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Acta Astronautica

Acta Astronautica 83 (2013) 216–231

0094-57

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journal homepage: www.elsevier.com/locate/actaastro

Hypervelocity impact testing of advanced materials and structuresfor micrometeoroid and orbital debris shielding$

Shannon Ryan a,n, Eric L. Christiansen b

a Defence Science and Technology Organisation, Australiab NASA Johnson Space Center, USA

a r t i c l e i n f o

Article history:

Received 9 January 2012

Received in revised form

12 September 2012

Accepted 19 September 2012Available online 20 November 2012

Keywords:

Hypervelocity impact

Space debris

Micrometeoroids

MMOD

65/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.actaastro.2012.09.012

s paper was presented during the 62nd IAC i

esponding author. Tel.: þ61 39626 7706.

ail addresses: shannon.ryan@dsto.defence.gov

ristiansen@nasa.gov (E.L. Christiansen).

a b s t r a c t

A series of 66 hypervelocity impact experiments have been performed to assess the

potential of various materials (aluminium, titanium, copper, stainless steel, nickel,

nickel/chromium, reticulated vitreous carbon, silver, ceramic, aramid, ceramic glass,

and carbon fibre) and structures (monolithic plates, open-cell foam, flexible fabrics,

rigid meshes) for micrometeoroid and orbital debris (MMOD) shielding. Arranged in

various single-, double-, and triple-bumper configurations, screening tests were

performed with 0.3175 cm diameter Al2017-T4 spherical projectiles at nominally

6.8 km/s and normal incidence. The top performing shields were identified through

target damage assessments and their respective weight. The top performing candidate

shield at the screening test condition was found to be a double-bumper configuration

with a 0.25 mm thick Al3003 outer bumper, 6.35 mm thick 40 PPI aluminium foam

inner bumper, and 1.016 mm thick Al2024-T3 rear wall (equal spacing between

bumpers and rear wall). In general, double-bumper candidates with aluminium plate

outer bumpers and foam inner bumpers were consistently found to be amongst the top

performers. For this impact condition, potential weight savings of at least 47% over

conventional all-aluminium Whipple shields are possible by utilizing the investigated

materials and structures. The results of this study identify materials and structures of

interest for further, more in-depth, impact investigations.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Due to the increasing population of orbital debris innear Earth environments, the required performance ofmicrometeoroid and orbital debris (MMOD) protectionsystems for future manned vehicles can be expected toincrease. Depending on the vehicle and mission profile,this increase in performance will either be in added capabi-lity (i.e. stopping larger debris), or improved efficiency(i.e. equal protection with less weight). In [1] Christiansen

ll rights reserved.

n Cape Town.

.au (S. Ryan),

evaluated the performance of 15 different materials usedin place of the baseline aluminium alloy as the bumper in aWhipple shield configuration. The goals of the study wereto demonstrate the feasibility of using alternative materialsto increase MMOD shield performance without increasingmass, or, provide comparable levels of performance withlighter weight configurations. Candidate materials wereselected for their predicted ability to, for example: gen-erate large shock pressures in the impacting projectile,thus vaporizing or fragmenting it into small particles moreeffectively; increase the debris cloud dispersion angle;disrupt the projectile without contributing hazardousfragments to the debris cloud; etc. A number of alternatematerials, particularly double-bumper shields containingaluminium meshes, were found to be superior to the

Nomenclature

AD Areal density (g/cm2)BLE Ballistic Limit EquationFOM Figure Of MeritMMOD Micrometeoroid and Orbital Debrisnm Not measuredNP Not perforated or spalledP PerforatedPPI Pore Per (linear) InchRVC Reticulated Vitreous CarbonSP SpalledSS Stainless SteelWC Whipple Candidate

WP Witness Platedc Critical projectile diameter (cm)deff Effective projectile diameter (cm)dh Clear hole diameter (cm)dp Projectile diameter (cm)dsp Spall diameter (cm)Dmax Maximum diameter of damaged areaNh Number of perforationsPeff Effective penetration depth (cm)S Spacing (cm)tb Bumper thickness (cm)tob Outer bumper thickness (cm)tr Residual thickness (cm)tw Rear wall thickness (cm)

Fig. 2. Ligament cross section shape variation with relative density

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231 217

baseline Al6061-T6 plate under the impact conditioninvestigated. Furthermore, graphite/epoxy composite wasfound to be superior to an equal areal density aluminiumplate as an intermediate bumper behind a disrupting meshouter bumper.

With similar goals to the 1987 study, an extensive testprogram was undertaken by NASA JSC between 2003 and2005 to investigate the hypervelocity impact performanceof new structures and materials, particularly metallicopen-cell foams. Metallic foams are characterised by theirlow density and novel physical, mechanical, thermal,electrical and acoustic properties. They offer significantperformance gains in light, stiff structures for the efficientabsorption of energy, thermal management, etc. [2]. Forthis study, open cell foams were selected in preference ofclosed cell foams as they are generally of lower weightand provide a higher degree of homogeneity. Open cellfoams are generally defined in terms of relative density tothe base material (as a percentage) and pore density interms of pores per linear inch (PPI). In Fig. 1 foam cellsand pores are defined; cells are typically 14-facetedpolyhedral or solid tetrakaidecahedrons, while pores arethe individual windows between the interconnected foamligaments. Pore density controls the number and nominalsize of foam ligaments, and relative density controls theircross-sectional form and actual size, shown in Fig. 2.Preliminary investigations of the hypervelocity impactperformance of metal foam structures [3–5] have demon-strated their potential, particularly in comparison with

Fig. 1. Definition of open cell foam pore and cell size (& ERG Aerospace).

traditional structural panels (such as honeycomb coresandwich panels).

This paper presents the results of initial screeningtests performed on multi-wall configurations incorpor-ating advanced materials, particularly metallic open cellfoams. Results of the study are intended to informselection of promising materials and configurations forfurther investigation.

2. Defining the target baseline

For evaluating the performance of the candidate mate-rials a baseline aluminium Whipple shield was used,nominally identical to that in [1]. This baseline config-uration, shown in Fig. 3, consisted of a 0.0254 cm thickAl6061-T6 bumper plate spaced 5.08 cm from an Al2024-T3 rear wall. The thickness of the rear wall was varied inorder to determine the ballistic limit for a 0.3175 cmdiameter Al2017-T4 spherical projectile, with a nominalvelocity of 6.8 km/s at normal incidence (i.e. normal to thetarget surface). Shield failure was defined as the onset of

(& ERG Aerospace).

Fig. 3. Baseline aluminium Whipple shield.

Table 1Details of the baseline Whipple shield impact experiments.

Target

no.

Test

no.

Rear wall Total AD

(g/cm2)

Velocity

(km/s)

Result

[P/SP/NP]

Rear wall

dsp (cm)

WP dh

(cm)Material tw (cm) AD (g/cm2)

W-1 4311 Al2024-T3 0.127 0.344 0.562 6.52 SP 15 –

W-2 4312 Al2024-T3 0.160 0.438 0.657 6.69 SP 12.5 –

W-3 4313 Al2024-T3 0.180 0.492 0.710 6.52 SP 13.6 –

W-4 4369 Al2024-T3 0.127 0.346 0.565 6.85 SP 14.6 –

W-5 4370 Al6061-T6 0.229 0.603 0.821 6.74 SP 14 2.4

W-6 4429 Al2024-T3 0.254 0.700 0.918 6.62 SP 13 –

W-7 4430 Al2024-T3 0.318 0.899 1.119 6.91 NP 15 –

Table 2Details of the single-bumper candidate shield configurations.

Target no. HITF no. Bumper Rear wall Total

Material tb (cm) AD (g/cm2) Material tw (cm) AD (g/cm2) S (cm) AD (g/cm2)

WC-1 4310 RCM-NC- foam 0.500 0.339 Al2024-T3 0.127 0.345 5.08 0.684WC-2 4333 Silver foam 0.670 0.600 Al2024-T3 0.041 0.113 5.08 0.713WC-3 4334 45 PPI ceramic foam 0.635 0.246 Al2024-T3 0.127 0.350 5.08 0.596

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231218

material ejection into the simulated vehicle interior(i.e. detached spall of the rear wall). Clear hole perforationand through-cracking are considered more comprehen-sive failures.

Results of the baseline Whipple shield ballistic limitcharacterisation tests are presented in Table 1. The firstsix tests resulted in detached spallation failure, whiletest W-7 passed. As such, for this impact condition,the ballistic limit of the baseline Whipple shield isat a rear wall thickness between 0.254 cm and 0.318 cm(corresponding to a total areal density, ADtot, between0.918 g/cm2 and 1.119 g/cm2). For the six tests thatresulted in detached spall failure, there was minimaldifference in the rear wall damage (both front and rearside). Target W-5 is considered to have performed worsethan the other spalled targets, as the witness plate waspenetrated (indicating a more lethal spall fragment). Thisis likely due to the use of Al6061-T6 for the rear wallinstead of Al2024-T3, which has a higher hardness andyield strength.

