electric Propulsion/Chemical Propulsion Crewed Mars Mission

The high specific impulse (Isp) of Nuclear Electric Propulsion (NEP) technology offers the potential for advanced space mission capabilities. However, the five critical technology elements of NEP vehicles have yet to prove technical maturity levels for consideration into mission design. In response to the critical reviews by the NASA Engineering and Safety Center (NESC) and the National Academies of Sciences, Engineering, and Medicine (NASEM), NASA’s Space Nuclear Propulsion (SNP) project created an NEP Technology Maturation Plan (TMP) for focused development of NEP technology. The TMP called for a coordinated set of technology development efforts to meet this objective. The Modular Assembled Radiators for NEP VehicLes (MARVL) Early Career Initiative (ECI) project was initiated to develop a portion of the fifth Critical Technology Element (CTE) of the NEP vehicle: the Primary Heat Rejection Subsystem (PHRS). A target application of a 2039 human-rated Mars mission was outlined in the TMP. For the outlined mission, a NEP vehicle will experience several thermal environments which will impact the design and operation of the PHRS. To maintain radiator temperatures within the required effective temperature range, the effect of natural, induced, and NEP internally generated heat loads on the radiator panel must be well understood. Furthermore, this analysis is critical for analyzing the influence of various orientations and positions of the NEP vehicle relative to nearby celestial bodies throughout the mission. This study conducted a complete enveloping analysis of the thermal environments influencing the NEP vehicle throughout the mission. Thermal analysis was conducted for the radiator panels based on the defined mission environments. This thermal analysis concludes with the selection of ideal radiator orientations for the NEP vehicle, and the identification of worst case hot and cold environmental sink temperatures throughout the mission. For the target application, the environmental sink temperature while the reactor is powered OFF or powered ON ranges from 30 K to 353 K and 2.7 K to 243 K respectively. When considering interplanetary space, the minimum environmental sink temperature when the reactor is powered OFF and the radiators are oriented “edge to Sun” is 2.7 K. The environmental thermal models generated in this study will be used for future studies with the full vehicle system model. The environmental sink temperature curves generated will be used for future radiator and component analysis to predict transient performance in the space environment. The environmental sink temperature and heat rejection capability curves will inform the trade between commissioning orbits that are in consideration. The model may also serve as a useful tool as reference for future crewed space missions, missions involving radiators or temperature sensitive equipment, or other missions requiring analysis of natural orbital thermal environments.

Nuclear Electric Propulsion↗
DOE OSTI2026

Surrogate modeling of Monte Carlo radiation transport with convolutional neural networks for shielding optimization

Here, we present a machine learning (ML)-based surrogate model using convolutional neural networks (CNN) designed to emulate the attenuation of neutron fields as they pass through various shielding materials. This model can compute the outgoing neutron flux almost instantaneously and achieves reasonable accuracy compared to traditional Monte Carlo (MC)-based codes, which are computationally intensive. This emulator alleviates the complexity of neutron radiation transport through shielding materials by reducing the dimensionality and enables shielding optimization for a known radiation environment. This optimization process, which would have taken an unrealistic timeline due to several complex radiation transport simulations, can now be achieved in minutes, thus increasing computational capabilities in radiation shielding assessment. We demonstrate the applications of this emulator in computing effective dose rates and optimizing shielding solutions for a heavy-ion accelerator facility, such as the Facility for Rare Isotope Beams, where secondary neutrons produced via beam interactions dominate the radiation environment.

accelerator shielding↗
NASA NTRS1990

Gaseous Optical Contamination of the Spacecraft Environment: A Review

Interactions between the ambient atmosphere and orbiting spacecraft, sounding rockets, and suborbital vehicles, and with their effluents, give rise to optical (extreme UV to LWIR) foreground radiation which constitutes noise that raises the detection threshold for terrestrial and celestial radiations, as well as military targets. Researchers review the current information on the on-orbit optical contamination. Its source species are created in interaction processes that can be grouped into three categories: (1) Reactions in the gas phase between the ambient atmosphere and desorbates and exhaust; (2) Reactions catalyzed by exposed ram surfaces, which occur spontaneously even in the absence of active material releases from the vehicles; and (3) Erosive excitative reactions with exposed bulk (organic) materials, which have recently been identified in the laboratory though not as yet observed on spacecraft. Researchers also assess the effect of optical pumping by earthshine and sunlight of both reaction products and effluents.

