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AERO2705 Space Engineering 1 Assignment 4

By

Cheema, Prasad (311212875)

Chen, Tsung-Kuang (311268781)

Cheung, Martin (311183999)

Lee, Ju-Heon (311247156)

Medina Correa, Alexandre (312168594)

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Contents 1 Mission Overview .................................................................................................................................. 5

1.1 Launch Journey ............................................................................................................................. 5

2 Scientific Package - ALICE ...................................................................................................................... 6

3 Structure ............................................................................................................................................... 7

4 Communications ................................................................................................................................... 9

4.1 Transponder .................................................................................................................................. 9

4.2 Antennas ....................................................................................................................................... 9

4.2.1 Antenna Choice Justification ............................................................................................... 10

4.3 Amplifier ...................................................................................................................................... 10

4.4 Specifications .............................................................................................................................. 10

4.5 Tracking ....................................................................................................................................... 10

4.6 Calculations for Transmissions from the High Gain Antenna ...................................................... 11

5 Power generation, storage and regulation.......................................................................................... 12

5.1 Requirement ............................................................................................................................... 12

5.2 Power distribution flow chart ..................................................................................................... 13

5.3 Generating Power ....................................................................................................................... 13

5.4 Storing Energy ............................................................................................................................. 16

5.5 Energy regulation ........................................................................................................................ 18

5.6 Mass determination .................................................................................................................... 18

5.7 Deploy Mechanism ..................................................................................................................... 19

6 Microcontroller ................................................................................................................................... 20

6.1 The crucial specification .............................................................................................................. 20

6.2 Table of microcontrollers: ........................................................................................................... 20

S3C2440(Samsung 2004) ........................................................................................................................ 20

SAK-C161PI(e Infineon, 1999) ................................................................................................................ 20

6.3 Memory ....................................................................................................................................... 21

6.4 BUS Structure .............................................................................................................................. 21

6.5 Computer Platform and dimension............................................................................................. 21

6.6 On Board Clock ............................................................................................................................ 22

7 Propulsion ........................................................................................................................................... 22

7.1 Apogee Engines ........................................................................................................................... 22

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7.2 Fuel Tank ..................................................................................................................................... 23

7.3 Fuel Requirement ........................................................................................................................ 24

8 Thermal Control .................................................................................................................................. 25

8.1 Thermal Balance ......................................................................................................................... 27

9 Attitude control ................................................................................................................................... 29

9.1 1N Thrusters ................................................................................................................................ 30

9.2 Gyroscopic Microwheels ............................................................................................................. 31

10 Landing Sensor ................................................................................................................................ 32

10.1 Introduction ................................................................................................................................ 32

10.2 Design Description ...................................................................................................................... 32

10.3 Circuit Diagram ............................................................................................................................ 33

10.4 Derivation .................................................................................................................................... 33

11 Prototype ........................................................................................................................................ 34

11.1 Testing and Calibration ................................................................................................................ 35

11.2 Results of Tests ............................................................................................................................ 35

12 Conclusion ....................................................................................................................................... 36

12.1.1 X Appendix .......................................................................................................................... 37

12.1.2 X. 1 Motivation and Method for Mass Moment of Inertia Calculations ............................. 37

12.2 X.2 Internal Components and Corresponding Mass and Dimensions......................................... 38

12.3 X.3 Internal Components and their Individual Mass Moments of Inertia .................................. 39

12.4 X.4 Internal Components and their Deviation from Mass Centre ............................................... 40

12.5 X.5 Internal Components and their Final Mass Moments of Inertia Relative to Mass Centre ... 41

12.6 X.6 Centre of Mass ...................................................................................................................... 41

X.7 Labelled Figures Corresponding to Inertia Table Numbers ............................................................... 42

13 References ....................................................................................................................................... 47

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Part A- Design of a Comet Intercepting Spacecraft 1 Mission Overview The aim of the mission it is to study the composition of the comet, and how its nucleus, tail and coma

interact, in order to try and verify the validity of the Oort cloud. The hypothesis is that most comets

today come from the Oort cloud, and so we shall determine this comet’s properties using the ALICE

spectrometer. (Note that the name ALICE is not an acronym, it is simply a name that its principal

investigator enjoys). We will obtain these results and compare them to previous studies on comets and

see if comet composition and properties are similar. If so, it may lead to suggest that they came from the

source, the hypothetical Oort cloud.

This satellite’s main objective is to therefore observe the UV electromagnetic waves produced by the

comet as it travels. In addition to this it shall search for thermal markers in the comet via the UV

spectrum. These thermal markers are noble gases. Because of the noble gases’ inability to chemically

combine with other chemicals, they will indicate the approximate temperature the comet formed. For

example if Neon appears to part of the comet’s original material, one can imply that the comet originally

formed in a region of space of which the temperature was less than 16K. This will give us a strong clue in

regards to the Oort cloud theory. After achieving the main purpose of the comet interception and

compositional analysis, the satellite shall enter phase B operation to get approach the comet to within

one centimetre, almost contacting the comet. A conceptual contact sensor can be found towards the

end of the report.

Once this operational period of the satellite ends it will mark the official End Of Mission (EOF) whence

the comet and satellite will pass the mean orbit of Mars around sun. In order to achieve the operations

described above, modular and redundant subsystems are developed and formulated, tackling various

solutions to an operational satellite.

1.1 Launch Journey The launch trajectory from earth to the satellite will follow one of the flight path planned out in previous

stages using Atlas IIA as the carrier vehicle. The launch vehicle will perform all velocity change necessary

from the surface of planet earth to around 50 km away and 50m/s velocity difference of the comet. This

will include inclination change, orbital change, and velocity change including reduction where necessary.

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2 Scientific Package - ALICE ALICE is a unique UV Spectrometer which allows UV Mapping within the sensors Field of Vision (FOV),

used originally at the NASA´s Rosetta Orbiter. The sensor works by allowing UV light to enter through the

Aperture door which is then reflected off to an Entrance Slit via Off Axis Parabola mirror (OAP mirror).

From the slit, the light hits the toroidal holographic grating which is then dispersed onto a micro channel

plate detector (MCP) that uses a double delay readout scheme to save the image. By having multiple

shots we can determine the elemental emission of comet with respect to time.

The Sensor itself is actually controlled by an independent microcontroller (SA 3865), which can of cause

be removed and attached to our own microcontroller if so desired. However, leaving the microcontroller

does have some benefits. The biggest advantage is that the sensing is not multiplexed with other sensors

aboard the satellite, and its RAM can be purely dedicated to the UV sensing.

(ALICE placement in the Satelite)

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(Detail drawing of ALICE)

3 Structure The mechanical structure for the satellite is of the upmost importance as it will act as:

1. The primary shield from radiation via the panel 2. Provide a house for our components and payload 3. Act as a shield and energy dissipater against external mechanical shocks.

In order for the above criterion to be satisfied the mechanical design shall be constructed as follows:

The fuel shall be stored in a Ethylene Propylene Diene Monomer (EPDN) bladder tank (Astrium® standard material)

Around the bladder tank there shall be a box housing the bladder tank made of an aluminium-aluminium honey comb structure. This is because aluminium has high strength to weight ratio, and the honey comb structure further strengthen the structure (in an axial direction relative to the honeycomb) with very little material density.

