Advances in Spacecraft Technologies Part 5 pptx

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150
Amount methanol in water (%)
0 1020304050
ADN solubility (%)
56
58
60
62
64
66
68
70
72
Specific Impulse (Ns/kg)
1600
1700
1800
1900
2000
2100
2200
2300
2400
2500
2600
T = 0
o
C

Fig. 12. Specific impulse and ADN solubility in water/methanol mixtures at 0°C. p
c
=
2.0 MPa,
ε
= 50.
Low volatile fuels such as 1,4-butanediol, glycerol, ethylene glycol and trimethylol propane
where studied to minimize the amount of ignitable and/or toxic fumes. First glycerol was
chosen due to the superior thermal ignition properties of the ADN/glycerol/water-blend.
This monopropellant formulation was called LMP-101 (Anflo et al., 2000). However, it was
discovered that LMP-101 suffered from poor thermal stability, and as a consequence it was
rejected from further development. During the years, several different ADN-based
monopropellants have been developed (Wingborg et al., 2004; Wingborg and Tryman, 2003).
Two formulations, LMP-103S and FLP-106 have received particular attention. LMP-103S has
been selected by SSC and FLP-106 has been selected by FOI as the main monopropellant
candidate for further development efforts.
4.2 Properties of ADN liquid monopropellant formulation FLP-106
FLP-106 is a low-viscous yellowish liquid, as seen in Fig. 13, with high performance, low
vapour pressure and low sensitivity. It is based on a low volatile fuel, water and 64.6 %
ADN. The development, characterization and selection of FLP-106 are reported elsewhere
(Wingborg and de Flon, 2010; Wingborg et al., 2004; Wingborg et al., 2006; Wingborg et al.,
2005). Some of the properties of FLP-106 are shown in Tables 10 and 11, and its mass density
as function of temperature is shown in Fig. 14.


Fig. 13. Monopropellant FLP-106.
Green Propellants Based on Ammonium Dinitramide (ADN)

151

Hydrazine FLP-106
Specific impulse
b
(s) 230 (Brown, 1995) 259
Density (g/cm
3
) 1.0037 1.357
Temp. in chamber (°C)
1120 1880
T
min

c
(°C)

2.01 0.0
Viscosity (cP, mPas) 0.913 3.7
Thermal expansion
coefficient (1/K)
9.538·10
-4
6.04·10
-4

Heat capacity (J/gK) 3.0778 2.41
Table 10. Properties of hydrazine and FLP-106
a
.
a) All properties at 25 °C. Hydrazine data from Schmidt (Schmidt, 2001) and FLP-106 data from

Wingborg et al. (Wingborg and de Flon, 2010; Wingborg et al., 2004; Wingborg et al., 2006; Wingborg et
al., 2005).
b) Calculated Isp. Pc = 2.0 MPa, Pa = 0.0 MPa, ε = 50.
c) Minimum storage temperature determined by freezing (hydrazine) or precipitation (FLP-106).

A
e
/A
t
50 100 150 200
I
sp
(s)
a
259 264 266 268
Table 11. Vaccum specific impulse at different nozzle area expansion ratios.
a) Pc = 2.0 MPa

Temperature (
o
C)
0 102030405060708090
Density (g/cm
3
)
1,30
1,32
1,34
1,36
1,38

FLP-106
ρ =1.378-8.2e
-4
T

Fig. 14. Mass density of FLP-106 as a function of temperature.
4.3 FLP-106 manufacturing and batch control
FLP-106 is manufactured in two steps; first the fuel is dissolved in water and secondly ADN
is mixed in the fuel/water blend. The temperature drops substantially during the
dissolution of ADN and thus it takes some time before all ADN has dissolved. To speed up
the dissolution, the mixture can be heated using a warm water bath. The ADN used was
procured from EURENCO Bofors in Sweden. The purity of the material is above 99 %.
However, small amounts of insoluble impurities are present, which is clearly seen when
dissolving ADN. The purity can be improved by recrystallization. In this way insoluble
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152
impurities are removed, but the content of ammonium nitrate increases due to ADN
degradation. To prevent this, the prepared propellant is instead purified in-situ by filtration
using a 0.45 µm PTFE filter, and a completely clear liquid propellant of high purity is
formed.
When manufacturing batches of FLP-106 it is important to verify it has been prepared
correctly and conforms to the specification. Apart from visual examination, each batch of
propellant is analysed with respect to density using a Mettler Toledo DE40 density meter. It
is estimated that the ADN content in this way can be determined within ±0.05 %. The high
precision is possible due to the low volatility of FLP-106.
4.3 FLP-106 material compatibility
The compatibility between the propellant and different construction materials used in
propulsion systems have been assessed (Wingborg and de Flon, 2010). The materials
considered are shown in Table 12. The tests were performed using a Thermometric TAM

2277 heat flow calorimeter. Pieces of respective test material were immersed in
approximately 0.2 g FLP-106 in 3 cm
3
glass ampoules. The measurements were performed at
75 °C for 19 days. All the tested materials were supplied by Astrium GmbH, Bremen, except
sample no. 13, which was cut out from a Nalgene bottle.

Sample no. Materials
1 Metal, AISI 304L
2 Metal, AISI 321
3 Metal, AISI 347
4 Metal, Inconel 600
5 Metal, AMS 4902
6 Metal, AMS 4906
7 Metal, Nimonic 75
8 Polymer, PTFE
9 Rubber, EPDM
10 O-ring, Kalrez 4079, Du Pont
11 O-ring, Kalrez 1050LF, Du Pont
12 O-ring, 58-00391, Parker Hannifin GmbH
13 Polymer, PETG, Nalgene
Table 12. Materials used in the compatibility assessment.
In all cases the heat flow induced by the tested materials were below 0.1 µW/mm
2
(Wingborg and de Flon, 2010). Based on the heat flow measurements all materials tested are
considered to be compatible with FLP-106. However, EPDM and PETG samples both
showed a slight colour shift. This might be due to thermal degradation of the materials.
Since the tests were performed at substantially harsher conditions than, for instance the
NASA Test 15 (test time 48 h, test temp 71 °C) (NASA, 1998), it is not clear that the colour
shift detected is an issue.

