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At least 343 records · Page 19

Mapping Aerosol Lidar Ratios Over Ocean Using Constrained Retrievals and A Global Aerosol Model

The current NASA Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) algorithms assign one lidar ratio (i.e., extinction-to-backscatter ratio; LR) value globally for each of the seven tropospheric aerosol types. In a future data products release, the CALIPSO project aims to improve these algorithms through the development of regional and seasonal LR climatologies. In this work, aerosol LRs are inferred through Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) backscatter profiles constrained by collocated aerosol optical depth (AOD) from Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) data. This analysis is subsampled for those profiles that are cloud-free and contain only one CALIOP-classified aerosol type (e.g., marine). The CALIOP profiles are then collocated with aerosol volume fractions obtained through Goddard Chemistry Aerosol Radiation and Transport (GOCART) model simulations. In this presentation, we show that the twelve-year (June 2006-August 2018) mean spatial distributions of inferred aerosol LRs for CALIOP-classified marine aerosols correspond inversely with patterns of GOCART sea salt volume fraction (SSVF). For example, smaller SSVFs (< 65%) and larger LRs (> 55 sr), are found near land masses. This is indicative of the influence of over-land aerosols (e.g., pollution and biomass burning smoke). In the remote oceans (i.e., regions likely less impacted by non-sea salt aerosols), larger SSVFs (> 95%) and smaller LRs (< 25 sr) are found. The developed relationship between the GOCART SSVFs and MODIS AOD constrained LRs (polynomial fit intersect values of ~56 sr for SSVF of 0% and ~21 sr for SSVF of 100%) is used to produce model-assisted climatological LR maps on seasonal scales. Additionally, we show maps of inferred LRs from constrained retrievals using the CALIPSO Ocean Derived Column Optical Depth (ODCOD) product and comparisons with those from the MODIS analyses. The technique demonstrated in this study not only benefits CALIPSO in the near-term, but similar methods can be applied to future spaceborne elastic backscatter lidars with collocated passive sensors, such as those associated with the upcoming NASA Atmosphere Observing System (AOS).

Travis Toth↗

Mapping Aerosol Lidar Ratios Over Ocean for CALIPSO Using Modis AOD-Constrained Retrievals and A Global Aerosol Model

The CALIPSO aerosol algorithms currently assign one lidar ratio value for each of the seven tropospheric aerosol types. In a future data products release, the CALIPSO project aims to improve these algorithms by developing regional and seasonal lidar ratio climatologies. In this study, aerosol lidar ratios are inferred through Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) backscatter profiles constrained by collocated aerosol optical depth from Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) datasets. The analysis is subsampled for only those profiles that are cloud-free and contain one aerosol type (based on CALIOP feature classification). In addition, the CALIOP profiles are collocated with aerosol volume fractions simulated by the Goddard Chemistry Aerosol Radiation and Transport (GOCART) model. In this talk, the twelve-year (2006-2017) mean spatial distributions of inferred aerosol lidar ratios for CALIOP-classified marine aerosols and the corresponding modeled sea salt volume fractions (SSVF) will be shown. Model-assisted climatological lidar ratio maps on a seasonal scale will also be presented, developed from the empirical relationship found between the modeled SSVF and lidar ratios. A comparison with past studies will be provided as well as results of a sensitivity study regarding the variability of retrieved lidar ratios as a function of horizontal averaging resolution. While the majority of this talk will focus on lidar ratios for CALIOP-classified marine aerosols, preliminary results will be shown for other aerosol types over ocean, such as dust and elevated smoke.

Travis Toth↗

Airborne Lidar Measurements of Ozone and Aerosol Profiles Over Major US Metropolitan Areas

