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Numerical Modeling of Shatter Cones Development in Impact Craters

Shatter cones are the characteristic forms of rock fractures in impact structures. They have been used for decades as unequivocal fingerprints of meteoritic impacts on Earth. The abundant data about shapes, apical angles, sizes and distributions of shatter cones for many terrestrial impact structures should provide insights for the determination of impact conditions and characteristics of shock waves produced by high-velocity projectiles in geologic media. However, previously proposed models for the formation of shatter cones do not agree with observations. For example, the widely accepted Johnson-Talbot mechanism requires that the longitudinal stress drops to zero between the arrival of the elastic precursor and the main plastic wave. Unfortunately, observations do not support such a drop. A model has been also proposed to explain the striated features on the surface of shatter cones but can not invoked for their conical shape. The mechanism by which shatter cones form thus remains enigmatic to date. In this paper we present a new model for the formation of shatter cones. Our model has been tested by means of numerical simulations using the hydrocodes SALE 2D enhanced with the Grady-Kipp-Melosh fragmentation model.

Baratoux, D.

Comparison of the Atomic Oxygen Erosion Depth and Cone Height of Various Materials at Hyperthermal Energy

Atomic oxygen readily reacts with most spacecraft polymer materials exposed to the low Earth orbital (LEO) environment. If the atomic oxygen arrival comes from a fixed angle of impact, the resulting erosion will foster the development of a change in surface morphology as material thickness decreases. Hydrocarbon and halopolymer materials, as well as graphite, are easily oxidized and textured by directed atomic oxygen in LEO at energies of approx.4.5 eV. What has been curious is that the ratio of cone height to erosion depth is quite different for different materials. The formation of cones under fixed direction atomic oxygen attack may contribute to a reduction in material tensile strength in excess of that which would occur if the cone height to erosion depth ratio was very low because of greater opportunities for crack initiation. In an effort to understand how material composition affects the ratio of cone height to erosion depth, an experimental investigation was conducted on 18 different materials exposed to a hyperthermal energy directed atomic oxygen source (approx.70 eV). The materials were first salt-sprayed to provide microscopic local areas that would be protected from atomic oxygen. This allowed erosion depth measurements to be made by scanning microscopy inspection. The polymers were then exposed to atomic oxygen produced by an end Hall ion source that was operated on pure oxygen. Samples were exposed to an atomic oxygen effective fluence of 1.0x10(exp 20) atoms/sq cm based on Kapton H polyimide erosion. The average erosion depth and average cone height were determined using field emission scanning electron microscopy (FESEM). The experimental ratio of average cone height to erosion depth is compared to polymer composition and other properties.

Waters, Deborah L.

Ensemble Forecasting of Coronal Mass Ejections Using the WSA-ENLIL with CONED Model

The combination of the Wang-Sheeley-Arge (WSA) coronal model, ENLIL heliospherical model version 2.7, and CONED Model version 1.3 (WSA-ENLIL with CONED Model) was employed to form ensemble forecasts for 15 halo coronal mass ejections (halo CMEs). The input parameter distributions were formed from 100 sets of CME cone parameters derived from the CONED Model. The CONED Model used image processing along with the bootstrap approach to automatically calculate cone parameter distributions from SOHO/LASCO imagery based on techniques described by Pulkkinen et al. (2010). The input parameter distributions were used as input to WSA-ENLIL to calculate the temporal evolution of the CMEs, which were analyzed to determine the propagation times to the L1 Lagrangian point and the maximum Kp indices due to the impact of the CMEs on the Earth's magnetosphere. The Newell et al. (2007) Kp index formula was employed to calculate the maximum Kp indices based on the predicted solar wind parameters near Earth assuming two magnetic field orientations: a completely southward magnetic field and a uniformly distributed clock-angle in the Newell et al. (2007) Kp index formula. The forecasts for 5 of the 15 events had accuracy such that the actual propagation time was within the ensemble average plus or minus one standard deviation. Using the completely southward magnetic field assumption, 10 of the 15 events contained the actual maximum Kp index within the range of the ensemble forecast, compared to 9 of the 15 events when using a uniformly distributed clock angle.

