Section III Presentation - Purdue University

Section III PresentationFebruary 27, 2020

1

Eli SitchinFebruary 27, 2020

Discipline: CADVehicle and Systems Group: Cycler

2

The Problem: Determine the Cycler Vehicle Habitation Layout

Requirements

• The cycler habitation must satisfy the hygiene, nutrition, sleep, and psychological

needs of 70 passengers.

• At least 7500 m2 must be devoted to food production (i.e. a greenhouse).

• Passengers must be able to access and maintain all onboard utilities.

Assumptions

• 2 passengers per bedroom

• 4 habitation modules and 2 habitation interfaces

Need to Determine

• Sizing and layout of quarters, bathrooms, greenhouse, dining and common areas,

gym, elevators, hallways, and utilities.

3

Interior Design

Layout

• Quarters: Purple-Grey

• Bathroom: Aquamarine

• Utilities: Red

• Kitchen/Common Area: Tan

• Greenhouse: Green

• Gym: Gold

• Hallway: White

• Elevators and External Structure:

Aluminum

Total Floor Area: 6798 m2

Total Habitable Volume: 17100 m3

Number of 2-Person Bedrooms: 36

• 9 per habitation module; 1 to be left

vacant

CAD: Eli Sitchin

4

Habitation Interior

(2 total)

Habitation Module

Habitation

Interface

Erick SmithFebruary 27, 2020

CAD: Landing TrackStructures: Mass Driver

Martian Taxi Catching SystemCradle

Information

Mass 100 tons

Material Aluminum 6061

T6

Length 25 meters

Magnet Width 15 meters

Width 36 meters

Images by Erick Smith

Mass Driver Materials & Structural Analysis

Mass Driver Parts Materials

Rails Iron, Wrought or

Rhenium beams

Vacuum Casing Iron, Wrought

Magnets 15 Lanthanides

Scandium

Yttrium

Niobium Titanium

ReBCO

Next Steps

• Animation sequence for the Martian Taxi

grab system

• More research on the Electrodynamic

Suspension System.

• Researching ways use a combination of

magnets from all 5 materials.

• Researching coolants to increase the

magnetic fields.

• Fixing design to add wheels for the cradle

to be complient with the EDS system.

Nicholas DeAngeloFebruary 27th, 2020

Communications –Taxi System

Problem – Radome Material

• Due to extreme reentry temperatures, Taxi needs internal antenna with high

heat resistant radome material• Material needs to withstand temperatures up to 2700℉ [1]

• Solution – Quartz Fibre• Extreme heat resistance, outstanding electromagnetic properties, and high strength

to weight ratio makes Quartz Fibre a perfect option [2]

• Used in many aerospace systems in both military and civilian industry [2]

• Resin called prepreg

is combined with

fibre and a mold to

form the Radome [2]

Image taken from Saint-Gobain [3]

Radome Analysis/Capabilities

Parameter Value

Nose Cone Surface

Area*33.5 m

Radome thickness [6] 0.0254 m

Quartz Fibre

composite density

[4][5]

1850 𝑘𝑔

𝑚3

Radome mass 1.574 Mg

2

Parameter Value

Dielectric

Constant3.74

Loss tangent 0.0002

Moving Forward

• Radome Loss in Link Budget

• Determine best Quartz Fibre/Resin

composite ratio

* Nose Cone Surface Area taken from Will from CAD Team

Adam WootenFebruary 27th, 2020

Communications Team LeadCycler (Optic), ED Tether (RF)

The Problem

Given Requirements

• Continuous Communication

• 1 Gbps HD Communication

Requirements Flowdown

• 4 dB Gain Margin

• Redundancy (See figure)

• Power < 500W

Drawing By: Adam Wooten

*Not To Scale*

ED Tether RF Communication Hardware

Mass (kg) 150.

Power (W) 150.

Volume (m3) 3.0

Antenna Diameter (m) 1.00

Gain Margin Min for

ED-GEO (dB)

4.45

Gain Margin Max for

ED-Earth (dB)

38.43

Antenna Characteristics

Comm System Mass, Power, Volume

Drawing By: Adam Wooten Drawing By: Adam Wooten

ED – GEO

Max DistanceED Tether - Earth

Distance

*Not To Scale* *Not To Scale*

Sidharth PrasadFebruary 27, 2020

Taxi Martian EntryControls

Controlling Martian Entry

• Downrange variance is significant without control

• At Olympus Mons height 150 km, at ground 350 km

Controlling Martian Entry

• Bank Angle Control

𝑅𝑝 = 𝑅𝑅𝑒𝑓 +𝜕𝑅

𝜕𝐷𝐷 − 𝐷𝑅𝑒𝑓 −

𝜕𝑅

𝜕 ሶ𝑟ሶ𝑟 − ሶ𝑟𝑟𝑒𝑓

𝐿

𝐷 𝐶=

𝐿

𝐷 𝑅𝑒𝑓+𝐾3(𝑅 − 𝑅𝑝)

𝜕𝑅/𝜕𝐿𝐷

𝜙𝐶 = 𝑐𝑜𝑠−1𝐿/𝐷𝐶𝐿/𝐷

∗ 𝐾2𝑅𝑂𝐿𝐿

Mendeck, Gavin & Craig, Lynn. (2011). Entry Guidance for the 2011 Mars Science

Laboratory Mission. AIAA Atmospheric Flight Mechanics Conference 2011.

10.2514/6.2011-6639.

BREAKResume at 2:10

Brady WalterFebruary 27, 2020

Communication Satellite Attitude Control Analysis

Reaction Wheel Control

Requirements

• Accurate sizing based on external torques

• Desaturation

• Backup plan in event of failure

Communication Satellite Torque Ceilings

GEO 1.3052x10-6 N-m

Earth L4/L5 3.2200x10-7 N-m

AREO 1.0050x10-6 N-m

Mars L4/L5 1.1597x10-7 N-m

Reaction Wheel Control

• Nominal Functionality: PID Controller

• Desaturation: RCS Thrusters

• Pyramid orientation allows for control after failure

• Sizing shown below

α 45°

B 42°

Mass Radius Maximum Power

GEO/AREO 23 kg 0.24 m 113 W

Earth/Mars L4/L5 11.1 kg 0.17 m 113 W

Beverley K.W. YeoFebruary 27th, 2020

ControlsCycler – Stability Analysis, Perturbations

also: Webmaster

Cycler stability against perturbations

Problem: Spin stability infeasible

Small torque but constantly acting on cycler

→ Spin rate required increases over time

Solution: 3-axis stability

→ gyros (4 CMGs) and thrusters (RCTs) (?)

Sum of external

torques

Near Earth

(Nm)

Interplanetary

(Nm)

Near Mars

(Nm)

X-axis 0 0 0

Y-axis 0 0 0

Z-axis 9.3035 1.0564 3.1527

[1] Cycler drawn by CAD (Eli Sitchin, Aaron Engstrom)

[2] CAD document, value as of 13 Feb

Near Earth Interplanetary Near Mars

1.4985x10-11 0.1701x10-11 0.5078x10-11

[1]

Internal torques excluded (fuel sloshing, human factors)

Assumed radiation and particle forces act at center of area

Website updates

Report requirements (from Purdue – need WCAG 2.0 AA level):

• Good descriptive captions for all images, charts (use alternative text feature)

• All abbreviations need to be defined before usage

(e.g. AAE → Aeronautical & Astronautical Engineering (AAE))

• Cross-referencing, table of contents etc. must be hyperlinked

Good caption example: describes

exactly what is shown in the figure

Bad caption example: says what

the picture is, but not what is in it

Caption examples from K.W. Yeo et al. (2020) Flow transitions in collisions between vortex-rings and density interfaces.

