The methodology used to assess the probability of no impact of space debris and meteoroids on a spacecraft structure is applied to the Space Station solar array assembly. Starting with the space debris and meteoroids flux models, the projected surface area of the solar cell string circuit of the solar array panel and the mast longeron, and the design lifetime, the possibility of no impact on the solar array mast and solar cell string circuits was determined as a function of particle size. The probability of no impact on the cell string circuits was used to derive the probability of no open circuit panel. The probability of meeting a certain power requirement at the end of the design lifetime was then calculated as a function of impacting particle size. Coupled with a penetration and damage models/correlations which relate the particle size to the penetration depth and damage, the results of this analysis can be used to determine the probability of meeting the lower power requirement given a degree of redundancy, and the probability of no impact on the solar array mast

Nahra, Henry K.

English

NASA Technical Reports Server

NASA Technical Memorandum 101315
Assessment of the Effects of Space Debris
and Meteoroids Environment on the Space
Station Solar Array Assembly
(MSA-IM-1C1315) ASSiSSMIKl CF IflB BPfECIS N88-26S59
GI SPACE DEEBIS £ KB BElIOEGIIJi IK\IIONBEK1
CK THE SFflCI S111IOS SCXAE 1E£AI ASSEBBIX
(KASfi) 11 p CSC1 22B Dnclas
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 G3/18 0161702
Henry K. Nahra
Lew/5 Research Center
Cleveland, Ohio
Prepared for the
20th Photovoltaic Specialists Conference
sponsored by the Institute of Electrical and Electronics Engineers
Las Vegas, Nevada, September 26-30, 1988
NASA
https://ntrs.nasa.gov/search.jsp?R=19880019575 2020-03-20T05:18:46+00:00Z
Trade names or manufacturers' names arc used in this report for identification
only. This usage does not constitute an official endorsement, either expressed or
implied, by the National Aeronautics and Space Administration.
ASSESSMENT OF THE EFFECTS OF SPACE DEBRIS AND METEOROIDS ENVIRONMENT ON THE SPACE
STATION SOLAR ARRAY ASSEMBLY
Henry K. Nahra.
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
ABSTRACT
In this paper, the methodology used to assess
the probability of no impact of space debris and
meteoroids on a spacecraft structure was applied
to the space station solar array assembly. Start-
ing with the space debris and meteoroids flux
models, the projected surface area of the solar
cell string circuit of the solar array panel and
the mast longeron, and the design lifetime, the
probability of no Impact on the solar array mast
and solar, cell string circuits was determined as
a function of particle size. The probability of
no impact on the cell string circuits was used to
derive the probability of no open circuit panel.
The probability of meeting a certain power require-
ment at the end of the design lifetime was then
calculated as a function of impacting particle
size. Coupled with a penetration and damage
models/correlations which relate the particle size
to the penetration depth and damage, the results
of this analysis can be used to determine the prob-
ability of meeting the power requirement given a
degree of redundancy, and the probability of no
impact on the solar array mast.
INTRODUCTION
The meteoroids and debris environments consist
of particles of different diameter and density
moving at high velocities in the space environ-
ment. Micrometeoroids range in size from 10~^ to
10 cm, with a mean density of 0.5 g/cm3, and a
mean velocity of about 20 km/sec. Although micro-
meteoroids originate from cometary and lunar
sources, space debris are man made and range in
size from microscopic particles to particles of
100 cm in effective diameter. Since space debris
originate from useless orbiting spacecrafts, they
exhibit an average orbital velocity of 9 to
10 km/sec depending on the orbital Inclination,
with an average mass density of 2.8 g/cm3 for par-
ticles less than 1 cm in diameter. Micrometeo-
roids and space debris flux models (F1g. 1) can
be used to estimate the flux of certain particle
diameter or greater (1). The concern for the
damage resulting from the impact of particles mov-
ing with hypersonic velocities necessitates the
assessment of the number of impacts and their
effects on the space station photovoltaic solar
array integrity and performance.
