- Email: [email protected]
Comparison of fragments created by low- and hyper-velocity impacts
Available online at www.sciencedirect.com
Advances in Space Research 41 (2008) 1132–1137 www.elsevier.com/locate/asr
Comparison of fragments created by low- and hyper-velocity impacts T. Hanada
a,b,*
, J.-C. Liou
c
a
Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan JAXA/ISAS, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan ESCG/ERC, Mail Code JE104, 2224 Bay Area Blvd., Houston, TX 77058, USA b
c
Received 1 November 2006; received in revised form 18 May 2007; accepted 18 May 2007
Abstract This paper summarizes two new satellite impact experiments. The objective of the experiments was to investigate the outcome of lowand hyper-velocity impacts on two identical target satellites. The first experiment was performed at a low-velocity of 1.5 km/s using a 40-g aluminum alloy sphere. The second experiment was performed at a hyper-velocity of 4.4 km/s using a 4-g aluminum alloy sphere. The target satellites were 15 cm · 15 cm · 15 cm in size and 800 g in mass. The ratios of impact energy to target mass for the two experiments were approximately the same. The target satellites were completely fragmented in both experiments, although there were some differences in the characteristics of the fragments. The projectile of the low-velocity impact experiment was partially fragmented while the projectile of the hyper-velocity impact experiment was completely fragmented beyond recognition. To date, approximately 1500 fragments from each impact experiment have been collected for detailed analysis. Each piece has been weighed, measured, and analyzed based on the analytic method used in the NASA Standard Breakup Model (2000 revision). These fragments account for about 95% of the target mass for both impact experiments. Preliminary analysis results will be presented in this paper. 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Space debris; Satellite impact; Fragmentation
1. Introduction A commonly used model to describe the outcome of satellite fragmentation is the NASA Standard Breakup Model (Johnson et al., 2001). The model includes the size and area-to-mass distributions of fragments after an explosion or collision. It also includes the ejection velocity distribution of the fragments with respect to the parent object. The NASA model is an empirical model based on ground-based experiments and on-orbit breakups. The database for the collisions includes two non-catastrophic and three catastrophic impact experiments, and one onorbit catastrophic collision, as summarized in Table 1 (see also Liou et al., 2002). The outcome of a catastrophic collision is the total fragmentation of the target object, *
Corresponding author. Address: Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan. E-mail address: [email protected] (T. Hanada).
whereas a non-catastrophic collision only results in minor physical damage to the target. The transition from non-catastrophic to catastrophic collisions appears to occur when the ratio of impact kinetic energy to target mass exceeds 40 J/g (Johnson et al., 2001). As can be seen from Table 1, the experiments and events were all in the hyper-velocity impact regime, applicable to most potential on-orbit collisions in the Low-Earth Orbit (LEO) region. A simple functional fit to the six fragment size distributions yield the following power-law equation, 1:71 N cum ¼ 0:1 M 0:75 tot Lc
ð1Þ
where Ncum is the number of fragments larger than a given characteristic length, Lc (in m), and Mtot is the total mass of the target and projectile (in kg). Overall, Eq. (1) provides a reasonable fit to the six data sets, over more than 12 orders of magnitude in mass, or more than four orders of magnitude in size. For the area-to-mass ratio and ejection velocity distributions, the NASA collision model was
0273-1177/$34 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.05.062
T. Hanada, J.-C. Liou / Advances in Space Research 41 (2008) 1132–1137
1133
Table 1 Database for NASA’s collision breakup model Name Bess 1 Bess 2 PSI 1 PSI 2 SOCIT P78/Solwind a
Target mass a
– –a 26 kg 26 kg 34.5 kg 850 kg
Projectile mass
Impact velocity (km/s)
Catastrophic?