Surrounding this shall be a frame structure built of ten carbon fibre reinforced plastic struts (type GY 70). This framework shall provide the necessary interface to connect to the six side panels of the cubesat-like structure. Moreover, because of its frame design it will allow spacing for wiring and components to be fitted with adequate space.

The six side panels shall be composed of aluminium face integrated about an aluminium honeycomb structure. The panels are removable for an appropriate integration of units into the structure, allowing modular design approach.

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Along the carbon fibre internal framework there shall be thin strips of magnesium metal (Elektron 21) physically bonded to the carbon fibre and allowing a structure for the aluminium based panels to be bolted to. (The aluminium cannot be bolted to the carbon fibre, due to the brittle nature of carbon fibre).

Carbon Fibre Frame

Aluminium Honey Comb Panel Covered in Kapton

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4 Communications The factors that have been considered for the communications subsystem include:

Data transmission rate

Power consumption

Size of communications components

Directional considerations of transmissions

Interference due to Earth’s atmosphere.

4.1 Transponder The transponder that will be used is the X/X Deep

Space Transponder, produced by Thales Alenia Space

(2012). X-band frequency signals shall be

transmitted, as higher data rates can be transmitted,

although it will require more power. The

transponder’s uplink frequency is in the range 7145-7235 MHz, and the downlink frequency is 8400-

8500 MHz. S, X and Ku-band frequencies were considered. However, X-band frequencies were chosen as

they allow greater data transmission rates and although Ku-band frequencies have even greater data

rates, they are sensitive to interference by water droplets in the atmosphere. These frequencies are fully

compatible with the Deep Space Network stations in Canberra, Madrid and California.

4.2 Antennas The Antennas that will be used include four Low Gain Antennas, for receiving and transmitting signals to

and from Earth (uplink and downlink). Four LGAs have been decided upon so that there will always by an

antenna receiving signal from Earth, regardless of the spacecraft’s attitude. In addition, a 0.6m- (mean)

diameter High Gain Antenna will be responsible for transmitting data back to Earth (downlink). As the

spacecraft travels towards the comet, the Low Gain Antenna, which is omnidirectional, will be used for

tracking the spacecraft and sending simple correctional thrust commands to the spacecraft. After

analysing the comet’s composition and making measurements using the scientific instruments, the Low

Gain Antenna will be used to receive commands to rotate its attitude so that the High Gain Antenna,

which is unidirectional, faces the Earth, at which point, the High Gain Antenna will transmit all the

scientific data (such as images and spectral observations) back to Earth (telemetry). This was decided

because High Gain Antennas can transmit far higher data rates than Low Gain Antennas, over a long

distance, and therefore Low Gain Antennas will be used for small data transmissions such as tracking and

command.

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4.2.1 Antenna Choice Justification

For the high gain antenna, a 1.5 m diameter antenna paraboloid antenna will be used, similar to the one

used on the NEAR Spacecraft mission. This specific antenna has been chosen as it is relatively light (6.3

kg), consisting of a graphite-resin material on a Nomex honeycomb core. The antenna is also very

efficient with 63% at 7.2 GHz and 58% at 8.4 GHz.

(Bokulic et al. 1998)

As for the Low Gain Antenna, four Microstrip patch

antennas, one on each of four faces of the spacecraft,

will be used due to its very low mass and small size,

which is good as weight must be minimised. It will only

take up a 5 cm square of area on each face, but it will

have a beamwidth of 90 degrees, allowing full

reception at all attitudes. The operating temperature

range is from -65 degrees to 100 degrees, making it

suitable to place on the outside of the spacecraft.

(Antdevco 2009)

4.3 Amplifier The transponder has an in-built input filter to filter out high-noise signal, and a power amplifier that will

amplify signals which would have been weaken during transmission, due to the inverse square law.

4.4 Specifications

Mass Power Consumption Dimensions

Transponder 3.3 kg Receive: 8 W, Transmit: 38 W

258 x 148 x 195 mm

High Gain Antenna 6.3 kg Depends on transponder 1.5 m diameter

Microstrip Patch Antenna (uplink

specified at about 7200MHz) (Antdevco

2009)

50 g x 4 Can handle at least 10 W of power

50x50x3 mm

4.5 Tracking The tracking of the spacecraft involves Doppler, Ranging and Delta Differential One-way Ranging. In

order to calculate the velocity of the spacecraft, the Deep Space Network control centre will measure

the Doppler shift of the frequency of the signal that is being transmitted from the Spacecraft (NASA

2012). In order to determine the range of the spacecraft, the time that it takes for the signal to travel

from the ground station to the spacecraft is measured. Delta Differential One-way Ranging (Delta-DOR)

involves using two widely-separated ground antennas (two of the Deep Space Network Complexes) on

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Earth to track the spacecraft in order to measure the time difference between the signals. As this delay

measurement is affected by various sources such as the interference by the ionosphere or solar plasma,

in order to provide calibration for these errors, a Quasar, which is a well-known radio source in the sky, is

also tracked. The delay time of the quasar is subtracted from that of the spacecraft's to provide the

delta-DOR measurement, or the angular separation of the Quasar from the spacecraft. This

measurement is accurate to 5-50 nanoradians. (NASA 2012)

4.6 Calculations for Transmissions from the High Gain Antenna The power transmitted to Earth’s Deep Space Network from the spacecraft’s High Gain Antenna can be

approximated by the following equation:

2

2 2Watts

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T T R

received

P G GP

d

Where:

TP =Power transmitted (W),

RP =Power received (W),

TG =Gain of transmitting antenna,

RG =Gain of receiving antenna, d =distance between antennas (m), =wavelength (m)

The power transmitted (T

P ) from the antenna is 38 W (from transponder specifications). The gain of the

transmitting antenna (T

G ) is estimated to be about 38.6dB (UHF Satcom), as the Dawn spacecraft, which

was launched in 2007, had used a similar 1.5 m high gain antenna. This corresponds to a voltage gain of

85.1 from the formula 10( ) logPower dB VoltageGain . The Deep Space Network antenna in

Goldstone, California, which has a diameter of 70 m, has a gain of approximately 85.87 dB. This is

equivalent to a voltage gain of about 19658.2, from the formula above. The wavelength transmitted ( )

is about 0.035 m (taking the transmitted frequency as 8500 MHz). The maximum distance between

antennas ( d ) will be assumed to be twice the distance from the Earth to the Sun, because, at the comet

intercept point, the spacecraft and the Earth will be approximately on opposite sides of the sun.

Therefore, d will be taken as 62 150 10 km (NASA n.d.).

As such, the Power received at the Deep Space Network can be determined:

2

21

22 9

38 85.1 19658.2 0.035Watts 5.48 10

16 2 150 10received

P W

The power received is very small, in the order of 10-21, in accordance with the inverse square law. This

strengthens the need for power amplifiers to be used in Deep Space Network complexes to receive data

from our spacecraft.

