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At least 217 records · Page 12

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NASA NTRS1990

Structure function calculations for Ostwald Ripening processes

A program for computing the structure function for configurations involved in Ostwald Ripening was written. The basic algorithms are derived from a mathematical analysis of a two-dimensional model system developed by Bortz, et. al. (1974). While it is expected that the values form the computer simulations will reflect Ostwald Ripening, at this point the program is still being tested. Some preliminary runs seem to justify the expectations.

Hassan, Razi A.↗

NASA NTRS1993

Stability of mixing layers

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Tam, Christopher↗

NASA NTRS1993

An onboard star identification algorithm

The paper presents the autonomous Initial Stellar Acquisition (ISA) algorithm developed for the X-Ray Timing Explorer for prividing the attitude quaternion within the desired accuracy, based on the one-axis attitude knowledge (through the use of the Digital Sun Sensor, CCD Star Trackers, and the onboard star catalog, OSC). Mathematical analysis leads to an accurate measure of the performance of the algorithm as a function of various parameters, such as the probability of a tracked star being in the OSC, the sensor noise level, and the number of stars matched. It is shown that the simplicity, tractability, and robustness of the ISA algorithm, compared to a general three-axis attiude determination algorithm, make it a viable on-board solution.

Ha, Kong↗

NASA NTRS1993

Impacts, tillites, and the breakup of Gondwanaland

Mathematical analysis demonstrates that substantial impact crater deposits should have been produced during the last 2 Gy of Earth's history. Textures of impact deposits are shown to resemble textures of tillites and diamictites of Precambrian and younger ages. The calculated thickness distribution for impact crater deposits produced during 2 Gy is similar to that of tillites and diamictites of 2 Ga or younger. We suggest, therefore, that some tillites/diamictites could be of impact origin. Extensive tillite/diamictite deposits predated continental flood basalts on the interior of Gondwanaland. Significantly, other investigators have already associated impact cratering with flood basalt volcanism and continental rifting. Thus, it is proposed that the breakup of Gondwanaland could have been initiated by crustal fracturing from impacts.

Oberbeck, Verne R.↗

NASA NTRS1922

Syphon Diaphragms : A Method for Predicting Their Performance for Purposes of Instrument Design

Here, the purpose is to show that the characteristic performance of a syphon diaphragm can be predicted from a knowledge of its stiffness and of its dimensions. The proof is based on a mathematical analysis of this type of diaphragm, together with enough experimental data to prove the validity of the assumptions and the sufficiency of the analysis. Equations are developed for the performance of syphons under various conditions of loading, both for concentrated loads and for hydrostatic pressure.

Eaton, H N↗

NASA NTRS1943

Torsion Tests of 24S-T Aluminum-alloy Noncircular Bar and Tubing

Tests of 24S-T aluminum alloy have been made to determine the yield and ultimate strengths in torsion of noncircular bar and tubing. An approximate basis for predicting these torsional strength characteristics has been indicated. The results show that the torsional stiffness and maximum shearing stresses within the elastic range may be computed quite closely by means of existing formulas based on mathematical analysis and the membrane analogy.

Moore, R L↗

NASA NTRS1948

Effect of Centrifugal Force on the Elastic Curve of a Vibrating Cantilever Beam

A study was made to determine the effect of rotation on the dynamic-stress distribution in vibrating cantilever beams. The results of a mathematical analysis are presented together with experimental results obtained by means of stroboscopic photographs and strain gages. The theoretical analysis was confined to uniform cantilever beams; the experimental work was extended to include a tapered cantilever beam to simulate an aircraft propeller blade. Calculations were made on nondimensional basis for second and third mode vibration; the experiments were conducted on beams of various lengths, materials, and cross sections for second-mode vibration. From this investigation it was concluded that high vibratory-stress positions are unaffected by the addition of centrifugal force. Nonrotating vibration surveys of blades therefore are valuable in predicting high vibratory-stress locations under operating conditions.

