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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.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Martin, Michael A.↗
NASA NTRS2004

Assessing the Effectiveness of a Mathematics-Focused, Instructional Technology Program for Grades 6-8: A 5-Year Trend Analysis of NASA CONNECT(tm) Evaluation Data

NASA CONNECT is a research-, inquiry, and standards-based, integrated mathematics, science, and technology series of 30-minute instructional distance learning (television and web-based) programs for students in grades 6 8. Respondents who evaluated the programs in the series over the first five seasons (1998-99 through 2002-03) reported that (1) they used the programs in the series; (2) the goals and objectives for the series were met; (3) the programs were aligned with the national mathematics, science, and technology standards; (4) the program content was developmentally appropriate for the grade level; and (5) the programs in the series enhanced and enriched the teaching of mathematics, science, and technology.

Glassman, Nanci A.↗
NASA NTRS1989

A mathematical model of physiological processes and its application to the study of aging

The behavior of a physiological system which, after displacement, returns by homeostatic mechanisms to its original condition can be described by a simple differential equation in which the "recovery time" is a parameter. Two such systems, which influence one another, can be linked mathematically by the use of "coupling" or "feedback" coefficients. These concepts are the basis for many mathematical models of physiological behavior, and we describe the general nature of such models. Next, we introduce the concept of a "fatal limit" for the displacement of a physiological system, and show how measures of such limits can be included in mathematical models. We show how the numerical values of such limits depend on the values of other system parameters, i.e., recovery times and coupling coefficients, and suggest ways of measuring all these parameters experimentally, for example by monitoring changes induced by X-irradiation. Next, we discuss age-related changes in these parameters, and show how the parameters of mortality statistics, such as the famous Gompertz parameters, can be derived from experimentally measurable changes. Concepts of onset-of-aging, critical or fatal limits, equilibrium value (homeostasis), recovery times and coupling constants are involved. Illustrations are given using published data from mouse and rat populations. We believe that this method of deriving survival patterns from model that is experimentally testable is unique.

Aging/physiology↗
NASA NTRS2005

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Seymour, David C.↗
NASA NTRS2009

A Mathematical Basis for the Safety Analysis of Conflict Prevention Algorithms

In air traffic management systems, a conflict prevention system examines the traffic and provides ranges of guidance maneuvers that avoid conflicts. This guidance takes the form of ranges of track angles, vertical speeds, or ground speeds. These ranges may be assembled into prevention bands: maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for all maneuvers. Without conflict prevention information, a pilot might perform a maneuver that causes a near-term conflict. Because near-term conflicts can lead to safety concerns, strong verification of correct operation is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information. This paper examines multiple mathematical approaches: iterative, vector algebraic, and trigonometric. The correctness theories are structured first to analyze conflict prevention information for all aircraft. Next, these theories are augmented to consider aircraft which will create a conflict within a given lookahead time. Certain key functions for a candidate algorithm, which satisfy this mathematical basis are presented; however, the proof that a full algorithm using these functions completely satisfies the definition of safety is not provided.

Maddalon, Jeffrey M.↗
NASA NTRS2009

A Verification-Driven Approach to Traceability and Documentation for Auto-Generated Mathematical Software

Model-based development and automated code generation are increasingly used for production code in safety-critical applications, but since code generators are typically not qualified, the generated code must still be fully tested, reviewed, and certified. This is particularly arduous for mathematical and control engineering software which requires reviewers to trace subtle details of textbook formulas and algorithms to the code, and to match requirements (e.g., physical units or coordinate frames) not represented explicitly in models or code. Both tasks are complicated by the often opaque nature of auto-generated code. We address these problems by developing a verification-driven approach to traceability and documentation. We apply the AUTOCERT verification system to identify and then verify mathematical concepts in the code, based on a mathematical domain theory, and then use these verified traceability links between concepts, code, and verification conditions to construct a natural language report that provides a high-level structured argument explaining why and how the code uses the assumptions and complies with the requirements. We have applied our approach to generate review documents for several sub-systems of NASA s Project Constellation.

Denney, Ewen W.↗
NASA NTRS2011

Mathematical Model and Experimental Results for Cryogenic Densification and Sub-Cooling Using a Submerged Cooling Source

Among the many factors that determine overall rocket performance, propellant density is important because it affects the size of the rocket. Thus, in order to decrease the size of a rocket, it may be desirable to increase the density of propellants. This study analyzes the concept of increasing the propellant density by employing a cooling source submerged in the liquid propellant. A simple, mathematical model was developed to predict the rate of densification and the propellant temperature profile. The mathematical model is generic and applicable to multiple propellants. The densification rate was determined experimentally by submerging a cooling source in liquid oxygen at constant, positive pressure, and measuring the time rate of change in temperature with respect to vertical position. The results from the mathematical model provided a reasonable fit when compared to experimental results.

Partridge, J. K.↗
NASA NTRS2017

Mathematical Modeling of Electrodynamics Near the Surface of Earth and Planetary Water Worlds

An interesting feature of planetary bodies with hydrospheres is the presence of an electrically conducting shell near the global surface. This conducting shell may typically lie between relatively insulating rock, ice, or atmosphere, creating a strong constraint on the flow of large-scale electric currents. All or parts of the shell may be in fluid motion relative to main components of the rotating planetary magnetic field (as well as the magnetic fields due to external bodies), creating motionally-induced electric currents that would not otherwise be present. As such, one may expect distinguishing features in the types of electrodynamic processes that occur, as well as an opportunity for imposing specialized mathematical methods that efficiently address this class of application. The purpose of this paper is to present and discuss such specialized methods. Specifically, thin-shell approximations for both the electrodynamics and fluid dynamics are combined to derive simplified mathematical formulations describing the behavior of these electric currents as well as their associated electric and magnetic fields. These simplified formulae allow analytical solutions featuring distinct aspects of the thin-shell electrodynamics in idealized cases. A highly efficient numerical method is also presented that is useful for calculations under inhomogeneous parameter distributions. Finally, the advantages as well as limitations in using this mathematical approach are evaluated. This evaluation is presented primarily for the generic case of bodies with water worlds or other thin spherical conducting shells. More specific discussion is given for the case of Earth, but also Europa and other satellites with suspected oceans.

