Journal of Geophysical Research: Planets

Asymmetry of ejecta flow during oblique impacts using three-dimensional particle image velocimetry

Authors


Abstract

[1] Three-dimensional particle image velocimetry (3D PIV) applied to impact cratering experiments allows the direct measurement of ejecta particle positions and velocities within the ejecta curtain as the crater grows. Laboratory experiments were performed at the NASA Ames Vertical Gun Range with impact velocities near 1 km/s (6.35-mm diameter aluminum spheres) into a medium-grained (0.5 mm) particulate sand target in a vacuum at 90° and 30° from the horizontal. This study examines the first 50% of crater growth, during which the crater has grown to one half its final radius. From the 3D PIV data, the ballistic trajectories of the ejecta particles are extrapolated back to the target surface to determine ejection velocities, angles, and positions. For vertical impacts these ejection parameters remain constant in all directions (azimuths) around the crater center. The 30° impacts exhibit asymmetries with respect to azimuth that persist well into the excavation-stage flow. These asymmetries indicate that a single stationary point source is not adequate to describe the subsurface flow field during an oblique impact.

1. Introduction

[2] The majority of impact craters are produced during oblique, as opposed to vertical, impacts [Gilbert, 1892; Shoemaker, 1962]. Impact angle affects the excavation flow field as well as the final form of the crater and ejecta deposit as observed in both experiments and the planetary record [Gault and Wedekind, 1978; Schultz and Gault, 1985; Schultz and Anderson, 1996; Schultz and D'Hondt, 1996; Cheng and Barnouin-Jha, 1999]. The final crater shape in map view is relatively symmetric for experimental impacts into loose particulates, even down to impact angles as low as 15° [Gault and Wedekind, 1978]. Consequently, crater-scaling relations for diameter and displaced mass can adequately accommodate the impact-angle effects by using only the vertical velocity component [Gault and Wedekind, 1978; Chapman and McKinnon, 1986]. Other scaling relations, however, such as the ejecta deposit thickness and aerial extent, will depend heavily on initial asymmetries in the cratering flow field induced by oblique impacts [Schultz, 1999; Schultz and Mustard, 2001].

[3] Experimental studies provide a basis for crater and ejecta scaling laws, which then can be used to interpret larger planetary craters. Several experimental studies of oblique impacts into particulate targets have been described previously [Gault and Wedekind, 1978; Schultz and Gault, 1985; Schultz, 1999] and recent numerical models have incorporated impact-angle effects at early times [Pierazzo and Melosh, 1999, 2000a], but a detailed description of the cratering flow field in different directions around the impact point has not been made. The effect of impact angle has important implications for crater growth and excavation [Gault and Wedekind, 1978], peak-pressure history [Dahl and Schultz, 2001], material transport and mixing [e.g., Schultz and Gault, 1985; Li and Mustard, 2000; Haskin et al., 2003], impactor survival and the potential escape of material from a planetary surface [e.g., O'Keefe and Ahrens, 1986; Schultz and Gault, 1990; Pierazzo and Melosh, 2000b].

[4] Various studies describe the fundamental processes of impact cratering where the subsurface flow is initiated by a vertical impact [e.g., Gault et al., 1968]. At the moment of impact, the projectile begins transferring its momentum and energy downward and into the target material. The resulting shock in the target travels downward and outward, thereby compressing the target material and inducing radial flow of material away from the impact point. Also at the moment of impact, another shock wave travels upward through the projectile. The compression stage continues until the shock wave in the projectile has reached its back surface. By this time during a vertical impact, the projectile has deposited most of its kinetic energy and momentum into the target, either to be consumed as internal heating (waste heating, compression or comminution) or expended in crater excavation. Following the initial shock wave in the target material, a series of rarefaction waves decompresses the target material and bends the radial streamlines upward toward the surface such that subsurface particles may eventually be ejected from the growing crater. During this excavation stage, the shock and attendant rarefaction waves create a flow field that excavates material in a systematic way. After leaving the target surface, the ejecta follow independent ballistic trajectories that at any given moment comprise the outward-moving ejecta curtain.