4.4 Ignition of FLP-106
One important aspect in the development of a new monopropellant is the ignition. State of
the art hydrazine thrusters use catalytic ignition, which is simple and reliable. To replace
Green Propellants Based on Ammonium Dinitramide (ADN)

153
hydrazine, ADN-based monopropellants must be as easy to ignite. However, a
disadvantage of the ADN-based monopropellants is the high combustion temperature,
which is approximately 800°C higher than hydrazine, as seen in Table 10. The combustion
temperature is in the same range as for HAN-based monopropellants, and it has been
reported that the current state of the art hydrazine catalyst (Shell 405) cannot withstand such
high temperatures (Reed, 2003; Zube et al., 2003). This and the fact that hydrazine and ADN-
based liquid propellants are very different, both physically and chemically, require
development of new ignition methods, or new catalysts. When dripping the FLP-106 on a
hot plate, with a temperature in the range of 200 to 250°C, it ignite and burn fast. This
clearly shows that thermal ignition is possible and thermal ignition might thus be a feasible
ignition method. Three different methods of heating the propellant to the ignition
temperature have been identified:
• Pyrotechnic (by forming hot gases using a solid energetic material which in turn will
heat the propellant)
• Thermal conduction (by spraying the propellant on a hot object which in turn is heated
by electric means)
• Resistive (ADN is a salt and the propellants thereby possess a relatively high electric
conductivity. This means that an ADN-based monopropellant can be resistively heated)
Development of catalytic (Scharlemann, 2010), thermal (Wingborg et al., 2006), and resistive
(Wingborg et al., 2005) ignition methods is ongoing.
4.5 FLP-106 compared to LMP-103S
Both FLP-106 and LMP-103S are compatible with materials currently used in propulsion
systems. They both also have similar oral toxicity and should be considered as harmful, but
not toxic. However, FLP-106 has a substantial lower vapour pressure and requires no

respiratory protection during handling. They are not sensitive to shock initiation and
should, from this point of view, not be considered as hazard class 1.1 materials (ECAPS,
2010; Wingborg and de Flon, 2010). The advantage using FLP-106, apart from its lower
volatility, is its higher performance and higher density as shown in Table 13. The specific
impulse for FLP-106 is 7 s higher compared to LMP-103S, and the density-impulse (ρ·I
sp
) is
13 % higher.

Propellant FLP-106 LMP-103S
I
sp
(s)
a
259 252 (ECAPS, 2009)
ρ (g/cm
3
)
b
1.362 1.240 (ECAPS, 2010)
ρ·I
sp
(gs/cm
3
) 353 312
Table 13. Properties of ADN-based monopropellants.
a) at a nozzle area expansion ratio of 50.
b) at 20 °C
.
5. Concluding remarks

Ammonium dinitramide, ADN, seems promising as a green substitute for both ammonium
perchlorate, AP, and for monopropellant hydrazine. A solid ADN propellant has been
formulated and test fired successfully and a high performance liquid ADN-based
monopropellant has been developed.
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Future work concerning solid ADN-based propellants will focus on improving the
mechanical properties and to characterize the sensitivity.
Future work concerning liquid ADN-based monopropellants will focus on ignition and
thruster development.
6. Acknowledgements
The authors like to acknowledge all colleagues at FOI involved in the ADN development
and the Swedish Armed Forces for financial support.
7. References
Agrawal, J. P. & Hodgson, R. D. (2006). Organic Chemistry of Explosives, Wiley, Chichester.
Anflo, K., Grönland , T. A. & Wingborg, N. (2000). Development and Testing of ADN-Based
Monopropellants in Small Rocket Engines. 36th AIAA/ASME/SAE/ASEE Joint
Propulsion Conference, 16-19 July 2000, Huntsville, AL, USA.
ASTRIUM. (2007). Aestus Rocket Engine.

[Accessed 2010-08-25].
ATSDR. (1997). Hydrazine cas # 302-01-2; 1,1-dimenthylhydrazine cas # 57-14-7; 1,2-
dimenthylhydrazine cas # 540-73-8. Agency for Toxic Substances and Disease
Registry, USA. [Accessed 2010-08-25].
Bathelt, H., Volk, F. & Weindel, M. (2004). ICT - Database of Thermochemical Values.
Version 7.0 ed.: Fraunhofer-Institut für Chemische Technologie (ICT).
Bombelli, V., Ford, M. & Marée, T. (2004). Road Map for the Demonstration of the Use of
Reduced-Hazard Monopropellants for Spacecraft. 2nd International Conference on
Green Propellants for Space Propulsion, 7-8 June 2004, Chia Laguna, Sardinia, Italy.

Bombelli, V., Simon, D. & Marée, T. (2003). Economic Benefits of the use of Non-Toxic
Monopropellants for Spacecraft Applications. 39th AIAA/ASME/SAE/ASEE Joint
Propulsion Conference, 20-23 July 2003, Huntsville, AL, USA.
Bottaro, J. C., Penwell, P. E. & Schmitt, R. J. (1997). 1,1,3,3-Tetraoxy-1,2,3-triazapropene
Anion, a New Oxy Anion of Nitrogen: The Dinitramide Anion and Its Salts. Journal
of the American Chemical Society, 119, 9405-9410.
Brown, C. D. (1995). Spacecraft Propulsion, AIAA, Washington.
Christe, K. O., Wilson, W. W., Petrie, M. A., Michels, H. H., Bottaro, J. C. & Gilardi, R. (1996).
The Dinitramide Anion, N(NO2)2 Inorganic Chemistry, 35, 5068-5071.
DoD (2009). DoD Workshop Advanced Strategy for Environmentally Sustainable Energetics, 24-25
March 2009, Rockaway, NJ, USA.
ECAPS. (2009). Green Propellant Technology on the Prisma Satellite. Swedish Space Corporation
Group. [Accessed 2010-08-25].
ECAPS. (2010). Monopropellant LMP-103S. Swedish Space Corporation Group.

[Accessed 2010-08-25].
Eldsäter, C., de Flon, J., Holmgren, E., Liljedahl, M., Pettersson, Å., Wanhatalo, M. &
Wingborg, N. (2009). ADN Prills: Production, Characterisation and Formulation.
40th International Annual Conference of ICT, 23-26 June 2009, Karlsruhe, Germany.
Green Propellants Based on Ammonium Dinitramide (ADN)

155
EPA. (2005). Perchlorate Treatment Technology Update. United States Environmental Protection
Agency, USA.
[Accessed 2010-08-25].
Gordon, S. & McBride, B. J. (1994). Computer program for calculation of complex chemical
equilibrium compositions and applications. I. Analysis. NASA.
Hurlbert, E., Applewhite, J., Nguyen, T., Reed, B., Baojiong, Z. & Yue, W. (1998). Nontoxic
Orbital Maneuvering and Reaction Control Systems for Reusable Spacecraft. Journal
of Propulsion and Power, 14, 676-687.

