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NASA NTRS2014

Upgrade of the NASA 4STAR (Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research) to its Full Science Capability of Sun-Sky-Cloud-Trace Gas Spectrometry in Airborne Science Deployments

The objectives of this task in the AITT (Airborne Instrument Technology Transition) Program are to (1) upgrade the NASA 4STAR (Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research) instrument to its full science capability of measuring (a) direct-beam sun transmission to derive aerosol optical depth spectra, (b) sky radiance vs scattering angle to retrieve aerosol absorption and type (via complex refractive index spectra, shape, and mode-resolved size distribution), (c) zenith radiance for cloud properties, and (d) hyperspectral signals for trace gas retrievals, and (2) demonstrate its suitability for deployment in challenging NASA airborne multiinstrument campaigns. 4STAR combines airborne sun tracking, sky scanning, and zenith pointing with diffraction spectroscopy to improve knowledge of atmospheric constituents and their links to air pollution, radiant energy budgets (hence climate), and remote measurements of Earth's surfaces. Direct beam hyperspectral measurement of optical depth improves retrievals of gas constituents and determination of aerosol properties. Sky scanning enhances retrievals of aerosol type and size distribution. 4STAR measurements are intended to tighten the closure between satellite and ground-based measurements. 4STAR incorporates a modular sun-tracking/sky-scanning optical head with fiber optic signal transmission to rack mounted spectrometers, permitting miniaturization of the external optical head, and future detector evolution. 4STAR test flights, as well as science flights in the 2012-13 TCAP (Two-Column Aerosol Project) and 2013 SEAC4RS (Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys) have demonstrated that the following are essential for 4STAR to achieve its full science potential: (1) Calibration stability for both direct-beam irradiance and sky radiance, (2) Improved light collection and usage, and (3) Improved flight operability and reliability. A particular challenge for the AITT-4STAR project has been conducting it simultaneously with preparations for, and execution of, ARISE (Arctic Radiation - IceBridge Sea&Ice Experiment), a NASA airborne science deployment (unplanned when AITT-4STAR was selected for funding) in which 4STAR will deploy to Thule, Greenland, and Fairbanks, Alaska, on the NASA C- 130. This presentation describes progress to date in accomplishing AITT-4STAR goals, and plans for project completion.

Sun-Sky-Cloud-Trace↗
NASA NTRS2019

Informing Algorithms from Ground Validation: The GPM Combined Algorithm

Ground validation (GV) for the Global Precipitation Measurement (GPM) mission encompasses in-situ (e.g., gauge, disdrometer) measurements, ground radar products, and comprehensive datasets from dedicated airborne field campaigns. These datasets are used for direct validation of the precipitation products from GPM as well as to inform assumptions used by the algorithms that produce these products. This presentation will focus on current and potential such uses of GV data in the GPM combined radar-radiometer algorithm.The GPM combined algorithm, by virtue of using data from the Dual-frequency Precipitation Radar (DPR) and GPM Microwave Imager (GMI), is the most well-constrained instantaneous precipitation product from GPM. It also plays an important in role the passive microwave algorithms as a basis for the construction of brightness temperature-precipitation profile databases and is a calibrator for the multi- satellite gridded product IMERG. Since both radar and radiometer data are used as observational inputs, and even with these data the retrievals are underconstrained, microphysical properties of the hydrometeor profile that are relevant over the range of GMI and DPR wavelengths and incidence angles need to be assumed by the algorithm forward models. Such properties include the normalized intercept parameter (N w ) and shape parameter () of the particle size distribution, ice size-density relationship, and particle size-aspect ratio relationships. The sub-beam variability must also be prescribed in order to accurately simulate the observed radar reflectivity profiles without introducing significant biases. The sensitivity of the algorithm to these parameters, along with their mean values and variability, will be discussed. Examples of future directions include refinement with new data (particularly the assumptions related to ice), and seeking relationships between assumptions and observable or environmental data.

