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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

An optimized finite-difference scheme for wave propagation problems

Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.

Zingg, D. W.↗
NASA NTRS2019

Evaluation of a Multizone Impedance Eduction Method

A computational study is used to evaluate the PyCHE impedance eduction method developed at the NASA Langley Research Center. This method combines an aeroacoustic duct propagation code based on numerical solution to the convected Helmholtz equation with a global optimizer that uses the Differential Evolution algorithm. The efficacy of this method is evaluated with acoustic pressure data simulated to represent that measured with one-zone, two-zone, and three-zone liners mounted in the NASA Langley Grazing Flow Impedance Tube. The PyCHE method has a normalized impedance error of approximately 0.2 for (uniform) one-zone liners with a length of at least 5”, and produces quite reasonable results for liners as short as 2”. Whereas the impedance of the liner has an effect on eduction accuracy, the amount of attenuation is shown to be the dominant parameter. Similar results are observed for two-zone liners, for which the impedance of each zone is unique. The two-zone results also indicate it is more difficult to accurately educe resistance than reactance, and a zone length of at least 6” (slightly longer than for uniform liners) is needed to limit the normalized error to 0.2. The PyCHE method is also demonstrated to successfully educe the impedances for each zone of a three-zone liner. These results are sufficiently encouraging to warrant the continued usage of the PyCHE impedance eduction method for single and multizone liners.

Jones, M. G.↗
NASA NTRS1981

Saturn gravity results obtained from Pioneer 11 tracking data and earth-based Saturn satellite data

Improved gravity coefficients for Saturn, its satellites and rings are calculated on the basis of a combination of Pioneer 11 spacecraft Doppler tracking data and earth-based determinations of Saturn natural satellite apse and node rates. Solutions are first obtained separately from the coherent Doppler tracking data obtained for the interval from August 20 to September 4, surrounding the time of closest approach, with the effects of solar plasma on radio signal propagation taken into account, and from secular rates for Mimas, Enceladus, Tethys, Dione, Rhea and Titan determined from astrometric data by Kozai (1957, 1976) and Garcia (1972). Combination of the data by the use of the Pioneer solution and corresponding unadjusted covariance matrix as a priori information for a secular rate analysis results in values for the total ring mass of essentially zero at a standard error level of 1.7 x 10 to the -6th Saturn masses, a ratio of solar mass to that of the Saturn system of 3498.09 + or - 0.22, masses of Rhea, Titan and Iapetus of 4.0 + or - 0.9, 238.8 + or - 3, and 3.4 + or - 1.3 x 10 to the -6th Saturn masses, respectively, and second and fourth zonal harmonics of 16,479 + or - 18 and -937 + or - 38, respectively. The harmonic coefficients are noted to be important as boundary conditions in the modeling of the Saturn interior.

Null, G. W.↗
NASA NTRS1989

Lifetime predictions for the Solar Maximum Mission (SMM) and San Marco spacecraft

Lifetime prediction techniques developed by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) are described. These techniques were developed to predict the Solar Maximum Mission (SMM) spacecraft orbit, which is decaying due to atmospheric drag, with reentry predicted to occur before the end of 1989. Lifetime predictions were also performed for the Long Duration Exposure Facility (LDEF), which was deployed on the 1984 SMM repair mission and is scheduled for retrieval on another Space Transportation System (STS) mission later this year. Concepts used in the lifetime predictions were tested on the San Marco spacecraft, which reentered the Earth's atmosphere on December 6, 1988. Ephemerides predicting the orbit evolution of the San Marco spacecraft until reentry were generated over the final 90 days of the mission when the altitude was less than 380 kilometers. The errors in the predicted ephemerides are due to errors in the prediction of atmospheric density variations over the lifetime of the satellite. To model the time dependence of the atmospheric densities, predictions of the solar flux at the 10.7-centimeter wavelength were used in conjunction with Harris-Priester (HP) atmospheric density tables. Orbital state vectors, together with the spacecraft mass and area, are used as input to the Goddard Trajectory Determination System (GTDS). Propagations proceed in monthly segments, with the nominal atmospheric drag model scaled for each month according to the predicted monthly average value of F10.7. Calibration propagations are performed over a period of known orbital decay to obtain the effective ballistic coefficient. Progagations using plus or minus 2 sigma solar flux predictions are also generated to estimate the despersion in expected reentry dates. Definitive orbits are compared with these predictions as time expases. As updated vectors are received, these are also propagated to reentryto continually update the lifetime predictions.

