centurion final design document

Conceptual Design for an Orbit Transfer Vehicle

FDR Report

Prepared for:

The American Institute of Aeronautics and Astronautics

Undergraduate Team 4 Space Design – AE443S

April 14th, 2015

Prepared by:

Mruthyum (Jay) Mulakala

Samip Shah

Bentic Sebastian

Benjamin Wilson

Derek Awtry

Kevin Lohan

Yu Guan

Engineering Team

Jay Mulakala Lead Systems Engineer

Pgs. 1-8, 69-77

X .

Derek Awtry Orbital Engineer

Pgs. 8-20

X .

Benjamin Wilson Propulsion Systems Engineer

Pgs. 20-29

X .

Yu Guan Structural Engineer

Pgs. 30-43

X .

Bentic Sebastian Power and Thermal Systems Engineer

Pgs. 38-43, 53-61

X .

Samip Shah ADCS Engineer

Pgs. 38-53

X .

Kevin Lohan Launching and Docking Engineer

Pgs. 61-69

X .

Table of Contents

List of Figures ............................................................................................................................................. i List of Tables .............................................................................................................................................. ii List of Acronyms .......................................................................................................................................iii

1. Executive Summary .................................................................................................................................... 1

1.1 Mission Timeline .................................................................................................................................. 7 2. Orbital Systems ........................................................................................................................................... 8

2.1. Design Approach ................................................................................................................................. 8 2.2. Concept Development ......................................................................................................................... 9

Trajectory to L1 ........................................................................................................................... 9

Trajectory to L2 ......................................................................................................................... 12

Station-keeping Analysis ........................................................................................................... 16

Orbital Maintenance in LEO ...................................................................................................... 17

Aerobraking maneuvers ............................................................................................................. 18

End of Life Summary ................................................................................................................. 19

2.3. Critical Design Issues ........................................................................................................................ 20 Computation of Halo Orbits and Insertion Velocities ................................................................ 20

Computation of Invariant Manifolds .......................................................................................... 20

3. Propulsion Systems ................................................................................................................................... 20

3.1. Design Approach ............................................................................................................................... 20 3.2. Concept Development ....................................................................................................................... 21

Main Propulsion System ............................................................................................................ 21

Attitude Control Propulsion System .......................................................................................... 28

4. Structural Definition .................................................................................................................................. 30

4.1 Design Approach ................................................................................................................................ 30 4.2 Concept Development ........................................................................................................................ 30

Material Selection ...................................................................................................................... 30

Mass Estimation ......................................................................................................................... 33

Vehicle Internal Volume ............................................................................................................ 34

Vehicle Structural Design .......................................................................................................... 34

Structural Testing ....................................................................................................................... 39

4.3 Critical Design Issues ......................................................................................................................... 40 5. Communication and Systems .................................................................................................................... 40

5.1 Frequency Band Selection .................................................................................................................. 40 5.2 Radiometric Tracking ......................................................................................................................... 41 5.3 Antenna Selection ............................................................................................................................... 44

6. Attitude Determination and Control Systems ............................................................................................ 45


Sensor Selection ......................................................................................................................... 46

Actuator Selection ...................................................................................................................... 50

Onboard Processing and Control Methods................................................................................. 53

7. Spacecraft Power Management Systems ................................................................................................... 55


Power generation and distribution ............................................................................................. 55

Power Storage ............................................................................................................................ 57

Radiation shielding .................................................................................................................... 59

Emergency mode ....................................................................................................................... 59

8. Spacecraft Thermal Systems ..................................................................................................................... 60


Thermal Control of Nuclear Reactors ........................................................................................ 60

Thermal Control of Fuel Tanks .................................................................................................. 62

Thermal control of Systems Module .......................................................................................... 63

Thermal Control of Solar Panels ................................................................................................ 65

9. Launching and Docking ............................................................................................................................ 65


Launch Vehicle .......................................................................................................................... 66

Discussion .................................................................................................................................. 68

Docking System ......................................................................................................................... 69

Refueling Procedure ................................................................................................................... 72

9.3 Critical Design Issues ......................................................................................................................... 73 10. Risk and Cost Analysis ............................................................................................................................ 73

10.1 Risk Analysis and Mitigation .......................................................................................................... 73 10.2 Cost Estimation ............................................................................................................................... 76

11. Conclusion ............................................................................................................................................... 81

12. References ............................................................................................................................................... 82

i

List of Figures

Figure 1-1. Earth-Moon Lagrange Points [1] .................................................................................................. 1 Figure 1-2. Illustration of Centurion OTV in Earth Orbit ............................................................................... 2 Figure 1-3. Detailed Illustration of Centurion OTV ........................................................................................ 4 Figure 1-4. Illustration of Centurion OTV ...................................................................................................... 5 Figure 1-5. Illustration of Centurion OTV Trajectory ..................................................................................... 6 Figure 1-6. Long Term Mission Timeline ....................................................................................................... 7 Figure 2-1. Side view of the trajectory to L1 ................................................................................................ 13 Figure 2-2. View of L1 from the perspective of the Moon............................................................................ 13 Figure 2-3. Zoomed view of the halo orbit at L1 .......................................................................................... 13 Figure 2-4. L2 trajectory as seen from the Earth ........................................................................................... 15 Figure 2-5. L2 halo orbit as seen from the Moon .......................................................................................... 15 Figure 2-6. L2 trajectory in the Earth-Moon rotating axis ........................................................................... 16 Figure 3-1. Basic LANTR schematic [23].................................................................................................... 22 Figure 3-2. Aerojet R-1E thrusters [30]......................................................................................................... 29 Figure 4-1. PAMG-XR1 5056 Aluminum honeycomb ................................................................................. 32 Figure 4-2. CYCOM 5320-1 toughened epoxy resin prepreg system [37] .................................................... 32 Figure 4-3. Systems Module with outer casing removed .............................................................................. 35 Figure 4-4. Hinged Radiator for Systems Module [38] ................................................................................. 36 Figure 4-5. Cryogenic Propellant Tank ......................................................................................................... 37 Figure 4-6. Propulsion System with outer casing removed ........................................................................... 37 Figure 4-7. Deployable radiator [39] ............................................................................................................. 38 Figure 4-8. Stress Analysis of cryogenic propellant tank .............................................................................. 40 Figure 5-1. Atmospheric attenuation as a function of frequency [43] ........................................................... 41 Figure 5-2. Number of missions using NEN vs. DSN [47] ........................................................................... 42 Figure 5-3. NEN performance compared to DSN using the S-Band [47] ..................................................... 43 Figure 5-4. EIRP of NEN compared to DSN in the S-Band [47] .................................................................. 44 Figure 5-5. High Gain Antenna with parabolic reflector ............................................................................... 45 Figure 6-1. Layout of ADCS Components .................................................................................................... 47 Figure 6-2. Surrey Rigel-L ............................................................................................................................ 48 Figure 6-3. Adcole Course Sun Sensor Pyramid ........................................................................................... 49 Figure 6-4. Configuration of attitude control thrusters .................................................................................. 51 Figure 6-5. Triple Mode Redundancy Configuration .................................................................................... 55 Figure 7-1. Power schematic of He-Xe gas for electricity production [71] ................................................... 56 Figure 7-2. Power distribution schematic. ..................................................................................................... 57 Figure 7-3. BFO (blood-forming-organ) dose [74] ....................................................................................... 59 Figure 8-1. Close-up of the radiators ............................................................................................................. 62 Figure 8-2 Braytpn Cycle for ESCORT System [24] .................................................................................... 61 Figure 8-3. Detailed wireframe of the OTV .................................................................................................. 63 Figure 8-4 Solar panels at system module. .................................................................................................... 65 Figure 0-1. Conceptual Design for NASA Docking System [81] ................................................................. 70 Figure 0-2. Modified Dextre Robot [86] ....................................................................................................... 72 Figure 9-1. Technology Risk Analysis .......................................................................................................... 74 Figure 9-2. Operational Risk Analysis .......................................................................................................... 75 Figure 9-3. Number of Falcon 9 launches required to transport fuel for 10 missions ................................... 79 Figure 9-4. Total project costs using Centurion versus conventional technologies ....................................... 80

ii

List of Tables

Table 1.1. AIAA Mission Requirements ......................................................................................................... 2 Table 2.1. Hohmann Transfer Burns and Insertions, adapted from [10] ....................................................... 10 Table 2.2. Delta V's for different orbits, table adapted from [10] ................................................................. 10 Table 2.3. Total mission ΔV for varying z-amplitudes .................................................................................. 11 Table 2.4. Transfer times to L1 and halo orbit durations for varying z-amplitudes ...................................... 11 Table 2.5. Total mission ΔV for varying z-amplitudes .................................................................................. 14 Table 2.6. Transfer times to L2 and halo orbit durations for varying z-amplitudes ...................................... 15 Table 2.7. Station-keeping values for L1 halo orbits..................................................................................... 17 Table 2.8. Station-keeping values for L2 halo orbits..................................................................................... 17 Table 2.9. Delta V's of possible altitudes at which to aerobrake with a 10 meter heat shield. ...................... 19 Table 3.1. Potential Main Propulsion System Technologies ......................................................................... 21 Table 3.2. Fuel Consumption to and from L2 [Isp = 911s] ............................................................................. 27 Table 3.3. Potential ACS propulsion technologies ........................................................................................ 28 Table 3.4. Potential ACS propellant tanks .................................................................................................... 29 Table 4.1. Comparison of common material for space vehicles [16] ............................................................ 31 Table 5.1. NEN Frequency Band Characteristics [2] .................................................................................... 41 Table 5.2. Near Earth Network Tracking Characteristics [20] ...................................................................... 42 Table 5.3. Types of antenna for space communication [11] .......................................................................... 44 Table 6.1. Characteristics of common star trackers [22] [23] [24] ................................................................ 48 Table 6.2. Characteristics of common IMUs [26] [27] [28] .......................................................................... 48 Table 6.3. Characteristics of common sun sensors [5] .................................................................................. 49 Table 6.4. Capture Tolerances for Docking and Berthing [29] ..................................................................... 49 Table 6.5. Demonstrated Accuracy of AOS Proximity Sensors [30] ............................................................ 50 Table 6.6. Characteristics of common thrusters [31] [32] [33] [34] .............................................................. 51 Table 6.7. Characteristics of commonly used control moment gyroscopes [37] [38] [39] ............................ 52 Table 6.8. Estimated Source Lines of Code [41] ........................................................................................... 53 Table 6.9. Characteristics of radiation hardened flight processors [42] [43] [44] ......................................... 54 Table 7.1. Batteries and their characteristics [36] ......................................................................................... 58 Table 8.1. Diagram of upper casing, lower casing, and fuel tank.................................................................. 63 Table 8.2. Heat Dissipation among components ........................................................................................... 64 Table 9.1. Comparison of Potential Launch Vehicles for Centurion ............................................................. 67 Table 9.2. Launch Vehicle Selection Factors and Weighting........................................................................ 67 Table 9.3. Trade Study of the Viable Launch Vehicles ................................................................................. 68 Table 9.4. IDSS Docking Compatability [57] [6].......................................................................................... 71 Table 10.1. Risk Analysis Criteria ................................................................................................................ 73 Table 10.2. Technology Risk Analysis .......................................................................................................... 74 Table 10.3. Operational Risk Analysis .......................................................................................................... 75 Table 10.4. Development and Mission Costs ................................................................................................ 78

iii

List of Acronyms

ADCS – Attitude Determination and Control Systems

AIAA – American Institute for Astronautics and Aeronautics

AMSL – Above Mean Sea Level

APAS – Androgynous Peripheral Attachment System

ATCS – Active Thermal Control System

BLS – Boeing Launch Services

BNTR – Bimodal Nuclear Thermal rocket

CALT – China Academy of Launch Vehicle Technology

CECE – Common Extensible Cryogenic Engine

CIS – Commonwealth of Independent States

CMG – Control Moment Gyroscope

CR3BP – Circular restricted three body problem

EML – Earth-Moon Lagrangian Point

ESA – European Space Agency

FDR – Final Design Report

Isp – Specific Impulse

L1 – Lagrnage point 1

L2 – Lagrange point 2

LANTR – Liquid Oxygen Augmented Nuclear thermal rocket

LEO – Low Earth Orbit

LH2 – Liquid Hydrogen

LOX – Liquid Oxygen

NASA – National Aeronautics and Space Administration

NDS – NASA Docking System

NERVA – Nuclear Engine for Rocket Vehicle Applications

NTR – Nuclear Thermal Rocket

OTV – Orbit Transfer Vehicle

PDR – Preliminary Design Report

PTCS – Passive Thermal Control System

QFD – Quality Function Deployment

RCS – Reaction Control Systems

RRM – Robotic Refueling Mission

SNRE – Small Nuclear Rocket Engine

STPO – Space Transportation Project Office

TFU – Theoretical First Unit

TRL – Technology Readiness Level

XE – Experimental Engine

1

1. Executive Summary

Hyperion Ventures’ aims to provide a transportation vehicle that satisfies the requirements set forth by the

American Institute for Astronautics and Aeronautics (AIAA). The task was to develop an Orbital Transfer Vehicle

(OTV) capable of transporting payloads between Low Earth Orbit (LEO) and two Lagrange points, either EML1 or

EML2. There are currently 5 Lagrange points around Earth, as shown in Figure 1-1. Two of these five positions offer

an area where the combined gravitational pull of the Earth and Moon offer a stable orbit configuration, while the other

3, L1, L2, and L3 are unstable but offer the ideal location for a potential space station due to their positioning and

accessibility [1].

Several missions have been planned over the

past few decades to utilize these points, from a Deep

Space Climate Observatory to the James Webb Space

Telescope to a design proposed by Boeing that would

serve as a refueling depot and servicing station. The

platform would serve as a base for deep space

exploration, robotic relay stations for moon rovers,

telescope servicing, and even mars base missions. In

order to meet these growing demands, Hyperion

Ventures is tasked with developing an Orbit Transfer

Vehicle (OTV) capable of transporting unmanned and

manned payloads between Low Earth Orbit (LEO) and

Earth-Moon Lagrangian points L1 (EML1) or L2 (EML2). The benefits for these points have been researched for

decades and motivation for development at these Lagrange points have grown. The American Institute of Aeronautics

and Astronautics’ (AIAA) Request for Proposal (RFP) clearly dictates the constraints and requirements for an OTV

mission to these Lagrangian points for potential use in future missions. The specific design constraints are listed in

Table 1.1. To satisfy these constrains, Hyperion Ventures has designed a vehicle to satisfy the AIAA criteria, called

Centurion, Figure 1-2.

Figure 1-1. Earth-Moon Lagrange Points [1]

2

Table 1.1. AIAA Mission Requirements

Number Condition: Reference:

1 The OTV will be stationed in 400 km AMSL circular LEO with 28° inclination. Section 2

2 The OTV payload capability shall be 50,000 lbs from LEO to EML1 and 15,000 lbs

from EML1 to LEO.

Section 3

3 The OTV must be capable to remain at EML1 or EML2 for at least 30 days. Section 2

4 Each transfer should not exceed 6 days. Section 2

5 The life of the OTV shall be 5 years and the OTV shall be capable of at least 10 missions

to EML1 or EML2.

Section 4

Centurion is a modular design vehicle equipped with some of the latest technologies, including a nuclear

thermal propulsion system. The structure weighs approximately 89,000 kg of which about 49,000 kg is the fuel

onboard the vehicle. It is capable of docking with a variety of payloads and capsules and has the ability to transport

that cargo to Lagrange points L1 or L2. The total cost to design, fabricate, and launch Centurion would be about $2.5

billion, with subsequent missions costing about $95 million each.

Centurion redefines modularity and simplicity. The vehicle is composed of different modules designed

specifically for this mission, the optimal attitude determination and control systems for the vehicle, power and thermal

systems that reduce the weight of Centurion while not compromising safety, an orbital plan that can almost cut travel

time in half compared to conventional technologies, a revolutionary new propulsion system never before used in

action, and a launching and docking mechanism that allows the vehicle to dock with ease.

Figure 1-2. Illustration of Centurion OTV in Earth Orbit

3

The primary structure of Centurion is composed of aluminum and titanium. Concerns regarding failure under

stress and thermal conditions have been taken into consideration to reduce stress concentrations while maintaining a

strong, stable structure. The base of the vehicle consists of three nuclear thermal engines supplied by a large liquid

hydrogen fuel tank containing over 49,000 kg of fuel. Liquid hydrogen was chosen as the primary fuel due to its low

cost and low molecular weight necessary for use in the nuclear thermal engines.

The nuclear thermal propulsion system is one of the key, distinguishable aspects of Centurion. The

technology was initially proposed in 1955 by the Hungarian engineer, Theodore von Karman [2]. This new system

was then tested in 1960 through the Nuclear Engine for Rocket Vehicle Application or NERVA program. These tests

validated the applicability of a nuclear thermal engine on rockets. The benefits for such an engine range from fuel

savings to reduced costs, and cut the cost of our missions by a factor of 3. The reactor core is composed of highly

enriched uranium–carbide fuel in a graphite matrix. Liquid hydrogen is injected into the core where it is heated to

above 2200°C and ejected out of the nozzle. The main concerns surrounding the use of a nuclear thermal propulsion

system include the political hurdles in gaining approval to send an active nuclear reactor into space and maintain the

safety of crew members from the intense neutron and gamma-ray radiation fields produced by the reactor. Radiation

concerns can be addressed through the application of radiation shields around the reactor and can further be reduced

through a combination of a tungsten and lithium hydrogen shield. The cost to develop this engine in 1971 was

estimated to be around $2.2 billion in FY1971 dollars, but within the past few decades, that price has gone down by

more than 90% due to increased research by numerous companies and development by Pratt & Whitney [3]. The

highly advanced nuclear thermal propulsion system is the solution that Hyperion Ventures’ proposes to address the

high costs and fuel associated with a mission to EML1 or EML2.