Munchak, Joe.↗
NASA NTRS1972

The process of crater removal in the lunar maria, part P

Near-terminator photography from the Apollo 14 and 15 missions is used as a basis to evaluate the processes by which craters disappear from the lunar surface. From observations and analyses it is concluded that: (1) The erosion of lunar craters in the size range of 10 m to 1 km is effected principally by small impacts producing minute changes in crater form up to the point where the crater is worn to an interior slope of approximately 1 degree. Below that slope, the annihilation process is dominated by the formation of younger overlapping craters. (2) The distribution of shapes of craters in this size range can be explained as resulting from impact generated processes.

Soderblom, L. A.↗
NASA NTRS1988

Contraction design for small low-speed wind tunnels

An iterative design procedure was developed for 2- or 3-dimensional contractions installed on small, low speed wind tunnels. The procedure consists of first computing the potential flow field and hence the pressure distributions along the walls of a contraction of given size and shape using a 3-dimensional numerical panel method. The pressure or velocity distributions are then fed into 2-dimensional boundary layer codes to predict the behavior of the boundary layers along the walls. For small, low speed contractions, it is shown that the assumption of a laminar boundary layer originating from stagnation conditions at the contraction entry and remaining laminar throughout passage through the successful designs is justified. This hypothesis was confirmed by comparing the predicted boundary layer data at the contraction exit with measured data in existing wind tunnels. The measured boundary layer momentum thicknesses at the exit of four existing contractions, two of which were 3-D, were found to lie within 10 percent of the predicted values, with the predicted values generally lower. From the contraction wall shapes investigated, the one based on a 5th order polynomial was selected for newly designed mixing wind tunnel installation.

Bell, James H.↗
NASA NTRS2012

Detection Thresholds of Falling Snow from Satellite-Borne Active and Passive Sensors

Precipitation, including rain and snow, is a critical part of the Earth's energy and hydrology cycles. Precipitation impacts latent heating profiles locally while global circulation patterns distribute precipitation and energy from the equator to the poles. For the hydrological cycle, falling snow is a primary contributor in northern latitudes during the winter seasons. Falling snow is the source of snow pack accumulations that provide fresh water resources for many communities in the world. Furthermore, falling snow impacts society by causing transportation disruptions during severe snow events. In order to collect information on the complete global precipitation cycle, both liquid and frozen precipitation must be collected. The challenges of estimating falling snow from space still exist though progress is being made. These challenges include weak falling snow signatures with respect to background (surface, water vapor) signatures for passive sensors over land surfaces, unknowns about the spherical and non-spherical shapes of the snowflakes, their particle size distributions (PSDs) and how the assumptions about the unknowns impact observed brightness temperatures or radar reflectivities, differences in near surface snowfall and total column snow amounts, and limited ground truth to validate against. While these challenges remain, knowledge of their impact on expected retrieval results is an important key for understanding falling snow retrieval estimations. Since falling snow from space is the next precipitation measurement challenge from space, information must be determined in order to guide retrieval algorithm development for these current and future missions. This information includes thresholds of detection for various sensor channel configurations, snow event system characteristics, snowflake particle assumptions, and surface types. For example, can a lake effect snow system with low (approx 2.5 km) cloud tops having an ice water content (IWC) at the surface of 0.25 g / cubic m and dendrite snowflakes be detected? If this information is known, we can focus retrieval efforts on detectable storms and concentrate advances on achievable results. Here, the focus is to determine thresholds of detection for falling snow for various snow conditions over land and lake surfaces. The results rely on simulated Weather Research Forecasting (WRF) simulations of falling snow cases since simulations provide all the information to determine the measurements from space and the ground truth. Sensitivity analyses were performed to better ascertain the relationships between multifrequency microwave and millimeter-wave sensor observations and the falling snow/underlying field of view. In addition, thresholds of detection for various sensor channel configurations, snow event system characteristics, snowflake particle assumptions, and surface types were studied. Results will be presented for active radar at Ku, Ka, and W-band and for passive radiometer channels from 10 to 183 GHz.

