The VASCAT uses batteries for energy storage. Batteries have high energy densities and extensive space heritage. Battery life decreases with the amount that the battery is discharged and is quantified by a value of depth of discharge (DOD). Long lifetime systems require a low DOD. Figure 12 shows the relationship between DOD and life cycles.^{14}
Nickel metalhydride (NiMH) batteries have longer lifetimes than nickel cadmium (NiCd) batteries at the same DOD. They last the necessary 17,000 cycles for a DOD of 25%. Nickel cadmium batteries require a DOD of around 13% to last this lifetime and therefore, more battery mass. Nickel metalhydride batteries are chosen for the VASCAT. The battery cells chosen are produced by Sanyo (HR4/3FAU 4500).
Summing the energy column in Table 19 gives the total energy the VASCAT needs each eclipse period:
2.5 Thermal
The thermal subsystem of the VASCAT keeps all components within their operational temperature limits. A thermal control system (TCS) achieves this goal as efficiently as possible by minimizing power consumption, complexity, and mass. A passive TCS, which requires no power or control, is the best solution to minimize these criteria.
A preliminary thermal analysis determines the temperature variations the satellite experiences on orbit. This analysis is presented in Table 20. It assumes a spherical satellite with uniform surface properties. The minimum and maximum power dissipations are estimates from the preliminary power budget. The other values presented are discussed in more detail later in this section chapter.
Table 20: Design parameters for preliminary VASCAT thermal analysis
Symbol

Value

Units

Description

A

1.1

m^{2}

Surface area

D

0.593

m

Diameter of sphere with equal surface area

A_{C}

0.276

m

Crosssectional area of spherical satellite


5.67 × 10^{8}

W/m^{2}K^{4}

StefanBoltzmann constant

Q_{w,max}

88

W

Max power dissipation

Q_{w,min}

56

W

Min power dissipation

H

400

km

Altitude

R_{E}

6378

km

Radius of Earth


1.20

rad

Angular radius of Earth

K_{a}

0.998


Albedo correction

q_{l,max}

258

W/m^{2}

Max Earth IR emission at surface

q_{l,min}

216

W/m^{2}

Min Earth IR emission at surface

G_{S}

1420

W/m^{2}

Direct solar flux

a

35%



Albedo


0.8



Emissivity


0.8



Absorptivity

F

0.331



View factor

T_{max}

58

°C

Worst case hot temperature

T_{min}

53

°C

Worst case cold temperature

Generalized component temperature limits are given in Table 21.
Table 21: VASCAT Temperature Limits (°C)
Description

Cold Limit

Hot Limit

Structural members

45

65

Batteries

0

40

Electronics

0

50

MAPS

0

25

A detailed thermal analysis is performed to better characterize the VASCAT. A thermal model provides information about specific components, such as the MAPS instrument. The VASCAT thermal model is created by dividing the satellite into nodes. Analytically, every node obeys the basic heat transfer equation:

217^{4}

In this equation Q is the net heat flux into the node, C_{p} is the specific heat capacity, which is a measure of how the temperature of the node changes relative to energy input, T is the temperature of the node, and t is change in time. This equation is solved for the temperature of the node if the heat flux is known. Each pertinent component, as well as the bus structure side panels, is assigned to a node. The specific heat of each node is calculated by multiplying the component mass by the specific thermal capacitance of its primary material (typically aluminum).
Nodes transfer heat between themselves by conduction. Conduction couplings are a measure of how a node transfers heat to another node that is touching it. The following equation is the governing conduction heat transfer equation:

218^{4}

The kA/L term is the conduction coupling value, G, in W/K. As shown, G is a function of the contact area between nodes, A, the heat path length, l, and the material thermal conductivity, k. The conduction couplings are calculated using the geometry of the satellite and knowledge of the materials used.
Radiation heat exchange takes place between nodes and space. For the purposes of this analysis, internal radiation between components is neglected. The internal surfaces of the satellite are painted black, which minimizes internal radiative heat transfer. Only radiation from the bus external surfaces to space is considered. Radiation heat transfer is given by:

219^{4}

In this equation A is the surface area, is the SteffanBoltzmann constant, and is the emissivity of the surface. The emissivity of the node is determined from the properties of its thermal coating, and the surface area is found from geometry.
Generation of a thermal model requires knowledge of the heat fluxes (see Equation 217) in addition to the heat transfer paths. Nodal heat fluxes are determined from the internal component dissipations and environmental inputs. Hot and cold cases are considered. The hot case includes the maximum or peak power dissipations from each of the components and the maximum orbit averaged fluxes on the satellite. Likewise, the cold case includes the minimum operational power dissipations and the minimum orbit averaged fluxes.
The internal dissipations are determined by the mission operation requirements and are obtained from the power subsystem. The component dissipations used for each of the cases are given in Table 22.
Table 22: Component internal power dissipations

Total power (W)

Description

Hot

Cold

MAPS

27.2

16.2

Momentum Wheel

25

7

Magnetic Torque Bars

16.2

12.6

Magnetometer

0.001

0.0008

Earth Sensors

16

16

Sun Sensors

5

5

Rate Gyros

6.3

6.3

The orbit averaged fluxes are calculated from information about the satellite’s orbit. The external heat sources are direct solar energy, Earth infrared (IR) and albedo. Albedo is a measure of how much of the sun’s energy is reflected from the Earth’s atmosphere and surface back into space, and is usually given as a percentage.^{6} The cold case analysis assumes the satellite is in eclipse and the only external heat source is from the Earth. The environmental fluxes are shown in Table 23.
Table 23: Environmental fluxes in space (W/m^{2})
Source