Simpkinson, Scott H↗

NASA NTRS1957

Seat Design for Crash Worthiness

A study of many crash deceleration records suggested a simplified model of a crash deceleration pulse, which incorporates the essential properties of the pulse. The model pulse is considered to be composed of a base pulse on which are superimposed one or more secondary pulses of shorter duration. The results of a mathematical analysis of the seat-passenger deceleration in response to the airplane deceleration pulse are provided. On the basis of this information, presented as working charts, the maximum deceleration loads experienced by the seat and passenger in response to the airplane deceleration pulse can be computed. This maximum seat-passenger deceleration is found to depend on the natural frequency of the seat containing the passenger, considered as a mass-spring system. A method is presented that shows how to arrive at a combination of seat strength, natural frequency, and ability to absorb energy in deformation beyond the elastic limit that will allow the seat to serve without failure during an airplane deceleration pulse taken as the design requirement.

Pinkel, I Irving↗

NASA NTRS1993

Computer-controlled float zone crystal growth

A PC-based computer control system to automate a high-temperature float zone growth of titanium carbide is reported. The control strategy of the computer control system relies on the relations derived from a combination of empirical relations and results from detailed mathematical analysis of the physical transports of the entire float zone assembly. A system control computer program was written to establish real-time determination of the size of the molten zone from a thermal image, control parameters from established relationships, and collected processed data to achieve control objectives. We found that the developed computer control allows the growth process to be operated nearer the stability limit. Any slight variations in growth conditions can be corrected in time to avoid any instability growth, which otherwise cannot be adjusted via manual control.

Chan, Y. T.↗

NASA NTRS1994

Preparation of course materials: Elementary mathematics of powered flight

Non-science students at William and Mary will soon be required to take a mathematics course in order to earn a bachelor's degree. A standard menu of technique courses is the usual way in which universities provide for this requirement: Trigonometry, probability, geometry for teachers, and the like. In this work, we attempt to break away from these largely unsuccessful choices. Our intent is to prepare material that sets a variety of simple mathematical procedures in the context of a commonly experienced part of students' lives: riding in commercial airplanes. The work, begun last summer at Langley, is now close to completion and trial in upcoming fall term at William and Mary. As of this writing, the narrative is complete for 12 to 14 projected sections. We have prepared material on wind triangles, wind roses, navigation maps, drag induced loss of velocity for unpowered missiles (tennis balls), luggage and its effect on center of gravity, localized magnetic declination and VOR orientation, geometry of great circles, terminal velocity for falling bodies, pressure vessels: tires and balloons and blimps, global structure of declination lines, map projections (mercator, azimuthal equidistant, Lambert), ears and their reaction to altitude change. The next section will treat lift, drag and thrust. The last will treat control surfaces. The entire approach avoids any effort to investigate mathematical topics that arise in the solution of problems. And by the same token, we avoid any organized attempt to explain aeronautical engineering, even on an elementary level. We look only at enough mathematics to do a problem and we select only engineering topics that permit some kind of (elementary) mathematical analysis. In the end, we will think of the material as successful if two things happen: Students must come away with some confidence that even lay people can quantify parts of their surroundings. Other potential instructors must be willing to gain enough familiarity with the physical content of the material so that it can be used at other universities.

Rublein, George T.↗

NASA NTRS1995

Subband/Transform MATLAB Functions For Processing Images

SUBTRANS software is package of routines implementing image-data-processing functions for use with MATLAB*(TM) software. Provides capability to transform image data with block transforms and to produce spatial-frequency subbands of transformed data. Functions cascaded to provide further decomposition into more subbands. Also used in image-data-compression systems. For example, transforms used to prepare data for lossy compression. Written for use in MATLAB mathematical-analysis environment.

