Small Satellite Thermal Design, Test and Analysis !

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ABSTRACT

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!1. INTRODUCTION

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2. FASTRAC SATELLITES

2.1. FASTRAC Satellite Description

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3. METHODOLOGY !3.1. Thermal Design

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3.2. Space Environment

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3.2.1. Orbit Sun/Shade Estimation

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3.2.2. Spacecraft Orientation

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3.3. Thermal Analysis

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3.3.4. Thermal Blanket Simulation

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:>6!>#->!?63F65%?.56@!#3#?%?#&-!?>6!@.&&A!@#/6!0D!?>6!057#?!;656!@#3.$%?6/!;#?>!@#E!HbII!8!#&D5%56/!X]TY!$%3F@!F$%96/!0&!?>6!>6E%-0&%$!D%96@!%&/!D0.5!H1III!8!#&D5%56/!$%3F@1!?;0!0&!6%9>!6&/(!!:>6!$09%?#0&!0D!?>6!>6%?!$%3F@!9%&!76!@66&!#&!'#-.56!HI(!!!!:>6! $0;! ?63F65%?.56@1! #3#?%?#&-! ?>6!69$#F@6/!@#/61!;656! @#3.$%?6/!;#?>!%!90$/!@>50./!900$6/!7A! $#g.#/!&#?50-6&(! !:>6!C%9..3!9>%3765!;%$$@!;656!%$@0!900$6/!;#?>!$#g.#/!&#?50-6&(!!'#-.56!HH!@>0;@!?>6!@%?6$$#?6!F$%96/!#&!V>%3765!U(!!

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Emissivity I(MObNb! I(Mf! I(MM!

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3.4.4. Test Description

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!

-100

-80

-60

-40

-20

0

20

40

60

80

Time

Tem

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(ºC

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!!

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4. RESULTS !4.1. Thermal Tests Results

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-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30Time (Hours)

Tem

pera

ture

(ºC

)

40

T-Drop In Min./Max. Acceptable Temp.!

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0

5

10

15

20

25

30

35

40

45

50

0 10 20 30Time (Hours)

Tem

pera

ture

(ºC

)

40

Batteries Max/Min Acceptable Temp.

!!

'#-.56!HO`!!S%??65A!:63F65%?.56!/.5#&-!:V:!!

-10

0

10

20

30

40

50

60

70

80

0 10 20 30 4Time (Hours)

Tem

pera

ture

(ºC

)

0

Inside COM Box Max/Min Acceptable Temp.!

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!!

-20

0

20

40

60

80

100

120

0 10 20 30 40

Time (Hours)

Tem

pera

ture

(ºC

)

Voltage Regulator Max/Min Acceptable Temp.!

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!!

4.2. Test Thermal Analysis

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f!@>0;@!?>6!?#36!>#@?05A!?63F65%?.56!0D!?>6!S,:!70E!30/6$!%&/!?6@?!/%?%(!!:>6!30/6$!>%@!?>6!@%36!@>%F61!@$0F6@!%@!?>6!?6@?!/%?%!%&/!?>6!?63F65%?.56!F6%Q@!099.5!%?!?>6!@%36!?#361!7.?!?>656!;656!?63F65%?.56!/#DD656&96@!76?;66&!?>63(!!:>#@!?63F65%?.56!/#DD656&96!;%@!9%.@6/!7A!?>6!@#3F$#D#9%?#0&!0D!?>6!30/6$!903F%56/!?0!?>6!903F$6E#?A!0D!?>6!@%?6$$#?6(!!:>6!?63F65%?.56!0D!?>6!30/6$!#@!$0;65!?>%&!?>6!?6@?#&-!?63F65%?.56!7A!%&!%C65%-6!0D!HIiV(!!!

4.3. Orbit Thermal Analysis

:>6! 7%??65#6@! ;656! %7$6! ?0! ;#?>@?%&/! ?>6! 90$/! 9%@6! ?63F65%?.56@1! 7.?! 0C65>6%?6/! /.5#&-! ?>6! >0?! 9%@6! ?63F65%?.56@(!!'.5?>65!@#3.$%?#0&!@>0;6/!?>%?!%//#&-!%!@3%$$!50?%?#0&!?0!?>6!@%?6$$#?6!%&/!#&956%@#&-!?>6!?#36!#&!?>6!@>%/61!6&%7$6@!?>6!7%??65#6@!?0!@?%A!;#?>#&!?>6#5!?63F65%?.56!$#3#?@(!!!

!

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40Time (hours)

Tem

pera

ture

( º

C)

MLI Temperature History Model MLI Temperature History

!!