1.65 g 0.37 g 237 g 237 g 150 g 16 kg
3.0 4.5 5.9 3.3 6.0 7.6
No No Yes Yes Yes Yes
The target was a simulated spacecraft wall.
derived based on additional on-orbit fragmentation data and the Satellite Orbital Debris Characterization Impact Experiment (SOCIT) data (Johnson et al., 2001). Yasaka et al. (2000) were investigating low-velocity impact phenomena, applicable for on-orbit collisions in the Geosynchronous Earth Orbit (GEO) region, while Johnson et al. (2001) was developing the NASA model described above. Yasaka et al. (2000) hit a simulated spacecraft wall with a solid stainless steel sphere at a speed of 300 m/s or lower to develop a low-velocity collision model in a similar manner to what had been done in the area of hyper-velocity impacts. The cumulative distribution of fragments was expressed in mass by the following power-law equation, N cum ¼ 0:78 ðM f =M e Þ
0:68
ð2Þ
where Ncum is the number of fragments weight more than a given mass, Mf (in g), and Me is the total mass of fragments (in g). They also provided the ejection velocity distribution of the fragments with respect to the parent object based on an empirical equation derived by Su (1990) and McKnight (1991) from a variety of on-orbit fragmentation data. Many international communities working on orbital debris evolutionary models for the GEO region have adopted their low-velocity collision model as well. Hanada et al. (2005) reanalyzed the low-velocity impact data obtained by Yasaka et al. (2000) based on the analytic method used in the NASA model, and then compared the results with the NASA model. It was concluded that the NASA model could be applied to low-velocity collisions with some simple modifications. Their conclusion has encouraged us to develop a wide velocity range collision model. The low-velocity impact experiments conducted by Yasaka et al. (2000) were categorized as a non-catastrophic collision, characterized primarily by fragmentation of the projectile and by crater or hole on the target, however. The purpose of this paper is to investigate the outcome of low- and hyper-velocity catastrophic impacts on two identical target satellites. One was hit with a 40-g aluminum alloy sphere at a low-velocity of 1.5 km/s, whereas the other was hit with a 4-g aluminum alloy sphere at a hyper-velocity of 4.4 km/s. The ratios of impact energy to target mass for the two experiments were approximately the same (55 J/g). The target satellites were completely fragmented in both experiments, consistent with the NASA
criterion mentioned previously. Approximately 1500 fragments from each impact experiment have been collected to be weighed, measured, and analyzed based on the analytic method used in the NASA model. Preliminary analysis results presented in this paper will encourage the development of a general-purpose mass distribution model applicable for a wide impact velocity range and a sizebased material density distribution model. 2. Impact experiments 2.1. Target satellites and projectiles The targets for the two impact experiments were identical micro satellites, 15 cm · 15 cm · 15 cm in size with a communication antenna on the top and solar cells on a side (see Fig. 1). The main structure of each micro satellite was composed of five layers (top, bottom, and three internal layers parallel to the top and bottom layers) and four side panels. Unlike the target prepared for the previous impact experiment that was a cylindrical-shaped micro satellite without side panels (see also Nakashima et al., 2005), this
Fig. 1. Target micro satellite before impact. The target satellite is 15 cm · 15 cm · 15 cm in size and 800 g in mass.
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new structure made the targets more realistic. The layers and panels were made of Carbon Fiber-Reinforced Plastics (CFRP), assembled by angle bars made of an aluminum alloy. The thickness of the five layers was 2 mm while that of the four side panels was 1 mm. The interior of each micro satellite was equipped with fully functional wireless radios, lithium-ion batteries, communication circuit, electric power supply circuit, and command and data handling circuit. The total mass of each micro satellite was approximately 800 g. Two different solid spheres, made of an aluminum alloy, were prepared as projectiles. One was 3 cm in diameter and 40 g in mass, whereas the other was 1.4 cm in diameter and 4 g in mass. The projectiles were launched from a two-stage light gas gun at Kyushu Institute of Technology. The first experiment was performed at a low-velocity of 1.5 km/s using the 40-g aluminum alloy solid sphere. The second experiment was performed at a hyper-velocity of 4.4 km/s using the 4-g aluminum alloy sphere. The NASA Standard Breakup Model has defined if the ratio is equal to or greater than 40 J/g, then the impact is catastrophic (Johnson et al., 2001). The ratios of impact kinetic energy to target mass for the two experiments were approximately
Fig. 2. Fragment collection box. The box is covered with Styrofoam plates to collect generated fragments without any secondary damages. The target satellite is fixed inside the box with thin wires.
