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All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

LANDSAT-D MSS/TM tuned orbital jitter analysis model LDS900

The final LANDSAT-D orbital dynamic math model (LSD900), comprised of all test validated substructures, was used to evaluate the jitter response of the MSS/TM experiments. A dynamic forced response analysis was performed at both the MSS and TM locations on all structural modes considered (thru 200 Hz). The analysis determined the roll angular response of the MSS/TM experiments to improve excitation generated by component operation. Cross axis and cross experiment responses were also calculated. The excitations were analytically represented by seven and nine term Fourier series approximations, for the MSS and TM experiment respectively, which enabled linear harmonic solution techniques to be applied to response calculations. Single worst case jitter was estimated by variations of the eigenvalue spectrum of model LSD 900. The probability of any worst case mode occurrence was investigated.

Pollak, T. E.↗
NASA NTRS2005

Turbulence Hazard Metric Based on Peak Accelerations for Jetliner Passengers

Calculations are made of the approximate hazard due to peak normal accelerations of an airplane flying through a simulated vertical wind field associated with a convective frontal system. The calculations are based on a hazard metric developed from a systematic application of a generic math model to 1-cosine discrete gusts of various amplitudes and gust lengths. The math model simulates the three degree-of- freedom longitudinal rigid body motion to vertical gusts and includes (1) fuselage flexibility, (2) the lag in the downwash from the wing to the tail, (3) gradual lift effects, (4) a simplified autopilot, and (5) motion of an unrestrained passenger in the rear cabin. Airplane and passenger response contours are calculated for a matrix of gust amplitudes and gust lengths. The airplane response contours are used to develop an approximate hazard metric of peak normal accelerations as a function of gust amplitude and gust length. The hazard metric is then applied to a two-dimensional simulated vertical wind field of a convective frontal system. The variations of the hazard metric with gust length and airplane heading are demonstrated.

Stewart, Eric C.↗
NASA NTRS2018

SLS Navigation Model-Based Design Approach

The SLS Program chose to implement a Model-based Design and Model-based Requirements approach for managing component design information and system requirements. This approach differs from previous large-scale design efforts at Marshall Space Flight Center where design documentation alone conveyed information required for vehicle design and analysis and where extensive requirements sets were used to scope and constrain the design. The SLS Navigation Team has been responsible for the Program-controlled Design Math Models (DMMs) which describe and represent the performance of the Inertial Navigation System (INS) and the Rate Gyro Assemblies (RGAs) used by Guidance, Navigation, and Controls (GN&C). The SLS Navigation Team is also responsible for the navigation algorithms. The navigation algorithms are delivered for implementation on the flight hardware as a DMM. For the SLS Block 1-B design, the additional GPS Receiver hardware is managed as a DMM at the vehicle design level. This paper provides a discussion of the processes and methods used to engineer, design, and coordinate engineering trades and performance assessments using SLS practices as applied to the GN&C system, with a particular focus on the Navigation components. These include composing system requirements, requirements verification, model development, model verification and validation, and modeling and analysis approaches. The Model-based Design and Requirements approach does not reduce the effort associated with the design process versus previous processes used at Marshall Space Flight Center. Instead, the approach takes advantage of overlap between the requirements development and management process, and the design and analysis process by efficiently combining the control (i.e. the requirement) and the design mechanisms. The design mechanism is the representation of the component behavior and performance in design and analysis tools. The focus in the early design process shifts from the development and management of design requirements to the development of usable models, model requirements, and model verification and validation efforts. The models themselves are represented in C/C++ code and accompanying data files. Under the idealized process, potential ambiguity in specification is reduced because the model must be implementable versus a requirement which is not necessarily subject to this constraint. Further, the models are shown to emulate the hardware during validation. For models developed by the Navigation Team, a common interface/standalone environment was developed. The common environment allows for easy implementation in design and analysis tools. Mechanisms such as unit test cases ensure implementation as the developer intended. The model verification and validation process provides a very high level of component design insight. The origin and implementation of the SLS variant of Model-based Design is described from the perspective of the SLS Navigation Team. The format of the models and the requirements are described. The Model-based Design approach has many benefits but is not without potential complications. Key lessons learned associated with the implementation of the Model Based Design approach and process from infancy to verification and certification are discussed

