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NASA NTRS2010

Advanced Aerobots for Scientific Exploration

The Picosat and Uninhabited Aerial Vehicle Systems Engineering (PAUSE) project is developing balloon-borne instrumentation systems as aerobots for scientific exploration of remote planets and for diverse terrestrial purposes that can include scientific exploration, mapping, and military surveillance. The underlying concept of balloon-borne gondolas housing outer-space-qualified scientific instruments and associated data-processing and radio-communication equipment is not new. Instead, the novelty lies in numerous design details that, taken together, make a PAUSE aerobot smaller, less expensive, and less massive, relative to prior aerobots developed for similar purposes: Whereas the gondola (including the instrumentation system housed in it) of a typical prior aerobot has a mass of hundreds of kilograms, the mass of the gondola (with instrumentation system) of a PAUSE aerobot is a few kilograms.

Behar, Alberto↗
NASA NTRS2014

Central Africa Energy: Utilizing NASA Earth Observations to Explore Flared Gas as an Energy Source Alternative to Biomass in Central Africa

Much of Central Africa's economy is centered on oil production. Oil deposits lie below vast amounts of compressed natural gas. The latter is often flared off during oil extraction due to a lack of the infrastructure needed to utilize it for productive energy generation. Though gas flaring is discouraged by many due to its contributions to greenhouse emissions, it represents a waste process and is rarely tracked or recorded in this region. In contrast to this energy waste, roughly 80% of Africa's population lacks access to electricity and in turn uses biomass such as wood for heat and light. In addition to the dangers incurred from collecting and using biomass, the practice commonly leads to ecological change through the acquisition of wood from forests surrounding urban areas. The objective of this project was to gain insight on domestic energy usage in Central Africa, specifically Angola, Gabon, and the Republic of Congo. This was done through an analysis of deforestation, an estimation of gas flared, and a suitability study for the infrastructure needed to realize the natural gas resources. The energy from potential natural gas production was compared to the energy equivalent of the biomass being harvested. A site suitability study for natural gas pipeline routes from flare sites to populous locations was conducted to assess the feasibility of utilizing natural gas for domestic energy needs. Analyses and results were shared with project partners, as well as this project's open source approach to assessing the energy sector. Ultimately, Africa's growth demands energy for its people, and natural gas is already being produced by the flourishing petroleum industry in numerous African countries. By utilizing this gas, Africa could reduce flaring, recuperate the financial and environmental loss that flaring accounts for, and unlock a plentiful domestic energy source for its people. II. Introduction Background Africa is home to numerous burgeoning economies; a significant number rely on oil production as their primary source of revenue. Relative to its size and population density, the continent has a wealth of natural resources, including oil and natural gas deposits. The exploration of these resources is not a new endeavor, but rather one that spans decades, up to a century in some places. Their resources, if realized, could provide a great means of economic and social mobility for the people of Africa. Currently, Africa represents about 12 % of the energy market, yet at the same time, consumes only 3 % of the world's energy (Kasekende 2009). The higher

Jones, Amber↗
NASA NTRS2016

Magnetohydrodynamic Turbulence and the Geodynamo

Recent research results concerning forced, dissipative, rotating magnetohydrodynamic (MHD) turbulence will be discussed. In particular, we present new results from long-time Fourier method (periodic box) simulations in which forcing contains varying amounts of magnetic and kinetic helicity. Numerical results indicate that if MHD turbulence is forced so as to produce a state of relatively constant energy, then the largest-scale components are dominant and quasistationary, and in fact, have an effective dipole moment vector that aligns closely with the rotation axis. The relationship of this work to established results in ideal MHD turbulence, as well as to models of MHD turbulence in a spherical shell will also be presented. These results appear to be very pertinent to understanding the Geodynamo and the origin of its dominant dipole component. Our conclusion is that MHD turbulence, per se, may well contain the origin of the Earth's dipole magnetic field.