Glover, D.↗

NASA NTRS1995

Formal methods in the design of Ada 1995

Formal, mathematical methods are most useful when applied early in the design and implementation of a software system--that, at least, is the familiar refrain. I will report on a modest effort to apply formal methods at the earliest possible stage, namely, in the design of the Ada 95 programming language itself. This talk is an 'experience report' that provides brief case studies illustrating the kinds of problems we worked on, how we approached them, and the extent (if any) to which the results proved useful. It also derives some lessons and suggestions for those undertaking future projects of this kind. Ada 95 is the first revision of the standard for the Ada programming language. The revision began in 1988, when the Ada Joint Programming Office first asked the Ada Board to recommend a plan for revising the Ada standard. The first step in the revision was to solicit criticisms of Ada 83. A set of requirements for the new language standard, based on those criticisms, was published in 1990. A small design team, the Mapping Revision Team (MRT), became exclusively responsible for revising the language standard to satisfy those requirements. The MRT, from Intermetrics, is led by S. Tucker Taft. The work of the MRT was regularly subject to independent review and criticism by a committee of distinguished Reviewers and by several advisory teams--for example, the two User/Implementor teams, each consisting of an industrial user (attempting to make significant use of the new language on a realistic application) and a compiler vendor (undertaking, experimentally, to modify its current implementation in order to provide the necessary new features). One novel decision established the Language Precision Team (LPT), which investigated language proposals from a mathematical point of view. The LPT applied formal mathematical analysis to help improve the design of Ada 95 (e.g., by clarifying the language proposals) and to help promote its acceptance (e.g., by identifying a verifiable subset that would meet the needs of safety-critical applications). The first LPT project, which ran from the fall of 1990 unti the end of 1992, produced studies of several language issues: optimization, sharing and storage, tasking and protected records, overload resolution, the floating point model, distribution, program erros, and object-oriented programming. The second LPT project, in 1994, formally modeled the dynamic semantics of a large part of the (almost) final language definition, looking especially for interactions between language features.

Guaspari, David↗

NASA NTRS1996

A Digital Control Algorithm for Magnetic Suspension Systems

An ongoing program exists to investigate and develop magnetic suspension technologies and modelling techniques at NASA Langley Research Center. Presently, there is a laboratory-scale large air-gap suspension system capable of five degree-of-freedom (DOF) control that is operational and a six DOF system that is under development. Those systems levitate a cylindrical element containing a permanent magnet core above a planar array of electromagnets, which are used for levitation and control purposes. In order to evaluate various control approaches with those systems, the Generic Real-Time State-Space Controller (GRTSSC) software package was developed. That control software package allows the user to implement multiple control methods and allows for varied input/output commands. The development of the control algorithm is presented. The desired functionality of the software is discussed, including the ability to inject noise on sensor inputs and/or actuator outputs. Various limitations, common issues, and trade-offs are discussed including data format precision; the drawbacks of using either Direct Memory Access (DMA), interrupts, or program control techniques for data acquisition; and platform dependent concerns related to the portability of the software, such as memory addressing formats. Efforts to minimize overall controller loop-rate and a comparison of achievable controller sample rates are discussed. The implementation of a modular code structure is presented. The format for the controller input data file and the noise information file is presented. Controller input vector information is available for post-processing by mathematical analysis software such as MATLAB1.

Britton, Thomas C.↗

NASA NTRS1994

The Determination of Forces and Moments on a Gimballed SRM Nozzle Using a Cold Flow Model

The Solid Rocket Motor Air Flow Facility (SAF) at NASA Marshall Space Flight Center was used to characterize the flow in the critical aft end and nozzle of a solid propellant rocket motor (SRM) as part of the design phase of development. The SAF is a high pressure, blowdown facility which supplies a controlled flow of air to a subscale model of the internal port and nozzle of a SRM to enable measurement and evaluation of the flow field and surface pressure distributions. The ASRM Aft Section/Nozzle Model is an 8 percent scale model of the 19 second burn time aft port geometry and nozzle of the Advanced Solid Rocket Motor, the now canceled new generation space Shuttle Booster. It has the capability to simulate fixed nozzle gimbal angles of 0, 4, and 8 degrees. The model was tested at full scale motor Reynolds Numbers with extensive surface pressure instrumentation to enable detailed mapping of the surface pressure distributions over the nozzle interior surface, the exterior surface of the nozzle nose and the surface of the simulated propellant grain in the aft motor port. A mathematical analysis and associated numerical procedure were developed to integrate the measured surface pressure distributions to determine the lateral and axial forces on the moveable section of the nozzle, the effective model thrust and the effective aerodynamic thrust vector (as opposed to the geometric nozzle gimbal angle). The nozzle lateral and axial aerodynamic loads and moments about the pivot point are required for design purposes and require complex, three dimensional flow analyses. The alignment of the thrust vector with the nozzle geometric centerline is also a design requirement requiring three dimensional analyses which were supported by this experimental program. The model was tested with all three gimbal angles at three pressure levels to determine Reynolds number effects and reproducibility. This program was successful in demonstrating that a measured surface pressure distribution could be integrated to determine the lateral and axial loads, moments and thrust vector alignment for the scaled model of a large space booster nozzle. Numerical results were provided which are scaleable to the full scale rocket motor and can be used as benchmark data for 3-D CFD analyses.