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5 Power generation, storage and regulation

5.1 Requirement

Power will need to be generated to support the on-board electronics of the satellite to carry out the

mission. This energy will be generated by solar panels made by Emcore, and will be used to charge up a

set of batteries. The batteries will act as a power bus generating enough power to supply energy to:

Communication systems – 62W max

Central control systems – 45W

Science instruments - 4W

Positioning and attitude control electronics – 48.25W average, additional 100 max

The average power requirement is about 160W given the energy needed for the above electronic

systems, to have some margin of safety, power requirement will be aimed at 200W, and the peak power

delivery will be taken care by the on-board battery.

The following table is the overall scope of the power requirements for each component, summarising all

parts of the report where power is needed.

Category Component Power Voltage Requirements

Comms X/X Deep Space Transponder Receiver: <14W, Transmitter: 38W 22-35 V

Low gain antenna 10 W 22-35 V

attitude Astrix 200 6W per channel (4 channels) 22-50 V

1N Hydrazine Astrium Thrusters 6.4W + 6.5W 16V-strict

100SP-O SSTL min-1.2W, av- 10W, max- 113W 17-35V

sun sensor 1.35W peak 5-50V, average 7.5mA, 27mA peak

science Alice 4.0W 5~7V

control Bus Structure 40W 19-25V

System Clock 5.0 W 10V-strict

Total Power ≈160W 22V for most of them

Devises will have an average voltage requirement of 25V as an estimate from the table, so the average

current needed will be

𝑐𝑢𝑟𝑟𝑒𝑛𝑡 =𝑝𝑜𝑤𝑒𝑟

𝑣𝑜𝑙𝑡𝑎𝑔𝑒=160

25= 6.4 𝐴

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5.2 Power distribution flow chart

The above is a power bus structure illustrating how the power is distributed around the satellite. The

power generated will be all stored into the battery set via a protective circuit shown later in this section.

The set of batteries, due to the set output voltage they have and the range of voltages some of the

components can have, are connected either directly to the components or via a set of voltage regulators.

The on-board computer will also be connected to both power regulators for use, and to monitor in the

case of voltage regulator failure and switch to the backup ones

5.3 Generating Power

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To generate power, space-rated high efficiency solar panels, the ZJT triple junction photovoltaic cells

(Emcore 2011), are chosen to power the comet intercepting satellite. The ZJT has 29.5% minimum

average efficiency compared to average solar panels performing about 17% at best (SRoeCo Solar 2012).

It also has very low cell mass, at 84mg/cm^2, making it ideal for space applications.

To provide infrastructure and protection to the solar cells, aluminium and Gorilla Glass (Corning 2008)

are used with density of 2.7g/cm^3 and 2.45g/cm^2 respectively. Aluminium is selected for its high

strength to mass ratio and Gorilla Glass is very hard to abrade, meaning a large amount of photons can

still be converted into electricity over time even if debris does graze the surface.

Given the above information, calculations are carried out to find out the surface area needed to power

the satellite system. The satellite will fly further away from the sun, by our intercepting trajectory,

therefore the mission duration is estimated to be the window between the satellite’s meeting point with

the comet until they pass together beyond the orbit of Mars, at which point solar panels are deemed to

be insufficient to power the entire system. With redundancy of power generated, the system will most

likely continue to operate even beyond this point, but the satellite requirement will be based on this

point and mark it as the intended end of mission (EOM) for this satellite.

Graph of light intensity verse distance

The above plot is the light intensity (W/m^2) decay plot from Earth to Mars, so if the power is sufficient

at Mars’ average orbit around the sun which is the estimated EOM of the satellite, then the sun’s light

intensity will have a parabolic increase any point before EOM.

While the solar panels will operate at 29.5% efficiency, the intensity of light at Mars is 589.2 W/m^2

(NASA n.d.) and light transmission through the protective glass on board the solar cells is about 90%

(Corning 2008), thus the minimum surface area of solar panel required at a mean distance to Mars orbit

can be calculated as follows:

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𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 ∗ 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 ∗ 𝑙𝑖𝑔ℎ𝑡 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑

= 589.2 ∗ 0.295 ∗ 0.9 = 156.43 𝑊 𝑚−2

Therefore, to achieve 200 watts of power, 1.3 meter squares of solar panel will be needed

200

156.43= 1.2785 ≈ 1.3 𝑚2

This power has degeneracy so the solar panels will ensure sufficient power well after designed EOM. This

is also necessary to account for damaged of solar cells and decrease in efficiency over time.

(Emcore 2011)

As can be seen in the above I-V plot, maximum power will be generated at 2.41V and 16.5 mA/cm^2,

with a solar cell area of 26.6 cm^2. Therefore to generate the average 25V needed we will need about 11

of these solar cells connected in series.

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2.41= 10.37 = 11(𝑟𝑜𝑢𝑛𝑑 𝑢𝑝)

One cell will generate 16.5x26.6=438.9mA≈0.44A, so to have the required 6A, will need about 14 cells

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0.44= 13.64 = 14(𝑟𝑜𝑢𝑛𝑑 𝑢𝑝)

These shall be placed in series with each row producing 25V. Therefore the total number of cells will be

14x11=154 cells.

Which translates to only 0.41 m^2, but the solar cells are about 30% efficient so total area required will

be 1.35m^2 which coincides the area needed to generate the total power needed at 1.3 m^2.

462 𝑐𝑒𝑙𝑙𝑠 𝑖𝑛 𝑡𝑜𝑡𝑎𝑙

To achieve this efficiency, the optimal voltage/current will need to be drawn from the solar panel and

this will be controlled by Maximum Power Point tracer (MPPT) (Iannello n.d.) which will be incorporated

into power control system in the micro controller.

5.4 Storing Energy

The electrical energy generated will then be stored into a series of Polymer Li-ion battery so all the

power output is from the battery to regulate voltage supplied. It is chosen for its high power density per

unit mass that it has 6Ah capacity for only 122g. Appropriate voltage regulators will be incorporated to

deliver correct voltage to different electrical components which will be discussed in the subsequent

section. Also, the batteries will be designed to supply power to the entire satellite system should the

solar panels be not facing the sun directly during attitude change, for up to 10 hours.

The battery Chosen is shall be the XK-605068*3P by Xingke Professional Li-ion Battery Co., ltd. (XTD n.d.)

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Given that the system needs 6A in total, and the max discharge current for the battery is 2A, then 3 will

be connected in parallel. To deliver the 25V required, number in series will be 25/3.7≈7 so,

𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑡𝑡𝑒𝑟𝑦 = 3 ∗ 7 = 21

This will allow nominal capacity of 12Ah which will last the system for 20 hours without any solar

radiation. The battery is also rated to charge at least 300 times, since the system is using power bypass,

so there is will be very small charge/discharge cycles

The battery set also has built-it protective circuits to prevent over charge when the satellite is still near

earth’s orbit around sun, using transistors and diodes limiting directions of current and act as switches

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Overall, the power generating system is designed to have a certain degree of redundancy so that the

area to capture light is larger than the actual power needed; in other words the light intensity shall be

larger than the intensity used to calculate for most part of the mission; the batteries will function as

backups rather than actual power supplies because there should not be obstructions to sunlight.