the same (55 J/g), and placed the outcome as catastrophic according to the NASA criterion. A fragment collection box shown in Fig. 2 was prepared to collect all fragments generated, without any secondary damages. The box was framed by angle bars and all sides except the front side covered with a clear acrylic plate to observe fragmentation process were covered with Styrofoam plates. The target satellite was fixed inside the box with thin wires attached to each corner. This box was set up inside the vacuum chamber of the two-stage light gas gun. 3. Data analysis and discussion 3.1. Overview of impact experiment results Fig. 3 shows the fragmentation of the target satellite right after the impact experiment. Both target satellites were completely fragmented after the impact, consistent with the NASA criterion mentioned previously. The projectile of the low-velocity impact was partially fragmented while the projectile of the hyper-velocity impact was completely fragmented beyond recognition. Figs. 4 and 5 compare the layers and the side panels of the target satellites recovered after the impact experiment, respectively. The projectiles traveled from left to right in Fig. 4, while they traveled from top to bottom in Fig. 5. Even though the projectile of the low-velocity impact experiment was fragmented, the projectile shot through the all five layers to damage. However, any damages like on the layers cannot be observed on the side panels. On the other hand, the projectile of the hypervelocity impact experiment seems not to shoot through the bottom layer. However, some side panels were damaged like the three internal layers between the top and bottom layers. It is easy to assume that the projectile was completely fragmented and then expanded rapidly to damage side panels. It should be noted that the hole on the first side panel from the left in Fig. 5 is for the antenna, not due to the impact.
Fig. 3. Fragmentation of the micro satellites right after the impact experiment. The target satellites were completely fragmented in both impact experiments, consistent with the NASA criterion. (a) Low-velocity impact. (b) Hyper-velocity impact.
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Fig. 4. Recovered layers of the target satellite after the impact experiment. The projectile traveled from the left side to the right side. The projectile was not able to shoot through the bottom layers in the hyper-velocity impact. (a) Low-velocity impact. (b) Hyper-velocity impact.
Fig. 5. Recovered side panels of the target satellite after the impact experiment. The projectile traveled from the top to the bottom. Some side panels also are damaged as well in the hyper-velocity impact. (a) Low-velocity impact. (b) Hyper-velocity impact.
Fig. 6 compares the 500 largest fragments from each impact experiment. The CFRP side panel and layer fragments are easily recognizable among the pieces. The overall characteristics of the two fragment sets are similar, although some differences exist. For example, many lineshaped fragments were generated by the hyper-velocity impact (compare fragments at the lower right in Fig. 6), whereas only a few line-shaped fragments were generated by the low-velocity impact. Such a difference may lead to differences in fragment properties as described later.
3.2. Fragment properties To date, approximately 1500 fragments from each impact experiment have been collected for detailed analysis. Each piece has been weighed, measured, and analyzed
based on the analytic method used in the NASA model. These fragments account for about 95% of the target mass for both impact experiments.
3.2.1. Mass and size distributions The cumulative distribution of collision fragments can be expressed in characteristic length or in mass. The characteristic length of an object is defined as the average of three orthogonal dimensions, x, y, and z, where x is the longest dimension, y is the longest dimension in the plane perpendicular to x, and z is the longest dimension perpendicular to both x and y. In terms of mass distribution, the two fragment groups are similar in both cumulative (number of fragments equal to or greater than a given mass) and differential (number if fragments per mass bin) distributions, as shown in Fig. 7. In terms of size distribution, there
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Fig. 6. Five hundred largest fragments from each impact experiment. Hyper-velocity impact generates more line-shaped fragments than low-velocity impact does (compare fragments at the lower right). (a) Low-velocity impact. (b) Hyper-velocity impact.
104
104 HVI (Ncum) HVI (Ndiff) LVI (Ncum) LVI (Ndiff)
103 Number
Number
103
102
102
101
101
10-2
10-1 100 Mass [g]
101
100 100
102
Fig. 7. Mass distributions of the two fragment sets. Both the cumulative and differential distributions are shown. Fragments from hyper-velocity and low-velocity impacts (abbreviated as HVI and LVI, respectively) have very similar distributions.