Johansson, M., de Flon, J., Pettersson, Å., Wanhatalo, M. & Wingborg, N. (2006). Spray
Prilling of ADN, and Testing of ADN-Based Solid Propellants. 3rd International
Conference on Green Propellants for Space Propulsion, 17-20 September 2006, Poitiers,
France.
Kinkead, E. R., Salins, S. A., Wolfe, R. E. & Marit, G. B. (1994). Acute and Subacute Toxicity
Evaluation of Ammonium Dinitramide. Mantech Environmental Technology.
Langlet, A., Östmark, H. & Wingborg, N. 1997. Method of Preparing Dinitramidic Acid and
Salts Thereof. Patent No: WO 97/06099.
McBride, B. J. & Gordon, S. (1996). Computer program for calculation of complex chemical
equilibrium compositions and applications. II. Users manual and program
description. NASA.
Meinhardt, D., Brewster, G., Christofferson, S. & Wucherer, E. J. (1998). Development and
Testing of New, HAN-based Monopropellants in Small Rocket Thrusters. 34th
AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 13-15 July 1998, Cleveland, OH,
USA.
Meinhardt, D., Christofferson, S. & Wucherer, E. (1999). Performance and Life Testing of
Small HAN Thrusters. 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 20-
24 June 1999, Los Angeles, CA, USA.
Mittendorf, D., Facinelli, W. & Sarpolus, R. (1997). Experimental Development of a
Monopropellant for Space Propulsion Systems. 33rd AIAA/ASME/SAE/ASEE Joint
Propulsion Conference, 6-9 July 1997, Seattle, WA, USA.
NASA (1998). Flammability, odor, offgassing, and compatibility requirements and test
procedures for materials in environments that support combustion. NASA, USA.
Östmark, H., Bemm, U., Bergman, H. & Langlet, A. (2002). N-Guanylurea-dinitramide: A
New Energetic Material with Low Sensitivity for Propellants and Explosives
Applications. Thermochimica Acta, 384, 253-259.
Östmark, H., Bemm, U., Langlet, A., Sandén, R. & Wingborg, N. (2000). The Properties of
Ammonium Dinitramide (ADN): Part 1, Basic Properties and Spectroscopic Data.
Journal of Energetic Materials, 18, 123-128.
Palaszewski, B., Ianovski, L. S. & Carrick, P. (1998). Propellant Technologies: Far-Reaching

Benefits for Aeronautical and Space-Vehicle Propulsion. Journal of Propulsion and
Power, 14, 641-648.
Perez, M. (2007). Bulletin de Analyses. Produit: PAG (polyazoture de glycidyle). Lots: 76S04.
EURENCO France.
Pettersson, B. (2007). ADN Safety Data Sheet. EURENCO Bofors.
Reed, B. D. (2003). On-Board Chemical Propulsion Technology. 10th International Workshop
on Combustion and Propulsion, 21-25 September 2003, Lerici, La Spezia, Italy.
Ritz, B., Zhao, Y. X., Krishnadasan, A., Kennedy, N. & Morgenstern, H. (2006). Estimated
effects of hydrazine exposure on cancer incidence and mortality in aerospace
workers. Epidemiology, 17, 154-161.
Advances in Spacecraft Technologies

156
Scharlemann, C. (2010). GRASP- A European Effort to Investigate Green Propellants for
Space Application. Space Propulsion 2010, 3-6 May 2010, San Sebastian, Spain.
Schmidt, E. W. (2001). Hydrazine and its Derivatives, Wiley-Interscience.
STANAG (2002). Explosives, Nitrocellulose Based Propellants, Stability Test Procedure and
Requirements Using Heat Flow Calorimetry. NATO Standardisation Agreement
STANAG 4582 (First Draft)
Stephenson, D. D. & Willenberg, H. J. (2006). Mars ascent vehicle key elements of a Mars
Sample Return mission. IEEE Aerospace Conference, 4-11 March 2006, Big Sky, MT,
USA.
Sutton, G. P. & Biblarz, O. (2001). Rocket Propulsion Elements, John Wiley & Sons, New York.
Talawar, M. B., Sivabalan, R., Anniyappan, M., Gore, G. M., Asthana, S. N. & Gandhe, B. R.
(2007). Emerging Trends in Advanced High Energy Materials. Combustion,
Explosion, and Shock Waves, 43, 62-72.
Teipel, U. (2004). Energetic Materials: Particle Processing and Characterization, Wiley-VCH,
Weinheim.
Urbansky, E. T. (2002). Perchlorate as an Environmental Contaminant. Environ Sci & Pollut
Res, 9, 187-192.

Venkatachalam, S., Santhosh, G. & Ninan, K. N. (2004). An Overview on the Synthetic
Routes and Properties of Ammonium Dinitramide (ADN) and Other Dinitramide
Salts. Propellants, Explosives, Pyrotechnics, 29, 178-187.
Wingborg, N. (2006). Ammonium Dinitramide-Water: Interaction and Properties. J. Chem.
Eng. Data, 51, 1582-1586.
Wingborg, N. & de Flon, J. (2010). Characterization of the ADN-based liquid
monopropellant FLP-106. Space Propulsion 2010, 3-6 May 2010, San Sebastian, Spain.
Wingborg, N., de Flon, J., Johnson, C. & Whitlow, W. (2008). Green Propellants Based on
ADN. Space Propulsion 2008, 5-8 May 2008, Heraklion, Crete, Greece. ESA, 3AF,
SNPE.
Wingborg, N., Eldsäter, C. & Skifs, H. (2004). Formulation and Characterization of ADN-
Based Liquid Monopropellants. 2nd International Conference on Green Propellants for
Space Propulsion, 7-8 June 2004, Chia Laguna, Sardinia, Italy.
Wingborg, N., Johansson, M. & Bodin, L. (2006). ADN-Based Liquid Monopropellants:
Propellant Selection and Initial Thruster Development. 3rd International Conference
on Green Propellants for Space Propulsion, 17-20 September 2006, Poitiers, France.
Wingborg, N., Larsson, A., Elfsberg, M. & Appelgren, P. (2005). Characterization and
Ignition of ADN-Based Liquid Monopropellants. 41st AIAA/ASME/SAE/ASEE Joint
Propulsion Conference, 10-13 July 2005, Tucson, AZ, USA.
Wingborg, N. & Tryman, R. (2003). ADN-Based Monopropellants for Spacecraft Propulsion.
10th International Workshop on Combustion and Propulsion, 21-25 September 2003,
Lerici, La Spezia, Italy.
Wucherer, E. J. & Christofferson, S. (2000). Assessment of High Performance HAN-
Monopropellants. 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 16-19
July 2000, Huntsville, AL, USA.
Zube, D. M., Wucherer, E. J. & Reed, B. (2003). Evaluation of HAN-Based Propellant Blends.
39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference
, 20-23 July 2003, Huntsville,
AL, USA.