Therefore the power generating system will ensure power availability on average, as well as whenever

there is a power surge. All power consumptions of the component are taken at the maximum for the

purpose of the calculation apart from the attitude change gyros which will have additional 100W when

activated on full torque, but this will be covered by the redundant battery system and it will only rarely

enter such mode of operation. This redundancy is necessary to take into account for degradation or

damage to the solar panel and reductions in storage capacity of batteries over time, to ensure a

continued operation of the satellite.

5.5 Energy regulation While most of the components will work at 25V, there are a few that work at a smaller voltage and some

have no range and will have to have a strict voltage to operate. Therefore the subsystems that can take in

variable voltage will be directly powered by the battery, the others will use a voltage regulator such as

the HS-117RH by Intersil (2012).

This will be used to regulate sensitive instruments and act as step down transformers to components

require lower voltages and divert power out from the power bus. This is radiation hardened, 300 krad (Si)

(Max) (Intersil 2012), to prevent damage, because if this is damaged then the subsequent component.

Due to the small size, this can be made redundant and make duplicate component to allow proper

functionality of satellite should any of the regulators fail.

5.6 Mass determination Given all the density of the glass, aluminium frame, cells and the individual mass of the batteries, the

total mass contribution will be, using the equation:

𝑚𝑎𝑠𝑠 = 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 ∗ 𝑣𝑜𝑙𝑢𝑚𝑒

Where the volume is found using the area of the solar panel, taking the thickness of frame to be 1 cm

and glass to be 0.5 cm. all calculated values are rounded up to consider for the edges of the solar panel

assembly. Results are the following:

Photovoltaic cells

1.1kg

Glass cover

16kg

Frame of solar cells

36kg

Batteries

2.6kg

Voltage regulator

A few grams only so negligible

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5.7 Deploy Mechanism

Each solar panel will have three parts, 2 folded panels (diagram only for illustration) and one rail holding

the panel out to prevent damage from the attitude control thrusters. The unfolding process will be

passive, using springs in tension to pull the panels and rails outwards until it is perpendicular to the

satellite. With details shown above.

Due to the temperature that the hinge will likely to freeze a thermo-foil will be attached to each hinge

and these will be powered directly from the solar panels in order to ensure the solar panels will properly

unfold. To not waste power after unfolding is complete, a switch will be in place of the hinge between

the two folded panels and once contact it locks the structure of the panels in place and cuts the current

to the thermo-foil to conserve power. Also solar panel deployment will happen during early stage of the

mission when the satellite is still close to the sun so power requirement of the thermo-foil will not be a

problem.

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6 Microcontroller Choosing a microcontroller for any application (including satellite operation) is completely subjective.

Every microcontroller has their own gamut of unique properties(Duane Benson 2012). That being said,

most microcontrollers’ operational details carry similar characteristics, and therefore similar in the

manner they work. They all use PORTs to control I/O devices, and uses bus to network the data from

memory to CPU to the actual I/O devices themselves.

Due to this objectivity, we are going to make the assumption that we can obtain any sufficiently skilled

programmer to code our software. This will allow us to solely pick our microcontroller based on specs

alone.

6.1 The crucial specification Power consumption: Because we are working with limited power supply, all our sub-system

must be power efficient.

Radiation Hardened: despite our satellite already built to reflect radiation, we need to

guarantee that the microcontroller will not malfunction because of radiation.

Temperature Range: similar reason to Radiation Harden

E-Clock Frequency: higher the frequency, the faster the codes executes

6.2 Table of microcontrollers: Microcontroller Power consumption (power

consumptions are approximate) Temperature range

E-Clock Frequency

Radiation Hardened

TC1775(Infineon, 2005)

137.5 mW ( = ∑ =

2.75 50 𝑚𝐴)

-40~125 40 MHz Unknown

80C32ERP(Space electronics Inc. 1999)

275 mW ( = ∑ =

5.5 50 𝑚𝐴) (for 36MHz)

-65~150 1~12 MHz Yes (>100 Krad)

SuperH RISC(RENESAS 2012)

720 mW( = ∑ =

3.6 200 𝑚𝐴)

-40~85 50~100 MHz No

S3C2440(Samsung 2004)

368 mW -40~85 66 MHz Unknown

SAK-C161PI(e Infineon, 1999)

275 mW ( = ∑ =

5.5 50 𝑚𝐴)

-40~125 1~50MHz (depending on the mode)

Unknown

As shown above, we see that 80C32ERP has the least power consumption as well as being sufficiently radiation-hardened. The E-clock frequency is the smallest out of the group, meaning its processing speed is the slowest out of the group. However this is not a huge problem, since this will only control the satellite’s thrusters while all the work done by the spectrometer will be done via its own microcontroller – the SA 3865.

Hence choosing the 80C32ERP is the best choice out of the 5 listed microcontrollers.

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PORT1: Thrusters

PORT2: Gyroscopic

reaction wheel

PORT3: FOG

PORT4: Range sensor

NOTE: Although power consumption is 275 mW, this is when there is there is no hardware connected to the PIN. We will assume that once all the sensor and hardware are connected, it will consume 40W (which is approximately the power consumption of a small laptop).

6.3 Memory As for the memory, any RAM which has been radiation hardened will suffice, as we do not require large

computational power to control the satellite. As for the flash memory which will provide storage for the

data, a radiation hardened 25 GB Solid State Drive should be used for fast data writing and reliability

(Glassmeier ).

6.4 BUS Structure

6.5 Computer Platform and dimension All these components (save for the SSD which will be integrated separately to accommodate SA 3865)

will be put together on a platform which can be custom made by Etratech. The board’s dimension will be

20x15x5 cm to allow room for RAM (Micah McDunnigan, 2012), pins and the microcontroller itself.

Transponder

Antenna

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6.6 On Board Clock The on-board clock that shall be used is a Miniature Rubidium Atomic Clock known as the SA.32m. The

SA.32m consumes 5W of power in a steady state condition. Moreover the SA.32m is rated to an

accuracy of between +/- 1.5 ms.

7 Propulsion

7.1 Apogee Engines The satellite will be launched from the Atlas IIA after the launch system arrives at the Comet´s orbit. The

satellite will be launched from a transport rocket, which will make the proper arrangement of position

and velocity, and then the satellite will be launched with a difference of 50m/s relative to the comet, in

the same direction. Thus, we need a powerful apogee engine to launch the satellite from the launch

vehicle to the comet’s orbit. The engine must be designed for long term steady state, and also pulse

mode if necessary during positioning corrections at comet’s orbit.

The 400N Hydrazine Thruster CHT400 designed by Astrium® (Astrium 2012, 400N Thruster) is going to be

used in the mission, since it is a heavy duty thruster designed for injection of spacecraft payloads into

their initial orbits. The propellant used is Hydrazine, which gives us a maximum ISP of 224 seconds (214 –

224s), this high specific impulse is good for producing enough thrust for the orbit transfer and for fuel

saving, since we can produce a big amount of thrust with not so much propellant. Moreover the

hydrazine does not require a liquid oxidiser in order to operate in the space environment. All that is

needed is a heated catalyst bed for the hydrazine to pass through. This catalyst is typically of a high

surface area alumina-iridium nature.