Smith, E. A.↗
NASA NTRS1992

The global structure of the annual and semiannual sea surface height variability from Geosat altimeter data

Two years of data from the Geosat Exact Repeat Mission are employed to study the annual and semiannual variability of sea-surface height on a global basis. The data are treated with atmospheric corrections and interpolations, and the orbit error of about 40 cm RMS is purged. The spatial variability of the Geosat data is constructed for particular frequencies, and the estimate of the M2 tidal error indicates that the error is aliased to 1.15 cycles/yr and has an unusual spatial pattern. Sine and cosine coefficients are derived for the annual and semiannual frequencies by means of a least squares fit yielding the amplitude and phase of the changes in sea-surface height. A 180-deg phase difference is noted between the Northern and Southern Hemispheres for the annual variability, and large-scale westward propagating waves are identified. The Geosat data also indicate the phase relationships between major current systems and the systems of variations at work in the Intertropical Convergence Zone.

Jacobs, Gregg A.↗
NASA NTRS2005

Computation of Sound Propagation by Boundary Element Method

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Guo, Yueping↗
NASA NTRS1973

Implementation of a self-controlling heater

Temperature control of radiation sensors, targets, and other critical components is a common requirement in modern scientific instruments. Conventional control systems use a heater and a temperature sensor mounted on the body to be controlled. For proportional control, the sensor provides feedback to circuitry which drives the heater with an amount of power proportional to the temperature error. It is impractical or undesirable to mount both a heater and a sensor on certain components such as ultra-small parts or thin filaments. In principle, a variable current through the element is used for heating, and the change in voltage drop due to the element's temperature coefficient is separated and used to monitor or control its own temperature. Since there are no thermal propagation delays between heater and sensor, such control systems are exceptionally stable.

Strange, M. G.↗
NASA NTRS1983

Simulation and analysis of differential global positioning system for civil helicopter operations

A Differential Global Positioning System (DGPS) computer simulation was developed, to provide a versatile tool for assessing DGPS referenced civil helicopter navigation. The civil helicopter community will probably be an early user of the GPS capability because of the unique mission requirements which include offshore exploration and low altitude transport into remote areas not currently served by ground based Navaids. The Monte Carlo simulation provided a sufficiently high fidelity dynamic motion and propagation environment to enable accurate comparisons of alternative differential GPS implementations and navigation filter tradeoffs. The analyst has provided the capability to adjust most aspects of the system, the helicopter flight profile, the receiver Kalman filter, and the signal propagation environment to assess differential GPS performance and parameter sensitivities. Preliminary analysis was conducted to evaluate alternative implementations of the differential navigation algorithm in both the position and measurement domain. Results are presented to show that significant performance gains are achieved when compared with conventional GPS but that differences due to DGPS implementation techniques were small. System performance was relatively insensitive to the update rates of the error correction information.

Denaro, R. P.↗
NASA NTRS1994

Comparison of TOPEX sea surface heights and tide gauge sea levels

TOPEX sea surface height data from the first 300 days of the mission are compared to sea level data from 71 tide gauges. The initial comparison uses sea surface height data processed according to standard procedures as defined in the users handbook. It is found that the median correlations for island and for coastal tide gauges are 0.53 and 0.42, respectively. The analogous root mean square (RMS) differences between the two data sets are 7.9 and 10.4 cm. The comparisons improve significantly when a 60-day harmonic is fit to the differences and removed. This period captures aliased M(sub 2) and S(sub 2) tidal energy that is not removed by the tide model. Making this correction and smoothing the sea surface height data over 25-km along-track segments results in median correlations of 0.58 and 0.46 for the islands and coastal stations, and median RMS differences of 5.8 and 7.7 cm, respectively. Removing once per revolution signals from the sea surface heights results in degraded comparisons with the sea levels. It is also found that a number of stations have poor comparisons due to propagating signals that introduce temporal lags between the altimeter and tide gauge time series. A final comparison is made by eliminating stations where this propagation effect is large, discarding two stations that are suspected to have problems with the sea level data, smoothing over 10-day intervals, and restricting attention to islands gauges. This results in a set of 552 data pairs that have a correlation of 0.66 and a RMS difference of 4.3 cm. The conclusion is that on timescales longer than about 10 days the RMS sea surface height errors are less than or of the order of several centimeters.