[5] The description of an oblique impact differs fundamentally from this standard view of a vertical impact. Oblique impacts transfer a momentum component horizontal to the target surface and initially create an asymmetric shock within the target. Vertical impacts induce symmetric flow around the impact point, thereby obscuring the downward-directed impactor momentum. The independent motions of the ejecta particles within the ejecta curtain are completely determined by the subsurface cratering flow field, which in turn is heavily affected (especially in the initial stages) by impact angle. The effect of the horizontal momentum component in an oblique impact is expressed by ejecta asymmetries [Gault and Wedekind, 1978; Schultz, 1999], subsurface flow and resultant shock-related damage [Schultz and Anderson, 1996], and direct measurements of peak stresses [Dahl and Schultz, 2001]. The same response is seen in finite element codes [Pierazzo and Melosh, 1999].

[6] Initially, the oblique-impact ejecta curtain is extremely asymmetric, with low curtain (and ejection) angles downrange and high angles uprange [Schultz and Anderson, 1996]. This asymmetry results from the initially downrange-directed projectile momentum affecting the subsurface flow field. With time, both uprange and downrange curtain angles become more symmetric. If the impact angle is not too oblique (generally 30° or higher for hypervelocity impacts into particulate targets), the near-rim ejecta deposit appears symmetric, but at very low impact angles (for example, 15° from horizontal), ejecta deposits exhibit a distinctive uprange zone of avoidance [Gault and Wedekind, 1978]. This uprange zone of missing ejecta further expresses the downrange-driven effect of projectile momentum on the excavation process. For these angles, the cratering flow field is affected by the projectile's downrange-directed momentum to such an extent that little material is ejected (and thus deposited) uprange of the crater. Such asymmetries in the ejecta pattern extend to planetary scales and are indicative of highly oblique impacts [Gault and Wedekind, 1978; Schultz and Lutz-Garihan, 1982; Schultz, 1992].

[7] The cratering flow field completely determines the ejecta motions above the target surface (in the absence of an atmosphere). Thus, if ejecta velocities and positions are measured in the laboratory and a general flow-field geometry is assumed, the subsurface cratering flow field for that impact can be inferred. Measurements of impact ejecta dynamics typically have used high-speed imaging [e.g., Braslau, 1970; Stöffler et al., 1975; Gault and Wedekind, 1978; Schultz and Gault, 1985]. Another approach captured ejecta at certain positions around the growing crater and used ballistic equations (along with film records) to reconstruct ejection parameters in the evolving curtain [e.g., Stöffler et al., 1975; Hartmann, 1985; Schultz, 1999].

[8] Oberbeck and Morrison [1976] performed one of the first impact experiments designed to isolate and directly observe groups of ejecta particles composing the ejecta curtain. In their experiments a vertical plate intercepted the advancing ejecta curtain at the expected position of the crater rim. Wires placed across the width of a vertical slit in the plate broke the ejecta curtain into distinguishable packets of ejecta. High-speed film captured these ejecta packets along their ballistic trajectories and allowed Oberbeck and Morrison [1976] to calculate average ejection velocities and angles. Housen et al. [1983] later argued that this experimental apparatus affected the ejecta particle trajectories (most notably, the fastest ejecta) such that the results did not follow power law ejecta scaling relations. Thus a less intrusive method of imaging individual ejecta particles was needed to better quantify ejecta behavior in the laboratory.

[9] Following earlier experimental studies of explosion cratering [Piekutowski et al., 1977], Cintala et al. [1999] developed a non-intrusive imaging technique to observe individual ejecta particles in flight during vertical impacts. In their experiments, a vertical laser plane passed through the impact point perpendicular to a camera. Pulses of the laser illuminated individual particles moving along ballistic trajectories within the narrow laser plane. Individual trajectories could then be mapped and ejection angle and velocity measured directly. These experiments confirmed that ejection velocities decrease following a power law as the crater grows, as predicted using dimensional analysis [Housen et al., 1983]. Since only one radial direction from the impact point could be analyzed at a time, azimuthal variations in ejecta behavior (such as those produced by oblique impacts) are difficult to quantify using this system.

[10] The present paper describes an experimental technique new to impact cratering: three-dimensional particle image velocimetry (3D PIV). This technique directly measures three-dimensional ejecta particle positions and velocities within the ejecta curtain in real time as the crater grows. Used in combination with the oblique-angle capabilities of the NASA Ames Vertical Gun Range, 3D PIV captures a three-dimensional, quantitative portrait of the crater excavation process for vertical and oblique impacts.