The lower module of Centurion, containing the nuclear thermal engines and the fuel, is completely covered

in radiation shielding and thermal shielding to protect the various components and computers aboard the vehicle, and

to protect the payload and other external and internal structures. Water will be used as a secondary cooling system to

ensure the engines do not overheat and to maintain a safe temperature. The primary concern for nuclear thermal

engines include crew safety and component deterioration due to radiation exposure. The nuclear thermal engines come

with their own radiation shielding to shield surrounding components from accidental radiation exposure. Additional

thermal shielding surrounds the fuel tanks and engines to protect the vehicle and other internal instruments. For our

missions, safety is a high priority, and has been taken into consideration in every aspect of Centurion’s design.

4

Figure 1-3. Detailed Illustration of Centurion OTV

5

The central and upper modules of the OTV consists of the communication systems, the Attitude

Determination and Control Systems, the power systems, sensors, and the docking module. Star trackers are used as

the absolute attitude determination sensors due to their accuracy [4]. Inertial Measurement Units (IMU) and sun

sensors are used as redundancy systems in the case of failure [5]. Thrusters and control moment gyroscopes have also

been implemented on Centurion due to the large amount of torque that can be generated and the fine attitude control

that will be essential when docking. Autonomous control systems will be used as control methods to analyze the sensor

data, implement control algorithms, and send instructions to the various actuators. Necessary computers have been

implemented on Centurion to handle these demands.

At the top of OTV is the current NASA Docking System (NDS). It was a docking system initially designed

by the United States in 1996 and redesigned in 2012 for future space exploration vehicles and serves as the

international spacecraft docking standard. It is also known as the international low impact docking system due to its

ability to dock safely and securely without damage to either vehicle [6]. It has been used in the past and is currently

in operation aboard the International Space Station. The system itself is androgynous, combining low impact docking

technology with the ability to both dock and berth. Once the payload and vehicle are docked, power, data, commands,

communications, water, and fuel can be transferred between the payload and vehicle, allowing for manned payload

missions. The NDS serves as the best docking system for Centurion mission due to its versatility and compatibility

with international standards, allowing Centurion to accommodate a wider range of payloads.

Figure 1-4. Illustration of Centurion OTV

6

Centurion’s primary mission is to transport cargo to and from Lagrange points EML1 or EML2, depending

on the mission. It will be docked with a refueling station in Low Earth Orbit (LEO) and will conduct its missions from

that base. For missions to L1, the OTV will take a minimum of 3.6 days to travel from LEO to EML1. For missions

to L2, the OTV will take a minimum of 5.2 days to travel from LEO to EML2. Once at EML1 or EML2, the OTV

will spend about 30 days to deploy and setup the payload. Once back in LEO, Centurion will refuel and will be ready

for its next mission.

Figure 1-5. Illustration of Centurion OTV Trajectory

In order to assemble and deploy the OTV to the refueling station in LEO, the vehicle will be launched from

Cape Canaveral, Florida to maintain the 28 degree inclination. This site has served as a great launching point for

many other missions in the past and serves as the perfect point to reach the desired inclination. This launch site is also

ideal for its location and limited collateral damage in the case of an emergency, allowing for debris to be dropped into

the ocean and to avoid human causalities. Centurion will be launched using a Delta IV launch vehicle for assembly.

It is expected to be in production by 2025 and would allow the mission to stay on track [7]. This vehicle would best

serve as our launch vehicle due to its large weight capacity and date for production. The launch vehicle would be

capable of carrying up to 125,000 kg into orbit and would be able to reduce the number of launches required to

assemble Centurion. For payloads, our design allows for a large range of various payloads to dock with the vehicle,

7

allowing it to be versatile and adaptable over time. These payloads can be launched using a variety of different launch

vehicles, but the Falcon 9 Heavy is recommended due to its versatility and compatibility.

Centurion uses some of the most advanced systems that puts it above the competition. From the nuclear

thermal engines to the modified NASA docking system, Centurion is at the forefront of space exploration. All of these

systems working cohesively together make up Centurion, a revolutionary new vehicle that will enable future deep

space missions.

1.1 Mission Timeline

Figure 1-6. Long Term Mission Timeline

Figure 1-6 showcases the long term timeline for the mission. The OTV is expected to be in operation by

2027. The major limiting factors in the development of our timeline is the development of the Nuclear Bi-Modal

thrusters and the further development of the NASA docking system. The nuclear thrusters should be in production by

2023. The NASA docking system is currently in production, but further research and development will be committed

to ensure a longer lifetime of the docking system. This should be completed by 2019, allowing us to maintain our

expected 2027 deadline for the launch of Centurion.

Orbital Assembly will begin around mid-2025 as mission tests are completed. Assembly of Centurion will

take place at Fort Lauderdale, Florida. Due to the small size of Centurion with its greatly reduced fuel mass as

compared to conventional solution, the entire completed assembly will be positioned on a Delta IV fairing. This would

allow for the most cost efficient launch and will only require a single launch to put Centurion in Orbit. Once in orbit,

Centurion will serve for a minimum of 5 years, transporting cargo to and from EML1 or EML2 for a minimum of 10

missions. The projection lifespan of Centurion far exceeds the 10 missions, but will be used as a guideline to maintain

the timeline. By 2032, Centurion will begin its orbital decommissioning. The OTV will take one final cargo to EML1.

8

After delivering its cargo, the OTV will reposition itself and head to EML4. At this point, the OTV will remain for

the duration of its life as to ensure safety from the nuclear material aboard the OTV and proper disposal of nuclear

fuel.

2. Orbital Systems

2.1. Design Approach

Hyperion Ventures is tasked with developing an Orbit Transfer Vehicle (OTV) capable of transporting

unmanned and manned payloads between Low Earth Orbit (LEO) and Earth-Moon Lagrangian points L1 (EML1) or

L2 (EML2) and back. Each mission to and from the Lagrange points can, at the most, take 6 days. Once at L1 or L2,

Centurion will need to stay there for at least 30 days, return to LEO, refuel and repeat the mission. 10 missions will

need to be completed in a matter of 5 years.

In order to get to L1, a few different orbital transfer methods were considered. First, the Hohmann Transfer

was considered, as it is the most efficient orbital transfer method (one that requires the lowest ΔV) to transfer between

two points in space. For three body dynamics, the Hohmann transfer will not give the most accurate results, but they

will be very close for initial estimates [8]. The reason for the inaccuracy is that as the spacecraft gets closer to the

Moon, its path will be perturbed by the Moon’s gravitational field. Next, the invariant manifolds were considered as

a low energy transfer option. The Earth-Moon manifolds, however, are not accessible from LEO. The manifolds are

generally over 75,000 km above Earth’s surface [8], so it would require two burns to get to L1 and another burn to

insert the spacecraft into a halo orbit. Finally, another three burn transfer was considered, where the initial LEO

departure burn would take the spacecraft close to the Moon, and then the spacecraft would make another burn to get

itself on a path to L1, then make one more burn to insert itself into an orbit around L1. For transfers to the second

Lagrange point, the same general process was followed.

The orbits that will be considered at the Lagrange point will be halo orbits and quasi halo orbits -- also known

as Lissajous orbits. Because Centurion does not need to stay at the Lagrange point for a very long amount of time,

Centurion will only be able to orbit a Lagrange point a couple times, as long as the orbit has a large enough period.

By extension, station-keeping costs when in an orbit around L1 or L2 will be small, because of the short amount of

time in orbit.

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2.2. Concept Development

It takes less time to reach L1 then it does to reach L2 because of the relative distances of each. A direct transfer

to L1 requires about 4 days, with a ΔV around 3.7 km/s. An efficient transfer to L2 requires about 6 days, with a ΔV

around 4.0 km/s. From these figures alone, the transfer time to get to L2 is just under the maximum required time limit

of a transfer to or from a Lagrange point. An investigation into the various trajectories and halo orbits to get to L1 and

L2 will be discussed in the following section.

Trajectory to L1

To get to L1, three different trajectories were considered. Fist, a simple Hohmann transfer was used to get to

the Lagrange point. In order to calculate the Hohmann transfer ΔV and the TOF required to get there, the vis-viva

equation was used. A modified form of this equation is shown in Equation (2-1),

ΔVH = √𝜇 (2

𝑟1

−1

𝑎𝐻

) − √𝜇 (1

𝑟1

) (2-1)

where 𝑟1 is the radius of the perigee of the Hohmann transfer, 𝑎𝐻 =𝑟1+𝑟2

2 is the semi major axis of the Hohmann

transfer (with 𝑟2 being the distance from the Earth to L1), and 𝜇 is the gravitation parameter of the Earth [9]. When

the Moon is closest to the Earth, the distance between the two is around 362,600 km, and therefore points L1 and L2

lie at 308,079.4 km and 423,198.8 km respectively. These Lagrange points were found by computing the force balance

between the Earth and the Moon, and seeing where those two forces are in equilibrium at each point (see MATLAB

code Lag1.m and Lag2.m for computation). With these values, a Hohmann transfer will have a ΔV of 3.0616 km/s.

The second burn at apoapsis of the transfer will be the insertion burn into the halo or quasi-halo orbit. The TOF is

another variable of interest, because the transfer time has to be less than 6 days. Equation (2-2) shows the TOF for a

Hohmann transfer.

𝑡𝐻 = 𝜋 (𝑎𝐻

3

𝜇)

12

(2-2)

where all the parameters are the same as in Equation (2-1). The time of flight for a Hohmann transfer to L1 with the

Moon at periapsis is 3.597 days, which is well within the 6 day limit. In Table 2.1, proposed halo orbit insertion burns

(represented by ΔV2) for different types of orbits are shown. These types of orbits were taken from [10], where orbit

1 is a halo orbit, orbit 2 is a medium quasi-halo orbit, and orbit 3 is a large quasi-halo orbit. Originally, the orbits

10

proposed started from an Earth altitude of 200 km, but substituting in a 400 km burn, ΔV1 will decrease and thus total

ΔV will decrease as well.

Table 2.1. Hohmann Transfer Burns and Insertions, adapted from [10]

Orbit Option 𝚫𝐕𝟏 (km/s) 𝚫𝐕𝟐 (km/s) Total 𝚫𝐕

1 3.059 0.5807 3.6397

2 3.059 0.5646 3.6236

3 3.059 0.5491 3.6081

The next transfer method considered is the three burn transfer around the Moon. The first burn is the initial

burn from LEO to a 200 km lunar altitude, the second burn is from the 200 km lunar altitude to the Lagrange point,

and the third burn is the insertion burn into the halo orbit. Using data from [10], it can be seen in Table 2.2 that there

is an opportunity to use less energy to get to L1 while still being under the required time limit, and this means less

fuel consumption thus driving the cost down.

Table 2.2. Delta V's for different orbits, table adapted from [10]

Orbit Option 𝚫𝐕𝟏 (km/s) 𝚫𝐕𝟐 (km/s) 𝚫𝐕𝟑 (km/s) Total 𝚫𝐕 (𝐤𝐦

𝐬) TOF

(days)

4 3.117 0.26887 0.30131 3.6872 4.87

5 3.117 0.27180 0.2721 3.66701 5.09

6 3.117 0.27158 0.24842 3.6370 5.42

7 3.117 0.26690 0.21310 3.5970 5.80

Note that these results were based on an initial 200 km altitude LEO, so when calculated with an initial 400 km altitude

orbit, the totals for fuel consumption should go down across the board, and the TOF will increase.

2.2.1.1. STK Analysis to L1

In terms of modeling a two burn transfer to L1, STK/Astrogator was used. A tutorial was initially used to

simulate the satellite’s path to L1 [11], and then that tutorial was modified for this project’s specific parameters. The

Launch targeter was changed to an initial conditions targeter, where a perigee altitude of 400 km and a 28 degree

inclination were used to find the orbit from which Centurion would need to start. The Astrogator targeter then found

the trajectory to get to L1, used a differential corrector to model a 3 revolution halo orbit, and exited the Lagrange

point orbit to get back into a circular orbit around the Earth at a 400 km altitude and a 28 degree inclination.

Multiple trajectories were modeled in STK to simulate different halo orbits in L1. Table 2.3 shows the data

obtained from these simulations, in which only the z-amplitude was varied. ΔV1 is the halo orbit insertion burn, ΔV2

11

is the halo orbit exit burn, and ΔV3 was the total mission ΔV (to and from L1). The initial burn to LEO and from LEO

was 3.069 km/s and 3.058 km/s respectively.

Table 2.3. Total mission ΔV for varying z-amplitudes

Orbit Option Amplitude (km) 𝚫𝐕𝟏 (m/s) 𝚫𝐕𝟐 (m/s) 𝐓𝐨𝐭𝐚𝐥 𝚫𝐕𝟑 (m/s)

8 5,000 620.017 644.108 7411.944

9 7,500 622.213 644.063 7421.159

10 10,000 625.070 647.151 7422.128

11 15,000 632.660 654.051 7446.725

12 20,000 642.570 663.845 7482.638

Note that the simulations included two station-keeping burns, which will be discussed in a later section. The

highlighted option shows that the orbit with the 5,000 km z-amplitude had the lowest total ΔV, and thus the orbit that

will be utilized in our mission. Table 2.4 shows the transfer times to and from L1, as well as the amount of time

Centurion spent in the halo orbit. Each halo orbit modeled was 3 revolutions long.

Table 2.4. Transfer times to L1 and halo orbit durations for varying z-amplitudes

Orbit Option Amplitude (km) 𝐓𝐢𝐦𝐞 𝐭𝐨 𝐋𝟏 (𝐝𝐚𝐲𝐬) 𝐓𝐢𝐦𝐞 𝐋𝟐 (days) 𝐇𝐚𝐥𝐨 𝐎𝐫𝐛𝐢𝐭 (𝟑 𝐫𝐞𝐯)

8 5,000 4.482 4.227 35.999

9 7,500 4.352 4.352 36.146

10 10,000 4.348 4.349 36.108

11 15,000 4.340 4.342 36.079

12 20,000 4.329 4.327 36.140

Each trajectory simulated was in the halo orbit for over 30 days, and each transfer was under 6 days meeting all the

requirements. Figure 2-1 and Figure 2-2 show the trajectory of orbit option 8 as seen from different reference frames.

Figure 2-1 shows the trajectory to L1 from a rotating reference frame. Because the Moon’s orbit is not

circular, the Moon’s position with relation to the Earth will move back and forth, and the position of L1 will do the

same. Figure 2-2 shows the trajectory as viewed form the Earth-Moon plane. A zoomed in view of just the halo orbit

is shown in Figure 2-3. This specific halo orbit had a z-amplitude (above the Earth-Moon plane) of 5,000 km.

12

For this simulation, a Hohmann like transfer to L1 was automatically performed by the targeter, and the initial

burn had a ΔV of 3.069 km/s to get to L1. As you’ll recall, the analytic solution using a Hohmann transfer to L1 was

3.0616 km/s, which is a difference of only 0.0074 km/s from the simulation. This means that the results obtained from

calculating a simple Hohmann transfer were very accurate.

Trajectory to L2

For a maneuver to L2, similar methodology as the maneuver to L1 was used, where a few types of transfers

were considered: the Hohmann transfer, and the three burn transfer. The three burn transfer around the Moon was

almost immediately ruled out because the TOF was too large. The fastest transfer using this method took 14.7 days,

which is well over the 6 day limit for a transfer [10].

Next, a straight Hohmann transfer to L2 was computed. When the Moon is closest to the Earth, the distance

from the Earth to L2 is 423,198.8 km. Using Equation (2-1), the ΔVH was calculated to be 3.0920 km/s, a slightly

higher ΔV than for a transfer to L1. Using Equation (2-2), the time of flight to L2 would be 5.741 days, which is just

barely under the 6 day limit. Much like the trajectories considered to L1, this trajectory also takes into account that

the L2 insertion happens when the Moon is closest to the Earth. Of course, this Hohmann transfer calculation does not

take into account the Moon’s gravity, and the perturbations that it causes. That being said, the total ΔV when

considering the gravitational effects will be lower. This Hohmann transfer is the lowest energy transfer to get to L2.

Some transfers have been proposed that would put the spacecraft into a low lunar altitude then the velocity of the

spacecraft would then go around the Moon and to the Lagrange point. These transfers, first proposed by Robert

Farquhar in 1972, were also ruled out because of the TOF being around 212 hours or 8.83 days – well over the 6 day

limit [12].

13

Figure 2-1. Side view of the trajectory to L1

Figure 2-2. View of L1 from the perspective of the Moon

Figure 2-3. Zoomed view of the halo orbit at L1

14

In terms of the halo insertion burns, those could be on the order of 800 m/s [10] [13]. Possible halo orbits

and quasi-halo orbits around L2 have been proposed, with periods of around 15 days. This means that only 2 full

revolutions would be required to meet the minimum 30 day limit at the Lagrange point. The z-amplitudes for insertion

could range anywhere from 2,600 km to 11,000 km for a quasi-halo orbit, and 8,000 km for a halo orbit [13]. This

means that the required burn at LEO would not have to change much from the original calculation, bringing the total

ΔV of the L2 mission to around 7.8 km/s.

2.2.2.1. STK Analysis to L2

The trajectory was modeled to L2 using STK/Astrogator, and it used the same start conditions as the model

to L1. The orbit started out in a 400 km altitude, 28 degree inclined orbit, and then the orbit was propagated to EM-

L2. The only difference was the Trans-Lunar Injection (TLI) ΔV was changed to reflect the increased distance to L2

in relation to L1.

Multiple trajectories were modeled to L2, much like the procedure for L1. Table 2.5 shows different mission

ΔV’s for varying halo orbits. ΔV1 represents the halo orbit insertion burn, ΔV2 is the halo orbit exit burn, and total ΔV

is the total mission ΔV to L2 and back. The burn from LEO is 3.094 km/s, and the return ΔV is 3.099 km/s.

Table 2.5. Total mission ΔV for varying z-amplitudes

Orbit Option Amplitude (km) 𝚫𝐕𝟏 (m/s) 𝚫𝐕𝟐 (m/s) 𝐓𝐨𝐭𝐚𝐥 𝚫𝐕 (m/s)

13 5,000 1124.806398 1018.229755 8352.291161

14 7,500 1122.051898 1030.947916 8372.583998

15 10,000 1118.016671 1003.734879 8339.402704

16 15,000 1106.846749 988.600830 8321.101857

17 20,000 1097.023643 974.495641 8306.030167

These simulations also included two station-keeping burns, which will be discussed in more detail later.

