Drag force scaling for penetration into granular media

Effect of skull morphology on fox snow diving

Certain fox species plunge-dive into snow to catch prey (e.g., rodents), a hunting mechanism called mousing. Red and arctic foxes can dive into snow at speeds ranging between 2 and 4 m/s. Such mousing behavior is facilitated by a slim, narrow facial structure. Here, we investigate how foxes dive into snow efficiently by studying the role of skull morphology on impact forces it experiences. In this study, we reproduce the mousing behavior in the lab using three-dimensional (3D) printed fox skulls dropped into fresh snow to quantify the dynamic force of impact. Impact force into snow is modeled using hydrodynamic added mass during the initial impact phase. This approach is based on two key facts: the added mass effect in granular media at high Reynolds numbers and the characteristics of snow as a granular medium. Our results show that the curvature of the snout plays a critical role in determining the impact force, with an inverse relationship. A sharper skull leads to a lower average impact force, which allows foxes to dive head-first into the snow with minimal tissue damage.

Penetration of a spinning sphere impacting a granular medium

We investigate experimentally the influence of rotation on the penetration depth of a spherical projectile impacting a granular medium. We show that a rotational motion significantly increases the penetration depth achieved. Moreover, we model our experimental results by modifying the frictional term of the equation describing the penetration dynamics of an object in a granular medium. In particular, we find that the frictional drag decreases linearly with the velocity ratio between rotational (spin motion) and translational (falling motion) velocities. The good agreement between our model and our experimental measurements offers perspectives for estimating the depth that spinning projectiles reach after impacting onto a granular ground, such as happens with seeds dropped from aircraft or with landing probes.

High speed impact on granular media: breakdown of conventional inertial drag models

In this study, we extensively explore the impact process on granular media, particularly focusing on situations where the ratio of impact speed to acoustic speed is on the order of 0.01-1. This range significantly exceeds that considered in existing literature (0.0001-0.001). Our investigation involves a comprehensive comparison between our simulation data, obtained under high-speed conditions, and the established macroscopic drag models. In the high-speed regime, conventional drag force models prove inadequate, and the drag force cannot be separated into a depth-dependent static pressure and a depth-independent inertial drag, as suggested in previous literature. A detailed examination of the impact process in the high-speed limit is also presented, involving the spatio-temporal evolution of the force chain network, displacement field, and velocity field at the particle length scale. Unlike prior works demonstrating the exponential decay of pulses, we provide direct evidence of acoustic pulses propagating over long distances, reflecting from boundaries, and interfering with the original pulses. These acoustic pulses, in turn, induce large scale reorganization of the force chain network, and the granular medium continuously traverses different jammed states to support the impact load. Reorientation of the force chains leads to plastic dissipation and the eventual dissipation of the impact energy. Furthermore, we study the scaling of the early stage peak forces with the impact velocity and find that spatial dimensionality strongly influences the scaling.

Finite size effects during the penetration of objects in a granular medium

In many industrial or geotechnical applications, objects move through a granular medium and an important issue is the prediction of the force that develops during the motion of the intruder. In this paper, we experimentally study the vertical penetration of intruders into granular media and analyze both the average force and the fluctuations during motion. We investigate configurations where the size of the intruder becomes close to a few grain sizes, a regime that has not been studied before. Finite size effects are observed, showing that both the mean force and the fluctuations significantly increase when decreasing the ratio of the intruder size to the particle size, and scaling laws are identified to characterize this effect. The role of a conical tip in front of the cylinder to facilitate the penetration is also studied, showing that it is more efficient when the aspect ratio between the intruder size and the grain size is low.

Force on a sphere suspended in flowing granulate

We investigate the force of flowing granular material on an obstacle. A sphere suspended in a discharging silo experiences both the weight of the overlaying layers and drag of the surrounding moving grains. In experiments with frictional hard glass beads, the force on the obstacle was practically flow-rate independent. In contrast, flow of nearly frictionless soft hydrogel spheres added drag to the gravitational force. The dependence of the total force on the obstacle diameter is qualitatively different for the two types of material: It grows quadratically with the obstacle diameter in the soft, low-friction material, while it grows much weaker, nearly linearly with the obstacle diameter, in the bed of glass spheres. In addition to the drag, the obstacle embedded in flowing low-friction soft particles experiences a total force from the top as if immersed in a hydrostatic pressure profile, but a much lower counterforce acting from below. In contrast, when embedded in frictional, hard particles, a strong pressure gradient forms near the upper obstacle surface.