Tran, N. H.↗
DOE OSTI2026

Material-dependent photon ionizing radiation effects in Si and GaAs PIN diodes: A numerical investigation

We present a finite-element drift-diffusion-Poisson model in the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework to compare the radiation response of silicon (Si) and gallium arsenide (GaAs) PIN diodes under high-energy photon irradiation. The model solves coupled carrier continuity and Poisson’s equations with Shockley-Read-Hall recombination, and is verified against standard analytical J-V behavior. Using a simplified 1D geometry with ideal Ohmic contacts, we quantify device response under forward and reverse bias with a 100 MeV photon flux. Under forward bias, Si exhibits markedly greater radiation sensitivity than GaAs, including larger increases in current density, stronger local field and carrier-product perturbations, and higher recombination. Under reverse bias, GaAs shows larger radiation-induced photocurrent and broader current-density peaks near junctions, indicating an advantage for photodetection. Integrated steady-state recombination is consistently higher in Si across voltages. Under periodic photon pulses, GaAs produces higher-amplitude photoresponse and settles more rapidly than Si. These results highlight material-dependent trade-offs for radiation-tolerant, high-speed optoelectronics and provide guidance for selecting PIN architectures in aerospace, nuclear, and high-energy physics environments.

36 MATERIALS SCIENCE↗
NASA NTRS2026

Mechanical Properties of Carbon Fiber Reinforced Composites Exposed to Cryogenic Conditions and Space Radiation via Simulation and Testing

As NASA missions extend beyond low Earth orbit, increasing reliance is placed on carbon fiber reinforced polymer (CFRP) composites for spacecraft structures where mass efficiency, durability, and long-term reliability are critical. In service, these materials are subjected to a combination of ultraviolet radiation, vacuum, ionizing radiation, atomic oxygen, and extreme thermal excursions under sustained mechanical loading. Flight systems such as the Boeing Starliner and SpaceX Dragon employ external composite structures that will experience these environments for extended durations. Although prior spaceflight and ground studies have reported limited changes in bulk mechanical properties, the synergistic effects of these environments on composite microstructure, particularly at the fiber matrix interphase, remain insufficiently characterized and represent a potential qualification and reliability risk. This study investigates the effects of short-term cryogenic exposure on a radiation shielding carbon epoxy composite, SC2020, as a ground-based analog for space relevant thermal extremes. The SC2020 material system has previously flown on the International Space Station under the Materials International Space Station Experiment (MISSE) program. Composite specimens were exposed to liquid nitrogen for 6 and 24 hours and evaluated using a multiscale characterization framework that combined ASTM D3039 tensile testing, Atomic Force Microscopy (AFM) based interphase analysis, and helium gas permeability measurements. Tensile testing showed no statistically significant or permanent degradation in global strength or modulus following cryogenic exposure. In contrast, AFM measurements revealed reductions in interphase modulus, weakened adhesion, and increased nanoscale heterogeneity, indicating localized degradation mechanisms not captured by conventional bulk testing. Gas permeability measurements showed a progressive increase in helium diffusion with exposure duration, consistent with micro-void formation or partial interfacial debonding. The results indicate that cryogenic exposure initiates degradation at the fiber matrix interphase while leaving global mechanical properties largely unchanged over short durations. These findings underscore the importance of multiscale diagnostics for identifying early-stage damage mechanisms that may influence long term performance and qualification margins for spaceflight composite structures. The data presented establish a cryogenic baseline for comparison with forthcoming MISSE flight exposure results and support ongoing NASA Established Program to Stimulate Competitive Research (EPSCoR) efforts aimed at improving composite qualification methodologies, risk assessment, and reliability prediction for space environments.

composite reliability↗
NASA NTRS1990

Interactions Between the Space Station and the Environment: A Preliminary Assessment of EMI