Highlighted is the orbit with the lowest mission ΔV, and thus the orbit chosen for the mission. Table 2.6 shows the

halo orbit duration and the time to and from L2.

15

Table 2.6. Transfer times to L2 and halo orbit durations for varying z-amplitudes

Orbit Option Amplitude (km) 𝐓𝐢𝐦𝐞 𝐭𝐨 𝐋𝟏 (days) 𝐓𝐢𝐦𝐞 𝐋𝟐 (days) 𝐇𝐚𝐥𝐨 𝐎𝐫𝐛𝐢𝐭 (𝐝𝐚𝐲𝐬)

13 5,000 5.269 5.868 44.277

14 7,500 5.267 5.860 45.089

15 10,000 5.266 5.895 45.171

16 15,000 5.269 5.925 44.985

17 20,000 5.275 5.958 44.841

Note that every orbit simulated had a time back from L2 under 6 days and each halo orbit lasted for 44 to 45 days,

thus meeting the requirements. In terms of modeling this orbit,

Figure 2-4 shows entire trajectory of orbit option 17, and

Figure 2-5 shows a closer view of the 20,000 km amplitude, 3 revolution halo orbit.

Figure 2-4. L2 trajectory as seen from the Earth

Figure 2-5. L2 halo orbit as seen from the Moon

16

Figure 2-6. L2 trajectory in the Earth-Moon rotating axis

Seen in

Figure 2-6 is a view of the Earth and the Moon as seen from the Earth-Moon rotating axis, with Centurion

almost at its closest approach to the Moon and the Earth. Because the Moon is shifting, L2 will also shift from being

closer and farther away from the Earth. Therefore Centurion, if it is to orbit L2, will not stay in the same position with

relation to the Earth. This specific halo orbit’s period is 44.841 days.

Station-keeping Analysis

Since Centurion will only be in a halo or quasi-halo orbit for a minimum of 30 days, station-keeping costs of

our mission will be very low, on the order of 10 m/s [13]. The STK targeter included a station-keeping maneuver.

Table 2.7 shows all the station-keeping values obtained for all the L1 trajectory simulations.

17

Table 2.7. Station-keeping values for L1 halo orbits

Orbit Option 𝚫𝐕𝟏 (m/s) 𝚫𝐕𝟐 (m/s)

8 9.586 9.952

9 13.588 13.069

10 7.352 14.37

11 7.834 24.048

12 10.311 37.805

Table 2.8 shows the station-keeping burns needed to keep Centurion in an orbit around L2. These values were also

obtained using the STK simulations.

Table 2.8. Station-keeping values for L2 halo orbits

Orbit Option 𝚫𝐕𝟏 (m/s) 𝚫𝐕𝟐 (m/s)

13 8.385644 6.922246

14 8.729282 16.927658

15 9.412483 14.138888

16 12.764731 18.727220

17 17.744123 22.860030

Note that all of these values are very low, considering the entire mission is on the order of multiple km/s, and these

values are all on the order of 0.01-0.02 km/s. These values are by no means negligible, but they are low enough so

that a variation in any of these numbers would not be detrimental to the mission design.

Orbital Maintenance in LEO

When our spacecraft gets back into LEO after a mission from L1 or L2, the spacecraft will stay there for

approximately 4 to 4.5 months. The orbit would degrade over that period approximately 12 km in altitude, assuming

that the vehicle starts at a 400 km altitude orbit with an empty fuel tank. The meaning the ΔV required to get back to

a 400 km altitude orbit would be 6.7974 m/s. The amount of fuel lost would be on the order of 50 kg, using (2-3). If

instead the vehicle refueled immediately when back in LEO, the orbit would only degrade 3 km due to the larger

overall mas, and the ΔV required to get back to the 400 km orbit would be 1.697 m/s. The amount of fuel lost due to

just the burn would be on the order of 10 kg At first glance it seems that refueling immediately would save the most

fuel, but the amount of fuel boiled off needs to be accounted for. Centurion would lose on the order of 2000 more

18

kilograms of fuel due to boil off if it were to refuel immediately. Therefore, the vehicle will refuel at the end of the 4

months between missions to save the most fuel.

Aerobraking maneuvers

Included in this section are the details on aerobraking - the calculations and feasibility of the aerobrake from

L1. The time required to get back from L2 will be too close to the maximum allowable limit to even consider

aerobraking. Some things that need to be considered for this proposal are the risks involved with aerobraking, the time

it takes to aerobrake, and the overall effect on the entire system.

In order to calculate the savings in fuel of the aerobrake, a simple equation was used,

ΔV = kρo√2𝜋𝜇 (1 + 𝑒

√𝑒) √𝐻 (2-3)

where k = ballistic coefficient of heat shield, 𝜌𝑜 = density of air at periapse, 𝜇 = the gravitation constant of the earth,

𝑒 = eccentricity of the orbit, and 𝐻 =𝑅𝑇

𝑔 is the scale height, where T is the temperature at periapsis. The ballistic

coefficient is a function of the coefficient of drag, surface area, and the mass of the vehicle, namely,

𝑘 =𝐶𝑑𝑆

2𝑚

(2-4)

where 𝐶𝑑 is the coefficient of drag, S is the surface area, and m is the mass [14].

Using values from the HPOP STK density models and thermodynamic tables at different altitudes and initial

guesses for the spacecraft and orbital trajectories - a heat shield diameter of 10 meters, coefficient of drag of around

2, total mass of around 70,000 kg, and an eccentricity of .96 - values for the ΔV of an aerobrake come out to very low

numbers. Table 2.9 shows the ΔV values and the altitude at which they were calculated.

19

Table 2.9. Delta V's of possible altitudes at which to aerobrake with a 10 meter heat shield.

Altitude (km) Density (kg/km^3) 𝚫V (m/s)

50 102700.0 1,026.4

60 30960.0 295.6152

80 18449.456 157.9763

100 560.276 4.7543

120 22.234 0.2563

140 3.839 0.552

Note that the Jacchia 1960 density model from STK was used for altitudes above 80 km, and thermodynamic tables

from [15] were used for altitudes below 80 km. Also, these values were computed using a MATLAB code, which can

be found in Appendix 12.1. The only way that aerobraking will be able to have a tangible effect on our system is that

if the ΔV savings were on the order of 1 km/s, which only happens at an altitude of 50 km. This is way too low for

our spacecraft if we want the spacecraft to stay intact and be reusable, because the density at that altitude would be

very large and thus cause the spacecraft to heat up and either start breaking apart or fail completely.

End of Life Summary

Since Centurion has an active nuclear thermal propulsion system, a viable and safe end of life plan has been

implemented so that the vehicle will never again be able to get near the atmosphere of the Earth. Therefore, at the end

of 10 missions, Centurion will be able to take a payload on a one way trip to L1, drop it off, and then maneuver to the

Earth-Moon Lagrange Point 4 (L4). L4 was chosen because it is stable, unlike L1, L2, and L3. Anything within a

certain vicinity of L4 will stay there, and therefore it is a good spot to place Centurion. Since this is only a one way

mission, the payload to L1 would probably be some sort of satellite or science mission that would study the moon, or

beyond.

The ΔV required to get to L2 was found by using a minimum energy transfer trajectory using Lambert’s

theorem [9]. The transfer trajectory ΔV was found to be around 682 m/s from L1, bringing the total mission ΔV to

4.914 km/s for a mission to L4 with a pit stop at L1. Note that the transfer ellipse was calculated using the Moon’s

sphere of influence and therefore doesn’t take into account three body dynamics. For this reason the ΔV is not

completely accurate, but is a good first cut estimation of the ΔV required to get there. Even so, the ΔV required to get

to L4 would be far less than the ΔV required to return to LEO from L1.

20

2.3. Critical Design Issues

Computation of Halo Orbits and Insertion Velocities

There are many different ways to compute halo orbit periods and trajectories, but all of these methods are

complex. These periodic orbits are solutions to the circular restricted three body problem (CR3BP). Once an

approximation is achieved (by way of finding different amplitudes and constants associated with the orbit), a full

solution to the CR3BP can be found through various techniques [9]. These solutions and their initial guesses will be

tabulated and analyzed to determine the best possible transfer and orbit combination for the mission.

Computation of Invariant Manifolds

The invariant manifolds that exist between the Earth and the Moon, or any three body system in general, are

associated with a type of periodic solution to the CR3BP, i.e. a halo orbit. So once a possible orbit is known, the

invariant manifolds can be computed based on this [9]. As mentioned earlier, for the Earth-Moon case, the invariant

manifolds exist some 75,000 km above the Earth’s surface, and are therefore not able to be immediately utilized. A

transfer between LEO and these invariant manifolds will be considered as a possible transfer option. A transfer

between LEO to Low Lunar Orbit and then to the invariant manifolds to L2 will also be considered.

3. Propulsion Systems


To engineer a propulsion system that must carry a 22,500 kg payload from Low Earth orbit to an Earth-Moon

Lagrange point in an efficient and timely manner is no small feat. Centurion Orbital Transfer Vehicle (OTV) must be

able to travel to and from LEO to either Earth-Moon Lagrange point 1 (EML1) or Earth-Moon Lagrange point 2

(EML2) a minimum of five times. A one way trip must be executed in six days or less. To accommodate the constraint

of a six day transit time to and from EML1 or EML2 Centurion must be able to produce a total of 8.31 kilometers per

second of ∆V per round trip, section 2. Additionally, Centurion’s propulsion systems must be able to complete all

mission requirements while using minimal propellant mass.

Centurion will have two independent propulsion systems. The two systems will be the main propulsion

system and the attitude control propulsion system. The main propulsion system will be responsible for all major orbit

transfer maneuvers. Such maneuvers include: leaving LEO, arriving at the Lagrange point, leaving the Lagrange point,

and returning to LEO. For the main propulsion system a Bimodal Nuclear Thermal Rocket (BNTR) called Escort has

21

been selected. Separate from the main propulsion system will be the attitude control propulsion system. The attitude

control propulsion system will be responsible for coarse attitude adjustments and will work in conjunction with control

moment gyroscopes to meet all of the requirements of the attitude control system. For the attitude control propulsion

system Aerojet R-1E bipropellant thrusters have been chosen.


While developing the concept of Centurion several types of propulsion were considered for both the main

and attitude control systems. For the main system, ion chemical, and nuclear thermal propulsion technology were

considered. When developing the attitude control system, ion, cold gas, and chemical were considered.

Main Propulsion System

Technologies considered for use in the main propulsion system were compared using a few key parameters,

some of which can be found in the Risk Analysis Section. First was the fuel mass required to perform a round trip.

Because of the large payload any solution will require a large fuel mass. By placing fuel consumption as a primary

design driver, second only to safety, it could be ensured that Centurion would have the most cost effective design.

Second was the thrust rating of the engine. Again, with a large, potentially manned, payload this was an important

factor. Too large of a thrust could be harmful to the crew and too small of a thrust could make the mission take too

long. Thus, the last major consideration was the time it would take to achieve the largest ΔV, however, this is not

included in Table 3.1 because it was only useful for ruling out ion thrusters.

Table 3.1. Potential Main Propulsion System Technologies [16] [17] [18] [19] [20] [21] [3] [22]

Type Thruster Isp

[s]

Propellant Max Thrust

[N]

Fuel Mass to L2

[kg]

Ion Aerojet NEXT 4100 Xenon 0.235 8,700

Busek BHT-20k 2320 Xenon 0.807 16,600

NASA NSTAR 3195 Xenon 0.094 11,600

Bipropellant CALT YF-73 420 LOX/LH2 44,150 229,000

Astrium Aestus 324 N2O4/MMH 29,600 436,000

Aerojet CECE 465 LOX/H2 111,000 183,000

Monopropellant Aerojet MR-80B 225 Hydrazine 3780 1,410,000

AMPAC MONARC 445 235 Hydrazine 445 1,190,000

Nuclear Thermal CIS NTR 955 LH2 66,700 47,500

NERVA XE 850 LH2 1,112,000 62,500

Escort 911 LH2 333,600 49,600

Table 3.1 illustrates the strengths and weaknesses of each propulsion technology considered. Ion thrusters

are the most fuel efficient due to their high specific impulses. However, they produce so little thrust that thousands of

22

them would be required to be competitive with the weakest chemical thruster considered. Bipropellant chemical

thrusters provide appropriate levels of thrust but their specific impulse is comparatively low. Because of this the fuel

mass required for a round trip is prohibitively large. Monopropellant chemical thrusters follow a similar pattern, with

even lower specific impulses than bipropellants and lower thrust ratings they were quickly out of the running. Nuclear

thermal propulsion technology has none of these issues. With specific impulses nearing 1000 seconds and thrust

ratings that rival bipropellant thrusters these engines are the perfect match.

3.2.1.1. Nuclear Thermal Propulsion Systems

Nuclear thermal propulsion systems are fairly simple. In a standard thrust producing system there are three

main parts; the fuel tank and feed system, the reactor, and the nozzle. The fuel tank and fuel system house the liquid

hydrogen propellant and delivers it to the reactor. The reactor provides heat to expand the liquid hydrogen. Once

heated, the hydrogen is forced through the nozzle to produce thrust just like in a conventional chemical thruster. In

fact, the only aspect of a nuclear thermal propulsion system that differs from a traditional chemical system is that

nuclear systems are driven by nuclear fission rather than chemical combustion. The advantage of nuclear propulsion

comes from the fact that nuclear fission occurs at higher temperatures than combustion reactions. This increase in

temperature directly translates to the increased fuel efficiency of nuclear systems.

There are four types of thermonuclear propulsion systems that can be used. As a baseline there is the simple

thrust producing version. Second is the liquid oxygen augmented nuclear thermal rocket (LANTR), Figure 3-1. This

Figure 3-1. Basic LANTR schematic [23]

23

system produces more thrust than conventional NTR systems by using liquid oxygen as an afterburner [23]. Third is

the bimodal system. This is the type of system that has been selected for use on Centurion. Bimodal systems make use

of the high temperatures in the reactor to generate electric power by means of a closed Brayton cycle generator. Finally

there is the trimodal system. This system uses the liquid oxygen afterburner and closed Brayton cycle generator for

increased thrust production while generating power for the vehicle as well [24].

3.2.1.2. Past and Present Nuclear Thermal Systems

The Rover and NERVA (Nuclear Engine for Rocket Vehicle Application) programs stand as the most

significant endeavor in creating a flight ready nuclear thermal propulsion system to date. In 1955 the Rover program

began investigating the feasibility of using nuclear reactors for space propulsion. Out of Los Alamos National Labs

the Rover program succeeded in creating a series of liquid hydrogen cooled nuclear reactors called Kiwi. These

reactors served as the basis for the NERVA program. In 1961 NERVA began using the Kiwi reactors to create flight

ready nuclear thermal propulsion systems [25]. Aerojet and Westinghouse were contracted to develop the flight ready

systems. Early on it was decided that the most important design driver should be safety. After safety the team was

concerned with producing a specific impulse of around 760 seconds, the capability of the engine to start without

external aid (called a bootstrap start), and the engine should be capable of producing around 337kN of thrust while

minimizing weight [2].

Two sets of engine tests were conducted throughout the lifetime of the NERVA program. First was the NRX

(Nuclear Reactor Experimental) series of tests conducted in February 1966. This series of tests was concerned with

proving the capability of a bootstrap start, investigating the stability of the system during a wide variety of operational

modes, and observing the endurance of reactor components. These objectives were all achieved. The reactor was

started a number of times under varying conditions and was shown to be highly controllable and predictable. Overall

the NRX series was highly successful and led to the Ground Experimental Engine (XE) test series [2]. The XE engine

was designed to be flight ready and represents the most complete systems ever constructed. Testing of the XE series

went much the same as the NRX series. A total of 28 bootstrap starts were accomplished and the engine ran for a total

of 115 minutes with no sign of failure. The tests were a complete success [26].

Current nuclear thermal propulsion concepts are based extensively on the NERVA program’s findings but

are focused on smaller and more fuel efficient systems. Advances in nuclear fuels have led to the ability to produce

higher chamber temperatures which increases fuel efficiency [3].

24

3.2.1.3. Escort System Specifics

Centurion will be using a system proposed by Pratt and Whitney called the Escort system. Escort uses three

bimodal nuclear thermal propulsion units to provide thrust and power to the vehicle. Each unit is designed with its

own closed Brayton cycle generator for power production as well as shielding and all necessary turbomachinery.

Escort also comes equipped with radiators capable of dissipating the large thermal load generated by the fission

reactor. In the reactor the fission of 235U is used to generate thermal energy. The uranium is suspended in a tungsten

cermet (W-UO2) [27]. Tungsten is a dense element capable of withstanding high temperatures and can mitigate the

effects of gamma radiation. In addition tungsten is highly resistive to corrosion due to hydrogen, which increases the

durability and lifetime of the reactor.

In the foldout on page 26, there is a basic representation of the Escort system. Beginning at the liquid

hydrogen tank in the upper left corner the propellant is drawn out of the tank by means of a turbopump driven by an

expander cycle. To accomplish expansion and drive the pump liquid hydrogen is first injected into the nozzle and runs

up the nozzle and into the control drum. This cools the nozzle and control drum as well as drives the pump. After the

expansion the propellant is injected into reactor where it is heated and expanded further to produce thrust.

Separately, the closed Brayton cycle generator uses a fluid mixture of helium and xenon to extract heat from

the reactor to generate electric power. A series of valves allows the HeXe mixture to flow from its storage tank into

the reactor where it is heated and then forced through a turbine to generate power. Once through the turbine, the fluid

enters a radiator where the majority of the remaining heat from the reactor is dissipated.

Inside the reactor are the hexagonal tungsten uranium dioxide fuel elements. A cross section of these fuel

elements can be seen in the fold out. The yellow circles on the cross section represent the paths that the hydrogen

propellant takes through the reactor. In the center of the image the green circles represent the coaxial flow paths of the

helium xenon generator fluid. And the red area is the W-UO2 cermet fission material.

In the bottom right of the fold out is a model of the reactor and generator system. Of particular importance

in this image is the external shield on top of the reactor. This shield is made of lead and protects any potential crew

from the harmful effects of gamma rays produced in the reactor.