This propulsion system also has good reliability since it was used on all Ariane 5 versions to date. The

manufacturer guarantees us a cycle life of 6000 cycles, or at least 1745 seconds of accumulated burn life.

(Although one should always be wary of the manufacturers’ claims). The system is also covered with

thermal insulation for an optimum start up condition, but it is also qualified for multiple cold starts. The

inlet supports pressure from 6.0 to 26.0 bars.

23

Figure Y.1 400 N Hydrazine Thruster in Feedthrough Housing [Astrium 2012, 400 N Thruster]

7.2 Fuel Tank For this mission, the system needs about 450kg of hydrazine to achieve the comet’s orbit from launch at

LEO and then make position and attitude correction for the mission objective. The better option is using

a bladder tank. This is a flexible tank that decreases the internal volume as fuel is consumed.

Our tank is going to be based on Astrium® BT01-0 bladder tank [Astrium 2012, BT01-0 39L tank]. The

tank should have a 400l internal storage, then, based on the BT01-0 specifications, it should have a 500l

volume and 40kg. The tank structure is made of titanium and has a spherical geometry.

The pressure gas will be helium. The bladder is made of Ethylene=Propylene-Diene Monomer (EPDM),

this synthetic elastomer have a high resistance to polar substances, heat and have excellent electrical

insulating properties, good for the storage of hydrazine. The model is very reliable since it was used on

the Ariane 5ACS project in a combination with clusters of the 400N CHT400 thruster.

Figure Y.2 – BT01-0 Bladder Tank [Astrium 2012, BT01-0 Tank]

24

7.3 Fuel Requirement The satellite will be launched from the transport rocket with a difference of 50m/s with the Comet´s

velocity. For calculate the fuel requirement for the transfer we must use the following equation

[Braeunig, 2009, Impulse and Momentum eq.1.20]:

𝑀0 = 𝑀𝑓 ∗ 𝑒𝛥𝑉

𝐼𝑆𝑃∗𝑔𝑜

Then, making the proper arrangements:

𝑀𝑓 =𝑀𝑜

𝑒𝛥𝑉

𝐼𝑆𝑃∗𝑔𝑜

𝑀 𝑟𝑜 𝑒𝑙𝑙𝑎 = 𝑀𝑠𝑎 𝑒𝑙𝑙 𝑒 ∗ (1 −1

𝑒𝛥𝑉

𝐼𝑆𝑃∗𝑔𝑜

)

Then, for our satellite we have the following equation, using an average ISP for Hydrazine 400N Thruster

of approximately 220s at vacuum for facilitate the calculations. The surface gravity of Sun is 274m/s²

[NASA 2012, Sun Fact Sheet].

𝑀 𝑟𝑜 𝑒𝑙𝑙𝑎 = 𝑀𝑠𝑎 𝑒𝑙𝑙 𝑒 ∗ (1 −1

𝑒50

230∗9.81

) = 0.0219 ∗ 𝑀𝑠𝑎 𝑒𝑙𝑙 𝑒

Considering that our dry satellite mass approximately 340kg and that we are carrying 400l of hydrazine

(1.021g/cm³), corresponding 320kg, we have a total mass of approximately 660kg. For this total mass,

we have enough fuel to launch the satellite from the transport rocket with a velocity of 50m/s from the

comet´s velocity, and then arrive on the comet at same velocity, after that we have enough fuel for

corrections and changes of position and attitude and also for control during the approximation to less

than one meter towards the comet surface. Using this bus structure and carrying this total amount of

fuel is sufficient to able our satellite to make a velocity change of more than 2600m/s, as we can see

below:

𝛥 = 𝑆 ∗ 𝑔0 ∗ 𝐿𝑁𝑀𝑜

𝑀𝑓→ 𝛥 ~2600

𝑚

𝑠= 𝟐. 𝟔

𝒌𝒎

𝒔

25

8 Thermal Control The thermal control of the satellite must maintain temperature stability for the payload structure,

principally for the sensors and detectors, which are the most sensible parts of the satellite. First we need

to check both operational and survival temperature for each kind of component; the satellite will be

built under Earth’s temperature and atmosphere, so we have to maintain the best range of temperature

variation. For long-term temperature requirements, generally the system will be at 20⁰±2⁰C when the

payload is operational. Then, we have to use proper thermal enclosures to balance the temperature

from internal and external disturbances.

Using general values of temperature range, we must set our satellite to operate between 0⁰C and 35⁰C,

the minimum and maximum temperatures over the survival temperature that make all components

operational (Table X.1). Most of the heat will came from internal heat transfer and solar radiation, since

we don’t have “friction” since most part of the flight will be at vacuum.

Table X.1 – Components Survival and Operating Temperature

Since the satellite will be under solar radiation exposure, we need to apply a proper insulation to prevent

heat transfer to inside the structure. Then, the solution is using a Multi-Layer Insulation (MLI). In this

case, we are going to use a Dunmore™ MLI. The MLI must have a very low conductivity, a good

dimensional stability, low cost and weight. The best option is using a 13 layers Dunmore™ Two-sided

Aluminized Polyester Combination MLI [Dunmore, n.d.] that combines, strength and easy conformable

with just 0.059kg/m² with a emissivity of 3.5%. Since it contains a metalized surface, it will reflect the

radiation of the sun, preventing overheating of the internal components, as well as keeping the heat

produced by the components inside the satellite.

Internally, we must use a cryogenic insulation on the fuel tanks to prevent internal heat transfer. The fuel

must be under a low temperature, less than the operational temperature to maintain the system under

an optimum temperature. To prevent this heat flow, the solution is using insulation for the fuel tank. A

RUAG™ Coolcat 1 [RUAG, n.d.] fills the requirements since we can apply insulation from 300K to 77K

(27⁰C to -196⁰C). The blanket is very light and the conductivity less than 1W/m².

26

Although, just using insulation will not maintain the temperature by itself. All the components of the

payload and system produce heat when operating, for that we need to use other kind of thermal

components to distribute the heat inside the satellite, and even to dissipate waste heat from the device.

For prevention of over-heating components as louvers and thermal radiators can dissipate the waste

heat and maintain the temperature optimized for the components operation. The radiator must have an

effective thermal conductivity, then the best option is using a Thermacore ™ k-Core® passive high-

performance solid conduction system [Thermacore, 2010, k-Core®]. The k-Core® is lighter than

aluminum, which also helps to fill mass requirements, that is possible because the radiator is made of

Annealed Pyrolytic Graphite (APG). The radiator has more than 1500W/(m.K) of thermal conductivity

and also is very strong since it uses aluminum as shell material of the structure. They have a reliable

operation within -40°C to +72°C. On the satellite we will use 3.38 kg/m³ radiators with 1.5mm thick.

Thermal Louvers (fig.X.1) are high-efficient devices for controlling the temperature of a satellite. The

system is activated by sensing the temperature of a space radiator and react to control the temperature.