Impact craters formed by spinning granular projectiles

Craters formed by the impact of agglomerated materials are commonly observed in nature, such as asteroids colliding with planets and moons. In this paper, we investigate how the projectile spin and cohesion lead to different crater shapes. For that, we carried out discrete element method computations of spinning granular projectiles impacting onto cohesionless grains for different bonding stresses, initial spins, and initial heights. We found that, as the bonding stresses decrease and the initial spin increases, the projectile's grains spread farther from the collision point, and in consequence, the crater shape becomes flatter, with peaks around the rim and in the center of the crater. Our results shed light on the dispersion of the projectile's material and the different shapes of craters found on Earth and other planetary environments.

Imperfect bodies sink imperfectly when settling in granular matter

From Mars rovers to buildings, objects eventually sink and tilt into a fluidized granular bed due to gravity. Despite the irregular shape of realistic granular intruders, most research focus on the settling of "perfect" objects like spheres and cylinders. Here, we systematically explore the penetration of "imperfect" solids-from stones to bodies with carefully controlled asymmetries-into granular beds. A cylinder with two halves of different roughnesses rotates toward the granular region next to the smoother surface and deviates from the vertical direction. We demonstrate that even small irregularities in the surface of an object may produce substantial changes in the penetration process. Using computer simulations, we show that defects concentrate granular force chains, thus producing decisive forces on the intruder. Furthermore, we demonstrate that tilting and migration of sinking bodies can be correctly predicted by a simple mechanical model based on a unified force law.

Roles of packing fraction, microscopic friction, and projectile spin in cratering by impact

From small seeds falling from trees to asteroids colliding with planets and moons, the impact of projectiles onto granular targets occurs in nature at different scales. In this paper, we investigate open questions in the mechanics of granular cratering, in particular, the forces acting on the projectile and the roles of granular packing, grain-grain friction, and projectile spin. For that, we carried out discrete element method computations of the impact of solid projectiles on a cohesionless granular medium, where we varied the projectile and grain properties (diameter, density, friction, and packing fraction) for different available energies (within relatively small values). We found that a denser region forms below the projectile, pushing it back and causing its rebound by the end of its motion, and that solid friction affects considerably the crater morphology. Besides, we show that the penetration length increases with the initial spin of the projectile, and that differences in initial packing fractions can engender the diversity of scaling laws found in the literature. Finally, we propose an ad hoc scaling that collapsed our data for the penetration length and can perhaps unify existing correlations. Our results provide new insights into the formation of craters in granular matter.

Learning quadrupedal locomotion on deformable terrain

Simulation-based reinforcement learning approaches are leading the next innovations in legged robot control. However, the resulting control policies are still not applicable on soft and deformable terrains, especially at high speed. The primary reason is that reinforcement learning approaches, in general, are not effective beyond the data distribution: The agent cannot perform well in environments that it has not experienced. To this end, we introduce a versatile and computationally efficient granular media model for reinforcement learning. Our model can be parameterized to represent diverse types of terrain from very soft beach sand to hard asphalt. In addition, we introduce an adaptive control architecture that can implicitly identify the terrain properties as the robot feels the terrain. The identified parameters are then used to boost the locomotion performance of the legged robot. We applied our techniques to the Raibo robot, a dynamic quadrupedal robot developed in-house. The trained networks demonstrated high-speed locomotion capabilities on deformable terrains: The robot was able to run on soft beach sand at 3.03 meters per second although the feet were completely buried in the sand during the stance phase. We also demonstrate its ability to generalize to different terrains by presenting running experiments on vinyl tile flooring, athletic track, grass, and a soft air mattress.

Near-zero cohesion and loose packing of Bennu's near subsurface revealed by spacecraft contact

When the OSIRIS-REx spacecraft pressed its sample collection mechanism into the surface of Bennu, it provided a direct test of the poorly understood near-subsurface physical properties of rubble-pile asteroids, which consist of rock fragments at rest in microgravity. Here, we find that the forces measured by the spacecraft are best modeled as a granular bed with near-zero cohesion that is half as dense as the bulk asteroid. The low gravity of a small rubble-pile asteroid such as Bennu effectively weakens its near subsurface by not compressing the upper layers, thereby minimizing the influence of interparticle cohesion on surface geology. The underdensity and weak near subsurface should be global properties of Bennu and not localized to the contact point.