Gail Skofronick-Jackson↗
NASA NTRS2018

Net Radiative Effects of Dust in the Tropical North Atlantic Based on Integrated Satellite Observations and in Situ Measurements

In this study, we integrate recent in situ measurements with satellite retrievals of dust physical and radiative properties to quantify dust direct radiative effects on shortwave (SW) and longwave (LW) radiation (denoted as DRESW and DRELW, respectively) in the tropical North Atlantic during the summer months from 2007 to 2010. Through linear regression of the CERES-measured top-of atmosphere (TOA) flux versus satellite aerosol optical depth (AOD) retrievals, we estimate the instantaneous DRESW efficiency at the TOA to be -49+/-7.1 W/sq.m AOD(exp -1) and -36+/-4:8W/sq.m AOD(exp -1) based on AOD from MODIS and CALIOP, respectively. We then perform various sensitivity studies based on recent measurements of dust particle size distribution (PSD), refractive index, and particle shape distribution to determine how the dust microphysical and optical properties affect DRE estimates and its agreement with the above-mentioned satellite-derived DREs. Our analysis shows that a good agreement with the observation-based estimates of instantaneous DRESW and DRELW can be achieved through a combination of recently observed PSD with substantial presence of coarse particles, a less absorptive SW refractive index, and spheroid shapes. Based on this optimal combination of dust physical properties we further estimate the diurnal mean dust DRE(sub SW) in the region of -10W/sq.m at TOA and -26W/sq.m at the surface, respectively, of which ~30% is canceled out by the positive DRE(sub LW). This yields a net DRE of about -6:9 and -18.3 W/sq.m at TOA and the surface, respectively. Our study suggests that the LW flux contains useful information on dust particle size, which could be used together with SW observations to achieve a more holistic understanding of the dust radiative effect.

Song, Qianqian↗
NASA NTRS1989

Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space.

Henning, TH.↗
NASA NTRS1988

Contraction design for small low-speed wind tunnels

An iterative design procedure was developed for two- or three-dimensional contractions installed on small, low-speed wind tunnels. The procedure consists of first computing the potential flow field and hence the pressure distributions along the walls of a contraction of given size and shape using a three-dimensional numerical panel method. The pressure or velocity distributions are then fed into two-dimensional boundary layer codes to predict the behavior of the boundary layers along the walls. For small, low-speed contractions it is shown that the assumption of a laminar boundary layer originating from stagnation conditions at the contraction entry and remaining laminar throughout passage through the successful designs if justified. This hypothesis was confirmed by comparing the predicted boundary layer data at the contraction exit with measured data in existing wind tunnels. The measured boundary layer momentum thicknesses at the exit of four existing contractions, two of which were 3-D, were found to lie within 10 percent of the predicted values, with the predicted values generally lower. From the contraction wall shapes investigated, the one based on a fifth-order polynomial was selected for installation on a newly designed mixing layer wind tunnel.

Bell, James H.↗
NASA NTRS2002

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗
NASA NTRS2003

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗
NASA NTRS1982

Selection of USSR foreign similarity regions

The similarity regions in the United States and Canada were selected to parallel the conditions that affect labeling and classification accuracies in the U.S.S.R. indicator regions. In addition to climate, a significant condition that affects labeling and classification accuracies in the U.S.S.R. is the proportion of barley and wheat grown in a given region (based on sown areas). The following regions in the United States and Canada were determined to be similar to the U.S.S.R. indicator regions: (1) Montana agrophysical unit (APU) 104 corresponds to the Belorussia high barley region; (2) North Dakota and Minnesota APU 20 and secondary region southern Manitoba and Saskatchewan correspond to the Ural RSFSR barley and spring wheat region; (3) Montana APU 23 corresponds to he North Caucasus barley and winter wheat region. Selection criteria included climates, crop type, crop distribution, growth cycles, field sizes, and field shapes.

Disler, J. M.↗
NASA NTRS1990

Constraints on early events in Martian history as derived from the cratering record

Constrains on early events in Martian history are derived using the planet's cratering record. Variations in the shapes of the crater size-frequency distribution curves are interpreted as indicative of the size-frequency distribution of the production populations, thus providing information about the age of the unit relative to the end of the heavy bombardment period. Results from the analysis of craters superposed on heavily cratered units across the Martian surface provide constraints on the hemispheric dichotomy and the early erosional conditions on Mars.