During field missions in 2021 and 2023, the airborne NASA Langley Research Center High Spectral Resolution Lidar 2 (HSRL 2) measured the temporal and spatial evolution of ozone and aerosol distributions impacting urban air quality over the four most populated cities in the United States. HSRL-2 measurements in 2021 were acquired over the Houston metropolitan region, including Galveston Bay and the Houston Ship Channel, as part of the NASA Tracking Aerosol Convection Experiment – Air Quality (TRACER-AQ) mission conducted in collaboration with the Department of Energy. HSRL-2 measurements were acquired over Los Angeles, Chicago, and New York City in 2023 as part of the NASA Synergistic TEMPO Air Quality Science (STAQS) mission conducted in collaboration with the NOAA Atmospheric Emissions and Reactions Observed from Megacities to Marine Areas (AEROMMA) mission. HSRL 2 provided nadir vertical profiles of ozone, aerosol backscatter, extinction, and depolarization as the aircraft flew lawnmower type patterns at 9 km for several hours over these urban areas. HSRL-2 measured profiles of aerosol extinction and aerosol optical depth (AOD) via the HSRL technique at 355 and 532 nm and profiles of aerosol backscatter and depolarization at 355, 532, and 1064 nm. Mixed Layer Heights (MLH) were derived by locating sharp vertical gradients in the profiles of aerosol backscatter. The flights were comprised of up to three repeating lawnmower patterns over each city showing the evolution of the ozone and aerosol distributions from the morning through the afternoon. The HSRL-2 measurements reveal ozone enhancements near the surface as well as in the free troposphere above the mixed layer. Some lidar measurements over Chicago and New York City show the daytime boundary layer growing into elevated layers of biomass burning aerosol. These layers complicate efforts to use column-integrated satellite measurements to infer surface air quality. As expected, mixed layer height (MLH) typically increased significantly during the day; however, during some flights, particularly over the Houston area, MLH also showed large spatial variability associated with changes in surface cover and/or small scale circulations. Often HSRL-2 measurements of AOD also showed large spatial and temporal variability throughout the day over these cities. We discuss how the ozone and aerosol profiles are averaged over different vertical and horizontal scales near the surface for use in assessments of regional air quality models and near-surface ozone retrievals from NASA’s recently launched Tropospheric Emissions: Monitoring Pollution (TEMPO) satellite.

Lidar↗

HSRL-2 Observations over the Houston, TX Region during TRACER-AQ

During field missions in 2021 and 2023, the airborne NASA Langley Research Center High Spectral Resolution Lidar 2 (HSRL 2) measured the temporal and spatial evolution of ozone and aerosol distributions impacting urban air quality over the four most populated cities in the United States. HSRL-2 measurements in 2021 were acquired over the Houston metropolitan region, including Galveston Bay and the Houston Ship Channel, as part of the NASA Tracking Aerosol Convection Experiment – Air Quality (TRACER-AQ) mission conducted in collaboration with the Department of Energy. HSRL-2 measurements were acquired over Los Angeles, Chicago, and New York City in 2023 as part of the NASA Synergistic TEMPO Air Quality Science (STAQS) mission conducted in collaboration with the NOAA Atmospheric Emissions and Reactions Observed from Megacities to Marine Areas (AEROMMA) mission. HSRL 2 provided nadir vertical profiles of ozone, aerosol backscatter, extinction, and depolarization as the aircraft flew lawnmower type patterns at 9 km for several hours over these urban areas. HSRL-2 measured profiles of aerosol extinction and aerosol optical depth (AOD) via the HSRL technique at 355 and 532 nm and profiles of aerosol backscatter and depolarization at 355, 532, and 1064 nm. Mixed Layer Heights (MLH) were derived by locating sharp vertical gradients in the profiles of aerosol backscatter. The flights were comprised of up to three repeating lawnmower patterns over each city showing the evolution of the ozone and aerosol distributions from the morning through the afternoon. The HSRL-2 measurements reveal ozone enhancements near the surface as well as in the free troposphere above the mixed layer. Some lidar measurements over Chicago and New York City show the daytime boundary layer growing into elevated layers of biomass burning aerosol. These layers complicate efforts to use column-integrated satellite measurements to infer surface air quality. As expected, mixed layer height (MLH) typically increased significantly during the day; however, during some flights, particularly over the Houston area, MLH also showed large spatial variability associated with changes in surface cover and/or small scale circulations. Often HSRL-2 measurements of AOD also showed large spatial and temporal variability throughout the day over these cities. We discuss how the ozone and aerosol profiles are averaged over different vertical and horizontal scales near the surface for use in assessments of regional air quality models and near-surface ozone retrievals from NASA’s recently launched Tropospheric Emissions: Monitoring Pollution (TEMPO) satellite.