Shebalin, John V.↗
NASA NTRS2017

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Galaxies↗
NASA NTRS2017

Structure in the 3D Galaxy Distribution: III. Fourier Transforming the Universe: Phase and Power Spectra

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Galactic clusters↗
NASA NTRS2017

Cassini Spacecraft Strategy for Recovering from a Complete Loss-Of-Signal Condition

Unlike other faults where the space craft’s automated Fault Protection (FP) routines can be relied upon to provide a carrier signal and telemetered data to the ground-based Spacecraft Operations Flight Support (SOFS) team to facilitate vehicle acquisition, diagnosis, and fault recovery, a complete Loss-of-Spacecraft-Signal (LOS) condition will yield no information at all to help re-acquire the vehicle and resolve the fault. For any FP response activation, the spacecraft’s downlink signal must be acquired via the Deep Space Network (DSN) on the expected (post-fault) Radio Frequency Subsystem (RFS) device configuration commanded by the FP; data that will not be attainable in the case of a complete LOS condition since there is no signal available for the ground station to lock onto. In the case of the Cassini Mission-to-Saturn spacecraft, numerous fault possibilities exist that can cause a LOS condition. Activations of the onboard RFS-related FP can reconfigure the post-fault RFS states, impeding the ground team’s ability to acquire the spacecraft’s downlink signal

Morgan, Paula S.↗
NASA NTRS2020

A New Crater Near Insight: Implications for Seismic Impact Detectability on Mars

A new 1.5 m diameter impact crater was discovered on Mars only ~40 km from the InSight lander. Context camera images constrained its formation between 21 February and 6 April 2019; follow-up High Resolution Imaging Science Experiment images resolved the crater. During this time period, three seismic events were identified in InSight data. We derive expected seismic signal characteristics and use them to evaluate each of the seismic events. However, none of them can definitively be associated with this source. Atmospheric perturbations are generally expected to be generated during impacts; however, in this case, no signal could be identified as related to the known impact. Using scaling relationships based on the terrestrial and lunar analogs and numerical modeling, we predict the amplitude, peak frequency, and duration of the seismic signal that would have emanated from this impact. The predicted amplitude falls near the lowest levels of the measured seismometer noise for the predicted frequency. Hence, it is not surprising this impact event was not positively identified in the seismic data. Finding this crater was a lucky event as its formation this close to InSight has a probability of only ~0.2, and the odds of capturing it in before and after images are extremely low. We revisit impact-seismic discriminators in light of real experience with a seismometer on the Martian surface. Using measured noise of the instrument, we revise our previous prediction of seismic impact detections downward, from ~a few to tens, to just ~2 per Earth year, still with an order of magnitude uncertainty.

I. J. Daubar↗
NASA NTRSDate not supplied

Coastal Land Change Due to Tectonic Processes and Implications for Relative Sea-Level Rise in the Samoan Islands

Of the major coastal land change mechanisms responsible for relative sea-level change, tectonic subsidence is generally quoted as ranging from < mm/yr to 1 cm/yr. However, we documented coseismic and ongoing post-earthquake surface displacements from continuous GPS and tide gauge/altimetry data that indicated rapid subsidence on two of the major Samoan Islands of 12 - 20 cm during and following the 8.1 2009 Tonga-Samoa earthquake. Earlier results and our modeling of GRACE-derived gravimetric data provided a preliminary forecast of future relative sea-level rise through rapid land subsidence [Han et al., 2019]. Of course these numerical forecasts of time-dependent deformation are only as good as our input observations and our assumed rheological models. As part of our current NASA Earth Surface and Interior study, we are obtaining a wider range of data to constrain and test alternate models of ongoing postseismic deformation across American Samoa and Upolu, Samoa: (1) times series of altimetry plus tide gauge data processed to complement the cGPS data available to provide high-temporal resolution, point measurements of uplift/subsidence, (2) InSAR derived observations of surface deformation across the highly vegetated Samoan Islands, (3) evaluating and using NASA satellite lidar data (ICESat-I & ICESat-II, GEDI) for fusion with multi-source topographic data sets and for estimating topographic change on the decadal time scale. We are evaluating and using these new observations to better understand and separate out local, island-wide, and multi-island subsidence patterns and to evaluate the high impact of rising sea-level in a tectonically active region.