Added-mass force in dry granular matter

From two-dimensional (2D) numerical simulations of the motion of a circular intruder into a dry granular packing, we provide evidence for a specific force term in the case of unsteady motion in addition to the force corresponding to a steady motion. We show that this additional term is proportional to the acceleration of the intruder relative to the grains as the added-mass force known for simple fluids. This force term corresponds to a variation in the kinetic energy of the surrounding flow and is characterized by a coefficient C_{AM} which is intrinsically linked to the nature of the granular media. An analytical calculation of the added-mass coefficient C_{AM} is developed based on the specific velocity field known for 2D granular flow around a cylinder. The theoretical value is shown to depend on the grain-cylinder size ratio, in good agreement with the measurements from our unsteady simulations.

How head shape and substrate particle size affect fossorial locomotion in lizards

Granular substrates ranging from silt to gravel cover much of the Earth's land area, providing an important habitat for fossorial animals. Many of these animals use their heads to penetrate the substrate. Although there is considerable variation in head shape, how head shape affects fossorial locomotor performance in different granular substrates is poorly understood. Here, head shape variation for 152 species of fossorial lizards was quantified for head diameter, slope and pointiness of the snout. The force needed to penetrate different substrates was measured using 28 physical models spanning this evolved variation. Ten substrates were considered, ranging in particle size from 0.025 to 4 mm in diameter and consisting of spherical or angular particles. Head shape evolved in a weakly correlated manner, with snouts that were gently sloped being blunter. There were also significant clade differences in head shape among fossorial lizards. Experiments with physical models showed that as head diameter increased, absolute penetration force increased but force normalized by cross-sectional area decreased. Penetration force decreased for snouts that tapered more gradually and were pointier. Larger and angular particles required higher penetration forces, although intermediate size spherical particles, consistent with coarse sand, required the lowest force. Particle size and head diameter effect were largest, indicating that fossorial burrowers should evolve narrow heads and bodies, and select relatively fine particles. However, variation in evolved head shapes and recorded penetration forces suggests that kinematics of fossorial movement are likely an important factor in explaining evolved diversity.

Intrusion into Granular Media Beyond the Quasistatic Regime

The drag force exerted on an object intruding into granular media is typically assumed to arise from additive velocity and depth dependent contributions. We test this with intrusion experiments and molecular dynamics simulations at constant speed over four orders of magnitude, well beyond the quasistatic regime. For a vertical cylindrical rod we find velocity dependence only right after impact, followed by a crossover to a common, purely depth-dependent behavior for all intrusion speeds. The crossover is set by the timescale for material, forced to well up at impact, to subsequently settle under gravity. These results challenge current models of granular drag.

Ricochets on Asteroids: Experimental study of low velocity grazing impacts into granular media

Spin off events and impacts can eject boulders from an asteroid surface and rubble pile asteroids can accumulate from debris following a collision between large asteroids. These processes produce a population of gravitational bound objects in orbit that can impact an asteroid surface at low velocity and with a distribution of impact angles. We present laboratory experiments of low velocity spherical projectiles into a fine granular medium, sand. We delineate velocity and impact angles giving ricochets, those giving projectiles that roll-out from the impact crater and those that stop within their impact crater. With high speed camera images and fluorescent markers on the projectiles we track spin and projectile trajectories during impact. We find that the projectile only reaches a rolling without slipping condition well after the marble has reached peak penetration depth. The required friction coefficient during the penetration phase of impact is 4-5 times lower than that of the sand suggesting that the sand is fluidized near the projectile surface during penetration. We find that the critical grazing impact critical angle dividing ricochets from roll-outs, increases with increasing impact velocity. The critical angles for ricochet and for roll-out as a function of velocity can be matched by an empirical model during the rebound phase that balances a lift force against gravity. We estimate constraints on projectile radius, velocity and impact angle that would allow projectiles on asteroids to ricochet or roll away from impact, finally coming to rest distant from their initial impact sites.