8
Use of Space Thermal Factors
by Spacecraft
N. Semena
Space Research Institute RAS,
Russia
1. Introduction
All the equipment used by the man can work in the limited temperature range. The
necessary ambient temperature and the intensive convective mechanism help to solve a
thermostabilization problem on the Earth. But in the space the decision of this problem is
much more difficult by reason of the extreme thermal conditions and vacuum. Now
thermostabilization of space devices is provided with special thermoregulation systems,
which failure leads to emergency end of mission. These systems depend from spacecraft (Sc)
electrical system which supplies energy heaters and from Sc orientation system, which
doesn't allow to heat up a radiator solar or planetary irradiance.
In article it will be shown that using of very simple technical decisions allows to make Sc
thermoregulation systems independent of other Sc systems and from variation of space
thermal factors. In addition it is shown how Sc thermal systems can be used for determine of
its orientation.
2. Analysis of shortcomings of the conventional system for ensuring the
thermal regime
To solve the problem of thermal stabilization of space equipment sufficiently efficient
systems of thermal regulation were developed whose basic elements are the radiator—
emitter, which is a surface emitting the excessive heat flux to space, and the electric heater
— the element heating the equipment if necessary.
The process for maintaining the temperature of an equipment used in space generally
consists of the maintenance of a necessary temperature level of the heat balance between the
heat flux irradiated from the radiator surface and the integral heat capacity of the device
including heat release of the equipment, heat release of the heater and the heat flux
absorbed by the external surface of the radiator-emitter. The scheme of the simplest system

of thermal regulation is presented in Fig. 1.
To investigate the influence of external and internal thermal factors on the temperature
regime of such a system one can use an assessment thermal model which does not account
for secondary factors: the non-isothermicity of thermal nodes, heat flux across the external
thermal insulation, the difference from zero of the effective temperature of space, and a
possible shielding of the radiator-emitter by the structure external elements. The above
factors do not affect the qualitative result of modelling but complicate the solution. Thus, the
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158

Fig. 1. Scheme of a conventional system for thermal regulation of the devices for space
application.
assessment thermal model of the presented system includes two thermal nodes (node No. 1
is the heat releasing equipment, including the heater, nodes No. 2 is the radiator-emitter)
and is governed by the system of two equations:
1
1
()()
11 21
12
1
4
2
(())(),
222222212222
21
dT
CQQ TT
Н

dR
dT
CEpAsEsEspSTTTS
dR
τ
εεσ
τ
=+ − −
=+ + + −−

where C
1
, C
2
, T
1
, and T
2
are the heat capacities and temperatures of the device and the
radiator,
τ
is the time, Q
1
and Q
H
are the heat releases of the device and the heater, S
2
,
ε
2

and
As
2
are the area, emissivity factor, the coefficient of absorption of solar radiation and the
external surface of the radiator-emitter, Ep
2
and Es
2
+Esp
2
are the infrared and solar radiant
fluxes incident onto the external surface of the radiator-emitter, R
12
and R
21
are the thermal
resistance of the heat-conducting duct from the equipment to radiator and from the radiator
to the equipment (usually R
12
= R
21
),
σ
is the Stefan — Boltzmann constant.
An analysis of the presented thermal model shows the shortcomings of the conventional
system for ensuring the thermal regime, which is employed in present-day devices of space
application.
1. Such a system is very sensitive to external heat fluxes falling onto the radiator- emitter
surface. The reason for this is that the only model element, at the expense of
Use of Space Thermal Factors by Spacecraft

159
which the heat is removed is ε2σT24S2, therefore, the system can function efficiently only at
such a level of external heat fluxes (Ep, Es+Esp), which ensure, for a given temperature of
the equipment (T1), the satisfaction of inequality (ε2Ep2 + As2(Es2+Esp2))S2 << At the
equality of these two elements, the radiator-emitter stops functioning, and at a sign change
of the inequality to the opposite sign the radiator-emitter reverts into a heater and stabilizes
the system at a higher temperature as compared to the one, which is required for the
equipment operation. This indeed means that the spacecraft must not be oriented in such a
way that a highly intense external flux from the sun and a planet falls during a long time
onto the radiator-emitter. The orientation constraints in their turn lead to a restriction of the
spacecraft functional capabilities.
2. The system is sensitive to the internal heat release of the equipment because a small
oscillation of temperature around the mean value is ensured only under the condition Q
1
+
Q
H
≈ const. This means that at a reduction of the useful power consumption of equipment
the freed power must be directed to the heater feeding to maintain a constant level of the
total heat release. This leads, in its turn, to the fact that the power supply system of
spacecraft must always be tuned to a peak power consumption, which is very wasteful
under the conditions of an electric power shortage on the spacecraft.
A seeming possibility of the first factor compensation at the expense of the second one leads
to an even higher loading on the power supply system, which must compensate in this case
both for a non-uniformity of the internal heat release of the equipment and non-uniformity
of the external radiant flux absorbed by the radiator-emitter. Thus, if a spacecraft is
composed of several independent devices each of which is equipped with an autonomous
system for ensuring the thermal regime and the given devices are switched on at different
times, then one can ensure, at first glance, the electric power saving by directing it only to

those devices, which must be switched on. However, this is impossible when using the
conventional systems for ensuring the thermal regime because the specified temperature of
the equipment is ensured only at a constant maximum power supply to each device.
3. Universal mechanism of self-regulation
The self-regulation mechanism of a passive system for ensuring the thermal regime must
ensure the temperature independence of thermally stabilized equipment of the external heat
flux variability and of its internal heat release variability in the absence of active elements.
At first sight, these are mutually exclusive conditions. If one considers, however, the
spacecraft as an element included in the entire thermal balance of the Solar system, then one
can conclude that the presence of a stable heating source, the sun, and a stable cooling
source, the open space, enables the given problem solution.
If the radiator is partitioned into six parts oriented at the right angle with respect to one
another (Fig. 2), then independently of the direction in which the sun or a planet lies the
integral heat flux absorbed by six radiators will vary weakly:
7
(()
2
i
E
p
As Es Es
p
SConst
ii i i ii
i
ε
=
++≈
∑
=