Oliver, T. Emerson↗
NASA NTRS2018

SLS Model Based Design: A Navigation Perspective

The SLS Program has implemented a Model-based Design (MBD) and Model-based Requirements approach for managing component design information and system requirements. This approach differs from previous large-scale design efforts at Marshall Space Flight Center where design documentation alone conveyed information required for vehicle design and analysis and where extensive requirements sets were used to scope and constrain the design. The SLS Navigation Team is responsible for the Program-controlled Design Math Models (DMMs) which describe and represent the performance of the Inertial Navigation System (INS) and the Rate Gyro Assemblies (RGAs) used by Guidance, Navigation, and Controls (GN&C). The SLS Navigation Team is also responsible for navigation algorithms. The navigation algorithms are delivered for implementation on the flight hardware as a DMM. For the SLS Block 1B design, the additional GPS Receiver hardware model is managed as a DMM at the vehicle design level. This paper describes the models, and discusses the processes and methods used to engineer, design, and coordinate engineering trades and performance assessments using SLS practices as applied to the GN&C system, with a particular focus on the navigation components.

Oliver, T. Emerson↗
NASA NTRS1989

Modal identities for multibody elastic spacecraft: An aid to selecting modes for simulation

The question: Which set of modes furnishes a higher fidelity math model of dynamics of a multibody, deformable spacecraft (hinges-free or hinges-locked vehicle modes) is answered. Two sets of general, discretized, linear equations of motion of a spacecraft with an arbitrary number of deformable appendages, each articulated directly to the core body, are obtained using the above two families of modes. By a comparison of these equations, ten sets of modal identities are constructed which involve modal momenta coefficients and frequencies associated with both classes of modes. The sums of infinite series that appear in the identities are obtained in terms of mass, and first and second moments of inertia of the appendages, core body, and vehicle by using certain basic identities concerning appendage modes. Applying the above identities to a four-body spacecraft, the hinges-locked vehicle modes are found to yield a higher fidelity model than hinges-free modes, because the latter modes have nonconverging modal coefficients; a characteristic proved and illustrated.

Hablani, Hari B.↗
NASA NTRS1986

Bearing tester data compilation analysis, and reporting and bearing math modeling

Integration of heat transfer coefficients, modified to account for local vapor quality, into the 45 mm bearing model has been completed. The model has been evaluated with two flow rates and subcooled and saturated coolant. The evaluation showed that by increasing the flow from 3.6 to 7.0 lbs/sec the average ball temperature was decreased by 102 F, using a coolant temperature of -230 F. The average ball temperature was decreased by 63 F by decreasing the inlet coolant temperature from saturated to -230 F at a flow rate of 7.0 lbs/sec. Since other factors such as friction, cage heating, etc., affect bearing temperatures, the above bearing temperature effects should be considered as trends and not absolute values. The two phase heat transfer modification has been installed in the 57 mm bearing model and the effects on bearing temperatures have been evaluated. The average ball temperature was decreased by 60 F by increasing the flow rate from 4.6 to 9.0 lbs/sec for the subcooled case. By decreasing the inlet coolant temperature from saturation to -24 F, the average ball temperature was decreased 57 F for a flow rate of 9.0 lbs/sec. The technique of relating the two phase heat transfer coefficient to local vapor quality will be applied to the tester model and compared with test data.

Cody, J. C.↗
NASA NTRS2005

Foundations of Tensor Analysis for Students of Physics and Engineering With an Introduction to the Theory of Relativity

Tensor analysis is one of the more abstruse, even if one of the more useful, higher math subjects enjoined by students of physics and engineering. It is abstruse because of the intellectual gap that exists between where most physics and engineering mathematics leave off and where tensor analysis traditionally begins. It is useful because of its great generality, computational power, and compact, easy to use, notation. This paper bridges the intellectual gap. It is divided into three parts: algebra, calculus, and relativity. Algebra: In tensor analysis, coordinate independent quantities are sought for applications in physics and engineering. Coordinate independence means that the quantities have such coordinate transformations as to leave them invariant relative to a particular observer s coordinate system. Calculus: Non-zero base vector derivatives contribute terms to dynamical equations that correspond to pseudoaccelerations in accelerated coordinate systems and to curvature or gravity in relativity. These derivatives have a specific general form in tensor analysis. Relativity: Spacetime has an intrinsic geometry. Light is the tool for investigating that geometry. Since the observed geometry of spacetime cannot be made to match the classical geometry of Euclid, Einstein applied another more general geometry differential geometry. The merger of differential geometry and cosmology was accomplished in the theory of relativity. In relativity, gravity is equivalent to curvature.

