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NASA NTRS2003

Structural Reliability Using Probability Density Estimation Methods Within NESSUS

A reliability analysis studies a mathematical model of a physical system taking into account uncertainties of design variables and common results are estimations of a response density, which also implies estimations of its parameters. Some common density parameters include the mean value, the standard deviation, and specific percentile(s) of the response, which are measures of central tendency, variation, and probability regions, respectively. Reliability analyses are important since the results can lead to different designs by calculating the probability of observing safe responses in each of the proposed designs. All of this is done at the expense of added computational time as compared to a single deterministic analysis which will result in one value of the response out of many that make up the density of the response. Sampling methods, such as monte carlo (MC) and latin hypercube sampling (LHS), can be used to perform reliability analyses and can compute nonlinear response density parameters even if the response is dependent on many random variables. Hence, both methods are very robust; however, they are computationally expensive to use in the estimation of the response density parameters. Both methods are 2 of 13 stochastic methods that are contained within the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) program. NESSUS is a probabilistic finite element analysis (FEA) program that was developed through funding from NASA Glenn Research Center (GRC). It has the additional capability of being linked to other analysis programs; therefore, probabilistic fluid dynamics, fracture mechanics, and heat transfer are only a few of what is possible with this software. The LHS method is the newest addition to the stochastic methods within NESSUS. Part of this work was to enhance NESSUS with the LHS method. The new LHS module is complete, has been successfully integrated with NESSUS, and been used to study four different test cases that have been proposed by the Society of Automotive Engineers (SAE). The test cases compare different probabilistic methods within NESSUS because it is important that a user can have confidence that estimates of stochastic parameters of a response will be within an acceptable error limit. For each response, the mean, standard deviation, and 0.99 percentile, are repeatedly estimated which allows confidence statements to be made for each parameter estimated, and for each method. Thus, the ability of several stochastic methods to efficiently and accurately estimate density parameters is compared using four valid test cases. While all of the reliability methods used performed quite well, for the new LHS module within NESSUS it was found that it had a lower estimation error than MC when they were used to estimate the mean, standard deviation, and 0.99 percentile of the four different stochastic responses. Also, LHS required a smaller amount of calculations to obtain low error answers with a high amount of confidence than MC. It can therefore be stated that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ and the newest LHS module is a valuable new enhancement of the program.

Chamis, Chrisos C.↗
NASA NTRS2000

The density of apical cells of dark-grown protonemata of the moss Ceratodon purpureus

Determinations of plant or algal cell density (cell mass divided by volume) have rarely accounted for the extracellular matrix or shrinkage during isolation. Three techniques were used to indirectly estimate the density of intact apical cells from protonemata of the moss Ceratodon purpureus. First, the volume fraction of each cell component was determined by stereology, and published values for component density were used to extrapolate to the entire cell. Second, protonemal tips were immersed in bovine serum albumin solutions of different densities, and then the equilibrium density was corrected for the mass of the cell wall. Third, apical cell protoplasts were centrifuged in low-osmolarity gradients, and values were corrected for shrinkage during protoplast isolation. Values from centrifugation (1.004 to 1.015 g/cm3) were considerably lower than from other methods (1.046 to 1.085 g/cm3). This work appears to provide the first corrected estimates of the density of any plant cell. It also documents a method for the isolation of protoplasts specifically from apical cells of protonemal filaments.

NASA Discipline Plant Biology↗
NASA NTRS2004

A Plasmaspheric Mass Density Model and Constraints on its Heavy Ion Concentration

The first empirical model of the equatorial mass density of the plasmasphere is constructed using ground-based ULF wave diagnostics. Plasmaspheric mass density between L=l.7 and L=3.2 has been determined using over 5200 hours of data from pairs of stations in the MEASURE array of ground magnetometers. The least-squares fit to the data as a function of L shows that mass density falls logarithmically with L. Average ion mass as a function of L is also estimated by combining the mass density model with plasmaspheric electron density profiles determined from the IMAGE Radio Plasma Imager (RPI). Additionally, we use the RPI electron density database to examine how the average ion mass changes under different levels of geomagnetic activity. We find that average ion mass is greatest under the most disturbed conditions. This result indicates that heavy ion concentrations are enhanced during large geomagnetic disturbances, and therefore play an important role in storm-time plasmaspheric dynamics. The average ion mass is also used to constrain the concentrations of He(+) and O(+). Estimates of the He(+) concentration determined this way can be useful for interpreting IMAGE Extreme Ultraviolet Imager (EUV) images.