,
where i is the radiator number. This leads in its turn to that the external radiant flux absorbed
by radiators is taken into account at the choice of the radiator areas as a constant heat addition,
which does not lead to oscillations of temperatures of the thermal model nodes.
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160

Fig. 2. Six-radiator system for ensuring equipment the thermal regime.
The given method is very efficient for compensation of the variability of radiant flux onto
the spacecraft external surface under its arbitrary variable orientation.
This method also enables a partial compensation of the internal heat release variability. A
constant external heat inflow into the system will enable the maintenance of the equipment
temperature at a minimally allowed level even at its switch-off and a non- functioning
heater, that is at Q
1
+ Q
H
= 0. The necessary heat balance may be ensured at the expense of
choosing the optical characteristics (As
i
,
ε
i
) of the external surface of radiators-emitters. The
use of a many-radiator system enables one in some cases to refuse completely the use of
heater.
As a rule, it is impossible to mount six radiators on a device because of a limited angular
coefficient of the space survey and design constraints. Such a system may be used with a
lesser number of radiators, but also with a lower efficiency.

4. Special mechanisms of self-regulation
The above presented mechanism of self-regulation is universal, it enables the maintenance
of temperature of the heat-stabilized equipment within the given limits under the spacecraft
orientation variation and under a drop of internal heat release, for example, at an accident
switch-off of the equipment. There is, however, an equipment, which operates under
specific thermal conditions, for example, under considerable single increases in heat release
or at a very low level of temperatures. A simple solution using the separation and different
orientation of radiators-emitters is insufficient for thermal stabilization of such an
equipment. The advanced adjustable passive heat pipes, the gas- regulated heat pipes
(GRHP) and thermal diodes (TD) [5], must be used within the system for ensuring the
thermal regime of such an equipment. In the heat pipe, the heat transport occurs at the
expense of the motion of evaporated heat-transfer agent from evaporation zone to
Use of Space Thermal Factors by Spacecraft

161
condensation zone. The return of condensed heat-transfer agent to evaporation zone occurs
at the expense of capillary forces. The heat pipe edge to which the heat flux is supplied is
usually the evaporation zone, and the opposite edge is the condensation zone. The
condensation zone may, however, shift in GRHP along the heat pipe length depending on
the value of a heat flux fed to the evaporation zone. Since effective heat transport is
performed in the heat pipe only between the zones of evaporation and condensation, the
GRHP represents a heat pipe of variable length. Thus, a radiator-emitter with a variable
effective emissive area depending on the supplied heat flux value may be constructed based
on a heat pipe and a plate with limited thermal conductivity (Fig. 3). The thermal diode is a
heat pipe with a unidirectional conductivity. The given element may be used for a low-
temperature system of ensuring the heat regime, if there is a need in minimizing the reverse
heat inflow from the radiator-emitter.

1— GRHP, 2— a plate with limited longitudinal thermal conductivity, S’
P
—the effective emissive area
of the radiator (the active area), S
P
is the radiator maximum area, T
P
is the temperature of the radiator
active zone, X is the GRI-IP active part length
Fig. 3. Radiator with an adjustable effective emissive area.
5. Efficiency of self-regulation mechanisms
With regard for the partition of the radiator-emitter into separate differently directed
elements, the introduction in the system for ensuring the thermal regime of adjustable
radiators based on GRHP and the plates with limited thermal conductivity as well as the use
of the TD, the assessment mathematical model of a passive system for ensuring the thermal
regime with introduced self-regulation mechanisms will be as follows:
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1
1
()
11 1
()
2
11
1
2
(())()()
222222221 12

()
21 12
4
()
22221
1
(())()()
11
()
11
4
(),
1
n
dT
CQ TT
i
dRT
i
ii
dT
CEpAsEsEspST TT
dRT
TS T
dT
n
CEpAsEsEspST TT
nnnnnnnn n
dRT
nn

TS T
nnnn
τ
ε
τ
εσ
ε
τ
εσ
=− ⋅−
∑
Δ
=
=
⋅+⋅ + ⋅Δ+ ⋅−−
Δ
−⋅⋅ ⋅ Δ
⋅⋅⋅
=
⋅+⋅ + ⋅Δ+ ⋅−−
Δ
−⋅⋅ ⋅ Δ

where C
1
, T
1
, and Q
1
are the heat capacity, the temperature, and heat release of the

equipment, τ is the time, i = 2 n is the number of radiators, C
i
, and T
i
are the heat
capacity and the temperature of the i-th radiator, S
i
(
Δ
T
i1
) is the effective emissive area of
the i-th radiator, which is a function of the heat flux to it or, what is the same, of the
difference T
i
— T
1
,
ε
i
and As
i
are the emissivity factor, the coefficient of the solar radiation
absorption by the external surface of the i-th radiator, Ep
i
and Es
i
+Esp
i
are the infrared and

solar radiant fluxes falling onto the external surface of the i-th radiator, R
1n
(
Δ
T
i1
) and
R
n1
(
Δ
T
i1
) are the thermal resistance of the heat-conducting duct from the equipment to the
i-th radiator and from the radiator to the equipment, what in the case of using a thermal
diode depends on the heat flux direction, or, what is the same, on the sign of the
difference T
i
— T
1
.
All the self-regulation mechanisms are presented in the given model. It is enough to use in
real systems one of the proposed techniques, which will be in terms of its characteristics the
closest one to the requirements made by the thermally stabilized equipment.
The model was used for determining the efficiency of techniques proposed for self-
regulation. To this end the real situations were modeled, which are critical for the
conventional system of ensuring the thermal regime. An electronic block with the
parameters typical of the present-day equipment was the thermal regulation object: its mass
was 10 kg (C1≈ 900 J/K) and heat release Q = 10 W. The conventional system of ensuring the
thermal regime for such a block must have a radiator with area S

