VOL. 76, NO. 23
JOURNAL OF GEOPHYSICAL RESEARCH
AUGUST 10, 1971
Craters Produced by Missile Impacts
H.J. Moore
U.S. Geological Survey Menlo Park, California 94025
Craters produced by missiles with oblique trajectories and kinetic energies between 2.1 * 1016 and 81 * 1014 ergs produce craters 2 to 10 meters across. The craters and their ejecta are typically bilaterally symmetrical about the plane of the trajectory. Crater dimensions are strongly dependent on target material and kinetic energy of the missile. Craters in wet targets are significantly larger than those in dry porous targets. Displaced masses of the craters are proportional to the kinetic energies of the missiles (adjusted for, angles of impact) raised to a power larger than 1, and near 1.5. In a general sense, sizes of craters produced by missile impacts are about the same size as craters produced by chemical explosives with shallow depths of burial. The problem of equivalent scaled depth of burst for an impact crater is not resolved, however.
A study of craters produced by the impact of missiles is being conducted by the U.S. Geological Survey, The purposes of the crater study are to extend our knowledge of experimental impact craters to those produced by projectiles with large kinetic energies, to compare the dimensions and characteristics of the craters with craters produced by chemical explosives, and to apply the knowledge pained from the impact craters to lunar problems. This paper provides data on missile impact craters about 2 to 10 meters across produced by missiles with kinetic energies between 2.1 * 1016 and 81 * 1014 impacting along oblique trajectories and compares the impact data with explosive data.
Procedures
Missiles with kinetic energies between 2.1 * 1016 and 81 * 1014 ergs impacted dry to moist sand, alluvium, colluviuin, and gypsum lake sediments along oblique trajectories with angles between 25° and 58° from the local horizontal. Some of the missiles have velocities at impact near 2.6 km/sec and larger [Moore, 1968]. The missiles contain no explosives, so that only the kinetic energy of the missile is available to form the crater. Target densities measured using techniques outlined in U.S. Bureau of Reclamation [19G3] range from 1.0 g/cm3 for some gypsifer-ous alluvium to 1.98 g/cm3 for gypsum lake beds and to 2.5 g/cm3 for sandstone.
Topographic maps of the craters are prepared using a telescopic alidade, plane table, stadia rod, and tape at scales of 1:24 and 1:48, depending on the size of the crater. Part of the ejecta and limits of throw-out are mapped at smaller scales. Crater dimensions are obtained from the topographic maps. Crater volumes are calculated using areas obtained with a compensating planimeter from the topographic maps and the known contour interval. The volumes include only that portion of the crater below the original ground surface. Displaced mass is computed by multiplying the density of the target material and crater volume.
Description
Craters and ejecta distributions invariably reflect the oblique trajectories of the missiles. They are bilaterally symmetrical about the plane of the trajectory. Crater rims are low to nonexistant beneath the trajectory (up-range side of the trajectory), and well developed on the opposite (down-range side of the trajectory) side (Figure 1).
Slopes of crater walls beneath the trajectory are typically steeper than those on the opposite wall, where most of the material is cohesionless fragmental material at the angle of repose. The flank of the crater beneath the trajectory is often the original ground surface, whereas the flank on the opposite side of the crater is tilted and slopes gently away from the crater rim. Mirror image rims, crater walls, and gently outward-sloping crater flanks are found at right angles to the trajectory plane.
Generally, six mappable units are exposed in and around the craters (Figures 2 and 3): (1) target material (tm), (2) thick ajecta (te), (3) thin to discontinuous ejecta (td), (41 tilted and broken target material (tb), (5) shattered and fractured target material (sf), and (6) slope material (sm). Each of these units is briefly described below. '
Target material' is undeformed intact target material surrounding the crater and underlying part of the ejecta. "Thick ejecta" is a blanket of debris about 5 to 30 cm thick deposited from the rim to distances of several meter with bilateral symmetry about the plane of the missile trajectory. Thick ejecta is composed of debris ranging in, size from a powder to sizeable fragments. In some materials, blocks may be as large as 0.75 meters. Most of the ejecta are disaggregated and fragmented target material but as much as 20 to 30% of the ejecta may be sheared and compressed fragments, along with scattered fragments of the missile. In most cases, where the target material is layered, the sequence of the original layering is preserved in the frag-mental ejecta but inverted (Figure 4).