The purpose of this paper is to analytically
assess the probability of success of the space
station solar array components (or subassemblies
such as the solar array mast and blanket) as a
function of the Impacting particle diameter for
both meteoroids and debris environments. Prob-
ability of success of the mast is defined as the
probability that the mast meets the lifetime
requirement with no impact-induced failure. Prob-
ability of success of the blanket 1s defined as
the probability that the blanket meets the power
requirement over the mission duration. Determina-
tion of the penetrating particle size and correla-
tion of the particle size and damage are not
presented in this paper due to the lack of such
data as applied to the solar array structure and
materials.
DESCRIPTION OF THE SPACE STATION SOLAR ARRAY
The space station solar array consists of two
photovoltaic blankets for power generation, a mast
for blanket deployment, a canister for mast stow-
age, two blanket boxes for blanket stowage during
launch, and a deployment mechanism for on-orbit
array deployment. Each blanket consists of active
panels structurally connected by hinge pins. Each
panel contains solar cells Interconnected by print-
etched copper circuits encapsulated between two
Kapton' layers. The cells are welded to the copper
pads and mounted on the Kapton substrate by an
adhesive (2). The space station solar array is
illustrated in Fig. 2 (3). Figure 3 shows the
repeating units that were used to analyze the
probability of success (or probability of meeting
a power or lifetime requirement) of the mast and
blanket of the solar array. These units are the
mast bay and the cell string of the panel.
ANALYSIS
Solar Array Mast
The mast and blanket subassemblies of the
solar array were under consideration in this anal-
ysis. To quantify the impact assessment on the
1 Registered trademark of E.I. Dupont De
Nemours and Co., Inc.
solar array mast, the probability of no impact on
the mast S-glass epoxy longerons was calculated
from the flux estimate, the projected surface area
and the design lifetime. In estimating the micro-
meteoroids flux, a defocusing factor of 0.98 which,
accounts for the defocusing of the particle flux
by the Earth gravitation was used to correct for
this effect. Similarly, a flux factor (1) of 1.5
which accounts for the directionality of the
debris flux with respect to the solar array normal
and the velocity vector was used. It was assumed
in this computation that a particle impact is dam-
aging, and damage of one or more of the three
longerons in one bay results in the mast failure.
From the above assumptions, the damage criterion
can be conservatively construed as the complete
loss of mechanical properties of the impacted
longeron which results in mast failure. Prob-
ability of impact of at most n particles can
be calculated from the cumulative Poisson
distribution (1)
P(n) = [e(-A*F*T)* (A*T*F)']/r! (1)
where F(particles/m2-year) is the flux, A(m2) is
the exposed area, T(year) Is the time and. r is
the summation index. Probability of no impact
(or zero impact) reduces Eq. 1 to
P(0) -A*F*T (2)
Given PI as the probability of no impact of the
ith longeron in one bay, and Qj is the probabil-
ity of one or more impacts on the ith longeron in
the same bay, the following is true (4),
and,
P.
N!
x!(N-x)!
- 0,
x(N-x)
(3)
(4)
where N = 3 because there are three longerons in
parallel in one bay. Considering the impact of
one or more longerons in a bay as a bay failure,
the probability of one bay meeting the lifetime
requirement is • .
P(bay) 1 - 3) x(3-x)
x=
x!(3-x>!
p<o>- -3*A*F*T (5)
Moreover, since there are 75 bays in one mast, and
since the failure of one bay affects the whole
mast, the probability of the mast meeting the
lifetime requirement is given by (5),
P(mast) = P(bay)75 (6)
Solar Array Blanket
The back surface of the solar cell string,
(consisting of eight cells in series and one
bypass diode in parallel as shown in Fig. 3), was
considered for probability of impact analysis of
panels and blanket of the solar array. Impacts
on the front surface of the solar cells were not
assessed because the solar cell is much thicker
than the Kapton substrate. Using the geometry
depicted in Fig. 3, the probability of no open
circuit panel due to meteoroids and debris impact
was calculated from the probability of no impact
on both the photo-etched circuits connecting two
consecutive cells and the circuits connecting
cells with the bypass diode. The probability of
no open string that, when open, results in an
open panel can be summarized by,
P(string) =
(,- - e 2a ) (l - e 3 }
-2A..FT, -2A-FT
e He (7)
where the areas AI , A2i, A2S, and A3 are shown
in Fig. 3. Since there are 25 strings/panel which
can be modeled in series, the probability of no
open panel in the meteoroids and debris environ-
ments becomes (5),
P(panel) = P(str.ing)25 (8)
Since there are N panels in one blanket-.