Barlow, Nadine G.↗
NASA NTRS1982

Macrostructure and microphysics of Saturn's E-ring

Observed optical and infrared properties of Saturn's E-ring are explained in terms of Mie scattering by a narrow distribution of ice spheres with an effective diameter of 2 to 2.5 microns, and an effective variance of 0.1 to 0.15. The spherical shape of the ring particles and their narrow size distribution imply that they had a molten origin, followed by quick freezing. Continued replenishment of the E-ring by volcanic eruptions on Enceladus seems plausible. The vertical structure of the E-ring consists of many layers. The stratification of the particles may be due to electrostatic levitation, similar to that experienced by particles in the spokes.

Pang, K. D.↗
NASA NTRS1991

Urban light pollution - The effect of atmospheric aerosols on astronomical observations at night

The transfer of diffuse city light from a localized source through a dust-laden atmosphere with optical depth less than 0.5 has been analyzed in the source-observer plane on the basis of an approximate treatment. The effect on several types of astronomical observation at night has been studied, considering different size distributions and amounts as well as particle shapes of the aerosols. The analysis is made in terms of the signal-to-noise ratios for a given amount of aerosol. The model is applied to conditions at the Wise Astronomical Observatory in the Negev desert, and limiting backgrounds for spectroscopy, photometry, and photography of stars and extended objects have been calculated for a variety of signal-to-noise ratios. Applications to observations with different equipment at various distances from an urban area of any size are possible. Due to the use of signal-to-noise ratios, the conclusions are different for the different experimental techniques used in astronomy.

Joseph, Joachim H.↗
NASA NTRS2000

What we Hope to Learn about Global Mineral Dust Aerosols from EOS Multi-Angle Imaging SpectroRadiometer (MISR)

On global scales, just a few broad atmospheric aerosol compositional groups are commonly observed. Of these, "mineral dust" is the only group which both contains non-spherical particles, and typically has size distributions with enough large particles for particle shape to affect its visible-light-scattering properties. The MISR instrument is scheduled for launch into a 10:30 AM sun-synchronous, polar orbit aboard the EOS Terra satellite in 1999. MISR will measure the upwelling visible radiance from Earth in 4 spectral bands centered at 446, 558, 672, and 866 nm, at each of 9 emission angles spread out in the forward and aft directions along the flight path at +/-70.5 deg, +/-60.0 deg, +/-45.6 deg, +/-26.1deg, and nadir. Over a period of 7 minutes, as the spacecraft flies along, a 360 km wide swath of Earth will successively be viewed by each of the cameras, allowing MISR to sample a very large range of scattering angles; in mid latitudes, the instrument will observe scattering angles between about 60 deg and 160 deg. Global coverage will be acquired about once in 9 days at the equator; the nominal mission lifetime is 6 years. The distinction in single scattering phase function between natural distributions of spherical and randomly oriented, non-spherical particles, with a broad range of aspect ratios, shows up strongly for scattering angles ranging from about 90 deg to near 180 deg. For non-spherical particle distributions, single scattering phase functions tend to be much flatter in this region than for spherical particles. Since MISR samples the relevant range of scattering angles very well, we expect to be able to make critical distinctions between natural distributions of spherical and randomly oriented, non-spherical particles with MISR data. We anticipate that the new multiangle, multispectral data from MISR will also contain other information about particle properties, a major step beyond current spacecraft remote sensing retrievals, which obtain aerosol optical depth based on entirely assumed particle microphysical properties. According to simulations over cloud-free, calm ocean, for pure particles with natural ranges of optical depth, particle size, and indices of refraction, MISR should retrieve column optical depth for all but the darkest particles, to an uncertainty of at most 0.05 or 20%, whichever is larger, even if the particle properties are poorly known. For one common particle type, soot, constraints on the optical depth over dark ocean are very poor. The simulated measurements also should allow us to separate two to four compositional groups based on indices of refraction, and to identify three to four distinct size groups between 0.1 and 2.0 microns characteristic radius at most latitudes. The technique is most sensitive to particle microphysical properties in the "accumulation mode" sizes. where particle scattering undergoes the transition from Rayleigh to large-particle regimes for the MISR wavelengths. Based on these results, we expect to distinguish air masses containing different aerosol types, routinely and globally, with multiangle remote sensing data. Such data complements in situ and field data, which can provide details about aerosol size and composition locally that are needed to assess the radiative effects of aerosols quantitatively. Both field data and correlations in space and time with likely source and sink regions will also be helpful in developing a global picture of mineral dust aerosol budgets. Further work on the expected sensitivity of MISR to natural mixtures of pure particles, including climatologically likely mineral dust components, is currently underway.

