Scaling Relationships for Microscale to Megascale Impact Craters
Scaling relationships for microscale to megascale impact craters formed in liquids, rocks, and metals
SCALING↗
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Similitude requirements and scaling relationships as applied to model testing
The similitude requirements for the most general test conditions are presented. These similitude requirements are considered in relation to the scaling relationships, test technique, test conditions (including supersonic flow), and test objectives. Particular emphasis is placed on satisfying the various similitude requirements for incompressible and compressible flow conditions. For free flying models tests, the test velocities for incompressible flow are scaled from Froude number similitude requirements and those for compressible flow are scaled from Mach number similitude requirements. The limitations of various test techniques are indicated, with emphasis on the free flying model.
Wolowicz, C. H.↗
Scaling relationships for mercury and gaseous propellant ion thrusters
A model describing the doubly charged ion densities in argon and xenon ion thrusters is presented. Doubly charged ions are shown to be produced in significant numbers from both the neutral and singly ionized states. Doubly-to-singly charged ion density ratios calculated using this model are compared to experimental values of this ratio measured in the 15 cm multipole thruster using both propellants. Agreement between theory and experiment is shown to be good. Using this doubly charged ion model, and a similar one obtained previously for mercury, together with the constant neutral loss rate theory, Child's current density law and accelerator grid fabrication limitations, a set of scaling relationships are developed. These relationships show the propellant utilizations, thrust densities and discharge power levels that can be expected as thruster diameter and/or specific impulse are increased and doubly charged ion densities are held at acceptably low values.
Wilbur, P. J.↗
The scaling relationship between telescope cost and aperture size for very large telescopes
Cost data for ground-based telescopes of the last century are analyzed for trends in the relationship between aperture size and cost. We find that for apertures built prior to 1980, costs scaled as aperture size to the 2.8 power, which is consistent with the precious finding of Meinel (1978). After 1980, 'traditional' monolithic mirror telescope costs have scaled as aperture to the 2.5 power. The large multiple mirror telescopes built or in construction during this time period (Keck, LBT, GTC) appear to deviate from this relationship with significant cost savings as a result, although it is unclear what power law such structures follow. We discuss the implications of the current cost-aperture size data on the proposed large telescope projects of the next ten to twenty years. Structures that naturally tend towards the 2.0 power in the cost-aperture relationship will be the favorable choice for future extremely large apertures; out expectation is that space-based structures will ultimately gain economic advantage over ground-based ones.
telescope costs↗
Event-scale relationships between surface velocity, temperature and chlorophyll in the coastal ocean, as seen by satellite
The overall goal of this project was to increase our understanding of processes which determine the temporally varying distributions of surface chlorophyll pigment concentration and surface temperature in the California Current System (CCS) on the time-scale of 'events', i.e., several days to several weeks. We also proposed to investigate seasonal and regional differences in these events. Additionally, we proposed to evaluate methods of estimating surface velocities and horizontal transport of pigment and heat from sequences of AVHRR and CZCS images. The four specific objectives stated in the original proposal were to: (1) test surface current estimates made from sequences of both SST and color images using variations of the statistical method of Emery et al. (1986) and estimate the uncertainties in these satellite-derived surface currents; (2) characterize the spatial and temporal relationships of chlorophyll and temperature in rapidly evolving features for which adequate imagery exist and evaluate the contribution of these events to monthly and seasonal averages; (3) use the methods tested in (1) to determine the nature of the velocity fields in the CCS; and (4) compare the currents, temperature, and currents in different seasons and in different geographic regions.
