NASA / TMQ2001-210949 2001-01-2340

Mathematical Analysis of Space Radiator

Segmenting for Increased Reliability

and Reduced Mass

Albert J. Juhasz

Glenn Research Center, Cleveland, Ohio

Prepared for the

31st International Conference on Environmental Systems

sponsored by the Society of Automotive Engineers

Orlando, Florida, July 9-12, 2001

National Aeronautics and

Space Administration

Glenn Research Center

June 2001

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Mathematical Analysis of Space Radiator Segmenting for

Increased Reliability and Reduced Mass

Albert J. Juhasz

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

ABSTRACT

Spacecraft for long duration deep space missions will

need to be designed to survive micrometeoroid

bombardment of their surfaces some of which may

actually be punctured. To avoid loss of the entire mission

the damage due to such punctures must be limited to

small, localized areas. This is especially true for power

system radiators, which necessarily feature large surface

areas to reject heat at relatively low temperature to the

space environment by thermal radiation. It may be

intuitively obvious, that if a space radiator is composed of

a large number of independently operating segments,

such as heat pipes, a random micrometeoroid puncture

will result only in the loss of the punctured segment, and

not the entire radiator. Due to the redundancy achieved

by independently operating segments, the wall thickness

and consequently the weight of such segments can be

drastically reduced. Probability theory is used to estimate

the magnitude of such weight reductions as the number

of segments is increased. An analysis of relevant

parameter values required for minimum mass

segmented radiators is also included.

INTRODUCTION

The literature on space radiator survivability (e.g.,

English and Guentert 1961; Juhasz 1998) confirms

logical reasoning by indicating that if a space radiator

were composed of a multiplicity of independently

operating segments, a random micrometeoroid puncture

of the radiator would result in the loss of only the

punctured segment, not the entire radiator. Hence, the

strategic advantage of segmented radiators for space

service applications is obvious. Such parallel redundancy

can be achieved with pumped loop heat rejection

radiators dividing a single closed circuit carrying cooling

fluid into a number of independent parallel circuits. But

the need for separate circulating pumps, valves, and fluid

ducts makes such a system unwieldy for more than a

few redundant loops. A much more efficient approach is

to utilize the inherent parallel redundancy that heat pipes

offer for space heat rejection applications. Since each

heat pipe with its extended heat transfer surface fins can

be considered as a radiator element that is independent

of all other elements and thus expendable the advantage

of a heat pipe radiator in terms of modularity and

minimum complexity is apparent. Since the design of a

space radiator can accommodate the loss in functionality

of a certain fraction of elements over the life of a given

mission, much thinner walls can be specified. As a result

dramatic savings in weight can be realized when

compared to a nonsegmented radiator having the same

overall survival probability.

Hence there is a clear strategic advantage of segmenting

large surface area radiators for space applications. The

purpose of this paper is to use basic probability theory in

examining the tradeoff between number of segments and

the segment wall thickness in order to achieve minimum

radiator mass, subject to certain assumptions regarding

the total number of segments N, that are required to

survive till completion of a mission. An analysis of

requirements for minimum mass systems is also

included in the appendix to resolve some initial

discrepancies with results reported in the literature.

MATHEMATICAL ANALYSIS

The tradeoff between the number of segments and the

segment wall thickness, in order to achieve minimum

radiator weight, can be derived on the basis of a simple

probability analysis:

If we assume that for each of N identical radiator

segments the probability of not being punctured is p,

then the probability S of having at least IV, segments not

punctured during the spacecraft radiator's design life is

given by the cumulative binomial distribution as

n=N NW

s= (1)

For each segment the probability p of no puncture is

given by

_.., fin(I/pip = e , or ln(l/p) = hat ; and h =L _-

(2)

where h is the average puncture rate per unit time and

unit area; a is the vulnerable area of each segment; and t

NASA/TM--2001-210949 l
is the required useful life of the radiator. Note, that for

large numbers of segments N, the value of p ~ IV,/N. W~(Nsa)w(Nsat) 1/3 (6)