2. Experimental Methods

[11] The experiments described here were performed at the NASA Ames Vertical Gun Range (AVGR) (see description by Gault and Wedekind [1978]), a national impact facility capable of firing small (≤6.35 mm) projectiles up to 6.5 km/s into a chamber where atmospheric pressure can be varied from vacuum to just below 1 atmosphere. The launch-tube assembly can be elevated in 15° increments to allow for oblique impacts ranging from 15° to 90° from horizontal. In the present experiments, 6.35-mm diameter aluminum spheres impacted a medium-grained (0.5 mm) particulate quartz sand target at impact angles of 90° (vertical) and 30° above horizontal. The projectiles impacted with velocities near 1.0 km/s into a vacuum of less than 7 x 10−4 atmospheres. This study focuses on obtaining data through the first 50% of crater growth.

[12] Three-dimensional particle image velocimetry (3D PIV) was originally designed for use in wind tunnels to provide measurements of fluid flow [Raffel et al., 1998]. 3D PIV employs a system of lasers, digital cameras and algorithms to calculate three-dimensional velocity vectors in a two-dimensional plane corresponding to the motion of particles traveling within a given flow. It should be noted that the technique described here as “3D PIV” is currently referred to as “3C PIV” or “three-component PIV” by the fluid-flow measurement community. 3C PIV refers to the method that determines three-component (U, V, W) vector velocities on a plane. New volumetric methods for determining vector velocities are referred to as “three-dimensional PIV” by that community. Here “3D PIV” is used to emphasize the three-dimensional nature of the velocity vectors obtained during crater formation and to differentiate this work from other experimental works that were able to obtain two-dimensional velocity vectors [Cintala et al., 1999].

[13] Within the large experimental chamber of the AVGR, 3D PIV enables the measurement of three-dimensional velocities of particles within the moving ejecta curtain [Schultz et al., 2000; Heineck et al., 2002]. The 3D PIV system projects a horizontal laser plane a few centimeters (in these cratering experiments, 8.4 cm) above the target surface (Figure 1). The laser plane thickness can be adjusted but for these experiments it is 6 mm thick. At a given instant, the laser plane illuminates ejecta particles within the growing ejecta curtain. Two CCD cameras located above the target chamber image the illuminated ring of particles twice in rapid succession thereby capturing the particles in slightly different positions within the laser plane. The time between image pairs ranges from 1 to 1000 μs, depending on the velocity of the particles. Thus four images are obtained for each time step: two images from each of two cameras.

Figure 1.

Sketch of the 3D PIV setup within the AVGR facility. The target is located on a platform within the large vacuum chamber. The projectile enters through one of several ports in the chamber (this sketch shows a projectile trajectory entering at 30° above horizontal). The impact creates an ejecta curtain that moves across the target surface as the crater grows. A horizontal laser sheet is projected into the vacuum chamber at a given height (a few centimeters) above the target surface. Two CCD cameras are located above the vacuum chamber and image the ring of illuminated ejecta particles. Modified from Heineck et al. [2002].

[14] A special software package [Lourenco and Krothapalli, 1998] cross-correlates image pairs from each camera in order to track small groups of particles. The position of the correlation peak with respect to a specified origin gives the average amount of particle displacement observed by each camera. This yields two arrays of two-dimensional displacement vectors or vector fields, one for each camera. Through the use of photogrammetric equations, the vertical displacement is calculated from the two-dimensional vector fields. The time delay between frames is incorporated into the displacements resulting in a final grid of three-dimensional velocity vectors, each representing a small group of ejecta particles within the laser plane. The software does not trace single particles; rather, it cross-correlates small regions in the first and second images for each camera, the centers of which lie on a mesh of specific spacing. The regions, known as interrogation windows, have at least 10 particle images to obtain statistically significant mean displacements. The mesh is specified to overlap the interrogation windows by 50%, resulting in four-fold oversampling. The resolution of the cameras yielded a pixel resolution of 0.2 mm in the region of interest. At any given time, the ejecta are traveling along nearly the same ballistic trajectories in the relatively small space recorded in the interrogation window. Therefore the average motion of such a small group of particles is representative of the individual motions within that area. The software is accurate to within 2% for horizontal velocities and 4% for vertical velocities within the laser plane [Heineck et al., 2002].