Lidar↗

Explore Information Content Efficiently from Current and Future Hyperspectral Satellite Missions using a Spectral Fingerprinting Method

Hyperspectral remote sensors from current and future missions provide measurements of the Top of Atmosphere (TOA) radiance or reflectance spectra with high information content. For example, the Atmospheric Infrared Sounder (AIRS), together with the Cross-track Infrared Sounder (CrIS), and the Infrared Atmospheric Sounding Interferometer (IASI) have provided more than 20 years radiance measurements with thousands of spectral channels. These measurements will be continued for the next two decades with the same or more advanced hyperspectral sensors. The upcoming missions such as NASA’s CLARREO Pathfinder (CPF) and ESA’s TRUTHS will provide unprecedented accurate TOA hyperspectral radiance measurements in solar spectral region. Traditional ways to derive Climate Data Records (CDRs) from these measurements are performing spatial and temporal averages of the retrieved Level-2 products. However, it is a time-consuming process to generate decades of Level-2 data from Level-1 data. Furthermore, the differences in Level-2 algorithms used for different satellite sensors will introduce errors in derived CDRs. In this presentation, we will describe a spectral fingerprinting method to generate high-quality CDRs directly from spatiotemporally averaged Level-1 data. By using consistent radiative kernels which contain the spectral information of various atmospheric and surface CDRs, we can reduce the errors due to algorithm inconsistency. Additionally, the spectral fingerprinting method reduces the time needed to generate CDRs by more than three orders of magnitude. This makes it easy to reprocess CDRs once the Level-1 data from different satellites have been improved via either re-calibrations or inter-satellite calibrations. We will present results of applying spectral fingerprinting method to 20-years of AIRS and CrIS data. The resulting CDRs include: 1) vertical profiles of atmospheric temperature and water vapor, 2) cloud properties such as optical depth, effective size, and height, 3) vertical profiles or column amounts for atmospheric trace gases such as O3 and CO, and 4) surface emissivity spectra and skin temperatures. These CDRs will be publicly available at NASA GES DISC in late 2024. The same fingerprinting method is planned to be applied to future CPF and TRUTHS data for solar spectral region.

hyperspectral remote sensing↗

An airborne study of boundary layer heat and moisture fluxes for project FIFE

A summary of work accomplished during the first International Satellite Cloud Climatology Project (ISLSCP) Field Experiment is presented. The Wyoming King Air participated in Intensive Field Campaigns (IFCs) 3 and 4 in 1987, which were committed to a combination of airborne sensible and latent heat flux measurements and soil moisture mappings, with the University of Kansas' X-band side-looking airborne radar (SLAR). A total of 9 flux missions were flown in 1987 using several different flight designs. A critical decision in the first round of aircraft flux analyses, agreed to by all the flux aircraft investigators, was to pass the aircraft data through a high-pass filter prior to the eddy-correlation flux calculations. Several conclusions were drawn from this study: (1) boundary layer (BL) profiles of heat fluxes were usually linear; (2) high-pass filtering applied to the aircraft data did not add to the disagreement between the profile; (3) undersampling at high frequencies could have accounted for as much as a 15 percent underestimate of surface fluxes; (4) disagreement between the aircraft and surface latent heat fluxes changed signs between summer and fall; (5) magnitude and sign of disagreement between aircraft and surface heat fluxes varied systematically with BL depth or height of aircraft profile; and (6) Bowen ratios from both detrended and filtered aircraft data agreed with surface values better for moist, summer cases than for dry cases.

Kelly, Robert D.↗

Mapping Aerosol Lidar Ratios Over Ocean using MODIS AOD Constrained Retrievals and GOCART Model Simulations