(N = 82 for the space station solar array) and
since the panels are protected by blocking diodes,
the probability of at least K unopen panels from
the N panels/blanket can be obtained by (4.and
5), . .
(N-x)
(9)
(10)
P(P(panel); K,N) = V (£)?(pane 1>XQ<panel)
where (1 is the binomial factor given by,
N!
x!(N-x)!
RESULTS
Solar Array Mast
Results from Eq. (6) are displayed as the
probability of the mast success as a function of
the particle diameter of meteoroids or debris.
Figures 4 and 5 show the aforementioned results
for 15 years. Assuming that the damaging parti-
cle size is known, and the damaging criterion
already defined applies, the aforementioned
figures can be used to determine the probability
of the mast in meeting the design lifetime
requirement.
Solar Array Blanket CONCLUDING REMARKS
Equation (9) is used to calculate the proba-
bility that at the end of life, at least K
panels (from N panels/blanket at the beginning
of life) are functional in the meteoroids and
debris environments. For a space station solar
array blanket, N was taken as 82 and K as 80
panels. Results of analyzing the cases for 15 and
4 year lifetimes are shown in Figs. 6 and 7 for
the meteoroids and debris environments.
Figures 8 and 9 show the probability of suc-
cess of the solar array blanket (which is the
probability of success of at least K panels at
the end of life from N panels at the beginning
of life) for different particle size and different
levels of redundancy. It is apparent that the
probability Increases with redundancy and particle
size. The increase with particle size is due to
the lower flux at larger diameter. Figure 8 shows
that over the design lifetime of 4 years, and for
impacting particles of 0.003 and 0.004 cm in diam-
eter, the calculated probability of success of a
blanket with 10 redundant panels is practically
zero. This is explained by the higher meteoroids
flux impinging on the back surface of the blanket.
The same feature is illustrated by Fig. 9 for the
debris environment for particle size of 0.001 cm
or smaller. To calculate the mission time at
which the blanket probability of success (or the
probability of meeting the power requirement with
a specific redundancy) decreases significantly,
Eqs. 7 to 9 were evaluated for different life-
times, and F1gs. 10 and 11 were generated.
Figure 10 shows the probability of success of
at least 80 panels at the end of life from 90
panels at the begining of life, as function of
mission time for the two meteoroid size particles
of 0.003 and 0.004 cm. It is shown from this fig-
ure that the probability decreases significantly
at approximately 0.5 and 1.25 years for the 0.003
and 0.004 cm particle diameter respectively. Fig-
ure 11 displays the same type of information with
10 redundant panels and no redundancy for a debris
particle size of 0.001 cm in diameter. From
Fig. 11, the probability was shown to decrease
rapidly at approximately 0.35 and 2.5 years of
design lifetime for a blanket with no redundancy
and with 10 redundant panels respectively.
An analysis was performed to assess the proba-
bility of success of the space station solar array
subassemblies in the meteoroids and debris envi-
ronment as a function of particle diameter. This
analysis could complement a penetration model
which determines the damaging particle size, and
a damage model which correlates the particle size
with the damaged areas. Therefore, a penetration
and damage models are needed for the mast and sub-
strate of the solar array blanket in order to com-
pute the probability of the array meeting the
power requirement in the meteoroids and debris
environment. Such information will help determine
the adequacy of the blanket design and the meteo-
roids and debris environmental oversizing factors
used to size the space station solar array.
ACKNOWLEDGMENT
The author wishes to acknowledge all the
reviewers of this paper from the Photovoltaic
Power Module Division and especially D.J. Hoffman
from the System Engineering and Integration Divi-
sion of the Space Station Directorate for their
time and constructive comments.
REFERENCES
1. N. Elfer, and G. Kovacevlc, "Design for Space
Debris Protection," in Man's Permanent Pres-
ence in Space. AIAA, New York, 1985.
2. "Solar Array Flight Experiment," Lockheed Mis-
siles and Space Company, NASA Contract NAS
8-31352,'Submitted to NASA Marshall Space
Flight Center, Apr. 1986.
