As the target size distribution and porosity were the same for all the COLLIDE and PRIME campaigns, we combined the collected data sets. This section presents how we analyzed the impacts and the results we obtained, integrating all the data collected.
The platforms used to collect data in microgravity induced residual accelerations on the experiment hardware attached to them. These accelerations were around 10 −3g in the Space Shuttle (Colwell and Taylor 1999) and 10 −2g on the parabolic aircraft (Colwell 2003) and on Blue Origin’s New Shepard rocket (Wagner and DeForest 2016). The free-floating experiment boxes of PRIME-3 offered the best microgravity quality: with only air drag acting on the box moving at very low speeds (< 1 mm/s), no residual acceleration could be detected from our video data. This implies that these experiment runs were performed at residual accelerations under our detection threshold, 10 −4g. In addition to these microgravity experiment runs, the PRIME-3 flights also allowed us to perform seven experiment runs at 0.05g.
Across all the data collected, four types of collision outcome were observed:
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Collisions producing ejecta with an embedded projectile (squares in Fig. 5): in these collisions, no motion of the projectile after the impact is detected. Either the ejecta blanket or individual particles could be tracked and their speed determined.
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Collisions producing ejecta with projectile rebound (triangles in Fig. 5): the projectile can be tracked after the collision. In addition to the ejecta speeds, a coefficient of restitution could be measured for the projectile.
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Collisions with no ejecta but projectile rebound (diamonds in Fig. 5). The coefficient of restitution for the projectile could be measured.
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Collisions with no ejecta and embedded projectile (circles in Fig. 5).
Figure 5 shows these outcomes as a function of the impact velocity. In this graph, all impacts not producing any ejecta were placed at a mean ejecta velocity of 1 cm/s. This is for the purpose of representing all the data on the same graph only, as no speed could be measured on absent ejecta (and a representation at 0 is not possible on a logarithmic scale). The following paragraphs give some additional details on these results for quartz sand and JSC-1 target materials.
JSC Mars-1 behaved similarly to quartz sand in reduced gravity (the JSC Mars-1 data points seen in Fig. 5 are mostly from the PRIME-1 campaign; see Table 1 in Colwell et al. (2008)). This can be explained by the similar grain shape between these two simulants (Fig. 3a, b). In microgravity, only one impact was available for data analysis, which was not enough for analyzing this set of data.
Ejecta production
Impacts in COLLIDE-2, COLLIDE-3, PRIME-1, and PRIME-3 resulted in the production of an ejecta blanket. In the PRIME-1 and most of the COLLIDE-2 data (Colwell 2003), individual ejecta particles could not be distinguished due to the low camera resolution. However, features of the ejecta blanket, in particular the fastest particles forming the upper edge of the blanket (named “corner” in Colwell et al. (2008)), were identified and allowed for the measurement of the upper end of the ejecta velocity distribution.
In PRIME-3, the camera resolution allowed for the individual tracking of ejecta particles. For these experiments, we were able to measure a mean ejecta velocity by directly tracking 30 particles for each impact, using the Spotlight software developed at NASA Glenn Research Center (Klimek and Wright 2006). However, due to the nature of the video data collected, the tracking of individual particles is limited to optically thin portions of the ejecta blanket. This includes but is not restricted to the ejecta “corner” mentioned above. Particle tracking was performed by three people independently in order to reduce the measurement errors. The ejecta grain velocity distribution obtained for each impact was normal and could be fit by a Gaussian curve. Details on the tracking methods can be found in Colwell et al. (2016) (see their Figs. 5 and 6). For PRIME-3 and COLLIDE-3, the characteristic ejecta velocity was chosen to be the Gaussian mean of velocity distribution of the tracked particles.
Figure 6 shows the results of the ejecta speed measurements for PRIME-1 and PRIME-3. The 1- σ error bars for the Gaussian mean determination are shown for the PRIME-3 data points. COLLIDE-3 produced ejecta for only one impact, and the target material was JSC Mars-1. As stated above, JSC Mars-1 behaved similarly to quartz sand, and we are not including JSC Mars-1 results here. The plateau formed by the PRIME-1 microgravity data points (black asterisks representing quartz sand impacts) around 10 cm/s for impact energies below 104 ergs is due to the residual accelerations induced by the parabolic aircraft on the experiment boxes (on the order of 10 −2g). Only particles ejected with energies able to overcome the effect of this ambient gravity field were lifted from the target. For this reason, the slowest moving ejecta has a minimum speed, set by this g-level, and the measured velocities follow a plateau. This plateau also formed in PRIME-3 microgravity data, but at ejecta velocities around a few centimeters per second, indicating that residual accelerations were successfully reduced by the free-floating hardware configuration, compared to PRIME-1, which was attached to the aircraft frame.