3. Target configurations

A total of 66 candidate shields were tested for com-parison with the baseline Whipple shield, consisting ofsingle-, double-, and triple-bumper configurations. Alltests were performed at conditions nominally identicalto those performed on the baseline Whipple shield(i.e. 0.3175 cm diameter Al2017-T4 sphere, 6.8 km/s, 01incidence). An overview of the candidate shields is givenin Table 2 (single-bumper), Table 3 (double-bumper), andTable 4 (triple-bumper). For all candidate shields the totalspacing was maintained nominally equal to that of thebaseline Whipple shield (i.e. 5.08 cm) and an effort wasmade, where possible, to maintain a constant total arealdensity. Internal spacing measurements (i.e. S1, S2) aremade from rear surface to front surface of the target

components, e.g. S2 is measured from the rear of the 2ndbumper to the front of the 3rd bumper. Target spacingmeasurements of zero (e.g. WC-20) indicate that thecomponents were flush. Examples of double- and triple-bumper target configurations are given in Fig. 4.

4. Test results

The results of the impact tests are given in Table 5(single-bumper), Table 6 (double-bumper), and Table 7(triple-bumper). Measurements are provided for spalldiameter (dsp), clear hole diameter (dh), All three testson the single-bumper candidates resulted in perforationof the shield rear wall, with WC-3 also having perforationof the witness plate. Of the 38 double-bumper candidates,22 were perforated and 16 successfully passed (no per-foration or detached spall). Of the 25 triple-bumpercandidate, there were 6 perforation results and 19 passresults.

5. Analysis

During the test program, impact experiments wereperformed on candidate shields with:

�

Varying number of bumper plates: 1/2/3 � Varying areal density: 0.419–0.713 g/cm2

�

Varying bumpers types/materials � Varying spacing of intermediate bumpers � Varying rear wall thicknesses

As such, directly assessing the performance of aparticular candidate relative to the other configurationsis difficult. Towards this goal three approaches have beendefined, each with their own strengths and weaknesses.By evaluating the targets using all three approaches, the

Table 3Details of the double-bumper shield configurations.

Target no. HITF no. 1st bumper 2nd bumper Rear wall Totals

Material tob

(cm)

AD

(g/cm2)

Material tb

(cm)

AD

(g/cm2)

S1

(cm)

Material tw

(cm)

AD

(g/cm2)

Spacing

(cm)

AD

(g/cm2)

WC-4 4306 90 PPI INCO Ni foam 0.230 0.101 90 PPI INCO Ni foam 0.23 0.103 2.132 Al 2024-T3 0.127 0.346 5.08 0.550WC-5 4307 RCM-Ni foam 0.30 0.171 90 PPI INCO Ni foam 0.23 0.100 2.097 Al 2024-T3 0.127 0.346 5.08 0.616WC-6 4308 RCM-NC foam 0.30 0.128 90 PPI INCO Ni foam 0.17 0.052 2.157 Al 2024-T3 0.127 0.346 5.08 0.526WC-7 4309 90 PPI INCO Ni foam 0.17 0.054 RCM-NC foam 0.30 0.125 2.157 Al 2024-T3 0.127 0.346 5.08 0.525WC-8 4323 2�100 PPI SS foam 0.127 0.105 2�100 PPI Ti foam 0.127 0.113 2.350 Al 2024-T3 0.127 0.348 5.08 0.566WC-9 4324 60 PPI Ti foam 0.127 0.120 60 PPI Ti foam 0.127 0.115 2.350 Al 2024-T3 0.127 0.347 5.08 0.583WC-10 4325 60 PPI SS foam 0.127 0.089 2�60 PPI SS foam 0.254 0.165 2.286 Al 2024-T3 0.127 0.349 5.08 0.603WC-11 4326 2�60 PPI SS foam 0.254 0.155 60 PPI SS foam 0.127 0.082 2.286 Al 2024-T3 0.127 0.349 5.08 0.586WC-12 4328 3�80 PPI RVC foam 1.905 0.101 3�80 PPI RVC foam 1.905 0.103 0.572 Al 2024-T3 0.127 0.348 5.08 0.551WC-13 4329 Al 2024-T3 0.03 0.075 80 PPI ceramic foam 0.635 0.154 2.144 Al 2024-T3 0.127 0.347 5.08 0.576WC-14 4330 80 PPI ceramic foam 0.635 0.151 Al 2024-T3 0.031 0.076 2.144 Al 2024-T3 0.127 0.347 5.08 0.574WC-15 4331 Al 2024-T3 0.03 0.075 10 PPI Al foam 0.635 0.133 2.144 Al 2024-T3 0.127 0.349 5.08 0.557WC-16 4332 10 PPI Al foam 0.635 0.124 Al 2024-T3 0.031 0.076 2.144 Al 2024-T3 0.127 0.348 5.08 0.548WC-17 4371 2�100 PPI Cu foam 0.127 0.116 2�100 PPI Cu foam 0.127 0.111 2.350 Al 2024-T3 0.127 0.347 5.08 0.575WC-18 4372 2�100 PPI Ti foam 0.127 0.101 2�100 PPI Ti foam 0.127 0.111 2.350 Al 2024-T3 0.127 0.350 5.08 0.563WC-19 4386 Al 2024-T3 0.03 0.082 80 PPI ceramic foam 0.635 0.136 2.160 Al 2024-T3 0.1016 0.279 5.09 0.497WC-20 4387 Al 2024-T3 0.03 0.084 80 PPI ceramic foam 0.635 0.097 0 Al 2024-T3 0.127 0.352 5.09 0.533WC-21 4388 Al 2024-T3 0.03 0.082 80 PPI ceramic foam 0.635 0.109 1.270 Al 2024-T3 0.127 0.350 5.09 0.540WC-22 4389 Al 2024-T3 0.03 0.082 80 PPI ceramic foam 0.635 0.105 3.023 Al 2024-T3 0.127 0.353 5.09 0.539WC-23 4390 Al 2024-T3 0.03 0.081 80 PPI ceramic foam 0.635 0.160 4.293 Al 2024-T3 0.127 0.352 5.09 0.593WC-24 4393 Al mesh (|¼0.016 in.) 0.076 0.058 80 PPI ceramic foam 0.635 0.192 2.108 Al 2024-T3 0.127 0.353 5.08 0.603WC-25 4394 100 PPI Ti foam 0.64 0.058 80 PPI ceramic foam 0.635 0.163 2.108 Al 2024-T3 0.127 0.351 5.07 0.572WC-26 4395 Al 2024-T3 0.030 0.083 40 PPI Al foam 0.635 0.142 2.134 Al 2024-T3 0.127 0.349 5.09 0.574WC-27 4396 Al 2024-T3 0.030 0.082 20 PPI Al foam 0.635 0.145 2.134 Al 2024-T3 0.127 0.350 5.09 0.578WC-28 4397 Al 2024-T3 0.030 0.082 10 PPI Al foam 0.635 0.149 2.159 Al 2024-T3 0.1016 0.279 5.09 0.511WC-29 4420 Al 6061-T6 w/ 100 PPI SS foam 0.094 0.123 80 PPI RVC foam w/ 2�Kevlar KM2 0.635 0.081 2.969 Al 2024-T3 0.127 0.340 5.08 0.544

WC-30 4422 Al6061-T6 w/ SS mesh (|¼0.009 in.) 0.094 0.133 4�Kevlar KM2 nm 0.091 3.225 Al 2024-T3 0.127 0.345 5.08 0.569

WC-31 4436 Al 6061-T6 0.041 0.107 7�Carbon fabric 0.16 0.119 3.259 Al 2024-T3 0.127 0.348 5.08 0.574

WC-32 4455 100 PPI Cu foam 0.064 0.066 40 PPI Al foam 0.635 0.140 2.999 Al 2024-T3 0.127 0.350 5.08 0.557

WC-33 4456 100 PPI Cu foam 0.064 0.058 40 PPI Al foam 0.635 0.140 2.999 Al 2024-T3 0.1016 0.276 5.08 0.474

WC-34 4457 100 PPI Cu foam 0.152 0.058 40 PPI Al foam 0.635 0.137 2.910 Al foam sandwicha 0.665 0.294 5.08 0.489

WC-35 4458 100 PPI Ti foam 0.064 0.050 40 PPI Al foam 0.635 0.140 2.999 Al 2024-T3 0.1016 0.276 5.08 0.465

WC-36 4459 100 PPI Cu foam 0.064 0.058 40 PPI Al foam 0.635 0.144 2.999 Al 2024-T3 0.0813 0.220 5.08 0.423

WC-37 4460 100 PPI SS foam 0.064 0.050 40 PPI Al foam 0.635 0.137 2.999 Al 2024-T3 0.1016 0.276 5.08 0.463

WC-38 4461 Al 3003-O 0.025 0.068 40 PPI Al foam 0.635 0.138 3.037 Al 2024-T3 0.1016 0.276 5.08 0.482

WC-39 4462 Al mesh (|¼0.013 in.) 0.097 0.055 40 PPI Al foam 0.635 0.143 2.966 Al 2024-T3 0.1016 0.276 5.08 0.474

WC-40 4463 100 PPI Cu foam 0.064 0.058 9�Carbon fabric 0.19 0.156 2.999 Al 2024-T3 0.1016 0.276 5.08 0.490

WC-41 4464 100 PPI Cu foam 0.064 0.062 40 PPI Al foam 0.635 0.139 2.999 Al foam w/ Al6061-T6b 0.686 0.269 5.08 0.470

a 6.35 mm thick 40 PPI Al foam with 0.3048 mm thick Al 6061-T6 facesheets.b 6.35 mm thick 40 PPI Al foam with 0.508 mm thick Al 6061-T6 flush on back.

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Table 4Details of the triple-bumper shield configurations.

Target

no.

Test

no.