Mitchum, Gary T.↗
NASA NTRS2023

Extended Kalman Filter Performance on the Artemis-1 Mission

The Artemis Program is NASA’s campaign to explore the Moon and beyond. Artemis-1, the uncrewed exoLEO test flight of the Orion spacecraft, was completed in 2022. There were four navigation Extended Kalman Filters (EKFs) that are part of the Orion navigation system. The Atmospheric Extended Kalman Filter (ATMEKF) estimates the vehicle position, velocity, and attitude (referred to as the vehicle state) during the ascent and entry phases of flight. Once Orion is outside of Earths atmosphere, the Earth Orbit Extended Kalman Filter (EOEKF) and CisLunar Extended Kalman Filter (CLEKF) estimate the translational states, depending on the phase of flight, while the Attitude Extended Kalman Filter (ATTEKF) estimates the rotational state of the vehicle. The Kalman filters propagate the vehicle state forward in time using a combination of dynamics models and the output data from the Inertial Measurement Unit (IMU). The filters update the vehicle states and associated uncertainties, in the form of the covariance matrix, using pseudorange measurements from GPS (in ATMEKF/EOEKF), optical navigation measurements of the Earth or Moon (in CLEKF), and star tracker measurements (in ATTEKF). Simultaneously, the Kalman filters estimate error sources in the sensors, which are included in the state vectors as Exponentially Correlated Random Variables (ECRVs). This paper will summarize the performance of these filters during the Artemis-1 mission.

Artemis-1↗
NASA NTRS1983

Data analysis for dual-polarized communication link experiments

The effect of the propagation medium on the performance of dual-polarized radio links operating in the microwave and millimeter wave regions is analyzed, with particular reference to rain and ice depolarization. Three methods of displaying measured cross-polarization discrimination (XPD) versus the attenuation (A) are examined: mean, median, and equiprobable. The mean and median values are shown to be essentially the same, while equiprobable data are sensitive to many errors. Ice depolarization alone or imbedded in rain depolarization can shift the entire XPD vs A relationship for equiprobable data. It is concluded that XPD vs A sets from different experiments can be compared with confidence when mean and median values are used. However, caution must be exercised with equipotential data sets, particularly when ice effects are involved.

Stutzman, W. L.↗
NASA NTRS1995

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Goodrich, John W.↗
NASA NTRS1995

Accuracy of wet troposphere radio path delay estimated from infrared emission

Several radio science applications require determination of the excess radio-propagation path delay caused by the Earth's atmosphere. These include very long baseline interferometry, spacecraft tracking, and potentially, detection of gravitational waves utilizing a link to a distant interplanetary spacecraft. At Ka band, the major source of variability of path delay is the fluctuations in the moisture content of the troposphere. The path delay characterization requirements for a planned gravitational wave experiment are novel and challenging. the error contribution to the phase observations due to path delay variation must be reduced by nearly two orders of magnitude over that occurring naturally on time scales of 100 to 10,000 seconds. Current approaches relying on microwave water vapor radiometry with ancillary data can deliver one order of magnitude calibration of these fluctuations, and more advanced systems are under development within the 2001-2002 time frame of the Cassini Mission to Saturn. The current work evaluates the potential for an alternative observational approach, using a ground-based Fourier transform spectrometer.

Parker, J. W.↗
NASA NTRS1981

Monte-Carlo model of pitch-angle scattering in solar cosmic ray events

Monte Carlo simulations of the propagation of solar cosmic-rays in interplanetary space are reported, including the effects of pitch-angle scattering and adiabatic focusing. Time intensity profiles agree well with the corresponding spatial diffusion approximation for models close to those used by Gombosi and Owens (1980). Monte Carlo simulations of the same model problem yield results that disagree with those of Gombosi and Owens, and the most likely possible source of error in the Monte Carlo simulation is considered to be in the region near the 90 deg pitch angle where the finite step size introduces certain inconsistencies.

Palmer, I. D.↗
NASA NTRS1984

Rocket observations of electron density in the nighttime E region using Faraday rotation

A rocket radio propagation experiment is described in which the electron density profile of the nighttime E region is obtained with an accuracy of 100 per cu cm. The factors limiting the accuracy of the experiment are found to be related to atmospheric and receiver noise and to the use of a magnetometer to determine the spin rate of the rocket. The Fourier analysis used for the frequency measurement may also contribute error under conditions of steep electron density gradients. The accuracy being achieved appears to be adequate for present applications of the experiment.