The puncture rate h is a function of both the depth of

penetration and the rate of flux of meteoroids. Summers

and Charters (1959) observed that the wall thickness, T_,

which a meteoroid will barely penetrate, is proportional to

the cube root of the meteoroid mass, m. Moreover,

Whipple (1958) showed that the meteoroid flux (number

frequency) is inversely proportional to meteoroid size

(i.e., mass). Assuming that the meteoroid velocity is

essentially independent of mass, we can express these

trends as a simple relationship:

h- m -1 ~ Tw3" or Tw = h -1/3 (3)

Using (2) the wall thickness can be written as

=IIn(1/p)]-l/3

Tw [_]

(3.1)

Multiplying the numerator and denominator of (3.1) by

(Ns)-'J3permits rewriting the approximation as

Since the required radiator area at the end of the mission

and the required mission life are input parameters for the

analysis and thus are known a priori, the product (N s a t)

can be considered a constant. Segmenting influences

the weight per unit area (W/N, a) required at the end of

life by affecting the relative weight term w. The term w,

that is relative weight per unit segment area, decreases

continually as the number of segments increases.

A brief paper on radiator segmenting by English and

Guentert (1961) reported, without showing assumptions

or calculation details, that for large values of N the

minimum weight per unit segment area will occur at

(N s / N)mi n = e -1/4 = 0.7788 (7)

This result differed somewhat with the detailed analysis

performed by the author (Juhasz 1998) under the

constraint that a constant number of surviving segments

Ns was required. In this case, the value of N,/N for

minimum weight per unit segment area was found to be

Tw = [N s In(l/p)]-1/3 [Nsat]l/3 (3.2) (N s / N)mi n = e-1/3 = 0.7165 (8)

With the objective of minimizing the initial weight of the

vulnerable radiator surface material while ensuring a

specified nonpunctured area at the end of radiator design

life, we can write the following expression:

W/Nsa=pTwN/Ns (4)

Equation (4) can be recast as

To resolve the discrepancy the minimum relative mass

calculations are performed here in detail for the

alternative constraint of a constant number of initial

segments N. Two alternate approaches for each of the

two constraint assumptions are included in the

Appendix of this report. As shown in section B of the

appendix, holding the initial number of segments

N constant, will indeed result in minimum w at N/N =

e-_/' -=0.7788.

W = (Nsa)p(N/Ns)'l" w (4.1)

where W is the initial weight, p is the density of the

radiator surface material, and N s a is the required final

area. In minimizing W/(N, a), for simplicity, only the

weight of the vulnerable surface area is considered. The

fin area, manifold ducting, and structure are not taken

into account. However, since the mass ratio of such

peripheral components to vulnerable radiator mass can

be readily determined, one can apply the proper

correction factor to arrive at an overall radiator mass.

Also, since material density, p, may be assumed to be a

constant for a given radiator, it becomes an invariant in

the analysis. Using (4) and (3.2) a relative weight w can

then be defined as

w =-(N/N s )IN s In(I/p)]-1/3 (5)

Then by substituting (5) and (3.2) into (4.1) the expression

for total weight shown can be approximated as

NASA/TM--2001 -210949

Both assumptions, constant IV, or constant N are valid.

But the case that specifies a required number of

surviving segments N, is somewhat more conservative,

since the number of initial segments for a minimum mass

system would have to be about 8 percent. However, the

relative mass versus segment ratio curves are fairly flat

near their minimum values, and both assumptions yield

results which are approximately within a +4 percent band

of 0.75. Hence, for design guidelines, the value of Ns/N

for minimum weight per unit segment area can be

assumed as

(N s / N)mi n ~ 0.75 (9)