A review of the interactions between proposed Space Station systems/payloads and the environment that contribute to electromagnetic interference was performed. Seven prime sources of interference have been identified. These are: The Space Station power system; active experiments such as beam injection; ASTROMAG; ram and wake density gradients; pick up ions produced by vented or offgassed clouds; waves produced by current loops that include the plasma and structure; arcing from high voltage solar arrays (or possible ESD in polar orbit). This review indicates that: minimizing leakage current from the 20 kHz power system to the structure; keeping the surfaces of the Space Station structure, arrays, and radiators nonconducting; minimizing venting of payloads or systems to non-operational periods; careful placement of payloads sensitive to magnetic field perturbations or wake noise; and designing an operational timeline compatible with experiment requirement are the most effective means of minimizing the effects of this interference. High degrees of uncertainty exist in the estimates of magnitudes of gas emission induced EMI, radiation of 20 kHz and harmonics, ASTROMAG induced interference, and arc threshold/frequency of the solar array. These processes demand further attention so that mitigation efforts are properly calibrated.

G B Murphy↗
NASA NTRS1997

Radiation Temperature and Extinction of Transient Gaseous Diffusion Flames in Microgravity

The absence of buoyancy-induced flows in micro-g and the resulting increase in the reactant residence time significantly alters the fundamentals of many combustion processes. Substantial differences between 1-g and micro-g flames have been reported in experiments on candle flames, flame spread over solids, droplet combustion and others. These differences are more basic than just in the visible flame shape. Longer residence times and higher concentration of combustion products in the flame zone create a thermochemical environment which changes the flame chemistry and the heat and mass transfer processes. Processes such as flame radiation (and its interaction with flame chemistry), that are often ignored under normal gravity, become very important and sometimes even controlling. This is particularly true for conditions at extinction of a micro-g diffusion flame.

Arvind Atreya↗
NASA NTRS2017

Europa Propulsion Valve Seat Material Testing

The Europa mission and spacecraft design presented unique challenges for selection of valve seat materials that met the fluid compatibility requirements, and combined fluid compatibility and high radiation exposure level requirements. The Europa spacecraft pressurization system valves will be exposed to fully saturated propellant vapor for the duration of the mission. The effects of Nitrogen Tetroxide (NTO) and Monomethylhydrazine (MMH) propellant vapors on heritage valve seat materials, such as Vespel SP-1 and Polychlorotrifluoroethylene (PCTFE), were evaluated to determine if an alternate material is required. In liquid system applications, Teflon is the only available compatible valve seat material. Radiation exposure data for Teflon in an air or vacuum environment has been previously documented. Radiation exposure data for Teflon in an oxidizer environment such as NTO, was not available, and it was unknown whether the effects would be similar to those on air-exposed samples. Material testing was conducted by Marshall Space Flight Center (MSFC) and White Sands Test Facility (WSTF) to determine the effects of propellant vapor on heritage seat materials for pressurization valve applications, and the effects of combined radiation and NTO propellant exposure on Teflon. The results indicated that changes in heritage pressurization valve seat materials' properties rendered them unsuitable for the Europa application. The combined radiation and NTO exposure testing of Teflon produced results equivalent to combined radiation and air exposure results.

Brad M Addona↗
DOE OSTI1988

Nuclear Safety [Vol. 29, No. 1, January-March 1988]