3. "Planar Solar Arrays for Space Station,"
Lockheed Missiles and Space Company, Inc.,
Sunnyvale, CA, 1984.
4. J.P. Wright, "Optimization of Large Heat Pipe
Radiators for Long Life Heat Rejection Mis-
sions," ASME Paper 79-ENAS-25, July 1979.
5. I. Miller, and J.E. Freund, Probability and
Statistics for Engineers. Second Ed., Engle-
wood Cliffs, NJ: Prentice-Hall, 1977.
S
OC
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-2
-3
-5
-6
-7
\ 1 990 ' S AVERAGE EN V I RONMENT
\
\
500 KM ALTITUDE
_ \\ 30° INCLINATION
METEOROIDS
DENSITY =0.5 GM/CC
-8
10,-2
/-SPACE DEBRIS
DENSITY =2.8 GM/CC
10r1 KT' 101
PARTICLE DIAMETER, CM
FIGURE 1. - FLUX OF METEOROIDS AND SPACE DEBRIS
AS A FUNCTION OF DIAMETER FOR A 500 KM ORBIT.
THE METEOROID FLUX IS CORRECTED FOR EARTH
SHIELDING.
BLANKET BOX
/-HINGE PIN
/-PANEL
DEPLOY-
ABLE / , .. .— «. ^ ^ .
MAST ^  \^ >^ ^^ \ s- HARNESS
CANISTER
FIGURE 2. - DEPLOYABLE RETRACTABLE SOLAR ARRAY
STRUCTURE FOR THE SPACE STATION PHOTOVOLTAIC
POWER MODULE.
/-BYPASS
/
 DIODE
STIFFENER
SOLAR CELL-
a'i
*j u
/' V
\» o*
4
i*
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^ PHOTO-ETCHED
COPPER CIRCUIT
(A) SOLAR CELL STRING INVESTIGATED FOR OPEN CIRCUIT
PROPABILITY DUE TO PARTICLE IMPACTS.
LONGERON
EXTENDED
P O R T I
° ' / f
TRANSITION "- ^[
PORTION
RETRACTED
PORTION
BAY
MAST-CANISTER
INTERFACE THREADS
OF NUT SUPPORT
ROLLER LUGS
CANISTER
(B) LONGERON, BAY AND MAST STRUCTURE
INVESTIGATED FOR IMPACT PROBABILITY.
FIGURE 3. - REPEATING STRUCTURES IN THE SOLAR ARRAY MAST AND BLANKET CONSIDERED FOR PROBABILITY OF IMPACT
ANALYSIS.
.001
PROBABILITY OF NO IMPACT ON LONGERON
IN ONE BAY
PROBABILITY OF NO IMPACT ON THREE
LONGERONS IN ONE BAY
PROBABILITY OF NO IMPACT ON ALL
BAYS IN ONE MAST
.01 .1
DEBRIS DIAMETER, CM
FIGURE 1. - PROBABILITY OF SUCCESS VERSUS DEBRIS
FOR LONGERON, BAY AND SOLAR ARRAY MAST FOR 15
YEARS DESIGN LIFETIME.
.001
O PROBABILITY OF NO IMPACT ON ONE LONGERON
IN ONE BAY
* PROBABILITY OF NO IMPACT ON THREE LONG-
ERONS IN ONE BAY
D PROBABILITY OF NO IMPACT ON ALL BAYS IN
ONE MAST
-D—D
.01 .1
MICROMETEOROID DIAMETER, CM
FIGURE 5. - PROBABILITY OF SUCCESS VERSUS MICRO-
METEOROID DIAMETER FOR LONGERON, BAY, AND SOLAR
ARRAY MAST FOR 15 YEARS DESIGN LIFETIME.
1— 1
3
1
Q-
1 .U
.8
.6
.4
.2
A
/TCMO-U o n o
—
-
£
k
n/
O
0 ,15 YEARS LIFETIME,
A 1 YEARS LIFETIME
1 1 1
.001 .01 .1
PARTICLE DIAMETER
1.0
FIGURE 6. - PROBABILITY OF SUCCESS VERSUS DEBRIS
DIAMETER FOR A SPACE STATION SOLAR ARRAY BLANKET
WITH TWO REDUNDANT PANELS.