25

3.2.1.4. Nuclear Reactor Safety

Nuclear thermal propulsion is the enabling technology that will lead to more ambitious missions to more

distant places in the solar system. Unfortunately, the public opinion of nuclear technology is that it is dangerous and

we should stay away from it. But the truth is that when handled properly thermonuclear rocket systems are no more

dangerous than conventional chemical propulsion systems. That being said, there are numerous precautions that must

be followed to ensure safety while handling nuclear devices.

A main point of concern is mitigating the effects of the nuclear radiation being emitted from the reactor core.

There are three types of radiation that must be dealt with; alpha particles, beta particles, and gamma rays. Both alpha

and beta particles are not damaging and can be easily stopped with a thin sheet of aluminum [28]. Gamma rays are

high energy (~1 MeV) photons that are emitted as a byproduct of fission. The gamma rays emitted from fission of

235U have energy of about 13.3 MeV. Considering the reactor runs at a peak power of around 500MW, the level of

gamma radiation from the reactor is potentially dangerous [29]. However there are numerous ways in which these

affects will be mitigated and kept to safe levels. First, there is a 3cm thick lead radiation shield positioned above the

reactor. Second, when docking with the payload or while nearby any life forms, the reactors will be run at a

dramatically decreased rate such that a safe distance from the reactor will be greater than or equal to 25 meters.

Other safety protocols are concerned with the timing of the operation of the nuclear fission reactors. When

launching Centurion, the reactors will not be run in a critical state before leaving the atmosphere. This will ensure that

if any problems occur they will not endanger any population on Earth. In addition, the reactors will not be allowed to

return to Earth after being run at a critical state [65]. For this reason, at the end of the ten missions Centurion will be

placed at EML4 indefinitely.

3.2.1.5. Main Propellant/Tankage

A number of inert gasses could be used in conjunction with the nuclear thermal propulsion system to

produce thrust. However, when equation (3-1) is considered, it is clear that Hydrogen is the ideal choice because it

has the lowest molecular weight M [65].

27

𝑰𝒔𝒑 = 𝑨𝑪𝒇√𝑻𝒄 𝑴⁄

(3-1)

The parameters A and Cf are constants and properties of the fuel and nozzle respectively. The important part of the

equation is under the radical. Tc is the temperature of combustion in the “combustion” chamber and M is the molecular

weight of the fuel. In this case the combustion chamber is where the inert hydrogen gas is heated to produce thrust,

the hydrogen is not combusted. The lower the molecular weight of the gas being expelled from the nozzle, the higher

the chamber temperature then the specific impulse will be greater. For this reason, and considering Hydrogen gas has

the lowest molecular weight of all gasses, Hydrogen was chosen as the fuel for the main propulsion system of

Centurion. To calculate the mass of fuel needed to make a round trip to the L1 and L2 the following equations were

used:

𝑴𝒑 = 𝑴𝒑𝟏 + 𝑴𝒑𝟐 + 𝑴𝒑𝟑 + ⋯ + 𝑴𝒑𝟏𝟏 (3-2)

where

𝑴𝒑𝒊 = ∑ 𝑴𝒊(𝒆∆𝑽𝒊

𝒄 − 𝟏) (3-3)

Mp is the total mass of the propellant and each Mpi is the mass of the propellant needed to achieve each major burn. Mi

is the combined mass of the structure, payload, and fuel, ∆Vi is the change in velocity needed to make a major

maneuver, and c is the exit velocity of the propellant. A tabulated version of this calculation is provided in Table 3.2.

The four major orbit transfer burns occur at stages 1, 3, 9, and 11. Theses maneuvers represent 99% of total fuel

consumption for a trip to L2. The remaining losses are due to halo orbit correction burns and boil off.

Table 3.2. Fuel Consumption to and from L2 [Isp = 911s]

Stage Description ∆V [m/s] Time

Elapsed

Mi (Includes

Payload) [kg]

Mpi Propellant

Spent [kg]

1 Departing LEO 3095 10 Minutes 87,745 25,682

2 Transit to L2 0 5.3 Days 62,063 42

3 Arrive at L2 1097 3 Minutes 62,021 7,165

4 Halo orbit 1 0 15 days 32,177 83

5 Halo Correction 1 18 6 Seconds 32,094 64

6 Halo Orbit 2 0 15 days 32,030 83

7 Halo Correction 2 23 6 Seconds 31,947 82

8 Halo Orbit 3 0 15 days 31,866 83

9 Depart L2 974 2 Minutes 38,588 3,986

10 Transit to LEO 0 6 days 34,602 25

11 Arrive at LEO 3099 4 Minutes 34,577 10,133

Final Mass = 24,444 ∑ 𝑀𝑝𝑖 = 47,428

28

To store the liquid hydrogen propellant, Centurion will make use of a custom fabricated 700 cubic meter

aluminum tank with active and passive thermal control. Hydrogen must be stored at or below 20 Kelvin in order to be

a liquid. Such a low temperature is possible to be maintained but requires robust thermal control. The Escort system

is designed to operate alongside a zero boil off cryogenic storage system. However, in order to better model a real

system Centurion was designed to compensate for boil off rate of 1% loss per month. For a trip to EML2 this comes

to a total loss of just over 316 kg of propellant.

Attitude Control Propulsion System

The attitude control propulsion system will be responsible for providing small amounts of ΔV needed to

adjust the orientation of Centurion. Thrusters will be used in conjunction with control moment gyroscopes to

accomplish the goals of the attitude control system. The propulsive portion of the attitude control system will mainly

be used for slewing maneuvers while docking and refueling.

Table 3.3. Potential ACS propulsion technologies [16] [17] [30] [31] [32]

Type Engine Fuel Isp

[s]

Thrust

[N]

Propellant

Mass[kg]

Ion Aerojet NEXT Xenon 4100 0.235

Busek BHT-20k Xenon 2320 0.807

Cold Gas MOOG 58-118 Unknown 72 3.5 560

AMPAC SVT01 Xenon 45 0.05 900

Monopropellant AMPAC

MONARC -90 Hydrazine 235 90 170

Aerojet MR-107N Hydrazine 232 109-296 180

Bipropellant

EADS 10N

NTO, MON-1, MON-

3 and MMH 291 10 140

Aerojet R-1E MMH/NTO 280 111 144

Table 3.3 shows technologies considered for use in the attitude control propulsion system. Ion thrusters were

considered for their high specific impulse. However, they were not chosen based on their low thrust (<1N). Cold gas

thrusters are the simplest type of thruster and are thus the most reliable. Unfortunately they are not very efficient and

for this reason were not chosen. Monopropellant and bipropellant chemical thrusters are very comparable in their

reliability but bipropellants are more efficient. For this reason the Aerojet R-1E thrusters were chosen.

29

3.2.2.1. Aerojet R-1E

The Aerojet R-1E is a versatile and reliable thruster.

Previously used on the space shuttle this thruster is dependable

and flight proven many times over. Each thruster has a mass of

just 2 kg and can produce a steady state thrust of 111N. Every

thruster is capable of firing 330,000 times with no limitations on

the duration of the burn [30]. By using these engines for the

attitude control propulsion system in conjunction with control

moment gyroscopes a two point failure system has been created. This ensures that Centurion will always be able to

adjust its attitude.

3.2.2.2. ACS Propellant/Tankage

As a bipropellant thruster the Aerojet R-1E requires a mixture of Mono Methyl Hydrazine (MMH) and

Nitrogen Tetra Oxide (NTO), where MMH is the fuel and NTO is the oxidizer. These fuels mix optimally at a mass

mixture ratio (O:F) of 1:6. To calculate the mass of propellant required for the attitude control propulsion system a

ΔV of 10 m/s was used. This represents the total amount of ΔV required for the entire lifetime of the OTV.

The fuel tanks of the attitude control propulsion system were selected based on three criteria; the volume of

the tank, mass of the tank and how many tanks would be required to house the propellants, as shown in Table 3.4.

Table 3.4. Potential ACS propellant tanks [33] [34] [35]

Tank Propellant Volume (L) Mass (kg) Tanks Required

MOOG GEO Sat. Hydrazine 220 27 4

ATK 80505-1 Any 134 16 4

Astrium OST 31/0 MON/MMH 235 16 4

The volume required for the MMH is 84 Liters and the volume required to house the NTO is 82 Liters. With these

constraints in mind ATK’s 80505-1 tank was selected for use. This tank is made of 6AL-4V titanium with a rubber

diaphragm at the mid sphere location.

Figure 3-2. Aerojet R-1E thrusters [30]

30

4. Structural Definition

4.1 Design Approach

According to the mission requirements, Centurion should have payload capacity of 50,000 lbs to LEO and

service lifetime of 5 years or 10 missions. Our vehicle will stay in orbit and dock with manned Orion capsule or cargo

payloads.

The structure of Centurion consists of a systems module, fuel tank, and propulsion module. The systems

module houses various equipment and sensors from ADCS, Communication, Thermal & Power, and Docking

subsystems. It is responsible for controlling the operation of the entire Orbital Transfer Vehicle as well as

communicating with the ground station. The middle section of the OTV is allocated as the fuel tank for both the main

propulsion system and the attitude control propulsion system. Due to the cryogenic nature of liquid hydrogen fuel,

specifically designed thermal shielding is installed around the fuel tank and the structural wall to minimize the effect

of boil-off. The bottom of the OTV is the bimodal thermal nuclear propulsion system utilizing a nuclear reactor and

three thrusters. Most radiators from the Thermal subsystem will also be installed in this section to effectively manage

the thermal performance of the entire OTV.

4.2 Concept Development

Material Selection

The structure of Centurion is divided into three major categories: the truss structure, the fuel tank wall, and

the outer casing. The material selection process for each part are discussed in the following sections.

After comparing the properties listed in Table 4.1, aluminum alloys were considered for the outer casing as

well as inner truss structure of Centurion while composite was considered for the cryogenic fuel tank. Aluminum

honeycomb offers unparalleled stiffness and one of the highest strength-to-weight ratios of any structural core

materials currently available. When treated with chemical conversion coating, the aluminum honeycomb becomes

resistant to corrosion and moisture. It would be the ideal material for the outer casing of Centurion. Aluminum-lithium

alloys, despite its often toxic and dangerous manufacturing process, are great in weight reduction and possess excellent

tensile strength and cryogenic strength. Since the thrusters of Centurion would be burning liquid hydrogen, aluminum-

lithium alloys would be great material for providing overall thermal shielding to the OTV. Propellant tanks have been

traditionally fabricated out of metals. Switching from metallic to composite propellant tank construction dramatically

increases the performance capabilities of the OTV through a significant reduction in weight.

31

Table 4.1. Comparison of common material for space vehicles [36]

Material Advantages Disadvantages

Composites - Low density

- Good strength in tension in appropriate

direction

- Can be tailored for high stiffness,

strength, and low coefficient of thermal

expansion

- Insufficient in compression and tension in

incorrect direction

- Brittle

- Costly to machine in small numbers

- Behaves poorly in environments with high

levels of radiation

Beryllium - High stiffness per density ratio

- Strength close to that of steel

- Alloys of Beryllium are extremely stiff

and lightweight

- Retains its properties up to 1000 degree

Fahrenheit

- Low ductility, fracture toughness, and

impact resistance

- Cannot be primary structural material

- Difficult to fabricate: costly

- Extremely toxic to humans

- Susceptible to surface damage during

machining due to brittleness

Titanium - High strength

- High stiffness to density ratio

- Low weight

- Low coefficient of thermal expansion

- Can replace Al in higher temperature

environments up to 1200 degree

Fahrenheit

- Suitable for cryogenic applications

- Hard and costly to machine

- Low fracture toughness

- Not as light or durable as Al

- Can become brittle at low temperatures or

when placed under repeated loads

- Touching fluids/lubricants can degrade

- Poor resistance to wear

Magnesium - Low density, lighter than Aluminum

- Useful for lower strength, lightweight

applications up to 400 degree Fahrenheit

- Prone to corrosion, needs protective

coatings

- Low yield strength

- Cannot be used in primary structure or areas

subject to wear, abrasion/erosion, or in

contact with moisture

Steel - High strength

- Treatment gives good range of strength,

hardness, and ductility

- High density

- Difficult to machine

- Most alloys are magnetic

Aluminum &

its alloys - Low density, high strength per weight

ratio

- Easy to manufacture/machine

- If anodized, low surface

absorption/emission properties

- Good in compression

- High coefficient of thermal expansion

- Low hardness

- Cannot be used above 400 degree

Fahrenheit

The PAMG-XR1 5056 Aerospace Grade Aluminum Honeycomb Core from Plascore Inc. were chosen as

the material for the outer casing of Centurion. PAMG-XR1 5056 honeycomb is made from 5056 aluminum alloy

foil and meets all the technical requirements of AMS C7438 Rev A.

32

Figure 4-1. PAMG-XR1 5056 Aluminum honeycomb

Besides the excellent strength, its density of 129.75 𝑘𝑔/𝑚3 would shed significant weight from the outer

casing of Centurion.

The cryogenic fuel tank of the OTV would be constructed from the CYCOM® 5320-1 toughened epoxy resin

prepreg system from Cytek Industries Inc. This epoxy resin system is chosen by NASA because of their high

performance composite cryotank due to its low-cost, lightweight, and superior strength. At 1310𝑘𝑔/𝑚3, its density is

only a fraction of metallic materials traditionally used for cryotank construction.

Figure 4-2. CYCOM 5320-1 toughened epoxy resin prepreg system [37]

33

Mass Estimation

Mass estimates of all components from all the subsystems were obtained and tabulated. The total dry mass

of the OTV is approximately 15950 kg. The launch mass was estimated by adding the fuel mass as well as the required

payload to LEO. At launch, the fully fueled OTV carrying max payload has a total mass of 88225 kg.

Table 4.2. Mass estimates of Centurion and its components

Subsystem Component Quantity Mass estimate/kg

Structures &

Communication

fuel tank 1 6000

wall + shielding 1 2000

antenna+supporting truss 2 120

ADCS

attitude thruster 4 32

CMG 4 138

CPU 1 3

Proximity Sensor 1 4

star tracker 2 4

attitude thruster fuel tank 4 120

sun sensor 2 2

Thermal & Power

battery 3 120

Radiator + supporting coolant

equipment 65 372

solar panel 2 20

Docking NASA docking system 1 340

Propulsion main thrusters+nuclear

reactors 3 6675

Total Dry Mass

15950

Fuel Mass

49595

Payload Mass

22680

Total Mass

88225

34

Vehicle Internal Volume

According to the dimensions indicated on Figure 1-2, the outer diameter and total length of Centurion are 7

m and 26.24 m respectively. This ensures that Centurion could fit into the fairing of different launch vehicles, like the

Falcon 9. Due to the amount of liquid hydrogen fuel required for mission to L2, the bulk of the internal volume of the

OTV would be used for cryogenic propellant storage. With propellant tank wall and thermal and radiation shieldings,

the internal volume of the cryogenic propellant tank is 625 𝑚3, which is more than enough for the entire mission from

LEO to L2.

Vehicle Structural Design

As shown in Figure 1-3, the OTV was divided into three segments, namely systems module, cryogenic

propellant tank, and propulsion system. The structural design of each segment was an iterative process since numerous

revisions were made during the entire project to meet evolving requirements from the other subsystems.

4.2.4.1. Systems Module

Despite the relatively small size of the systems module, it provides structural support to power systems, flight

computers, attitude control thrusters, and various other delicate equipment. At the same time, the systems module will

dock with payload modules from our clients. As a result, the top priority in the structural design process is ensuring

its structural integrity as well as normal operations of the equipment it protects. Also, it is desirable to design the

structure of the systems module with a large margin of safety to prevent possible failures. For Centurion, as shown

in Figure 4-3 below, the inner truss connects the NASA docking system to the cryogenic propellant tank. It also

provides mounting planes as well as structural support to the IMU, CMG, batteries, CPU, sun sensors, star tracker

cameras, radiators, solar panels and the antenna. The top plane and bottom corners of the inner truss are welded onto

the NASA docking system and the main propellant tank respectively. A pair of sun sensors and a pair of star tracker

cameras are bolted onto the top plate of the inner truss, with each pair arranged on opposite sides of the circumference.

Inside the truss, delicate components like the CPU, IMU, and CMG are securely attached to additional mounting

surfaces. On opposite sides of the truss, there are two aluminum truss arms, each of which carries a parabolic reflector

antenna, a hinged radiator, and a solar panel. The truss arm would extend outside the outer casing of the systems

module so that the radiators, solar panels, and antennas could have an unobstructed field of view in space. There are

also two sets of attitude control thrusters in the systems module. Two bipropellant fuel tanks are fixed to the inner

truss while connected to two attitude thrusters via fuel lines.

35

Figure 4-3. Systems Module with outer casing removed

Not shown in Figure 4-3 is the outer casing of systems module. The outer casing consists of two layers, one being

made of aluminum honeycomb for structural support, and the other being an aluminum lithium alloy for thermal

shielding.

In order to reject excess internal heat generated by the onboard equipment, the Alpha Deployable Radiator

(ADP) manufactured by Swales Aerospace was hinged onto the truss arm. ADP is designed to be attached to the

spacecraft through spherical-bearing hinges, pyrotechnic, or paraffin release actuators and snubbers.

36

Figure 4-4. Hinged Radiator for Systems Module [38]

4.2.4.2. Cryogenic Propellant Tank

By using liquid hydrogen as the propellant for the main propulsion system, thermal shielding becomes

equally important as structural support. As a cryogenic fluid, liquid hydrogen must be stored at approximately -423

F° and properly shielded to prevent a phenomenon known as boil-off.

As shown in Figure 4-5, the propellant tank consists of two half spheres and one cylinder. This configuration

is generally preferred to use for pressurized structures. Meanwhile, it also provides a total internal volume of 625 𝑚3

which is the amount of liquid hydrogen fuel required for the mission.

37

Figure 4-5. Cryogenic Propellant Tank

4.2.4.3. Propulsion Systems

The propulsion system is found at the very bottom of the OTV. The bimodal thermal nuclear propulsion

system would be housed and shielded in this segment of the structure. As shown in Figure 4-6, three reactor-thruster

sets are separated, by a layer of radiation shielding, from the upper section of Centurion. This ensures the rest of the

OTV would not be adversely affected by the nuclear radiation from the thermal nuclear reactors.

