Meteoritics & Planetary Science 1–19 (2017) doi: 10.1111/maps.12873 A numerical assessment of simple airblast models of impact airbursts * Gareth S. COLLINS , Elliot LYNCH, Ronan MCADAM, and Thomas M. DAVISON Department of Earth Science and Engineering, Impact and Astromaterials Research Centre, Imperial College, London SW7 2AZ, UK *Corresponding author. E-mail: [email protected] (Received 17 August 2016; revision accepted 02 March 2017) Abstract–Asteroids and comets 10–100 m in size that collide with Earth disrupt dramatically in the atmosphere with an explosive transfer of energy, caused by extreme air drag. Such airbursts produce a strong blastwave that radiates from the meteoroid’s trajectory and can cause damage on the surface. An established technique for predicting airburst blastwave damage is to treat the airburst as a static source of energy and to extrapolate empirical results of nuclear explosion tests using an energy-based scaling approach. Here we compare this approach to two more complex models using the iSALE shock physics code. We consider a moving-source airburst model where the meteoroid’s energy is partitioned as two- thirds internal energy and one-third kinetic energy at the burst altitude, and a model in which energy is deposited into the atmosphere along the meteoroid’s trajectory based on the pancake model of meteoroid disruption. To justify use of the pancake model, we show that it provides a good fit to the inferred energy release of the 2013 Chelyabinsk fireball. Predicted overpressures from all three models are broadly consistent at radial distances from ground zero that exceed three times the burst height. At smaller radial distances, the moving-source model predicts overpressures two times greater than the static-source model, whereas the cylindrical line-source model based on the pancake model predicts overpressures two times lower than the static-source model. Given other uncertainties associated with airblast damage predictions, the static-source approach provides an adequate approximation of the azimuthally averaged airblast for probabilistic hazard assessment. INTRODUCTION Tunguska event, which caused extensive tree damage over a 2200 km2 area (e.g., Ben-Menahem 1975; Chyba The breakup of a large asteroid or comet (meteoroid) et al. 1993; Boslough and Crawford 2008; Artemieva and due to aerodynamic stresses releases the majority of the Shuvalov 2016) and more recently the ~0.5 Mt, 2013 meteoroid’s kinetic energy into the atmosphere Chelyabinsk fireball, which occurred over a densely (Artemieva and Shuvalov 2016). As the meteoroid breaks populated region of Russia, injuring more than 1600 up, the surface area exposed to the air increases and the people and breaking windows in the surrounding towns body’s retardation and fragmentation increases (Popova et al. 2013). Although often less damaging than exponentially—resulting in an explosive release of energy crater-forming impacts, airbursts are far more common— (Passey and Melosh 1980; Chyba et al. 1993; Collins with a Tunguska-scale event expected to have an average et al. 2005). The largest airbursts release energies in the recurrence interval in the range 100–2000 yr (Brown megaton (Mt) to tens-of-megatons range (one ton of et al. 2013). TNT is equivalent to 4.184 gigajoules, 4.184 9 109) and, As atmospheric nuclear explosions have been if the majority of the energy release occurs sufficiently observed to produce blast waves similar to those low in the atmosphere, the strength of the resultant observed or inferred for impact airbursts (Glasstone and atmospheric blast wave can cause damage on the ground. Dolan 1977), an established technique for fast calculation Examples of such airbursts include the 3–15 Mt, 1908 of airburst blastwave damage is to treat the airburst as a 1 © 2017 The Authors. Meteoritics & Planetary Science published by Wiley Periodicals, Inc. on behalf of The Meteoritical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. 2 G. S. Collins et al. static source of energy, equivalent to a nuclear explosion disruption in the atmosphere (Shuvalov et al. 2013) to (e.g., Toon et al. 1997; Collins et al. 2005). For instance, establish the strengths and weaknesses of each modeling the protocol adopted by Collins et al. (2005) comprises approach. Our focus is to refine protocols for fast three parts (1) a model of atmospheric disruption to estimation of airburst blastwave damage on the ground determine the approximate burst altitude and energy (the that can be used in probabilistic hazard assessment. pancake model), (2) a scaling procedure for relating the airburst scenario (burst altitude and energy) to a PANCAKE MODEL OF METEOROID representative