1st bumper 2nd bumper 3rd bumper Rear wall Total

Type AD

(g/cm2)

Type AD

(g/cm2)

S1

(cm)

Type AD

(g/cm2)

S2

(cm)

Material tw

(cm)

AD

(g/cm2)

S

(cm)

AD

(g/cm2)

WC-44 4327 45 PPI RVC foam 0.127 45 PPI RVC foam 0.059 0 45 PPI RVC foam 0.036 0 Al 2024-T3 0.127 0.347 5.08 0.568WC-45 4349 100 PPI SS foam 0.047 Al 2024-T3 0.108 1.57 100 PPI Ti foam 0.050 1.6 Al 2024-T3 0.127 0.350 5.03 0.555WC-46 4350 100 PPI Ti foam 0.202 Al 2024-T3 0.112 1.57 100 PPI SS foam 0.049 1.6 Al 2024-T3 0.127 0.347 5.03 0.558WC-47 4351 100 PPI Cu foam 0.066 Al 2024-T3 0.110 1.57 80 PPI RVC foam 0.031 1.6 Al 2024-T3 0.127 0.350 5.03 0.557WC-48 4352 80 PPI RVC foam 0.031 Al 2024-T3 0.112 1.57 100 PPI Cu foam 0.072 1.6 Al 2024-T3 0.127 0.350 5.03 0.565

WC-49 4364 100 PPI Cu foam 0.058 Al 2024-T3 0.112 1.57 100 PPI SS foam 0.042 1.6 Al 2024-T3 0.127 0.348 5.03 0.560WC-50 4365 45 PPI RVC foam w/Al 6061-0

facesheets

0.155 Al 6061-0 0.056 1.17 45 PPI RVC foam w/

2�Kevlar

0.134 1.17 Al 2024-T3 0.127 0.351 5.05 0.696

WC-51 4366 100 PPI SS foam 0.050 Al 2024-T3 0.112 1.57 SS mesh w/ Kevlar 0.078 1.57 Al 2024-T3 0.127 0.347 5.07 0.589WC-52 4367 SS mesh (|¼0.01 in.) 0.123 Al 2024-T3 0.112 1.57 100 PPI SS foam w/ Kevlar 0.068 1.57 Al 2024-T3 0.127 0.348 5.07 0.651WC-53 4368 SS mesh (|¼0.01 in.) 0.125 Al 2024-T3 0.112 1.57 SS mesh 0.056 1.57 Al 2024-T3 0.127 0.347 5.03 0.640

WC-54 4385 Al 2024-T3 0.113 SS mesh

(|¼0.01 in.)

0.055 1.57 100 PPI SS foam 0.047 1.57 Al 2024-T3 0.127 0.342 5.03 0.556

WC-55 4391 Al 3003-0 0.028 SS mesh

(|¼0.01 in.)

0.056 0 80 PPI ceramic foam 0.125 2.1 Al 2024-T3 0.127 0.351 5.05 0.560

WC-56 4392 Al 3003-0 0.028 Al mesh

(|¼0.01 in.)

0.059 0 80 PPI ceramic foam 0.156 2.1 Al 2024-T3 0.127 0.350 5.05 0.593

WC-57 4413 100 PPI Cu foam 0.066 Al 6061-T6 0.075 1.685 100 PPI Cu foam 0.056 1.653 Al 2024-T3 0.127 0.344 5.16 0.542WC-58 4414 Al 6061-T6 0.083 100 PPI Cu foam 0.060 1.668 100 PPI Cu foam 0.059 1.653 Al 2024-T3 0.127 0.343 5.15 0.545WC-59 4415 100 PPI SS foam 0.054 Al 6061-T6 0.106 1.680 100 PPI SS foam 0.052 1.637 Al 2024-T3 0.127 0.344 5.15 0.557WC-60 4416 100 PPI SS foam 0.050 Al 6061-T6 0.305 1.685 80 PPI RVC foam w/

2�Kevlar

0.061 1.335 Al 2024-T3 0.127 0.349 5.15 0.536

WC-61 4417 Al 6061-T6 0.076 100 PPI SS foam 0.047 1.668 80 PPI RVC foam w/

2�Kevlar

0.059 1.352 Al 2024-T3 0.127 0.343 5.15 0.526

WC-62 4418 100 PPI Cu foam 0.054 Al 6061-T6 0.076 1.685 3�Kevlar 0.068 1.622 Al 2024-T3 0.127 0.346 5.15 0.544

WC-63 4419 100 PPI SS foam 0.047 Al 6061-T6 0.075 1.685 4�Kevlar 0.090 1.607 Al 2024-T3 0.127 0.329 5.15 0.541

WC-64 4421 100 PPI Cu foam 0.062 Al 2024-T3 0.112 1.680 80 PPI RVC foam 0.035 1.351 Al 2024-T3 0.127 0.345 5.15 0.553

WC-65 4431 100 PPI Cu foam 0.050 Al 2024-T3 0.112 1.680 80 PPI RVC foam 0.034 1.351 Al 2024-T3 0.813 0.223 5.15 0.419

WC-66 4432 Al mesh (|¼0.009 in.) 0.041 Al 6061-T6 0.075 1.255 4�Kevlar 0.092 2.447 Al 2024-T3 0.127 0.348 5.13 0.556

WC-67 4434 100 PPI Ti foam 0.058 Al 6061-T6 0.076 1.685 3�Kevlar 0.068 1.622 Al 2024-T3 0.127 0.350 5.15 0.553

WC-68 4435 5� carbon fabric 0.085 4� carbon fabric 0.071 1.654 5� carbon fabric 0.086 1.586 Al 2024-T3 0.127 0.343 5.20 0.584

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bias of each approach has less weight on the finalcandidate ranking.

5.1. Approach 1: Weight-based

The simplest way to assess the top performing shieldsis to rank them in terms of their total areal density, i.e. thetop performing shield was that which passed with thelowest weight. In Fig. 5 all shield candidates are plotted interms of their total areal density and the test result. Thetop performing shields are seen to be (in order): WC-38(HITF04461), WC-40 (HITF04463), WC-59 (HITF04417),and WC-58 (HITF04416). WC-38 provides a reduction inweight of at least 47% from the baseline Whipple shieldconfiguration (0.482 g/cm2 vs. 0.918 g/cm2).

5.2. Approach 2: Figure of merit (FOM)

A simple weight-based ranking of shield performanceis ideal if the ballistic limit of the competing candidates iswell characterized. For comparing target performancebased on single shots, it fails to take into account damageto the rear wall (effectively, how close the target is tofailure). For instance, a shield with a total areal density of0.5 g/cm2 may pass the test with a marginal safety factor,while a second, slightly heavier candidate (e.g. 0.51 g/cm2)may pass with little or no damage to the rear wall. In thiscase, a weight-based assessment will rank the 0.50 g/cm2

above the clearly better performing, yet slightly heavier,configuration.

A figure of merit can be used to rank the performanceof the shields with varying areal densities, rear wall

Al2024-T3plate

Al2024-T3plate

80 PPI ceramic foam

WC-19

21.6 mm 21.6 mm

Fig. 4. Examples of double-bumper (left, WC-19) and triple-bumper

(right, WC-50) candidate shields.

Table 5Details of the single-bumper candidate shield impact experiments.

Target no. HITF no. Velocity

(km/s)

Result

[P/NP/SP]

Rear wall

dh (mm)

WC-1 4310 6.66 P 1.5�1.7WC-2 4333 6.90 P 22.9�14.WC-3 4334 6.94 P 3.0�3.0

thicknesses, number of bumpers, and standoffs. Initially,this ranking is performed according to the test result, i.e.:perforated (P), spalled (SP), not perforated or spalled (NP).For ranking performance within the three result cate-gories, the following methodology is applied:

�

5

Perforated (P): initially based on the witness platedamage (P/SP/NP), subsequently on the diameter ofthe largest perforation hole, Ah (calculated using mea-surements of the minor and major axis);

� Spalled (SP): initially based on the witness plate

damage (P/SP/NP), subsequently on the diameter ofthe spalled area, dsp (measured);

� Not perforated or spalled (NP): based on how close the

rear wall is to failure.

To assess how close a rear wall is to failure, twoconditions are considered: cratering-type failure andimpulsive-type failure. Cratering-type failure is inducedby the impact of solid fragments, and impulsive-typefailure is a result of tensile loads generated by impact ofa molten/gaseous debris cloud. The FOM provides esti-mates of the rear wall failure limit for each mode, andassesses how close the respective test articles are to thoselimits. These estimates are not expected to be quantita-tively accurate estimates of failure thresholds, however,they provide a consistent and traceable methodology incomparing performance of the candidate shields.

5.2.1. Cratering-type failure

The impact of solid fragments upon the shield rearwall leads to a cratering-type failure that can be evaluatedwith semi-infinite plate cratering relationships. Cour-Palais defined the penetration depth into a semi-infinitetarget, PN, as (from [6]):

P1 ¼ 5:24d19=18p HB�1=4

ðrp=rwÞaðVcos y=CÞ2=3

ð1Þ

where dp is the projectile diameter (cm), HB is the targethardness (HB), rp is the projectile density (g/cm3), rw

is the target density (g/cm3), V is the projectile velocity(km/s), C is the target soundspeed (km/s), y is the impactangle (deg.), and

a¼1=2, f or ðrp=rwÞo1:5

2=3, f or ðrp=rwÞZ1:5

(ð2Þ

For metals, it was reported in [6] that spallationoccurred for plates with thicknesses less than 3 timesthe crater depth. Spall fragments became detached fromthe plate rear side when thicknesses decreased below 2.2

Witness plate

Nh dsp (mm) Dmax (mm) dh (mm) Nh

8 n/a nm nm nm

1 n/a nm n/a n/a

8 n/a nm o1 4

Table 6Details of the double-bumper candidate shield impact experiments.