Berube, D.↗
NASA NTRS1995

Estimates of volumetric bone density from projectional measurements improve the discriminatory capability of dual X-ray absorptiometry

To determine whether estimates of volumetric bone density from projectional scans of the lumbar spine have weaker associations with height and weight and stronger associations with prevalent vertebral fractures than standard projectional bone mineral density (BMD) and bone mineral content (BMC), we obtained posteroanterior (PA) dual X-ray absorptiometry (DXA), lateral supine DXA (Hologic QDR 2000), and quantitative computed tomography (QCT, GE 9800 scanner) in 260 postmenopausal women enrolled in two trials of treatment for osteoporosis. In 223 women, all vertebral levels, i.e., L2-L4 in the DXA scan and L1-L3 in the QCT scan, could be evaluated. Fifty-five women were diagnosed as having at least one mild fracture (age 67.9 +/- 6.5 years) and 168 women did not have any fractures (age 62.3 +/- 6.9 years). We derived three estimates of "volumetric bone density" from PA DXA (BMAD, BMAD*, and BMD*) and three from paired PA and lateral DXA (WA BMD, WA BMDHol, and eVBMD). While PA BMC and PA BMD were significantly correlated with height (r = 0.49 and r = 0.28) or weight (r = 0.38 and r = 0.37), QCT and the volumetric bone density estimates from paired PA and lateral scans were not (r = -0.083 to r = 0.050). BMAD, BMAD*, and BMD* correlated with weight but not height. The associations with vertebral fracture were stronger for QCT (odds ratio [QR] = 3.17; 95% confidence interval [CI] = 1.90-5.27), eVBMD (OR = 2.87; CI 1.80-4.57), WA BMDHol (OR = 2.86; CI 1.80-4.55) and WA-BMD (OR = 2.77; CI 1.75-4.39) than for BMAD*/BMD* (OR = 2.03; CI 1.32-3.12), BMAD (OR = 1.68; CI 1.14-2.48), lateral BMD (OR = 1.88; CI 1.28-2.77), standard PA BMD (OR = 1.47; CI 1.02-2.13) or PA BMC (OR = 1.22; CI 0.86-1.74). The areas under the receiver operating characteristic (ROC) curves for QCT and all estimates of volumetric BMD were significantly higher compared with standard PA BMD and PA BMC. We conclude that, like QCT, estimates of volumetric bone density from paired PA and lateral scans are unaffected by height and weight and are more strongly associated with vertebral fracture than standard PA BMD or BMC, or estimates of volumetric density that are solely based on PA DXA scans.

Non-NASA Center↗
NASA NTRS1992

Age-related decrements in bone mineral density in women over 65

Age-related changes in bone density contribute to the risk of fractures. To describe the relationship between age and bone mass in elderly women, we studied a large cohort of women over age 65 years who were recruited from population-based lists in four cities in the United States. Bone density in g/cm2 was measured by single-photon absorptiometry (SPA) and dual x-ray absorptiometry (DXA) at the distal and proximal radius, the calcaneus, the lumbar spine, and the proximal femur. Centralized data collection was used to control data quality and consistency. We found a strong inverse relationship between bone density and age for most sites. Decrements in bone density between women aged 65-69 years and women 85 years and older exceeded 16% in all regions except the spine, where the difference between the two age groups was 6%. Ward's triangle and the calcaneus exhibited the largest decrements, with 26 and 21%, respectively. The estimates of annual changes in bone mineral density by linear regression at sites other than the spine ranged from -0.82% at the femoral neck and trochanter to -1.30% at Ward's triangle. Correlations between the different regions ranged from r = 0.51 between the proximal radius and Ward's triangle to r = 0.66 between the distal radius and calcaneus. We conclude that the inverse relationship between age and bone mass measured by absorptiometry techniques in white women continues into the ninth decade of life. The relationship is strongest for bone density of Ward's triangle and the calcaneus and weakest for the spine.