'#-.56!HM`!!"=]!:63F65%?.56!V03F%5#@0&!

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40

Time (hours)

Tem

pera

ture

(ºC

)

Model Battery Box Temperature Actual Battery Box Temperature!

!'#-.56!Hf`!!S%??65A!S0E!:63F65%?.56!V03F%5#@0&!

!4.3.1. Hot Orbit Simulation

).5#&-! ?>6! >0?! 9%@61! #&! ;>#9>! ?>6! @%?6$$#?6! ;%@! %?! %&! #&9$#&%?#0&! 0D! OLi! %&/! %?! %&! %$?#?./6! 0D! NII! Q31! ?>6! @%?6$$#?6!#336/#%?6$A!769%36!>0?1!%&/!F%@@6/!?>6!>0?!?63F65%?.56!$#3#?!0D!?>6!7%??65A!0D!JIiV1!%@!@66&!#&!'#-.56!GI(!!:>6!30/6$!@?%5?6/!%?!%!?63F65%?.56!0D!GOiV1!%&/!HM!057#?@!;656!@#3.$%?6/(!!<C6&!;#?>!%&!%C65%-6!/#DD656&96!0D!HIiV!76?;66&!?>6!30/6$! %&/! ?>6! ?6@?! /%?%1! %&/! %&! %C65%-6! ?63F65%?.56! /#DD656&96! 76?;66&! ?>6! #&@#/6! %&/! 0.?@#/6! 0D! ?>6! 7%??65A! 70E! 0D!N(LOiV!/.5#&-!?>6!>0?!9A9$6@1!?>6!?63F65%?.56!0D!?>6!7%??65A!F%@@6@!?>6!3%E#3.3!7%??65A!$#3#?(!!

10

20

30

40

50

60

70

0 500 1000 1500 2000

Time (min)

Tem

pera

ture

(ºC

)

BAT Model Temperature History

!!

'#-.56!GI`!P0?!V%@6!Z57#?!K#3.$%?#0&!;#?>!ZC65>6%?#&-!S%??65A!:63F65%?.56!P#@?05A!

20

22

24

26

28

30

32

34

36

38

40

0 500 1000 1500 2000

Time (min)

Te

mp

era

ture

(ºC

)

BAT Model Temperature History

BAT Model with 10ºC Correction

!!

'#-.56!GH`!P0?!V%@6!Z57#?!K#3.$%?#0&!;#?>!S%??65A!:63F(!P#@?05A!;#?>#&!:63F65%?.56!=#3#?@!

!).5#&-!?>6!>0?!9%@61!%!50?%?#0&!;%@!#&?50/.96/!;>656!?>6!@%?6$$#?6!50?%?6/!%70.?!?>6!):!&053%$!X@66&!#&!'#-.56!OY!%?!%!5%?6!%?! HI! 56C0$.?#0&@! F65! 057#?! XI(HIb! 56C0$.?#0&@! F65! 3#&.?6Y1! ?>50.->! GG! 057#?@(! ! :>#@! 50?%?#0&!3#->?! 099.5! /.5#&-! ?>6!/6F$0A36&?!0D!?>6!@%?6$$#?6!D503!?>6!$%.&9>!C6>#9$6(!!',K:T,V!3.@?!&0?!>%C6!%!50?%?#0&!5%?6!-56%?65!?>%&!N!56CR3#&1!%@!#?!;0.$/!&0?!76!%7$6!?0!%9g.#56!4WK1!;>#9>!#@!95.9#%$!D05!3#@@#0&!@.996@@(!!,&!#&956%@6!0D!?>6!@>%/6/!56-#0&!0D!?>6!057#?!;%@!%$@0!&696@@%5A!?0!/6956%@6!?>6!7%??65A!?63F65%?.56(!!'05!?>6!7%??65A!?0!76!;#?>#&!?>6!?63F65%?.56!$#3#?1!Nfm!0D!?>6!057#?!>%/!?0!76!#&!?>6!@>%/6(!!:>6!7%??65A!?63F65%?.56!>#@?05A!9%&!76!@66&!#&!'#-.56!GH(!!