[15] Although the laser plane thickness is 6 mm for these experiments, the software assumes that all of the particles are located at the laser height, in this case 8.4 cm above the target surface. During much of excavation for the present study, ejecta particles within the laser plane are moving fast enough that the difference in velocity between the bottom and top of the laser plane is minimal. For example, a particle with a vertical velocity component of 20 m/s in the center of the laser plane is moving only 1.5 mm/s slower than it was when it entered the laser plane (on the order of one hundredth of a percent change from bottom to top of the laser plane). Ejecta with a vertical velocity component in the center of the laser plane of 1 m/s is only 25 mm/s slower than when it entered the bottom of the laser plane (a 2.5% difference). Particles entering or leaving the laser plane between the two camera images cannot be measured; consequently, those particles on the very edges of the laser plane have little affect on the calculation. Hence the effect of the laser plane thickness at the latest times measured in this study contributes at most a few percent of variation to the velocity measurements.

[16] The experiments presented here were performed in a vacuum. Hence the individual ballistic trajectory of each particle is completely defined by the three-dimensional location and velocity of that particle at any point along its trajectory. The velocity and position of a particle within the laser plane, as determined using 3D PIV, establish its entire ballistic trajectory (Figure 2). The intersection of the ballistic trajectory and the pre-impact surface defines the ejection position, vector velocity and angle. It should be noted that the “ejection velocity” and the “velocity within the laser plane” are not the same for a given particle. The “velocity within the laser plane” is what is measured by the 3D PIV system. The “ejection velocity”, however, is derived from the ballistic equations and represents the velocity at which the particle passes through the target surface. The ballistic equations of motion in vector form are:

equation image

where the ejection position ro = (xo, yo, 0), the ejection velocity vo = (Uo, Vo, Wo) and the acceleration a = (0, 0, -g). There are six measured parameters: the position within the laser plane rl = (xl, yl, h), where h is the laser height above the target surface, and the particle velocity within the laser plane vl = (Ul, Vl, Wl). The six unknowns are the ejection position ro = (xo, yo, 0), the time at which the particles arrive in the laser plane (tl) and the ejection velocity vo = (Uo, Vo, Wo). Since there is no acceleration in either the x or y directions and no atmospheric interactions, the measured laser plane velocities Ul and Vl are constant and equal to their corresponding horizontal ejection velocity components. The other unknowns can be solved as:

equation image
Figure 2.

At a given time during crater formation, the three-dimensional velocities of ejecta particles within the laser plane are measured using 3D PIV (arrows). These three-dimensional velocities and positions uniquely define each particle's ballistic trajectory (dashed lines). The intersection of this trajectory with the pre-impact surface defines the ejection position, velocity and angle. At a later time, the process is repeated, thereby following the evolution of the ejecta curtain through time by analyzing a series of horizontal ejecta curtain cross sections.

[17] The 3D PIV system design currently does not allow for video framing during crater formation. Consequently, the evolution of ejection parameter asymmetries must be tracked by performing and analyzing a series of nearly identical impact experiments imaged in consecutive time steps. It is impossible to recreate each shot to be an exact replicate of all the others. Slight variations in impact velocity and rifling of the projectile, as well as the arrangement of the sand target grains lead to minor variations in the timing of the camera system as well as the subsurface flow field. However, by examining the 3D PIV data obtained during two very nearly identical shots imaged at nearly the same time, it is possible to assess the errors that arise by comparing different time steps taken during extremely similar, yet subtly varying impact experiments. When the 3D PIV data is compared between the closest identical shots obtained in this study, the differences between the data (in terms of calculated ejection velocities and angles versus azimuth) are less than 2%, independent of impact angle. Thus this method of using a number of similar experiments to reconstruct a time series for a single impact is valid despite slight variations between the individual impacts used.

[18] The final data obtained by using 3D PIV in these cratering applications provide direct measurements of ejection position, velocity and angle of ejected particles while the crater is growing. Incorporating the oblique impact angle capabilities of the AVGR, it is possible to study the variation of these parameters as the crater grows and in all azimuthal directions for oblique impacts and compare them with similar data for vertical impacts.