Figure 4-6. Propulsion System with outer casing removed

38

The extreme heat generated by the reactors and thrusters is another major concern during the design process

of the propulsion system structure. In order to effectively dissipate the heat to space, a deployable radiator system

developed by Lockheed Martin was chosen for this purpose. It uses active, mechanically pumped liquid ammonia

loops to transport heat out to space. With a total surface area of 65 m2, the pair of double-sided radiators could be

folded for launch and then unfolded into their extended form for final deployment once in space.

Figure 4-7. Deployable radiator [39]

4.2.4.4. Thermal Shielding

Table 4.3. Temperature limits for common materials [40]

39

The highest temperatures affecting structural design typically arise from atmospheric entry or robust

propulsion systems. These conditions require the use of special materials, tailored insulation, or both [41]. The

Space Shuttle uses tile insulation on its exposed aerodynamic surfaces. Most of these areas have normal aluminum

skin-stringer or honeycomb panels beneath, though the most critical locations (e.g., stagnation points) use titanium.

4.2.4.5. Radiation Shielding

Electromagnetic and particle radiation, such as protons and electrons from radiation belts, solar emissions,

and cosmic radiation, can remove structural material. The amount is usually no more than 1 mg/𝑐𝑚2, which has no

serious effect on the design of most structures. Thin films, however, such as a solar sails, must account for this

degradation. Radiation also reduces the ductility of most materials. This must be anticipated for long-duration or high-

exposure missions since the design life time of the Centurion is expected to be 5 years or 10 missions. Another major

source of radiation is the thermal nuclear reactor onboard. Since relevant shielding will come with the thermal nuclear

propulsion system, we assume the internal radiation to be at the minimal level and would not pose any threat to

onboard equipment as well as payload capsule.

Structural Testing

Besides being the most massive structural component onboard Centurion, the cryogenic propellant tank

serves as the key component connecting the systems module with the main propulsion system. It must be able to

withstand various loads during launch, orbital transfers, and other maneuvers. A brief structural analysis of the

propellant tank was performed in PTC Creo to simulate a simplified model to equivalent loads.

The worst loading on the propellant tank would occur during burn times as the tank was subjected to massive

compressive loads. The fully fueled propellant tank was subjected to internal pressure, top and bottom structural loads,

and gravitational loads estimated at 6 Gs according to the user’s manual from SpaceX [42]. As shown in Figure 4-8,

a maximum stress of approximately 33 MPa was found along the cylindrical segment of the wall. Comparing this

value with the critical value given in the datasheet of CYCOM 5230-1, it is apparent that the propellant tank is

structurally safe.

40

Figure 4-8. Stress Analysis of cryogenic propellant tank

4.3 Critical Design Issues

Since aluminum honey combs will be the primary structure of Centurion, consideration must be made to

ensure they will not fail due to thermal cycling. As Centurion will experience repeated thermal loading and unloading

during its mission to L2, potential damages caused by thermal cycling must be studied and tested to ensure the

structural integrity of its primary structure. Also, because the thermal-nuclear propulsion system is still in

development, its reliability and radiation effects on the overall structural integrity of Centurion is difficult to gauge.

5. Communication and Systems

5.1 Frequency Band Selection

The Near Earth Network (NEN) provides several bands for uplink and downlink including S-band, X-band,

and Ka-band. These bands correspond to a certain operating frequency range. A higher frequency corresponds to

higher data rates, however with this increase comes increases in power requirements and pointing accuracy. Table 6.1

summarizes the bands available for use with the NEN.

41

Table 5.1. NEN Frequency Band Characteristics [2]

Band Frequency (GHz)

S-band 2-3

X-band 7-11

Ka- band 18-30

As Centurion is not transmitting data that would require very high bandwidth, very high frequency bands are

not required. Figure 5-1 depicts the relationship between atmospheric attenuation of a signal and signal frequency.

There is very little attenuation in the lower frequencies that S and X support, however for higher bands such as Ka

there begins to be a much higher level of attenuation. The higher the attenuation of a signal the less reliably the signal

goes through. As Centurion does not require the high speed data transmissions that Ka-band allows, it is much safer

to utilize the two lower frequency bands of S and X. Both of these bands are thoroughly supported on the NEN.

Figure 5-1. Atmospheric attenuation as a function of frequency [43]

5.2 Radiometric Tracking

The NEN provides several services for position and velocity determination that will be useful for Centurion.

These services include Doppler, range, and angle tracking. These services will enable accurate orbit determination

which is vital for orbital transfer maneuvers as well as for docking maneuvers. A spacecraft’s range is measured by

round trip travel time of a sequence of sinusoidal tones originating at one of many different ground-based stations.

The trip time is then divided by the speed of light to calculate the position of the spacecraft. As this signal travels to

and from the spacecraft, its frequency is slightly modified by Doppler shift. Comparing the modified signal to the

42

original signal allows the velocity of the spacecraft to be determined [44]. Angle tracking uses a similar method to

ranging, however, it requires two ground antennas rather than just one. Each satellite calculates range from the

spacecraft by using the distance between the antennas and the angle in the sky [45].

Table 5.2. Near Earth Network Tracking Characteristics [46]

Characteristics Value

Ranging Accuracy 10 Meters (1 sigma)

Doppler Accuracy 1 millimeter per second (1 sigma), 5 second

integration time

Angle Accuracy 0.1 Degrees

Maximum Velocity 2.0 Degrees/second (az and el)

Table 5.2 shows the accuracy capabilities of the NEN. The values that are particularly useful are the ranging

and Doppler accuracies. These values are important for orbital transfers because they allow Centurion to perform

accurate ΔV maneuvers and orbital transfer maneuvers. While the ranging capabilities are not accurate enough for

docking maneuvers they are accurate enough to get in close enough proximity to the fuel depot and the payloads for

the proximity sensors to allow even finer accuracies of range and velocity.

Comparing the NEN(Near Earth Network) with the DSN(Deep Space Network), Figure 5-2 shows that more

vehicles in lunar orbit and L1/l2 orbits use the DSN compared to NEN. This is therefore an opportunity for Centurion

to take advantage of the lack of trraffic in the NEN.

Figure 5-2. Number of missions using NEN vs. DSN [47]

43

NEN can operate optimally at the L1 and L2 ranges, just as well as DSN. G/T is a measure for the antenna gain

accounting for differences in noise measurements at different distances from Earth. G/T is frequently used as a

measure of performance. Figure 5-3 shows that NEN, represented by the red plot, can provide up to 25 dB/Kelvin in

the S-Band. This large range means that NEN can be used to provide communication for vehicles in L1 and L2 orbits

without a significant degradation in the quality of signal.

Figure 5-3. NEN performance compared to DSN using the S-Band [47]

EIRP(Equivalent Isotropically Radiated Power) is another measure of the performance of a communication

network. In Figure 5-4, DSN provides a higher EIRP compared to NEN in the S-band region, which means that DSN

signals are stronger than NEN. However, the graph shows that NEN signals are strong enough to be used at L1 and

L2 orbits, with NEN having a maximum EIRP of about 85 dBm/W.

44

Figure 5-4. EIRP of NEN compared to DSN in the S-Band [47]

NEN has G/T and EIRP values that allow it to be used effectively in communication in vehicles in the L1 and L2

regions, such as Centurion. The largest advantage of using the NEN lies in the smaller number of vehicles currently

using NEN, which provides a larger of communication frequencies that can be used.

5.3 Antenna Selection

As listed in Table 5.3, parabolic reflector is the ideal choice of antenna configuration for Centurion as it

provides the highest gain with reasonable max gain. The high gain antenna is able to transmit data to Earth on two

frequency channels, on at roughly 8.4 gigahertz and the other at around 2.3 gigahertz. The 8.4 GHz channel is the X-

band that sends scientific and engineering data whereas the 2.3 GHz channel is the S-band that relays status of

Centurion to Earth.

Table 5.3. Types of antenna for space communication [11]

Antenna Type Typical Max Gain/ dBI Mass /kg

Parabolic Reflector 15-65 10-30

Helix 5-20 10-15

Horn 5-20 1-2

Array 5-20 20-40

45

Figure 5-5. High Gain Antenna with parabolic reflector

6. Attitude Determination and Control Systems

6.1 Design Approach

The attitude determination and control system (ADCS) capabilities for such a versatile mission must be

comprehensive. The systems of Centurion must be able to perform with high accuracy in low earth orbit (LEO), while

in transit to Lagrange points 1 and 2 (L1 and L2, respectively), while station keeping at those points, and while docking

with the fuel depot and payload module. In addition to performance requirements, these systems must also be power

efficient, cost efficient, and have a lifespan suitable for this mission. To achieve the goals of the ADCS subsystems a

variety of sensors and actuators were considered. Centurion’s attitude sensors must be able to collect accurate attitude

data under any flight condition and at any position along its route. Its actuators must be able to orient the spacecraft

accurately for docking procedures and when the spacecraft is at its peak mass. Furthermore, the control system design

46

must be able to provide fairly high frequency attitude control and stabilization. Overall, the main design drivers of the

ADCS subsystems are accuracy, reliability, speed, and redundancy.


Sensor Selection

The sensors of Centurion are very important for precise knowledge of the orientation and position of the

spacecraft. These parameters need to be known to a fine degree in order to correctly maneuver the spacecraft. In order

to get the maximum resolution of Centurion’s attitude a variety of sensors were will be included on Centurion,

including star trackers, IMUs, and sun sensors.

Modern star trackers operate by capturing an image of a star field and cross referencing it to a catalog of

known star positions. The relative position of the stars help reduce errors and improve accuracy. Table 6.1 shows a

comparison of a variety of readily available star trackers on the market. Important factors to consider with a star tracker

are lifetime, resolution, update rate, and tracking rate. As the mission lifetime is 5 years, all of the listed star trackers

are more than adequate. For most mission procedures all of these trackers would be more than accurate enough;

however, for procedures such as docking, very accurate attitude determination is necessary. While the trackers that

provide the highest accuracy attitude information are the Terma HE-5AS and the Jena Optronik ASTRO APS, the

Surrey Rigel-L seems to be the best star tracker overall. While it does not have the highest resolution, it excels in its

update rate and tracking rates. In addition, multiple star trackers can be used to reduce the possibility of sensor error

and malfunctions. This star tracker also features full autonomous tracking which allows it to output readily useable

quaternion angles rather than raw star positions. Autonomous tracking greatly reduces the strain and computational

requirements of onboard computers. The cost of the 2-unit pack is $910,600. Figure 6-2 illustrates the Surrey Rigel-L

Star Tracker. A star tracker will be mounted on two opposite sides of the spacecraft as shown in Figure 6-1.

47

Figure 6-1. Layout of ADCS Components

48

Table 6.1. Characteristics of common star trackers [48] [49] [50]

Manufacturer/Model Lifetime

(yrs)

Max Resolution

(arc sec)

Update

Rate (Hz)

Tracking Rate

(deg/s)

Surrey/Rigel-L 7+ X/Y < 3

Z < 25

1-16 6

Terma/HE-5AS - RMS pitch, yaw <1

RMS roll <5

4 0.5-2.0

Jena Optronik/ASTRO APS >18 X/Y < 1

Z < 8

10 0.3-3

Inertial measurement units (IMUs) and gyroscopes provide relative attitude. Relative attitude sensors require

an initial attitude as well as corrections from an absolute attitude sensor to correct noise, inaccuracies, and drift.

Gyroscopes detect changes in angle of rotation. IMUs contain gyroscopes as well as accelerometers in order to detect

changes in position in addition to changes in rotation. For precise maneuvering of Centurion, the pointing requirements

are very high and will require detailed knowledge of both angle and position.

Table 6.2 lists the characteristics of several commonly used

IMUs. Bias stability measures how stable the output of the gyro is, bias

repeatability measures the accuracy of the output after powering on the

device, angular random walk (ARW) measures the noise of the device,

and scale factor measures accuracy of output when varying rotation input

or velocity input. The IMU that perform best in all of these categories is

the Honeywell HG9848. For the purposes of the mission, it is very

important to maintain angular accuracy while docking, and for this reason this sensor seems to perform best overall.

IMUs tend to have a higher failure rate than many components and for this reason there will be a redundant IMU

onboard. Each unit costs roughly $50,000, putting the total cost of IMUs at $100,000 [51].

Table 6.2. Characteristics of common IMUs [52] [53] [54]

Manufacturer/Mo

del

Gyro Bias

Repeatability/

Stability (deg/h)

Gyro ARW

(deg/√hr)

Gyro Scale

Factor

(ppm)

Accel Bias

Repeatability

(μg)

Scale

Factor

(ppm)

Northrop

Grumman/

LN-200S

1/<0.1 <0.07 100 300 300

Honeywell/

HG9848

<0.005 <0.005 <10 <50 150

Kearfott/

KI-4901

0.005/0.003 .003 50 400 500

Figure 6-2. Surrey Rigel-L

Star Tracker

49

Sun sensors determine the direction of the sun and report body angles relative to the sun. Sun sensors are not

very effective at high angular rates. Accuracy of sun sensor body angles can vary from several degrees down to below

one degree depending on quality of sensor. These sensors require an unimpeded view of the sun therefore multiple

sun sensors are required on a spacecraft. As sun sensors shall be a secondary sensor for this mission and mainly

required for just solar array pointing, accuracy is not of huge importance.

Table 6.3 lists specifications of several common sun sensors. The most

attractive type seems to be the Adcole course sun sensor pyramid as this sensor

requires no power input and the lowest number of units for a full sphere of coverage.

Each sun sensor has a cost of $60,000, therefore the total cost of these sensors is

$120,000. Figure 6-3 illustrates the configuration of the sun sensor pyramid and Figure

6-1 shows where these sun sensors will be mounted.

Table 6.3. Characteristics of common sun sensors [5]

Manufacturer/Model Field of View Accuracy (deg) # required for full coverage

Adcole/

Digital Sun Sensor

+/- 64 deg 0.25 5

Adcole/Course Sun Sensor Pyramid 2π steradians 1 2

The requirements for the docking and berthing capture system employed by Centurion are listed in Table 6.4.

These tolerances, and in particular the lateral alignment requirements, cannot be achieved without accurate knowledge

of the relative distance between Centurion and what it is docking with. In addition to sensors for general attitude

knowledge, additional sensors are required to assist with docking maneuvers.

Table 6.4. Capture Tolerances for Docking and Berthing [55]

Operation Approach

Velocity (m/s)

Lateral

Alignment (m)

Lateral

Velocity (m/s)

Angular

Misalignment (deg)

Angular Rate

(deg/s)

Docking 0.3 0.2 0.05 5 0.25

Berthing 0.01 0.5 < 0.01 < 10 < 0.1

Proximity sensors are vital for the autonomous docking procedures performed by Centurion. Table 6.5 lists the

tracking accuracy of the proximity sensor system to be used on Centurion. In particular, the accuracy in the X, Y, Z

and range that this proximity sensor provides enables the requirements of the capture system to be fulfilled.

Figure 6-3. Adcole Course

Sun Sensor Pyramid

50

Table 6.5. Demonstrated Accuracy of AOS Proximity Sensors [56]

Distance to Target X (m) Y (m) Z (m) Pitch (deg) Yaw (deg) Roll (deg) Range (m)

2m 0.0003 0.0007 0.0029 0.25 0.09 0.06 0.003

30m 0.0098 0.0039 0.0061 1.04 0.81 0.33 0.012

Of the sensors considered, star trackers are the best absolute attitude determination sensor in terms of

accuracy and for this reason alone two of these sensors will be used. Some downside of this sensor is that star trackers

tend to provide attitude data at fairly low rates and can fail to determine attitude in certain conditions. One way to

work with this is to combine star tracker data with IMU data. The star tracker will provide an absolute attitude for

which the IMU to integrate off of. In case the star tracker cannot determine attitude the IMU can continue be used

while capabilities return to the star tracker. In addition to these two sensors, sun sensors will be included. Sun sensors

are fairly inexpensive and provide a straightforward means of course attitude knowledge. In addition to these attitude

sensors, a proximity sensor will be used in order to enable docking and refueling maneuvers.

Actuator Selection

The actuators of Centurion are very important for a variety of maneuvers including orbital transfers, slewing,

and docking. Some of these maneuvers require very fast maneuvering while some maneuvers require very fine

accuracy. In order to satisfy these requirements, a variety of actuators were considered, including thrusters, reaction

wheels, magnetic torque rods, and control moment gyroscopes. Reaction wheels will not be able to meet the pointing

requirements of Centurion due to the low amounts of torque produced by these actuators. Similarly, due to fact that

Centurion will not always be in LEO and will require much higher torques than torque rods can provide, magnetic

torque rods will also not be used in the final design of Centurion.

Thrusters create a reaction force by expelling mass from the spacecraft. In addition to providing thrust,

thrusters are useful for attitude control; for this purpose the thrusters must be arranged along each axis in pairs that

point in opposite directions and are located along a line that passes through the spacecraft’s center of mass. This type

of control is known as a reaction control system (RCS). RCS systems typically use a combination of large and small

thrusters in order to obtain both large and minute adjustments.

Table 6.6 lists several characteristics of interest for a variety of available thrusters. Several types of propellant

were considered including cold gas, monopropellant, and bipropellant. Cold gas thrusters produce very small amounts

of thrust and would be insufficient for this mission as the full mass of Centurion is very large. A larger thrust is

51

required for this spacecraft, so that monopropellant and bipropellant thrusters are acceptable. Of these two fuels,

bipropellant is far more reliable and less prone to degradation. Of the remaining thrusters considered, the Aerojet R-

1E has the best balance of available thrust and specific impulse. These thrusters are found on the space shuttle for

attitude control and are quite reliable.

There will be four such clusters with two at the forward part section of the

spacecraft and two at the rear as shown in Figure 6-1. This configuration will allow

for thrust in the forward and reverse direction as well as attitude changes in the roll,

pitch, and yaw. The thrust produced by these thrusters is more than adequate for both

large and small attitude changes.