Strub, P. Ted↗
Statistical scaling relationships and size effects in the strength and creep rupture of fibrous composites
In this presentation we discuss a new theoretical model and supporting experimental results for the strength and lifetime in creep rupture of unidirectional, carbon fiber/epoxy matrix composites at ambient conditions. First we review the 'standard' Weibull/power-law methodology that has been standard practice. Then we discuss features of a recent model which build on the statistical aspects of fiber strength, micromechanical aspects of stress transfer around fiber breaks, and time-dependent creep of the matrix. The model is applied to 'microcomposites' consisting of seven fibers in a matrix for which strength and creep-rupture data are available. The model yields Weibull distributions in an envelope format for both strength and lifetime. The respective shape, scale and power-law parameters depend on such parameters as the Weibull shape parameter for fiber strength, the exponent for matrix creep, the effective load transfer length (which grows in time due to matrix creep) and the critical cluster size for failed fibers. The experimental results are consistent with the theory, though time-dependent debonding appears to be part of the failure process.
Phoenix, S. Leigh↗
Preliminary Sizing Completed for Single- Stage-To-Orbit Launch Vehicles Powered By Rocket-Based Combined Cycle Technology
Single-stage-to-orbit (SSTO) propulsion remains an elusive goal for launch vehicles. The physics of the problem is leading developers to a search for higher propulsion performance than is available with all-rocket power. Rocket-based combined cycle (RBCC) technology provides additional propulsion performance that may enable SSTO flight. Structural efficiency is also a major driving force in enabling SSTO flight. Increases in performance with RBCC propulsion are offset with the added size of the propulsion system. Geometrical considerations must be exploited to minimize the weight. Integration of the propulsion system with the vehicle must be carefully planned such that aeroperformance is not degraded and the air-breathing performance is enhanced. Consequently, the vehicle's structural architecture becomes one with the propulsion system architecture. Geometrical considerations applied to the integrated vehicle lead to low drag and high structural and volumetric efficiency. Sizing of the SSTO launch vehicle (GTX) is itself an elusive task. The weight of the vehicle depends strongly on the propellant required to meet the mission requirements. Changes in propellant requirements result in changes in the size of the vehicle, which in turn, affect the weight of the vehicle and change the propellant requirements. An iterative approach is necessary to size the vehicle to meet the flight requirements. GTX Sizer was developed to do exactly this. The governing geometry was built into a spreadsheet model along with scaling relationships. The scaling laws attempt to maintain structural integrity as the vehicle size is changed. Key aerodynamic relationships are maintained as the vehicle size is changed. The closed weight and center of gravity are displayed graphically on a plot of the synthesized vehicle. In addition, comprehensive tabular data of the subsystem weights and centers of gravity are generated. The model has been verified for accuracy with finite element analysis. The final trajectory was rerun using OTIS (Boeing Corporation's trajectory optimization software package), and the sizing output was incorporated into a solid model of the vehicle using PRO/Engineer computer-aided design software (Parametric Technology Corporation, Waltham, MA).
Roche, Joseph M.↗
Migration of the Cratering Flow-Field Center with Implications for Scaling Oblique Impacts
Crater-scaling relationships are used to predict many cratering phenomena such as final crater diameter and ejection speeds. Such nondimensional relationships are commonly determined from experimental impact and explosion data. Almost without exception, these crater-scaling relationships have used data from vertical impacts (90 deg. to the horizontal). The majority of impact craters, however, form by impacts at angles near 45 deg. to the horizontal. While even low impact angles result in relatively circular craters in sand targets, the effects of impact angle have been shown to extend well into the excavation stage of crater growth. Thus, the scaling of oblique impacts needs to be investigated more thoroughly in order to quantify fully how impact angle affects ejection speed and angle. In this study, ejection parameters from vertical (90 deg.) and 30 deg. oblique impacts are measured using three-dimensional particle image velocimetry (3D PIV) at the NASA Ames Vertical Gun Range (AVGR). The primary goal is to determine the horizontal migration of the cratering flow-field center (FFC). The location of the FFC at the time of ejection controls the scaling of oblique impacts. For vertical impacts the FFC coincides with the impact point (IP) and the crater center (CC). Oblique impacts reflect a more complex, horizontally migrating flow-field. A single, stationary point-source model cannot be used accurately to describe the evolution of the ejection angles from oblique impacts. The ejection speeds for oblique impacts also do not follow standard scaling relationships. The migration of the FFC needs to be understood and incorporated into any revised scaling relationships.