4.3.2. Cold Orbit Simulation

).5#&-!?>6!90$/!9%@61!?>6!7%??65#6@!;656!%7$6!?0!@?%A!;#?>#&!?>6!70.&/%5A!?63F65%?.56@(!!'#-.56!GG!@>0;@!?>6!?63F65%?.56!0D!?>6!7%??65A!70E!9A9$#&-!?>50.->!GN!057#?@!@?%5?#&-!%?!%!?63F65%?.56!0D!LiV(!!:>6!%C65%-6!?63F65%?.56!D#5@?!$0;65@!%&/!?>6&!#&956%@6@!-6&?$A(!!:>#@!#&956%@6!#&!?63F65%?.56!76D056!07?%#&#&-!?>6!?>653%$!7%$%&96!0D!?>6!@F%9695%D?!#@!9%.@6/!7A!?>6!?>653%$!7$%&Q6?!?5%FF#&-!#&!?>6!>6%?(!!:>6!?>653%$!7%$%&96!#@!%9>#6C6/!;>6&!?>6!>6%?!5%/#%?6/!?0!?>6!@%?6$$#?6!#@!6g.%$!?0!?>6!>6%?!5%/#%?6/!7A!?>6!@%?6$$#?6(!

:>6!3#&#3.3!7%??65A!?63F65%?.56!#@!OiV!;>#$6!9>%5-#&-(!!,@!@>0;&!#&!K69?#0&!J(G!X'#-(!HfY1!?>6!3#&#3.3!?63F65%?.56!0D!?>6!30/6$!#@!$0;65!?>%&!?>6!?6@?#&-!?63F65%?.56!7A!%&!%C65%-6!0D!HIiV(!!]&!%//#?#0&1!/.5#&-!?>6!?6@?!?>6!0.?@#/6!0D!?>6!7%??65A!70E!;%@!%?!%!$0;65!?63F65%?.56!?>%&!?>6!#&@#/6!0D!?>6!7%??65A!70E!/.5#&-!?>6!90$/!9A9$61!7A!%&!%C65%-6!0D!N(OiV!/.5#&-!?>6!90$/!@0%Q(!!SA!%//#&-!%&!%C65%-6!0D!HN(OiV!?0!?>6!?0?%$!30/6$!?63F65%?.561!;6!07?%#&!%!?63F65%?.56!;#?>#&!?>6!7%??65A!$#3#?@(!!!

!

0

2

4

6

8

10

12

14

16

18

0 500 1000 1500 2000 2500

Time (min)

Tem

pera

ture

(ºC

)

BAT Model Temperature History

BAT Model with 10ºC Correction

!

'#-.56!GG`!V0$/!V%@6!Z57#?!K#3.$%?#0&!;#?>!S%??65A!:63F(!P#@?05A!;#?>#&!:63F65%?.56!=#3#?@!

35.5

36

36.5

37

37.5

38

38.5

39

39.5

40

40.5

0 10 20 30 40 50 60

Inclination (deg)

Perc

en

tag

e o

f O

rbit

in

th

e

Sh

ad

e

300 Km Altitude

330 Km Altitude

360 Km Altitude

!!

'#-.56!GN`!!]&9$#&%?#0&!C@(!W6596&?%-6!0D!?>6!Z57#?!#&!?>6!K>%/6!D05!)#DD656&?!Z57#?!,$?#?./6@!

!

4.3.3. Acceptable Orbits

:>6! @%?6$$#?6! 3.@?! >%C6! %?! $6%@?! Nfm! 0D! ?>6! 057#?! #&! ?>6! @>%/6(! ! '#-.56! GN! @>0;@! @6C65%$! 057#?! %$?#?./6@! %?! /#DD656&?!#&9$#&%?#0&@!;>#9>!>%C6!%&!%C65%-6!F6596&?%-6!0D! ?>6!057#?! %70C6!Nfm(! !:>6!3%E#3.3!%996F?%7$6!057#?! %$?#?./6! #@!0D!NbIQ3(!!S6?%!%&-$6@!;656!9%$9.$%?6/!?0!D#&/!?>6!0F?#3%$!$%.&9>!;#&/0;@1!7.?!?>6A!/#/!&0?!%DD69?!?>6!%C65%-6!F6596&?%-6!0D!?>6!057#?!?>6!@%?6$$#?6!;0.$/!563%#&!#&!?>6!@>%/6(!!S69%.@6!0D!$0;!#&9$#&%?#0&@!0D!?>6!%996F?%7$6!057#?@1!76?%!%&-$6@!/0!&0?!$%5-6$A!%DD69?!?>6!@%?6$$#?6!@>%/6/!?#36(!!!!

5. CONCLUSIONS !:>6! @%?6$$#?6! F65D0536/! ;6$$! /.5#&-! ?6@?#&-! %&/! %&%$A@#@(! ! "0@?! 0D! ?>6! @.7@A@?63@! @>0;6/! -00/! ;05Q3%&@>#F! %&/!56%/#&6@@!D05!@F%96D$#->?(!!'05!',K:T,V_@!3#@@#0&!?0!76!@.996@@D.$1!?>6!@%?6$$#?6!3.@?!>%C6!%?!$6%@?!Nfm!0D!?>6!057#?!#&!?>6!@>%/6(!!:>#@!$#3#?@!?>6!5%&-6!0D!%$?#?./6!%&/!#&9$#&%?#0&@!0D!?>6!@%?6$$#?6_@!057#?(!!!