Journal of Visualization (under review)

Emily SchottFebruary 27, 2020

Human Factors: Taxi/TetherMitigating Disorientation

Disorientation in the Tether Gondolas

Multiple changes in acceleration

and orientation over a short

period of time from the tether to

the cycler

The motion of the gondola

simulates a standard-rate turn

in an aircraft

• Fluid in the inner ear

stabilizes and causes

disorientation [1]

• Static head position is not a

factor, only rapid changes Centripetal Acceleration and Angular

Velocity profile for the Phobos Tether

Gondola Seating

Acceleration cannot be controlled, but the direction of acceleration can

• “Eyeballs in” is most tolerable [Kevin Huang, HF]

Sitting “backwards” will be the best option

• Acceleration is felt downwards while at rest on Phobos/Luna/Mars,

“eyeballs in” at the tip of the tether, and downward in the taxi

Gondola →Top view

Side view

𝝎

Alexey ZeninFebruary 27, 2020

Discipline: Human FactorsVehicle/Systems: Cycler

Topic: Bioregenerative Life Support System (BLSS)

Problem: Crops Species Cultivated on Board

Objective:

• Update Mass, Power, and Volume requirements for the system

• Finalize the list of the crops for balanced vegetarian diet

Cycler’s BLSS Requirements

Food Regeneration 0.7 kg/day-person

Water Regeneration 3.2 kg/day-person

Carbon Dioxide reduction 1 kg/day-person

Oxygen Regeneration 0.84 kg/day-person

EstimationsCrops Diurnal

Needs

[g/person]

Crops Area

[m2/person]

Wheat 174 13.2

Chufa 78 2.87

Pea 17 1.3

Carrot 74 0.4

Radish 37 0.3

Beets 44 0.3

Kohlrabi 60 0.34

Onion 40 0.2

Dill 10 0.03

Tomatoes 50 0.4

Cucumbers 34 0.14

Potatoes 84 2.4

Per 35 Crew Members*

PHYTOFY

Power

0.6 MW

Volume: 4900 m3

Area 2450 m2

Total Mass: 165 Mg

Structural Mass 28.6 Mg

Water Mass 165 Mg

PHYTOFY Mass 51.917 Mg

*Multiply by 2 to get values for the whole cycler

Michael PorterFebruary 27, 2020

Discipline: Mission DesignVehicle & System: Taxi

The Problem: Determine ∆𝑉𝑠 Accounting for Rendezvous

• Previous Work

• ∆𝑉𝑠 estimated using transfers along closest

approach geometry

• Need to account for phasing during rendezvous

• Assumptions

• State vector data for various bodies are inertial

• Sun is central body

• Constraints

• TOF < 4 days

Figure created by Michael Porter

The Solution: Lambert Algorithm

Insert

𝑟𝑑𝑒𝑝𝑟𝑎𝑟𝑟𝑇𝑂𝐹𝜇

Generate via

Lambert Algorithm

𝑎𝑃

𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑇𝑦𝑝𝑒𝑇𝐴 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑎𝑛𝑔𝑙𝑒

Generate using Keplerian

Equations, f and g functions, and

Rotation Matrices

ҧ𝑣𝑑𝑒𝑝,𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 ҧ𝑣𝑑𝑒𝑝,𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝜔 𝑖Ω 𝑒

∆𝑉𝑡𝑜𝑡∆𝑉𝑑𝑒𝑝∆𝑉𝑎𝑟𝑟

Future Work

• ∆𝑉𝑚𝑖𝑛 𝑓𝑜𝑟 𝑔𝑖𝑣𝑒𝑛 𝑇𝑂𝐹 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡• 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑝𝑙𝑎𝑛𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 𝑡𝑒𝑡ℎ𝑒𝑟𝑠 𝑢𝑠𝑖𝑛𝑔

𝑖𝑛𝑐𝑙𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡• 𝐶𝑎𝑛 𝑓𝑢𝑟𝑡ℎ𝑒𝑟 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑝𝑟𝑜𝑝𝑒𝑙𝑙𝑎𝑛𝑡 𝑏𝑦 𝑤𝑒𝑖𝑔ℎ𝑡𝑖𝑛𝑔

∆𝑉 𝑡𝑜𝑤𝑎𝑟𝑑𝑠 𝑝𝑟𝑜𝑝𝑒𝑙𝑙𝑎𝑛𝑡𝑙𝑒𝑠𝑠 𝑎𝑠𝑝𝑒𝑐𝑡𝑠

BREAKResume at 2:44

Valentin RichardFebruary 27, 2020

Mission DesignMars Tether Sling

How will Mars rotation interfere with the motion of the tether?

- Influence of the rotating planet and gravity on the tether’s gyroscopic effect ?

- Need to predict the tether behavior to perform rendezvous analysis, spin-downs…

Assumptions:

Massless, Inextensible Tether

No tangential acceleration

Centripetal acceleration = 2g

Tether is placed on Olympus

Mons

18.65 °N

Mars

All figures are from V. Richard

𝛼 : in-plane angle

𝛽 : out-of-plane angle

* Figure based on S.G. Tragesser and L. G. Baars

Numerical model simulation

- Simulation time : ¼ of Martian day

0 50 100 150 200 250 300 350 400

Time (min)

-3

-2

-1

0

1

2

3

Dis

tan

ce

fro

m s

urf

ace (

m)

105 Payload distance to Mars surface over time

Plot made by Valentin RICHARD

Conclusion: A fraction of the torque

needs to be used to keep the Tether

steady

Equatorial view

Isometric view

Pierre VEZIN02/26/2020

Mission Design – ElectrDyn. Tether(DeltaV calc, Dynamic Simulation, Orbit degradation, Optimal LEO)

What is the optimal LEO orbit for the ED Tether ?

Requirements:

- Regular Transfer Windows to LUNA only

- Allow for Reboost after every launch:

Assumptions:

- Tether orbit is circular

- Magnetic field = perfect, non tilted dipole [2]

- Luna orbit inclination = 18-28° wrt Equator [1]

LOW

Altitude

Figure by P.VEZIN

2

[3]

(CC) Recht hand regel

What is the optimal LEO orbit for the ED Tether ?

Inclination 28° 18°

Prec. Rate -5.3°/day -5.7°/day

Conclusion :

1/ ED Thrust is only possible at 2

points on the orbit in lunar plane

2/ Orbit is very unstable

3/ Luna orbital plane not even

intertially fixed

→ more trouble

Equatorial LEO better suited

because:

1/ No Nodal precession

2/ Launch windows still open

every 13 days

3/ Thrust conditions are met 100%

all around the equator.

Moving forward : Will be looking into the rendez-vous sequence

using a pre spun up tether. (relative velocities…)

Figure by P.VEZIN

3

Melissa WhitcombFebruary 27, 2020

Mission Design

Orbital ∆v Calculations

Finding All The Pieces…

Image copyright © 2020 by DjSadhu.com. All Rights Reserved.

Arrows added by Melissa Whitcomb.

https://www.djsadhu.com/

Time of Flight and ∆v Values

Assumptions:

• ∆v values will take inclination into account (3D)

• Tethers are located on the north poles of the moon

and Phobos.