Anderson, J. L. B.↗
Subsurface Morphology and Scaling of Lunar Impact Basins
Impact bombardment during the first billion years after the formation of the Moon produced at least several tens of basins. The Gravity Recovery and Interior Laboratory (GRAIL) mission mapped the gravity field of these impact structures at significantly higher spatial resolution than previous missions, allowing for detailed subsurface and morphological analyses to be made across the entire globe. GRAIL-derived crustal thickness maps were used to define the regions of crustal thinning observed in centers of lunar impact basins, which represents a less unambiguous measure of a basin size than those based on topographic features. The formation of lunar impact basins was modeled numerically by using the iSALE-2D hydrocode, with a large range of impact and target conditions typical for the first billion years of lunar evolution. In the investigated range of impactor and target conditions, the target temperature had the dominant effect on the basin subsurface morphology. Model results were also used to update current impact scaling relationships applicable to the lunar setting (based on assumed target temperature). Our new temperature-dependent impact-scaling relationships provide estimates of impact conditions and transient crater diameters for the majority of impact basins mapped by GRAIL. As the formation of lunar impact basins is associated with the first approximately 700 Myr of the solar system evolution when the impact flux was considerably larger than the present day, our revised impact scaling relationships can aid further analyses and understanding of the extent of impact bombardment on the Moon and terrestrial planets in the early solar system.
Miljkovic, K.↗
A Comparison of Crater-Size Scaling and Ejection-Speed Scaling During Experimental Impacts in Sand
Non‐dimensional scaling relationships are used to understand various cratering processes including final crater sizes and the excavation of material from a growing crater. The principal assumption behind these scaling relationships is that these processes depend on a combination of the projectile's characteristics, namely its diameter, density, and impact speed. This simplifies the impact event into a single point‐source. So long as the process of interest is beyond a few projectile radii from the impact point, the point‐source assumption holds. These assumptions can be tested through laboratory experiments in which the initial conditions of the impact are controlled and resulting processes measured directly. In this contribution, we continue our exploration of the congruence between crater‐size scaling and ejection‐speed scaling relationships. In particular, we examine a series of experimental suites in which the projectile diameter and average grain size of the target are varied.
Anderson, J. L. B.↗
Target and Projectile: Material Effects on Crater Excavation and Growth
Scaling relationships allow the initial conditions of an impact to be related to the excavation flow and final crater size and have proven useful in understanding the various processes that lead to the formation of a planetary-scale crater. In addition, they can be examined and tested through laboratory experiments in which the initial conditions of the impact are known and ejecta kinematics and final crater morphometry are measured directly. Current scaling relationships are based on a point-source assumption and treat the target material as a continuous medium; however, in planetary-scale impacts, this may not always be the case. Fragments buried in a megaregolith, for instance, could easily approach or exceed the dimensions of the impactor; rubble-pile asteroids could present similar, if not greater, structural complexity. Experiments allow exploration into the effects of target material properties and projectile deformation style on crater excavation and dimensions. This contribution examines two of these properties: (1) the deformation style of the projectile, ductile (aluminum) or brittle (soda-lime glass) and (2) the grain size of the target material, 0.5-1 mm vs. 1-3 mm sand.