1.0
.8
5 .6
n • 4
O 4 YEARS LIFETIME
A 15 YEARS LIFETIME
.01 .1 , 1.0
METEOROID DIAMETER
FIGURE 7. - PROBABILITY OF SUCCESS VERSUS METEO-
ROID DIAMETER FOR A SPACE STATION SOLAR ARRAY
BLANKET WITH TWO REDUNDANT PANELS.
1.000 I—
g
o
a.
0 2 4 6 8 1 0
NUMBER OF REDUNDANT PANELS PER SOLAR ARRAY BLANKET
FIGURE 8. - PROBABILITY OF SUCCESS VERSUS RE-
DUNDANCY OF SOLAR ARRAY BLANKET FOR 4 YEARS
DESIGN LIFETIME IN THE METEOROIDS ENVIRONMENT.
o
V
O
D
DIAMETER,
CM
.00100
.00125
.00150
.00175
.00200
.00300
.00400
.00600
0 2 •- .4 •
 ; , 6 8 10
NUMBER OF REDUNDANT PANELS PER SOLAR ARRAY BLANKET
FIGURE 9. - PROBABILITY OF SUCCESS VERSUS REDUN-
DANCY OF SOLAR ARRAY BLANKET FOR 4 YEARS DE-
SIGN LIFETIME IN THE DEBRIS ENVIRONMENT.
1.000
o
£ .800
LU
§ .600
o
P .400
i
•B .200
DIAMETER,
CM
.003
.004
*
*
I \ I
.5 1.0 1.5 2.5
MISSION TIME IN YEARS
FIGURE 10. - PROBABILITY OF SUCCESS VERSUS MISSION
TIME OF A SOLAR ARRAY BLANKET FOR TWO METEOROID
DIAMETERS AND 10 REDUNDANT PANELS/BLANKET.
1§
ce
UJ
1.000
.800
.600
9 .400
5 .200
1
NO REDUNDANCY
10 REDUNDANT
PANELS
\
\
\
•^  I
1 2 3 4
MISSION TIME IN YEARS
FIGURE 11. - PROBABILITY OF SUCCESS VERSUS MISSION
TIME FOR .001 CM DEBRIS PARTICLE DIAMETER.
NASA
National Aeronautics and
Space Administration
Report Documentation Page
1. Report No.
NASA TM-101315
2. Government Accession No. 3. Recipient's Catalog No.
4. Title and Subtitle 5. Report Date
Assessment of the Effects of Space Debris and Meteoroids
Environment on the Space Station Solar Array Assembly 6. Performing Organization Code
7. Author(s)
Henry K. Nahra
8. Performing Organization Report No.
E-4310
10. Work Unit No.
482-55-52
9. Performing Organization Name and Address
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191
11. Contract or Grant No.
12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, D.C. 20546-0001
13. Type of Report and Period Covered
Technical Memorandum
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared for the 20th Photovoltaic Specialists Conference sponsored by the Institute of Electrical and
Electronics Engineers, Las Vegas, Nevada, September 26-30, 1988.
16. Abstract
In this paper, the methodology used to assess the probability of no impact of space debris and meteoroids on a
spacecraft structure was applied to the space station solar array assembly. Starting with the space debris and
meteoroids flux models, the projected surface area of the solar cell string circuit of the solar array panel and the
mast longeron, and the design lifetime, the probability of no impact on the solar array mast and solar cell string
circuits was determined as a function of particle size. The probability of no impact on the cell string circuits was
used to derive the probability of no open circuit panel. The probability of meeting a certain power requirement at
the end of the design lifetime was then calculated as a function of impacting particle size. Coupled with a
penetration and damage models/correlations which relate the particle size to the penetration depth and damage,
the results of this analysis can be used to determine the probability of meeting the power requirement given a
degree of redundancy, and the probability of no impact on the solar array mast.
17. Key Words (Suggested by Author(s))
Micrometeroids; Mast; Space debris; Longerons;
Solar array; Photo-etched circuit; Blanket
18. Distribution Statement
Unclassified — Unlimited
Subject Category 18
19. Security Classif. (of this report)
Unclassified
20. Security Classif. (of this page)
Unclassified
21. No of pages
10
22. Price*
A02
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Assessment of the effects of space debris and meteoroids environment on the space station solar array assembly

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