are some noticeable differences between the two groups (see Fig. 8). The hyper-velocity impact appears to produce more larger fragments than low-velocity impact does. The numbers of fragments larger than 1 cm are 486 (hypervelocity) and 241 (low-velocity), respectively. Fig. 9 shows the size versus mass distribution of the 1500 fragments from the hyper-velocity impact experiment. They can be separated into two groups, high and low material density. The former includes fragments with metallic components while the latter includes CFRP pieces. The high and low material density groups are also recognizable among low-velocity impact fragments, although the separation is less obvious (see Fig. 10). The fact that there exist two material density groups in the size versus mass distribution can be applied to the development of a size-based material density distribution model. 3.2.2. Area-to-mass ratio distribution Figs. 11 and 12 show the area-to-mass ratio distribution of the 1500 fragments from each impact experiment in terms of size (characteristic length). They can also be separated into two groups, high and low material density, as in
101 Characteristic Length [mm]
102
Fig. 8. Size (characteristic length) distributions of the two fragment sets. Both the cumulative and differential distributions are shown. Hypervelocity impact (HVI) produces more fragments in the 1 cm and larger size regime than low-velocity (LVI) impact does.
103 102 101 Mass [g]
100 10-3
HVI (Ncum) HVI (Ndiff) LVI (Ncum) LVI (Ndiff)
100 10-1 10-2 10-3 100
101 102 Characteristic Length [mm]
103
Fig. 9. Size versus mass distribution of the hyper-velocity impact fragments. They can be separated into two groups, one with a higher material density distribution and the other with a lower material density distribution.
Figs. 9 and 10. The hyper-velocity impact appears to produce more fragments with a higher area-to-mass ratio than the low-velocity impact does. The numbers of fragments with an area-to-mass ratio larger than 10 m2/kg are 229
T. Hanada, J.-C. Liou / Advances in Space Research 41 (2008) 1132–1137
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than 1 m2/kg are, not much different, 896 (hyper-velocity) and 861 (low-velocity).
103 102
4. Conclusions Mass [g]
101 100 10-1 10-2 10-3 100
101 102 Characteristic Length [mm]
103
Fig. 10. Size versus mass distribution of the low-velocity impact fragments. They can still be separated into two groups, although the separation is not as clear as that for hyper-velocity impact fragments.
This paper has summarized two new satellite impact experiments conducted to investigate the outcome of low- and hyper-velocity impacts on two identical satellites. One was hit with a 40-g aluminum alloy sphere at a low-velocity of 1.5 km/s, whereas the other was hit with a 4-g aluminum alloy sphere at a hyper-velocity of 4.4 km/s. The target satellites were completely fragmented in both impact experiments. Approximately 1500 fragments from each impact experiment have been weighed, measured, and analyzed based on the analytic method used in the NASA Standard Breakup Model. The results presented in this paper have indicated the following conclusions:
2
Area-to-Mass Ratio [m /kg]
102
1. The similarity in mass distribution of fragments between low- and hyper-velocity impacts encourages the development of a general-purpose distribution model applicable for a wide impact velocity range. 2. The fact that there exist two material density groups in the size versus mass distribution of fragments suggests the development of a size-based material density distribution model.
101
100
10-1
10-2 100
101 102 Characteristic Length [mm]
103
Fig. 11. Size versus area-to-mass ratio distribution of the hyper-velocity impact fragments. They can also be separated into two groups as in Figs. 9 and 10.
Acknowledgements The authors acknowledge the generous support of the NASA Orbital Debris Program Office on the experiments. The authors also acknowledge the delegated work done by Mr. Yoshihiro Tsuruda, a graduate student of Kyushu University, on the experiments and data analysis.
102
2
Area-to-Mass Ratio [m /kg]
References 101
100
10-1
10-2 100
101 102 Characteristic Length [mm]
103
Fig. 12. Size versus area-to-mass ratio distribution of the low-velocity impact fragments. The low-velocity impact produces less fragments with an area-to-mass ratio of 10 m2/kg or higher.