Anderson, J. L. B.↗
Testing the Reliability of Cluster Mass Indicators with a Systematics Limited Dataset
We present the mass X-ray observable scaling relationships for clusters of galaxies using the XMM-Newton cluster catalog of Snowden et al. Our results are roughly consistent with previous observational and theoretical work, with one major exception. We find 2-3 times the scatter around the best fit mass scaling relationships as expected from cluster simulations or seen in other observational studies. We suggest that this is a consequence of using hydrostatic mass, as opposed to virial mass, and is due to the explicit dependence of the hydrostatic mass on the gradients of the temperature and gas density profiles. We find a larger range of slope in the cluster temperature profiles at radii 500 than previous observational studies. Additionally, we find only a weak dependence of the gas mass fraction on cluster mass, consistent with a constant. Our average gas mass fraction results also argue for a closer study of the systematic errors due to instrumental calibration and modeling method variations between analyses. We suggest that a more careful study of the differences between various observational results and with cluster simulations is needed to understand sources of bias and scatter in cosmological studies of galaxy clusters.
Juett, Adrienne M.↗
Crater population on asteroid (101955) Bennu indicates impact armouring and a young surface
The impactor-to-crater size scaling relationships that enable estimates of planetary surface ages rely on an accurate formulation of impactor–target physics. An armouring regime, specific to rubble-pile surfaces, has been proposed to occur when an impactor is comparable in diameter to a target surface particle (for example, a boulder). Armouring is proposed to reduce crater diameter, or prevent crater formation in the asteroid surface, at small crater diameters. Here, using measurements of 1,560 craters on the rubble-pile asteroid (101955) Bennu, we show that the boulder population controls a transition from crater formation to armouring at crater diameters ~2–3m, below which crater formation in the bulk surface is increasingly rare. By combining estimates of impactor flux with the armouring scaling relationship, we find that Bennu’s crater retention age (surface age derived from crater abundance) spans from 1.6–2.2Myr for craters less than a few meters to ~10–65Myr for craters >100m in diameter, reducing the maximum surface age by a factor of >15 relative to previous estimates. The range of crater retention ages, together with latitudinal variations in large-crater spatial density, indicate that ongoing resurfacing processes render the surface many times younger than the bulk asteroid.
E. B. Bierhaus↗
Crater Population on Asteroid (101955) Bennu Indicates Impact Armouring and a Young Surface
The impactor-to-crater size scaling relationships that enable estimates of planetary surface ages rely on an accurate formulation of impactor–target physics. An armouring regime, specific to rubble-pile surfaces, has been proposed to occur when an impactor is comparable in diameter to a target surface particle (for example, a boulder). Armouring is proposed to reduce crater diameter, or prevent crater formation in the asteroid surface, at small crater diameters. Here, using measurements of 1,560 craters on the rubble-pile asteroid (101955) Bennu, we show that the boulder population controls a transition from crater formation to armouring at crater diameters ~2–3 m, below which crater formation in the bulk surface is increasingly rare. By combining estimates of impactor flux with the armouring scaling relationship, we find that Bennu’s crater retention age (surface age derived from crater abundance) spans from 1.6–2.2 Myr for craters less than a few meters to ~10–65 Myr for craters >100 m in diameter, reducing the maximum surface age by a factor of >15 relative to previous estimates. The range of crater retention ages, together with latitudinal variations in large-crater spatial density, indicate that ongoing resurfacing processes render the surface many times younger than the bulk asteroid.
Asteroids↗
Applications of the GPCP Satellite-Gauge Merged Precipitation Data Set to the Goals of PACS and GCIP
Recently, under the direction of GEWEX/GCIP there has been an attempt to link North American monsoon rainfall to precipitation in the Great Plains for the purposes of predictability on the seasonal time scale. Rain gauge analyses have been used to show continental-scale relationships. However, the interannual variability of warm season precipitation over the United States is linked to the east Pacific climate system. The Global Precipitation Climatology Project (GPCP) satellite estimates of precipitation over oceans add a vital piece of information towards the goals of PACS and GCIP. This preliminary study will begin by focusing on the East Pacific sector. El-Nino-Southern Ossilation (ENSO) modulates the position and strength of the Inter-Tropical Convergence Zone (ITCZ), which affects the precipitation source for the Mexican monsoon. For example, the five driest summers in coastal Mexico occurred during the five strongest El Ninos (as determined by positive values of Nino 3.4) since 1979. Previous work has investigated lag-lead relationships between the North American monsoon and continental rainfall. GPCP has the potential to extend these relationships to a global scale. Finally data sets with a finer time and space scale, including Tropical Rainfall Measurement Mission (TRMM) products, will be used to examine wave dynamics. Kelvin waves, in particular, may be trigger mechanisms for the onset of the North American monsoon.