NASA Discipline Musculoskeletal↗
NASA NTRS2004

Automated Processing of ISIS Topside Ionograms into Electron Density Profiles

Modeling of the topside ionosphere has for the most part relied on just a few years of data from topside sounder satellites. The widely used Bent et al. (1972) model, for example, is based on only 50,000 Alouette 1 profiles. The International Reference Ionosphere (IRI) (Bilitza, 1990, 2001) uses an analytical description of the graphs and tables provided by Bent et al. (1972). The Alouette 1, 2 and ISIS 1, 2 topside sounder satellites of the sixties and seventies were ahead of their times in terms of the sheer volume of data obtained and in terms of the computer and software requirements for data analysis. As a result, only a small percentage of the collected topside ionograms was converted into electron density profiles. Recently, a NASA-funded data restoration project has undertaken and is continuing the process of digitizing the Alouette/ISIS ionograms from the analog 7-track tapes. Our project involves the automated processing of these digital ionograms into electron density profiles. The project accomplished a set of important goals that will have a major impact on understanding and modeling of the topside ionosphere: (1) The TOPside Ionogram Scaling and True height inversion (TOPIST) software was developed for the automated scaling and inversion of topside ionograms. (2) The TOPIST software was applied to the over 300,000 ISIS-2 topside ionograms that had been digitized in the fkamework of a separate AISRP project (PI: R.F. Benson). (3) The new TOPIST-produced database of global electron density profiles for the topside ionosphere were made publicly available through NASA s National Space Science Data Center (NSSDC) ftp archive at . (4) Earlier Alouette 1,2 and ISIS 1, 2 data sets of electron density profiles from manual scaling of selected sets of ionograms were converted fiom a highly-compressed binary format into a user-friendly ASCII format and made publicly available through nssdcftp.gsfc.nasa.gov. The new database for the topside ionosphere established as a result of this project, has stimulated a multitude of new studies directed towards a better description and prediction of the topside ionosphere. Marinov et al. (2004) developed a new model for the upper ion transition height (Oxygen to Hydrogen and Helium) and Bilitza (2004) deduced a correction term for the I N topside electron density model. Kutiev et al. (2005) used this data to develop a new model for the topside ionosphere scale height (TISH) as a function of month, local time, latitude, longitude and solar flux F10.7. Comparisons by Belehaki et al. (2005) show that TISH is in general agreement with scale heights deduced from ground ionosondes but the model predicts post-midnight and afternoon maxima whereas the ionosonde data show a noon maximum. Webb and Benson (2005) reported on their effort to deduce changes in the plasma temperature and ion composition from changes in the topside electron density profile as recorded by topside sounders. Limitations and possible improvements of the IRI topside model were discussed by Coisson et al. (2005) including also the possible use of the NeQuick model, Our project progressed in close collaboration and coordination with the GSFC team involved in the ISIS digitization effort. The digitization project was highly successful producing a large amount of digital topside ionograms. Several no-cost extensions of the TOPIST project were necessary to keep up with the pace and volume of the digitization effort.

Reinisch, bodo W.↗
NASA NTRS2004

Progress in High Power Density SOFC Material Development for Aerospace Applications

Solid oxide fuel cell (SOFC) systems for aircraft applications require order of magnitude increase in specific power density and long life under aircraft operating conditions. Advanced SOFC materials and fabrication processes are being developed at NASA GRC to increase specific power density and durability of SOFC cell and stack. Initial research efforts for increasing specific power density are directed toward increasing the operating temperature for the SOFC system and reducing the weight of the stack. While significant research is underway to develop anode supported SOFC system operating at temperatures in the range of 650 - 850 C for ground power generation applications, such temperatures may not yield the power densities required for aircraft applications. For electrode-supported cells, SOFC stacks with power densities greater than 1.0 W/sq cm are favorable at temperatures in excess of 900 C. The performance of various commercial and developmental anode supported cells is currently being evaluated in the temperature range of 900 to 1000 C to assess the performance gains and materials reliability. The results from these studies will be presented. Since metal interconnects developed for lower temperature operation are not practical at these high temperatures, advanced perovskite based ceramic interconnects with high electronic conductivity and lower sintering temperatures are being developed. Another option for increasing specific power density of SOFC stacks is to decrease the stack weight. Since the interconnect contributes to a significant portion of the stack weight, considerable weight benefits can be derived by decreasing its thickness. Eliminating the gas channels in the interconnect by engineering the pore structure in both anode and cathode can offer significant reduction in thickness of the ceramic interconnect material. New solid oxide fuel cells are being developed with porous engineered electrode supported structures with a 10 - 20 micron thin electrolyte. The performance data for advanced SOFC cells with engineered porosity in both electrodes will be presented.