Upcoming:

TOF’s (min) for taxi orbits to outbound cyclers (1 & 2)

Journey segment ∆v min

(km/s)

Earth surface to LEO 4.119

Moon surface to LLO 0.580

LLO to Cycler 1 3.640

Cycler to LMO 0.868

Mars surface to LMO 1.634

LMO to Phobos 1.911

Sources:

[1] NASA Planetary Fact Sheets

https://nssdc.gsfc.nasa.gov/planetary/planetfact.html

[2] ESA Mars Express https://sci.esa.int/web/mars-

express/-/31031-phobos

[3] Dr. Jekan Thanga, Purdue guest lecturer,

1/27/2020.

https://nssdc.gsfc.nasa.gov/planetary/planetfact.html

https://sci.esa.int/web/mars-express/-/31031-phobos

Peter Salek February 4, 2020

Discipline: Power and ThermalPower and Magnetic Drag on the Mass Driver

1

Problem

Requirements:

• Examine the magnitude of Air Drag

and Magnetic Drag on the power

requirements

• Investigate if magnetic drag can be

neglected at high speed applications

● Power consumption peaks at the Taxis top speed when drag force is at a maximum

● Power is stored in batteries and used when solar panels can no longer keep up with the

required power

● VVVF (Variable Voltage, Variable Frequency) power is provided to support the power

needs of the MagLev

SolutionMars

Peak Power Consumption (GW) 30.1

Peak Air Drag Power Consumption

(GW)

4

Peak Air Drag Power Consumption

(KW)

350

Total Energy Consumption (GJ) 3600

• Air Drag contributes a significant amount to the

power requirements and should be reduced

• Magnetic Drag is multiple magnitudes lower and

can continue to be neglected

Josh SchmeidlerFebruary 27th, 2020

Power & ThermalTaxi Vehicle - Thermal Protection System (TPS)

Taxi Vehicle Heating During Mars Entry

Problem

• Aerodynamic heating during atmospheric entry

Requirements

• Thermal protection during descent

• Reusability a key factor

• Maximum heating rate = 84.84 𝑊

𝑐𝑚2

• Heating Load = 6.314 𝑘𝐽

𝑐𝑚2

Thermal Protection System

Silicon Carbide Layer

Fibrous Silicon

Solution

• Ceramic Tile TPS• Strengthened silicon outer layer

• Fibrous silicon insulation inner layer

• TPS Mass = 3.823 Mg• Thickness of around 6.35 cm

• Approximately 18000 tiles

• TPS Volume = 26.53 𝑚3

BREAKResume at 3:20

Joe TiberiFebruary 6th, 2020

Propulsion Team LeadED Tether

Tether Sling Design And Release Perturbation

• On release of the taxi, there is

angular momentum relative to the

Taxi

Tether Design Guide

• Next steps

• Discuss with Taxi RCS

team to determine if it is

worth adding a device to

the tethers to counteract

the perturbation.

Tether System Angular Velocity of Taxi

at Release

ED Tether 0.90 deg/s

Luna Tether 0.60 deg/s

Phobos Tether 0.83 deg/s

Taxi Rotation Results

Shuting YangFebruary 27, 2020

PropulsionPhobos and Luna Tether Slings

Propellant Analysis

469

264

248

216

185

123

76

72

64

57

0 50 100 150 200 250 300 350 400 450 500

LOX/LH2

NTO/MMH

LOX/RP-1

NTO/Aerozine 50

HTPB

Pro

pe

llan

t T

yp

e

Mass Ratio (MR) of Tether to Chemical Propellants

Phobos

Luna

𝑀𝑅𝑡𝑝

Problem: Refine Key Dimensions for Tether Slings

𝑀𝑅𝑡𝑝: MR of tether to chemical propellants

Solution:

𝑀𝑡: Tether Mass

L: Tether Length


∆V

(km/s)

Decreased

∆V (%)

Decreased

𝑴𝑹𝒕𝒑 (%)

Decreased

𝑴𝒕 (%)

Decreased

L (%)

Decreased

𝑨𝟎 (%)

3.6 3 10 14 6 11

3.5 6 18 25 11 20

3.2 14 38 50 25 40

5 3 17 21 6 19

4.5 13 53 63 24 57

4 22 72 82 40 76

∆V: Velocity Change from Phobos/Luna to Cycler

𝐴𝑡: Cross section area at the end/tip of the tether

𝐴0: Cross section area at the start/base of the tether

Varied Input:

∆V only

Tether MaterialDecreased

𝑴𝑹𝒕𝒑 (%)

Decreased

𝑴𝒕 (%)

Decreased

𝑨𝒕 (%)

Decreased

𝑨𝟎 (%)

Carbon Nanotube 98 98 95 99

Boron -5,325 -5,309 -7 -3,261

m-Si -44 -44 52 37

Carbon Nanotube 99 99 91 100

Carbides 20 20 2 19

m-Si -168 -168 17 -98

Varied Input:

Tether material only

Tether Material 𝑴𝑹𝒕𝒑

Dyneema 123

Carbon Nanotube 2

Monocrystalline

Silicon (m-Si)177

Boron 6673

Zylon 469

Carbon Nanotube 3

Carbides 377

m-Si 1256

Phobos

Luna

Natasha Yarlagadda February 27, 2020

Propulsion Team - Mass Driver(Levitation Technology)

Problem:

Assumptions:- 50% of taxi mass for weight of cradle

- System operating at 27.77 m/s

- Guidance forces not considered

Electrodynamic Suspension (EDS)[1]

Magnetic Levitation has 3 axes of motion:

Propulsion (± y)

Levitation (± z)

Guidance (± x)

Requirements:

1) Flevitation

2) Technology for levitation

3) Specs of chosen technology

Image by: Natasha Yarlagadda

References cited and calculations shown in backup slides

Solution: Null Flux Coils and Superconducting Magnets

- Power requirements for coils

- Cooling propellant for HTS[6]

- Guidance analysis

- Detailed effects of high speed/large mass

Mass of System (Mg) 300

F_levitation (MN) 1.11

REBCO HTS Magnet[3]

# Magnets Dimensions (m)[4]

80 0.5 x 1.07

Null Flux Coils

# Coils Dimensions (m)[5]

2.8 million 0.31 x 0.55

Specifications:Technology[2]:

Next Steps:

Image by: Natasha Yarlagadda

References cited and calculations shown in backup slides

Rachel RothFebruary 27, 2020

StructuresCommunication Satellites

Slide 1 of 3

Problem – Resizing, Subsystem Int., Internal Layout

Slide 2 of 3

x

y3 m

3 m

3 m

x

y

4 m

2 m

4 m

GEO/AREO Sun-Earth L4/L5 / Sun-Mars L4/L5

Bus resizing

Subsystem integration

Internal layout

Total masses update

prop

prop

reaction wheels at c.m.

computer

LCS

thrustersSolution

Total Satellite Mass Mass (𝐌𝐠)Volume

available (𝐦𝟑)

GEO 1.757 22.501

Sun-Earth L4/L5 2.016 12.387

Sun-Mars L4/L5 1.981 12.387

AREO 1.629 12.316

Slide 3 of 3

Next steps:

• More detailed

internal layout

• External devices

attachment details

• Thermal integration

5 cm

Backup SlidesFebruary 27, 2020

Eli Sitchin Backup SlidesFebruary 27, 2020

Discipline: CADVehicle and Systems Group: Cycler

63

Backup Slide: General Dimensions

Considerations

• All “private” facilities, such as bathrooms and sleeping quarters, placed in the

habitation modules.

• All communal facilities - with the exception of the kitchens - placed in the

habitation interface.