2
=0.03 m with optical
characteristics As
2
= 0.2, ε
2
= 0.9, provided that the solar radiation does not fall on the
radiator. While using the universal self-regulation mechanism it is necessary to employ six
radiators, each of which must have the following characteristics: S
i
= 0.015, As
i
= 0.9,
ε
i
=0.9,
i=2 7.
Figure 4 shows the temperature variation of the thermal regulation object mounted on an
orbital spacecraft (the time of a single revolution is 90 mm) at an orbit turn of 90° with
respect to the direction to the sun (it occurs at the expense of the orbit precession). The
application of six radiators in this situation is seen in Fig. 4 to enable the preservation of the
thermal regulation object temperature within the range 21.7±0.1°C, whereas in the case of
using a single radiator the temperature increases from 21 to 38°C.
Use of Space Thermal Factors by Spacecraft

163

The systems supplied with radiators: one radiator (A), six radiators (B).
Fig. 4. Temperature variation of the thermal regulation object at an orbit rotation of the
spacecraft.

Figure 5 shows the temperature drop of the same object at a switch-off of the electric power
during 900 mm (a possible situation at the electric power shortage).


The systems supplied with radiators: one radiator (A), six radiators (B).
Fig. 5. Temperature drop of the thermal regulation object at a switch-off of electric power.
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164
The presented dependence shows that at an electric power switch-off the object temperature
will drop from 21 to -0.7°C when using six radiators and to —20 °C when using a single
radiator. At the operation of space equipment, a periodic considerable increase in power
consumption by the equipment is also possible. In this case, it is necessary to use a radiator
with an adjustable effective radiating area. Figure 6 shows the temperature variation of the
regulation object at an increase in heat release from 10 to 20 W during 900 min while using a
conventional system for ensuring the thermal regime and a system with an adjustable
radiator.


The systems supplied with radiators with constant (I) and adjustable (2) emissive areas.
Fig. 6. Temperature variation of the thermal regulation object with increasing power
consumption.
It is seen from the presented dependence that the adjustable radiator is capable in this case
of ensuring a nearly constant temperature of the equipment, whereas at the use of the
conventional system the temperature increases from 21 to 60
O
C.
Figure 7, which presents the temperature increase of a thermal regulation object cooled to
—100°C (the temperature typical of infrared and X-ray detectors) and mounted on the
orbital spacecraft, demonstrates the efficiency of using thermal diodes in a low- temperature

system at a turn by 90° of the orbit plane with respect to the direction to the sun similarly to
the turn shown in Fig. 4.
The given dependence shows that when the radiator-emitter orientation changes the
temperature of the thermal regulation object cooled to —100°C increases up to —43 °C
during 1800 mm at the use of a standard system of thermal regulation and up to —64 °C at
the introduction of a thermal diode into the system.
Use of Space Thermal Factors by Spacecraft

165

The systems supplied with radiators: with one radiator (1), one radiator and thermal diode (2).
Fig. 7. Temperature variation of the thermal regulation object cooled down to —100 °C at a
rotation of the spacecraft orbit
.
6. Use of space thermal factors for determination of the space vehicle orbit
orietation
In the previous sections the decisions have been shown, allowing to make Sc
thermoregulation system the tolerant to anisotropy of a space thermal factors. But this
anisotropy contains the information about a direction on external heat sources – the sun and
a planet and hence, can be used for definition of Sc orientation.
As an example consider parameters of radiant flows in near-earth space. Specificity of the
direct solar radiation is conditioned by significant remoteness of the Sun from Sc. In
practical calculations the Sun can be considered as an infinitely distant radiation source.
Therefore, its radiant flow over the near-earth orbit has characteristics that do not depend
on the orbit parameters: constant small local divergence (32’); similar direction at a specific
moment (solar radiation is parallel in volumes commensurable with Sc dimensions);
constant irradiance Es ~ 1400 W/m
2
, with weak seasonal variations or zero intensity at Sc
approaching the Earth shadow.

Self-radiation of the Earth, on the contrary, due to its proximity to Sc has characteristics
depending on the actual height over the Earth: significant (up to 150°) angle of radiation
divergence and irradiance up to 230 W/m
2
. The Sun radiation reflected from the Earth also
depends on the orbit height and, besides, on the time since intensity of such radiation
depends on the variable in time positional relationship of the Sun, the Earth and the Sc.
Irradiance of Sc frame elements by direct solar radiation reflected from the Earth can vary in
time at the orientation of the Sc to the Earth or its constant orientation to the Sun. Irradiation
of various Sc frame elements by the Sun radiation reflected from the Earth is, vice versa,
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166
constant in time at Sc orientation to the Earth and variable at its orientation to the Sun.
Spectrum distribution of direct and reflected from the Erath solar radiation lies mostly in the
visible area. Self-radiation of the Earth is infrared.
The following shall be noted. If on the ground temperature of the external surface of any
body is conditioned by a large number of random factors (wind velocity, air humidity,
present nearby objects, soil temperature, etc.) in outer space the body orientation in relation
to the Sun appears to be the principal external factor forming its surface field temperature.
To identify interdependence of orientation and thermal mode of Sc surface its thermal
mathematical model can be used that is demonstrated by an example of the simplest located
on the Earth orbit Sc being the cube with known conductive bounds between the facets (fig. 8).