Smith, L. G.↗
NASA NTRS1993

On-board closed-loop congestion control for satellite based packet switching networks

NASA LeRC is currently investigating a satellite architecture that incorporates on-board packet switching capability. Because of the statistical nature of packet switching, arrival traffic may fluctuate and thus it is necessary to integrate congestion control mechanism as part of the on-board processing unit. This study focuses on the closed-loop reactive control. We investigate the impact of the long propagation delay on the performance and propose a scheme to overcome the problem. The scheme uses a global feedback signal to regulate the packet arrival rate of ground stations. In this scheme, the satellite continuously broadcasts the status of its output buffer and the ground stations respond by selectively discarding packets or by tagging the excessive packets as low-priority. The two schemes are evaluated by theoretical queuing analysis and simulation. The former is used to analyze the simplified model and to determine the basic trends and bounds, and the later is used to assess the performance of a more realistic system and to evaluate the effectiveness of more sophisticated control schemes. The results show that the long propagation delay makes the closed-loop congestion control less responsive. The broadcasted information can only be used to extract statistical information. The discarding scheme needs carefully-chosen status information and reduction function, and normally requires a significant amount of ground discarding to reduce the on-board packet loss probability. The tagging scheme is more effective since it tolerates more uncertainties and allows a larger margin of error in status information. It can protect the high-priority packets from excessive loss and fully utilize the downlink bandwidth at the same time.

Chu, Pong P.↗
NASA NTRS2008

Assessment of Current Jet Noise Prediction Capabilities

An assessment was made of the capability of jet noise prediction codes over a broad range of jet flows, with the objective of quantifying current capabilities and identifying areas requiring future research investment. Three separate codes in NASA s possession, representative of two classes of jet noise prediction codes, were evaluated, one empirical and two statistical. The empirical code is the Stone Jet Noise Module (ST2JET) contained within the ANOPP aircraft noise prediction code. It is well documented, and represents the state of the art in semi-empirical acoustic prediction codes where virtual sources are attributed to various aspects of noise generation in each jet. These sources, in combination, predict the spectral directivity of a jet plume. A total of 258 jet noise cases were examined on the ST2JET code, each run requiring only fractions of a second to complete. Two statistical jet noise prediction codes were also evaluated, JeNo v1, and Jet3D. Fewer cases were run for the statistical prediction methods because they require substantially more resources, typically a Reynolds-Averaged Navier-Stokes solution of the jet, volume integration of the source statistical models over the entire plume, and a numerical solution of the governing propagation equation within the jet. In the evaluation process, substantial justification of experimental datasets used in the evaluations was made. In the end, none of the current codes can predict jet noise within experimental uncertainty. The empirical code came within 2dB on a 1/3 octave spectral basis for a wide range of flows. The statistical code Jet3D was within experimental uncertainty at broadside angles for hot supersonic jets, but errors in peak frequency and amplitude put it out of experimental uncertainty at cooler, lower speed conditions. Jet3D did not predict changes in directivity in the downstream angles. The statistical code JeNo,v1 was within experimental uncertainty predicting noise from cold subsonic jets at all angles, but did not predict changes with heating of the jet and did not account for directivity changes at supersonic conditions. Shortcomings addressed here give direction for future work relevant to the statistical-based prediction methods. A full report will be released as a chapter in a NASA publication assessing the state of the art in aircraft noise prediction.

Hunter, Craid A.↗
NASA NTRS2007

Active Correction of Aberrations of Low-Quality Telescope Optics

A system of active optics that includes a wavefront sensor and a deformable mirror has been demonstrated to be an effective means of partly correcting wavefront aberrations introduced by fixed optics (lenses and mirrors) in telescopes. It is envisioned that after further development, active optics would be used to reduce wavefront aberrations of about one wave or less in telescopes having aperture diameters of the order of meters or tens of meters. Although this remaining amount of aberration would be considered excessive in scientific applications in which diffraction-limited performance is required, it would be acceptable for free-space optical- communication applications at wavelengths of the order of 1 m. To prevent misunderstanding, it is important to state the following: The technological discipline of active optics, in which the primary or secondary mirror of a telescope is directly and dynamically tilted, distorted, and/or otherwise varied to reduce wavefront aberrations, has existed for decades. The term active optics does not necessarily mean the same thing as does adaptive optics, even though active optics and adaptive optics are related. The term "adaptive optics" is often used to refer to wavefront correction at speeds characterized by frequencies ranging up to between hundreds of hertz and several kilohertz high enough to enable mitigation of adverse effects of fluctuations in atmospheric refraction upon propagation of light beams. The term active optics usually appears in reference to wavefront correction at significantly lower speeds, characterized by times ranging from about 1 second to as long as minutes. Hence, the novelty of the present development lies, not in the basic concept of active or adaptive optics, but in the envisioned application of active optics in conjunction with a deformable mirror to achieve acceptably small wavefront errors in free-space optical communication systems that include multi-meter-diameter telescope mirrors that are relatively inexpensive because their surface figures are characterized by errors as large as about 10 waves. Figure 1 schematically depicts the apparatus used in an experiment to demonstrate such an application on a reduced scale involving a 30-cm-diameter aperture.

Hemmati, Hamid↗