Using the equations of this analysis, to solve for S, p, w,

and T_, and arbitrarily defining the weight and wall

thickness as unity for a non-segmented radiator with a

survival probability of 0.999, a computer code was

developed to tabulate (see Table 1) and plot relative

weight w and wall thickness TWfor values of N (ranging

from 10 to 1000) as a function of N,/N, as shown in
TABLE 1: COMPARISON OF RESULTS FOR OVERALL SYSTEM RELIABILITY S

(a) Constant N._=717 (b) Constant N =

Ns/N P Relative Relative N

Weight Thickness

w 7,

.30000 .32928 .03597 .01079 2390.0

.40000 .43591 .02972 .01189 1792.0

.50000 .54038 .02627 .01314 1434.0

.60000 .64273 .02445 .01467 1195.0

.68000 .72296 .02392 .01626 1054.0

.69000 .73264 .02390 .01649 1039.0

.70000 .74257 .02391 .01674 1024.0

.71000 .75275 .02394 .01700 1009.0

.71500 .75760 .02396 .01713 1002.0

.71700 .75899 .02394 .01717 1000.0

.75000 .79094 .02416 .01812 956.0

.77880 .81897 .02455 .01912 920.0

.80000 .83867 .02493 .01994 896.0

.90000 .92960 .02971 .02674 796.0

1.0000 1.0000 1.0000 1.0000 717.0

= 0.999

1000

NJN P Relative Relative No

Weight Thickness

w T,

.30000 .34549 .04880 .01464 300.0

.40000 .44791 .03651 .01460 400.0

.50000 .54824 .02986 .01493 500.0

.60000 .64660 .02606 .01564 600.0

.68000 .72379 .02437 .01657 680.0

.69000 .73334 .02423 .01672 690.0

.70000 .74286 .02411 .01688 700.0

•71000 .75236 ,02401 .01705 710.0

•71500 .75710 .02396 .01713 715.0

•71700 .75899 .02394 .01717 717.0

•75000 .79008 .02376 .01782 750.0

.77880 .81714 .02379 .01853 779.0

.80000 .83655 .02392 .01914 800.0

•90000 .92621 .02710 .02439 900.0

1.00000 1.0000 1.0000 1.0000 1000.0

.1=

3

nr

1.0

.8

.6

.4

.2

.1

.08

.06 -

.04 _'__0

r _ 1ooo

.o21(a) , , •

Number of /

segments, N j /

/

I I I

.4 .5 .6 .7 .8 .9 1.0

Proportion of segments surviving, Ns/N

t

/

/

/

/

1.0

.8

.6

.4

.2

(/)

_)

r"

•- .1

® .08

._>

__ .06

.04

.O2

Number of

segments, N

10

20

40

100

300

1000

.01 I I

.4 .5 .6 .7 .8 .g 1.0

Proportion of segments surviving. Ns/N

Figure 1.--Segmented heat pipe radiator characteristics for survival probability S = 0.999. (a) Relative

weight of vulnerable surface (nonsegmented = 1 ). (b) Relative wall thickness (nonsegmented = 1 ).

figure 1. Note the dramatic reduction in both weight and wall

thickness that accrues because of radiator segmenting,

even for as few as 10 segments, butespeciallyby increasing

the number of segments N to 1000.

To verify the theoretically derived IV,/N ratios at which

minimum relative weight is achieved, table 1 shows

results for relative weight and thickness for 1,000

segments (N = 1,000). Note that the minimum w value

(bold number) for constant N, = 717 occurs at

N,/N ~ 0.69, rather than the 0.717 value derived in the

appendix. Similarly, for constant N = 1000, the minimum

occurs at N, /N -0.75 rather than the predicted e-'_"