Target no. HITF no. Velocity

(km/s)

Result

[P/NP/SP]

Rear wall Witness plate

dh (mm) Nh dsp (mm) Dmax (mm) dh (mm) Nh

WC-4 4306 6.72 P 6.0�6.5 4 n/a 80�75 nm nm

WC-5 4307 6.78 P 1.6�1.5 1 n/a 95�110 nm nm

WC-6 4308 6.71 P 3.1�1.6 2 n/a 100�120 nm nm

WC-7 4309 6.78 P 7.2�8.6 1 n/a 120�110 nm nm

WC-8 4323 5.976 P 2.0�2.1 1 n/a 105�90 n/a 0

WC-9 4324 6.93 P 1.6�1.4 2 n/a 115�110 n/a 0

WC-10 4325 6.75 P 2.5�1.6 1 n/a 130�120 n/a 0

WC-11 4326 6.77 NP n./a 0 n/a 130�120 n/a 0

WC-12 4328 6.78 P 6.2�6.2 1 n/a 70�70 2.1�1.6 41

WC-13 4329 6.92 NP n/a 0 n/a 85�85 n/a 0

WC-14 4330 6.76 P 7.3�4.7 3 n/a 65�65 n/a 0

WC-15 4331 6.707 NP n/a 0 n/a 80�90 n/a 0

WC-16 4332 6.716 P 2.3�2.5 4 n/a 75�55 n/a 0

WC-17 4371 6.52 NP n/a 0 n/a 50�55 n/a 0

WC-18 4372 6.78 NP n/a 0 n/a 66�65 n/a 0

WC-19 4386 6.76 P 2.7�2.1 1 n/a 55�55 n/a 0

WC-20 4387 6.97 P 4.8�5.6 1 n/a 80�90 o0.1 1

WC-21 4388 6.96 P 2.0�2.0 1 n/a 46�52 n/a 0

WC-22 4389 6.796 NP n/a 0 n/a 41�37 n/a 0

WC-23 4390 6.94 NP n/a 0 n/a 34�33 n/a 0

WC-24 4393 6.89 NP n/a 0 n/a 56�52 n/a 0

WC-25 4394 6.94 P n/a 0 n/a 56�53 n/a 0

WC-26 4395 6.89 NP n/a 0 n/a 115�98 n/a 0

WC-27 4396 6.87 NP n/a 0 n/a 80�85 n/a n/a

WC-28 4397 6.86 P 1.0�1.0 2 n/a 70�65 65�60 0

WC-29 4420 6.94 NP n/a 0 n/a 44�48 n/a n/a

WC-30 4422 6.75 NP n/a 0 n/a 44�42 n/a n/a

WC-31 4436 6.84 NP n/a 0 n/a 70�70 n/a n/a

WC-32 4455 6.56 P 2.5�2.2 1 n/a 105�110 84�86 0

WC-33 4456 6.78 P 0�0 2 n/a 115�110 65�45 0

WC-34 4457 6.82 P 22�25 1 n/a 75�75 75�80 0

WC-35 4458 6.78 P 5.0�3.5 3 n/a 80�80 100�105 0

WC-36 4459 6.8 P 3.3�4.3 1 n/a 70�70 110�95 0

WC-37 4460 6.75 P 3.1�1.8 1 n/a 75�70 60�65 n/a

WC-38 4461 6.88 NP n/a 0 n/a 86�80 n/a n/a

WC-39 4462 6.68 P 1.8�2.4 2 n/a 75�75 80�70 0

WC-40 4463 6.7 NP n/a 0 n/a 60�60 n/a n/a

WC-41 4464 6.61 P 22.5�21 1 n/a 82�80 85�100 0

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231222

times the crater depth, and extension of the crater intothe spall region (i.e. perforation) occurred when thethickness was reduced to 1.8 times that of the craterdepth and below.

The ballistic limit of a plate subject to cratering can becalculated in terms of critical projectile diameter, dc:

dc ¼tw

kU

HB1=4ðrw=rpÞ

a

5:24ðVcos y=CÞ2=3

" #18=19

ð3Þ

where tw is the plate thickness (cm) and k is a constantrelated to failure mode (¼3.0, 2.2, and 1.8 for incipientspall, detached spall, and perforation respectively).

To estimate how close a target wall is to cratering-typefailure, the residual thickness, tr, is measured at thelocation of the deepest crater (see Fig. 6) using a digitalneedle point thickness gauge.

The residual thickness provides an approximation ofthe effective penetration depth, Peff, where:

Pef f ¼ tw�tr ð4Þ

The effective projectile diameter, deff, is then calculatedfrom Eq. (1) as:

def f ¼ ½ðPef f =5:24ÞHB1=4ðrw=rpÞ

aðC=Vcos yÞ2=3

�19=18 ð5Þ

From Eqs. (3) and (5) an approximation can be made ofhow close the target rear wall was to failing impulsively,i.e.:

f ailCR ¼def f

dc� 100 ð6Þ

where failCR is a percentage which approaches 100% as therear wall approaches cratering-type failure.

5.2.2. Impulsive-type failure

For impacts that lead to complete fragmentation andmelting of the projectile and bumper fragments the rearwall is loaded by a finely dispersed, molten/gaseous cloudthat imposes a pressure load on the shield rear wall,comparable to the action of a blast wave. This pressurewave induces plastic deformation in the form of bulging,leading to tearing and petalling of the rear wall at failure.

Table 7Details of the triple-bumper candidate shield impact experiments.

Target no. HITF no. Velocity (km/s) Result [P/NP/SP] Rear wall Witness plate

dh (mm) Nh dsp (mm) Dmax (mm) dh (mm) Nh

WC-42 4327 6.88 P 9.8�10.0 1 n/a 75�75 – 0

WC-43 4349 6.55 NP – 0 n/a 80�100 n/a n/a

WC-44 4350 6.76 P 1.3�0.8 2 n/a 48�54 – 0

WC-45 4351 6.78 NP – 0 n/a 60�56 n/a n/a

WC-46 4352 6.86 NP – 0 n/a 65�70 n/a n/a

WC-47 4364 6.82 NP – 0 n/a 70�60 n/a n/a

WC-48 4365 7.08 NP – 0 n/a 36�33 n/a n/a

WC-49 4366 7.00 NP – 0 n/a 54�52 n/a n/a

WC-50 4367 6.98 NP – 0 n/a 57�49 n/a n/a

WC-51 4368 6.85 NP – 0 n/a 75�75 n/a n/a

WC-52 4385 7.09 NP – 0 n/a 30�32 n/a n/a

WC-53 4391 6.98 P 1.7�1.8 1 n/a 52�52 – 0

WC-54 4392 6.76 P 1.7�2.2 1 n/a 55�50 – 0

WC-55 4413 6.76 NP – 0 n/a 60�60 n/a n/a

WC-56 4414 6.75 NP – 0 n/a 73�71 n/a n/a

WC-57 4415 6.86 NP – 0 n/a 60�55 n/a n/a

WC-58 4416 6.82 NP – 0 n/a 31�28 n/a n/a

WC-59 4417 6.78 NP – 0 n/a 22�22 n/a n/a

WC-60 4418 6.78 NP – 0 n/a 30�30 n/a n/a

WC-61 4419 6.74 NP – 0 n/a 33�32 n/a n/a

WC-62 4421 6.86 NP – 0 n/a 49�37 n/a n/a

WC-63 4431 6.89 P 8.0�8.0 1 n/a 43�47 – 0

WC-64 4432 6.74 NP – 0 n/a 20�22 n/a n/a

WC-65 4434 6.91 NP – 0 n/a 25�23 n/a n/a

WC-66 4435 6.73 P 1.3�2.1 1 n/a 42�45 – 0

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0 10 20 30 40 50 60 70

Candidate number

Are

al d

ensi

ty (g

/cm

2)

Pass (DB)Pass (TB)Fail (SB)Fail (DB)Fail (TB)

WC-38

WC-40

WC-58

WC-59

Fig. 5. Summary of the test results, plotted in terms of candidate total areal density, ADtot. The four top performing candidates are identified.

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231 223

In order to analyze the amplitude of impulsive loadingon the shield rear wall an analytical procedure developedby Angel and Smith [7] was applied. This technique isbased on a simply supported plate of radius r, modelled asa perfectly-plastic material, subject to a uniform trans-verse load P(t) applied over an area with radius R, shown

in Fig. 7. The load P(t) has a rectangular time profile(shown in Fig. 8), indicating an instantaneous load ofmagnitude Pm applied over a duration T, following whichit returns instantaneously to zero.

When the plate is loaded over its entire area (i.e. r¼R)with a total distributed load equal to Pm, the static

Fig. 6. Measurement of residual thickness.

Fig. 7. Plate subject to a uniform transverse load.

Fig. 8. Profile of the assumed impulsive load.

Table 8Figure of merit calculations for the candidate shields (NP test results).