Kolecki, Joseph C.↗
NASA NTRS2005

Software Template for Instruction in Mathematics

Intelligent Math Tutor (IMT) is a software system that serves as a template for creating software for teaching mathematics. IMT can be easily connected to artificial-intelligence software and other analysis software through input and output of files. IMT provides an easy-to-use interface for generating courses that include tests that contain both multiple-choice and fill-in-the-blank questions, and enables tracking of test scores. IMT makes it easy to generate software for Web-based courses or to manufacture compact disks containing executable course software. IMT also can function as a Web-based application program, with features that run quickly on the Web, while retaining the intelligence of a high-level language application program with many graphics. IMT can be used to write application programs in text, graphics, and/or sound, so that the programs can be tailored to the needs of most handicapped persons. The course software generated by IMT follows a "back to basics" approach of teaching mathematics by inducing the student to apply creative mathematical techniques in the process of learning. Students are thereby made to discover mathematical fundamentals and thereby come to understand mathematics more deeply than they could through simple memorization.

Shelton, Robert O.↗
NASA NTRS1987

Aerobic fitness in women and responses to lower body negative pressure

The role of tolerance to orthostatic stress in the maintenance of high aerobic fitness in women was investigated by examining the responses of heart rate, stroke volume, cardiac output, Heather index of contractility, arterial pressure, peripheral resistance, change in calf circumference, and thoracic impedance of healthy female subjects to lower body negative pressure (LBNP) applied for 5 min at -50 mm Hg or until a subject became presyncopal. The testing protocol involved a stepwise reduction in pressure and consisted of two parts: an LBNP test in supine position followed by a treadmill test to peak aerobic capacity. Women were found to exhibit the same response pattern to LBNP as was previously reported by Convertino et al. (1984) for men. The results do not support the hypothesis that orthostatic tolerance in women is inversely related to aerobic fitness, as demonstrated by a finding that the peak aerobic capacity of subjects who became presyncopal did not differ from the peak of the tolerant subjects, and that hemodynamic responses to LBNPL were not a function of aerobic capacity.

Frey, Mary Anne Bassett↗
NASA NTRS1993

Tumuli and tubes: Teaching scientific techniques

Planetary and space science is the best way to teach basic chemistry, physics, and math. Einstein once said that 'man is drawn to the mysterious and it is from that that we achieve true art and science.' Planets and the processes that shape them are especially mysterious and fascinating to students, young and old, and because of this planetary geology kindles interest that draws them further into the world of science. At the very least, they are engaged enough to learn how science works, a key ingredient in scientific literacy. A project involving field measurements on Kilauea volcano, Hawaii, by a Geology 101 honors class is described. Hawaii is blessed with spectacular, active, accessible, and relatively safe basaltic eruptions. The study of volcanoes, the landforms they produce, and the processes that operate on and in volcanoes, combined with the study of volcanoes on the other planets, is an excellent way to link aspects of Hawaiian geology to the planets. During the past year we have taken advantage of our setting to organize a NASA field workshop for junior investigators and senior graduate students, made field trips and planetary volcanism the centerpieces of our annual Summer Workshop for Teachers, and led a field trip around Kilauea Volcano during the Challenger Center Faculty Development conference, held on the island of Hawaii last summer. An activity for the honors Geology 101 class (all undergraduates) at the University of Hawaii is presently being planned. Our goal is to give them some hands on experience working on a field project and applying what they have learned to planetary volcanoes. The work will include qualitative observations and quantitative measurements on volcanic lava flows. Follow-up activities will involve data analysis. The trip requires planning (at least 3 months before hand) everything from accommodations and insurance to the actual activities we will be doing. Our goal is to stimulate interest and awareness in the students' surroundings, in this case, volcanoes, and to include planetary applications and how studies of terrestrial geology greatly aids studies of the other planets. Two studies are planned both of which are active research projects being conducted by the authors. These projects, tumuli in pahoehoe flow fileds and lava tube cross-secational areas, are described.

Tatsumura, Michelle J.↗
NASA NTRS1994

Multi-application controls: Robust nonlinear multivariable aerospace controls applications

This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented as a method for analyzing robust performance and the mu-synthesis method will be presented as a method for synthesizing a robust control system. The paper concludes with the author's expectations regarding future applications of robust nonlinear multivariable controls.

Enns, Dale F.↗