Whitesides, R. Harold↗

NASA NTRS1998

Design and Calibration of the X-33 Flush Airdata Sensing (FADS) System

This paper presents the design of the X-33 Flush Airdata Sensing (FADS) system. The X-33 FADS uses a matrix of pressure orifices on the vehicle nose to estimate airdata parameters. The system is designed with dual-redundant measurement hardware, which produces two independent measurement paths. Airdata parameters that correspond to the measurement path with the minimum fit error are selected as the output values. This method enables a single sensor failure to occur with minimal degrading of the system performance. The paper shows the X-33 FADS architecture, derives the estimating algorithms, and demonstrates a mathematical analysis of the FADS system stability. Preliminary aerodynamic calibrations are also presented here. The calibration parameters, the position error coefficient (epsilon), and flow correction terms for the angle of attack (delta alpha), and angle of sideslip (delta beta) are derived from wind tunnel data. Statistical accuracy of' the calibration is evaluated by comparing the wind tunnel reference conditions to the airdata parameters estimated. This comparison is accomplished by applying the calibrated FADS algorithm to the sensed wind tunnel pressures. When the resulting accuracy estimates are compared to accuracy requirements for the X-33 airdata, the FADS system meets these requirements.

Whitmore, Stephen A.↗

NASA NTRS1999

Cardiovascular Deconditioning in Humans: Alteration in Cardiovascular Regulation and Function During Simulated Microgravity

Alterations in cardiovascular regulation and function that occur during and after space flight have been reported. These alterations are manifested, for example, by reduced orthostatic tolerance upon reentry to the earth's gravity from space. However, the precise physiologic mechanisms responsible for these alterations remain to be fully elucidated. Perhaps, as a result, effective countermeasures have yet to be developed. In this project we apply a powerful, new method - cardiovascular system identification (CSI) - for the study of the effects of space flight on the cardiovascular system so that effective countermeasures can be developed. CSI involves the mathematical analysis of second-to-second fluctuations in non-invasively measured heart rate, arterial blood pressure (ABP), and instantaneous lung volume (ILV - respiratory activity) in order to characterize quantitatively the physiologic mechanisms responsible for the couplings between these signals. Through the characterization of all the physiologic mechanisms coupling these signals, CSI provides a model of the closed-loop cardiovascular regulatory state in an individual subject. The model includes quantitative descriptions of the heart rate baroreflex, autonomic function, as well as other important physiologic mechanisms. We are in the process of incorporating beat-to-beat fluctuations of stroke volume into the CSI technique in order to quantify additional physiologic mechanisms such as those involved in control of peripheral vascular resistance and alterations in cardiac contractility. We apply CSI in conjunction with the two general protocols of the Human Studies Core project. The first protocol involves ground-based, human head down tilt bed rest to simulate microgravity and acute stressors - upright tilt, standing and bicycle exercise - to provide orthostatic and exercise challenges. The second protocol is intended to be the same as the first but with the addition of sleep deprivation to determine whether this contributes to cardiovascular alterations. In these studies, we focus on the basic physiologic mechanisms responsible for the alterations in cardiovascular regulation and function during the simulated microgravity in order to formulate hypotheses regarding what countermeasures are likely to be most effective. Compared to our original proposal, the protocol we are using has been slightly modified to lengthen the bed rest period to 16 days and streamline the data collection. These modifications provide us data on a longer bed rest period and have enabled us to increase our subject throughput. Based on review of our preliminary data we have decided to test a countermeasure which is applied the very end of the bed rest period. We will use the same bed rest protocol to test this countermeasure. We anticipate completing the baseline data collection in our first protocol plus testing of the countermeasure in an additional eight subjects, at which time we plan to initiate the second protocol which includes sleep deprivation. In future studies, we plan to apply CSI to test other potential countermeasures in conjunction with the same bed rest, sleep deprivation and acute stressor models. We also anticipate applying CSI for studying astronauts before and after space flight and ultimately, during space flight. The application of CSI is providing information relevant to the development and evaluation of effective countermeasures allowing humans to adapt appropriately upon re-exposure to a gravity field, and to live and work for longer periods of time in microgravity.