After 17 years, the NASA Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission ceased science operations in August 2023. For the final CALIPSO data products release (Version 5), the CALIPSO project seeks to improve the accuracy of its aerosol extinction by advancing knowledge of aerosol lidar ratios (i.e., extinction-to-backscatter ratios; LRs) for various aerosol types. The current algorithm assigns one LR value globally for each of the seven tropospheric aerosol types. The CALIPSO team aims to improve the retrieval algorithm through the development of regional and seasonal LR climatologies for the same aerosol types. In this study, aerosol LRs are inferred through Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) backscatter profiles constrained by collocated aerosol optical depth (AOD) from Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) data over oceans during daytime. This analysis is subsampled for those profiles that are cloud-free and contain only one CALIOP-classified aerosol type. The CALIOP profiles are then collocated with aerosol volume fractions obtained through Goddard Chemistry Aerosol Radiation and Transport (GOCART) model simulations. This presentation will reveal findings that the 12-year (June 2006-August 2018) mean spatial distributions of inferred aerosol LRs for CALIOP-classified marine and dusty marine aerosols correspond inversely with patterns of GOCART sea salt volume fraction (SSVF). For example, smaller SSVFs (< 65%) and larger LRs (> 55 sr), are found near land masses (Fig. 1). This indicates the influence of advected anthropogenic aerosols (e.g., pollution and biomass burning smoke). In the remote oceans (i.e., regions likely less impacted by non-sea salt aerosols), the SSVFs are larger (> 95%) and the LRs are smaller (< 25 sr) (Fig. 1). A polynomial fit of the MODIS AOD constrained LRs to the corresponding GOCART SSVFs (intersect values of ~58 sr for SSVF of 0% and ~21 sr for SSVF of 100%) is further used to produce model-assisted climatological LR maps on seasonal scales. Additionally, we will show results of a LR validation analysis for which we compare the revised CALIPSO AODs obtained by applying the seasonal/regional constrained LRs against CALIPSO Version 4.51 Ocean Derived Column Optical Depth (ODCOD). While the majority of the presentation will focus on LRs for CALIOP-classified marine and dusty marine aerosols, an overview of LR results will show preliminary results for other aerosol types over ocean, such as dust and elevated smoke. The technique demon-strated in this study highlights the benefits not only to the final planned CALIPSO data release in 2025, but similar methods can be applied to future spaceborne elastic backscatter lidars with collocated passive sensors (e.g., such as those associated with NASA’s proposed Atmosphere Observing System).

Travis D Toth↗

Arc Jet Test and Analysis of Asbestos Free Solid Rocket Motor Nozzle Dome Ablative Materials

Asbestos free solid motor internal insulation samples were recently tested at the MSFC Hyperthermal Arc Jet Facility. Objectives of the test were to gather data for solid rocket motor analog characterization of ablative and in-depth thermal performance of rubber materials subject to high enthalpy/pressure flow conditions. Tests were conducted over a range of convective heat fluxes for both inert and chemically reactive sub-sonic free stream gas flow. Active instrumentation included use of total calorimeters, in-depth thermocouples, and a surface pyrometer for in-situ surface temperature measurement. Post-test sample forensics involved determination of eroded depth, charred depth, total sample weight loss, and documentation of the general condition of the eroded profile. A complete Charring Material Ablator (CMA) style aero thermal analysis was conducted for the test matrix and results compared to the measured data. In general, comparisons were possible for a number of the cases and the results show a limited predictive ability to model accurately both the ablative response and the in-depth temperature profiles. Lessons learned and modeling recommendations are made regarding future testing and modeling improvements that will increase understanding of the basic chemistry/physics associated with the complicated material ablation process of rubber materials.

Clayton, J. Louie↗

Test and Analysis of Solid Rocket Motor Nozzle Ablative Materials

Asbestos free solid motor internal insulation samples were tested at the MSFC Hyperthermal Facility. Objectives of the test were to gather data for analog characterization of ablative and in-depth thermal performance of rubber materials subject to high enthalpy/pressure flow conditions. Tests were conducted over a range of convective heat fluxes for both inert and chemically reactive sub-sonic free stream gas flow. Instrumentation included use of total calorimeters, thermocouples, and a surface pyrometer for surface temperature measurement. Post-test sample forensics involved measurement of eroded depth, charred depth, total sample weight loss, and documentation of the general condition of the eroded profile. A complete Charring Material Ablator (CMA) style aero-thermal analysis was conducted for the test matrix and results compared to the measured data. In general, comparisons were possible for a number of the cases and the results show a limited predictive ability to model accurately both the ablative response and the in-depth temperature profiles. Lessons learned and modeling recommendations are made regarding future testing and modeling improvements that will increase understanding of the basic chemistry/physics associated with the complicated material ablation process of rubber materials.

Clayton, J. Louie↗

Radar Cuts Subsoil Survey Costs

Soil features located with minimum time and labor. Ground-penetrating radar (GPR) system supplements manual and mechanical methods in performing subsurface soil survey. Mobile system obtains graphic profile of soil discontinuities and interfaces as function of depth. One or two test borings necessary to substantiate soil profile. GPR proves useful as reconnaissance tool.