Habitation Module Height (Cross-track1, m) 6

Habitation Module Height (Along-track1, m) 75.7

Habitation Interface Height (Cross-track1, m) 50

Habitation Interface Width (Along-track1, m) 50.3

Ceiling Height from Floor (m) 2.5 [1]

64

Human for Scale

1 Cross-Track: Parallel to axis of rotation

Along-Track: Perpendicular to axis of rotation and radial axis

Habitation Module

Hallway Width: 1.5 m [2]

Backup Slide: Habitation Interface Design

Considerations

• All crops on board, with the exception of tomatoes, require 1 m

or less of vertical space2. Thus, the greenhouse will primarily

consist of two layers of plant beds to reduce the greenhouse

floor area per habitation interface from 3500 m2 to 2060 m2.

• The variable hallway width accounts for the presence of the

elevators placed at the center of the habitation interface.

Greenhouse Area per Interface (m2) 2060

Gym Area per Interface (m2) 125

Hallway Minimum Width (m) 2.5

Hallway Maximum Width (m) 5

65

Greenhouse

Gym

Hallway

Elevators

Utilities

2 Information courtesy of Alexey Zenin (Human Factors)

Backup Slide: Passenger Quarters Design

Considerations

• Designed for 2 passengers to sleep and

store their belongings.

• Dimensions based on those of university

dormitories [3].

• Each passenger will sleep on a twin bed3.

Room Width (Along-Track, m) 4 [3]

Room Length (Cross-Track, m) 4.5 [3[

Room Volume (m3) 45

66

4 Rows of 9

Rooms Total

3 Information courtesy of Kait Hauber (Human Factors)

Backup Slide: Bathroom Design

Toilets per Habitation Module4 4

Showers per Habitation Module4 3

Bathroom Length (Along-Track, m) 10

Bathroom Width (Cross-Track, m) 4.5

Toilet/Shower Width (Along-Track, m) 1

Toilet Depth (Cross-Track, m) 1.5

Shower Depth (Cross-Track. m) 1

Toilets

67

Showers

4 Information courtesy of Kait Hauber (Human Factors)

Backup Slide: Kitchen/Common Area Design

Considerations

• The common area includes both dining tables and

passenger entertainment (TV, VR headsets, etc.)

Kitchen Length (Along-Track,

m)

5

Common Area Length (Along-

Track, m)

13.6

Kitchen/Common Area Depth

(Cross-Track, m)

4.5

Common Area

Kitchen

68

References

[1] Rosen, M., Appel, C., and Ritchie, H., “Human Height,” Our World in Data,

2019.

[2] “Part 36 - Nondiscrimination on the Basis of Disability by Public

Accommodations and in Commercial Facilities,” Americans With Disabilities

Act, Jul. 1991.

[3] “Shreve Room Layout,” Housing at Purdue University Available:

https://www.housing.purdue.edu/Housing/Residences/Shreve/layout.html.

69

Backup Slides References Erick Smith

He, J. L. (n.d.). Publications on Maglev Technologies. Retrieved from

https://www.osti.gov/servlets/purl/5435648

Ohsaki, H. (n.d.). Review and update on MAGLEV. Retrieved from OR3-1%20Ohsaki%20Publication.pdf

https://www.osti.gov/servlets/purl/5435648

Backup Slides DeAngelo

[4]

[5]

References

• [1] - “Entry, Descent and Landing.” NASA, NASA, 22 Nov. 2018,

mars.nasa.gov/insight/entry-descent-landing/.

• [2] - “Home.” Saint, www.quartz.saint-gobain.com/news/using-quartz-fiber-

aerospace-radomes.

• [3] -“Home.” Quartz Fiber | Fused | Thermal Insulation, www.quartz.saint-

gobain.com/products/quartzel.

• [4] - Tecknowledge, LLC. “Worldwide Hub for Composite Materials.” 900GPa,

www.900gpa.com/en/product/fiber/QF_00826957EC?u=metric.

• [5] - 2001, Written by AZoMAug 3. “Epoxy Laminate; Carbon Fibre Prepreg.”

AZoM.com, 11 June 2013, www.azom.com/article.aspx?ArticleID=632.

• [6] - http://www.fastcomposites.ca/publications/CCI_Radome_Whitepaper_190813.pdf

http://www.fastcomposites.ca/publications/CCI_Radome_Whitepaper_190813.pdf

BACKUP: Required SNR Wooten

• Shannon-Hartley theorem

• C = data rate in bit/s

• B = Bandwidth in Hz

• S/N = Signal to Noise Ratio

C = B log2(1+S/N)

S/N = 2C/B-1

Data Rate (C) 1 Gb/s = 1E+9 bit/s

Bandwidth (B) 40E+9 Hz

S/N 1.75E-2

73

BACKUP: Noise from Solar Irradiance

• Solar irradiance @ 1550 nm ~300 mW m-2 nm-1

• Area of Receiver Aperture = (π DR2 )/4 m2

• N = Solar irradiance * Bandwidth * Area of Receiver Aperture

• This value is used in link budget analysis.

Telescope Diameter Noise Power, N

100 cm 0.03 W

74

Value for Solar irradiance from G. Thuillier, “The Solar Spectral Irradiance From 200 To

2400 nm As Measured By The Solspec Spectrometer From The Atlas and Eureca Missions”

BACKUP: Other Losses (Compiled by Eric Smith)Parameter Value

Pointing Loss (LPT) -3 dB

Atmospheric Loss (LATM) 0 dB

Polarization Loss (LPOL) 0 dB

Transmit Optics Efficiency (ηT) -0.969 dB

Aperture Illumination Efficiency (ηa) -0.969 dB

Receive Optics Efficiency (ηR) -0.969 dB

Total: -5.907 dB

These losses are estimates for our system from examples in Hamid Hemmati, “Deep Space Optical

Communications”.

75

BACKGROUND: ED_Tether.m

%% Calculate the Link Budget for RF Between ED Tether & GEO

% Written by Adam Wooten

lambda = 5e-3;% wavelength in m

d = 50e3; %distance between reciever and tranmitter in m 50,000km

B_nm = 500; %Bandwidth

C = 1e9; %Channel Capacity in bits/s

N0 = 0.3;%W/(m^2 nm)

Pt_Watts =150;

Dt = 1; %transmit aperature diameter in m

Dr = 2; %recive aperature diameter in m to GEO

margin = LinkBudget(lambda,d,B_nm,C,N0,Dt,Dr,Pt_Watts)

BACKGROUND: Code LinkBudget.mfu

nctio

n m

arg

in =

Lin

kB

udget(

lam

bda,d

,B_nm

,C,s

pectR

adia

nce,D

t,D

r,P

t_W

att

s)

%%

Calc

ula

te L

ink B

udget

with g

iven in

puts

% la

mbda =

wavele

ngth

of

carr

ier

% d

= d

ista

nce b

etw

een t

ransm

itte

r and r

eceiv

er

% B

_nm

= B

andw

idth

in

nanom

ete

rs

% C

= r

equired d

ata

rate

in

bits/s

% s

pecR

adia

nce =

spectr

al irra

dia

nce in

W/(

m^2

nm

)

% D

t =

Dia

mete

r of

transm

itte

r apert

ure

% D

r =

Dia

mete

r of

receiv

er

apert

ure

% P

t_W

att

ts =

tra

nsm

itte

r pow

er

in W

att

s

%%

c =

299792458;

%speed o

f lig

ht in

m/s

B =

c/(

B_nm

*1e

-9);

%B

andw

idth

in

Hz

SN

R_re

q =

2^(

C/B

)-1;

%R

equired S

NR

for

giv

en d

ata

rate

and b

andw

idth

Pt =

pow

2db(P

t_W

att

s);

%tr

ansm

it p

ow

er

in W

att

s

At =

Dt^

2 *

pi/4; %

Tra

nsm

itte

r A

pert

ure

Are

a

Ar

= D

r^2 *

pi/4;

% R

eceiv

er

Apert

ure

Are

a

Gt

= a

nte

nnaG

ain

(At,

lam

bda);

% R

eceiv

er

Ante

nna G

ain

in

dB

Gr

= a

nte

nnaG

ain

(Ar,

lam

bda);

% R

eceiv

er

Ante

nna G

ain

in

dB

Lfs

= s

paceLoss(d

,la

mbda);

%F

ree S

pace L

oss in

dB

N =

spectR

adia

nce*A

r*B

_nm

; %

nois

e p

ow

er

in W

att

s

P_re

q =

pow

2db(S

NR

_re

q *

N);

% r

equired p

ow

er

in d

B

eta

_t

= p

ow

2db(.