Nuclear Safety is a review journal that covers significant developments in the field of nuclear safety. Its scope includes the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, the safety aspects of the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. THE CHERNOBYL ACCIDENT: 1 Core History and Nuclide Inventory of the Chernobyl Core at the Time of Accident by Gerald Kirchner and Cornelius C. Noack; GENERAL SAFETY CONSIDERATIONS: 6 Nonprescriptive Nuclear Safety Regulation: The Example of Loss of Offsite Power by M. W. Golay, V. P. Manno, and C. Vlahoplus, Jr., 20 Nuclear Power Safety Goals in Light of the Chernobyl Accident by C. Whipple and C. Starr; ACCIDENT ANALYSIS: 29 Containment Loads from Severe Accidents—U.S. Program by W. Kerr and M. K. Dey; PLANT SAFETY FEATURES: 36 Safety Characteristics of Modern High-Temperature Reactors: Focus on German Designs by W. Kröger, H. Nickel, and R. Schulten; ENVIRONMENTAL EFFECTS: 49 Radiation Hormesis and Nuclear Safety by C. C. Congdon; OPERATING EXPERIENCES: 58 Evaluation of Nonradiological Water Chemistry at Power Reactors by Harvey Zibulsky, James J. Kottan, Walter J. Pasciak, Mary Ann Castrogivanni, and Sujit Banerjee, 64 Reactor Shutdown Experience Compiled by J. W. Cletcher, 67 Operating U.S. Power Reactors Compiled by E. G. Silver; RECENT DEVELOPMENTS: 85 General Administrative Activities Compiled by E. G. Silver, 94 Reports, Standards, and Safety Guides by D. S. Queener, 100 Status of Power-Reactor Projects Undergoing Licensing Review Compiled by E. G. Silver, 103 Proposed Rule Changes as of Sept. 30, 1987; ANNOUNCEMENTS: 5 Northwestern University Short Course on Radiation Safety, 28 International Approach to Nuclear Safety (After Three-Mile Island and Chernobyl), 57 RPI Short Course on Modern Developments in Boiling Heat Transfer and Two-Phase Flow, 107 20th DOE/NRC Nuclear Air Cleaning Conference, 110 Third International Topical Meeting on Nuclear Power Plant Thermal Hydraulics and Operations, 108 The Authors, 111 Indexes to Nuclear Safety, Volume 28.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2003

Introduction to Radiation Issues for International Space Station Extravehicular Activities: Chapter 1

The International Space Station (ISS) provides significant challenges for radiation protection of the crew due to a combination of circumstances including: the extended duration of missions for many crewmembers, the exceptionally dynamic nature of the radiation environment in ISS orbit, and the necessity for numerous planned extravehicular activities (EVA) for station construction and maintenance. Radiation protection requires accurate radiation dose measurements and precise risk modeling of the transmission of high fluxes of energetic electrons and protons through the relatively thin shielding provided by the space suits worn during EVA. Experiments and analyses have been performed due to the necessity to assure complete radiation safety for the EVA crew and thereby ensure mission success. The detailed characterization described of the material and topological properties of the ISS space suits can be used as a basis for design of space suits used in future exploration missions. In radiation protection practices, risk from exposure to ionizing radiation is determined analytically by the level of exposure, the detrimental quality of the radiation field, the inherent radiosensitivity of the tissues or organs irradiated, and the age and gender of the person at the time of exposure. During low Earth orbit (LEO) EVA, the relatively high fluxes of low-energy electrons and protons lead to large variations in exposure of the skin, lens of the eye, and tissues in other shallow anatomical locations. The technical papers in this publication describe a number of ground-based experiments that precisely measure the thickness of the NASA extravehicular mobility unit (EMU) and Russian Zvezda Orlan-M suits using medical computerized tomography (CT) X-ray analysis, and particle accelerator experiments that measure the minimum kinetic energy required by electrons and photons to penetrate major components of the suits. These studies provide information necessary for improving the understanding of the current ISS space suits and provide insights into improved approaches for the design of future suits. This chapter begins with a summary of the dynamic ionizing radiation environment in LEO space and introduces the concepts and quantities used to quantify exposure to space radiation in LEO. The space suits used for EVA and the experimental partial human phantom are described. Subsequent chapters report results from measured charged particle fields before and after incident protons and secondary particles are transported through the space suits and into organs and tissues.

M R Shavers↗
NASA NTRS1992

Development and application of a 3-D geometry/mass model for LDEF satellite ionizing radiation assessments

A computer model of the three dimensional geometry and material distributions for the LDEF spacecraft, experiment trays, and, for selected trays, the components of experiments within a tray was developed for use in ionizing radiation assessments. The model is being applied to provide 3-D shielding distributions around radiation dosimeters to aid in data interpretation, particularly in assessing the directional properties of the radiation exposure. Also, the model has been interfaced with radiation transport codes for 3-D dosimetry response predictions and for calculations related to determining the accuracy of trapped proton and cosmic ray environment models. The methodology is described used in developing the 3-D LDEF model and the level of detail incorporated. Currently, the trays modeled in detail are F2, F8, and H12 and H3. Applications of the model which are discussed include the 3-D shielding distributions around various dosimeters, the influence of shielding on dosimetry responses, and comparisons of dose predictions based on the present 3-D model vs those from 1-D geometry model approximations used in initial estimates.

B. L. Colborn↗