value. The reason for this is that the error in the

assumption inherent in the derivations, namely p ~ N/N,

was about 5.5 percent, as can be verified by comparing

the tabulated values of p and N,/N. In table 2 the p

values are more in agreement for the higher N values (N

= 3000) and the lower S value (used to reduce the

computations). Hence the minimum w values (bold

numbers) in table 2 do occur at N,/N values which are in

close agreement with the theory. As mentioned above,

NASA/TM--2001- 210949 3
TABLE 2: COMPARISON OF RESULTS FOR OVERALL SYSTEM RELIABILITY S = 0.600

(a) Constant N_=2151 * (b) Constant N = 3000 *

NJ N P Relative Relative N NS/N P Relative Rel_ive Ns

Weight Thickness Weight Thickness

w m_ w T,

.30000 .30131 .02431 .00729 7170.0 .30000 .30198 .03252 .00976 900.0

.40000 .40164 .01997 .00799 5377.0 .40000 .40211 .02427 .00971 1200.0

.50000 .50181 .01754 .00877 4302.0 .50000 .50215 .01979 .00989 1500.0

.60000 .60192 .01619 .00971 3585.0 .60000 .60209 .01718 .01031 1800.0

.68000 .68197 .01569 .01067 3163.0 .68000 .68197 .01597 .01086 2040.0

.69000 .69200 .01567 .01081 3117.0 .69000 .69195 .01587 .01095 2070.0

.70000 .70210 .01565 .01096 3072.0 .70000 .70193 .01577 .01104 2100.0

.71000 .71203 .01564 .01111 3029.0 .71000 .71191 .01569 .01114 2130.0

.71500 .71699 .01564 .01118 3008.0 .71500 .71689 .01565 .01119 2145.0

.71700 .71889 .01564 .01121 3000.0 .71700 .71889 .01564 .01121 2151.0

.75000 .75184 .01569 .01177 2868.0 .75000 .75181 .01546 .01159 2250.0

.77880 .78085 .01585 .01234 2761.0 .77880 .78072 .01541 .01200 2337.0

.80000 .80195 .01603 .01282 2688.0 .80000 .80165 .01544 .01235 2400.0

.90000 .90128 .01831 .01648 2390.0 .90000 .90117 .01697 .01527 2700.0

1.00000 .99976 .12512 .12512 2151.0 1.00000 .99983 .12512 .12512 3000.0

*Note that due to higher N and lower S, segment reliability

minimum relative weights (bold characters) are for N/Ns

p is very close to N/N_as assumed in theory. Hence

values as predicted.

the relative mass versus N,/N curves are fairly flat near

their minimum values, so that the condition shown in (9)

will be sufficiently accurate for most applications. The

reader may note, that in table 2 the relative mass value w

for the nonsegmented radiator (N,/N=I) is much lower

than unity. This is so because the weight of the

nonsegmented radiator at S = 0.6 is lower than that for a

nonsegmented one with S = 0.999. The relative weight

parameter w is referenced to a nonsegmented

configuration with a survival probability of 0.999.

Both, table 1 and figure 1 show that for a given number

of segments N, the relative weight will increase for

values of N, /N below the value given in equation (9),

even though the wall thickness decreases. This is

because as N, decreases, the vulnerable area of each

segment increases and p, the probability of no puncture

per segment, decreases.

As already mentioned in connection with the derivation of

equation (4), fin area, radiator fluid manifolds, and

structural weight were not included in this analysis.

Regarding fin area, the following observation can be

made: If a certain fraction of the vulnerable area a of

each segment represents the fin area not rendered

useless, even if penetrated by a micrometeoroid, then

the results of the present analysis will be conservative

(i.e., the relative weights and wall thicknesses will be

even lower than shown in fig. 1). However, since the

structure and manifolds will need to be protected by a

thicker wall or a bumper shield, the benefits provided by

fins will be offset to some degree, depending on the

particular design of the spacecraft radiator.

Nevertheless, the utilization of finned segments that

increase the radiating area without increasing the

vulnerable area will provide an additional margin in the

design of large segmented space radiators. The use of

heat pipes, each operating independently with selfcontained heat transport loops, will further facilitate the

space radiator design process.