Table 6.6. Characteristics of common thrusters [57] [58] [59] [60]

Manufacturer/Model Thrust (N) Specific Impulse (sec) Propellant

Vacco/2 LBF Cold Gas 8.9 - GN2

Moog/DST-11H 22 310 Hydrazine/MON

Aerojet/R-1E 111 280 MMH/NTO

Aerojet/MR-107V 67 229 Hydrazine

Control moment gyroscopes (CMGs) are similar in function to reaction wheels but are better suited to large

spacecraft such as the International Space Station. A control moment gyroscope consists of a rotor mounted on a single

or dual axis gimbal that tilts the rotor’s angular momentum. The tilt of the rotor creates a torque that rotates the

spacecraft. These actuators require only a small amount of power to produce a very large torque; however, they tend

to be fairly expensive. Similar to reaction wheels, desaturation maneuvers must periodically be executed in order to

rid the system of torque buildup [61]. In order to obtain three axis control of a spacecraft three single-axis CMGs are

required.

Table 6.7 lists several characteristics of common CMGs. All of the CMGs considered produce suitable

torques. Although the CMGs produced by L-3 produce the largest output torque, their rather large size, weight, and

price reduce their appeal. The Honeywell and Airbus CMGs are comparable; however, while the Honeywell CMGs

provide a higher output torque, they consume almost four times the power of the Airbus CMGs. Although this is a

significantly higher power consumption, the amount of power available on Centurion is more than adequate to fulfil

this amount of power consumption. The Honeywell M50 CMGs should be more than adequate for high precision

attitude maneuvers. Six CMGs will be used onboard to enable full mobility of Centurion while allowing for

Figure 6-4. Configuration of

attitude control thrusters

52

redundancy. The price of these will be estimated using the price of a similar CMG, the L-3 DGCMG. The price per

unit of this specific CMG is roughly $7 million [62]. Based on the weight of the Honeywell M50 and the one produced

by L-3, the price per unit is estimated at $700,000. Therefore the total price of the six CMGs is $4.2 million. The

location of the CMGs is shown in Figure 6-1.

Table 6.7. Characteristics of commonly used control moment gyroscopes [63] [64] [65]

Manufacturer/Model Angular Momentum

(N-m-s)

Output Torque

(N-m)

Weight

(kg)

Power Requirements

(W)

Honeywell/M50 25-75 0.075-75 28 95 @ peak torquing

L-3/DGCMG 4800/250 4760 258 272 -

Airbus/CMG 15-45s 15 45 18.4 25

One of the main jobs of the CMG is to mitigate environmental torques. While thrusters will be able to resist

these torques adequately, it will require very frequent thruster firings. CMGs will be able to actively resist these

torques. The type of torque that will play the largest role is solar radiation pressure. Equation (6-1 estimates the

maximum torque from solar radiation that must be mitigated, where Ts is the torque, Φ is the solar constant, c is the

speed of light, As is the sunlit surface area, q is the reflectance factor, φ is the angle of incidence, and cps and cm are

the centers of pressure and mass. Thus, the maximum total torque from solar radiation can be calculated as roughly 4

x 10-3 N-m. This torque will easily be mitigated.

𝑇𝑠 =𝛷

𝑐𝐴𝑠(1 + 𝑞)(𝑐𝑝𝑠 − 𝑐𝑚)cos𝜑

(6-1)

The CMGs will also allow for emergency situations in instances when thrusters cannot be used. Eq. (6-2)

was used to determine the capabilities of the CMGs onboard Centurion. From Table 6.4, the maximum angular

misalignment for docking maneuvers is 5 degrees while the maximum angular rate while doing these maneuvers must

be lower than 0.25 degree per second. Each CMG produces a maximum of 75 N-m of torque. With the selected CMGs

it will take at most around 25 minutes for Centurion to slew into any roll orientation. At the angular acceleration that

these CMGs produce the maximum angular velocity that is allowed by the docking mechanisms will not be surpassed.

To pitch or yaw 180o at maximum rate it will take Centurion roughly 40 using solely the CMGs. This is well within

the time requirement for orbital maneuvers.

53

𝜏 =4𝜃𝐼

𝑡2

(6-2)

Thrusters will be used as the main actuation method for orbital and docking maneuvers as well as for

momentum desaturation maneuvers. Eq. (6-3) were used to determine the torqueing capabilities of the selected thruster

systems. For slewing in the roll direction a rotation of 180o can be performed in as little as 4 minutes. For slewing in

the pitch or yaw directions a rotation of 180o can be performed in as little as 6 minutes. In the roll case the change in

velocity needed is 0.26m/s while in the yaw or pitch cases the change in velocity needed is roughly 0.36 m/s. As with

the CMGs, thrusters will be able to perform docking and refueling tasks with ease.

𝜏 = 𝐹𝑅 = 𝐼𝛼 (6-3)

These two actuation methods will provide Centurion with more than enough control to perform the

maneuvers critical to mission success.

Onboard Processing and Control Methods

Software development will be a major factor in the timetable and cost of Centurion.

Table 6.9 lists the estimated source lines of code (SLOC) for Centurion. While most of these are typical

values for a spacecraft the thermal control and power management are higher than average to accommodate for the

nuclear bimodal propulsion system and its accompanying power system. The total SLOC is estimated at 54,000 lines.

A comprehensive onboard flight computer will be employed on Centurion to ensure accurate control of the

spacecraft. Centurion does not require state-of-the-art processor specifications for attitude control. The majority of

processor resources will be used by the employment of a Kalman filter. Common Kalman filters have complexities

on the order of n3 flops per step where a flop is a multiplication and addition operation [66]. Assuming a Kalman filter

running at 10 kHz, the processing requirement is less than 3 MIPS. Table 6.9 lists several readily available radiation

hardened flight processors. All of the processors provide enough processing power for the needs of Centurion.

Although it is not the most powerful, the Rad750 is one of the most flight proven processors available and for this

reason it will be used on Centurion.

54

Table 6.8. Estimated Source Lines of Code [67]

Computer Software Component SLOC

Executive 1,000

Communications 2,000

Attitude/Orbit Sensor Processing

Sun Sensor 500

IMU 1,000

Star Tracker 2,000

Attitude Determination and Control

Kinematic Integration 2,000

Kalman Filter 8,000

Error Determination 1,000

Orbit Propagation 10,000

Attitude Actuator Processing

Thruster Control 1,000

CMG Control 1,500

Fault Detection 10,000

Utilities

Basic Mathematics 1,000

Transcendental Mathematics 1,500

Matrix Mathematics 2,300

Time Management & Conversion 700

Coordinate Conversion 2,500

Other Functions

Momentum Management 3,000

Power Management 2,000

Thermal Control 1,500

Total 54,500

% ADCS 45%

Table 6.9. Characteristics of radiation hardened flight processors [68] [69] [70]

Manufacturer/Model Speed (MIPS) Power (W) Flight Proven

IBM/Rad6000 35 10 Yes

IBM/Rad750 400 10 Yes

Proton300k 8000 12 Yes

Three flight computers will be used in conjugation to form a triple modular redundancy system. An error in

one computer can thus be outvoted by the other two computers. For the system to fail as a whole at least two computers

must produce identical errors which is highly improbable. Traditional systems use a single voting gate which allow

for the same failure modes as using a single flight computer. On Centurion, a redundant voting gate will be included

in case of a failure in the primary voting gate. This process is illustrated in Figure 6-5.

55

7. Spacecraft Power Management Systems


Centurion’s power system is posed as a solution to some key requirements. Firstly, the power system shall

provide enough power for all onboard computers and sensors, as well as the launching and docking mechanism.

Secondly, a source of power shall be available in the case of a failure of the power generation system. Thirdly, the

electronic components shall be protected against radiation. Fourthly, the power distribution system shall maintain a

suitable temperature for the onboard electronics.


Power generation and distribution

The main source of power will be generated by the Bimodal Nuclear Thermal Rocket System (BNTRS).

BNTRS is a propulsion system that uses nuclear power in order to propel the vehicle as well as to provide power when

required. The advantage of this system is its weight savings. There are two modes of operation for this system: the

thermal propulsion mode (when the vehicle is being propelled), and the power generation mode (when the vehicle is

not being propelled). During the power generation mode, shown in Figure 7-1, Helium-Xenon is heated in the nuclear

Figure 6-5. Triple Mode Redundancy Configuration

56

reactor, and then passes through the turbine, producing upto 25 kW of electric power. Excess heat in the He-Xe gas is

removed by passing it through a radiator, before getting heated once again by the reactor.

Figure 7-1. Power schematic of He-Xe gas for electricity production [71]

The ESCORT system is a BNTRS that has been chosen for Centurion. This system consists of three bimodal

nuclear reactors. Each reactor can produce a maximum of 25kW of power. At 2/3 of their maximum output, the three

reactors of ESCORT can produce 50kW of power. This energy supplies 50 times the minimum required power of the

mission, which is 1.4kW. The control rods can be used to control the amount of power to suit the needs of the mission,

which vary from 1.4 kW to 2kW, depending on the use of the docking system.

The electric energy that is generated by the nuclear reactor is sent to the front of the vehicle, where the system

module is present. The electric energy is sent at high voltage of about 124V to the system module, in order to reduce

heat loss [35]. At the system module, the voltage requirements vary significantly between system components. The

IBM/Rad750 computer uses the smallest voltage (between 2.5V and 3.3V).The Surrey/Rigel L star tracker uses the

highest voltage out of the components (between 16 and 50V).

Table 7-2. Voltage requirements for System module components.[29][31]

System component Voltage Required(V) Power Required(W)

Surrey/Rigel-L star tracker 16-50V 0.5-6.5W

Honeywell/HG9848 IMU 5V(+- 15V) 10W

Adcole/Coarse Sun Sensor Pyramid 0V 0W

Aerojet/R-1E attitude control thruster 28V 36W

Honeywell/M50 moment gyroscope 28V 11-113 W

IBM/Rad750 2.5-3.3V 5W

57

Figure 7-2. Power distribution schematic.

Since the voltage input varies from 2.5V to 50V, DC-DC convertors, similar to the ones used on the ISS [35]

will be used to bring the voltage down in order to supply the required voltages for the components. AC-DC Convertors

will also be used, as shown in Figure 7-2. The voltage drops from 124V to about 28V when it reaches the System

Module.

Power Storage

For this mission, the batteries had to satisfy four main parameters. The batteries were required to be as light

as possible, rechargeable, have a high energy density to power launching and docking with other space vehicles, and

have a design lifetime of at least 5 years. The best battery must also survive large range of temperatures that the vehicle

will be exposed to in lunar orbit. The temperature can vary greatly from -160C to 130C in lunar orbit [72]. Nickel-

hydrogen batteries are the current leader in “on orbit power storage” [73] . However lithium ion batteries hold a lot of

potential in the aerospace industry [73]. A variety of batteries were studied in order to find the most suitable one for

the mission. The criterion that held the most weight in the decision-making processing were the specific energy, energy

density, the operating temperature, and design life.

Li-ion batteries operate between the largest temperature ranges. They also have the highest energy density

and the second-highest specific energy (with Ag-Zn batteries coming first). The disadvantage of using lithium ion

batteries are the short design life. Lithium batteries last only for a year. This means that in order to power a five year

mission, there needs to be at least five batteries. There should be a redundant battery for each of the five, which means

there needs to be at least 10 batteries.

58

Table 7.1. Batteries and their characteristics [36]

Technology Specific

Density(Wh/kg)

Energy

Density(Wh/l)

Operating

temp.

Range(C)

Design

life(years)

Cycle life

Ag-Zn 100 191 -20 to 25 2 100

Ni-Cd 34 53 -10 to 25 3 25,000-

40,000

Super Ni-Cd 28-33 70 -10 to 30 5 58000

IPV Ni-H2 8-24 10 -10 to 30 6.5 At least 60000

CPV Ni-H2 30-35 20-40 -5 to 10 10-14 50,000

SPV Ni-H2 53-54 70-78 -10 to 30 10 At most

30,000

Lithium Ion 90 250 -20 to 30 1 At least 500

An advantage of IPV Nickel Hydrogen batteries is that they have longer design lifecycles than Lithium Ion

batteries [47]. However, the IPV Nickel Hydrogen battery has a specific energy of 24 Wh/kg [47], which is not high

enough for the energy requirements of this mission. The minimum power needed for Centurion is 1.4 kW. Assuming

a rough numbers of hours of flight time to be 720 hours and the station-keeping time to be 144 hours, and a total power

consumption of the vehicle to be 2kW, the weight of the Nickel hydrogen battery would have to be 83kg to provide

power for the complete duration of the mission. Using the same analysis for lithium batteries, the weight of the Lithium

battery needed is just 22kg. Another disadvantage of IPV Nickel-hydrogen batteries is that it also occupies a large

space because of its low volumetric energy density of 10wh/L, as observed in Table 7.1. Batteries and their

characteristics [36]. This means that a significant volume of the vehicle will need to be used to house the batteries

for this mission. In this regard, Lithium Ion batteries have a specific energy density of 250Wh/L. Lithium Ion batteries

will thus occupy a much smaller space than the IPV Nickel-Hydrogen batteries. The lithium ion batteries have a very

low cycle life compared to the Nickel-Hydrogen batteries.

Lithium Ion batteries are the most suitable for this mission, because they have a high energy density, and

work within a large operating range. A critical issue with Lithium Ion batteries is its short design life of one year.

Since the life span of the mission is five years, the batteries have to be replaced once a year. There will be redundant

batteries installed in the systems module to account for this issue.

Quallion is the manufacturer chosen for this mission, because of their innovative technology that can work

for up to a cycle life of 100,000 cycles at a capacity of 72 Ah [74]. 100,000 cycles are greater than the 6 year lifetime

of the mission specifics. The QL075KA battery has a maximum power output of 72*3.6=259.2 W. So in order to store

at least 1.4 W, we would need eight batteries. The QL075KA battery has an energy density of 142 Wh/kg, so the total

59

weight of the batteries needed for the duration of the mission would be about 9.86kg. Since these batteries have a long

cycle, which exceeds the lifetime of 5 years provided by the mission specifics, this battery does not need to be replaced.

So there will be eight batteries, weighing a total of 9.86kg, and there will an extra eight redundant batteries, bringing

the total weight of the batteries to 19.72kg.

Radiation shielding

Weight and thickness are key factors that have been used to find the best material for radiation shielding for

this mission. Aluminum is a good choice for shielding, as it has the highest density compared to hydrogen and water.

The main hazard to the onboard processor and the electronics is the radiation generated by the harsh space

environment, and of the radiation produced by the nuclear generator itself.

Figure 7-3. BFO (blood-forming-organ) dose [74]

As figure 7-3 shows, an Aluminum shield is the best choice for radiation shielding, since it has the highest

density. The three nuclear reactors will have radiation shielding of 40 cm each.

Emergency mode

A critical risk to be addressed by the power system is the consequence of the rare occurrence that the nuclear

system fails to produce power. Centurion’s power system will account for this possibility in emergency mode. If the

ESCORT nuclear system accidently shuts down, Centurion will no longer be able to produce both propulsion and

power for itself. In this event, it is very important to ensure that Centurion can be safely put into an orbit that would

60

not be a hazard to other spacecraft. This maneuver must done no more than 24 hours of the time of failure, so that

Centurion does not hinder the path of other spacecraft.

In order to provide power during the emergency mode, solar panels have been used. The minimum power

required for the functioning of the systems module is 1.4kW. This power consumption is mainly due to the onboard

computers, sensors, attitude control thrusters and the launching-docking system. The solar panels are placed close to

the systems module.

8. Spacecraft Thermal Systems


Centurion requires a thermal system that is robust and reliable. There are several requirements that the

thermal system would have to address. The thermal system should be able to control the temperature within the capsule

and the main vessel during all the phases of the trip, and during station-keeping. The thermal system should control

temperature within the Nuclear Reactors, the fuel tanks, the system module, and the solar panels.


Thermal Control of Nuclear Reactors

Centurion uses three ESCORT nuclear reactors for the mission. Helium-Xenon gas is used as the working

fluid within the reactor, as it very unreactive for temperatures up to 1300K, the peak temperature of the Helium-Xenon

within the reactor. Figure 8-2 shows the Brayton Cycle of the ESCORT System used for this mission. There are three

sets of turbines, alternators, and compressors within the three nuclear reactors. The three nuclear reactors require a

radiator with a total surface area of 65 meters squared. The reactors heat up the Helium-Xenon gas to a temperature

of 929K. The radiator has an emissivity of 0.9. Materials such as brass and copper have emissivity close to this value,

and therefore can be used as the main material for the radiators.

61

Figure 8-1 Brayton Cycle for ESCORT System [24]

62

In order to dissipate the excess heat, two radiators are placed on both sides of Centurion. The total surface

area of the radiators is 65 meters squared. The radiator can emit heat on its both sides, so there will effectively be four

radiating surfaces. Each radiator has dimensions of 3m by 5m, which results in the surface area of each radiator to be

15 meters squared. The radiators will use Beta gimbals in order to ensure that they are always perpendicular to the

direction of solar rays. A design for deployable radiators with ammonia coolant pipes, developed by Lockheed Martin,

will be used to implement the two radiators.

Figure 8-2. Close-up of the radiators

Thermal Control of Fuel Tanks

Although the top and bottom portions of the fuel tank is covered by casings, the middle section is left exposed

to the heat produced by the solar rays on its surface, as shown in Figure 8-1. The solar radiation will heat up all sides

of the fuel tank evenly. However, during the orbit around the moon, Centurion will face asymmetry of solar radiation,

resulting in uneven heating of the tank. The fuel tanks consist of Lithium Hydride, the propellant used by the ESCORT

63

system. The thermal system for the fuel tank has to ensure that the Lithium Hydride propellant is kept at low

temperatures ideal for storing the propellant with minimal boil-off.

The tank that stores Lithium hydride will be cryogenic, according to the specifications of the ESCORT

system. The ESCORT system uses about 60 layers of MLI (Multi-layer insulation) on the outer casing of the

Aluminum-Lithium tank. In addition, one foot of SOFI (Spray-on foam insulation) will be applied to the external

surface.