Tyler, Robert H.↗
NASA NTRS2021

A Mathematical Analysis of an Example Delay Tolerant Network using the Theory of Sheaves

NASA’s High-Data Rate Architecture (HiDRA) project is working towards a general yet practical toolkit and knowledge base to help usher in the era of new technologies for space systems communications, such as optical links. The High-Rate Delay Tolerant Networking (HDTN) implementation falls under the umbrellas of both the toolkit and the knowledge base, as its advancements illuminate more general areas of Delay Tolerant Networking (DTN) that need growth. The goal of this paper is to explore the usage of particular mathematical machineries, namely temporal flow networks and sheaves, to identify fundamental, underlying structures in DTN for space systems. Satellites, space assets, ground stations, etc. give rise to a disconnected network, and it is the goal of DTN to glue disparate links together into a cohesive system, that is, a network. Depending on a given link, the latencies might be beyond that which the Transmission Control Protocol (TCP) can handle, and contact times might have one-way light times in excess of minute (sometimes significantly longer). Some links might be periodic (say, due to orbital mechanics) or they might not be. This diversity has made it difficult to probe the underlying structure. An immediate consequence is that DTNs in practice today are controlled by globally distributed contact plans (schedules), which are the input to the contact graph routing (CGR) algorithm. While this is effective for smaller networks, it will be very difficult to scale for future networks. Deeper and more rigorous theory is needed to bring DTN to the next evolutionary step. To this end, this paper introduces and suggests a mathematical framework for DTN, and applies it to a space network that is simulated using an orbital analysis toolkit. The tag-line for the structure known as sheaves is that they are the mathematically precise way of gluing local data together into unique, global data. If we consider routing, we see that networking is a “sheafy” science. We then discuss a simplified sheaf model, known as the cellular sheaf. The sheaf-theoretic analysis is presented and discussed, as it is hoped that this and related papers will help form the primordial ooze of DTN theory. Finally there is a section of future work suggesting follow-on research.

Delay Tolerant Networking↗
NASA NTRS2018

Evaluation of the Validity of Bio-Mathematical Models in Predicting Fatigue in an Operational Environment

During long-duration spaceflight missions, crewmembers and ground-support staff experience irregular sleep schedules, erratic natural light patterns, and high workload due to mission demands. Such conditions can cause circadian misalignment and sleep loss, which in turn cause deficits in cognitive performance. While bio-mathematical models have been implemented within workplace settings to predict fatigue profiles, the accuracy of sleep-wake models under conditions of non-traditional shiftwork is little known. Thus, the present study aims to evaluate the validity of four sleep-wake models (e.g., SAFTE-FAST, the Unified Model of Performance, the Adenosine-Circadian Model, and the State-Space Model) designed to predict human performance and fatigue levels against objective measures of performance in a spaceflight analog. To accomplish this aim, we will collect Psychomotor Vigilance Task (PVT) data from four crews (n=16) in the Human Exploration Research Analog (HERA) over 45 days. HERA is a closed, 3-story habitat at Johnson Space Center where inhabitants are exposed to extreme space exploration scenarios under varying sleep-wake conditions. The PVT is a simple reaction time test that involves minimal learning, making it sensitive to the effects of sleep loss and circadian misalignment. Findings from this study will help inform work scheduling and implementation of effective countermeasures (e.g., caffeine, lighting) to improve work efficiency and combat fatigue, as well as offer valuable insight into the applicability of bio-mathematical fatigue models in future space exploration missions.

fatigue↗
NASA NTRS1971

Redundancy management of electrohydraulic servoactuators by mathematical model referencing

A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.

Campbell, R. A.↗
NASA NTRS1972

Goddard trajectory determination subsystem: Mathematical specifications

The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.

Wagner, W. E.↗
NASA NTRS1973

ASTP ranging system mathematical model

A mathematical model is presented of the VHF ranging system to analyze the performance of the Apollo-Soyuz test project (ASTP). The system was adapted for use in the ASTP. The ranging system mathematical model is presented in block diagram form, and a brief description of the overall model is also included. A procedure for implementing the math model is presented along with a discussion of the validation of the math model and the overall summary and conclusions of the study effort. Detailed appendices of the five study tasks are presented: early late gate model development, unlock probability development, system error model development, probability of acquisition and model development, and math model validation testing.

Ellis, M. R.↗
NASA NTRS1975

Attitude determination of a high altitude balloon system. Part 1: Development of the mathematical model

A mathematical model for predicting the three dimensional motion of the balloon system is developed, which includes the effects of bounce, pendulation and spin of each subsystem. Boundary layer effects are also examined, along with the aerodynamic forces acting on the balloon. Various simplified forms of the system mathematical model were developed, based on an order of magnitude analysis.

Nigro, N. J.↗
NASA NTRS1975

Mathematical techniques: A compilation

Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.

Source record↗
NASA NTRS1975

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Howard, J. C.↗