This inversion of layering has been described at Meteor Crater, Arizona [Shoemaker, 1000], and for ex- plosive craters with shallow depths of burial (Shoemaker [I960]; D. J. Roddy, unpublished data, 1971). 'Thin to discontinuous ejecta' surrounds the thick ejecta and may extend a small distance in the 'up' trajectory directions. Fragments in this unit are generally smaller than those in the thick ejecta and consist of the same three types of material. Fragments of this unit are scattered to distances near 12 to 10 motors at right angles to the plane of the trajectory and 20 motors or so in the forward direction when the crater diameter is near 5 to 6 meters . across. In some cases, small tongues of this unit extend small distances 'up' trajectory. The limit of throw-out, beyond which no fragments are found, extends about 130 meter- from the crater, but it may be as far as 330 meters for the larger orators. '
Tilted and broken target material' underlies the thick ejecta near the rim and beneath the flanks. Here target material is tilted upward and fractured (see Figure 4). Rotation and tilling rapidly decrease outward from the rim crest. Generally, upward tilting of the target material is absent on the 'up' trajectory side. 'Shattered and fractured target material' is found exposed on the steep crater wall beneath the trajectory and may include conjugate fractures. Open fractures concentric to the crater edge and downward faulting may occur near the crater edge. 'Slope material' is composed of cohesionless debris at the angle of repose on lower crater walls and as a covering on the crater floor. Pieces of broken target material, sheared and compressed material, and projectiles are found in this unit. Slope material is best developed on lower parts of crater walls, especially 'down' trajectory and at right angles to the plane of the trajectory.
A mixed breccia of sheared and compressed target, material and pieces of the projectile underlie the crater floor [Moore, 1969]. The mixed breccia is partly surrounded by sanded material with flow banding. Intensely fractured material surrounds, in turn, both the mixed breccia and the sanded material.
Significant, variations of crater form, ejecta distribution, and character of the ejecta occur for craters in different target materials. Rims completely surround craters in water-saturated lake beds and loose sand, whereas rims are absent on the 'up' trajectory side of craters in alluvium. Thick ejecta completely surrounds craters in water-saturated sediments, and no sheared and compressed target material is found in their ejecta. Thus the morphology of missile craters and their ejecta are dependent, on the target material.
Crater Size
Crater dimensions are a function of the kinetic energy of the missiles, angles of impact, and target material. Projectile density, shape, orien-tation, size and velocity may also affect crater dimensions | Denardo, 1968; Denardo et al., 1967: Cook and Mortensen, 1967; Culp and Hooper, 1961], but these variables, which are known, may not be specified for all the missile impact craters. Nevertheless, the effect of the kinetic energy and target, material on crater size can be illustrated by using crater radii and displaced masses. Crater rim radii, taken as 0.25 of the sum of the crater diameter from rim to edge in the trajectory plane and the crater di- ameter from rim to rim at right, angles to the plane, are approximately proportional to the 0.4 power of the kinetic energy (Figure 5) and differ significantly from cube-root pealing, which requires the 0.33 power. In comparing displaced masses with kinetic energies, the kinetic energies are corrected for angles of impact, on the basis of data on hypervelocity impact of steel pellets with lead targets [Bryan, 1962; see also Gault et al., 1965], by multiplying the kinetic energy of the missile and the sine of the angle of impact measured from the local impact surface.
Although there is considerable scatter in ihe data on displaced masses, they are not directly proportional to the corrected kinetic energies (Figure 6), but rather are proportional to the corrected kinetic energies raised to a power near 1.5. Such a conclusion is reached when considering six craters in moist gypsum lake beds, a relatively uniform target material (Figure 6).
The importance of target material is also pronounced (Figure 6). ('raters produced by missiles with equal energies and angles of impact in water-saturated gypsum lake beds are clearly larger than other craters produced in dry to moist targets such as sand, alluvium, colluvium, indurated gypsum sand, and moist gypsum lake beds. Those in moist gypsum lake beds also tend to be larger than those in sand, alluvium, and colluvium. It is noteworthy that craters in water-saturated lake beds are characterized by rims that completely surround the crater and ejecta devoid of sheared and compressed target material. Sheared and compressed target material is absent in ejecta from craters in moist gypsum lake beds, in marked contrast to the ejecta from craters in dry alluvium and dry indurated gypsum sand, where sheared and compressed target material is abundant. This suggests that compressibility, shear strength, and moisture content of the target material play important roles in the cratering process. The large size of craters in water-saturated gypsum when compared to craters in dry porous material may be due to several causes: (1) reduced target strength resulting from positive pore pressures during compression of target material that reduces the effective stress normal to failure planes [Hubbert and Rubey, 1959; Moore and Lugn, 1965], (2) increased fraction of energy delivered to target at impact [Gault and Heito-wit, 1903], and (3) decreased rate of energy loss behind expanding shock and stress waves.