Jeanne Sauber-Rosenberg↗
NASA NTRSDate not supplied

Direct Simulation Monte Carlo Studies of the Gas Sampling for the VATMOS-SR Mission Concept

VATMOS-SR (Venus ATMOSpheric - Sample Return) is a small spacecraft mission concept which would return a gas sample from the upper atmosphere of Venus to Earth for scientific analysis. This could be the first sample return mission for an extra-terrestrial atmosphere, and potentially the first sample return from an Earth-sized planet. The VATMOS-SR mission concept consists of a SmallSat atmospheric sampling probe (45 deg. sphere/cone geometry, <1 m diameter) that is designed to skim through the Venus upper atmosphere and acquire gas samples below the homopause altitude (around ~110 km altitude), where the different atmospheric gases are mixed. The velocity of the spacecraft where sampling would occur is expected to be between ~10.5 km/s and ~13.1 km/s, depending on the trajectory chosen. This presentation will discuss hypervelocity sampling in the upper atmosphere of Venus, with respect to the VATMOS-SR mission concept. VATMOS-SR would enable critical atmospheric measurements to form a full picture of how, why, and when Venus evolved to be so different from Earth and Mars. The abundances and isotopic compositions of volatile elements (such as N, C, S, O and the noble gases) in planetary atmospheres record volatile delivery during accretion, outgassing from planetary interiors, and atmospheric loss to space. Precise and accurate determinations of atmospheric volatile signatures are the key to understanding the origins and geodynamical evolution of Venus compared to the other terrestrial planets. Hypersonic sampling poses unique technical and scientific challenges. To ensure it is possible to relate the composition of the sampled gases to the free stream atmospheric composition, large-scale numerical simulations are employed to model the flow through the VATMOS-SR sampling system. In particular, an emphasis is placed on quantifying noble gas isotopic fractionation that occurs during the sample acquisition and transfer process in order to determine how measured isotopic ratios of noble gases in the sample compare to actual isotopic ratios in the Venusian atmosphere. The Direct Simulation Monte Carlo (DSMC) code SPARTA, an open source software package developed by Sandia National Laboratories, is used in this work. SPARTA, based on Bird’s DSMC method, is a molecular-level gas-kinetic technique. As SPARTA is able to model hypervelocity reacting flows in strong chemical and thermal non-equilibrium, this software package is well suited to determine relevant flow properties for the VATMOS-SR mission concept, and to numerically quantify the expected level of elemental and/or isotopic fractionation in the sample acquired by VATMOS-SR. This presentation will show results from 3D simulations correlating the noble gas isotopic fractionation in the gas acquired at hypervelocity speeds to its ambient atmosphere value. In particular, emphasis will be placed at Xenon isotopes of masses 128 and 130, as precise measurements of that ratio would yield a comparison to Earth’s atmosphere. Additionally, sensitivity studies that quantify the uncertainties due to the freestream parameters as well as the modeling parameters will be performed.