coronal mass

Tables for Supersonic Flow Around Right Circular Cones at Small Angle of Attack

The solution of supersonic flow fields by the method of characteristics requires that starting conditions be known. Ferri, in reference 1, developed a method-of-characteristics solution for axially symmetric bodies of revolution at small angles of attack. With computing machinery that is now available, this has become a feasible method for computing the aerodynamic characteristics of bodies near zero angle of attack. For sharp-nosed bodies of revolution, the required starting line may be obtained by computing the flow field about a cone at a small angle of attack. This calculation is readily performed using Stone's theory in reference 2. Some solutions of this theory are available in reference 3. However, the manner in which these results are presented, namely in a wind-fixed coordinate system, makes their use somewhat cumbersome. Additionally, as pointed out in reference 4, the flow component perpendicular to the meridian planes was computed incorrectly. The results contained herein have been computed in the same basic manner as those of reference 3 with the correct velocity normal to the meridian planes. Also, all results have been transferred into the body-fixed coordinate system. Therefore, the values tabulated herein may be used, in conjunction with the respective zero-angle-of-attack results of reference 5, as starting conditions for the method-of-characteristics solution of the flow field about axially symmetric bodies of revolution at small angles of attack. As in the zero-angle-of-attack case (ref. 5) the present results have been computed using the ideal gas value of 1.4 for the ratio of the specific heats of air. Solutions are given for cone angles from 2.5 deg to 30 deg in increments of 2.5 deg. For each cone angle, results were computed for a constant series of free-stream Mach numbers from 1.5 to 20. In addition, a solution was computed which yielded the minimum free-stream Mach number for a completely supersonic conical flow field. For cone angles of 27.5 deg and 30 deg, this minimum free-stream Mach number was above 1.5. Consequently, solutions at this Mach number were not computed for these two cone angles.

SUPERSONIC FLOW

Boundary-Layer-Transition and Heat-Transfer Measurements from Flight Tests of Blunt and Sharp 50 Degree Cones at Mach Numbers from 1.7 to 4.7

Boundary-layer-transition and heat-transfer measurements were obtained from flight tests of blunt and sharp cones having apex angles of 50 deg. The test Mach number range was from 1.7 to 4.7, corresponding to free-stream Reynolds numbers, based on cone base diameter, of 18. 3 x 10(exp 6) and 32.1 x 10(exp 6), respectively. Transition on both models occurred at a local Reynolds number of 1 x 10(exp 6) to 2 X 10(exp 6) based on distance from the stagnation point. Transition Reynolds numbers based on momentum thickness were between 320 and 380 for the blunt cone. The model surface roughness was 25 rms microinches or greater. Turbulent heat transfer to the conical surface of the blunt cone at a Mach number of 4 was 30 percent less than that to the surface of the sharp cone. Available theories predicted heat-transfer coefficients reasonably well for the fully laminar or turbulent flow conditions.

BLUNT BODY

The effect of angle of attack on boundary-layer transition on cones.

Boundary-layer transition on 5- and 15-deg half-angle cones was studied as a function of angle of attack (ranging from 0 to 20 deg) in a 3.5 ft hypersonic wind tunnel at a freestream Mach number of 7.4. It is shown that the influence of the angle of attack on the transition Reynolds number is a function of the meridian angle. On the windward ray of the 15-deg cone, transition Reynolds numbers show an initial slight increase and then a decrease with increasing angle of attack; leeward-ray Reynolds numbers for this cone decrease rapidly with angle of attack. Windward-ray transition Reynolds numbers increase monotonically with angle of attack on the 5-deg cone, but the effect of the angle of attack on the leeward ray is the same as for the 15-deg cone.

Mateer, G. G.

Subsonic wind-tunnel tests of a trailing-cone device for calibrating aircraft static pressure systems

A trailing-cone device for calibrating aircraft static-pressure systems was tested in a transonic wind tunnel to investigate the pressure-sensing characteristics of the device including effects of several configuration changes. The tests were conducted at Mach numbers from 0.30 to 0.95 with Reynolds numbers from (0.9 x one million to 4.1 x one million per foot). The results of these tests indicated that the pressures sensed by the device changed slightly but consistently as the distance between the device pressure orifices and cone was varied from 4 to 10 cone diameters. Differences between such device-indicated pressures and free-stream static pressure were small, however, and corresponded to Mach number differences of less than 0.001 for device configurations with pressure orifices located 5 or 6 cone diameters ahead of the cone. Differences between device-indicated and free-stream static pressures were not greatly influenced by a protection skid at the downstream end of the pressure tube of the device nor by a 2-to-1 change in test Reynolds number.

Jordan, F. L., Jr.