8);

% tra

nsm

itte

r optics e

ffic

iency in

dB

eta

_a =

pow

2db(.

8);

% a

pert

ure

illu

min

atio

n e

ffic

iency in

dB

L_poin

tin

g =

3;

%dB

estim

ate

for

now

L_atm

= 0

; %

no a

tmosphere

lo

ss b

ecause t

x/r

x b

oth

in

space

L_pol =

0;

%no p

ola

rizatio

n

eta

_r

= p

ow

2db(.

8);

% r

eceiv

er

optics e

ffic

iency in

dB

marg

in =

Pt+

eta

_t+

eta

_a+

Gt-

L_poin

tin

g-L

_atm

-L_pol-Lfs

+eta

_r+

Gr-

P_re

q;

% L

ink

Marg

in in

dB

end

77

BACKGROUND: Code spaceLoss.m & antennaGain.mfu

nctio

n F

SL

= s

pa

ce

Lo

ss(d

,la

mbd

a)

% C

alc

ula

tes th

e F

ree

Sp

ace

lo

ss in

dB

of a

sig

na

l o

f w

ave

len

gth

la

mb

da

,

% th

at tr

ave

ls th

e d

ista

nce

d.

FS

L =

pow

2db((

4*p

i*d/lam

bda)^

2);

end

fun

ctio

n G

_T

= a

nte

nn

aG

ain

(A_

eff,la

mbd

a)

%%

Co

de

to

ca

lcu

late

ga

in fo

r tr

an

sm

itting

an

ten

na

% W

ritt

en b

y E

ric S

mith

% A

_e

ff =

eff

ective

are

a o

f a

nte

nn

a

% la

mb

da

= w

ave

len

gth

of sig

na

l

% th

e u

nits o

f A

_e

ff m

ust b

e e

qu

al to

th

e

un

its o

f la

mb

da

^2

%%

G_

T =

po

w2

db

(4*p

i*A

_e

ff/(

lam

bda

^2))

;

end

78

BACKUP: References

Butterfield, A., & Szymanski, J. (2018). Shannon–Hartley theorem. In A Dictionary of Electronics and

Electrical Engineering. : Oxford University Press. Retrieved 29 Jan. 2020, from

https://www.oxfordreference.com/view/10.1093/acref/9780198725725.001.0001/acref-9780198725725-

e-4260.

Thuillier, Hersé, Labs, Foujols, Peetermans, Gillotay, . . . Mandel. (2003). The Solar Spectral Irradiance

from 200 to 2400 nm as Measured by the SOLSPEC Spectrometer from the Atlas and Eureca

Missions. Solar Physics, 214(1), 1-22.

Hemmati, H. (2006). Deep space optical communications (Deep-space communications and navigation

series). Hoboken, N.J.: Wiley-Interscience.

Satellite dish data sheet for a 1.2 m diameter antenna (used to estimate mass of antenna & systems) https://newerasystems.net/wp-content/uploads/2017/01/AvLModel12mModel1050PIBSpecSheet2015-07-31.pdf

79

https://newerasystems.net/wp-content/uploads/2017/01/AvLModel12mModel1050PIBSpecSheet2015-07-31.pdf

Brady WalterFebruary 27, 2020

Communication Satellite Attitude Control Analysis - Backup Slides

Backup Slides - Brady Walter






Thopil, G. A. “An Attitude and Orbit Determination and Control System for a Small Geostationary

Satellite”, University of Stellenbosch, December 2006. https://core.ac.uk/download/pdf/37321303.pdf

Lam, Quang. “Preserving Spacecraft Attitude Control Accuracy Using Theta-D Controller Subject to

Reaction Wheel Failures”, American Institute of Aeronautics and Astronautics, April 2010. https://www.researchgate.net/publication/268570670_Preserving_Spacecraft_Attitude_Control_Accuracy_Using_Theta-

D_Controller_Subject_to_Reaction_Wheel_Failures

“RSI 12 Momentum and Reaction Wheels”, Collins Aerospace, 2020. Accessed 5 Feb via https://www.rockwellcollins.com/Products-and-Services/Defense/Platforms/Space/RSI-12-Momentum-and-Reaction-Wheels.aspx

Konig, Wolfgang M; Longuski, James M; Todd, Richard E. “Survey of Nongravitational Forces and Space

Environmental Torques: Applied to the Galileo”, Purdue University, June 1992.

https://core.ac.uk/download/pdf/37321303.pdf

https://www.researchgate.net/publication/268570670_Preserving_Spacecraft_Attitude_Control_Accuracy_Using_Theta-D_Controller_Subject_to_Reaction_Wheel_Failures

https://www.rockwellcollins.com/Products-and-Services/Defense/Platforms/Space/RSI-12-Momentum-and-Reaction-Wheels.aspx

Appendix: Euler equations Beverly

Euler’s Equations [3]:

Small perturbations i.e. small → :

LHS → torques, calculated from perturbation forces

Moments of inertia are known/fixed → calculate angular acceleration

[3] Wertz, J. R. (1978). Spacecraft attitude determination and control. Dordrecht: Kluwer Academic Publishers.

Appendix: Perturbation Torques Calculation

• Forces [4] scaled individually using area ratio for each cycler component

(solar panel, habitation module, superstructure) according to area ratio and

assuming largest sun-facing area.

• Forces assumed to act at centre of each solar panel, habitation module,

superstructure

• Moment arm is distance of solar panel/habitation module

• Mars forces calculated using formulae in [4].

• Refer to MATLAB code in next slide

[4] Longuski, J. M., Todd, R. E., & Konig, W. W. (1992). Survey of nongravitational forces and space environmental

torques - Applied to the Galileo. Journal of Guidance, Control, and Dynamics, 15(3), 545–553. doi: 10.2514/3.20874

Appendix: MATLAB code for torque calculations (Earth)

1/5


2/5


3/5


4/5


5/5

rc

Appendix: MATLAB code of torque calculation (Mars)

1/4


2/4


3/4


4/4

rc

Appendix: Website – WCAG 2.0 AA Guidelines

• For level AA (what Purdue wants), need to fulfil all requirements for

both level A and level AA

• Guidelines:

https://www.w3.org/TR/WCAG20/?_ga=2.94914708.922866470.15

78261497-550133356.1574792175

• Covers both website itself and any PDFs we upload

• Videos need subtitles

• ZIP folders with code are fine

https://www.w3.org/TR/WCAG20/?_ga=2.94914708.922866470.1578261497-550133356.1574792175

Alexey ZeninFebruary 27, 2020

Backup Slides

Matlab Code with calculations

References

Ammann EC, Lynch VH. Gas exchange of algae. II. Effects of oxygen, helium, and argon

on the photosynthesis of Chlorella pyrenoidosa. Appl Microbiol. 1966

Jul;14(4):552–557.

Barbour MG, Burk JH, Pitts WD. 1987. Terrestrial plant ecology. 2nd ed. Menlo Park (CA):

Benjamin/Cummings Publishing Co.