Figure 8-1. Detailed wireframe of the OTV

Thermal control of Systems Module

The Systems Module is made up of onboard computers, lithium-ion batteries and other sensors. These

components have optimum working temperatures, and these temperatures have to be carefully monitored. The

following table shows the operating temperatures of all the components in the systems module. The temperature range

that will allow all the components to work at optimum conditions is between -20C and 15C.

Table 8.1. Diagram of upper casing, lower casing, and fuel tank.

System component Working temperature(C)

Surrey/Rigel-L star tracker -30C to 15C

Honeywell/HG9848 IMU -54C to 71C

Adcole/Coarse Sun Sensor Pyramid -30C to 15C

Aerojet/R-1E attitude control thruster -30C to 15C

Honeywell/M50 moment gyroscope -30C to 15C

IBM/Rad750 -55C to 125C

Lithium Ion batteries -20C to 30C

64

A good rule of thumb to decide which instruments would produce the most heat is to think about the voltages

that are being used by the components. From the Power section, it can be noted that the Honeywell/M50 moment

gyroscope has the highest power requirement, ranging between 11W and 130W.

A calculation will be done to determine the maximum temperature within the systems module. The Stefan-

Boltzmann law is stated as the rate of heat dissipation within the system module and can be found from the equation:

𝐽 = 𝐴 ∈ 𝜎𝑇4 (8-1)

Where J is the power dissipated by the radiator, A is the surface area of the radiator, ∈ is the emissivity of

the material. 𝜎 is the Stefan-Boltzmann constant(5.669x10-8), and T is the temperature of the radiator.

The equation can be re-arranged to make the temperature the subject of the equation.

𝑇 = √𝐽

𝐴∈𝜎

4 (8-2)

Using this law, it is possible to get an approximate value for the temperature that will be emitted by each

component in the system module. Max power is 130W from moment gyro.

Table 8.2. Heat Dissipation among components

In order to control the temperatures within the Systems Module, two small radiators will be used. These radiators will

be a smaller version of the radiators developed by Lockheed Martin. Based on extrapolation from Lockheed Martin’s

specifications chart, the total surface area of these radiators will be 22 metres squared. The dimensions chosen for the

two radiators are 2m by 0.2m.

System component Lower bound of Heat Dissipated

(K)

Upper bound of Heat

Dissipated (K)

Surrey/Rigel-L star tracker 424 804

Honeywell/HG9848 IMU 671 671

Adcole/Coarse Sun Sensor Pyramid NIL NIL

Aerojet/R-1E attitude control thruster NIL NIL

Honeywell/M50 moment gyroscope 169 302

IBM/Rad750 132 204

Lithium Ion batteries 187 365

65

Thermal Control of Solar Panels

The Solar Panels require thermal control in order to keep them cool in order to optimally provide energy to

the batteries. Since the two solar panels are not large (approximately 2m by 0.5m each ), they will heat up by a large

amount.

The minimum power required for a solar panel in the event of

an emergency is 1400W, which will keep the computers and the launch

and dock system. Without the launch system, the minimum power

required for Centurion is 1kW. During emergency mode, the maneuvers

that Centurion will make can take a longer period of time, and thus the

power supplied by the solar panels can be in the range of a 100W, in

order to provide some recharging capacity to the lithium batteries on

board. With an efficiency of 15%, which is common for most solar

panels [35], the amount of waste power generated during a cycle would

be approximately 566W.

Using the principle of Stephan-Boltzmann’s Law, the overall peak temperatures of the solar panels can be

calculated to be 16,000K, which is too high. In order to reduce the temperature of the panels, the surface area can be

increased.

With dimensions of 3.85m by 1m, the temperature of the surface of the solar panels will be 8462K, which is

much more manageable. In order to further reduce temperatures to the optimal temperatures required for effective

solar energy conversion, an active cooling system of ammonia coolant loops similar to the loops used on the Lockheed

Martin radiators next to the nuclear reactors will be added.

9. Launching and Docking

9.1 Design Approach

Centurion benefits from its ability to stay in space and act as a staging platform. This ability reduces the total

weight of launches into space, driving the cost to transport the payload down. This reduction in future cost comes at

an increase in a larger initial launch cost to get all systems into space. This benefit now raises two new issues; how

Figure 8-2 Solar panels at system module.

66

will Centurion dock with its payload, and how will Centurion be refueled? In solving these problems, the main priority

is to maximize the chance that the systems work reliably, and then to reduce the overall cost of system.

In selecting the launch vehicle, the primary foci were the cost per launch, the fairing geometry, and when the

rocket will be available for launch. Due to the large weight of Centurion, the best way to minimize the total cost of

the launch system is to determine which rocket gives the best cost per launch. This rocket also must have a large

fairing geometry, as Centurion will be a large system. The rockets that best satisfy these criteria are not currently in

production, and rather than rely on a proposed completion date. Emphasis will be placed on rockets which are currently

available, or near completion. Vehicles that can be launched from Cape Canaveral will be preferred since its launch

inclination is 28.5° which is nearest to the 28° inclination of the refueling station. As discussed in section 9.2.2.1, the

vehicle that best satisfies these requirements is the Delta IV Heavy. The Delta IV Heavy provides the most reliable

option to carry the OTV, as well as satisfy all launch criteria required to place Centurion into orbit. To launch the

payload and fuel for each mission SpaceX’s Falcon 9 heavy will be used since it provides a much lower cost compared

to current rockets, while maintaining a similar payload capacity.

Centurion will require the selection of a docking system that can both dock with the payload, and with a

refueling station. The docking system will be selected in accordance to the international docking standards, (IDSS).

As discussed in section 9.2.3.4, the best option for a docking mechanism is the NASA Docking System, which is

nearing completion.


Launch Vehicle

The size of Centurion dictates that there must either be a number of launches, or one launch of a large rocket

in order to get all of the components to orbit. The selection of launch vehicle determines the maximum sizes of each

component of Centurion since the fairing size is limited. With an increased fairing size, larger components may be

used on the OTV. Due to the high cost to launch a rocket into space, the launch vehicle will be a driving factor in the

total system cost. Proper vehicle selection becomes a critical component in determining the mission feasibility. The

statistics for current and future launch vehicles are summarized in Table 9.1.

67

Table 9.1. Comparison of Potential Launch Vehicles for Centurion

Vehicle Developer Launch Readiness Payload to

LEO (kg)

Cost Per Launch

(Millions US $)

Fairing

Diameter (m)

Falcon XX SpaceX In development 140,000 300 10

Falcon X

Heavy

SpaceX In development 125,000 280 10

Long March 9 CALT In development 100,000 350 8

SLS Alliant

Lockheed

In development 70,000 1,000 8

Falcon 9

Heavy

SpaceX In development 53,000 85 4.6

Angara A7 Khrunichev In development 40,500 140 5.1

Long March 5 CALT In development 25,000 105 5

Angara A 5 Khrunichev In development 24,500 105 4.3

Proton-M Khrunichev Operational 23,000 75 4.4

Delta IV

Heavy

BLS/ULA Operational 22,560 300 5

H-IIB LM CLS Operational 20,520 128 4.2

Ariane 5 ESA Operational 20,000 220 5.4

Angara A3 Mitsubishi Operational 19,000 114 4.6

[20], [76], [7], [77], [78]

The vehicle mass rules out current light and medium rocket classes because they would require a large

number of launches, and incur a high cost per launch. A trade study was conducted with the remaining launch vehicles

in order to determine the optimal choice. The variables to determining the optimal launch vehicle are the cost per

launch, the total payload carried to LEO, the fairing dimensions, the developer, and the projected debut date. These

variables are summarized in Table 9.2. The trade study is conducted and summarized in Table 9.3, with all of the

scores being determined from the statics in Table 9.1.

Table 9.2. Launch Vehicle Selection Factors and Weighting

Factor Weight Factor

Cost per Launch – The total cost of a launch. This will be a driving factor in the

system cost.

4

Payload to LEO – The total payload the rocket can carry to LEO. Large rockets can

send the OTV full of fuel into space.

3

Fairing dimensions – The dimensions of the fairing. The system will be large and

fairing size is limited

3

Developer – Who is responsible for the rocket? Influences the launch site, and

reliability

2

Launch readiness – How soon until the rocket is ready for a launch. Current rockets

will be emphasized.

5

68

Table 9.3. Trade Study of the Viable Launch Vehicles

Factor Weighting

Factor

Falcon

XX

Falcon

X Heavy

Long

March

9

SLS Falcon

9

Heavy

Angara

A7

Proton-

M

Delta

IV

Heavy

Cost Per

Launch

4 3 3 2 1 4 4 4 2

Payload to

LEO

3 5 5 4 4 3 2 2 2

Fairing

Dimensions

3 5 5 4 4 3 3 2 3

Developer 2 5 5 4 5 5 2 2 5

Launch

Readiness

5 1 1 2 2 3 3 5 5

Weighted

total

57 57 50 48 59 50 57 58

Discussion

9.2.2.1. Delta IV Heavy

The trade study shows that the Delta IV Heavy is the best choice for the OTV launch vehicle. The rocket will

be able to carry 22,560 kg of payload, which is above the estimated 16,000 kg of dry mass. The initial launch will

send the OTV into orbit only partially fueled since a Delta IV Heavy will not be able to carry a fully fueled system.

With a cost of $300 million per launch, the Delta IV Heavy is one of the more expensive options [76]. The main reason

that this cost is justified is because the Delta IV Heavy is an already proven launch vehicle. Since the first launch will

contain 3 nuclear engines, safety is the primary concern. In the case of failure radioactive material may be released

into the atmosphere. This could have potentially serious consequences so all possible precautions are taken in ensuring

that this does not happen. Future launch vehicles may provide cheaper options however until those vehicles prove

themselves as a reliable vehicle the risk of failure is too great.

The base fairing geometry is not big enough to hold the OTV so a custom fairing must be used. The standard

fairing size for a Delta IV Heavy has a 5m diameter, and is 19m tall. The United Launch Alliance, (ULA), has

conducted studies looking at the feasibility of carrying larger payloads. It was determined that the current Delta IV

Heavy could carry a payload as large as 7m in diameter, and 26.5m tall. These specifications are large enough to carry

Centurion into LEO. Potential future upgrades to the Delta IV can allow the rocket to carry more massive payloads

with even larger dimensions [78].

69

9.2.2.2. SpaceX Falcon 9 Heavy

In order to transport fuel to Centurion, SpaceX’s Falcon 9 Heavy will be used. The Falcon 9 Heavy will be

able to carry 53,000 kg to LEO at the lowest cost, $85 million. The mass to LEO for the Falcon 9 is well above the

50,000 lb, or 22670 kg, payload requirement. The fairing capacity is above even the fuel mass, 50,000kg, for the

nuclear thermal engines. The main factor in the selection of the Falcon 9 is its extremely low cost. The Falcon 9 only

costs $85 million per launch which is significantly lower than the Delta IV heavy, which is estimated at $330 million

[7] [76].

Docking System

Centurion will require one docking system, which must dock with the refueling station as well as with

whatever payload needs to be transferred. Since there are 5 missions, and several docking interactions during each

mission this docking system must also be reliable. Any docking interface requires two components, an active part and

a passive part. The active part is on the module which is moving towards the main vehicle, called the chaser module.

The other component is called the passive part, and that is on the main vehicle.

There are two types of docking. One type is when the chaser module moves in position to the assembly, and

it uses its thrusters to engage the docking system. A second type of docking called berthing, this is when a robotic arm

will perform the docking procedure [79]. In the case of Centurion there will not necessarily be a nearby structure with

a robotic arm, so berthing capabilities may not be possible. Therefore a berthing system will not be considered for

Centurion.

9.2.3.1. Probe and Drogue

The probe and drogue docking system is the simplest docking system. There is a probe on the active portion

which is a protruding probe. On the passive side there is a cone, which awaits the probe. The probe may hit anywhere

within the cone, and it will be deflected towards the center. This greatly increases the leeway on the incoming angle

of the spacecraft, and yields a high rate of success. This method will not allow for any transfer of materials or people

through the interface, as there are no pressurized components. This limits the applicability of the system, but increases

its effectiveness [80].

9.2.3.2. Androgynous Peripheral Attach System

Androgynous Peripheral Attach Systems, APAS, were developed by Russia as their docking system, which

was used to bridge the gap between the Apollo and Soyuz programs. The APAS systems differ from the probe and

70

drogue systems in that there is now an outer ring which docks two systems, and a hatch in the center. This difference

limits the error in alignment for the docking system to where only a 7° difference in incoming angle is acceptable. Yet

the hatch allows for the transfer of materials and humans, if the juncture is pressurized [81]. APAS systems, are the

current docking systems for the majority of satellites, and are used on main interfaces of the International Space Station

[79]. They also benefit from being androgynous which means that either side of the interface may act as the passive

or active portion. Their main drawback is their lack of compatibility with other systems. In order to dock a different

system to an APAS there must be some modification to the APAS receiver. Thus the APAS docking mechanism is

not favorable.

9.2.3.3. NASA Docking System

NASA Docking System (NDS) was

hypothesized to be the universal docking

mechanism for the future. NDS will be a soft

capture mechanism that allows for a high order

of accuracy. NDS will also be Androgynous so

either side may be active or passive. The active

component of NDS will survive for 2 active

docking cycles, or 231 days, before it must be

replaced. The passive mechanism will last

much longer, and is estimated to last for up to

15 years, or 50 passive docking cycles [82].

This docking system is severely limited by the

lifetime of the active portion

9.2.3.4. Discussion

The main factor in determining the docking system for Centurion is its compatibility with a variety of

systems. Due to the fact that it will take some time for Centurion to be developed it is important to look at future

docking systems, as many of the next generation vehicles will be equipped with these systems. To satisfy this issue a

standard has been developed called the international docking standard. These regulations ensure that no matter who

develops their own unique docking mechanism the connection ports will all be in the same place [83]. This allows for

Figure 9-1. Conceptual Design for NASA Docking System [81]

71

many different manufacturers to produce their own mechanism, and allow it to dock with another vehicle. Table 9.4

shows the international docking standards systems, IDSS, compatibility of the docking mechanisms described above.

Table 9.4. IDSS Docking Compatability [83] [6]

Docking System IDSS Compatibility

Probe and Drogue NO

APAS NO

NASA Docking System YES

As Table 9.4 shows NDS is the only compatible system with other IDSS. Thius makes the NDS the clear

choice for Centurion. There is still concern because of the limited number of active cycles. There is still a large number

of passive cycles. Centurion can take advantage of these passive cycles and act as the passive interface to preserve its

integrity. This forces the payload to act as the active interface. Having the payload act as the active portion is beneficial

since any maintenance on the docking mechanism may be done to the payload. This is a far easier solution because

the payload will be returned to LEO, or potentially to the Earth’s surface. To further improve the situation more

research and development may be done in order to improve the number of active cycles.

9.2.3.5. Docking Methods

There are two main methods to dock a spacecraft, R-bar approach and V-bar approach. The main difference

between the two is the direction that the module will dock with the structure. The R-bar approach is used when the

docking system will connect perpendicular to the velocity vector. This method will require two pulses, one to bring

the chaser module alongside of the main module, and another pulse to remove any excess velocity. After the positions

are lined up, then another maneuver must be performed in order to bring the two modules together, and dock [84].

The V-bar approach is used when the docking system will connect parallel to the velocity vector. This method

will yield more accurate results, due to the reduced number of maneuvers required to bring the two modules together

[85]. These methods are distinguished mainly by the direction that the piece needs to attach to the assembly. The

differences in the efficiency and accuracy of the two methods are similar, with the V-bar approach being slightly more

accurate.

72

Since Centurion is launched in one piece, the only docking it will have to do is with the payload and refueling

station. The docking interface will be place on the front of the OTV so all of the components will be in line with each

other. This makes it far simpler for a V-bar approach to be used compared to the R-bar.

Refueling Procedure

Centurion will require a new system to be developed in order to be refueled. Since the system will not return

to the surface of the Earth until after the 10 year life, there must be a new way to refuel Centurion. Currently there is

a refueling system being developed by NASA, called the Robotic Refueling Mission, (RRM).

This refueling system is still in the research and development

phase, but it will provide the basis for what to consider as a viable

option. The project required the modification of a Dextre robot, so that

it would be able to remove the seals on a spacecraft’s fuel tank.

Implementation of these modifications can be seen in Figure 0-2. First

a specialized tool cuts all of the tapes, and wires which seal the fuel

cap. Another tool is used to remove the cap, allowing for a hose to

attach and transfer fuel. Once the tank is loaded one final tool is used

to install a new cap on the satellite [86].

There was a successful test of the RRM during January 2014,

where RRM transferred Ethanol into the International Space Station [87]. This test acted as a proof of concept, and

will require more work until RRM is ready to refuel actual satellites. The project gives good insight into compatibility

requirements. The refueling station will having something similar to the RRM, and as such the nozzle that the fuel

will flow through must be compatible with the type of systems on RRM.

Further modifications to the Dextre robot used for RRM must be made to make the refueling procedure

feasible. It is estimated that the fuel flowed at a rate of 1L/min during the fuel transfer stage of RRM [86]. At that rate

it would take 571 days to fill Centurion full of fuel, 700,000L. If Centurion waits 571 days to refuel then it will not be

possible to complete 10 missions in 5 years. The flow rate will need to be increased for Centurion to be refueled in a

reasonable timeframe. Using a pump similar to those on aircraft for aerial refueling would satisfy this issue. Typically

jets are refueled at a rate of 2,000lbs/min, with a theoretical maximum rate of 6,000lbs/min [88]. By using .81kg/L as

Figure 9-2. Modified Dextre Robot [86]

73

the density of jet fuel, the flow rates can be written as 1120L/min with a maximum of 3360L/min. At these rates it

would take 10.5 hours to refuel Centurion, with a theoretical fastest time of 3.5 hours. In order to ensure a successful

refueling 12 hours will be allotted for the refueling procedure.

9.3 Critical Design Issues

The refueling procedure must be better established prior to ensuring Centurion will be successful. There has

never been an uncontrolled space refueling, so any system developed must encompass all possible scenarios which

could cause failure. More testing must also be done to ensure that the fuel transfer rate at the refueling station can be

increased to limit the time at the station.