Cable, Thomas L.↗
NASA NTRS2010

Modeling Neutral Densities Downstream of a Gridded Ion Thruster

The details of a model for determining the neutral density downstream of a gridded ion thruster are presented. An investigation of the possible sources of neutrals emanating from and surrounding a NEXT ion thruster determined that the most significant contributors to the downstream neutral density include discharge chamber neutrals escaping through the perforated grids, neutrals escaping from the neutralizer, and vacuum facility background neutrals. For the neutral flux through the grids, near- and far-field equations are presented for rigorously determining the neutral density downstream of a cylindrical aperture. These equations are integrated into a spherically-domed convex grid geometry with a hexagonal array of apertures for determining neutral densities downstream of the ion thruster grids. The neutrals escaping from an off-center neutralizer are also modeled assuming diffuse neutral emission from the neutralizer keeper orifice. Finally, the effect of the surrounding vacuum facility neutrals is included and assumed to be constant. The model is used to predict the neutral density downstream of a NEXT ion thruster with and without neutralizer flow and a vacuum facility background pressure. The impacts of past simplifying assumptions for predicting downstream neutral densities are also examined for a NEXT ion thruster.

Soulas, George C.↗
NASA NTRS2010

Persistent Longitudinal Variations of Plasma Density and DC Electric Fields in the Low Latitude Ionosphere Observed with Probes on the C/NOFS Satellite

Continuous measurements using in situ probes on consecutive orbits of the C/N0FS satellite reveal that the plasma density is persistently organized by longitude, in both day and night conditions and at all locations within the satellite orbit, defined by its perigee and apogee of 401 km and 867 km, respectively, and its inclination of 13 degrees. Typical variations are a factor of 2 or 3 compared to mean values. Furthermore, simultaneous observations of DC electric fields and their associated E x B drifts in the low latitude ionosphere also reveal that their amplitudes are also strongly organized by longitude in a similar fashion. The drift variations with longitude are particularly pronounced in the meridional component perpendicular to the magnetic field although they are also present in the zonal component as well. The longitudes of the peak meridional drift and density values are significantly out of phase with respect to each other. Time constants for the plasma accumulation at higher altitudes with respect to the vertical drift velocity must be taken into account in order to properly interpret the detailed comparisons of the phase relationship of the plasma density and plasma velocity variations. Although for a given period corresponding to that of several days, typically one longitude region dominates the structuring of the plasma density and plasma drift data, there is also evidence for variations organized about multiple longitudes at the same time. Statistical averages will be shown that suggest a tidal "wave 4" structuring is present in both the plasma drift and plasma density data. We interpret the apparent association of the modulation of the E x B drifts with longitude as well as that of the ambient plasma density as a manifestation of tidal forces at work in the low latitude upper atmosphere. The observations demonstrate how the high duty cycle of the C/NOFS observations and its unique orbit expose fundamental processes at work in the low latitude, inner regions of geospace.

Pfaff, R.↗
NASA NTRS2011

Propulsion Physics Using the Chameleon Density Model

To grow as a space faring race, future spaceflight systems will require a new theory of propulsion. Specifically one that does not require mass ejection without limiting the high thrust necessary to accelerate within or beyond our solar system and return within a normal work period or lifetime. The Chameleon Density Model (CDM) is one such model that could provide new paths in propulsion toward this end. The CDM is based on Chameleon Cosmology a dark matter theory; introduced by Khrouy and Weltman in 2004. Chameleon as it is hidden within known physics, where the Chameleon field represents a scalar field within and about an object; even in the vacuum. The CDM relates to density changes in the Chameleon field, where the density changes are related to matter accelerations within and about an object. These density changes in turn change how an object couples to its environment. Whereby, thrust is achieved by causing a differential in the environmental coupling about an object. As a demonstration to show that the CDM fits within known propulsion physics, this paper uses the model to estimate the thrust from a solid rocket motor. Under the CDM, a solid rocket constitutes a two body system, i.e., the changing density of the rocket and the changing density in the nozzle arising from the accelerated mass. Whereby, the interactions between these systems cause a differential coupling to the local gravity environment of the earth. It is shown that the resulting differential in coupling produces a calculated value for the thrust near equivalent to the conventional thrust model used in Sutton and Ross, Rocket Propulsion Elements. Even though imbedded in the equations are the Universe energy scale factor, the reduced Planck mass and the Planck length, which relates the large Universe scale to the subatomic scale.