Curtis, Scott↗
Airframe noise of a small model transport aircraft and scaling effects
Airframe noise of a 0.01 scale model Boeing 747 wide-body transport was measured in the Langley Anechoic Noise Facility. The model geometry simulated the landing and cruise configurations. The model noise was found to be similar in noise characteristics to that possessed by a 0.03 scale model 747. The 0.01 scale model noise data scaled to within 3 dB of full scale data using the same scaling relationships as that used to scale the 0.03 scale model noise data. The model noise data are compared with full scale noise data, where the full scale data are calculated using the NASA aircraft noise prediction program.
Shearin, J. G.↗
Experimental and analytical studies of advanced air cushion landing systems
Several concepts are developed for air cushion landing systems (ACLS) which have the potential for improving performance characteristics (roll stiffness, heave damping, and trunk flutter), and reducing fabrication cost and complexity. After an initial screening, the following five concepts were evaluated in detail: damped trunk, filled trunk, compartmented trunk, segmented trunk, and roll feedback control. The evaluation was based on tests performed on scale models. An ACLS dynamic simulation developed earlier is updated so that it can be used to predict the performance of full-scale ACLS incorporating these refinements. The simulation was validated through scale-model tests. A full-scale ACLS based on the segmented trunk concept was fabricated and installed on the NASA ACLS test vehicle, where it is used to support advanced system development. A geometrically-scaled model (one third full scale) of the NASA test vehicle was fabricated and tested. This model, evaluated by means of a series of static and dynamic tests, is used to investigate scaling relationships between reduced and full-scale models. The analytical model developed earlier is applied to simulate both the one third scale and the full scale response.
Lee, E. G. S.↗
Impact Experiments into Granular Targets Containing Solitary Blocks of Varying Strength and Size
Crater scaling relationships provide a means to correlate dimensions of laboratory-scale impact experiments to naturally formed craters at planetary scales. For relatively larger impact events, where gravity is the dominant arresting force against crater growth, these scaling relations are comparatively simple. For smaller craters, however, the target properties have increasing influence over the cratering process. Further complexities are easily envisaged when considering realistic surfaces that contain small-scale heterogeneities in cohesive strength, density, porosity, friction, as these properties will each have unequal effects on the resultant crater morphometry. Even when produced under controlled laboratory conditions, understanding (and controlling) the entire relevant parameter space is daunting, and deconvolution of the relevant contributors can be complicated even in the best-case scenario. To this end, we have begun an extensive series of impact experiments that will provide a nascent framework that will aid in the interpretation of craters observed on complex natural surfaces throughout the solar system. To start with the simplest configuration, experiments were performed with cylindrical PVC buckets that were filled with quartz sand and contained a single cubic block of synthetic sandstone. The blocks varied in size (14-33 mm) and unconfined compressive strength (0.5-7.4 MPa) and were placed in/on the sand along the trajectory of the incoming impactor and buried to different depths. All experiments were conducted using the vertical gun located in the Experimental Impact Lab at NASA Johnson Space Center with alumina projectiles that were accelerated to ~1.53 km s^-1 under a vacuum of 1 torr. After the impact, target containers were removed from the chamber are morphometric data were extracted by using a Peel 2 3D-scanner in combination with the open-source software, CloudCompare. Initial results show that block strength is a secondary effect on crater diameter and depth, but when at least one edge of the block is exposed and the surface (partial burial) the strength will dictate the number of surviving block fragments around the crater, as well as how much disrupted block material is retained within the crater walls.
Christopher J. Cline II↗