Fig. 8. Scheme of outer radiant flow effect on the near-earth cubical Sc.
Considering the cube facets as the thermal elements of Sc and assuming that Sc lacks
internal heat generation and reradiation between the facets (more complex configuration
and structure of the device would complicate the model having no impact on general results
of the analysis), its thermal model will be described by the following six equations:

(())
6
4
;
1( )
1 6,
dT
i
CEpAsEsEspS
iiiiiii
d
TT
ij
TS
iii
R
jij
ij
i
ε
τ
εσ
⋅
=⋅ + ⋅ + ⋅+
−
+−⋅⋅⋅
∑
=≠
=

Use of Space Thermal Factors by Spacecraft

167
where C
i
, T
i
⎯ values of heat capacity and temperature of six elements (cube facets), R
ij
⎯
heat resistance between i– and j– heat elements (cube facets), As
i
, ε
i
, S
i
⎯ values of the
coefficients of solar radiation absorption and degree of blackness and area of six cube facets,
Es
i
, Esp
i
, Ep
i
⎯ momentary values of irradiation by direct solar radiation, reflected from the
Earth the solar radiation and self-radiation of the Earth of six cube facets,
τ
⎯ time,
σ
⎯

Stefan-Bolzmann constant.
Directions to the principal heat sources – the Sun and the Earth – can be determined on the
basis of eighteen values of the outer radiant flows (Es
i
, Esp
i
, Ep
i
, i = 1…6). However, six
equations of thermal model for their determination are not sufficient. Therefore, the thermal
model shall be supplemented by no less than twelve equations. These equations can be
obtained under the condition of all cube facets radiation by two sources (the Sun and the
Earth) and constant mutual orientation of the facets in relation to each other.
Due to the specificity of direct solar radiation for the description of values Es
i

the simplest
mathematical model can be applied. Choosing directions coinciding with normals to the
first, second and third cube facets (see fig. 1) as axes X, Y, Z of the coordinates system bound
with Sc, we can draw up the following equations:
cos( );
1 6,
Es Es s
ii
i
δ
=⋅
=

where Es ⎯ normal irradiation by the solar radiation on the Earth orbit (the solar constant),

δ
s
1
,
δ
s
2
,
δ
s
3
⎯ angles between the positive directions of axes X, Y, Z of the coordinates
system bound with Sc and the direction to the Sun,
δ
s
4
,
δ
s
5
,
δ
s
6
⎯ angles between negative
directions of axes X, Y, Z of the coordinates system bound with Sc and the direction to the
Sun.
Value Es has seasonal variations from 1396 to 1444 W/m
2
, but at that, it is known with high

degree of certainty for any day for a year.
Cube facets irradiation by self-radiation of the Earth (Ep
1
,
… Ep
6
) is described in a more
complex way:
1
;
4
2
cos sin 0 ;
2
1
2
(cos sin ( arcsin( ))
2
22
sin cos
22
arcsin cos sin cos
sin
;
22
0;
2
1 6,
Ap
Ep Es

ii
ppпри pp
ii i
p p ctg p ctg p
ii i
pp
i
p
pp
i
p
i
при pp p
i
при pp
ii
i
φ
π
φδ θ δ θ
π
φδθ θδ
π
θδ
θ
θδ
δ
ππ
θδ θ
π

φθδπ
−
=⋅⋅
=⋅ ≤<−
=⋅ ⋅ ⋅ − ⋅ +
−
+−⋅−
−≤ <+
=+≤≤
=

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168
where Ар ⎯ average albedo of the Earth,
ϕ
i
⎯ angular coefficient of irradiation of the i-
facet of Sc by the planet,
δ
р
1
,
δ
р
2
,
δ
р
3

⎯ angles between positive directions X, Y, Z of the
coordinates system bound with Sc and the direction to the Earth center,
δ
р
4
,
δ
р
5
,
δ
р
6
⎯
angles between negative directions of axes X, Y, Z of the coordinates system bound with Sc
and the direction to the center of the Earth,
θ
р ⎯ angle of view of the planet from the center
of Sc.
The most complex model serves to describe cube facets irradiation by the solar radiation
reflected from the Earth.
';
' cos cos sin sin cos ;
23
1 6,
Esp Ap Es
ii
f
psf pss
ii i i

i
φ
φ
δγ δγβ
=⋅⋅
=⋅ ⋅ +⋅ ⋅ ⋅
=

where
ϕ
′
i
⎯ angular coefficient of irradiation of the part of the planet of i-facet of Sc, f
2

radiated by the Sun, f
3
⎯ auxiliary functions, γs ⎯ angle between directions to the Sun and
to Sc from the planet center, βs
i
⎯ two-facet angle with the vertex coinciding with the
straight going through the planet center and Sc, in one plane of which lies the normal to i-
facet of Sc and in another one – direction to the Sun.
Functions f
2
, f
3
are determined as follows.
If the plane of i-facet of Sc does not cross the planet:
4

cos 1 sin
1
23
( ) (1 sin 2 sin ln );
2
4 2 sin 1 sin
22
cos (3 sin ) 1 sin
() ln
3
16 sin 1 sin
2
(1 sin ) (3 3sin 2 sin )
;
8
pp
fp p p
pp
pp p
fp
pp
ppp
θθ
θθθ
θθ
θθ θ
θ
θθ
θθθ
−

=⋅+ +⋅ + ⋅
⋅+
⋅+ +
=⋅−
⋅−
−⋅+ +⋅
−

If the plane of i-facet of Sc crosses the planet:

()
2
(, ) ;
2
2
sin
(, ) () 0 ;
33
2
2
(, ) () ;
33
222
fp
fpp
ii
p
fpp fpпри pp
ii
pp

i
fpp fp при pp p
ii
p
θ
θδ φ
θ
π
θδ θ δ θ
π
θδ
ππ
θ
δθ θδθ
θ
=⋅
=≤≤−
+−
=⋅ −≤≤+
⋅

Missing equations can be obtained from the vector productions of unit vectors directed to
the Sun ⎯
123
(cos ,cos ,cos ),ss s s
δ
δδ
G
to the Earth ⎯
123

(cos , cos , cos ),
p
ppp
δ
δδ
G
and orts
⎯
(1,0,0), (0,1,0), (0,0,1):
GGG
xyz
eee

Use of Space Thermal Factors by Spacecraft

169
(
)
(
)
()()
;
;
.
see see e se
x
y
x
y
x

y
pee pee e pe
x
y
x
y
x
y
ee e
xy z
⋅⋅ =⋅⋅−⋅⋅
⋅⋅ =⋅⋅−⋅⋅
⋅=
⎡⎤
⎡⎤
⎣⎦
⎣⎦
⎡⎤
⎡⎤
⎣⎦
⎣⎦
⎡⎤
⎣⎦
G
GG GGG G GG
GGG GGG G GG
GG G

Thus, on the basis of the thermal mathematical model, the model that serves to calculate
angles between the axes of the coordinates system bound with Sc and directions to the Sun