SEGMENTED RADIATOR DESIGN EXAMPLES

Having discussed some of the theoretical basis for

segmenting radiators and for utilizing heat pipes as ideal

elements or building blocks, let us next discuss a few

advanced space radiator designs. The conical radiator

for the 0.1 MW. SP-100 thermoelectric (T/E) space

power system with a liquid-metal (lithium) cooled reactor

heat source (Juhasz, 1998) is shown in figure 2. The

radiator cone is composed of 12 panels, each of which is

a radiator segment consisting of 226 C--C heat pipes of

varying condenser length. These heat pipes are

essentially of the same design as discussed in this

report. The SP-100 radiator, designed for 7-yr survival

probability of 0.99, could provide the 2.4 MW, heat

rejection needs of the power system with only 11 of its

12 panels functioning, each with 75 percent of their

original number of heat pipes. Thus each of the twelve

panels could absorb the loss of about 56 heat pipes for a

total reduction of radiator area equal to that represented

by over 670 heat pipes, without significant impact on the

required output power. Note that additional losses in heat

pipe radiating surface area would result in a rise in T/E

cold junction temperature beyond the design value at the

end of life (EOL). As a result the thermal efficiency and

thus electric power output would be lowered. It should be

noted, however, that no drastic power system failure

would occur! Figure 3 shows a proposed heat rejection

subsystem for a 15-MW, closed-cycle gas turbine power

system with a nuclear high-temperature gas reactor heat

NASA/TM--2001-210949 4
Radiator panel

Evaporator _lkl

.7/ /I

Z-.--- }_====a/ I Design features

_ J I_ t_nel, conical radiator

_ Carbon-carbon heat pipes _i_'

Heat ipe • Integral fins Radiator _

with ePd cap s I: I._.t_ag_ lufimnsw°rking fluid configuratior

Figure 2.raSP-100 advanced heat pipe segmented radiator.

Inset: Edge view of double C-C face sheet configuration

Perspective edge view

Finned heat pipe condensers

B-B

Bifurcated

duct

Turbine discharge

flows

T1 T2 T3

t

i,I

C. C2 C3

Com_ }ressor inlet

flows

Figure 3.--Flat segmented heat pipe radiator for a nuclear triple loop gas turbine power system.

NASA/TM--2001-210949 5
t_

E

1400

1200

_ --0-- Fluid temperature --O-- Wall 1000

800 __

6O0

400

Nal K I Cs

I or S-I H20

m

J

200 I L I' I I I I I I I

0 0.2 0.4 0.6 0.8

Fractional radiator duct length

Figure 4.--Heat pipe radiator temperature profiles for a gas turbine power system. (Letters between lines

designate heat pipe working fluids.)

source (Juhasz et al., 1993). This segmented radiator

system is initially composed of 1600 finned heat pipe

segments of which 1200 are needed to survive until the

end of the mission. This radiator was designed to meet

the heat rejection requirements of three separate gas

turbine loops. A bifurcated manifold duct, which carries

the He turbine exhaust stream, communicates thermally

with 0.05-m diameter, 1.5-m long C-C heat pipe

evaporators by combined conduction-convection heat

transfer. The specific weight of such a radiator was

shown to be less than 1.5 kg/m 2 as compared to

-15 kg/m 2for state-of-the-art (SOA) technology.

The computed temperature profiles for the He gas and

the heat pipe evaporator wall along the radiator duct are

shown in figure 4. These profiles were computed under

the assumption of constant incremental radiator area

with incremental manifold duct length. To accommodate

the more than 800-K radiator temperature drop for this

high-temperature gas turbine power system (turbine inlet

temperature of 2000 K), the radiator was divided into five

temperature zones, each of which is defined by the

operating temperature range associated with a particular

heat pipe working fluid: sodium, potassium, cesium,

sulfur-iodine (in lieu of mercury), and water. Note that the

double C--C face sheet configuration suggested by the

perspective edge view offers even greater survivability

and structural rigidity at a somewhat higher weight,

depending on the thickness of the face sheets.