(hyper-velocity) and 67 (low-velocity), respectively. Many line-shaped fragments produced by the hyper-velocity impact may contribute to this difference. However, the numbers of fragments with an area-to-mass ratio lager
Hanada, T., Yasaka, T., Hata, H., et al. Using NASA standard breakup model to describe low-velocity impacts on spacecraft. J. Spacecraft 42 (5), 859–864, 2005. Johnson, N.L., Krisko, P.H., Liou, J.-C., et al. NASA’s new breakup model of EVOLVE 4.0. Adv. Space Res. 28 (9), 1377–1384, 2001. Liou, J.-C., Johnson, N.L., Krisko, P.H., et al. The new NASA orbital debris breakup model, in: Green, S.F., Williams, I.P., McDonnell, J.A.M., McBride, N. (Eds.), Dust in the Solar System and Other Planetary Systems. Pergamon Press, Oxford, UK, pp. 363–367, 2002. McKnight, D.S. Determination of breakup initial conditions. J. Spacecraft 28 (4), 470–477, 1991. Nakashima, K., Hanada, T., Akahoshi, Y., et al. Low-velocity catastrophic impact on micro satellite, in: Danesy, D. (Ed.), Proceedings of the Fourth European Conference on Space Debris, ESOC, Darmstadt, Germany, 18–20 April, 2005 (ESA SP-587, August 2005). ESA Publications Division, ESTEC, Noordwijk, The Netherlands, pp. 701–704, 2005. Su, S.-Y. The velocity distribution of collisional fragments and its effect on future space debris environment. Adv. Space Res. 10 (3–4), 389–392, 1990. Yasaka, T., Hanada, T., Hirayama, H. Low-velocity projectile impact on spacecraft. Acta Astronaut. 47 (10), 763–770, 2000.
Advances in Space Research 41 (2008) 1132–1137 www.elsevier.com/locate/asr
Comparison of fragments created by low- and hyper-velocity impacts T. Hanada
a,b,*
, J.-C. Liou
c
a
Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan JAXA/ISAS, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan ESCG/ERC, Mail Code JE104, 2224 Bay Area Blvd., Houston, TX 77058, USA b
c
Received 1 November 2006; received in revised form 18 May 2007; accepted 18 May 2007
Abstract This paper summarizes two new satellite impact experiments. The objective of the experiments was to investigate the outcome of lowand hyper-velocity impacts on two identical target satellites. The first experiment was performed at a low-velocity of 1.5 km/s using a 40-g aluminum alloy sphere. The second experiment was performed at a hyper-velocity of 4.4 km/s using a 4-g aluminum alloy sphere. The target satellites were 15 cm · 15 cm · 15 cm in size and 800 g in mass. The ratios of impact energy to target mass for the two experiments were approximately the same. The target satellites were completely fragmented in both experiments, although there were some differences in the characteristics of the fragments. The projectile of the low-velocity impact experiment was partially fragmented while the projectile of the hyper-velocity impact experiment was completely fragmented beyond recognition. To date, approximately 1500 fragments from each impact experiment have been collected for detailed analysis. Each piece has been weighed, measured, and analyzed based on the analytic method used in the NASA Standard Breakup Model (2000 revision). These fragments account for about 95% of the target mass for both impact experiments. Preliminary analysis results will be presented in this paper. 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Space debris; Satellite impact; Fragmentation
1. Introduction A commonly used model to describe the outcome of satellite fragmentation is the NASA Standard Breakup Model (Johnson et al., 2001). The model includes the size and area-to-mass distributions of fragments after an explosion or collision. It also includes the ejection velocity distribution of the fragments with respect to the parent object. The NASA model is an empirical model based on ground-based experiments and on-orbit breakups. The database for the collisions includes two non-catastrophic and three catastrophic impact experiments, and one onorbit catastrophic collision, as summarized in Table 1 (see also Liou et al., 2002). The outcome of a catastrophic collision is the total fragmentation of the target object, *
Corresponding author. Address: Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan. E-mail address: [email protected] (T. Hanada).
whereas a non-catastrophic collision only results in minor physical damage to the target. The transition from non-catastrophic to catastrophic collisions appears to occur when the ratio of impact kinetic energy to target mass exceeds 40 J/g (Johnson et al., 2001). As can be seen from Table 1, the experiments and events were all in the hyper-velocity impact regime, applicable to most potential on-orbit collisions in the Low-Earth Orbit (LEO) region. A simple functional fit to the six fragment size distributions yield the following power-law equation, 1:71 N cum ¼ 0:1 M 0:75 tot Lc
ð1Þ
where Ncum is the number of fragments larger than a given characteristic length, Lc (in m), and Mtot is the total mass of the target and projectile (in kg). Overall, Eq. (1) provides a reasonable fit to the six data sets, over more than 12 orders of magnitude in mass, or more than four orders of magnitude in size. For the area-to-mass ratio and ejection velocity distributions, the NASA collision model was
0273-1177/$34 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.05.062
T. Hanada, J.-C. Liou / Advances in Space Research 41 (2008) 1132–1137
1133
Table 1 Database for NASA’s collision breakup model Name Bess 1 Bess 2 PSI 1 PSI 2 SOCIT P78/Solwind a
Target mass a
– –a 26 kg 26 kg 34.5 kg 850 kg
Projectile mass
Impact velocity (km/s)
Catastrophic?