Bugbee BG, Salisbury FB. 1988. Exploring the limits of crop productivity. I. Photosynthetic

efficiency of wheat in high irradiance environments. Plant Physiology SR:869-878.

Bugbee BG, Spanarkel B, Johnson S, MonJe O, Koerner G. 1994. CO2 crop growth

enhancement and toxicity in wheat and rice. Advances in Space Research l 1: 2S7- 267.

Ensminger NE, Oldfield JE, Heinemann WW. 1990. Feeds and nutrition. 2nd ed. Clovis

(CA):Ensminger Publishing Co.

References

Gitelson JI, et al. 1989. Long-term experiments on man's stay in biological life support system.

Advances in Space Research 9: 65-71.

Salisbury FB, Clark MA. 1996. Choosing plants to he grown in a controlled environment life

support system (CELSS) based upon attractive vegetarian diets. Life Support and

Biosphere Science 2: 169-179.

Salisbury FB, Bingham GE, Campbell WF, Carman JG, Bubenhein DL, Yendler B, Jahns

G. 1995. Growing super-dwarf wheat in Svet on Mir. Life Support & Biosphere

Science 2: 31-39.

Michael Porter – BackupFebruary 27, 2020

Discipline: Mission DesignVehicle & System: Taxi

lambert_solver_with_tof.m -> equations utilized

Space Triangle

𝑇𝐴 = 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑎𝑛𝑔𝑙𝑒 = cos−1ഥ𝑟1 ∙ ഥ𝑟2ഥ𝑟1 | ഥ𝑟2|

𝑐 = ഥ𝑟12 + ഥ𝑟2

2 − 2 ഥ𝑟1 ഥ𝑟2 cos(𝑇𝐴)

𝑠 = 0.5 ( ഥ𝑟1 + ഥ𝑟2 + 𝑐)

𝑎𝑚𝑖𝑛 =𝑠

2

𝛼𝑚𝑖𝑛 = 𝜋

𝛽𝑚𝑖𝑛 = 2 sin−1𝑠 − 𝑐

2 ∗ 𝑎𝑚𝑖𝑛

Determining Elliptical or Hyperbolic Transfer

Type 1: TA < 180°Type 2: TA > 180°

𝐼𝑓 𝑇𝑦𝑝𝑒 1: 𝑇𝑂𝐹𝑝𝑎𝑟 =1

3

2

𝜇𝑠32 − 𝑠 − 𝑐

32

𝐼𝑓 𝑇𝑦𝑝𝑒 2: 𝑇𝑂𝐹𝑝𝑎𝑟 =1

3

2

𝜇𝑠32 + 𝑠 − 𝑐

32

𝐼𝑓 𝑇𝑂𝐹 > 𝑇𝑂𝐹𝑝𝑎𝑟: 𝑒𝑙𝑙𝑖𝑝𝑡𝑖𝑐𝑎𝑙 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 (see next slide 6)

𝐼𝑓 𝑇𝑂𝐹 < 𝑇𝑂𝐹𝑝𝑎𝑟: ℎ𝑦𝑝𝑒𝑟𝑏𝑜𝑙𝑖𝑐 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 (see slide 7)

lambert_solver_with_tof.m -> equations utilizedLambert Elliptical Case

𝜇 𝑡2 − 𝑡1 = 𝑎32 𝛼 − 𝛽 − sin 𝛼 − sin 𝛽

Where 𝛼 𝑎𝑛𝑑 𝛽 depend on the Ellipse Type are:

𝛼0 = 2 sin−1𝑠

2𝑎𝛽0 = 2 sin−1

𝑠 −𝑐

2𝑎

𝐼𝑓 1𝐴: 𝛼 = 𝛼0 𝛽 = 𝛽0 𝐼𝑓 1𝐵: 𝛼 = 2𝜋 − 𝛼0 𝛽 = 𝛽0𝐼𝑓 2𝐴: 𝛼 = 𝛼0 𝛽 = −𝛽0 𝐼𝑓 2𝐵: 𝛼 = 2𝜋 − 𝛼0 𝛽 = −𝛽0

And Ellipse Types are defined as follows:

𝑇𝑂𝐹𝑚𝑖𝑛 =𝑎32

𝜇𝛼𝑚𝑖𝑛 − 𝛽𝑚𝑖𝑛 − sin 𝛼𝑚𝑖𝑛 − sin 𝛽𝑚𝑖𝑛 (see slide 5 for 𝛼𝑚𝑖𝑛 𝑎𝑛𝑑 𝛽𝑚𝑖𝑛)

If Type A: TOF < 𝑇𝑂𝐹𝑚𝑖𝑛 IfType B: TOF > 𝑇𝑂𝐹𝑚𝑖𝑛


Lambert Hyperbolic Case

𝜇 𝑡2 − 𝑡1 = |𝑎|32 sinh𝛼′ − 𝛼′ − sinℎ 𝛽′ − 𝛽′

Where 𝛼′ 𝑎𝑛𝑑 𝛽′ depend on the Hyperbolic Type are:𝐼𝑓 1𝐻: 𝛼′ = 𝛼0′ 𝛽′ = 𝛽0′𝐼𝑓 2𝐴: 𝛼′ = 𝛼0′ 𝛽′ = −𝛽0′


Orbit Determination

If Hyperbolic:

𝑃1,2 =4 |𝑎𝑠𝑜𝑙𝑣𝑒𝑑| 𝑠 − 𝑟1 𝑠 − 𝑟2

𝑐2sinh2(

𝛼′ ± 𝛽′

2)

If Elliptical:

𝑃1,2 =4 𝑎𝑠𝑜𝑙𝑣𝑒𝑑 𝑠 − 𝑟1 𝑠 − 𝑟2

𝑐2sin2(

𝛼 ± 𝛽

2)

If type 1A, 1H, or 2B:𝑃𝑐ℎ𝑜𝑠𝑒𝑛 = max(𝑃1, 𝑃2)

If type 1B, 2H, 2A:𝑃𝑐ℎ𝑜𝑠𝑒𝑛 = m𝑖𝑛(𝑃1, 𝑃2)

Transfer_arc_creater.m -> equations utilizedOrbital Equations

𝑒 = 1 −𝑃

𝑎𝑃𝑒𝑟𝑖𝑜𝑑 = 2𝜋

𝑎3

𝜇𝑠𝑒𝑐𝑜𝑛𝑑𝑠 തℎ = ҧ𝑟 × ҧ𝑣

𝜃∗ = cos−11

𝑒

𝑝

𝑟− 1 ሶ𝑟 = ҧ𝑣 ∙ Ƹ𝑟 𝜔 = 𝜃 − 𝜃∗

𝐼𝑓 ሶ𝑟 > 0: 𝑎𝑠𝑐𝑒𝑛𝑑𝑖𝑛𝑔 𝐼𝑓 ሶ𝑟 < 0: 𝑑𝑒𝑠𝑐𝑒𝑛𝑑𝑖𝑛𝑔

F and g functions

ҧ𝑟 = 1 −𝑟

𝑝1 − cos( 𝜃∗ − 𝜃0

∗) ഥ𝑟0 +𝑟 𝑟0

𝜇 𝑝sin 𝜃∗ − 𝜃0

∗ 𝑣0

ҧ𝑣 =𝑟0 ∙ 𝑣0

𝑝 𝑟01 − cos( 𝜃∗ − 𝜃0

∗ ) −1

𝑟0

𝜇

𝑝sin( 𝜃∗ − 𝜃0

∗) 𝑟0 + 1 −𝑟0

𝑝[ 1 − cos 𝜃∗ − 𝜃0

∗ ] 𝑣0

Lambert_demonstrator.m -> equations utilizedOrbital Equations

𝑃 = 𝑎 ( 1 − 𝑒2) 𝑟 =𝑝

1+𝑒 cos 𝜃∗tan

𝜃∗

2= (

𝑒+1

1 −𝑒)1

2tan𝐸

2

𝜃∗ = cos−11

𝑒

𝑝

𝑟− 1 𝑀 = 𝐸 − 𝑒 sin 𝐸 𝜃 = 𝜔 + 𝜃∗

𝑀 =𝜇

𝑎3(𝑡 − 𝑡𝑝) 𝑟 = 𝑎 ( 1 − 𝑒 cos𝐸)