There are no power requirements since the actuators work by contraction of a bi-metallic sensor and

then it rotates the blades of the system to allow heat dissipation by reflection trough the highly polished

blade surface, also the system is capable of operation within an external environment range of -85°C to

120°C over 30,000 cycles with no degradation in performance.

Figure X.1 - Typical Thermal Louver Assembly Schematic [Orbital, n.d.]

We are going to use one Orbital® 61201 Thermal Louver [Orbital, n.d.] for each radiator, with 22 blades

to reflect and dissipate waste heat from the satellite.

The Thermal Control System of the satellite must also prevent the low internal temperature of the

components. Then, to maintain the components at a proper temperature we must add heaters to

prevent temperatures below the survival temperature of each component. For this case the solution is

use a light Kapton™ Insulated Heater. The Holroyd® Kapton™ Insulated Heater [Holroyd, n.d.] can fill this

requirement with polymide heater since they can suit any application requiring surface heating up to

200⁰C. The heater is made from a semi-transparent, flexible, thin material.

27

For the thermal balance inside the satellite we also are going to use heat transfer from hot areas (as

engine) to cold areas. This heat flow will be enabled by sing Thermacore® Therma-Loop® [Thermacore,

2010] passive heat pipes inside the satellite structure.

This type of pipe is flexible and also resists gravity loads (is capable of resisting 9g). The system can be

very simple, with a evaporator nearby the engine are, to take temperature from this area and

condensers spread into cold areas of the satellite (fig.X.2). As refrigerant we use Ammonia, since NH3

boils at −33.34 °C at a pressure of 1 atmosphere, the liquid must be stored under high pressure or at low

temperature [Wikipedia, 2012, Ammonia, para.2].

Figure X.2 - Loop Pipe Structure [Thermacore, n.d.]

8.1 Thermal Balance For the thermal balance of our system, the thermal control components must be capable to control the

heat inside, spread the heat that is not necessary and also maintain the proper temperature internally at

satellite. For long-term temperature requirements, generally the system will be at 20⁰±2⁰C (293.15±2K)

when the payload is operational.

We can also say that a suitable thermal balance requires that all the heat dissipated by electronics and

the energy absorbed from Sun radiation. Then, we can estimate the area of radiator panels to maintain a

temperature of approximately 295K, desired for an operational payload.

Since our satellite will be far away from Earth, we need to consider the Sun energy influence at our

satellite. Then, since we are going to intercept the comet nearby Earth´s orbit around the Sun, we can

consider that the distance between our satellite and Sun is approximately 1AU (Astronomical Unit, ~

149,597,871km). At this distance, the solar flux is approximately 1367W/m² [Poinas 2004]. We are going

to neglect Earth´s influence for now, since the aim is to get as closer as possible to the comet.

28

Figure X.3 – Solar Intensity x Sun Distance [Poinas 2004]

Then, since we are accounting just the Sun influence as external source, the power absorbed can be

calculated as:

= 𝐸𝑀𝐿𝐼 ∗ 𝐴𝑟𝑒𝑎 ∗ 𝑞𝑠

Where 𝐸𝑀𝐿𝐼 is the emissivity efficiency of our multi-layer insulation coat; 𝐴𝑟𝑒𝑎 is the area which is going

to receive the emissivity and 𝑞𝑠 is the solar flux. We are going to estimate a 2m² of the solar panels,

for security of the system. The emissivity of the Dunmore® MLI is approximately 3.5%. Hence, the power

absorbed can be calculated as:

= 0.035 ∗ 2 ∗ 1367 = 95.7𝑊

We can consider that the components are going to dissipate an approximately power of 130W. Then the

total power, absorbed and emitted, on the satellite will be 225.7W.

Then, the radiator must be efficient to emit the unnecessary heat from the satellite, hence, the power

emitted by the radiator can be calculated as:

𝑄 = 𝐴𝑟𝑎𝑑 ∗ 𝜎(𝑇14 − 𝑇2

4)

Where the power emitted depends on the area of the radiator, the required temperature, the external

temperature (cold space temperature, ~2.7K) and the Stefan-Boltzmann constant (5.67 ∗ 10−8𝑊/

𝑚2𝐾4). Then, since we have that the radiators must at least dissipated the produced and absorbed

power, the power emitted must be 225.7W. Then, the area required is:

𝐴𝑟𝑎𝑑 =225.7

[5.67 ∗ 10−8 ∗ (2954 − 2.74)]~0.525𝑚²

29

For the structure of the satellite we are using two 0.35m² radiators, with an emitting area of 0.7m². Then,

our radiators, allied with the heat pipes will be able to maintain the operational temperature inside the

satellite.

If we consider a minimum temperature of 0⁰C (~270K) we can see that the area will be:

𝐴𝑟𝑎𝑑 =225.7

[5.67 ∗ 10−8 ∗ (2704 − 2.74)]~0.7𝑚²

Then, for maintain a 0⁰C operational temperature; our radiators must operate at maximum capacity with

the louvers assistance. Although, most part of the satellite´s components are designed to operate under

Earth´s characteristics, then, we must set our operational temperature to 293.15±2K, a temperature

range which our thermal system operates under an optimum emissivity of heat.

9 Attitude control Satellite attitude determination is the process of estimating the orientation of the satellite through

remote observational techniques. The observational data obtained is typically a measurement of angular

rate relative to a fixed reference frame. These measurements shall be obtained quickly and accurately to

optimise the attitude of the satellite when required.

From attitude determination, one must use on board actuation systems to alter the orientation of the

satellite when necessary. These actuation controls may either result in fine control or slew (rough

realignment) controls.

Attitude determination:

For this satellite subsystem, a fibre optic gyroscope (FOG) shall be used for attitude determination. A

FOG, performs the same function as a typical mechanical gyroscope, but instead works through the

Sagnac effect (a beam travelling against a rotation will experience a slightly shorter path), rather than

gyroscopic momentum-based measurements from momentum wheels.

The FOG that shall be used is the Astrix® 200 from Astrium. This inertial measurement unit will provide a

three axis measurement of the satellite’s current rotational rate with incredible accuracy (0.001 arc

seconds). The mass of the Astrix® 200 is 10kg; it consumes up to 6W of power per channel (four channel

maximum, for four inertial measurements) and only dissipates a few mW of power (theoretically).

30

Moreover this unit has been specifically designed to be separated from processing electronics which will

enable it to be thermally regulated and avoid thermo-elastic effects on the fibre optic cables.

However to ensure redundancy of the attitude determination system several active pixel digital sun

sensors (from Selex Galileo) shall be positioned around the satellite. Although analog sun sensors are

more efficient, they will be highly unreliable for our required distance from the sun, even with the use of

collector plates to focus the sun’s rays onto the photovoltaic panels.

The APSS Active Pixel Sun Sensor shall be used as our digital sun sensors. Moreover they shall be placed

on four sides of our satellite to ensure that we need not necessarily waste a lot of fuel trying to orient

our sun sensors with sun.

This particular digital sun sensor works by passing the sun’s photons through a pinhole and projecting an

image onto the CMOS (complementary metal oxide sensor) imaging sensor. From here the centroid of

the projected sun’s image relative to the origin on the imager can be calculated and then the sunlight

incident angle can be calculated.

