Model of human-operator response to step transitions in controlled element dynamics
Derivation of analytical model to predict operator transition response
MATHEMATICAL MODEL↗
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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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Operating cost model for local service airlines
Several mathematical models now exist which determine the operating economics for a United States trunk airline. These models are valuable in assessing the impact of new aircraft into an airline's fleet. The use of a trunk airline cost model for the local service airline does not result in representative operating costs. A new model is presented which is representative of the operating conditions and resultant costs for the local service airline. The calculated annual direct and indirect operating costs for two multiequipment airlines are compared with their actual operating experience.
Anderson, J. L.↗
Investigation of traveler acceptance factors in short haul air carrier operations
The development of a mathematical model for human reaction to variables involved in transportation systems is discussed. The techniques, activities, and results related to defining certain specific inputs to the model are presented. A general schematic diagram of the problem solution is developed. The application of the model to short haul air carrier operations is examined.
A. R. Kuhlthau↗
The NATA code; theory and analysis. Volume 3: Programmer's manual
The present, third volume of the final report is a programmer's manual for the code. It provides a listing of the FORTRAN 4 source program; a complete glossary of FORTRAN symbols; a discussion of the purpose and method of operation of each subroutine (including mathematical analyses of special algorithms); and a discussion of the operation of the code on IBM/360 and UNIVAC 1108 systems, including required control cards and the overlay structure used to accommodate the code to the limited core size of the 1108. In addition, similar information is provided to document the programming of the NOZFIT code, which is employed to set up nozzle profile curvefits for use in NATA.
Bade, W. L.↗
Cartographic Modeling: Computer-assisted Analysis of Spatially Defined Neighborhoods
Cartographic models addressing a wide variety of applications are composed of fundamental map processing operations. These primitive operations are neither data base nor application-specific. By organizing the set of operations into a mathematical-like structure, the basis for a generalized cartographic modeling framework can be developed. Among the major classes of primitive operations are those associated with reclassifying map categories, overlaying maps, determining distance and connectivity, and characterizing cartographic neighborhoods. The conceptual framework of cartographic modeling is established and techniques for characterizing neighborhoods are used as a means of demonstrating some of the more sophisticated procedures of computer-assisted map analysis. A cartographic model for assessing effective roundwood supply is briefly described as an example of a computer analysis. Most of the techniques described have been implemented as part of the map analysis package developed at the Yale School of Forestry and Environmental Studies.
Berry, J. K.↗
A Structurally-Adaptive Framework for Distributed Airborne Sensing over Real-time Collaborative Information Sharing Networks
The emergence and maturation of wireless communication technologies continue to transform the aviation industry and are enabling new solutions to challenges faced by NASA’s Advanced Air Mobility (AAM) initiative. AAM is leading towards high-density autonomous aircraft operations in areas underserved by traditional aviation, such as over densely populated urban centers. In this paper, we build on concepts from Smart Spaces - where sensing, processing, and communication are embedded in an environment, and agents are operating within the space can exploit these capabilities in real-time through collaborative information sharing networks. Building from these concepts, we propose a framework to enable a dynamic, topologically-adaptive, and distributed estimation system for man-rated aviation to address challenges faced by autonomous AAM operations. This paper presents the initial concept of operations and system design for this framework, presents a mathematical formulation for abstraction of the problem, identifies requirements and constraints for operation, and presents algorithmic constructs and mathematical formalisms to demonstrate operation. The proposed framework will be evaluated on a regional AAM flight scenario and will focus on two initial applications: (1) GPS-free navigation supporting precision approach and landing (PAL), and (2) surveillance and conformance monitoring of aircraft in vertiport airspaces. Such approaches show promise in addressing gaps in current technologies needed to enable future AAM concepts, while promising greater capabilities, performance, robustness, and safety over current aviation systems and operations.