1.65 g 0.37 g 237 g 237 g 150 g 16 kg
3.0 4.5 5.9 3.3 6.0 7.6
No No Yes Yes Yes Yes
The target was a simulated spacecraft wall.
derived based on additional on-orbit fragmentation data and the Satellite Orbital Debris Characterization Impact Experiment (SOCIT) data (Johnson et al., 2001). Yasaka et al. (2000) were investigating low-velocity impact phenomena, applicable for on-orbit collisions in the Geosynchronous Earth Orbit (GEO) region, while Johnson et al. (2001) was developing the NASA model described above. Yasaka et al. (2000) hit a simulated spacecraft wall with a solid stainless steel sphere at a speed of 300 m/s or lower to develop a low-velocity collision model in a similar manner to what had been done in the area of hyper-velocity impacts. The cumulative distribution of fragments was expressed in mass by the following power-law equation, N cum ¼ 0:78 ðM f =M e Þ
0:68
ð2Þ
where Ncum is the number of fragments weight more than a given mass, Mf (in g), and Me is the total mass of fragments (in g). They also provided the ejection velocity distribution of the fragments with respect to the parent object based on an empirical equation derived by Su (1990) and McKnight (1991) from a variety of on-orbit fragmentation data. Many international communities working on orbital debris evolutionary models for the GEO region have adopted their low-velocity collision model as well. Hanada et al. (2005) reanalyzed the low-velocity impact data obtained by Yasaka et al. (2000) based on the analytic method used in the NASA model, and then compared the results with the NASA model. It was concluded that the NASA model could be applied to low-velocity collisions with some simple modifications. Their conclusion has encouraged us to develop a wide velocity range collision model. The low-velocity impact experiments conducted by Yasaka et al. (2000) were categorized as a non-catastrophic collision, characterized primarily by fragmentation of the projectile and by crater or hole on the target, however. The purpose of this paper is to investigate the outcome of low- and hyper-velocity catastrophic impacts on two identical target satellites. One was hit with a 40-g aluminum alloy sphere at a low-velocity of 1.5 km/s, whereas the other was hit with a 4-g aluminum alloy sphere at a hyper-velocity of 4.4 km/s. The ratios of impact energy to target mass for the two experiments were approximately the same (55 J/g). The target satellites were completely fragmented in both experiments, consistent with the NASA
criterion mentioned previously. Approximately 1500 fragments from each impact experiment have been collected to be weighed, measured, and analyzed based on the analytic method used in the NASA model. Preliminary analysis results presented in this paper will encourage the development of a general-purpose mass distribution model applicable for a wide impact velocity range and a sizebased material density distribution model. 2. Impact experiments 2.1. Target satellites and projectiles The targets for the two impact experiments were identical micro satellites, 15 cm · 15 cm · 15 cm in size with a communication antenna on the top and solar cells on a side (see Fig. 1). The main structure of each micro satellite was composed of five layers (top, bottom, and three internal layers parallel to the top and bottom layers) and four side panels. Unlike the target prepared for the previous impact experiment that was a cylindrical-shaped micro satellite without side panels (see also Nakashima et al., 2005), this
Fig. 1. Target micro satellite before impact. The target satellite is 15 cm · 15 cm · 15 cm in size and 800 g in mass.