Cinder cone growth modeled after Northeast crater, Mount Etna, Sicily

The structure, physical properties of ejecta, ballistics, and growth of Northeast crater, a young pyroclastic cone that originated in 1911 near the summit of Mount Etna, Sicily, were studied in order to form a model of volcano cinder cone growth. Four stages of growth were discerned: (1) a simple cone; (2) a cone with an outward-dipping talus slope; (3) destruction of rounded rim by the inward migration of the upper edge of the talus pile; and (4) extension of limits of talus pile beyond the ballistic limit of ejecta trajectories. The model is used to predict the features of lunar and Martian cones, assuming that they erupted under conditions qualitatively similar to Etna's Northeast crater.

Mcgetchin, T. R.

Physical properties of thin-film field emission cathodes with molybdenum cones

Field emission cathodes fabricated using thin-film techniques and electron beam microlithography are described, together with effects obtained by varying the fabrication parameters. The emission originates from the tip of molybdenum cones that are about 1.5 micron tall with a tip radius around 500 A. Such cathodes have been produced in closely packed arrays containing 100 and 5000 cones as well as singly. Maximum currents in the range 50-150 microamp per cone can be drawn. Life tests with the 100-cone arrays drawing 2 mA total emission (or 3 A per sq cm) have proceeded in excess of 7000 hr with about a 10% drop in emission current. Studies are presented of the emission characteristics and current fluctuation phenomena. It is tentatively concluded that the emission arises from only one or a few atomic sites on the cone tips.

Spindt, C. A.

Shatter cones - An outstanding problem in shock mechanics

Shatter cone characteristics are surveyed. Shatter cones, a form of rock fracture in impact structures, apparently form as a shock front interacts with inhomogeneities or discontinuities in the rock. Topics discussed include morphology, conditions of formation, shock pressure of formation, and theories of formation. It is thought that shatter cones are produced within a limited range of shock pressures extending from about 20 to perhaps 250 kbar. Apical angles range from less than 70 deg to over 120 deg. Tentative hypotheses concerning the physical process of shock coning are considered. The range in shock pressures which produce shatter cones might correspond to the range in which shock waves decompose into elastic and deformational fronts.

Milton, D. J.

Shatter cones formed in large-scale experimental explosion craters

In 1968, a series of 0.5-ton and 100-ton TNT explosion experiments were conducted in granitic rock near Cedar City, Utah, as part of a basic research program on cratering and shock wave propagation. Of special interest was the formation of an important type of shock metamorphic feature, shatter cones. A description is presented of the first reported occurrence of shatter cones in high explosion trials. A background to shatter cone studies is presented and attention is given to the test program, geology and physical properties of the test medium, the observed cratering, and the formational pressures for shatter cones. The high explosion trials conducted demonstrate beyond any doubt, that shatter cones can be formed by shock wave processes during cratering and that average formational pressures in these crystalline rocks are in the 20-60 kb range.

Roddy, D. J.

In-flight transition measurement on a 10 deg cone at Mach numbers from 0.5 to 2.0

Boundary layer transition measurements were made in flight on a 10 deg transition cone tested previously in 23 wind tunnels. The cone was mounted on the nose of an F-15 aircraft and flown at Mach numbers room 0.5 to 2.0 and altitudes from 1500 meters (5000 feet) to 15,000 meters (50,000 feet), overlapping the Mach number/Reynolds number envelope of the wind tunnel tests. Transition was detected using a traversing pitot probe in contact with the surface. Data were obtained near zero cone incidence and adiabatic wall temperature. Transition Reynolds number was found to be a function of Mach number and of the ratio of wall temperature to adiabatic all temperature. Microphones mounted flush with the cone surface measured free-stream disturbances imposed on the laminar boundary layer and identified Tollmien-Schlichting waves as the probable cause of transition. Transition Reynolds number also correlated with the disturbance levels as measured by the cone surface microphones under a laminar boundary layer as well as the free-stream impact.

Fisher, D. F.

The AKR emission cone at low frequencies

It is noted that certain of the ISEE-1 observations between the plasmasphere and the auroral zone have revealed the emission cone of auroral kilometric radiation (AKR) unaffected by plasmaspheric refraction. At some distance from the source, the cone produced a sharp low-frequency boundary in the AKR signals, which was displaced above the cyclotron frequency. The variation of this boundary, together with other aspects of the AKR signals, suggested that the AKR emission cone closed toward a hollow, roughly 45 deg limit cone with decreasing frequency, duplicating the behavior previously found with ISIS-1 at the opposite end of the AKR spectrum. It is pointed out that the hollow limit cone at low frequencies is a new feature, not previously reported.