Target no. HITF no. Cratering FOM Impuls

teff (cm) Peff (cm) dc (cm) Rank bmax (m

WC-26 4395 1.19 0.003 0.023 4 2.2

WC-52 4385 1.09 0.006 0.022 5 2.53

WC-65 4434 1.26 0.000 0.022 3 3.18

WC-30 4422 1.07 0.008 0.023 6 2.8

WC-22 4389 1.32 0.000 0.023 1 4.1

WC-38 4461 1.02 0.000 0.018 1 3.7

WC-31 4436 1.04 0.009 0.023 9 2.8

WC-64 4432 1.07 0.008 0.023 7 3.61

WC-60 4418 0.91 0.014 0.023 12 2.53

WC-29 4420 1.02 0.009 0.022 10 3.1

WC-58 4416 1.07 0.008 0.023 8 3.75

WC-45 4351 0.86 0.016 0.023 13 2.82

WC-27 4396 0.84 0.017 0.023 15 2.5

WC-23 4390 0.97 0.011 0.022 11 4.4

WC-59 4417 0.86 0.016 0.023 13 3.87

WC-56 4414 0.84 0.017 0.023 16 3.13

WC-15 4331 0.79 0.019 0.023 17 3.2

WC-47 4364 0.74 0.021 0.023 21 3.05

WC-49 4366 0.74 0.020 0.022 20 3.25

WC-61 4419 0.76 0.020 0.023 19 3.45

WC-13 4329 0.76 0.020 0.022 18 3.9

WC-57 4415 0.69 0.023 0.023 22 3.1

WC-55 4413 0.61 0.026 0.023 24 2.85

WC-43 4349 0.56 0.029 0.023 25 2.92

WC-50 4367 0.61 0.026 0.022 23 3.8

WC-62 4421 0.56 0.028 0.023 27 2.88

WC-48 4365 0.56 0.028 0.022 25 3.27

WC-11 4326 0.38 0.036 0.023 33 0.3

WC-24 4393 0.53 0.029 0.023 29 3.4

WC-51 4368 0.48 0.031 0.023 30 3.38

WC-40 4463 0.43 0.023 0.018 28 4.2

WC-18 4372 0.43 0.034 0.023 31 3.4

WC-17 4371 0.33 0.039 0.023 35 2.9

WC-25 4394 0.41 0.034 0.022 32 3.9

WC-46 4352 0.38 0.036 0.023 34 3.33

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231224

deflection at the centre of the plate, Ws, can be calculatedas (from [8]):

Ws ¼Pm

16pD

3þn1þn r2�R2ln

r

R�

7þ3n4ð1þnÞR

2

� �ð7Þ

where n is Poisson’s ratio (unitless) and D is the plateflexural rigidity (Pa m3),

D¼ 2Eh3=½3ð1�n2Þ� ð8Þ

Under dynamic loading, the deflection at the centre ofthe plate, Wd, is calculated as (from [9]):

Wd ¼I2ð3=2Þ�ðP0=PÞ� �

2UADUP0ð9Þ

where I is the impulse acting on the plate (Pa s), P is theapplied pressure (Pa), P0 is the pressure required toproduce plastic deformation (Pa), and AD is the mass perunit area of the middle surface (kg/m2) which can bewritten in the form:

dd ¼

0 , 0omo1

mðm�1Þ , 1omo2

m=4 3m�1� �

, 2om

8><>: ð10Þ

ive FOM score Rank

m) r (mm) d dn Rank

60 59.22 270.43 2 22 1

50 80.48 319.56 4 29 2

40 105.37 332.87 17 32 3

45 84.75 304.04 6 36 4

40 131.41 321.97 32 37 5

55 131.40 285.40 34 39 6

50 82.90 297.42 6 51 7

40 113.81 316.69 26 61 8

35 83.89 333.08 4 64 9

50 94.48 306.18 14 64 10

35 125.81 337.02 27 67 11

40 89.96 320.46 8 73 12

45 78.38 314.95 3 78 13

40 147.06 335.76 33 88 14

45 118.17 306.75 29 94 15

50 90.25 289.65 16 96 16

45 95.62 300.18 18 103 17

45 94.24 310.38 13 118 18

45 105.79 326.98 19 119 19

35 113.04 329.16 25 120 20

45 124.06 319.55 30 120 21

45 96.91 314.03 15 125 22

40 90.38 318.57 9 129 23

35 90.36 310.86 12 137 24

40 128.48 339.65 28 143 25

40 94.05 328.07 10 145 26

40 113.75 349.45 20 145 27

20 10.79 361.17 1 166 28

45 107.22 316.79 23 168 29

40 110.06 327.11 22 172 30

50 149.14 285.37 35 175 31

50 98.90 292.23 23 178 32

45 81.89 283.68 11 186 33

45 124.78 321.40 30 190 34

35 113.03 340.98 21 191 35

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231 225

where dd is the dimensionless deflection, ðrwr2=3s0hT2ÞWd;

m is the dimensionless load, Pm=6ps0h2; s0 is the static yieldstrength of the plate (Pa).

For static loading, the ratio of rear wall deflection for aplate loaded over part of its radius (as shown in Fig. 7) tothat of a plate loaded over its entire area is given by:

W ¼1

5þn4ð3þnÞ r

2

R2�4ð1þnÞln r

R

� ��ð7þ3nÞ

� �R2

r2ð11Þ

Thus, the dynamic deflection of a plate loaded over part ofits radius, W, can be estimated by the ratio W multipliedby the deflection Wd:

W ¼W �Wd ð12Þ

The dimensionless measure of permanent deflection, d,is now calculated as:

d¼rwr2

3s0hT2W ð13Þ

or, by considering the wall strength under dynamic ratherthan static loading:

d¼rwr2

3ls0hT2W ð14Þ

where l is the ratio of dynamic to static yield strength ofthe rear wall (unitless), l¼4.5.

The parameters of permanent rear wall deflection canbe expressed in terms of projectile and rear wall proper-ties (from [7]):

d¼1�K

3l 1þKð Þ2

rwV2

s0O ð15Þ

where K is the ratio of surface densities¼R2/(S2þR2), S is

the shield spacing (cm), and O is a measure of rear walldeformation (unitless), O¼W/h.

To evaluate the dimensionless permanent deflection atthe centre of the rear wall, the dynamic deflection W wasset to the measured bulge height, bmax. For rear wallfailure, Angel and Smith [7] empirically define a limitvalue of 15.82 for O (labelled as On). This value wasdetermined from experiments with spherical aluminiumprojectiles impacting on aluminium multi-shock shieldsat 6 km/s. For the multi-shock concept, Cour-Palais andCrews [10] found that repeated shocking of projectilefragments raised their thermal state, leading to fragmen-tation, melting, and vaporization at lower impact velo-cities than with a traditional Whipple shield. Fromobservations of target deposits, they considered thatimpact of a projectile at 6.3 km/s on an aluminiummulti-shock shield resulted in a projectile state equivalentto impact at 10 km/s on a standard aluminium Whippleshield. At 10 km/s, impact on an aluminium Whippleshield is expected to result in complete projectile melt,with a degree of vaporization, leading to impulsive failureof the shield rear wall. From the limit rear wall deforma-tion, On, a limit permanent deflection, dn, can be calcu-lated:

dn¼

1�K

3lð1�KÞ2rwV2

s0On

ð16Þ

The ratio of dimensionless permanent rear wall deflec-tion calculated in Eq. (15) to the limit permanent deflec-tion calculated in Eq. (16) gives an approximation of howclose the target rear wall is to failing impulsively, i.e.:

f ailIMP ¼ddn� 100 ð17Þ

where failIMP is a percentage which approaches 100% asthe rear wall approaches impulsive-type failure.

5.2.3. Figure of merit calculation

Of the 66 candidate shields tested there were 31perforation results. In all cases, failure was deemed tohave occurred as a result of cratering. As such, it isconsidered that for the test condition and target config-urations used in this investigation (nominal 6.8 km/s,normal incidence) the threshold of cratering-type failureis significantly more relevant than that of impulsive-typefailure. This is typical for metallic multi-wall shieldswithout intermediate blankets (such as multi-layer insu-lation (MLI) or ballistic/ceramic fabrics such as in stuffedWhipple shields, see e.g. [1]) at the velocity and incidencetested. As such, the factor C1 is introduced to the figure ofmerit calculation to bias the results in favour of config-urations well below the cratering-type failure threshold,i.e.:

FOM¼ f ailIMPþC1Uf ailCR ð18Þ

where C1¼5.0.The FOM calculations and rankings are given in Table 8

for the pass results (i.e. no perforation or detached spall),and Table 9 for the fail results (i.e. perforated or spalled).Of the top four performing candidate shields, two aredouble-bumper (WC-26, WC-30) and two are triple-bumper configurations (WC-52, W-65). It can be seen inTable 8 that the top weight-based ranking candidates aredifferent to the top FOM-based ones.

5.3. Approach 3: Ballistic-limit based

The FOM approach is inherently biased towards hea-vier shields, as these have a higher likelihood of prevent-ing perforation or detached spallation of the rear wall.Another method to compare shield performance is tocalculate the ballistic limit of an equivalent configurationof traditional materials and structures, and compare it tothe performance of the advanced configuration observedin the test. This approach should normalize, to a degree,the total areal density of competing candidateconfigurations.

5.3.1. Single-bumper shield ballistic limit equation

The ballistic limit of a single-bumper (or Whipple)shield can be calculated using the JSC Whipple Equation[11], defined as:

In the low velocity regime, i.e. VrVLV/cos y:

dc ¼twðs=40Þ1=2

þtb

0:6ðcos yÞ5=3r1=2p V2=3

" #18=19

ð19Þ

Table 9Figure of merit calculations for the candidate shields (P/SP test results).