𝑟𝜃ℎ𝐶𝑥𝑦𝑧 =

𝑐Ω 𝑐𝜃 − 𝑠Ω 𝑐𝑖 𝑠𝜃 −𝑐Ω 𝑠𝜃 − 𝑠Ω𝑠𝑖𝑐𝜃 𝑠Ω 𝑠𝑖𝑠Ω 𝑐𝜃 + 𝑐Ω 𝑐𝑖 𝑠𝜃 −𝑠Ω 𝑠𝜃 + 𝑐Ω 𝑐𝑖 𝑐𝜃 −𝑐Ω 𝑠𝑖

𝑠𝑖 𝑠𝜃 𝑠𝑖 𝑐𝜃 𝑐𝑖***Column Vector format

Backup slide: References Richard

Tether Dynamical equations:

Steven G. Tragesser, Luis G. Baars, "Dynamics and Control of a Tether Sling Stationed on a Rotating

Body", Journal of Guidance and Control, and Dynamics, Vol. 37, No. 1, January-February 2014

Backup slide: Additional figures (1)- Simulation Time: Entire Martian day

Top view Isometric view

Backup slide: Additional figures (2)- Simulation Time: Entire Martian day

0 500 1000 1500

Time (min)

-1200

-1000

-800

-600

-400

-200

0

200

Ou

t o

f p

lane

an

gle

s (°)

In and out of plane angles over time

beta

alpha

Plot made by Valentin RICHARD

Backup slide: EquationsComputation variables

Var Meaning Value

𝛼 In-plane angle output

𝛽 Out-of-plane angle output

𝜙 Latitude 18.65°

𝛺 Mars angular velocity 7.0777 * 10-5 rad.s-1

𝓵 Tether length 8.2477 * 105 m

𝓻 Hub radius 50 m

𝓰 Martian gravity accel. 3.71 m.s-2

𝜽 Hub Angular velocity 0.0049 rad.s-1

Backup slide: MATLAB Code (1)



Backup slide: Preliminary study on the effect of centripetal acceleration value

Before studying the behavior of the Martian Tether

Sling. I started doing a preliminary study on how the

centripetal acceleration value (the value that the

Tether Sling team is using now is 2g) will affect the

inclination of the Tether arm when located at the

poles.

The important result is that the angle drastically

decreases as the centripetal acceleration increases.

Using a 2g acceleration results in a 7.169°

inclination, which seems quite reasonable.

Backup Slides

Baseline: Momentum Conservation Vezin

• Let M1 be the mass of the tether system and V1 its velocity relative to Earth

• Let M2 be the mass of the SpaceCraft and V2 its velocity relative to Earth

• Let V be the orbital velocity of the entire system {tether + s/c} before release of S/C

The momentum conservation implies that:

P = M×V = constant = 𝑀1+𝑀2 𝑉 = M1 V1 + M2 V2

𝑉1 = 𝑉 +𝑀2

𝑀1× (𝑉 − 𝑉2)

Set ∆𝑉𝑆/𝐶= 𝑉2 − 𝑉 and 𝛿 =𝑀2

𝑀1

𝑉1 = 𝑉 − 𝛿 × ∆𝑉𝑆/𝐶 (1)

And finally

∆𝑉𝑡𝑒𝑡ℎ𝑒𝑟= 𝛿 × ∆𝑉𝑆/𝐶 → tether velocity loss is proportional to S/C deltaV and inversely to mass ratio.

• Deriving the relation V1 = 𝜇 (2

𝑟𝐿𝐸𝑂−

1

𝑎) we can express the tether’s perigee radius after release 𝑟𝑝 as a function

of initial circular radius rLEO & final speed V1

𝑎 =𝜇 𝑟𝐿𝐸𝑂

2𝜇− 𝑉12 𝑟𝐿𝐸𝑂(𝑎 =

𝑟𝑎+ 𝑟𝑝

2)

𝑟𝑝 =2 𝜇 𝑟𝐿𝐸𝑂

2𝜇 − 𝑟𝐿𝐸𝑂𝑉12 − 𝑟𝑎 and 𝑧𝑝 = 𝑟𝑝 − 𝑅𝐸𝑎𝑟𝑡ℎ (2)

Using this relation we can plot several curves for the perigee altitude of the tether after S/C separation, with mass ratio

and deltaV applied to the spacecraft as variables.

• What if the initial orbit is not circular but rather elliptical ? The apogee of the tether’s orbit would be higher than

1000km so when the S/C is released, it would drop but remain above 1000 km.

Impact on orbit Geometry: Momentum Conservation

Backup Slides

Elliptical initial Orbit• The variables : rLEO radius at time of release (1000 km); ra radius of apogee (before release); rp

radius of perigee (after release) (1000 km); Vpre velocity of tether before release (at the release

location); Vpost Velocity of tether after release (at release location); ∆𝑉𝑆𝐶 deltaV applied to payload

Backup Slides

Additionnal Plots

Backup Slides

Elliptical Initial orbitCircular Initial orbit

Software created

Useful metricsmu_earth = 398600.4415; %km^3/s^2 (gravitational parameter of Earth)

r_earth = 6378.136; %km (mean equatorial radius of Earth)

h_LEO = 1000; %km (altitude of LEO)

r_LEO = r_earth + h_LEO;

Compute Useful Valuesv_LEO = (mu_earth/r_LEO)^.5; %km/s (orbital velocity of circular LEO)

Orbit drop after releaseThe conservation of momentum allow us to express the orbital velocity of tether after release of S/C as a function of

initial speed (orbital speed in LEO), the mass ratio between the S/C and the whole tether system and the DeltaV

required for the payload

Assumptions : Delta V are colinear to prograde vector & Initial orbit is circular

Backup Slides

eta = [1 2 3 5 10 15 20 25 30 40 50].^-1; % Mass ratio payload/tether (range)dV = [2.95:0.05:4.3]; % Payload deltaV(range)-->(for moon, mars, cycler)

j=1;for mratio = eta % Mass ratio range(m(S/C) / m(tether))

i=1;for dv_sc = dV

% Velocity of tether after release in km/sV_tether(i,j) = v_LEO-mratio*dv_sc;

% Corresponding Perigee altitude (above Sea Level) in kmz_perigee(i,j) = 2*r_LEO*mu_earth/(2*mu_earth-r_LEO*V_tether(i,j)^2)-r_LEO-r_earth;i=i+1;

endj=j+1;

end

Software created

Backup Slides

Software createdfigure(9)plot(dV, V_tether)title('Final velocity of tether (after sep) vs. S/C DeltaV')xlabel('DeltaV (payload, km/s)')ylabel('Velocity of tether (km/s)')legend('mass Ratio = 1','2','3','5','10','15','20','25','30','40','50')grid

figure(10)plot(dV, z_perigee)title('Tether''s perigee altitude after release vs. S/C deltaV')xlabel('DeltaV (payload, km/s)')ylabel('Tether''s perigee (km above sea level)')legend('mass Ratio = 1','2','3','5','10','15','20','25','30','40','50')grid

Backup Slides

Software created% The perigee is PLUNGING, unless the mass ratio is immense (20+)% mratio = 20 implies that the tether is a least 20*100=2000 tonnes.% We will try to put the tether on a eccentrical orbit to store some energy% before the spin up and remain in stable circular orbit after release. This will also reduce the DeltaV requirements.