5.1. Thermal Vacuum Test

:>6!?>653%$!?6@?!#&/#9%?6/!?>%?!3%&A!@.7@A@?63@!;656!;#?>#&!?>6#5!?63F65%?.56!$#3#?@`!VZ"1!4WK1!Vk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

5.2. Thermal Model

:>6!30/6$!-%C6!?63F65%?.56!F6%Q@!%?!@#3#$%5!?#36@!?>%&!?>6!?6@?!/%?%(!!]?!%$@0!-%C6!@$0F6@!?>50.->!?>6!>0?!%&/!90$/!9A9$6@!@#3#$%5! ?0! ?>6! ?6@?!/%?%(! !:>6!30/6$! ?63F65%?.56@!/#/!&0?!90#&9#/6!6E%9?$A!;#?>! ?>6! ?63F65%?.56!/%?%1!%&/!%@@.3F?#0&@!;656!3%/6!?0!?>6!30/6$!;>6&!5.&&#&-!057#?!@#3.$%?#0&@1!7A!%//#&-!%?!$6%@?!LiV!?0!?>6!30/6$!#&!?>6!90$/!9%@6!@96&%5#0!%&/!%//#&-!HOiV!?0!?>6!>0?!9%@6!@96&%5#0(!!!

5.3. Orbit Thermal Analysis

:>656!;656!?;0!;05@?!9%@6!@96&%5#0@!?>%?!;656!30/6$6/!?0!#&C6@?#-%?6!?>6!?>653%$!56@F0&@6!0D!?>6!@%?6$$#?6`!>0?!%&/!90$/(!!:>6!S,:!70E!?63F65%?.56!#@!@6&@#?#C6!?0!?>6!6E?65&%$!>6%?!D$.E!D503!?>6!<%5?>1!K.&!%&/!%$76/0(!!:>#@!@6&@#?#C#?A!#@!9%.@6/!7A!?>6!F$%9636&?!0D!?>6!70E!&6%5!?>6!6E?65&%$!F%5?!0D!?>6!@?5.9?.56(!!SA!.@#&-!&0&!90&/.9?#C6!6F0EA!0&!?>6!7%??65#6@!;>6&!

F$%96/! 0&! ?>6! 7%??65A! >0$/65! 3#->?! /6956%@6! ?>6! ?63F65%?.56! @;#&-@! ?>6! 7%??65A! 3#->?! 07@65C6! /.5#&-! ?>6! 057#?(! ! ,!?>653%$! 7$%&Q6?!;#?>! $6@@! #&@.$%?#&-! $%A65@! 05!;#?>! -56%?65!0F6&! %56%@!3#->?! %$@0! >6$F! 0&! /6956%@#&-! ?>6! ?63F65%?.56!#&@#/6!?>6!@%?6$$#?6(!!5.3.1. Hot Case Orbit Simulation

).5#&-!?>6!>0?!9%@61!;#?>!?>6!@.5D%96!0D!?>6!7%??65A!70E!@.7@A@?63!/#569?6/!?0;%5/@!?>6!K.&!%?!%$$!?#36@1!?>6!7%??65A!70E!0C65>6%?6/(! ! '.?.56! %&%$A@#@! 3.@?! 76! 903F$6?6/! ?0! @>0;! ?>%?! 7A! 56/.9#&-! ?>6! &.3765! 0D! "A$%5! $%A65@! ?>6! %C65%-6!?63F65%?.56!0D!?>6!@%?6$$#?6!/6956%@6@(!!:>6!S,:!?63F65%?.56!/6956%@6/!D503!?>6!>0?!9%@6!@#3.$%?#0&!%?!I(HIb!5F31!%&/!?>6! ?#36! #&! ?>6! @>%/6! ;%@! #&956%@6/! ?0! Nfm! 0D! ?>6! 057#?(! ! ',K:T,V! $0;! 7%??65A! ?63F65%?.56! 5%&-61! /6956%@6@! ?>6!#&9$#&%?#0&!0&!;>#9>!?>6!@%?6$$#?6!9%&!76!#&@65?6/(!!!!5.3.2. Cold Case Orbit Simulation

',K:T,V!?>653%$!30/6$!;%@!%7$6!?0!;#?>@?%&/!;05@?!90$/!9%@6!@#?.%?#0&@1!;>#$6!?>6!@.5D%96!0D!?>6!@%?6$$#?6!;%@!/#569?6/!?0;%5/@!<%5?>!/.5#&-!?>6!K.&!@69?#0&!0D!?>6!057#?1!%&/!%;%A!D503!?>6!<%5?>!/.5#&-!?>6!@>%/6/!@69?#0&!0D!?>6!057#?(!!:>6!?>653%$!7$%&Q6?!?5%FF6/!>6%?!;>#9>!#&956%@6/!?>6!?63F65%?.56!0D!?>6!@%?6$$#?6!?>653%$!7%$%&96(!!