Ranking candidates with perforated rear walls is done initially according

to the state of the witness plate (P/SP/NP) and subsequently by the area

of the largest hole (Ah) in the shield rear wall.

Target no. HITF no. Rear wall WP Rank

Result Ah (mm2) Result Ah (mm2)

WC-33 4456 P 0 NP – 36WC-44 4350 P 3.1 NP – 37WC-28 4397 P 3.1 NP – 38WC-9 4324 P 7 NP – 39WC-5 4307 P 7.5 nma nm 40WC-1 4310 P 8 nma nm 41WC-66 4435 P 8.6 NP – 42WC-53 4391 P 9.6 NP – 43WC-54 4392 P 11.7 NP – 44WC-10 4325 P 12.6 NP – 45WC-21 4388 P 12.6 NP – 45WC-8 4323 P 13.2 NP – 47WC-39 4462 P 13.6 NP – 48WC-6 4308 P 15.6 nma nm 49WC-32 4455 P 17.3 NP – 50WC-37 4460 P 17.5 NP – 51WC-19 4386 P 17.8 NP – 52WC-16 4332 P 18.1 NP – 53WC-36 4459 P 44.6 NP – 54WC-35 4458 P 55 NP – 55WC-14 4330 P 107.8 NP – 56WC-4 4306 P 122.5 nma nm 57WC-7 4309 P 194.5 nma nm 58WC-63 4431 P 201.1 NP – 59WC-42 4327 P 307.9 NP – 60WC-2 4333 P 1041.9 NP – 61WC-41 4464 P 1484.4 NP – 62WC-34 4457 P 1727.9 NP – 63WC-3 4334 P 28.3 P o1 65WC-20 4387 P 84.4 P 0.01 64WC-12 4328 P 120.8 P 10.6 66

a Assumed NP result.

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231226

where

VLV ¼1:436ðtb=dpÞ

�1=3

2:60

, f or tb=dpo0:16

, f or tb=dpZ0:16

(

and tb is the bumper thickness (cm), tw (cm) is the rearwall thickness, rp is the density of the projectile material(g/cm3), s is the yield strength of the rear wall material(ksi), and y is the impact angle measured normal to theouter bumper surface (deg.).

In the hypervelocity regime, i.e. VZVHV/ cos y:

dc ¼ 3:918Fn

2

t2=3w S1=3

ðsy=70Þ1=3

r1=3p r1=9

b ðVcos yÞ2=3ð20Þ

where rb is the density of the bumper material (g/cm3)and S is the standoff between the bumper rear wall (cm).

The term F2n

acts as a de-rating factor for configurationswith insufficiently thick bumpers, and is calculated as:

Fn

2 ¼ rS=D�2ðtb=dpÞ

ðtb=dpÞcrit

ðrS=D�1Þþðtb=dpÞ

ðtb=dpÞcrit

� 2

ðrS=D�1Þ

ð21Þ

where

ðtb=dpÞcrit ¼0:2

0:25

, f or S=dpZ30

, f or S=dpo30

(

and

rS=D ¼twðtb ¼ 0Þ

tw tb=dp ¼ ðtb=dpÞcrit

� �Eq. (21) is valid for the case (tb/dp)o(tb/dp)crit. For

configurations with tb/dp ratios above the critical limit,the de-rating factor F2

nconverges to the NNO solution [12]

(i.e. F2n¼1).

For VLV/cos yoVo7/cos y, linear interpolation is used,i.e.:

dc ¼ dcðVLV Þþ½dcðVHV Þ�dcðVLV Þ�

VHV�VLV� ðV�VLV Þ ð22Þ

For non-aluminium plate bumpers, an equivalent platethicknesses, tb,eq is calculated from the areal densities ofthe actual bumper plate, i.e.:

teq ¼ ADb=rAl ð23Þ

5.3.2. Double-bumper shield ballistic limit equation

The ballistic limit of a double-bumper (or triple wall)shield can be calculated using the SRL triple wall equation[13,14], defined as:

In the low velocity (LV) regime, VrVLV/ cos y:

dc ¼ðt1=2

w þtbÞ=K3SUðs=40Þ1=2þtob

0:6ðcos yÞdr1=2p V2=3

" #18=19

ð24Þ

where tob is the outer bumper thickness (cm) and K3S is anempirical constant.

In the hypervelocity (HV) regime, VZVHV cos y:

dc ¼1:155ðS1=3

1 ðtbþKtwtwÞ2=3þKS2Sb2tgwðcos yÞ�eÞ

K2=33D r1=3

p r1=9ob V2=3

ðcos yÞdð70=sÞ1=3ð25Þ

where S1 is the standoff between the outer and innerbumpers (cm), S2 is the standoff between the innerbumper and rear wall (cm), K3D, KS2, and Ktw are empiricalconstants.

For VLV/cos yoVoVLV/cos y, linear interpolation isused (Eq. (25)).

dc ¼ dcðVLV Þþ½dcðVHV Þ�dcðVLV Þ�

VHV�VLV� ðV�VLV Þ ð26Þ

Impact regime transition velocities (VLV, VHV) aredependent on the outer bumper and projectile material.An overview of parameters applicable with the SRL triplewall equation is given in Table 10.

Similar to the process for single-bumper candidates(see Eq. (23)), weight equivalent aluminium plate thick-nesses must be calculated for the exotic bumper materials(i.e. fabrics, foams, meshes).

5.3.3. Triple-bumper shield ballistic limit equation

Evaluation of the triple-bumper shield performancein terms of predicted ballistic limit of an equivalentaluminium multi-wall structure is complicated by the

Fig. 9. Methodology of the EMI triple wall [15].

Table 10List of parameters for the SRL triple wall equation (Al projectile).

Outer bumper VLV VHV K3S K3D Ktw KS2 b d e g

Aluminium 3 7 1.4 0.4 1.5 0.1 2/3 4/3 if 451Zyr651 8/3 if 451Zyr651 1/3

5/4 if 451oy4651 10/4 if 451oy4651

CFRP 4.2 8.4 1.1 0.4 1 1 1/3 4/3 0 2/3

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231 227

fact that most multi-wall BLEs consider total bumperareal density and total spacing rather than individualmeasures, e.g. multi-shock equation, stuffed Whippleshield equation, etc. As such, they are incapable ofdiscriminating between the various materials/structuresused in the triple-bumper shields, or the various arrange-ments of intermediate bumper plate spacing (e.g. concen-trated towards the outer bumper vs. concentratedtowards the shield rear wall, etc.). Of the multi-wallequations commonly used in MMOD risk assessment,only the mesh double-bumper equation considersindividual components, but this is limited to the arealdensity of the internal layers in the low velocityregime, and as such, is also insufficient for this evalua-tion. The EMI triple wall equation [15] uses a differenttechnique, calculating an equivalent projectile (in termsof damage capability) from the fragment cloud gener-ated during impact of the projectile upon the outerbumper plate. The equivalent projectile is then propa-gated to impact upon a Whipple shield, representing the2nd bumper and rear wall of the triple wall configura-tion (see Fig. 9).

To calculate the ‘‘equivalent’’ projectile, the total massof the fragment cloud is assumed to consist of theprojectile material and the material coming from theouter bumper. Furthermore, it is assuming that no massis lost to the uprange ejecta, i.e. Normal impact:

mprim ¼ ðmpþmobÞ ¼mpþpD2

h

4tb1rb1 ð27Þ

For oblique impact:

mprim ¼mpþpDminUDmax

4tb1rb1 ð28Þ

where mp is the projectile mass (g), mb1 is the mass ofmaterial ejected from the outermost bumper (g), Dh is theoutermost bumper hole diameter (cm), and Dmin and Dmax

are the minor and major axes of the elliptical outermostbumper hole respectively (cm).

The mass of the equivalent projectile is assumed equalto the total primary fragment cloud mass, multiplied by afit function, C, where C is less than 1 and is experimentallydetermined. In [15] the fit function C is assumed to be afunction of the ratio of outermost bumper thickness, tb1,to projectile diameter, i.e.

C ¼ ftb1

dp

� ð29Þ

Although the EMI triple wall equation does not takeinto account the spacing between the outer and innerbumper walls, the fit factor C was derived from test dataon multiple configurations with different spacing. As aresult, it is expected that the equation would be biasedtowards configurations with greater spacing between theinner bumper and rear wall, given the relevance of thisparameter in the Whipple shield ballistic limit equation.To include the effect of spacing between the outermostbumper and second bumper plates (S1), the fit function ismodified:

C ¼ C1tb1

dp

� �1 S1

dp

� �1=3

ð30Þ

where C1 is an empirically-adjusted constant.The equivalent projectile diameter is then calculated

as:

dp,equiv ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi6UmprimUC

pUrp

3

sð31Þ

Now that an approximate technique is available tocalculate diameter of a projectile equivalent to a fragmentcloud following perforation of a thin aluminium bumper,it can be extended for application on the triple-bumpershield configurations by applying it with the SRL triplewall equation rather than the Whipple shield BLE. Similarto the Whipple and SRL equations, equivalent-weightaluminium bumper plates are used in the equation.

5.3.4. Ballistic-limit based ranking calculation

The critical projectile diameters of the weight equivalentsingle-, double-, and triple-bumper shield candidates arelisted in Table 11 and plotted in Fig. 10. For the triple-

Table 11Ballistic-limit based ranking calculation.