direct simulation Monte Carlo↗
NASA NTRSDate not supplied

The VATMOS-SR Mission Concept: DSMC Studies of the Gas Sampling

VATMOS-SR (Venus ATMOSpheric - Sample Return) is a small spacecraft mission concept that would return a gas sample from the upper atmosphere of Venus to Earth for scientific analysis. This could be the first sample return mission for an extra-terrestrial atmosphere and potentially the first sample return from an Earth-sized planet. The VATMOS-SR mission concept consists of a SmallSat atmospheric sampling probe (45 deg. sphere/cone geometry, <1 m diameter) that is designed to skim through the Venus upper atmosphere and acquire gas samples below the homopause altitude (around ~110 km altitude), where the different atmospheric gases are mixed. The velocity of the spacecraft where sampling would occur is expected to be between ~10.5 km/s and ~13.1 km/s, depending on the trajectory chosen. This presentation will discuss hypervelocity sampling in the upper atmosphere of Venus with respect to the VATMOS-SR mission concept. VATMOS-SR would enable critical atmospheric measurements to form a complete picture of how, why, and when Venus evolved to be so different from Earth and Mars. The abundances and isotopic compositions of volatile elements (such as N, C, S, O, and the noble gases) in planetary atmospheres record volatile delivery during accretion, outgassing from planetary interiors, and atmospheric loss to space. Precise and accurate determinations of volatile atmospheric signatures are the key to understanding the origins and geodynamical evolution of Venus compared to the other terrestrial planets. Hypersonic sampling poses unique technical and scientific challenges. To ensure it is possible to relate the composition of the sampled gases to the free stream atmospheric composition, large-scale numerical simulations are employed to model the flow through the VATMOS-SR sampling system. In particular, an emphasis is placed on quantifying noble gas isotopic fractionation that occurs during the sample acquisition and transfer process to determine how measured isotopic ratios of noble gases in the sample compared to actual isotopic ratios in the Venusian atmosphere. The Direct Simulation Monte Carlo (DSMC) code SPARTA, an open-source software package developed by Sandia National Laboratories, is used in this work. SPARTA, based on Bird’s DSMC method, is a molecular-level gas-kinetic technique. As SPARTA is able to model hypervelocity reacting flows in strong chemical and thermal non-equilibrium, this software package is well suited to determine relevant flow properties for the VATMOS-SR mission concept and to numerically quantify the expected level of elemental and/or isotopic fractionation in the sample acquired by VATMOS-SR. This presentation will show results from 3D simulations correlating the noble gas isotopic fractionation in the gas acquired at hypervelocity speeds to its ambient atmosphere value. In particular, emphasis will be placed on Xenon isotopes of masses 128 and 130, as precise measurements of that ratio would yield comparison to Earth’s atmosphere. Additionally, sensitivity studies that quantify the uncertainties due to the freestream parameters, as well as the modeling parameters, will be performed.

direct simulation Monte Carlo↗
NASA NTRSDate not supplied

Discontinuous Galerkin and Related Methods for ODE

Starting from the standard integral formulation, the DG method is derived here in differential form. The key ingredient is a polynomial called the correction function, which helps ‘correct’ the discontinuous solution by approximating the jump and yields a continuous one. Under the right Radau quadrature, this continuous solution is identical to the solutions by the right Radau collocation and the continuous Galerkin (CG) methods. Next, the correction function facilitates the construction of the associated implicit Runge-Kutta schemes (IRK-DG). Different quadratures for DG result in different IRK-DG methods: left Radau quadrature in Radau IA, right Radau quadrature in Radau IIA or right Radau collocation, and Gauss quadrature in a method called DG-Gauss. The construction of IRK-DG clarifies the meaning and facilitates the proofs of various 𝐵(𝑝), 𝐶(𝜂), and 𝐷(𝜁) conditions for accuracy. The two consequences of these conditions are that all 𝑠-stage IRK-DG methods are accurate to order 2𝑠− 1, and the IRK-DG methods of Radau type are unique. Numerical examples showing the behavior of the DG solutions are provided. In all, the correction function plays a key role and helps establish the relations among the DG, IRK DG, collocation, and CG methods.

Numerical Methods for Ordinary Differential Equati↗
NASA NTRS2009

The a(4) Scheme-A High Order Neutrally Stable CESE Solver

The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3

Chang, Sin-Chung↗
NASA NTRS1999

Noninvasive assessment of left atrial maximum dP/dt by a combination of transmitral and pulmonary venous flow