Hot

Cold

Solar

1418

0

Earth IR

258

216

Albedo

35%

25%

Totals

2172.3

216

The actual heat input depends on the surface properties of the satellite. Absorbtivity, , is a measure of how much external radiation is absorbed by the surface in question and is dependant upon the thermal coating applied. Emissivity characterizes how much heat the surface radiates according to Equation 219.^{20} The surface properties of various VASCAT external components are given in Table 24.^{6}
Table 24: Surface properties
Component

Coating / Material



Side Panels

Silicon

0.8

0.8

Nadir Panel

White Paint

0.3

0.9

Solar arrays

White Paint

0.3

0.9

The total input power is determined by:

220

In this equation the term in parenthesis is the total orbit average flux in W/m^{2}. View factor, , describes how the surface is oriented relative to the flux vector.
View factor is a parameter that varies depending upon the position of the satellite relative to the orbital frame. For example, the nadir panel of the satellite is Earthpointing, and therefore rarely has a full view of the sun. Therefore, the nadir panel view factor is approximately 0.2. The view factor is determined by the MATLAB code in Appendix A. This code determines the power output from bodymounted solar cells on a hexagonal cylinder at various positions in an orbit. It outputs the projected area that a surface will ‘see’ relative to the solar vector. This projected area is then used to determine the view factor for the external bus surfaces.
The thermal model is assembled after the heat transfer paths are identified and internal and external heat sources are considered. The thermal analysis requires simultaneous evaluation of Equations 217, 218, and 219 at each node. This evaluation is complex due to the nonlinear relationship between the temperature of a node and its resulting heat flux.^{9}
The Systems Integrated Numerical Differential Analyzer (SINDA), a thermal analysis package commonly used in industry, analyzes the VASCAT thermal model.^{3} This software package calculates nodal temperatures based on usergenerated conduction and radiation couplings and input fluxes. The program then uses an explicit forward solution method to evaluate the governing heat transfer equations. The explicit forward method uses the conditions at the current time step, or iterative loop, to calculate the temperature of each of the nodes in the system. It then performs an energy balance check on each of the nodes and varies the time step accordingly. The result is a steady state solution for nodal temperatures.
The MAPS instrument is the mission driver for the VASCAT, so several steps are taken to thermally control it. The instrument is conductively coupled to the nadir and zenith panels of the satellite. Additionally, the nadir and zenith panels are coated with white paint to increase their dissipation to space and reduce their incident heat flux.
The hot and cold case temperatures of the VASCAT components are listed in Table 25. Almost all component temperatures are within their specified limits. The exception is the MAPS instrument. In hot case conditions, MAPS operates at about 0.5 degrees over its hot limit. The model has temperature accuracy limits of ±1 degrees. Therefore, a 0.5 degree temperature violation is deemed acceptable within the scope of this analysis. However, the analysis shows that MAPS is a primary constraint driver for further design.
Table 25: Temperatures of the VASCAT components


Hot Case Temps (°C)

Cold Case Temps (°C)


Description

ID

Predicted

Limit

Predicted

Limit

Side Panel 1

1001

42.6

65

45

45


Side Panel 2

1002

38.4

65

45

45


Side Panel 3

1003

31.2

65

45

45


Side Panel 4

1004

37.3

65

45

45


Side Panel 5

1005

35.7

65

45

45


Side Panel 6

1006

36.5

65

45

45


Nadir Panel

1007

27.0

65

45

45


Top Panel

1008

29.3

65

45

45


MAPS

2001

30.5

30

0

5


Momentum Wheel

2101

38.4

50

0

0


Magnetic Torque Bar

2102

31.6

50

0

0


Magnetometer

2103

37.2

50

0

0


Earth Sensor

2104

35.2

50

0

0


Rate Gyro

2106

42.6

50

0

0


Computer

2201

36.2

50

10

10


Receiver

2202

28.5

65

20

20


Transmitter

2203

36.4

70

20

20


GPS

2204

35.5

65

20

20


Battery Box

2301

35.1

65

45

45


Batteries

2302

34.6

40

0

0


The exterior of the VASCAT is covered in solar cells. Therefore, it is not possible to incorporate a radiator into the design to help dissipate heat from MAPS. However, it may be possible to use conductive straps or fasteners to better transfer heat from the instrument to the satellite. Additionally, a doubler or cold plate might be used to thermally isolate the MAPS instrument from the rest of the satellite. These modifications are detailed design parameters and are therefore outside the scope of this analysis.
This analysis is preliminary and is based upon estimated values. A more indepth analysis should be performed on the VASCAT to determine if a passive thermal control system is indeed accurate. No detailed internal structural configuration has yet been defined. Therefore, the conduction paths are estimated from HokieSat’s internal configuration. In addition, the thermal masses of each of the components are estimates. Finally, a transient analysis, which takes into account the change in variations in temperature of the satellite over the course of an orbit, should be performed to ensure that a passive TCS is adequate.
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