⎯
δ
s
i
, and the planet ⎯
δ
p
i
, i. e. to determine orientation of Sc.
Thermal model shows, that general measurement system of external Sc surface can use for
determination of Sc orientation. This is possible at the condition of present plane
multidirectional zones with the following properties:
-
these zones shall have constant orientation in relation to the coordinates system bound
with Sc;
-
optical characteristics of these zones shall be known;
-
there shall be no screening of these zones from the space by other structural elements;
-
there shall be no less than six such zones, they shall be oriented so that each axis of the
coordinates system bound with Sc form with the normal to the surface at least one angle
less than 30 (theoretically less than 90) degrees in positive and negative directions;
-
it is desirable that thermal sensitivity of these zones to the spatial external factors be
much higher than to the internal heat factors of Sc;
-
thermal capacity of these zones shall be minimum.
In some Sc such zones already exist. In the devices where such zones are difficult to part
they can be created artificially as separate external elements set on the surface of the

spacecraft [3].
In the Space Research Institute (SRI) RAS the model of such device has been developed and
called a thermosensitive element (TSE).Orientation determination system based on
thermosensitive elements is called thermodynamical system of orientation determination
(TDSOD). The model of TSE has extremely reliable simple and inexpensive design. It
consists of (fig. 9):
-
heat receiving plate (1) from highly thermoconductive metal with special coating with
calibrated optical characteristics;
-
resistance thermometer (2), set in the center of the plate (1) so that thermal resistance
between them be minimum;
-
four-beam base (3), made of thin wall plate with low thermal conductivity (material ⎯
stainless steel or titanium), at the same time being a thermal bypass between the
thermosensitive plate and Sc frame;
-
fiber-glass plastic base (4) with electric outputs connected with the resistance
thermometer;
-
thermoisolating screen (5), decreasing radiation flow from the structural elements to the
heat receiving plate.
Thermosensitive elements of two types have been developed: solar and planetary (fig. 10),
differing by optical characteristics of the heat receiving plate coating. Solar TSE was
especially sensitive to the visible solar radiation for the account of the coating of “black
nickel” type with As = 0,9 and
ε
= 0,3. Planetary TSE had heightened sensitivity to infrared
radiation of the Earth for the account of the coating of АК-573 type with As = 0,2 and
ε

= 0,8.
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170

Fig. 9. TSE elements.


Fig. 10. General view of the solar (1) and planetary (2) TSE.
Thermodynamical system for orientation determination shall include not less than 12 such
elements, one planetary and one solar perpendicular to each axis bound with Sc of the
coordinates system in the positive and negative directions.
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171
To assess the possibility of TSE use as an element sensitive to the changing direction to the
Sun eight models of TSE differing by the parameters of thermosensitive plates which
characteristics given in the table experimental research has been carried out.
The TSE models were put into the vacuum chamber where main space thermal factors were
imitated: “cold”, “blackness”, solar and planetary radiation. The models were placed on the
rotary-support that served to turn TSE so that the angle between the normal to heat
receiving plate and the direction to the Sun change in the range from −90 to +90°. The device
at the same time appeared to be an imitator of the Sc frame coated with screen-vacuum
thermoisolation.
Initial angle between the normals to the heat receiving plates and the direction to the Sun
was equal to −90°. TSE turn from −90 to +90° was performed with different angular
velocities imitating possible rotation of Sc.
Dependence of the temperature of the heat receiving plates (for basic TSE № 1
and № 2) from an angle between the normal to them and the direction to the Sun is
presented in fig. 11: for rotation velocity 1,5 (а), 4 (b), 10 (с), 20 (d), 30 (е) ang.deg./min.

Characteristics of the heat receiving plate
Optical characteristics of
the coating
TSE
№
Size, mm
Thickness,
mm
Material
As
ε

TSE type
1
20×20
0,3 Alloy Д16 0,9 0,3 Solar
2
20×20
0,3 Alloy Д16 0,2 0,8 Planetary
3
20×20
0,5 Alloy Д16 0,9 0,3 Solar
4
20×20
0,5 Alloy Д16 0,2 0,8 Planetary
5
20×20
0,25 Cuprum 0,9 0,3 Solar
6

20×20
0,25 Cuprum 0,9 0,3 Solar
7
40×40
0,3 Alloy Д16 0,9 0,3 Solar
8
40×40
0,3 Alloy Д16 0,2 0,8 Planetary
Table 1. Characteristics of heat receiving plates of the studied TSE
Analysis of the presented experimental data shows that, first, the proposed TSE design
appears to be rather sensitive for orientation determination in relation to the Sun, second,
sensitivity of this method for orientation determination decreases at the increase of the
velocity of Sc rotation in relation to the Sun due to the increase of thermal inertia of heat
receiving plate.
To assess the possibility of orientation determination in relation to the Sun with the use of
TSE it is expedient to introduce the parameter binding differential temperature and angular
characteristics of TSE. Such parameter can be sensitivity K, showing temperature change of
the heat receiving plate of the thermosensitive elements at their turn in relation to the Sun
for one angular degree.
Dependence of TSE sensitivity K on the angle
α
between the normal to the heat receiving
plate and the direction to the Sun obtained on the basis of the experimental data is presented
in fig. 12.
Thus, at the average TSE sensitivity equal to 1,2°С/ang.deg., determination accuracy of the
direction to the Sun can be 5 arc min. at the measurement accuracy of the temperature of
0,1°С, that can be attained at the use of standard resistance thermometers and individual
calibration of each TSE.
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Fig. 11. Temperature dependence of the receiving plates of TSE № 1 and № 2 on the angle
between the normal to them and the direction to the Sun.


Fig. 12. Dependence of TSE sensitivity on the angle between the normal and heat receiving
plate and the direction to the Sun.
Use of Space Thermal Factors by Spacecraft

173
During the experiment we have also studied influence of the material, thickness and area of
thermoconductive plate on its sensitivity. It has been found out that replacement of the
aluminum alloy by cuprum at the production of the heat receiving plate practically has no
impact on TSE sensitivity (fig. 13).


Fig. 13. Temperature dependence of aluminum and copper heat receiving plates on the
angle between the normal to them and the direction to the Sun.
Increase of the area of heat receiving plate enlarges TSE sensitivity at the angle between the
normal to the plate and the direction to the Sun of less than 45°

(fig. 14). Increase of the
thickness of the heat receiving plate significantly reduces its reaction on the changing
direction of the solar radiation (fig. 15).


Fig. 14. Dependence of the temperature of heat receiving plates with the dimensions 20х20
and 40х40 mm on the angle between the normal to them and the direction to the Sun.