3. Results and Discussion

[19] Our initial study using 3D PIV addresses three main results: (1) a new method of viewing the ejecta curtain through cross-sectional images, (2) the evolution of ejection velocities as a function of azimuth and (3) the evolution of ejection angles as a function of azimuth. In each case, a comparison is made between vertical (90°) and 30° impacts in order to emphasize the amount of asymmetry present within even moderately oblique ejecta curtains. Each of these results highlights the need for caution when assuming that oblique impacts can be modeled using a single, stationary point source.

3.1. Ejecta Curtain Cross Sections

[20] Images produced by 3D PIV provide a unique cross-sectional view of the ejecta curtain parallel to the target surface (Figure 3). For vertical impacts, the horizontal cross section through the ejecta curtain forms a symmetric ring around the crater center, as shown in Figure 3a. With time, the curtain expands and retains its symmetry. A 30° impact, however, creates a very asymmetric ejecta curtain cross section at early times (Figure 3b). Initially, a large amount of material moves downrange at low angles. This is evidenced by the wider cross section through the downrange curtain; it is also documented in ejecta-capture experiments [Schultz, 1999] and illustrated using 3D PIV (discussed below). Uprange, little (if any) material is observed within the laser plane at very early times. The initial absence of uprange ballistic debris corresponds to the uprange zone of avoidance observed in ejecta deposits around craters produced by highly oblique impacts. As the effect of the downrange-directed momentum of the projectile decays, the subsurface flow field evolves and becomes more symmetric. The curtain eventually closes as the subsurface flow field begins ejecting material in the uprange direction and these slower uprange ejecta eventually reach the height of the laser plane. At these later times, the closure of the uprange curtain corresponds to ejecta deposited near the uprange crater rim, thereby partially masking the evidence of initial asymmetries. Even though the curtain has closed, the cross-sectional images continue to show the initial asymmetry in terms of curtain thickness and density variations. Later evolution of the subsurface flow field as expressed in the uprange and downrange ejecta velocities and angles increases the symmetry of the horizontal cross sections. The azimuthal differences in these cross-sectional images are direct results of the variations in ejection parameters between uprange, downrange and lateral curtain segments. The ejection parameter best understood in terms of dimensionless scaling is ejection velocity.

Figure 3.

This time series of raw 3D PIV images reveals the growth of the ejecta curtain, in horizontal cross section parallel to the target surface for (a) 90° and (b) 30° impacts. The four images in each series were taken at approximately the same times after impact of 5, 10, 30 and 80 msec. Note that the time after impact is not the same as the ejection time. Rather, the time after impact is the sum of the ejection time and the time needed for the particles to move ballistically from the surface into the laser plane (in this case a height of 84 mm). IP represents the position of the impact point, whereas CC is the location of the crater center (IP and CC are only significantly different for the 30° impacts). The viewing geometry is the same for all eight images. The laser sheet enters the images from the upper left corner and so intersects the left-hand side of the ejecta curtain first. The images have been inverted such that the illuminated particles appear dark on a white background. The relative brightness of all eight images, however, is the same with respect to each other. In other words, the intensity of one image can be accurately compared to the others. Note the azimuthal symmetry as the 90° curtain grows in time (a) compared to the initial highly asymmetric 30° curtain (b). The 30° curtain never attains a level of symmetry comparable to the vertical curtain. The last time step in this series corresponds to ejecta that left the target surface when the crater was half formed or at approximately 10% of crater formation time.

3.2. Ejection Velocities

[21] The scaling of ejection velocities is well documented and understood for vertical impacts [Housen et al., 1983]. 3D PIV now allows the comparison of ejection velocities for vertical and 30° impacts. After being processed, the raw cross-sectional images can be presented in terms of three-dimensional velocities. The same cross-sectional images shown in Figure 3 are given in terms of vector velocities within the laser plane in Figure 4. Clearly, velocities for the 30° impacts are asymmetric while the vertical impacts are very symmetric with respect to the crater center. These velocities within the laser plane are extrapolated back to the surface using standard ballistics to obtain ejection velocities. The average ejection velocities for each vertical impact are scaled according to Housen et al. [1983] and plotted versus average scaled ejection position (Figure 5). Data from a similar experiment performed by Cintala et al. [1999] are included for comparison. The 3D PIV ejection velocities show a power law relationship that supports previous experiments [Cintala et al., 1999] and is consistent with ejecta-scaling relations [Housen et al., 1983]. Although the slopes of the two data sets differ, both are within the bounds set by energy- or momentum-driven excavation. The difference most likely reflects the ratio of the projectile to target grain size [Barnouin-Jha et al., 2002]. The experiments presented here used target particles that were less than a tenth the size of the projectiles, whereas the experiments from Cintala et al. [1999] used target grain sizes only half the projectile size. The smaller target grain sizes in these experiments behaved more like a continuous medium for the shock wave, thereby producing higher ejection velocities closer to the crater center. With larger target grains, individual particle interaction effects may have dominated the excavation near the crater center during Cintala et al.'s [1999] experiments.