CONCLUDING REMARKS

A derivation of the mathematical relationships required to

evaluate weight and reliability advantage of radiator

segmenting was completed, including theoretical

analyses of conditions for minimum mass systems. A

computer code was also developed to generate analysis

results in tabular or graphical form. The drastic reduction

in mass and wall thickness required to achieve a

required overall reliability for segmented radiators was

demonstrated in theory. Several examples of segmented radiator designs utilizing heat pipe elements

were described. The advantage of heat pipe technology

in fabricating large surface area space radiator systems

with multiple redundancy, which achieve high mission

reliability at low specific weight, are pointed out in quantitative terms, as compared to non-segmented radiators.

REFERENCES

1. English, R.E. and Guentert, D.C. (1961): Segmenting

Radiators for Meteoroid Protection. ARS Journal,

August 1961.

2. Juhasz, A.J. (1998): Design Considerations for

Lightweight Space Radiators Based on Fabrication

and Test Experience with a Carbon-Carbon

Composite Prototype Heat Pipe. NASA/TP---1998-

207427, October, 1998.

3. Juhasz, A.J., EI-Genk, M.S. (1993), and Harper, W.B.:

"Closed Brayton Cycle Power System with a High

Temperature Pellet Bed Reactor Heat Source for NEP

Applications," Proc. of the l(J" Symposium on Space

Nuclear Power and Propulsion, AlP 271, Vol. 2, AlP,

New York, 1993, pp. 1055-1064. NASA TM-105933.

4. Summers, J.L. and Charters, A.C. (1959): HighSpeed Impact of Metal Projectiles in Targets of

Various Materials. Proc. Third Syrup. On

Hypervelocity Impact (Vol. 1, Armour Res. Foundation

of liT), Chicago, Feb. 1959.

5. Whipple, F.L. (1958): The Meteorite Risk to Space

Vehicles. 8" Internat. Astronautical Congress.

Springer Verlag 1958, pp. 418-428.

NASAffM--2001-210949 6
APPENDIX

Determination of Minimum Relative Radiator Mass

The expression for minimum radiator mass relative to an

non segmented configuration having a survival

probability S of 0.999 was shown in (5) as

w = (IV/N s )IN s In(l/p)]-l/3 (A1)

It was also stated, that for large values of N the value of

the probability of no puncture of an individual segment, p,

can be approximated by Ns/N, i.e., p = Ns/N.

Alternate Method:

The logarithmic form of (A2) is:

Inw=lny-llnNs- 1In(In y)

Differentiating (A2.0) leads to:

(A2.0)

1 aw_ 1 0-1(1/Y)=0 (A2.1)

way y 3 Iny

The analysis of two separate cases is of interest. Dividing (A2.1) by 1/y it is readily seen that

A. For a given value of surviving segments N s what value

of N s/N will minimize w ?

Letting y = N/N s = 1/p

The relative mass expression w can be written as

w = y[N s In y]-l/3 (A2)

The minimum of w is found by solving the equation

represented by o_w/by = 0.

bw/_Y=Ns1/3Iy[-l (Iny)-4/3 *y + l*_ny] -1/3 =0 [L 3

Which can be simplified to

_w / Oy = N_sl/3(In y)-4/3[-3 (In y)-l + l]=O

(A3)

(A4)

Iny=l/3

and Ns/N= e-1/3 -- 0.7|? (A2.2)

as obtained in (A5.1) above.

B. For a given value of initial segments, N, what value of

Ns/N will minimize w ?

With constant initial number of segments a more

convenient form of (A1) is

w = (N/N s )[N(N s / N)ln(1/p)] -1/3 (gl)

and with y = N/N s = l/p, wcan be written as

EN ]-1/3

w= y[ yln yJ (B2)

= N-1/3y4/3(in y)-1/3 (B3)

In (A4) the term in brackets yields:

In y = 1/3

1/3

or y= e

and, sincel/y = NJN, it follows that N,/N = e-'j_ (AS)

Differentiating (B3) and setting the result to zero leads to

_w/_y = N -1/3 *

which can be simplified to

or (N,/N) = 0.717 (A5.1)

From the above result one may conclude, that with the

assumption of a large number of segments, N, for which

the corollary condition p = N s/N also holds, the relative

mass w will minimize when the ratio of surviving number

of segments to initial number of segments is ~ 0.72 if the

desired number of surviving segments, Ns, is held

constant.