Calvert, W.

Cone sampling array models

A model is described for positioning cones in the retina. Each cone has a circular disk of influence, and the disks are tightly packed outward from the center. This model has three parameters that can vary with eccentricity: the mean radius of the cone disk, the standard deviation of the cone disk radius, and the standard deviation of postpacking jitter. Estimates for these parameters out to 1.6 deg are found by using measurements reported by Hirsch and Hylton (1985) and Hirsch and Miller (1987) of the positions of the cone inner segments of an adult macaque. The estimation is based on fitting measures of variation in local intercone distances, and the fit to these measures is good.

Ahumada, Albert J., Jr.

Study of open jet wind tunnel cones

Tests have been made by the National Advisory Committee for Aeronautics on the air flow in an open jet wind tunnel with various sizes, shapes, and spacings of cones, and the flow studied by means of velocity and direction surveys in conjunction with flow pictures. It was found that for all combinations of cones tested the flow is essentially the same, consisting of an inner core of decreasing diameter having uniform velocity and direction, and a boundary layer of more or less turbulent air increasing in thickness with length of jet. The energy ratio of the tunnel was obtained for the different combinations of cones, and the spilling around the exit cone causing undesirable air currents in the experiment chamber was noted. An empirical formula is given for the design of cones having no appreciable spilling.

Weick, Fred E

Laminar boundary layer on cone in supersonic flow at large angle of attack

The laminar boundary-layer flow about a circular cone at large angles of attack to a supersonic stream has been analyzed in the plane of symmetry by a method applicable in general to the flow about conical bodies. At the bottom of the cone, velocity profiles were obtained showing the expected tendency of the boundary layer to become thinner on the under side of the cone as the angle of attack is increased. At the top of the cone, the analysis failed to yield unique solutions except for small angles of attack. Beyond a certain critical angle of attack, boundary-layer flow does not exist in the plane of symmetry, thus indicating separation. This critical angle is presented as a function of Mach number and cone vertex angle.

Moore, Franklin K

THEMIS Observations of Pitted Cones in Acidalia Planitia and Cydonia Mensae

Analysis of Viking imagery revealed the presence of large numbers of pitted or cratered cones in the northern plains of Mars with the highest concentrations occurring in eastern Acidalia Planitia and Cydonia Mensae. Based largely on crater/cone diameter ratio comparisons, these features were hypothesized as being analogous to terrestrial pseudocraters (rootless cones) such as occur in the Lake Myvatn region of Iceland. Doubts remained about this connection given the disparity in mean diameters between these Martian features (mean diameter of approx. 600 m) and the Icelandic rootless cones (mean diameter of approx. 50 m). Recent analysis of MOC Narrow Angle camera images of Elysium Planitia, Amazonis Planitia and elsewhere have revealed another class of features with diameters commensurate with the Icelandic rootless cones. If the features in Acidalia and Cydonia are not rootless cones, what are they? Recent information on the thermophysical properties of these features as provided by the Mars Odyssey THEMIS instrument may help to answer this question.

W H Farrand

Variability in Morphology and Thermophysical Properties of Pitted Cones in Acidalia Planitia and Cydonia Mensae

The northern plains of Mars contain a number of unique landforms and are unique in terms of their topography and composition . Much of the speculation about the northern plains centers on whether there was ever a northern ocean, and if there was, was it long-lived or ephemeral? The northern plains also hosts the Vastitas Borealis Formation which has been variously interpreted as the residue from a northern ocean , and pre-existing material reworked by cold-weather processes . In this work we examine a set of unusual features resident on the northern plains, the pitted cones originally recognized in Viking data . Our focus is on the pitted cones in Acidalia and Cydonia regions. The pitted cones of the northern plains have been hypothesized as being equivalent to terrestrial cinder cones , rootless cones , pingos , and mud volcanoes . To examine the Acidalia and Cydonia regions, multispectral data from the Mars Odyssey THEMIS, gridded topography from Mars Global Surveyor (MGS) MOLA, images from MGS MOC, and mineralogic and thermal inertia information from MGS TES have been assembled in a Geographic Information System. Analysis of MOC Narrow Angle camera images

Farrand, W. H.