The scatter of the PRIME-1 data points towards higher ejecta velocities was induced by the observational bias produced by the tracking method used: tracking the ejecta “corner” described above limits the recorded speeds to the fastest moving particles and is therefore only representative of the upper end of the ejecta velocity distribution: there is therefore a tendency to measure higher ejecta velocities at the same impact energies. However, the data points show a trend followed by the lower limit of the measured velocities: to guide the eye, we fit a power law to the impacts into quartz sand in microgravity. The index obtained is 1.35. For all impacts into JSC-1, a fitted power law index is at 0.50. We collected only one data point for JSC-1 ejecta at microgravity levels, which lies below this power law fit. Further data collection on JSC-1 ejecta-producing impacts in microgravity will be required in order to evaluate if this point is indicative of a different ejecta behavior between the two gravity levels.
The ejecta speeds measured for impacts at 0.05g during the PRIME-3 campaign are of the same range as the ones measured during the PRIME-1 campaign, where microgravity parabolas were flown, but the experiment hardware was fixed to the aircraft frame. This demonstrates that the residual accelerations produced on the experiment when attached to the aircraft are comparable to 10 −2g and that our method for determining the average ejecta speeds provides similar values than the method used in Colwell et al. (2008).
We defined the effective coefficient of restitution of the impacts as the ratio between the average ejecta velocity and the projectile impact velocity and investigated its relationship to the impact velocity. These effective coefficients of restitution showed no correlation and a uniform distribution over the available range of impact velocities (Fig. 7). We calculated the overall average effective coefficient of restitution to be 0.39 ± 0.15. This value is about twice the one derived by Deboeuf et al. (2009) for impacts of centimeter-sized spheres into 100 μm glass bead beds. Deviations to our mean value were much higher than for the measurements performed in Deboeuf et al. (2009). When separating the impacts into quartz sand from the ones into JSC-1, we obtained average effective coefficients of restitution of 0.38 ± 0.15 and 0.45 ± 0.16, respectively. When separating between impacts in low gravity and microgravity, we obtained values of 0.43 ± 0.14 and 0.15 ± 0.04, respectively.
Projectile rebound
A number of impacts during the COLLIDE-1, COLLIDE-3, and PRIME-3 campaigns showed a rebound of the projectile after impact on the target and allowed for the measurement of a coefficient of restitution \(\epsilon =\frac {v_{f}}{v_{i}}\), vi and vf being the projectile velocities before (initial) and after (final) the impact, respectively (see Table 1). Figure 8 shows the measured coefficients of restitution as a function of the impact energy. For speeds above 30 cm/s, impacts systematically produced an ejecta blanket and coefficients of restitution of the projectile could either not be measured or were of the order of 10 −2.
At impact speeds between about 20 and 30 cm/s, both ejecta production and projectile rebound without ejecta were observed. Below 20 cm/s, only rebounds without ejecta were observed. In order to compare our results to the experimental work of Katsuragi and Blum (2017), we fit a power law to this set of data. In Katsuragi and Blum (2017), spherical projectiles of about 1 cm in diameter are dropped into aggregates composed of 750 μm SiO2 monomer grains with a packing density of Φ = 0.35. The index we obtain with our data is − 0.27, similar to the value of − 1/4 found by Katsuragi and Blum (2017). We note, however, that if we separate the data sets from COLLIDE and PRIME, we obtain indexes of − 0.10 and − 0.50, respectively, a difference mostly due to the two very low-energy impacts into JSC-1 of the COLLIDE-1 flight. As mentioned in Katsuragi and Blum (2017), this overall index value is twice as high as expected from the theory of an elastic sphere impacting a plane surface (Johnson 1985; Thornton and Ning 1998). This indicates that energy absorption in a bed of granular material is not entirely captured by the mechanics of elastic surfaces.