Comparison with Chemical Explosion Craters
Sizes of craters produced by missile impacts compare, in a general way, to those produced by chemical explosives when the kinetic energy of the missile is equal to the TNT equivalent energy release of the explosive {Moore et al., 1964; Moore, 1966]. Such a correlation has boon shown (or rocks [Gault ct a!., 1963, p. 29; Gault and Moore, 1965] and sand [Oberbeck, 1971]. The problem of exact comparisons for a variety of natural materials and projectile conditions is not resolved, however. The effects of target properties such as porosity, cohesion, friction angle, moisture content, and equation-of-state and projectile properties such as density, velocity, size, shape, and equation of state have not been studied in sufficient detail. This problem can be illustrated with a sequence of experiments using targets of diatomaceous earth with an un-confined compressive strength near 8 bars and a density near 1.0 g/cm3. A wide variety of results are obtained.
A projectile (BB) fired into diatomaceous earth at about 0.12 km/sec produces a tube in the diatomaceous earth about 3 BB diameters deep and 1 BB diameter across.. A 0.22 caliber bullet fired into diatomaceous earth at about 1.5 km/sec produces a cavity beneath the target surface filled with fragments of the target material and projectile. No crater is produced by the 0.22 projectile, and only a narrow hole connects the surface of the target with the breccia-filled cavity. This cavity is similar to camouflets produced by deeply buried charges of chemical explosives that do not make craters [see for example, US. Army Corps of Engineers, 1958]. An experiment conducted at the Ames Research Center Free Flight Range under the direction of D. E. Gault showed that craters are produced by 1/8-inch chrome steel spheres impacting diatomaceous earth at 4.4 km/see. In dense coherent rocks, such as basalt [Moore et at., 1965], small projectiles at velocities near 0XS to 7.3 km/sec produce craters, but BB's at velocities near 0.12 km/sec simply bounce at impact, and no crater is produced. Similar variations to those described above occur with missile impacts.
As part of a passive seismic study of missile impact [Latham ct at., 1970], explosive craters were produced in colluvium and alluvium immediately adjacent to missile-impact craters in colluvium and alluvium by using commercial explosives at shallow depths of burial. (Explosives used were 65% Amodyte 1, Atlas Chemical Industries, and 60% Amogel 1, Apache Powder Company.) Data from this study are plotted in Figure 7, where the energy equivalence of the explosives is near 1.77 x 1013 ergs/pound and the scaled depths of burial A are the depth of burial in feet divided by the cube root of the charge weight in pounds.
The data show that craters in the colluvium are larger than those in the alluvium and that the sizes of the missile-impact craters are comparable to the explosive craters. For the impact crater in colluvium there was no evidence of a camouflet; thus, it compares well with an explosive crater with a scaled depth of burial near 0.3S A. A large difference is noted for the impact craters in alluvium. Such a difference is related to projectile burial. Field evidence indicated that a substantial part of the missile, in pieces and fragments, remained beneath the surface of the small crater, whereas morn pieces were found at the surface for the larger crater. Thus simple generalizations about equivalent scaled depths of burst for impact craters are unjustified. A lack of simple correlations for various target materials can be expected for projectile velocities as large as 6.5 km/sec |see e.g. Gault et at., 1966, Figure 4].
Nevertheless, cratering experiments using chemical and nuclear explosives with shallow depths of burial provide the data for best estimates of energies of large natural objects producing large impact craters.
Summary
In summary, dimensions of craters produced by missile impacts are strongly dependent on the kinetic energies of the missiles and the target materials. Crater morphologies, ejecta distributions, and map units are typically bilaterally symmetrical about the plane of the oblique missile trajectory. Although there is a correspondence between sizes of craters produced by impacts and explosives with equivalent energies, the problem of equivalent scaled depth of burst of impact craters is unresolved. For an impact, the variables affecting equivalent scaled depth include projectile properties such as velocity, density, mass, and shape and target properties such as strength, porosity, and composition.
Acknowledgments.
The author is indebted to the Commanding General, White Sands Missile Range, New Mexico, for allowing access to the craters, furnishing data on the kinetic energies of the missiles, and providing ground and aerial photographs of the craters. Valuable suggestions and reviews were given by D. J. Roddy and V. R. Oberbeck. Rt. Kachadoorian and P. Margolin helped map most of the craters. Publication authorized by the Director, U.S. Geological Survey.
References
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