10. Risk and Cost Analysis

10.1 Risk Analysis and Mitigation

Space related missions always have a degree of risk associated with them, but by taking into consideration

the reliability of the components and potential of risk at different stages of the research, development, and launch, we

can mitigate those risks; reaching a much more acceptable safety factor. Centurion was developed while keeping the

safety of the mission and structural stability in mind. Redundant systems have been established for the most critical

components in the case of failure, including the duplicate communication systems, redundant computers, attitude

control systems, and power systems. The structure is also designed to enable continued operation in the case of a

minor structural failure. Table 10.1 itemizes the criteria for the probability of a failure and the impact it would have

on the larger mission.

Table 10.1. Risk Analysis Criteria

Consequence (C) Probability of Failure (POF) Value

Little Consequence Little to No Probability 1

Mild Consequence Mild Probability 2

Moderate Consequence Moderate Probability 3

High Consequence High Probability 4

Major Consequence Very High Probability 5

All of the technologies that were considered in this proposal were evaluated and ranked based on the impact

they have on the overall mission, and the probability of failure for each of the technologies. The technologies that

74

were considered for Centurion mission had a large impact on the mission, but a lower probability of failure, making

them great choices for this mission, as shown in Table 10.2.

Table 10.2. Technology Risk Analysis

TECHNOLOGY Consequence POF Short code

Star Trackers 3 3 [1]

IMU's 3 3 [2]

Magnetometer 1 3 [3]

Sun Sensor 1 4 [4]

Reaction Wheels 2 3 [5]

Magnetic Torque Rods 1 1 [6]

Control Moment Gyroscopes 4 2 [7]

Thrusters 3 4 [8]

Nickel-Hydrogen 4 2 [9]

Lithium-Hydride 3 2 [10]

Solar Panels 3 1 [11]

Chemical Thrusters 3 2 [12]

Nuclear Thermal Thrusters 5 3 [13]

Delta IV 5 2 [14]

NASA Docking System 4 3 [15]

Table 10.2 categorizes all of the potential risks that the mission and the vehicle could face. It is color coded

and ranked from risks that are entirely unacceptable to residual risk. Red labels unacceptable risks while the green

labels residual risks. Risks in the orange and red boxes must be resolved entirely before production even begins. Risks

in the yellow, light green, or green boxes can be tolerated, but evidence will be given on how to limit those risks and

how they will be handled. Using the short codes from Table 10.2, a comparison can be made between the technologies

that are worth the risk, and the ones that are not. The only technologies that were considered, are those in the green,

light green, and yellow regions, Figure 10-1.

Unacceptable Risk

Pro

bab

ilit

y

[4] [8] [9] High Risk

[3] [5] [1],[2] [15] [13] Moderate Risk

[10],[12] [7] [14] Low Risk

[6] [11]

Residual Risk

Consequence

Figure 10-1. Technology Risk Analysis

75

Following the technology risk analysis, an operational risk analysis was conducted based on the risks

associated with operating, launching, and decommissioning Centurion. These risks range from political risks,

funding setbacks, and operational hazards associated with this mission. They were then ranked based on the

consequence they would have on the overall mission and the probability of occurrence. The two major setbacks

include political setbacks due to using nuclear engines, and putting nuclear material in space. While these are major

concerns, the benefits that the nuclear engines provide to the overall mission, far outweigh the disadvantages.

Table 10.3. Operational Risk Analysis

Operations Consequence PO Short code

Political setbacks due to technologies 4 4 [1]

Use of nuclear power in space 4 4 [2]

Issues with nuclear power across nations 4 3 [3]

Improper disposal of nuclear fuel 5 1 [4]

Accidental failure of nuclear engines 5 2 [5]

Lack of funding to complete production 5 1 [6]

Improper decommissioning of Centurion 4 2 [7]

Launch vehicle failure 2 2 [8]

Inclement weather delaying launch 1 5 [9]

Launch failure 3 2 [10]

Components failing before expected date 1 3 [11]

Sabotage 4 2 [12]

Human error/negligence 3 3 [13]

In order to rectify concerns over the use of nuclear power in space, a detailed summary of this plan will be

presented to the governing authority as well as distributed to the managing team. This plan outlines the major

advantages of the use of nuclear engines in space and addresses minor concerns due to the use of nuclear power. A

detailed explanation of the advantages of using nuclear engines can be found in the following section.

[9]

Unacceptable Risk

Pro

bab

ilit

y

[1],[2] High Risk

[11] [13] [3], [12] Moderate Risk

[8] [10] [7] [5] Low Risk

[4], [6]

Residual Risk

Consequence

Figure 10-2. Operational Risk Analysis

76

10.2 Cost Estimation

The costs for Centurion mission include ground and launch operations, design, development, and production

of the OTV, and the launch of subsequent payloads. Some of the system’s cost drivers include the size of Centurion,

the complexity, technological innovations used in the vehicle, the lifetime of the design, and the timeline for the

mission as portrayed below. The largest costs for this mission would be the development of the nuclear thermal

thrusters and the development of the modified NASA Docking System. In order to develop an effective cost model,

the following equation must be followed:

(𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝐹𝑖𝑟𝑠𝑡 𝑈𝑛𝑖𝑡 𝑥 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦) − 𝑙𝑒𝑎𝑟𝑛𝑖𝑛𝑔 𝑐𝑢𝑟𝑣𝑒 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 + 𝑚𝑎𝑛𝑎𝑔𝑒𝑚𝑒𝑛𝑡 𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠+ 𝑡𝑒𝑐ℎ𝑛𝑜𝑙𝑜𝑔𝑖𝑐𝑎𝑙 𝑟𝑖𝑠𝑘 𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 = 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝐶𝑜𝑠𝑡

(10-1)

This cost modeling method effectively calculates the total component cost of each component aboard

Centurion, allowing for fairly accurate overall cost estimations for the entire mission. To begin, various launch

vehicles were considered.

The Falcon 9 costs an approximated $2111/lb per launch [72]. The Falcon 9 Heavy costs an approximated

$727/lb per launch. That is about a 34.4% discount rate. With a payload capacity of 53,000 kg, 116,845 lbs, the Falcon

9 Heavy was determined as optimal. For payload launches and fuel launches, the Falcon 9 Heavy would be the best

with a total cost per launch of $85M. Delivery of payload, set-up, loading of payload on site, and fuel would total

about $170 million per launch for our clients.

Calculating fuel costs, at about 40,000 kg (88,185 lbs) of fuel and about $3.60/kg of fuel, it will cost about

$400,000 per trip, which is negligible. These estimates were extrapolated from costs in the 1980’s and were adjusted

for inflation. At about 115,000 kg (330,693 lbs), the OTV would cost about $2.63 billion dollars to build. It would

cost $300 million to launch Centurion, $10 million for administrative costs, $250 million for miscellaneous expenses

including taxes, transportation, legal fees, and miscellaneous costs, bringing the total cost for the development of

Centurion to about $2.89 billion.

To calculate the Theoretical First Unit (TFU) and the adjusted total costs for Centurion, an adjusted total

costs model was chosen to be defined as:

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑇𝑜𝑡𝑎𝑙 = 𝑇 𝑥 𝑛(1+

ln (𝑆)ln (2) (10-2)

77

where T is the theoretical cost for the first unit, n is the number of units being purchased, and S is the discount

rate for purchasing multiple units. The discount rate is determined by analyzing the relationship between the

projected costs and actual costs of prior projects. Since Centurion is an unproven concept, we chose a discount

rate of 92% for each additional unit. A similar rate was used for the learning discount assumption that each

additional component to build would cost less since the labor would be more skilled to complete that task.

Inflation was taken into consideration when possible, but estimates are based on FY2015 dollars.

In addition to the learning curve and the discount rate, management reserves and technology risk

levels were also taken into consideration. The management reserves accounts for cost, schedule, time, and

material uncertainties. The newer, more custom a component is, the higher the reserve percentage. If that

component was off the shelf and the hardware currently exists with no modifications, it was given a 10%

reserve. If the component was completely new in design and hardware it was given a 50% reserve. The

nuclear thermal engines have currently been designed and are currently being tested, and as such were given

a 35% reserve. The technology risk reserves account for risks associated with implementing technologies of

lower readiness levels. The Technology Readiness Level (TRL) is ranked from 1 to 9. If the system is flight

proven through successful mission operations, it is given a 5% reserve. If the technology just showcases

basic principles and has not been developed or tested, it is given a 35% reserve. For components that have

been developed and tested in a simulated environment, they are given a 10% reserve. All of the components

that create Centurion have been categorized based on these specifications and have been tabulated in the

Development Costs Table 10.3.

Various other cost models were considered, such as the Mars Rover Engineering Costs, and the

Space Telescope model, but were rejected due to differences in their applications and final results. Other

expenses that were considered in these calculations include inflation, research and development, integration

and testing, source lines of code, labor and employees, overhead, and failures and replacements.

78

Table 10.4. Development and Mission Costs

Hyperion Ventures - Centurion Development Costs

Components # of Units

Units Theoretical

First Unit ($) Unadjusted Total Adjusted Total($)

Management Reserves

Additional Cost TRL

Reserves Additional Cost TOTAL COST

% of Total Budget

Ref

Structures (per unit) (per vehicle) (%) ($) (%) ($) ($) (%)

PLASCORE PAHD-XR1 10 48x96 in^2 $50,000.00 $500,000.00 $379,031.91 10 $37,903.19 5 $18,951.60 $435,886.69 0.02 [13]

PLASCORE PAMG-XR1 10 48x96 in^2 $50,000.00 $500,000.00 $379,031.91 10 $37,903.19 5 $18,951.60 $435,886.69 0.02 [13]

PLASCORE PAMG-XR1 10 48x96 in^2 $50,000.00 $500,000.00 $379,031.91 10 $37,903.19 5 $18,951.60 $435,886.69 0.02 [13]

CR III 5052 and 5056 8 48x96 in^2 $60,000.00 $480,000.00 $373,770.24 10 $37,377.02 5 $18,688.51 $429,835.78 0.02 [13]

ADCS

Sun Sensors 2 component $60,000.00 $120,000.00 $110,400.00 10 $11,040.00 5 $5,520.00 $126,960.00 0.01 [88]

ADCS Thrusters 16 component $540,000.00 $8,640,000.00 $6,189,635.17 10 $618,963.52 5 $309,481.76 $7,118,080.45 0.28 [57]

CMGs 6 component $700,000.00 $4,200,000.00 $3,385,650.95 10 $338,565.10 5 $169,282.55 $3,893,498.60 0.15 [89]

IMU 2 component $50,000.00 $100,000.00 $92,000.00 10 $9,200.00 5 $4,600.00 $105,800.00 0.00 [48]

Star Tracker 1 component $910,000.00 $910,000.00 $910,000.00 10 $91,000.00 5 $45,500.00 $1,046,500.00 0.04 [49]

Flight Computer 2 component $21,000.00 $42,000.00 $38,640.00 10 $3,864.00 5 $1,932.00 $44,436.00 0.00 [48]

Power and Thermal

Batteries 2 component $1,500.00 $3,000.00 $2,760.00 15 $414.00 10 $276.00 $3,450.00 0.00 [73]

Avionics 1 component $1,000.00 $1,000.00 $1,000.00 15 $150.00 10 $100.00 $1,250.00 0.00 [90]

Heat exchangers 1 component $4,500.00 $4,500.00 $4,500.00 15 $675.00 5 $225.00 $5,400.00 0.00 [91]

Radiators 2 component $2,000.00 $4,000.00 $3,680.00 15 $552.00 5 $184.00 $4,416.00 0.00 [92]

Pumps 3 component $1,500.00 $4,500.00 $3,942.92 15 $591.44 5 $197.15 $4,731.50 0.00 [93]

Solar Panels 4 Panel $2,000.00 $8,000.00 $6,771.20 10 $677.12 5 $338.56 $7,786.88 0.00

Propulsion Systems

Nuclear thermal eng. 3 engine $400,000,000.00 $1,200,000,000.00 $1,051,444,395.22 35 $368,005,538.33 20 $210,288,879.04 $1,629,738,812.59 64.71 --

Main propellant tanks 1 tank $5,000,000.00 $5,000,000.00 $5,000,000.00 15 $750,000.00 10 $500,000.00 $6,250,000.00 0.25 [34]

ACS propellant tanks 4 tank $1,000,000.00 $4,000,000.00 $3,385,600.00 15 $507,840.00 10 $338,560.00 $4,232,000.00 0.17 [70]

feed lines 1 cubic foot $100,000.00 $100,000.00 $100,000.00 10 $10,000.00 5 $5,000.00 $115,000.00 0.00 [70]

Valves 1 component $200,000.00 $200,000.00 $200,000.00 10 $20,000.00 5 $10,000.00 $230,000.00 0.01 [70]

Launching and Docking

Delta IV 2 vehicle $300,000,000.00 $600,000,000.00 $600,000,000.00 25 $150,000,000.00 15 $90,000,000.00 $840,000,000.00 33.35 [76]

NASA Docking System 1 component $10,000,000.00 $10,000,000.00 $10,000,000.00 15 $1,500,000.00 10 $1,000,000.00 $12,500,000.00 0.50 [86]

Manufacturing Costs

Administrative Costs 1500 employee $75,000.00 $112,500,000.00 $10,000,000.00 10 $1,000,000.00 5 $500,000.00 $11,500,000.00 0.46 --

Totals $2,518,665,617.00

Hyperion Ventures - Centurion Mission Costs

Components # of Units

Units Theoretical

First Unit ($) Unadjusted Total Adjusted Total($)

Management Reserves

Additional Cost TRL

Reserves Additional Cost TOTAL COST

% of Total Mission

Ref

Launching and Docking

(per unit) (per vehicle) (%) ($) (%) ($) ($) (%)

Falcon 9 Heavy 1 vehicle $85,000,000.00 $85,000,000.00 $85,000,000.00 5 $4,250,000.00 5 $4,250,000.00 $93,500,000.00 99.53 [73]

Propulsion Systems

Fuel 625 m^3 $640.00 $400,000.00 $400,000.00 5 $20,000.00 5 $20,000.00 $440,000.00 0.47 [70]

Totals $93,940,000.00

79

Centurion provides numerous benefits over the technologies and orbit transfer vehicle concepts that are

currently available. The nuclear thermal propulsion system and the modified NASA Docking System set this concept

apart from the competition. Primarily, Centurion’s significantly lower operating costs (lower fuel and launch

requirements) is the most significant advantage when compared to conventional bipropellant technologies. The liquid

hydrogen fuel used on the nuclear thermal engines of Centurion provide a huge fuel advantage, at less than 5 times

the cost of using bipropellant. By taking into consideration the cost to transport the fuel to LEO and disregarding cost

of the fuel entirely, we can see that the bipropellant costs almost 5 times more than transporting liquid hydrogen due

to the density of the bipropellant. Figure 10-3 illustrates the difference in these costs. This mission entails the use of

the Falcon 9 Heavy to launch the liquid hydrogen fuel to LEO. The use of the nuclear thermal engines allows the

mission to use much less fuel. For 10 missions, 10 Falcon 9 Heavy launches would be required. Considering the

bipropellant is also launched using Falcon 9 Heavys, 10 missions would require about 50 Falcon 9 Heavy launches.

Figure 10-3 clearly illustrates a $3.4 billion savings over the lifetime of the OTV, demonstrating the desirability of

Centurion.

Figure 10-3. Number of Falcon 9 launches required to transport fuel for 10 missions

80

In addition to the fuel transportation savings, Centurion cuts costs on fuel consumption, is energy efficient,

has a docking system with an extended lifespan, and uses some of the most advanced technologies available. The

nuclear thermal propulsion engines, the modified NASA Docking system, and the Delta IV are just a few. The nuclear

thermal engines have been conceptualized and designed, but never produced. The NASA Docking system can only

last 2 cycles. In order to advance the nuclear thermal and docking system technologies, a good portion of the Hyperion

Ventures’ budget has been allocated for the research and development of these technologies. The four nuclear thermal

engines are expected to cost about $1.6 billion to research and develop. The modified NASA Docking system is

expected to cost about $10 million to research and develop. These high R&D costs results in high capital expenses,

but low recurring costs, meaning Centurion would be more cost efficient with more missions. Figure 10-4 shows the

total project costs, including the initial development and recurring costs per mission, for Centurion versus conventional

technologies, which includes the current NASA Docking system, Falcon 9 Heavys, and a conventional bipropellant

engine. As can be seen from the graph, Centurion starts out expensive due to the extensive R&D, but it becomes the

most cost affordable option after just 4 missions. After 10 missions, Centurion would have saved about $2.9 billion

over the conventional design.

Figure 10-4. Total project costs using Centurion versus conventional technologies

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

To

tal

Pro

ject

Cost

(bil

lion $

)

# of Missions

Total Project Costs using

Centurion vs. Conventional

~$2.9 billion

81

11. Conclusion

Centurion meets the plan of action for an Orbital Transfer Vehicle constrained by the conditions set forth by

the AIAA RFP requirements. The OTV would offer clients the speed and reliability to transport both manned and

unmanned payloads to Lagrange points L1 or L2. Centurion offers the most innovative concept with the highest

quality, reliability, and sustainable design at the best price. While this plan was centered on the constraints set forth

by the AIAA RFP requirements, it can easily be expanded and optimized to meet increasing demands. The $2.3 billion

cost to develop Centurion may be higher compared to its competitors, but the $85 million operation costs per mission

sets it apart from conventional technologies, utilizing some of the most advanced technologies currently available.

Centurion’s nuclear thermal propulsion engines and the modified NASA Docking System sets Centurion

apart from the current competition, establishing itself as the premier option for payload transport to the Lagrange

points. While nuclear thermal technology is still under development, it is a very promising technology. Politics may

have held nuclear propulsion back but proponents of the technology believe that this technology would lead the path

for human transportation to mars, the rest of our solar system, and beyond. Nuclear technology has become much

more reliable and safe than it has ever been in history, proving its feasibility in this mission. With a modified docking

system, Centurion would be the first vehicle capable of transporting cargo to and from those Lagrange points, a feat

no other vehicle can currently accomplish. Hyperion Ventures’ solution, Centurion, surpasses the expectations set

forth by the RFP requirements and offers a unique solution to transport manned and unmanned payloads safely, and

economically.

82

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