Figure 4.

The same images as in Figure 3, this time presented as vector plots showing the velocities of particles within the laser plane as measured using 3D PIV (90° impacts in (a), 30° impacts in (b)). The color bars represent the measured velocities within the laser plane for each time step in meters per second (m/s). A different scale is used for each time step to emphasize the asymmetry present in the 30° impacts compared to the 90° impacts even in the latest data set shown. The vector lengths are scaled the same in all eight images and represent the magnitude of the velocity as well; therefore the vector lengths are directly comparable between all eight images. Each vector is three-dimensional, having a component that is perpendicular to the page; however, for simple comparison to Figure 3, the images are presented in the same orientation as in Figure 3 where the laser plane is in the plane of the paper. Note that these vectors do not represent the ejection velocities, but rather the velocities within the laser plane, slightly above the target surface.

Figure 5.

Scaled ejection velocities for vertical impacts plotted versus scaled ejection position. 3D PIV data are shown in solid circles, while data from a similar experiment presented by Cintala et al. [1999] are shown for comparison in open circles.

[22] The ability to capture quantitative data in all directions around the impact point demonstrates the power of 3D PIV, especially for studying azimuthal asymmetries during oblique impacts. Scaled ejection velocity data for 90° and 30° impacts are plotted as a function of azimuthal angle about the crater center (Figure 6). The flow-field center is assumed to be located at the crater center. At the earliest time measured during a vertical impact, there is a slight scatter in ejection velocities, but no discernible dependence on azimuth. These early-time data correspond to the first vertical curtain cross section shown in Figure 3a, in which the ejecta curtain exists at all azimuths. At this time, the ejecta number density is variable; i.e., the ejecta curtain is initially patchy. These patches reflect irregularities created during initial interactions and instabilities at the interface between projectile and target material. The ejection velocities for vertical impacts decrease yet remain constant in azimuth at any given time.

Figure 6.

Scaled ejection velocities versus azimuth for 90° (open symbols) and 30° impacts (solid symbols). Azimuthal angle is defined as 0° in the direction of the impactor trajectory (i.e., directly uprange) and increases clockwise around the ejecta curtain (180° corresponding to directly downrange). The lateral direction is defined to be perpendicular to the impactor trajectory (i.e., angles near 90° and 270° in azimuth). Average values of ejection velocity are determined for azimuthal bins of 10° increments. Data for the four time steps shown in Figures 3 and 4 are plotted. Note the continued asymmetry from downrange to uprange for the 30° impacts, even at the latest time shown. Error bars are shown (some may be smaller than the symbol).

[23] Ejection velocities for the 30° impacts vary as a function of azimuth around the crater center (Figure 6). At early times, the downrange scaled ejection velocities for 30° impacts are as much as 50% faster than the scaled 90° ejection velocities, whereas the 30° uprange data are similar to the vertical data. Although the 30° ejection velocities become more symmetric with respect to azimuth over time, the enhancement downrange persists, even at the latest time measured.

[24] The ratio of the downrange to the uprange ejection velocities (DR/UR) can be used as a reasonable measure of the asymmetry in each ejecta curtain. The azimuthal direction around the impact point is referenced here by the projectile trajectory. Uprange is defined as the direction of the incoming oblique projectile while downrange is the extrapolation of the projectile trajectory after impact. Although vertical impacts have no uprange or downrange direction, the same curtain segments are used when comparing vertical and 30° impacts. Vertical impacts should have a DR/UR ejection velocity ratio that is near unity because the vertical impacts are axi-symmetric about the crater center. Indeed, this is the case, as can be seen from the very flat azimuthal trends for vertical impacts in Figure 6. However, the same ratio for the 30° impacts exhibits a 40% increase in ejection velocity from uprange to downrange portions of the curtain. As the crater grows, the DR/UR ratio decreases initially for the 30° impacts, and then remains at a 20% ejection velocity enhancement downrange through the first half of crater growth. In general, the downrange ejection velocities are always 20–40% higher than the uprange ejection velocities for 30° impacts while there is no discernable difference between uprange and downrange velocities for the vertical impacts. This condition holds for all of the experiments presented here representing the first 50% of crater growth. These data indicate that low-velocity (1 km/s) oblique impacts retain their initial asymmetry in ejection velocity through at least half of crater growth.