Impact in granular matter: Force at the base of a container made with one movable wall

In geotechnics as well as in planetary science, it is important to find a means by which to protect a base from impacts of micrometeoroids. In the moon, for example, covering a moon base with regolith, and housing such regolith by movable bounding walls, could work as a stress-leaking shield. Using a numerical model, by performing impacts on a granular material housed in a rectangular container made with one movable sidewall, it is found that such wall mobility serves as a good means for controlling the maximum force exerted at the container's base. We show that the force exerted at the container's base decreases as the movable wall decreases in mass, and it follows a Janssen-like trend. Moreover, by making use of a dynamically defined redirecting coefficient K(X), proposed by Windows-Yule et al. [Phys. Rev. E 100, 022902 (2019)2470-004510.1103/PhysRevE.100.022902], which depends on the container's width X, we propose a model for predicting the maxima measured at the container's base. The model depends on the projectile and granulate properties, and the container's geometry.

The role of initial speed in projectile impacts into light granular media

Projectile impact into a light granular material composed of expanded polypropylene (EPP) particles is investigated systematically with various impact velocities. Experimentally, the trajectory of an intruder moving inside the granular material is monitored with a recently developed non-invasive microwave radar system. Numerically, discrete element simulations together with coarse-graining techniques are employed to address both dynamics of the intruder and response of the granular bed. Our experimental and numerical results of the intruder dynamics agree with each other quantitatively and are in congruent with existing phenomenological model on granular drag. Stepping further, we explore the ‘microscopic’ origin of granular drag through characterizing the response of granular bed, including density, velocity and kinetic stress fields at the mean-field level. In addition, we find that the dynamics of cavity collapse behind the intruder changes significantly when increasing the initial speed . Moreover, the kinetic pressure ahead of the intruder decays exponentially in the co-moving system of the intruder. Its scaling gives rise to a characteristic length scale, which is in the order of intruder size. This finding is in perfect agreement with the long-scale inertial dissipation type that we find in all cases.

A novel experimental setup for an oblique impact onto an inclined granular layer

We develop an original apparatus of the granular impact experiment by which the incident angle of the solid projectile and the inclination angle of the target granular layer can be systematically varied. Whereas most of the natural cratering events occur on inclined surfaces with various incident angles, there have not been any experiments on oblique impacts on an inclined target surface. To perform systematic impact experiments, a novel experimental apparatus has to be developed. Therefore, we build an apparatus for impact experiments where both the incident angle and the inclination angle can be independently varied. The projectile-injection unit accelerates a plastic ball (6 mm in diameter) up to v_i ≃ 100 m s^-1 impact velocity. The barrel of the injection unit is made with a three-dimensional printer. The impact dynamics is captured by using high-speed cameras to directly measure the impact velocity and incident angle. The rebound dynamics of the projectile (restitution coefficient and rebound angle) is also measured. The final crater shapes are measured using a line-laser profiler mounted on the electric stages. By scanning the surface using this system, a three-dimensional crater shape (height map) can be constructed. From the measured result, we can define and measure the characteristic quantities of the crater. The analyzed result on the restitution dynamics is presented as an example of systematic experiments using the developed system.

Millimetric granular craters from pulsed laser ablation

This Rapid Communication reports on an experimental study of granular craters formed by a mechanism, namely, optical energy, via a pulsed laser focused onto the surface of a granular bed. This represents an insight into granular cratering for two reasons; first, there is no physical contact between the initiation mechanism and the granular media (as typical for impact or explosion craters). Second, the resulting craters are millimetric in scale, which facilitates a test of energy scalings down to a previously unobserved lengthscale. Indeed, we observe a range of energy scalings conforming to D_{c}∼E^{β} with β≈0.31-0.43 depending on the characteristics of the granular media.

Impact-Induced Energy Transfer and Dissipation in Granular Clusters under Microgravity Conditions

The impact-induced energy transfer and dissipation in granular targets without any confining walls are studied by microgravity experiments. A solid projectile impacts into a granular target at low impact speed (0.045≤v_{p}≤1.6  m s^{-1}) in a laboratory drop tower. Granular clusters consisting of soft or hard particles are used as targets. Porous dust agglomerates and glass beads are used for soft and hard particles, respectively. The expansion of the granular target cluster is recorded by a high-speed camera. Using the experimental data, we find that (i) a simple energy scaling can explain the energy transfer in both soft-particle and hard-particle granular targets, (ii) the kinetic impact energy is isotropically transferred to the target from the impact point, and (iii) the transferred kinetic energy is 2%-7% of the projectile's initial kinetic energy. The dissipative-diffusion model of energy transfer can quantitatively explain these behaviors.