Robertson, Glen A.↗
NASA NTRS2004

Force Density Function Relationships in 2-D Granular Media

An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms

Youngquist, Robert C.↗
NASA NTRS2014

Effects of High-Density Impacts on Shielding Capability

Spacecraft are shielded from micrometeoroids and orbital debris (MMOD) impacts to meet requirements for crew safety and/or mission success. In the past, orbital debris particles have been considered to be composed entirely of aluminum (medium-density material) for the purposes of MMOD shielding design and verification. Meteoroids have been considered to be low-density porous materials, with an average density of 1 g/cu cm. Recently, NASA released a new orbital debris environment model, referred to as ORDEM 3.0, that indicates orbital debris contains a substantial fraction of high-density material for which steel is used in MMOD risk assessments [Ref.1]. Similarly, an update to the meteoroid environment model is also under consideration to include a high-density component of that environment. This paper provides results of hypervelocity impact tests and hydrocode simulations on typical spacecraft MMOD shields using steel projectiles. It was found that previous ballistic limit equations (BLEs) that define the protection capability of the MMOD shields did not predict the results from the steel impact tests and hydrocode simulations (typically, the predictions from these equations were too optimistic). The ballistic limit equations required updates to more accurately represent shield protection capability from the range of densities in the orbital debris environment. Ballistic limit equations were derived from the results of the work and are provided in the paper.

Christiansen, Eric L.↗
NASA NTRS2014

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.

corona↗
NASA NTRS2010

Estimation and Modeling of Enceladus Plume Jet Density Using Reaction Wheel Control Data

The Cassini spacecraft was launched on October 15, 1997 by a Titan 4B launch vehicle. After an interplanetary cruise of almost seven years, it arrived at Saturn on June 30, 2004. In 2005, Cassini completed three flybys of Enceladus, a small, icy satellite of Saturn. Observations made during these flybys confirmed the existence of a water vapor plume in the south polar region of Enceladus. Five additional low-altitude flybys of Enceladus were successfully executed in 2008-9 to better characterize these watery plumes. The first of these flybys was the 50-km Enceladus-3 (E3) flyby executed on March 12, 2008. During the E3 flyby, the spacecraft attitude was controlled by a set of three reaction wheels. During the flyby, multiple plume jets imparted disturbance torque on the spacecraft resulting in small but visible attitude control errors. Using the known and unique transfer function between the disturbance torque and the attitude control error, the collected attitude control error telemetry could be used to estimate the disturbance torque. The effectiveness of this methodology is confirmed using the E3 telemetry data. Given good estimates of spacecraft's projected area, center of pressure location, and spacecraft velocity, the time history of the Enceladus plume density is reconstructed accordingly. The 1 sigma uncertainty of the estimated density is 7.7%. Next, we modeled the density due to each plume jet as a function of both the radial and angular distances of the spacecraft from the plume source. We also conjecture that the total plume density experienced by the spacecraft is the sum of the component plume densities. By comparing the time history of the reconstructed E3 plume density with that predicted by the plume model, values of the plume model parameters are determined. Results obtained are compared with those determined by other Cassini science instruments.

Lee, Allan Y.↗
NASA NTRS2010

Estimation and Modeling of Enceladus Plume Jet Density Using Reaction Wheel Control Data

The Cassini spacecraft was launched on October 15, 1997 by a Titan 4B launch vehicle. After an interplanetary cruise of almost seven years, it arrived at Saturn on June 30, 2004. In 2005, Cassini completed three flybys of Enceladus, a small, icy satellite of Saturn. Observations made during these flybys confirmed the existence of a water vapor plume in the south polar region of Enceladus. Five additional low-altitude flybys of Enceladus were successfully executed in 2008-9 to better characterize these watery plumes. The first of these flybys was the 50-km Enceladus-3 (E3) flyby executed on March 12, 2008. During the E3 flyby, the spacecraft attitude was controlled by a set of three reaction wheels. During the flyby, multiple plume jets imparted disturbance torque on the spacecraft resulting in small but visible attitude control errors. Using the known and unique transfer function between the disturbance torque and the attitude control error, the collected attitude control error telemetry could be used to estimate the disturbance torque. The effectiveness of this methodology is confirmed using the E3 telemetry data. Given good estimates of spacecraft's projected area, center of pressure location, and spacecraft velocity, the time history of the Enceladus plume density is reconstructed accordingly. The 1-sigma uncertainty of the estimated density is 7.7%. Next, we modeled the density due to each plume jet as a function of both the radial and angular distances of the spacecraft from the plume source. We also conjecture that the total plume density experienced by the spacecraft is the sum of the component plume densities. By comparing the time history of the reconstructed E3 plume density with that predicted by the plume model, values of the plume model parameters are determined. Results obtained are compared with those determined by other Cassini science instruments.