Target no. HITF no. Result tb1,eq (cm) tb2,eq (cm) tb3,eq (cm) tw (cm) S1 (cm) S2 (cm) S3 (cm) dc (cm) dp/dc (cm) Rank

WC-40 4463 NP 0.021 0.056 n/a 0.102 2.54 2.54 n/a 0.185 1.713 1WC-38 4461 NP 0.254 0.05 n/a 0.102 2.54 2.54 n/a 0.186 1.705 2WC-46 4352 NP 0.011 0.041 0.026 0.127 1.6335 1.641 1.634 0.191 1.666 3WC-11 4326 NP 0.056 0.03 n/a 0.127 2.286 2.794 n/a 0.191 1.662 4WC-17 4371 NP 0.042 0.04 n/a 0.127 2.35 2.731 n/a 0.196 1.62 5WC-15 4331 NP 0.027 0.048 n/a 0.127 2.144 2.936 n/a 0.196 1.618 6WC-18 4372 NP 0.036 0.04 n/a 0.127 2.35 2.731 n/a 0.196 1.617 7WC-25 4394 NP 0.021 0.059 n/a 0.127 2.108 2.972 n/a 0.201 1.578 8WC-26 4395 NP 0.305 0.051 n/a 0.127 2.134 2.946 n/a 0.202 1.572 9WC-27 4396 NP 0.305 0.052 n/a 0.127 2.134 2.946 n/a 0.203 1.564 10WC-13 4329 NP 0.305 0.056 n/a 0.127 2.144 2.936 n/a 0.203 1.563 11WC-43 4349 NP 0.017 0.041 0.018 0.127 1.6335 1.641 1.634 0.203 1.562 12WC-29 4420 NP 0.044 0.029 n/a 0.127 3.38 1.7 n/a 0.203 1.561 13WC-30 4422 NP 0.048 0.033 n/a 0.127 3.38 1.7 n/a 0.204 1.553 14WC-24 4393 NP 0.021 0.069 n/a 0.127 2.108 2.972 n/a 0.206 1.544 15WC-49 4366 NP 0.018 0.041 0.028 0.127 1.6335 1.611 1.664 0.207 1.533 16WC-47 4364 NP 0.021 0.041 0.015 0.127 1.6335 1.641 1.634 0.207 1.532 17WC-31 4436 NP 0.406 0.043 n/a 0.127 2.54 2.54 n/a 0.208 1.528 18WC-58 4416 NP 0.018 0.03 0.022 0.127 1.7 1.7 1.7 0.208 1.525 19WC-45 4351 NP 0.024 0.041 0.011 0.127 1.6335 1.641 1.634 0.209 1.519 20WC-57 4415 NP 0.02 0.041 0.019 0.127 1.7 1.7 1.7 0.209 1.517 21WC-62 4421 NP 0.022 0.041 0.013 0.127 1.7 1.7 1.7 0.21 1.514 22WC-61 4419 NP 0.017 0.03 0.033 0.127 1.7 1.7 1.7 0.21 1.51 23WC-22 4389 NP 0.305 0.038 n/a 0.127 3.023 2.057 n/a 0.21 1.51 24WC-48 4365 NP 0.056 0.02 0.048 0.127 1.805 1.19 1.825 0.211 1.502 25WC-60 4418 NP 0.02 0.03 0.025 0.127 1.7 1.7 1.7 0.212 1.498 26WC-52 4385 NP 0.041 0.02 0.017 0.127 1.6106 1.634 1.664 0.212 1.495 27WC-65 4434 NP 0.021 0.03 0.025 0.127 1.7 1.7 1.7 0.214 1.487 28WC-64 4432 NP 0.015 0.03 0.033 0.127 1.27 2.54 1.27 0.215 1.477 29WC-55 4413 NP 0.024 0.03 0.02 0.127 1.7 1.7 1.7 0.216 1.473 30WC-51 4368 NP 0.045 0.041 0.02 0.127 1.6335 1.611 1.641 0.217 1.466 31WC-50 4367 NP 0.044 0.041 0.025 0.127 1.6335 1.611 1.664 0.218 1.457 32WC-59 4417 NP 0.03 0.017 0.021 0.127 1.7 1.7 1.7 0.221 1.436 33WC-56 4414 NP 0.03 0.022 0.021 0.127 1.7 1.7 1.7 0.221 1.435 34WC-23 4390 NP 0.305 0.058 n/a 0.127 4.293 0.787 n/a 0.227 1.399 35WC-2 4333 P 0.216 n/a n/a 0.0406 5.08 n/a n/a 0.124 2.56 36WC-20 4387 P 0.305 0.035 n/a 0.127 0 5.08 n/a 0.144 2.21 37WC-12 4328 P 0.036 0.037 n/a 0.127 0.572 4.508 n/a 0.149 2.129 38WC-36 4459 P 0.021 0.052 n/a 0.081 2.54 2.54 n/a 0.166 1.913 39WC-63 4431 P 0.018 0.041 0.012 0.081 1.7 1.7 1.7 0.167 1.899 40WC-21 4388 P 0.305 0.039 n/a 0.127 1.27 3.81 n/a 0.176 1.809 41WC-41 4464 P 0.022 0.05 n/a 0.097 2.54 2.54 n/a 0.178 1.782 42WC-37 4460 P 0.018 0.049 n/a 0.102 2.54 2.54 n/a 0.182 1.745 43WC-35 4458 P 0.018 0.05 n/a 0.102 2.54 2.54 n/a 0.183 1.738 44WC-33 4456 P 0.021 0.051 n/a 0.102 2.54 2.54 n/a 0.183 1.736 45WC-39 4462 P 0.02 0.052 n/a 0.102 2.54 2.54 n/a 0.183 1.735 46WC-6 4308 P 0.046 0.019 n/a 0.127 2.157 2.924 n/a 0.184 1.728 47WC-28 4397 P 0.305 0.054 n/a 0.102 2.159 2.921 n/a 0.184 1.721 48WC-19 4386 P 0.305 0.049 n/a 0.102 2.16 2.92 n/a 0.185 1.713 49WC-34 4457 P 0.021 0.049 n/a 0.106 2.54 2.54 n/a 0.186 1.705 50WC-5 4307 P 0.062 0.036 n/a 0.127 2.097 2.984 n/a 0.191 1.66 51WC-4 4306 P 0.036 0.037 n/a 0.127 2.132 2.949 n/a 0.191 1.658 52WC-8 4323 P 0.038 0.041 n/a 0.127 2.35 2.731 n/a 0.195 1.632 53WC-7 4309 P 0.02 0.045 n/a 0.127 2.157 2.924 n/a 0.195 1.627 54WC-9 4324 P 0.043 0.042 n/a 0.127 2.35 2.731 n/a 0.198 1.607 55WC-32 4455 P 0.024 0.051 n/a 0.127 2.54 2.54 n/a 0.203 1.568 56WC-42 4327 P 0.046 0.021 0.013 0.127 2.54 1.27 1.27 0.204 1.557 57WC-10 4325 P 0.032 0.059 n/a 0.127 2.286 2.794 n/a 0.204 1.556 58WC-44 4350 P 0.018 0.041 0.018 0.127 1.6335 1.641 1.634 0.205 1.552 59WC-66 4435 P 0.031 0.025 0.031 0.127 1.7 1.7 1.7 0.226 1.407 60WC-1 4310 P 0.122 n/a n/a 0.127 5.08 n/a n/a 0.253 1.25 61

WC-3 4334 P 0.089 n/a n/a 0.127 5.08 n/a n/a 0.261 1.21 62

WC-16 4332 P 0.045 0.305 n/a 0.127 2.144 2.936 n/a 0.299 1.061 63

WC-14 4330 P 0.055 0.305 n/a 0.127 2.144 2.936 n/a 0.3 1.06 64

WC-53 4391 P 0.01 0.02 0.045 0.127 0 2.186 2.735 0.318 1.625 65

WC-54 4392 P 0.01 0.021 0.056 0.127 0 2.186 2.735 0.318 1.589 66

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231228

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

0 10 20 30 40 50 60 70Candidate number

dp/d

c (-

)

Pass (DB)Fail (DB)Pass (TB)Fail (TB)Fail (SB)

WC-11

WC-38

WC-40

WC-46

Fig. 10. Ballistic limits (dp/dc) of all the candidate shields, plotted in terms of test result and number of bumpers. The top four performing candidates are

identified.

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231 229

bumper configurations, a value for C1 of 0.0665 was used,based on an equivalent demarcation of the pass/fail boundarydetermined for the double-bumper shields. In other words, adp/dc value of �1.56 was found to be the best demarcationbetween pass/fail results for the double-bumper shield. Assuch, the coefficient C1 was adjusted until a similar fit wasdetermined for the triple-bumper shields.

The top performing candidates, ranked in order (andidentified in Fig. 10) were found to be: WC-40 (HITF04463),WC-38 (HITF04461), WC-46 (HITF04352) and WC-11(HITF04326). Although none of the top four candidates wereamongst the top four in the FOM-ranking, two were at thetop of the weight-based ranks.