static 1 kt nuclear explosion scenario (yield DISRUPTION IN THE ATMOSPHERE scaling), and (3) a database of nuclear test data documenting blast pressure as a function of range for The motion of a meteoroid through the atmosphere static 1 kt atmospheric explosions at a range of altitudes and mass loss owing to ablation can be described by a (Glasstone and Dolan 1977). A simple approach such as set of four ordinary differential equations (e.g., Passey this is required for probabilistic impact hazard and Melosh 1980) up to the point that the meteoroid assessment, in which hundreds of thousands of scenarios fragments. Fragmentation is commonly assumed to must be considered (e.g., Reinhardt et al. 2016). occur when the ram pressure in front of the meteoroid Although the static-source approximation is a good (the local air density times the meteoroid velocity representation of nuclear blast waves, it has limitations squared), exceeds the meteoroid’s strength. Beyond the when applied to meteor phenomenon (Collins et al. fragmentation point, an additional equation is required 2005; Boslough and Crawford 2008; Shuvalov et al. to describe the increase in cross-sectional area of the 2013). The most obvious limitation of the disrupted rock mass as it deforms in response to approximation in this context is that the source is static, aerodynamic stresses, decelerates, and penetrates denser whereas at peak energy release, a meteor is still moving air (e.g., Chyba et al. 1993; Hills and Goda 1993; at hypersonic velocities—considerably faster than the Avramenko et al. 2014). speed at which the blast wave propagates—suggesting In the “pancake model” (Chyba et al. 1993; Collins that the static explosion analogy may underestimate et al. 2005), the spreading rate is defined by a force blast damage on the ground (Boslough and Crawford balance on the walls of the disrupted meteoroid, which 2008). In addition, recent data from Chelyabinsk is approximated as an incompressible, strengthless (Popova et al. 2013) suggest elliptical-shaped blast cylinder, deformed by an average differential stress damage contours with semimajor axes perpendicular to proportional to the ram pressure. The name of the the trajectory, which contrasts with the circular peak model refers to the tendency of the meteoroid to deform pressure contours predicted by the static-source model. into a thin pancake-like cylinder with a large cross- In this paper, we re-examine the static-source sectional area. In an unconstrained pancake model, the approximation as a procedure for estimating airburst meteoroid is allowed to expand without bound, while in blast damage using numerical modeling. First, we use a a constrained model, the cylinder radius is limited to a fast, semianalytical approximation of the pancake multiple of the initial diameter of the meteor—the so- model of a meteoroid’s atmospheric disruption— called pancake factor. In the similar “fragment cloud” modified to account for meteoroid ablation—to model of Hills and Goda (1993) spreading rate is constrain the range and likelihood of airburst altitude/ defined by equating the kinetic energy of the expanding energy combinations and the residual kinetic energy of fragments to the work done by the air to increase the the meteoroid at burst. We show that the 2013, ~500 kt area of the cloud of fragments. In this case, meteoroid Chelyabinsk airburst can be well described using the spreading ceases when the ram pressure in front of the pancake model and occurred at an altitude several meteoroid drops below the strength of the meteoroid. kilometers higher than the worst-case scenario expected Another, more recent meteoroid disruption model for this energy range. Second, we use the iSALE2D (Avramenko et al. 2014) derives an alternative shock physics code to simulate blastwave formation, spreading rate using dimensional analysis and a chain- attenuation, and interaction with the surface under reaction analogy for the cascading disruption of three simple energy deposition approximations: a meteoroid fragments. Like the fragment cloud model, spherical static source of internal energy equivalent to spreading is arrested when the ram pressure drops the impact energy, a spherical moving source with a below the fragments’ strength; however, in this case, the one-third kinetic-to-internal energy partitioning, and a strength of the fragments is assumed to increase with cylindrical line source with the energy per unit path time as fragment size decreases. length determined by the pancake model. We compare While these alternative models of meteoroid the results of our simulations to observations and disruption and deceleration in the atmosphere differ