Structurally-Adaptive↗
Phase operators and phase relations for photon states
For a quantized mode of the radiation field, the operator whose classical analog is the ordinary phase factor of the mode amplitudes has been shown to be nonunitary. A rigorous formulation of the phase P is given on the basis of the canonical factorization theorem. Many of the seemingly complex features of phase operators are found to be simple direct consequences of the general mathematical theory. It can be readily seen that P is a partial isometry but not a unitary operator. In contrast to the amplitude operator, it is found that P is not a spectral operator and that the set of phase eigenstates is not complete. Mathematically precise operator relations are developed, and a complete spectral analysis is given for each of the phase operators.-
Volkin, H. C.↗
Houston Operations Predictor/Estimator (HOPE) programming manual, volume 1
The programming techniques used to implement the equations and mathematical techniques of the Houston Operations Predictor/Estimator (HOPE) orbit determination program on the UNIVAC 1108 computer are described. Detailed descriptions are given of the program structure, the internal program structure, the internal program tables and program COMMON, modification and maintainence techniques, and individual subroutine documentation.
Daly, J. K.↗
Toward a mathematical formalism of performance, task difficulty, and activation
The rudiments of a mathematical formalism for handling operational, physiological, and psychological concepts are developed for use by the man-machine system design engineer. The formalism provides a framework for developing a structured, systematic approach to the interface design problem, using existing mathematical tools, and simplifying the problem of telling a machine how to measure and use performance.
Samaras, George M.↗
Exponential Formulae and Effective Operations
One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).
Mielnik, Bogdan↗
Define Minimum Safe Operational Volume for Aerial Vehicles in Upper Class E Airspace
The variety of vehicle performance in upper Class E airspace requires a method that can efficiently compute the minimum safe operational boundary between aircraft. This work presents a mathematical method to define the minimum safe operational boundary needed for aerial vehicles operating in upper Class E airspace. This method focuses on the extra separation required by vehicle maneuverability, communication delay, and control/operator response time. A sensitivity study is then performed to provide a general understanding of the impact of these factors on the extra separation needed. Experiments with pairwise encounters are conducted to verify the results generated by the proposed methods.
Separation standard↗
Define Minimum Safe Operational Volume for Aerial Vehicles in Upper Class E Airspace
The variety of vehicle performance in upper Class E airspace requires a method that can efficiently compute the minimum safe operational boundary between aircraft. This work presents a mathematical method to define the minimum safe operational boundary needed for aerial vehicles operating in upper Class E airspace. This method focuses on the extra separation required by vehicle maneuverability, communication delay, and control/operator response time. A sensitivity study is then performed to provide a general understanding of the impact of these factors on the extra separation needed. Experiments with pairwise encounters are conducted to verify the results generated by the proposed methods.
Separation↗
Dynamics and control of Stirling engines in a 15 kWe solar electric generation concept
This paper discusses the application of kinematic and free piston Stirling engines in a 15 kWe dish-electric approach for solar thermal electric generation. Initially, the principle of operation of Stirling engines in solar thermal electric generation is discussed. Then, under certain simplifying assumptions, mathematical models describing the dynamic operation of the kinematic and free piston Stirling engines are developed. It is found that the engine dynamics may be approximated by second order models. Control mechanisms for both types of Stirling engines are discussed. An approach based on the modulation of the working fluid mean pressure is presented. It is concluded that this approach offers a fast and effective means of control. The free piston Stirling engine, being a thermally driven mechanical oscillator, presents unique control requirements. These are discussed in this paper.
Das, R. L.↗
Smart Sensor System for NDE or Corrosion in Aging Aircraft
The extension of the operation life of military and civilian aircraft rather than replacing them with new ones is increasing the probability of aircraft component failure as a result of aging. Aircraft that already have endured a long srvice life of more than 40 years are now being considered for another 40 years of service.
monitoring system mathematical transformation oper↗
A series representation of the discrete fractional Laplace operator of arbitrary order
Although fractional powers of non-negative operators have received much attention in recent years, there is still little known about their behavior if real-valued exponents are greater than one. In this article, we define and study the discrete fractional Laplace operator of arbitrary real-valued positive order. Here a series representation of the discrete fractional Laplace operator for positive non-integer powers is developed. Its convergence to a series representation of a known case of positive integer powers is proven as the power tends to the integer value. Furthermore, we show that the new representation for arbitrary real-valued positive powers of the discrete Laplace operator is consistent with existing theoretical results.