[25] The oblique impact data presented in Figure 6 are further affected by the difference in ejection times of the uprange and downrange segments of the 30° curtains. Because the uprange and downrange ejecta are moving slower and faster (respectively) than the lateral ejecta, particles must leave the surface at different times in order to reach the laser plane together. Specifically, slower uprange ejecta must have left the surface before ejecta lateral to the trajectory, whereas faster downrange ejecta left the surface after the lateral ejecta. Ejection velocities decrease in every azimuthal direction as the crater grows. Consequently, it is possible to describe qualitatively what Figure 6 would look like if the same ejection time for all data could be specified. At the time of ejection of the lateral particles observed in the laser plane, the uprange ejecta would have been moving more slowly and had not yet reached the laser plane. The opposite is true of the downrange ejecta: the downrange ejecta leaving the surface at the same time as the lateral ejecta observed in the laser plane would have been moving faster and already passed through the laser plane at the time the image was captured. The asymmetry observed in Figure 6 for 30° impacts therefore is amplified when ejection times are required to be the same. Thus ejection velocities (Figure 6) and DR/UR ratios are minimum representations of the amount of asymmetry present during 30° impacts. Such data all indicate that ejecta curtains for these 30° impacts are “remembering” their origin as having come from an oblique impact well into the excavation stage after the curtain has closed and appears relatively symmetric. This conclusion reflects shock asymmetries created by oblique impact experiments through observed failure asymmetries [Schultz and Anderson, 1996] and direct measurements of early-time shock asymmetries that persist to late times in the far-field pressure wave [Dahl and Schultz, 2001].

[26] The ejection velocity data presented here suggest that 30° impacts (at low velocities) are never fully symmetric and cannot be approximated with a single point source, as is commonly assumed for excavation flow during oblique impacts. Rather, the initial conditions created by the impact angle continue to affect the excavation and deposition of the ejecta well into the excavation stage as evidenced by azimuthal variations in ejection velocities.

3.3. Ejection Angles

[27] Ejection angles (and also curtain angles) are commonly assumed to be fairly constant throughout crater growth [e.g., Housen et al., 1983]. Indeed, vertical impacts produce nearly the same ejection angles in azimuth at each time step, remaining between 45° and 55° degrees from horizontal (Figure 7). At early times for the 30° impacts, however, the ejection angles are low downrange and high uprange (Figure 7a). Ejection angles become more uniform in azimuth as the crater grows but retain their asymmetry well into the excavation stage at later times as shown in Figure 7. The DR/UR ratio of ejection angles (a measure of asymmetry) for vertical impacts again shows no asymmetry. The 30° impacts exhibit a relatively constant 20% decrease in ejection angle for the downrange curtain when compared to the uprange ejection angles as the crater grows. In general, the downrange and uprange ejection angles for the 30° impacts cluster around constant values near 40° and 50°, respectively. The basic shape of the ejection angle trend with azimuth for the 30° impacts remains the same but simply becomes less scattered as the crater grows. In all, the vertical impact ejection angles decrease almost 8 degrees in the first half of crater growth (as observed in these experiments). This increases the apparent symmetry between the data sets, but only by averaging out the asymmetry of the 30° impacts. Because asymmetries (this time in terms of ejection angles) again persist into the excavation stage, these results further demonstrate that the excavation-stage flow remembers its origin as an oblique impact and cannot be modeled as a single, stationary point source.

Figure 7.