Collision-based understanding of the force law in granular impact dynamics

We study the stopping force felt by an intruder impacting onto a granular medium. Variations in the shape of the intruder can influence the penetration depth by changing the inertial drag. We find this observed correlation can be explained by associating the velocity-dependent inertial drag to the energy dissipation that occurs through intermittent collisions of force-chain-like clusters, the mean behavior of which can be statistically described. In consequence, the stopping force can be captured through a proposed collisional model with good accuracy, and the observed impact dynamics data can be reproduced quantitatively.

Friction force regimes and the conditions for endless penetration of an intruder into a granular medium

An intruder penetrating into a granular column experiences a depth-dependent friction force F(z). Different regimes of F(z) have been measured depending on the experimental design: a nearly linear dependence for shallow penetrations, total saturation at large depths, and an exponential increase when the intruder approaches the bottom of the granular bed. We report here an experiment that allows us to measure the different regimes in a single run during the quasistatic descent of a sphere in a light granular medium. From the analysis of the resistance in the saturation zone, it was found that F(z) follows a cube-power-law dependence on the intruder diameter and an exponential increase with the packing fraction of the bed. Moreover, we determine the critical mass m_{c} required to observe infinite penetration and its dependence on the above parameters. Finally, we use our results to estimate the final penetration depth reached by intruders of masses m<m_{c}. The results indicate that an intruder of any density (larger than the density of the granular bed) can sink indefinitely into the granular medium if the bed packing fraction is smaller than a critical value.

Hopping Motion Estimation on Soft Soil by Resistive Force Theory

Various planetary terrains or asteroids, which are hard to traverse with wheeled platforms, are expected to be explored. Bekker’s model cannot be applied to estimate the motions of rovers without wheels, such as the hopping rover (hopper). In this paper, the resistive force theory (RFT) approach is introduced. This approach is not based on Bekker’s model, and is expected to apply to any platform. However, this RFT approach only applies to static or quasi-static motion, such as in the case of slow motions. To apply the RFT approach to dynamic motions, such as hopping, the effect of velocity as a dynamic variable is also studied. Through the hopping experiments, the effectiveness of RFT with the velocity-term approach is investigated and compared to the RFT approach.

Collisional model of energy dissipation in three-dimensional granular impact

We study the dynamic process occurring when a granular assembly is displaced by a solid impactor. The momentum transfer from the impactor to the target is shown to occur through sporadic, normal collisions of high force carrying grains at the intruder surface. We therefore describe the stopping force of the impact through a collisional-based model. To verify the model in impact experiments, we determine the forces acting on an intruder decelerating through a dense granular medium by using high-speed imaging of its trajectory. By varying the intruder shape and granular target, intruder-grain interactions are inferred from the consequent path. As a result, we connect the drag to the effect of intruder shape and grain density based on a proposed collisional model.

Drag law for an intruder in granular sediments

We investigate the drag experienced by a spherical intruder moving through a medium consisting of granular hydrogels immersed in water as a function of its depth, size, and speed. The medium is observed to display a yield stress with a finite force required to move the intruder in the quasistatic regime at low speeds before rapidly increasing at high speeds. In order to understand the relevant time scales that determine drag, we estimate the inertial number I given by the ratio of the time scales required to rearrange grains due to the overburden pressure and imposed shear and the viscous number J given by the ratio of the time scales required to sediment grains in the interstitial fluid and imposed shear. We find that the effective friction μ_{e} encountered by the intruder can be parametrized by I=sqrt[ρ_{g}/P_{p}]v_{i}, where ρ_{g} is the density of the granular hydrogels, v_{i} is the intruder speed, and P_{p} is the overburden pressure due to the weight of the medium, over a wide range of I where the Stokes number St=I^{2}/J≫1. We then show that μ_{e} can be described by the function μ_{e}(I)=μ_{0}+αI^{β}, where μ_{0}, α, and β are constants that depend on the medium. This formula can be used to predict the drag experienced by an intruder of a different size at a different depth in the same medium as a function of its speed.

Rheological characterization of digested sludge by solid sphere impact

An impact method was applied to investigate the rheological characteristics of digested sludge and reveal its transient dynamics. A high-speed camera allowed visualizing the dynamic impact process and observing interaction between impacting sphere and targeted sludge. A damping oscillation was observed after the impact. The crater diameter followed an exponential function, while the crater depth varied as a logarithmic function of both sphere diameter and free fall height. Furthermore, the viscosity and elasticity of digested sludge were evaluated by establishing a simplified impact drag force model. The impact elastic modulus was consistent with the Young's modulus measured by a penetrometer. The impact viscosity was reasonable as the estimated impact shear stress was greater than the yield stress of digested sludge resulting in the formation of crater. The impact method offers an alternative way to reveal the viscoelasticity of digested sludge through a dynamic process.

Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach

A theory for jammed granular materials is developed with the aid of a nonequilibrium steady-state distribution function. The approximate nonequilibrium steady-state distribution function is explicitly given in the weak dissipation regime by means of the relaxation time. The theory quantitatively agrees with the results of the molecular dynamics simulation on the critical behavior of the viscosity below the jamming point without introducing any fitting parameter.

Penetration depth scaling for impact into wet granular packings

We present experimental measurements of penetration depths for the impact of spheres into wetted granular media. We observe that the penetration depth in the liquid saturated case scales with projectile density, size, and drop height in a fashion consistent with the scaling observed in the dry case, but with smaller penetrations. Neither viscous drag nor density effects can explain the enhancement to the stopping force. The penetration depth exhibits a complicated dependence on liquid fraction, accompanied by a change in the drop-height dependence, that must be the consequence of accompanying changes in the conformation of the liquid phase in the interstices.

Origin of a depth-independent drag force induced by stirring in granular media

Experiments have shown that when a horizontal cylinder rotates around the vertical axis in a granular medium, the drag force in the stationary regime becomes independent of the depth, in contradiction with the frictional picture stipulating that the drag should be proportional to the hydrostatic pressure. The goal of this study is to understand the origin of this depth independence of the granular drag. Intensive numerical simulations using the discrete element method are performed giving access to the stress distribution in the packing during the rotation of the cylinder. It is shown that the rotation induces a strong anisotropy in the stress distribution, leading to the formation of arches that screen the hydrostatic pressure in the vicinity of the cylinder and create a bubble of low pressure.

Phase transition and flow-rate behavior of merging granular flows

Merging of granular flows is ubiquitous in industrial, mining, and geological processes. However, its behavior remains poorly understood. This paper studies the phase transition and flow-rate behavior of two granular flows merging into one channel. When the main channel is wider than the side channel, the system shows a remarkable two-sudden-drops phenomenon in the outflow rate when gradually increasing the main inflow. When gradually decreasing the main inflow, the system shows obvious hysteresis phenomenon. We study the flow-rate-drop phenomenon by measuring the area fraction and the mean velocity at the merging point. The phase diagram of the system is also presented to understand the occurrence of the phenomenon. We find that the dilute-to-dense transition occurs when the area fraction of particles at the joint point exceeds a critical value ϕ(c)=0.65±0.03.

Drag-force regimes in granular impact

We study the penetration dynamics of a projectile incident normally on a substrate comprising of smaller granular particles in three-dimensions using the discrete element method. Scaling of the penetration depth is consistent with experimental observations for small velocity impacts. Our studies are consistent with the observation that the normal or drag force experienced by the penetrating grain obeys the generalized Poncelet law, which has been extensively invoked in understanding the drag force in the recent experimental data. We find that the normal force experienced by the projectile consists of position and kinetic-energy-dependent pieces. Three different penetration regimes are identified in our studies for low-impact velocities. The first two regimes are observed immediately after the impact and in the early penetration stage, respectively, during which the drag force is seen to depend on the kinetic energy. The depth dependence of the drag force becomes significant in the third regime when the projectile is moving slowly and is partially immersed in the substrate. These regimes relate to the different configurations of the bed: the initial loose surface packed state, fluidized bed below the region of impact, and the state after the crater formation commences.

Depth-dependent resistance of granular media to vertical penetration

We measure the quasistatic friction force acting on intruders moving downwards into a granular medium. By utilizing different intruder geometries, we demonstrate that the force acts locally normal to the intruder surface. By altering the hydrostatic loading of grain contacts by a sub-fluidizing airflow through the bed, we demonstrate that the relevant frictional contacts are loaded by gravity rather than by the motion of the intruder itself. Lastly, by measuring the final penetration depth versus airspeed and using an earlier result for inertial drag, we demonstrate that the same quasistatic friction force acts during impact. Altogether this force is set by a friction coefficient, hydrostatic pressure, projectile size and shape, and a dimensionless proportionality constant. The latter is the same in nearly all experiments, and is surprisingly greater than one.