Attitude Actuation:

9.1 1N Thrusters The attitude actuation consists of two sections, a fine control and a slew control. For slew control, several small 1N Astrium® Hydrazine Thrusters shall be placed at critical points around the satellite in order to maximise the moment arm of thrusters relative to the centre of gravity (cg) of the satellite.

These critical points will in effect refer to two opposite corners of the satellite. This placing procedure will give us a minimum of three degrees of freedom, and a maximum of 6 degrees of freedom if the thrusters are used efficiently (serving as a viable back up should the main orbital thruster be unusable).

Another benefit of this placement is the symmetry of the placement. This is because instead of having one thruster to produce a net moment, two may work in collaboration to produce the same net moment with less fuel and power consumed.

31

This thruster can operate for a long term steady state and pulse mode, and it operates in a 5.5 to 22 bar

pressure range, enabling it for blow down. It also contains a design that operates as a heat barrier for the

propellant valve and system structure.

This monopropellant thruster system is highly reliable, as it was successfully used on the 365 flight units

of the Globalstar LEO constellation. The thruster have a specific impulse range from 200 to 223s

(nominal 220s) and the minimum impulse bit is 0.01N. Then, the accumulated total impulse is 112000Ns

in a 50 hours accumulated burn life, through an averaged 59000 cycles. For cold starts, below 10⁰C, it

can generate a maximum of 10N of thrust.

Figure Y.2 – 1N Hydrazine Astrium Thruster [Astrium 2012, 1N Mono-propellant Thruster]

9.2 Gyroscopic Microwheels

For fine attitude control, we shall use a system of gyroscopic reaction wheels. These reaction wheels shall be 100SP-0 microwheels developed by Surrey Space Technology. The positioning of these reaction wheels must allow for three-axis stabilization, thus three of the microwheels must be placed perpendicularly to one another, with a fourth one positioned skew to the remaining three. This fourth wheel shall function to remove spin saturation from any other, and also serve as a backup reaction wheel, should any of the others fail. These gyroscopes work by the conservation of angular momentum.

These microwheels are housed in a container shown in the above diagram. It uses a system of oil lubrication and each reaction wheel is rated for over a billion revolutions. The Surrey Space recommended nominal rotation rate range to maintain correct attitude during a 7.5 year space mission is 1000 to3000 rpm. Moreover these reaction wheels are internally protected from current overdraw, and shall be connected to the 24 -32 V bus.

32

Part B- Landing Sensor Device

10 Landing Sensor

10.1 Introduction A requirement of this mission is to get within close proximity of the comet. There are a number of

methods to achieve this aim and so, this section will describe the theory applied and the construction

and calibration of one prototype mechanical device that utilizes a circuit made with resistors and a

potentiometer that varies with the altitude of the satellite. The change of the resistance of the

potentiometer with height make a change in the voltage on each resistor, the aim is read this voltage and

uses it to find how high the device is. The prototype uses a potentiometer that varies linearly with the

angle variation.

10.2 Design Description The device was built using a 40cm rod, a potentiometer, 2x2KΩ resistors, a 9V battery and a button

switch to act as a bump sensor. This system is based upon the rotation of the rod as show in the diagram

below. It is this axis rotation which is responsible for the change of resistance on the potentiometer. The

rod itself is initially tilted a little to allow for a little moment to act on the potentiometer (referencing

that initial, slight rotation as the zero reference point in our analysis). When the spacecraft makes

contact with the comet (90 degrees rotation), the button switch will press down and open the circuit. At

this point, the voltage will drop to 0.

𝜃_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ∆𝜃 + 𝜃_𝑖𝑛𝑖𝑡𝑖𝑎𝑙

33

10.3 Circuit Diagram

10.4 Derivation The purpose of the resistors is to reduce the input voltage that will go through the potentiometer so that

our max voltage reading would not exceed 2.5V. Using the voltage divider equation, we see that the

voltage across the whole potentiometer is:

=𝑅2||𝑅

𝑅2||𝑅 + 𝑅1 =

5

11 9 =

45

11

As the potentiometer itself can be used as a voltage divider if we wire the 1st wire and the middle wire of

the potentiometer to a multimeter. In the diagram below, the input terminals A and B of the

potentiometer are connected to the rest of the circuit, so that the potentiometer is in parallel, while

terminals W and B in the diagram are connected to the voltmeter (in our experiment) or Analog to

Digital converter.

34

11 Prototype The prototype was built, tested and calibrated so that we could ensure that the output voltage was

between 0 cm and 2.5 cm, and that the voltage change with respect to theta was linear.

Below is an image of the prototype:

Resistor circuits in the sensor:

35

11.1 Testing and Calibration Three trials were conducted for each 5 cm increment of height and then an average voltage was

recorded. The height value was converted to an angle, Theta, which was plotted against the voltage

measurements in Excel. The main calibration aspect for the sensor was to produce a function of voltage

with respect to theta, and therefore voltage with respect to height.

11.2 Results of Tests The table below shows the results obtained from testing:

Height (cm) Theta (degrees) Average Voltage (V)

40 90 2.05

35 61.04498 1.58

30 48.59038 1.37

25 38.68219 1.23

20 30 1.08

15 22.02431 0.95

10 14.47751 0.83

5 7.180756 0.71

0 0 0.59

The relationship of voltage versus angle was plotted in Excel:

y = -0.0162x + 2.0493

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100

Vo

ltag

e (

V)

Theta (degrees)

Theta(degrees) Vs Voltage (V)

36

As shown above, there is a linear relationship given by V = −0.0162 θ + 2.0493. In order to obtain

a relationship of voltage versus height, height is related to angle by 𝜃 = cos−1( ℎ/40). Thus, we can

obtain a function of height in terms of voltage output.

V = −0.0162 cos−1( ℎ/40) + 2.0493

ℎ = 40𝑐𝑜𝑠 (−1

0.0162(V − 2.0493))

Thus, after receiving a voltage output from the sensor, the spacecraft will be able to use the function

above to find the corresponding height (and its distance from the comet).

12 Conclusion The sensor prototype extends to a maximum of 40 cm. The above tests show that the overall concept of

the sensor works for the intended purpose and that this sensor is scaled up to measure distances of up

to 1 m. The same linear function for 𝜃 (V = −0.0162 θ + 2.0493) can be applied, but for larger

distances, instead of the trigonometric ratio 𝜃 = cos−1( ℎ/40), the ratio will be 𝜃 =

cos−1(ℎ

𝑙𝑒 𝑔 ℎ 𝑜𝑓 𝑟𝑜𝑑). Therefore in order to scale up the sensor to measure larger distances the function

becomes ℎ = (𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑟𝑜𝑑) ∗ 𝑐𝑜𝑠 (−1

0.0162(V − 2.0493)).

13 Further implementation To fully implement the "landing" sensor, the design can duplicated and scaled up so the satellite will have 4 "legs", with these legs attaching to the same face as a camera. The camera will ensure the satellite is facing the correct way when landing. The differential change in the landing sensor can be programmed to actuate the attitude control sensors so the spacecraft will not lean on a particular side and damage solar panels.