Lee, Allan Y.↗
NASA NTRS2017

The Velocity and Density Distribution of Earth-Intersecting Meteoroids: Implications for Environment Models

Meteoroids are known to damage spacecraft: they can crater or puncture components, disturb a spacecraft's attitude, and potentially create secondary electrical effects. Because the damage done depends on the speed, size, density, and direction of the impactor, accurate environment models are critical for mitigating meteoroid-related risks. Yet because meteoroid properties are derived from indirect observations such as meteors and impact craters, many characteristics of the meteoroid environment are uncertain. In this work, we present recent improvements to the meteoroid speed and density distributions. Our speed distribution is derived from observations made by the Canadian Meteor Orbit Radar. These observations are de-biased using modern descriptions of the ionization efficiency. Our approach yields a slower meteoroid population than previous analyses (see Fig. 1 for an example) and we compute the uncertainties associated with our derived distribution. We adopt a higher fidelity density distribution than that used by many older models. In our distribution, meteoroids with TJ less than 2 are assigned to a low-density population, while those with TJ greater than 2 have higher densities (see Fig. 2). This division and the distributions themselves are derived from the densities reported by Kikwaya et al. These changes have implications for the environment: for instance, the helion/antihelion sporadic sources have lower speeds than the apex and toroidal sources and originate from high-T(sub J) parent bodies. Our on-average slower and denser distributions thus imply that the helion and antihelion sources dominate the meteoroid environment even more completely than previously thought. Finally, for a given near-Earth meteoroid cratering rate, a slower meteoroid population produces a comparatively higher rate of satellite attitude disturbances.

Moorhead, A. V.↗
NASA NTRS2019

Modeling Meteoroid Densities for Spacecraft Risk Assessment

This report describes the methodologies and algorithms that NASA’s Meteoroid Environment Office (MEO) currently utilizes to measure meteoroid densities. We discuss the needs for an accurate model for the meteoroid density distribution in its Meteoroid Engineering Model (MEM), and its potential implications for spacecraft design. The recently developed process is heavily derived from that of previous work, although subtle differences exist. A thorough comparison of the best-fit densities derived for sixty meteoroids in and with the process described here shows that discrepancies in final densities larger than a factor of two are measured for ∼ 20% of our test events. Such a level of discrepancy suggests that any density calculated using similar methods cannot be assumed to represent a unique fit to the data. Additional observational data for meteoroids beyond those utilized in this work will be essential for producing more reliable and repeatable density measurements.

Ehlert, Steven↗
NASA NTRS2021

Modeling the Effects of Liquid-to-Gas Density Ratio on Slosh Dynamics

Mechanical models are commonly used in Guidance, Navigation and Controls (GN&C) system-level models to represent propellant slosh forces on launch vehicles and spacecraft. The slosh model parameters are typically predicted using semi-empirical analytical methods that are based on experimental data for high liquid-to-gas density ratios (such as water and air at standard sea level conditions). Model parameter calculations typically neglect any contribution to slosh dynamics from the gas phase. However, some cryogenic propellant systems operate in conditions where the density ratio can be orders of magnitude smaller. Analytical and computational modeling was used in this effort to investigate the effects of liquid-to-gas density ratio on slosh dynamics. No experimental data nor previous studies are available at this time that quantify the effect of liquid-to-gas density ratio on slosh dynamics. However, in a recent CFD study, results showed that density ratio can have a significant effect on slosh model parameters. In this study, a dual pendulum slosh model was created that distinctly represents both liquid and gas phase dynamics. Solution of the model, which invokes the Euler-Lagrange equations of motion, demonstrates that slosh frequency is a combination of liquid slosh frequency and gas phase slosh frequency. Additionally, it shows that slosh mass is reduced due to the opposing motion of the gas phase with respect to that of the liquid phase. The slosh model parameter trends were verified using Computational Fluid Dynamics (CFD) analysis results for various liquid-to-gas density ratios, tanks, and fill levels.

Christopher D Moore↗