97 MATHEMATICS AND COMPUTING↗
Extending the operation range of a phase-sensitive optical time-domain reflectometer by using fibre with chirped Bragg gratings
>A record long external-disturbance detection distance of 140 km without employing optical amplifiers in the fibre line is demonstrated by a phase-sensitive optical time-domain reflectometer (Φ-OTDR) using a fibre section with inscribed chirped fibre Bragg gratings (CFBGs). This solution provides simultaneous operation of Φ-OTDR with a standard single-mode fibre at a distance of up to 100 km and with a CFBG fibre section located from the fibre line input point by at least 140 km. (paper)
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
An investigation for the development of an integrated optical data preprocessor
The successful fabrication and demonstration of an integrated optical circuit designed to perform a parallel processing operation by utilizing holographic subtraction to simultaneously compare N analog signal voltages with N predetermined reference voltages is summarized. The device alleviates transmission, storage and processing loads of satellite data systems by performing, at the sensor site, some preprocessing of data taken by remote sensors. Major accomplishments in the fabrication of integrated optics components include: (1) fabrication of the first LiNbO3 waveguide geodesic lens; (2) development of techniques for polishing TIR mirrors on LiNbO3 waveguides; (3) fabrication of high efficiency metal-over-photoresist gratings for waveguide beam splitters; (4) demonstration of high S/N holographic subtraction using waveguide holograms; and (5) development of alignment techniques for fabrication of integrated optics circuits. Important developments made in integrated optics are the discovery and suggested use of holographic self-subtraction in LiNbO3, development of a mathematical description of the operating modes of the preprocessor, and the development of theories for diffraction efficiency and beam quality of two dimensional beam defined gratings.
Verber, C. M.↗
Error Analysis System for Spacecraft Navigation Using the Global Positioning System (GPS)
The Flight Dynamics Division (FDD) at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) is currently developing improved space-navigation filtering algorithms to use the Global Positioning System (GPS) for autonomous real-time onboard orbit determination. In connection with a GPS technology demonstration on the Small Satellite Technology Initiative (SSTI)/Lewis spacecraft, FDD analysts and programmers have teamed with the GSFC Guidance, Navigation, and Control Branch to develop the GPS Enhanced Orbit Determination Experiment (GEODE) system. The GEODE system consists of a Kalman filter operating as a navigation tool for estimating the position, velocity, and additional states required to accurately navigate the orbiting Lewis spacecraft by using astrodynamic modeling and GPS measurements from the receiver. A parallel effort at the FDD is the development of a GPS Error Analysis System (GEAS) that will be used to analyze and improve navigation filtering algorithms during development phases and during in-flight calibration. For GEAS, the Kalman filter theory is extended to estimate the errors in position, velocity, and other error states of interest. The estimation of errors in physical variables at regular intervals will allow the time, cause, and effect of navigation system weaknesses to be identified. In addition, by modeling a sufficient set of navigation system errors, a system failure that causes an observed error anomaly can be traced and accounted for. The GEAS software is formulated using Object Oriented Design (OOD) techniques implemented in the C++ programming language on a Sun SPARC workstation. The Phase 1 of this effort is the development of a basic system to be used to evaluate navigation algorithms implemented in the GEODE system. This paper presents the GEAS mathematical methodology, systems and operations concepts, and software design and implementation. Results from the use of the basic system to evaluate navigation algorithms implemented on GEODE are also discussed. In addition, recommendations for generalization of GEAS functions and for new techniques to optimize the accuracy and control of the GPS autonomous onboard navigation are presented.
Truong, S. H.↗