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new structure made the targets more realistic. The layers and panels were made of Carbon Fiber-Reinforced Plastics (CFRP), assembled by angle bars made of an aluminum alloy. The thickness of the five layers was 2 mm while that of the four side panels was 1 mm. The interior of each micro satellite was equipped with fully functional wireless radios, lithium-ion batteries, communication circuit, electric power supply circuit, and command and data handling circuit. The total mass of each micro satellite was approximately 800 g. Two different solid spheres, made of an aluminum alloy, were prepared as projectiles. One was 3 cm in diameter and 40 g in mass, whereas the other was 1.4 cm in diameter and 4 g in mass. The projectiles were launched from a two-stage light gas gun at Kyushu Institute of Technology. The first experiment was performed at a low-velocity of 1.5 km/s using the 40-g aluminum alloy solid sphere. The second experiment was performed at a hyper-velocity of 4.4 km/s using the 4-g aluminum alloy sphere. The NASA Standard Breakup Model has defined if the ratio is equal to or greater than 40 J/g, then the impact is catastrophic (Johnson et al., 2001). The ratios of impact kinetic energy to target mass for the two experiments were approximately
Fig. 2. Fragment collection box. The box is covered with Styrofoam plates to collect generated fragments without any secondary damages. The target satellite is fixed inside the box with thin wires.
the same (55 J/g), and placed the outcome as catastrophic according to the NASA criterion. A fragment collection box shown in Fig. 2 was prepared to collect all fragments generated, without any secondary damages. The box was framed by angle bars and all sides except the front side covered with a clear acrylic plate to observe fragmentation process were covered with Styrofoam plates. The target satellite was fixed inside the box with thin wires attached to each corner. This box was set up inside the vacuum chamber of the two-stage light gas gun. 3. Data analysis and discussion 3.1. Overview of impact experiment results Fig. 3 shows the fragmentation of the target satellite right after the impact experiment. Both target satellites were completely fragmented after the impact, consistent with the NASA criterion mentioned previously. The projectile of the low-velocity impact was partially fragmented while the projectile of the hyper-velocity impact was completely fragmented beyond recognition. Figs. 4 and 5 compare the layers and the side panels of the target satellites recovered after the impact experiment, respectively. The projectiles traveled from left to right in Fig. 4, while they traveled from top to bottom in Fig. 5. Even though the projectile of the low-velocity impact experiment was fragmented, the projectile shot through the all five layers to damage. However, any damages like on the layers cannot be observed on the side panels. On the other hand, the projectile of the hypervelocity impact experiment seems not to shoot through the bottom layer. However, some side panels were damaged like the three internal layers between the top and bottom layers. It is easy to assume that the projectile was completely fragmented and then expanded rapidly to damage side panels. It should be noted that the hole on the first side panel from the left in Fig. 5 is for the antenna, not due to the impact.
Fig. 3. Fragmentation of the micro satellites right after the impact experiment. The target satellites were completely fragmented in both impact experiments, consistent with the NASA criterion. (a) Low-velocity impact. (b) Hyper-velocity impact.
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Fig. 4. Recovered layers of the target satellite after the impact experiment. The projectile traveled from the left side to the right side. The projectile was not able to shoot through the bottom layers in the hyper-velocity impact. (a) Low-velocity impact. (b) Hyper-velocity impact.
Fig. 5. Recovered side panels of the target satellite after the impact experiment. The projectile traveled from the top to the bottom. Some side panels also are damaged as well in the hyper-velocity impact. (a) Low-velocity impact. (b) Hyper-velocity impact.
Fig. 6 compares the 500 largest fragments from each impact experiment. The CFRP side panel and layer fragments are easily recognizable among the pieces. The overall characteristics of the two fragment sets are similar, although some differences exist. For example, many lineshaped fragments were generated by the hyper-velocity impact (compare fragments at the lower right in Fig. 6), whereas only a few line-shaped fragments were generated by the low-velocity impact. Such a difference may lead to differences in fragment properties as described later.
3.2. Fragment properties To date, approximately 1500 fragments from each impact experiment have been collected for detailed analysis. Each piece has been weighed, measured, and analyzed
based on the analytic method used in the NASA model. These fragments account for about 95% of the target mass for both impact experiments.
3.2.1. Mass and size distributions The cumulative distribution of collision fragments can be expressed in characteristic length or in mass. The characteristic length of an object is defined as the average of three orthogonal dimensions, x, y, and z, where x is the longest dimension, y is the longest dimension in the plane perpendicular to x, and z is the longest dimension perpendicular to both x and y. In terms of mass distribution, the two fragment groups are similar in both cumulative (number of fragments equal to or greater than a given mass) and differential (number if fragments per mass bin) distributions, as shown in Fig. 7. In terms of size distribution, there
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Fig. 6. Five hundred largest fragments from each impact experiment. Hyper-velocity impact generates more line-shaped fragments than low-velocity impact does (compare fragments at the lower right). (a) Low-velocity impact. (b) Hyper-velocity impact.