Cohen, Richard↗

NASA NTRS1996

Cascade Error Projection: A Learning Algorithm for Hardware Implementation

In this paper, we workout a detailed mathematical analysis for a new learning algorithm termed Cascade Error Projection (CEP) and a general learning frame work. This frame work can be used to obtain the cascade correlation learning algorithm by choosing a particular set of parameters. Furthermore, CEP learning algorithm is operated only on one layer, whereas the other set of weights can be calculated deterministically. In association with the dynamical stepsize change concept to convert the weight update from infinite space into a finite space, the relation between the current stepsize and the previous energy level is also given and the estimation procedure for optimal stepsize is used for validation of our proposed technique. The weight values of zero are used for starting the learning for every layer, and a single hidden unit is applied instead of using a pool of candidate hidden units similar to cascade correlation scheme. Therefore, simplicity in hardware implementation is also obtained. Furthermore, this analysis allows us to select from other methods (such as the conjugate gradient descent or the Newton's second order) one of which will be a good candidate for the learning technique. The choice of learning technique depends on the constraints of the problem (e.g., speed, performance, and hardware implementation); one technique may be more suitable than others. Moreover, for a discrete weight space, the theoretical analysis presents the capability of learning with limited weight quantization. Finally, 5- to 8-bit parity and chaotic time series prediction problems are investigated; the simulation results demonstrate that 4-bit or more weight quantization is sufficient for learning neural network using CEP. In addition, it is demonstrated that this technique is able to compensate for less bit weight resolution by incorporating additional hidden units. However, generation result may suffer somewhat with lower bit weight quantization.

Duong, Tuan A.↗

NASA NTRS2003

Modeling, Analyzing, and Mitigating Dissonance Between Alerting Systems

Alerting systems are becoming pervasive in process operations, which may result in the potential for dissonance or conflict in information from different alerting systems that suggests different threat levels and/or actions to resolve hazards. Little is currently available to help in predicting or solving the dissonance problem. This thesis presents a methodology to model and analyze dissonance between alerting systems, providing both a theoretical foundation for understanding dissonance and a practical basis from which specific problems can be addressed. A state-space representation of multiple alerting system operation is generalized that can be tailored across a variety of applications. Based on the representation, two major causes of dissonance are identified: logic differences and sensor error. Additionally, several possible types of dissonance are identified. A mathematical analysis method is developed to identify the conditions for dissonance originating from logic differences. A probabilistic analysis methodology is developed to estimate the probability of dissonance originating from sensor error, and to compare the relative contribution to dissonance of sensor error against the contribution from logic differences. A hybrid model, which describes the dynamic behavior of the process with multiple alerting systems, is developed to identify dangerous dissonance space, from which the process can lead to disaster. Methodologies to avoid or mitigate dissonance are outlined. Two examples are used to demonstrate the application of the methodology. First, a conceptual In-Trail Spacing example is presented. The methodology is applied to identify the conditions for possible dissonance, to identify relative contribution of logic difference and sensor error, and to identify dangerous dissonance space. Several proposed mitigation methods are demonstrated in this example. In the second example, the methodology is applied to address the dissonance problem between two air traffic alert and avoidance systems: the existing Traffic Alert and Collision Avoidance System (TCAS) vs. the proposed Airborne Conflict Management system (ACM). Conditions on ACM resolution maneuvers are identified to avoid dynamic dissonance between TCAS and ACM. Also included in this report is an Appendix written by Lee Winder about recent and continuing work on alerting systems design. The application of Markov Decision Process (MDP) theory to complex alerting problems is discussed and illustrated with an abstract example system.

Song, Lixia↗