N-l/3y1/3[ l (In y)-4/3 + 41n y * (In y)-4/3] = 03 (B5)

and

4/3 1 4

N-1/3yl/3(Iny) - [--_-+-_-In y] = 0 (B6)

NASA/TM--2001-210949 7
In (B6) the term in brackets yields

Iny =--t or y= el/4 (B7)

4

and since 1 = N s it follows that Ns = e -1/4 = 0.7788

y N N

(B8)

From the result shown in (B8) one may conclude, that

with the assumption of a large number of segments, N,

with the corollary condition p = Ns/N, the relative mass

w will minimize when the ratio of surviving number of

segments to initial number of segments is -0.78 if the

desired number of initial segments N is held constant.

Alternate Method: Writing the logarithmic form of (B3),

we have Inw=-llnN+41ny-lln(Iny) which can be

3 3 3 '

differentiated to yield

1 o_w_0+4, 1 1 1 • - =0

w o_y 3 y 3 Iny y

(B9)

1. el/4

which results in Iny = _- y = and

N s 1 e-1/4 = 0.7788 (B10)

N y

as obtained in (B8) above.

NASA/TM--2001-210949 8

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

June 2001

4. TITLE AND SUBTITLE

Mathematical Analysis of Space Radiator Segmenting for

Increased Reliability and Reduced Mass

6. AUTHOR(S)

Albert J. Juhasz

PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

3. REPORT TYPE AND Technical DATES Memorandum COVERED

5. FUNDING NUMBERS

WU-253--02-99-00

8. PERFORMING ORGANIZATION

REPORT NUMBER

E-12803

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM--2001-210949

2001-01-2340

11. SUPPLEMENTARY NOTES

Prepared for the 31 st International Conference on Environmental Systems sponsored by the Society of Automotive

Engineers, Orlando, Florida, July 9-12, 2001. Responsible person, Albert J. Juhasz, organziation code 5430,

216-433-6134.

12a. DISTRIBUTION/AVAILABILITYSTATEMENT 12b. DISTRIBUTION CODE

Unclassified - Unlimited

Subject Categories: 20, 65, and 38 Distribution: Nonstandard

Available electronically at http://gltrs._c.nasa.gov/GLTRS

This publication is available from the NASA Center for AeroSpace Information, 301-621-0390.

13. ABSTRACT (Maximum 200 words)

Spacecraft for long duration deep space missions will need to be designed to survive micrometeoroid bombardment of

their surfaces some of which may actually be punctured. To avoid loss of the entire mission the damage due to such

punctures must be limited to small, localized areas. This is especially true for power system radiators, which necessarily

feature large surface areas to reject heat at relatively low temperature to the space environment by thermal radiation. It

may be intuitively obvious, that if a space radiator is composed of a large number of independently operating segments,

such as heat pipes, a random micrometeoroid puncture will result only in the loss of the punctured segment, and not the

entire radiator. Due to the redundancy achieved by independently operating segments, the wall thickness and consequently

the weight of such segments can be drastically reduced. Probability theory is used to estimate the magnitude of such

weight reductions as the number of segments is increased. An analysis of relevant parameter values required for minimum

mass segmented radiators is also included.

14. SUBJECT TERMS

Space radiator reliability; Micro meteoroid survivability;

Radiator segmenting; Space power system radiators

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION

OF REPORT OF THIS PAGE

Unclassified Unclassitied

NSN 7540-01-280-5500

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

15. NUMBER OF PAGES

14

16. PRICE CODE

20. LIMITATION OF ABSTRACT

Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102