104
104 HVI (Ncum) HVI (Ndiff) LVI (Ncum) LVI (Ndiff)
103 Number
Number
103
102
102
101
101
10-2
10-1 100 Mass [g]
101
100 100
102
Fig. 7. Mass distributions of the two fragment sets. Both the cumulative and differential distributions are shown. Fragments from hyper-velocity and low-velocity impacts (abbreviated as HVI and LVI, respectively) have very similar distributions.
are some noticeable differences between the two groups (see Fig. 8). The hyper-velocity impact appears to produce more larger fragments than low-velocity impact does. The numbers of fragments larger than 1 cm are 486 (hypervelocity) and 241 (low-velocity), respectively. Fig. 9 shows the size versus mass distribution of the 1500 fragments from the hyper-velocity impact experiment. They can be separated into two groups, high and low material density. The former includes fragments with metallic components while the latter includes CFRP pieces. The high and low material density groups are also recognizable among low-velocity impact fragments, although the separation is less obvious (see Fig. 10). The fact that there exist two material density groups in the size versus mass distribution can be applied to the development of a size-based material density distribution model. 3.2.2. Area-to-mass ratio distribution Figs. 11 and 12 show the area-to-mass ratio distribution of the 1500 fragments from each impact experiment in terms of size (characteristic length). They can also be separated into two groups, high and low material density, as in
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Fig. 8. Size (characteristic length) distributions of the two fragment sets. Both the cumulative and differential distributions are shown. Hypervelocity impact (HVI) produces more fragments in the 1 cm and larger size regime than low-velocity (LVI) impact does.
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Fig. 9. Size versus mass distribution of the hyper-velocity impact fragments. They can be separated into two groups, one with a higher material density distribution and the other with a lower material density distribution.
Figs. 9 and 10. The hyper-velocity impact appears to produce more fragments with a higher area-to-mass ratio than the low-velocity impact does. The numbers of fragments with an area-to-mass ratio larger than 10 m2/kg are 229
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than 1 m2/kg are, not much different, 896 (hyper-velocity) and 861 (low-velocity).
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4. Conclusions Mass [g]
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Fig. 10. Size versus mass distribution of the low-velocity impact fragments. They can still be separated into two groups, although the separation is not as clear as that for hyper-velocity impact fragments.
This paper has summarized two new satellite impact experiments conducted to investigate the outcome of low- and hyper-velocity impacts on two identical satellites. One was hit with a 40-g aluminum alloy sphere at a low-velocity of 1.5 km/s, whereas the other was hit with a 4-g aluminum alloy sphere at a hyper-velocity of 4.4 km/s. The target satellites were completely fragmented in both impact experiments. Approximately 1500 fragments from each impact experiment have been weighed, measured, and analyzed based on the analytic method used in the NASA Standard Breakup Model. The results presented in this paper have indicated the following conclusions:
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1. The similarity in mass distribution of fragments between low- and hyper-velocity impacts encourages the development of a general-purpose distribution model applicable for a wide impact velocity range. 2. The fact that there exist two material density groups in the size versus mass distribution of fragments suggests the development of a size-based material density distribution model.
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Fig. 11. Size versus area-to-mass ratio distribution of the hyper-velocity impact fragments. They can also be separated into two groups as in Figs. 9 and 10.
Acknowledgements The authors acknowledge the generous support of the NASA Orbital Debris Program Office on the experiments. The authors also acknowledge the delegated work done by Mr. Yoshihiro Tsuruda, a graduate student of Kyushu University, on the experiments and data analysis.
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Fig. 12. Size versus area-to-mass ratio distribution of the low-velocity impact fragments. The low-velocity impact produces less fragments with an area-to-mass ratio of 10 m2/kg or higher.
(hyper-velocity) and 67 (low-velocity), respectively. Many line-shaped fragments produced by the hyper-velocity impact may contribute to this difference. However, the numbers of fragments with an area-to-mass ratio lager
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