Kahn, Ralph↗
NASA NTRS1987

Subcentimeter-size particle distribution functions in planetary rings from Voyager radio and photopolarimeter occultation data

Analysis of measurements of the scattered and direct components of Voyager 1 radio occultation signals at 3.5 and 13 cm wavelengths yield estimates of the distribution functions of supracentimeter-size particles and thickness of relatively broad regions in Saturn's rings. If mearurements of signal amplitude at a shorter wavelength are combined with the previously analyzed data, the shape of the distribution functions characterizing the smaller particles can be constrained. If size distributions of arbitrary form were considered, many solutions are found that are consistent with the three available observations of signal amplitude. The best-fit power law was calculated to the three observations at three wavelengths for several of the embedded Saturn ringlets. Mie scattering theory predicts that the measured phase of the radio occultation signal is highly sensitive to particles ranging from 0.1 to 1.0 wavelengths in size, thus additional constraints on the subcentimeter-size distribution functions for both the Saturn and Uranus rings can in principle be derived from radio phase measurements.

Zebker, Howard A.↗
NASA NTRS1997

Structure of potato tubers formed during spaceflight

Potato (Solanum tuberosum L. cv. Norland) explants, consisting of a leaf, axillary bud, and small stem segment, were used as a model system to study the influence of spaceflight on the formation of sessile tubers from axillary buds. The explants were flown on the space shuttle Columbia (STS-73, 20 October to 5 November 1995) in the ASTROCULTURE (TM) flight package, which provided a controlled environment for plant growth. Light and scanning electron microscopy were used to compare the precisely ordered tissues of tubers formed on Earth with those formed during spaceflight. The structure of tubers produced during spaceflight was similar to that of tubers produced in a control experiment. The size and shape of tubers, the geometry of tuber tissues, and the distribution of starch grains and proteinaceous crystals were comparable in tubers formed in both environments. The shape, surface texture, and size range of starch grains from both environments were similar, but a greater percentage of smaller starch grains formed in spaceflight than on Earth. Since explant leaves must be of given developmental age before tubers form, instructions regarding the regular shape and ordered tissue geometry of tubers may have been provided in the presence of gravity. Regardless of when the signalling occurred, gravity was not required to produce a tuber of typical structure.

manned↗
NASA NTRS1979

Computer design synthesis of a below knee-Syme prosthesis

A detailed design synthesis analysis of the BK Syme prosthesis is provided, to determine the socket's cutout orientation size and shape, cutout fillet shape, socket wall thickness distribution and the reinforced fiber distribution in the socket wall, for a minimally stressed structurally safe lightweight prosthesis. For analysis purposes, the most adverse socket loading is obtained at the push-off stage of gait; this loading is idealized as an axial in-plane loading on the bottom edge of the circular cylindrical socket shell whose top edge is considered fixed. Finite element stress analysis of the socket shell (with uniform and graded wall thickness) are performed for various orientations of the cutout and for various types of corner fillets. A lateral cutout with a streamline fillet is recommended. The wall material (i.e., thickness) distribution is determined so as to minimize the stresses, while ensuring that the wall material's stress limits are not exceeded. For such a maximally stressed lightweight socket shell, the panels in the neighborhood of the cutout are checked to ensure that they do not buckle under their acquired stresses. A fiber-reinforced laminated composite socket shell is also analyzed in order to recommend optimum variables in orientations and densities of reinforcing fibers.

Elangovan, P. T.↗