6. Discussion

The three ranking approaches (weight-based, FOM, BLE-based) are equally weighted, and the overall ranking isbased on the sum of the three rankings, given in Table 12.The top ranked shield, WC-38 (HITF04461) is a double-bumper configuration, with a 0.25 mm thick Al3003 outerbumper, 6.35 mm thick 40 PPI aluminium foam innerbumper, and 1.016 mm thick Al2024-T3 rear wall (equalspacing between bumpers and rear wall). The secondranked shield, WC-29 (HITF04420) is also a double-bumper configuration, with an Al6061-T6 and 100 PPI SSfoam outer bumper, an 80 PPI RVC and Kevlar fabric innerbumper, and a 1.27 mm thick Al2024-T3 rear wall. The thirdranked candidate, WC-26 (HITF04395) is another double-bumper configuration, with a 0.3 mm thick Al2024-T3 out-ermost bumper, 6.35 mm thick 40 PPI aluminium foamsecond bumper, and 1.27 mm thick Al2024-T3 rear wall.The top triple-ranked candidate is WC-58 (HITF04416) infifth place, however there is very little differentiating the3rd to 5th ranking scores. WC-58 is a 0.635 mm thick 100

PPI SS foam outermost bumper, a 0.305 mm thick Al6061-T6second bumper, an 80 PPI RVC foam and Kevlar thirdbumper, and a 1.27 mm thick Al2024-T3 rear wall.

In general, double-bumper configurations with analuminium plate outer bumper and foam inner bumperappears to be the most effective shielding configuration,with four of the seven top ranked shields (WC-38, WC-36,WC-22, and WC-15).

6.1. Uprange ejecta

Upon impact with the outer bumper of a MMODshielding configuration, an evacuation flow develops whichresults in the ejection of projectile and bumper materialuprange, commonly referred to as ejecta. In addition tocontributing to the pollution of the orbital environment,this ejecta can pose a continuing threat to the protectedstructure through secondary impacts with protrudingsurfaces. Therefore, it is of interest to the designer to limitthe generation of ejecta during hypervelocity impact. Inorder to evaluate the constitution and volume of ejectagenerated during the impact experiments in this study, anejecta catcher was placed uprange of the outer bumperplate and coloured blue in order to provide a highercontrast for visual inspection. For targets with an alumi-nium outer bumper plate, the ejecta catcher generallydisplayed a ring of craters and small perforation holes,with deposits trailing radially out to the target frame,shown in Fig. 11. However, for configurations with foam,mesh, or fabric outer bumper plates, there was generallyno perforation or cratering of the ejecta catcher. Christian-sen [16] recorded ejecta velocity and size during impact onvarious monolithic metallic, monolithic composite, andmesh bumper plates. Similar to the results observed in

Table 12Overall ranking of the candidate shields.

Target no. Type Ranking

Weight FOM BLE Total

WC-38 Double 1 6 2 1WC-29 Double 10 9 13 2WC-26 Double 23 1 9 3WC-40 Double 2 31 1 4WC-58 Triple 4 11 19 4WC-22 Double 9 5 24 6WC-15 Double 16 17 6 7WC-30 Double 22 4 14 8WC-60 Triple 7 9 26 9WC-65 Triple 11 3 28 9WC-52 Triple 15 2 27 11WC-61 Triple 5 20 23 12WC-43 Triple 13 24 12 13WC-31 Double 24 7 18 13WC-45 Triple 17 12 20 13WC-27 Double 27 13 10 16WC-64 Triple 14 8 29 17WC-59 Triple 3 15 33 17WC-47 Triple 19 18 17 19WC-13 Double 26 20 11 20WC-46 Triple 20 35 3 21WC-56 Triple 8 16 34 21WC-55 Triple 6 23 30 23WC-18 Double 21 32 7 24WC-62 Triple 12 26 22 24WC-57 Triple 18 22 21 26WC-11 Double 31 28 4 27WC-49 Triple 29 19 16 28WC-17 Double 28 33 5 29WC-25 Double 25 34 8 30WC-24 Double 32 29 15 31WC-23 Double 30 14 35 32WC-48 Triple 35 26 25 33WC-50 Triple 34 25 32 34WC-51 Triple 33 30 31 35WC-33 Double 43 36 45 36WC-36 Double 37 54 39 37WC-28 Double 45 38 48 38WC-37 Double 38 51 43 39WC-63 Triple 36 59 40 40WC-21 Double 49 45 41 40WC-39 Double 42 48 46 42WC-35 Double 39 55 44 43WC-6 Double 46 49 47 44WC-41 Double 41 62 42 45WC-19 Double 44 52 49 45WC-20 Double 48 64 37 47WC-44 Triple 53 37 59 47WC-34 Double 40 63 50 49WC-9 Double 60 39 55 50WC-5 Double 64 40 51 51WC-12 Double 52 66 38 52WC-8 Double 57 47 53 53WC-7 Double 47 58 54 54WC-4 Double 51 57 52 55WC-32 Double 55 50 56 56WC-66 Triple 59 42 60 56WC-53 Triple 54 43 65 58WC-2 Single 66 61 36 59WC-10 Double 63 45 58 60WC-16 Double 50 53 63 60WC-1 Single 65 41 61 62WC-54 Triple 61 44 66 63WC-42 Triple 56 60 57 64WC-14 Double 58 56 64 65WC-3 Single 62 65 62 66

Fig. 11. Typical ejecta plate damage from an aluminium (top) and foam/

mesh (bottom) outer bumper.

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231230

this study, it was found that almost no ejecta of anysignificance were observed for tests on aluminium meshes.

7. Further work

The reported work is the 1st phase of a proposed shieldmaterial evaluation study. The approach was to selectsuitable candidates based on availability of new materialsand the results of past analytical and experimental workand compare their performance to a baseline Whippleshield (same configuration from [1]). The next phase ofthe study will evaluate alternative materials for Nextel/Kevlar stuffed-Whipple shields used onboard the ISS.Future phases of the work will:

�

Select best candidates for further evaluation based ontheir MMOD performance, manufacturability, compat-ibility/serviceability, and cost. � Find the ballistic limit of the ‘‘best’’ shield candidate(s)

as function of velocity, angle, projectile density.

S. Ryan, E.L. Christiansen / Acta Astronautica 83 (2013) 216–231 231

�

Examine scale-up of ‘‘best’’ shield candidate(s) � Examine sensitivity of ‘‘best’’ shield ballistic limit to

changes: MLI, rear wall thickness, standoff/gaps, etc.

8. Conclusions

A series of 66 hypervelocity impact tests were performedon candidate shield configurations utilizing new andadvanced materials. The design of the candidate shields wasbased on an all-aluminium Whipple shield from [1]. Theimpact experiments were performed at nominally-identicalimpact conditions, with 0.3175 cm diameter aluminium alloyspheres at 6.8 km/s (normal incidence). Additionally, an effortwas made to maintain a constant areal density for all thecandidate shields, in order to facilitate comparison betweentheir respective performances.

The testing was performed as a preliminary investiga-tion of new shielding materials arranged in multi-wallconfigurations. In order to assess the respective perfor-mance of the respective materials or shielding configura-tions three ranking schemes were applied. The firstscheme (approach 1) was based on the total shieldweight, with the lighter shields that were successfullyable to defeat the test projectile given the highest rank-ings. For the second scheme (approach 2) a figure of meritwas calculated that, for the candidates able to defeat thetest projectile, assessed how close they were to failing bycratering, or impulsive loading. The third ranking scheme(approach 3) used ballistic limit equations to assess shieldperformance relative to that of equivalent weight all-aluminium configurations. The top performing shields atthe nominal condition tested were assessed to be:

1.

A double-bumper configuration, with a 0.25 mm thickAl3003 outer bumper, 6.35 mm thick 40 PPI aluminiumfoam inner bumper, and 1.016 mm thick Al2024-T3 rearwall (equal spacing between bumpers and rear wall).

2.

A double-bumper configuration, with an Al6061-T6and 100 PPI SS foam outer bumper, an 80 PPI RVCand Kevlar fabric inner bumper, and a 1.27 mm thickAl2024-T3 rear wall.

3.

A double-bumper configuration, with a 0.3 mm thickAl2024-T3 outermost bumper, 6.35 mm thick 40 PPIaluminium foam second bumper, and 1.27 mm thickAl2024-T3 rear wall.

In general, double-bumper configurations with analuminium plate outer bumper and foam inner bumper

performed extremely well, with four of the seven topranked shields. For the impact condition used in thisstudy, the top performing shields were capable of provid-ing equivalent protection to the baseline Whipple shieldat nearly half the weight (47% reduction is weightcompared to the baseline Whipple shield with a0.254 cm thick rear wall).

In addition to the performance ranking based on rearwall damage, a measurement of uprange ejecta was madeusing uprange witness plates. Aluminium plate outerbumpers were found to generate substantially moreuprange ejecta than foam, mesh, or fabric bumpers.

References

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[11] S. Ryan, E. Christiansen, A ballistic limit analysis programme forshielding against micrometeoroids and orbital debris, Acta Astro-naut. 69 (2011) 245–257.

[12] E. Christiansen, Design and performance equations for advancedmeteoroid and debris shields, Int. J. Impact Eng. 14 (1993) 145–156.

[13] S. Ryan, F. Schaefer, M. Lambert, A ballistic limit equation forhypervelocity impacts on CFRP/Al HC satellite structures, Adv.Space Res. 41 (2006) 1152–1166.

[14] F. Schaefer, S. Ryan, M. Lambert, R. Putzar, Ballistic limit equationfor equipment placed behind satellite structure walls, Int. J. ImpactEng. 35 (2008) 1784–1791.

[15] F. Schaefer, R. Putzar, Triple wall ballistic limit equation, in: FourthEuropean Conference on Space Debris, Darmstadt, 2005.

[16] E. Christiansen, Meteoroid/Debris Shielding, NASA Johnson SpaceCenter, Houston, 2003 NASA TP-2003-210788.