Johnson, R.↗

Constraints on the rate of discharge and duration of the Mangala Valles flood

Interest in Mangala Valles remains high within the planetary science community. This is justified because the survey mission images provide us with nearly complete coverage of the system at high resolution. Upcoming high resolution topography from the Mars Observer Laser Altimeter will enable the application of flood discharge models with an unprecedented level of detail. Previous work on the Mangala Valles problem has relied on the available low resolution topography. This has limited the ability of workers to constrain discharge calculations to only within several-order-of-magnitude estimates. Local determinations of channel depths via shadow length measurements and photoclinometric profiling are much more accurate, but can only be applied to steep slopes (and/or low sun elevations) in the case of shadow measurements, or across relatively short distances (to avoid changes in albedo along asymmetric photoclinometric profiles). We are taking stereo parallax measurements from medium resolution Viking Orbiter images, which provide a valuable intermediate check of the topography between those measurements made thus far and the upcoming Mars Observer data. The images used are from orbits 034A and 637A, and cover Mangala Valles from the source graben in Memnonia Fossae to the beginning of the bifurcated reach (at 9.5 deg lat., 151.5 deg lon.). These images are about 300 m/pixel and 250 m/pixel, respectively. Both sets of images were orthographically projected to 250 m/pixel. The separation angle between left-right pairs is approximately 52 degrees. This results in a vertical accuracy on the order of plus or minus 260 m. Though this is still somewhat coarse, the channel relief is clearly resolved. Preliminary profiles across Mangala Valles and the large topographic ridge to the east are shown on the following page. An east-west regional tilt that resulted from slight scaling differences in the digital data has been 'removed' by visually estimating a regional datum on the stereo pairs. North-south variations in scale have not yet been adjusted for, so the zero datum for each profile was simply taken to be the high water line of the channel itself. Our depth measurement for the source breach of about 750 m agrees reasonably well with values of 700-1000 m determined from shadow measurements.

Parker, T. J.↗

Slant-lidar aerosol extinction measurements and their relation to measured and calculated albedo changes

Lidar and albedo data for a single day on which aerosols increased the surface plus atmospheric albedo above values measured on two surrounding very clean days are presented. The slant-lidar extinction measurement technique used is described along with the equipment and operating procedures. The derivation of optical depths, backscatter-to-extinction ratios, and extinction profiles is addressed, and the use of the lidar-derived optical depths in calculating expected albedo change is considered. Measured and calculated albedo changes are compared, and the results are found to agree within experimental uncertainties.

Russell, P. B.↗

Use of Polarization Lidar for Investigation of Meteorological Formations

This paper presents the results of theoretical and experimental, investigations of depolarization characteristics of different meteorological formations. Experimental investigations are carried out with a monostatic lidar. The ruby laser radiation is polarized in a vertical plane. The radiation reflected is accepted by a lens system of 150 rom in diameter and a viewing angle of 12' and further it is divided by Wollaston prism into the components polarized orthogonally. In this case the principal plane of the prism is exposed parallel with the laser polarization plane. Investigations show the degree of radiation polarization, reflected from water clouds, to be changed within 1/0.7 (seldom up to 0.6) depending on their density. In most cases a signal reflected from the cloud leading edge is polarized completely. The time shift is observed between polarized and crosspolarized components of a Fignal, reflected from a cloud, depending on the density of a meteorological object. While penetrating into the cloud depth a degree of polarization decreases up to 0.8-0.7, and the character of this decrease is different for various types of clouds. For crystal clouds the shift between the components of the reflected signal is not observed and the magnitude of polarization degree amounts to 0.1/0.3 in comparison with water clouds. The polarization degree of radiation reflected by fog is not less than 0.6, and that in the rains of average intensity (about 5 mm/h) is always about 1. The authors have suggested an algorithm of numerical solution of nonstationary transfer equation in the vector form to forecast the influence of multiple scattering effects on polarization characteristics of the lidar light signal. The method of statistical simulation (Monte-Carlo technique) forms the basis of the algorithm. Numerical estimates obtained for a model of stratocumulus at lambda = 0.6943 microns under boundary conditions close to the conditions of natural experiment being discussed proved to be in a good agreement with the results of observation. Specifically, Fig. 1 shows the profiles of polarization (p) versus depth (L) of the following drop formations: fog (curve 1) with horizontal meteorological visibility of 4 km two stratocumulus at a height of 1100 m with the attenuation factors delta = 0.01m(exp -1) (curve 2) and delta = 0.05m(exp -1) (curve 3). Curve 3 shows the results of numerical estimates and the value of their statistical error.