Ejection angles versus azimuth for 90° (open symbols) and 30° impacts (solid symbols). Ejection angles are in degrees above horizontal. Azimuthal angle is defined as 0° in the direction of the impactor trajectory (i.e., directly uprange) and increases clockwise around the ejecta curtain (180° corresponding to directly downrange). The lateral direction is defined to be perpendicular to the impactor trajectory (i.e., angles near 90° and 270° in azimuth). Average values of ejection angle are determined for azimuthal bins of 10° increments. Symbols are the same as in Figure 6. Time of image acquisition after impact is approximately (a) 5 msec, (b) 10 msec, (c) 30 msec and (d) 80 msec (exact times are given in Figure 6). Straight lines in each case represent the average ejection angle for the vertical impacts. As the density of the vertical impact ejecta curtain increases with time, the laser intensity that reaches the right-hand side of the curtain decreases. This is reflected both in the relative intensity of the PIV images (Figure 3a) as well as in a slight lateral asymmetry in ejection angles with azimuth for the vertical impacts (c and d). Note the continuing asymmetry in ejection angle through time for the 30° impacts. Although the 30° impact ejection angles appear to become more symmetric with respect to the vertical impact ejection angles this actually reflects vertical impact ejection angles decreasing as the crater grows (see Figure 8).

[28] Ejection angles for vertical impacts are not constant throughout crater growth (Figure 8); rather, they evolve in a pattern that matches a similar experiment performed by Cintala et al. [1999] and are consistent with other experimental data [Schultz and Gault, 1985; Schultz and Anderson, 1996]. This implies that the point source for a vertical impact is also not stationary but rather moves in the vertical direction, as observed in strength-controlled numerical impact experiments and theory [Austin et al., 1981]. Consequently, the ejection angle and velocity data obtained using 3D PIV can be used to further refine the four-dimensional evolving point source region for both oblique and vertical impacts.

Figure 8.

Ejection angles for vertical impacts plotted versus scaled ejection position. 3D PIV data are shown in solid circles, while data from a similar experiment presented by Cintala et al. [1999] are shown for comparison in open circles.

4. Conclusions

[29] The following conclusions are made on the basis of these low-velocity impact experiments using 3D PIV to measure ejecta particle velocities and angles in gravity-controlled particulate targets. (1) The 3D PIV technique proves to be an extremely useful tool for directly measuring the excavation-stage flow of ejecta during impact experiments. (2) Asymmetries in curtain shape exist for 30° impacts, even though the final crater is relatively symmetric. (3) Asymmetries in ejection velocity and angle indicate that impact angle effects persist well into the first 50% of crater growth. (4) The measured asymmetries imply that a single point source is not adequate to represent oblique impacts. Moreover, the single point source is not stationary even for vertical impacts in gravity-controlled sand targets.

[30] Asymmetries in ejection velocity and angle, as well as curtain shape, thickness and density exist in low-velocity (1 km/s) 30° impacts through the first half of crater growth. Other studies demonstrate asymmetries throughout the entire excavation stage for oblique impacts as well. Dahl and Schultz [2001] have shown that initial asymmetries in the shock wave produced during oblique impacts persist to late times as measured in the far field. These continuing shock wave asymmetries persist throughout the excavation as expressed by ejecta asymmetries. For example, asymmetric ejecta deposit patterns are observed at both laboratory and planetary scales [Gault and Wedekind, 1978; Schultz and Anderson, 1996]. Uprange asymmetries are particularly persistent at planetary scales, whereas the high-velocity downrange ejecta component contributes unique signatures [Schultz, 1992]. Moreover, impact angle may have an effect on the levels of extinctions through geologic time [Schultz and Gault, 1990]. Even 30° impacts (usually assumed to be only moderately oblique) may affect crater excavation as reflected on planetary surfaces in the far-field ejecta, particularly the ejecta deposit morphometry in the uprange region. Future studies using 3D PIV will address more specifically the scaling of oblique impact ejecta dynamics and the four-dimensional evolution of the flow field during oblique impacts as a function of velocity, impact angle and target type in order to better understand the extent of these effects at planetary scales.

Acknowledgments

[31] We gratefully acknowledge the knowledge and assistance of the technicians at the NASA Ames Vertical Gun Range. We also greatly appreciate the insightful and helpful comments given by O. Barnouin-Jha and M. Cintala on this manuscript. This material is based upon work supported by a National Science Foundation Graduate Research Fellowship, a NASA-Rhode Island Space Grant Graduate Student Fellowship and NASA Grant No. NAG5-11538.

Ancillary