Projectile penetration depth
In the PRIME-3 video data, the resolution is high enough to determine the maximum penetration depth of the projectile into the target for 21 impacts. This maximum penetration depth is defined as the distance between the bottom of the projectile and the target surface. Figure 9 shows these results as a function of the equivalent total drop distance H. This distance was derived to be able to compare our results with the ones obtained by Katsuragi and Blum (2017): H=h+zmax, where h is the drop height (experiments in Katsuragi and Blum (2017) are performed in 1g, and the drop height is used to control the impact velocity), and zmax is the maximum penetration depth of the projectile into the target. As the impact velocity was not determined by the drop height in PRIME experiments, but by the stored potential energy in the spring of the projectile launcher, we calculate an equivalent h from the impact velocity vi by equating the 1g potential energy with our kinetic impact energy as follows:
$$ \begin{aligned} E_{1g} &= E_{0g} \\ mgh &= \frac{1}{2}mv_{i}^{2} \\ h &= \frac{v_{i}^{2}}{2g} \end{aligned} $$
(1)
with g = 9.81 m/s. As shown by the index 1 power law in Fig. 9, H is dominated by zmax in half of the impacts. This is due to the very low impact velocities, inducing equivalent drop heights h≪zmax, so that H∼zmax. We do not observe any correlation between the maximum penetration depth and the computed total equivalent drop distance. This is in contrast with the relation zmax∝H1/3 observed in Katsuragi and Blum (2017), representative of a scaling by impact energy. A scaling by momentum of the form \(z_{max} = Am_{p}^{\alpha }v_{i}^{\beta }\), with mp and vi being the projectile mass and impact velocity, respectively, and A, α, and β fit parameters, as performed in Güttler et al. (2009), was not successful either.
Grain behavior with decreasing gravity level
From the experimental results presented here, we observed differences in the response of the target to low-velocity impacts in reduced gravity (∼10−2g) and microgravity (<10−4g). Figure 5 shows that compared to the total number of impacts in reduced gravity (∼10−2g), only a few of them did not produce ejecta: the vast majority of impacts generated an ejecta curtain. In addition, none of the reduced-gravity impacts lead to a rebound of the projectile (no red triangles or diamonds). In particular, when no ejecta was produced around the lowest impact speeds observed (∼ 20 cm/s), only projectile embedding in the target could be seen. For the same impact speeds, a microgravity environment (<10−4g) lead to the rebound of the projectile. In fact, embedding into the target was only seen in the two impacts under 4 cm/s. All other impacts than those without ejecta showed a rebound of the projectile.
Projectile rebound was also observed in combination with an ejecta curtain in half of the impacts observed in microgravity (black triangles). Even though Fig. 8 shows that the coefficient of restitution of these rebounds is much smaller compared to the ones with no ejecta production (diamonds), this behavior demonstrates the differences in target response in reduced- and microgravity environments.
It can also be noted that for the same impact speed, ejecta is faster on average in reduced gravity compared to microgravity (red symbols are above black symbols in Fig. 5). In addition, less mass is ejected than in microgravity. Figure 10 shows the average ejecta speeds for four levels of ejected mass: as the ejecta mass cannot be measured after each experiment run (the return to 1g mixes the target material from the tray and the ejected particles), an estimation was performed from the video images. Four levels of ejecta mass were identified: no ejecta (0), individual particles detaching from the target (1), ejected mass of the order of the projectile mass (2), and ejected mass much higher than the projectile mass (3) (we followed the same numbering as in Colwell (2003)). In Fig. 10, the red symbols show reduced-gravity impacts (∼10−2g), and black symbols microgravity impacts (<10−4g). The impact velocity given for each target type and ejecta mass level is the average of all impacts that created the same amount of ejecta. From the sand targets, we can see that the same average impact speed results in higher ejecta masses in microgravity compared to reduced gravity. Together with Fig. 5, this shows that fewer target particles are ejected in reduced gravity, but their ejection speed is higher.
Figure 10 also shows that no ejecta blanket was observed in microgravity with JSC-1 targets. While this is also due to the fact that only very few impacts were performed in JSC-1 in microgravity at speeds > 50 cm/s, the nature of the target plays a role in the ejecta mass produced: compared to quartz sand particles, which are rounded and considered cohesionless in vacuum (once the air humidity is removed), JSC-1 particles are more angular and behave like a cohesive powder. Figure 5 shows that only two out of eight impacts into JSC-1 at > 10 cm/s resulted in ejecta production, and these were only individual particles detaching instead of an ejecta blanket. As we can see in Fig. 10, the impact speed does not seem to influence the production if these individual particles in JSC-1 targets, compared to quartz sand targets, which display a more consistent trend of increasing ejecta mass with increasing impact velocity. When an ejecta blanket is produced though, we can see that higher impact velocities result in higher ejected masses for both quartz sand and JSC-1 targets.