Balin, Yu. S.↗

Comparison of GEOS-5 AGCM Planetary Boundary Layer Depths Computed with Various Definitions

Accurate models of planetary boundary layer (PBL) processes are important for forecasting weather and climate. The present study compares seven methods of calculating PBL depth in the GEOS-5 atmospheric general circulation model (AGCM) over land. These methods depend on the eddy diffusion coefficients, bulk and local Richardson numbers, and the turbulent kinetic energy. The computed PBL depths are aggregated to the Koppen climate classes, and some limited comparisons are made using radiosonde profiles. Most methods produce similar midday PBL depths, although in the warm, moist climate classes, the bulk Richardson number method gives midday results that are lower than those given by the eddy diffusion coefficient methods. Additional analysis revealed that methods sensitive to turbulence driven by radiative cooling produce greater PBL depths, this effect being most significant during the evening transition. Nocturnal PBLs based on Richardson number are generally shallower than eddy diffusion coefficient based estimates. The bulk Richardson number estimate is recommended as the PBL height to inform the choice of the turbulent length scale, based on the similarity to other methods during the day, and the improved nighttime behavior.

AGCM↗

Shortwave Broadband Irradiance Computations Using Cloud Properties Combined from CALIPSO, CloudSat, and MODIS

In this study, cloud properties measured from the CALIPSO, CloudSat, and MODIS (CCM) are used for top-of-atmosphere (TOA) shortwave (SW) broadband (BB) irradiance computations. The CALIPSO and CloudSat active sensors provide detailed cloud vertical profiles, but these occasionally miss parts of the cloud columns due to the full attenuation of sensor signals, surface clutter, or insensitivity to a certain range of cloud particle sizes. As a result, the CCM-merged cloud extinction coefficient profiles can be underestimated. Therefore, we compare the column-integrated visible scaled cloud optical depth (VSCOD) of the CCM-merged cloud extinction coefficient profile with the MODIS-estimated VSCOD and apply a scaling factor to the CCM-merged cloud extinction profile. The VSCOD is defined as a visible cloud optical depth multiplied by (1¬–asymmetry parameter). The SW irradiances are computed using the scaled CCM-merged cloud extinction coefficient and effective radius profiles. It is shown that the multi-sensor-combined cloud profiles significantly reduce positive TOA SW BB biases, compared to those with MODIS-derived cloud properties only. The improvement is more pronounced for optically thick clouds, where MODIS ice particle effective radius is largely underestimated.

Cloud↗

An evaluation of flight data for the Apollo thermal protection system

A study was conducted to correlate Apollo ablation and thermal response flight data using advanced state-of-the-art analytical procedures. The agreement between flight data and predictions is consistently excellent for in-depth temperature distributions, char density profiles, and surface ablation, thus validating the analytical procedures.

Bartlett, E. P.↗

An analysis of atmospheric entry trajectories for manned and unmanned missions to the planet Venus

A unified atmospheric density model is presented for the planet Venus, and this model is compatible with Russian and American data obtained during the 1967 Venus launch opportunity. Trajectory characteristics involved in atmospheric entry are discussed with reference to roll-control modulation and entry corridor. Subsequent to a trajectory-oriented discussion of potential Venus mission characteristics, a parametric analysis of manned and unmanned vehicle entry trajectories into the Venusian atmosphere is presented. A sensitivity analysis with reference to atmospheric density deviations is included to show the dependence of corridor depth on the atmospheric density profile.

Craig, M. K.↗

The Crack-contact and the Free End Problem for a Strip Under Residual Stress

The plane problem for an infinite strip with two edge cracks under a given state of residual stress is considered. The residual stress is compressive near and at the surfaces and tensile in the interior of the strip. If the crack is deep enough to penetrate into the tensile zone, then the problem is one of crack-contact problem in which the depth of the contact area is an unknown which depends on the crack depth and the residual stress profile. The problem has applications to the static fatigue of glass plates and is solved for three typical residual stress profiles. In the limiting case of the crack crossing the entire plate thickness, the problem becomes a stress-free end problem for a semi-infinite strip under a given residual stress state away from the end. This is a typical stress diffusion problem in which decay behavior of the residual stress near and the nature of the normal displacement at the end of the semi-infinite strip are of special interest. For two typical residual stress states the solution is obtained, and some numerical results are given.

Bakioglu, M.↗