ACKNOWLEDGEMENTS !

:>#@!F%F65!;%@!3%/6!F0@@#7$6!7A!%$$!?>6!@?./6&?@!%&/!F50D6@@05@!%?!?>6!B&#C65@#?A!0D!:6E%@!%?!,.@?#&!;>0!>6$F6/!/6@#-&!%&/!7.#$/!',K:T,V(!!,$@01!3%&A!?>%&Q@!?0!U,K,_@!20>&@0&!KF%96!V6&?65!D05!$6??#&-!.@!.@6!?>6#5!D%9#$#?#6@!?>50.->0.?!?>6!?>653%$!9A9$6!?6@?(!!'#&%$$A1!?>6!-.#/%&96!D503!?>6!,#5!'0596!T6@6%59>!]&@?#?.?6!;%@!#&C%$.%7$6!?0!?>6!903F$6?#0&!0D!',K:T,V(!!

REFERENCES

H( P0$?!4(1!K?6;%5?!K(1!"%.$/#&!2(1!V%3F76$$!:(1!<9Q>0DD!W(1!<$3%@5#!P(1!<C%&@!S(1!4%5-!"(1!4566&7%.3!2(1!=#&D05/!"(1!W00$6!"(1!=#->?@6A!<(!4(1!T%\%!=(!=(1!nT6$%?#C6!U%C#-%?#0&1!"#950/#@9>%5-6!W$%@3%!:>5.@?651!%&/!)#@?5#7.?6/!V033.&#9%?#0&@!<EF65#36&?@!0&!?>6!',K:T,V!"#@@#0&o!HL?>!,&&.%$!,],,RBKB!V0&D656&96!0&!K3%$$!K%?6$$#?6@1!!GIIN!G( 86$9>1!2(8(1!n:>653%$!:6@?#&-!0D!K3%$$!V$%@@!V!KF%96![6>#9$6@`!,!K?./A1o!,],,!Gb?>!:>6530F>A@#9@!V0&D656&961!P0&0$.$.!P%;%##1!2.&6!HffH!N( P0DD3%&1!<5#9!2(1!'0.&?%#&1!4$6&!P(1!n:>6!KA@?63!,FF50%9>!?0!K.996@@D.$!KF%96!"#@@#0&!)6C6$0F36&?o1!20>&!P0FQ#&@!,W=!:69>&#9%$!)#-6@?1![0$.36!GI1!U.3765!J!XHfffY!J( )#%*+,-.%/01!"(!'(1!n'053%?#0&!,.?0&03A!KF%9695%D?!;#?>!:>5.@?!T6$%?#C6!U%C#-%?#0&1!,??#?./6!%&/!V50@@$#&Q!W50-5%3!:>653%$!:6@?!%&/!,&%$A@#@o1!:>6!B&#C65@#?A!0D!:6E%@!%?!,.@?#&1!:6E%@1!)6963765!GIIO!O( 4#$30561!)%C#/!4(!1nKF%9695%D?!:>653%$!V0&?50$!P%&/700Qo1!:>6!,650@F%96!W56@@1!<$!K6-.&/01!V,(1!GIIG!b( [%$$%/01!)(,(1!n'.&/%36&?%$!0D!,@?50/A&%3#9@!%&/!,FF$#9%?#0&@o1!G&/(!</#?#0&1!:>6!KF%96!:69>&0$0-A!=#75%5A1!GIIH!L( "#$$@1!,('(1!nP6%?!:5%&@D65o1!W56&?#96!P%$$1!K690&/!</#?#0&1!BFF65!K%//$6!T#C651!U(2(1!Hfff!M( K3#?>1!:5%C#@!T(1!n:>653%$!,&%$A@#@!0D!W,UK,:o1!U%C%$!W0@?-5%/.%?6!K9>00$1!"0&?656A1!V%$#D05&#%1!)6963765!HffL!f( "6A651!T./0$D!p(1!n<$636&?@!0D!KF%96!:69>&0$0-Ao1!,9%/63#9!W56@@1!K%&!)#6-01!Hfff!

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