The camera will also ensures the limitation of the sensor is not breached that it requires the satellite landing with the sensor side parallel to the surface of the comet.

37

14 Appendix

14.1.1 Appendix

14.1.2 Motivation and Method for Mass Moment of Inertia Calculations

An objects mass moment of inertia (not to be confused with ‘area’ moment of inertia) is a measure of an

object’s ability to resist a rotation once a moment is an applied. In essence, the mass moment of inertia

acts as a term that limits the angular acceleration of the object much like an object’s mass limits the

ability of an object accelerate once a force is applied.

The relationship between the mass moment of inertia and the applied moment is given by:

∑𝑴 = 𝑰𝜶

where,

The latter term describes the mass moment of inertia as being the square of the distribution of mass

relative to the mass centre.

For the satellite, the mass moment of inertia will be an indicator of the amount of thrust required to

cause a certain rotation. For example, if the satellite has a large moment of inertia about the x – axis,

then it would theoretically take a large amount of thrust to cause a rotation of the satellite about the x –

axis. Likewise, if the x – axis were to inherently have a small moment of inertia, then little thrust will be

required to result in a given rotation.

Although a small moment of inertia about any axis is desirable, it is difficult to make this number small

due to the amount of components that need to be placed around the satellite to make it function. On

another note, too small a moment of inertia can result in wide fluctuations in the angular momentum

vectors due to solar wind pressure.

In order to calculate the moments of inertia assumptions had to be made about the components. Most

of the components were assumed to be rectangular, spherical or cylindrical in nature. Moreover, they

were assumed to have a homogenous material and mass distribution. The only exception for these

simplifications was the high gain antenna which had to be assumed to be a paraboloidic shell for

accuracy.

38

14.2 Internal Components and Corresponding Mass and Dimensions

39

14.3 Internal Components and their Individual Mass Moments of Inertia

*Note that the numbers corresponding to (1), (2), (3) etc. will correspond to specific points on the

satellite. These points will be detailed on a diagram in Appendix page.

40

14.4 Internal Components and their Deviation from Mass Centre

41

14.5 Internal Components and their Final Mass Moments of Inertia Relative to Mass

Centre

14.6 Centre of Mass

Using Solidworks, it was possible to locate the centre of mass of the satellite

X (mm) Y (mm) Z (mm)

-11.54 310.49 -197.33

The centre of mass of the satellite is in fact very close to its centroid, which is highly beneficial for the

mission.

42

14.7 Labelled Figures Corresponding to Inertia Table Numbers

43

44

14.8 Table of Structural Parts and Mass

Component Dimensions (m3) Mass (kg)

Side Panel 2 x 2 x 0.138 12

Fuel Housing 1 x 1 x 1 cube hollowed with a

0.03 (offset)

16

Strut 2 x 0.031 x 0.031 3.5

14.9 Table of Structural Parts and Local Mass Moment of Inertias

Component Ixx' (kgm^2) Iyy' (kgm^2) Izz' (kgm^2)

Panel

(1) 4.028187325 8.0182 4.028187325

(2) 4.028187325 8.0182 4.028187325

(3) 8.0182 4.028187325 4.028187325

(4) 8.0182 4.028187325 4.028187325

(5) 4.028187325 4.028187325 8.0182

(6) 4.028187325 4.028187325 8.0182

Fuel Housing 26.6 26.6 26.6

Structural Bar

(1) 1.166946958 1.166946958 0.000560583

(2) 1.166946958 1.166946958 0.000560583

(3) 1.166946958 1.166946958 0.000560583

(4) 1.166946958 1.166946958 0.000560583

(5) 1.166946958 1.166946958 0.000560583

(6) 1.166946958 1.166946958 0.000560583

(7) 1.166946958 1.166946958 0.000560583

(8) 1.166946958 1.166946958 0.000560583

(9) 0.000560583 1.166946958 1.166946958

(10) 0.000560583 1.166946958 1.166946958

(11) 0.000560583 1.166946958 1.166946958

(12) 0.000560583 1.166946958 1.166946958

(13) 0.000560583 1.166946958 1.166946958

(14) 0.000560583 1.166946958 1.166946958

45

(15) 1.166946958 0.000560583 1.166946958

(16) 1.166946958 0.000560583 1.166946958

(17) 1.166946958 0.000560583 1.166946958

(18) 1.166946958 0.000560583 1.166946958

14.10 Table of Structural Parts and Mass Centre

Component Rx (m) Ry (m) Rz (m)

Panel

(1) 0.87 0.87 0.87

(2) -0.87 0.87 0.87

(3) 0.87 -0.87 0.87

(4) -0.87 0.87 -0.87

(5) 0.87 -0.87 -0.87

(6) -0.87 -0.87 -0.87

Fuel Housing 0.9 1 1.1

Structural Bar

(1) 0.4 0.4 0.4

(2) 0.4 -0.4 -0.9

(3) -0.4 0.4 0.9

(4) -0.4 -0.4 0.9

(5) 0.3 0.3 0.3

(6) -0.3 0.3 -0.3

(7) -0.3 -0.3 -0.9

(8) 0.3 0.3 -0.3

(9) 0 0.4 0.4

(10) 0 -0.4 0.9

(11) 0.4 0.4 0

(12) -0.4 -0.4 0

(13) 0.4 -0.4 0

(14) 0.4 -0.4 0

(15) 0.4 0 0.3

(16) -0.4 0 -0.3

(17) -1.1 0 0.9

(18) -1.1 0 0.9

46

14.11 Table of Structural Parts and Mass Moment of Inertia Relative to Mass Centre of

Satellite

Part Ixx (kgm^2) Iyy (kgm^2) Izz (kgm^2)

Panel

(1) 13.11098733 17.101 13.11098733

(2) 13.11098733 17.101 13.11098733

(3) 17.101 13.11098733 13.11098733

(4) 17.101 13.11098733 13.11098733

(5) 13.11098733 13.11098733 17.101

(6) 13.11098733 13.11098733 17.101

Fuel Housing 39.56 42.6 45.96

Structural Bar

(1) 1.726946958 1.726946958 0.560560583

(2) 1.726946958 1.726946958 2.835560583

(3) 1.726946958 1.726946958 2.835560583

(4) 1.726946958 1.726946958 2.835560583

(5) 1.481946958 1.481946958 0.315560583

(6) 1.481946958 1.481946958 0.315560583

(7) 1.481946958 1.481946958 2.835560583

(8) 1.481946958 1.481946958 0.315560583

(9) 0.000560583 1.726946958 1.726946958

(10) 0.000560583 1.726946958 4.001946958

(11) 0.560560583 1.726946958 1.166946958

(12) 0.560560583 1.726946958 1.166946958

(13) 0.560560583 1.726946958 1.166946958

(14) 0.560560583 1.726946958 1.166946958

(15) 1.726946958 0.000560583 1.481946958

(16) 1.726946958 0.000560583 1.481946958

(17) 5.401946958 0.000560583 4.001946958

(18) 5.401946958 0.000560583 4.001946958

47

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