OBJECTIVES: The study assessed whether hemodynamic parameters of left atrial (LA) systolic function could be estimated noninvasively using Doppler echocardiography. BACKGROUND: Left atrial systolic function is an important aspect of cardiac function. Doppler echocardiography can measure changes in LA volume, but has not been shown to relate to hemodynamic parameters such as the maximal value of the first derivative of the pressure (LA dP/dt(max)). METHODS: Eighteen patients in sinus rhythm were studied immediately before and after open heart surgery using simultaneous LA pressure measurements and intraoperative transesophageal echocardiography. Left atrial pressure was measured with a micromanometer catheter, and LA dP/dt(max) during atrial contraction was obtained. Transmitral and pulmonary venous flow were recorded by pulsed Doppler echocardiography. Peak velocity, and mean acceleration and deceleration, and the time-velocity integral of each flow during atrial contraction was measured. The initial eight patients served as the study group to derive a multilinear regression equation to estimate LA dP/dt(max) from Doppler parameters, and the latter 10 patients served as the test group to validate the equation. A previously validated numeric model was used to confirm these results. RESULTS: In the study group, LA dP/dt(max) showed a linear relation with LA pressure before atrial contraction (r = 0.80, p < 0.005), confirming the presence of the Frank-Starling mechanism in the LA. Among transmitral flow parameters, mean acceleration showed the strongest correlation with LA dP/dt(max) (r = 0.78, p < 0.001). Among pulmonary venous flow parameters, no single parameter was sufficient to estimate LA dP/dt(max) with an r2 > 0.30. By stepwise and multiple linear regression analysis, LA dP/dt(max) was best described as follows: LA dP/dt(max) = 0.1 M-AC +/- 1.8 P-V - 4.1; r = 0.88, p < 0.0001, where M-AC is the mean acceleration of transmitral flow and P-V is the peak velocity of pulmonary venous flow during atrial contraction. This equation was tested in the latter 10 patients of the test group. Predicted and measured LA dP/dt(max) correlated well (r = 0.90, p < 0.0001). Numerical simulation verified that this relationship held across a wide range of atrial elastance, ventricular relaxation and systolic function, with LA dP/dt(max) predicted by the above equation with r = 0.94. CONCLUSIONS: A combination of transmitral and pulmonary venous flow parameters can provide a hemodynamic assessment of LA systolic function.

NASA Discipline Cardiopulmonary↗
NASA NTRS2024

Comprehensive Observations and Geostatistics of Slope Streaks within the Olympus Mons Aureole

Slope streaks (SS) are enigmatic linear features characterized by relatively low-albedo features that appear and fade on high-albedo slopes on Mars. Despite numerous hypotheses proposed to explain their formation, the primary mechanism behind SS remains elusive. Here, we examine 702 SS features using 32 multitemporal Context Imager (CTX) images and mesoscale modeling data obtained from a site (centered at 31.230°N, 216.281°E) in the Olympus Mons Aureole region. Our investigation revealed several key findings that shed light on the dynamics of SS formation and fading. We discovered a significant preference for SS formation on south-facing (equator-facing) slopes compared to north-facing slopes, with SS being over seven times more likely to occur on the former. Furthermore, SS formation was found to be seasonal with significantly enhanced by a factor of ∼6 near the equinoxes (from solar longitude Ls 337°-42° and 136°-227°) compared to other times of the year. Our analysis also revealed a correlation between the rates of SS formation and fading, with scree slopes exhibited the fastest-fading SS also experiencing the highest rates of newly-formed SS. Additionally, we measured the median starting and stopping slopes of SS to be 23.4° and 14.9°, respectively, significantly below the angle of repose of sand. These low slopes suggest the necessity for an energetic trigger mechanism to initiate SS formation. Infrared spectroscopy revealed that the principal distinction between the material inside and outside of a SS lies in the reduced abundance of dust within the streak. Notably, this site demonstrates the highest rates of SS formation (a 29.6% increase in new SS per Mars year) and fading (a 12% fading of SS per Mars year) ever quantified. These elevated rates may be attributed to the site's topography, which facilitates calm surficial nighttime winds throughout the year, leading to widespread dust deposition. Daytime downhill winds near the ridgelines of S-facing slopes may then trigger movement of newly deposited dust aggregates or alternatively, a Knudsen pump phenomenon could serve as a potential trigger for SS. We propose that SS is inhibited during the northern summer solstice season due to the relatively clear aphelion atmosphere, which limits dust deposition. Similarly, the lack of triggering activity during the winter solstice is likely due to more moderate daytime winds. Overall, our findings are consistent with the wind-triggered dry avalanche hypothesis as a plausible explanation for SS formation.

D E Stillman↗
NASA NTRS1995

Is chemical heating a major cause of the mesosphere inversion layer?

A region of thermal enhancement of the mesosphere has been detected on numerous occasions by in situ measurements, remote sensing from space, and lidar techniques. The source of these 'temperature inversion layers' has been attributed in the literature to the dissipation relating to dynamical forcing by gravity wave or tidal activity. However, evidence that gravity wave breaking can produce the inversion layer with amplitude as large as that observed in lidar measurements has been limited to results of numerical modeling. An alternative source for the production of the thermal inversion layer in the mesosphere is the direct deposition of heat by exothermic chemical reactions. Two-dimensional modeling combining a comprehensive model of the mesosphere photochemistry with the dynamical transport of long-lived species shows that the region from 80 to 95 km may be heated as much as 3 to 10 K/d during the night and half this rate during the day. Given the uncertainties in our understanding of the dynamics and chemistry for the mesopause region, separating the two sources by passive observations of the mesosphere thermal structure looks to be difficult. Therefore we have considered an active means for producing a mesopause thermal layer, namely the release of ozone into the upper mesosphere from a rocket payload. The induced effects would include artificial enhancements of the OH and Na airglow intensities as well as the mesopause thermal structure. The advantages of the rocket release of ozone is that detection of these effects by ground-based imaging, radar, and lidar systems and comparison of these effects with model predictions would help quantify the partition of the artificial inversion layer production into sources of dynamical and chemical forcing.

Meriwether, John W.↗
NASA NTRS1981

Computation of hypersonic viscous flow around three-dimensional bodies at high angles of attack

A parabolized Navier-Stokes code capable of predicting steady viscous supersonic flows with cross-flow separation is applied to three-dimensional arbitrary geometries at high angles of attack. The numerical procedure, which is implicit, noniterative, and of second-order accuracy in the marching direction, has been used to compute complicated flow fields containing a relatively thick sonic layer and regions of strong viscous-inviscid interaction. A consistent and accurate procedure has also been developed to provide the necessary starting data through timewise integration of the equations of motion near the nose-tip region of the body. Numerical results obtained from the present method compare well with experiment for both the surface pressures and heat transfer.

Rizk, Y. M.↗
NASA NTRS1985

Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and nonlinear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of /y(dot) = f(y) for t greater than 0, y(0) given/ is typically reduced to the mth order (m is much less than n) problem of /z(dot) = g(z) for t greater than 0, z(0) given/ by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e-i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian and of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e., the columns of P.

Utku, S.↗
NASA NTRS2011

Analysis of Separation Corridors for Visiting Vehicles from the International Space Station

The International Space Station (ISS) is a very dynamic vehicle with many operational constraints that affect its performance, operations, and vehicle lifetime. Most constraints are designed to alleviate various safety concerns that are a result of dynamic activities between the ISS and various Visiting Vehicles (VVs). One such constraint that has been in place for Russian Vehicle (RV) operations is the limitation placed on Solar Array (SA) positioning in order to prevent collisions during separation and subsequent relative motion of VVs. An unintended consequence of the SA constraint has been the impacts to the operational flexibility of the ISS resulting from the reduced power generation capability as well as from a reduction in the operational lifetime of various SA components. The purpose of this paper is to discuss the technique and the analysis that were applied in order to relax the SA constraints for RV undockings, thereby improving both the ISS operational flexibility and extending its lifetime for many years to come. This analysis focused on the effects of the dynamic motion that occur both prior to and following RV separations. The analysis involved a parametric approach in the conservative application of various initial conditions and assumptions. These included the use of the worst case minimum and maximum vehicle configurations, worst case initial attitudes and attitude rates, and the worst case docking port separation dynamics. Separations were calculated for multiple ISS docking ports, at varied deviations from the nominal undocking attitudes and included the use of two separate attitude control schemes: continuous free-drift and a post separation attitude hold. The analysis required numerical propagation of both the separation motion and the vehicle attitudes using 3-degree-of-freedom (DOF) relative motion equations coupled with rigid body rotational dynamics to generate a large set of separation trajectories.

Zaczek, Mariusz P.↗