% Starting from here, r_LEO will be the radius of the tether’s location at release

perigee_min = 1000; %km Minimum Perigee alt after release (= tether perigee before release)rp_min = perigee_min+r_earth; %km Minimum Perigee radius after release

% Compute the speed required (after release) for the perigee to remain above Perigee_min kmv_post = (mu_earth*(2/r_LEO - 2/(r_LEO+rp_min)))^0.5

% The following loop calculates the initial speed required (at r_LEO) in% order to remain on an orbit with a perigee >rp_min after the release of% the spacecraft% This velocity (v_pre) is computed for all different value of mass ratio% and DeltaV applied to the payload% --> the lower the mass ratio, the higher the excess speed required will% be% --> the greater the delta V applied to the payload, the greater the% excess speed v_pre will need to be. Backup Slides

Backup Slides

Software createdj=1;for mratio = eta % Mass ratio range(m(S/C) / m(tether))

i=1;for dv_sc = dV % DeltaV range (encompasses dV for moon, mars and cycler)

v_pre(i,j) = mratio/(1+mratio)*(dv_sc + v_LEO + v_post/mratio);i=i+1;

endj=j+1;

end

% compute the altitude of apogee (before release) needed to limit perigee drop% --> function of mass ratio and deltaV of payloadz_apogee = -(v_pre.^2.*r_LEO - (2*mu_earth)).^-1 .*(2*mu_earth*r_LEO) - r_LEO - r_earth;

figure(11)plot(dV, z_apogee)title('Tether''s initial apogee altitude before release vs. DeltaV of payload')xlabel('DeltaV (payload, km/s)')ylabel('Tether''s apogee (km above sea level)')legend('mass Ratio = 1','2','3','5','10','15','20','25','30','40','50')grid

Backup Slides

Software created

% Compute the eccentricity of the initial orbit

e_initial = (z_apogee-h_LEO)./(z_apogee + r_earth + r_LEO);

figure(12)

plot(dV, e_initial)

title('Tether''s orbit initial eccentricity before release vs. DeltaV of payload')

xlabel('DeltaV (payload, km/s)')

ylabel('Tether''s orb. eccentricity')

legend('mass Ratio = 1','2','3','5','10','15','20','25','30','40','50')

grid

References

[1] «Modeling and analyis of the Electrodynamic tether» J.Longuski, M.Mueterthies

[2] «A Modular ME/ERT system architecture» R. Hoyt, J. Slostad, S. Frank

Additional Slides Salek

Power backup slides: Solar Radiation

Solar Radiation based on the following

equation:

Solar Irradiance = (Rsun2/Distance2)*Hsun

Hsun = 64*106 w/m2

Power backup slides: Power Consumption

Power for Mass Driver determined using

below equation:

First term represents magnetic drag and

was neglected until further research is

completed.

Power backup slides: Power Consumption

Backup Slides Schmeidler

References

[1] Benson, Tom. “Mars Atmosphere Model - Metric Units.” NASA, NASA,

12 Nov. 2014, www.grc.nasa.gov/WWW/K-12/rocket/atmosmrm.html.

[2] Dumoulin, Jim. “THERMAL PROTECTION SYSTEM.” NASA, NASA, 12 Jan.

1994, science.ksc.nasa.gov/shuttle/technology/sts-newsref/sts-tps.html#sts-

hrsi.

[3] Girija, Athul Pradeepkumar, et al. “Feasibility and Mass-Benefit Analysis of

Aerocapture for Missions to Venus.” Journal of Spacecraft and Rockets, vol. 57,

no. 1, 24 Jan. 2020, pp. 58–73., doi:10.2514/1.a34529.

Calculations

Tether Design Guide Code 1 Tiberi

Tether Design Guide Code 2

Tether Spin-up EOMs

Tether Velocity During Spinup

Power required during spin-up

Taxi Rotation Derivation

Shuting YangFebruary 27, 2020

PropulsionPhobos and Lunar Tether Sling

Backup Slides

Appendix A: References

1. Guide to Tensile Strength. (n.d.). Retrieved February 10, 2020, from

https://monroeengineering.com/info-general-guide-tensile-strength.php

2. Koppel, C. R. (1997). Optimal specific impulse of electric propulsion. European

Space Agency, (Special Publication) ESA SP, (398), 131-139.

3. Puigsuari, J., Longuski, J., & Tragesser, S. (1995). A tether sling for lunar and

interplanetary exploration. Acta Astronautica, 36(6), 291-295.

4. Rees, D. (2009). Mechanics of optimal structural design minimum weight

structures. Chichester, West Sussex, U.K. ; Hoboken: J. Wiley.

5. Robert, A. (2008). Rocket Propellants. Retrieved February 3, 2020, from

http://www.braeunig.us/space/propel.htm

6. “Ultra High molecular Weight Polyethylene fiber from DSM Dyneema,” eurofibers,

CIS YA100, January 2010.

https://monroeengineering.com/info-general-guide-tensile-strength.php

http://www.braeunig.us/space/propel.htm

Appendix B: Tables

∆V (km/s) Density (kg/𝑚3) UTS (GPa) 𝑀𝑝 (Mg) 𝑀𝑅𝑡𝑝 𝑀𝑡 (Mg) L (km) 𝐴𝑡 (𝑐𝑚2) 𝐴0 (𝑐𝑚2)

3.7053 970 3.325 193 123 3.4 x 104 700 113.85 843.41

3.6 970 3.325 193 111 3.0 x 104 660.78 113.85 753.89

3.5 970 3.325 193 101 2.6 x 104 624.58 113.85 679.72

3.2 970 3.325 193 76 1.7 x 104 522.09 113.85 506.99

3.7053 1340 62 193 2 6.3 x 104 700 6.11 7.08

3.7053 2460 3.1 193 6673 1.9 x 106 700 122.11 28348.3

3.7053 2330 7 193 177 4.9 x 104 700 54.08 531.31

∆V (%) Density (%) UTS (%) 𝑀𝑝 (%) 𝑀𝑅𝑡𝑝 (%) 𝑀𝑡 (%) L (%) 𝐴𝑡 (%) 𝐴0 (%)

3 0 0 0 10 14 6 0 11

6 0 0 0 18 25 11 0 19

14 0 0 0 38 50 25 0 40

0 -38 -1765 0 98 -85 0 95 99

0 -154 7 0 -5325 -5309 0 -7 -3261

0 -140 -111 0 -44 -44 0 52 37

Table 1. Variation of Inputs and the corresponding outputs for tether slings on Phobos.

Table 2. Convert table 1 data into the percentage form. A positive percentage represents the

decreased amount, and a negative number represents the increased amount.


𝑀𝑝: Payload Mass





UTS: Ultimate Tensile Strength

Appendix B: Tables

∆V (km/s) Density (kg/𝑚3) UTS (GPa) 𝑀𝑝 (Mg) 𝑀𝑅𝑡𝑝 𝑀𝑡 (Mg) L (km) 𝐴𝑡 (𝑐𝑚2) 𝐴0 (𝑐𝑚2)

5.1521 1550 5.8 193 469 2.2 x 105 1353.37 65.26 2264.93

5 1550 5.8 193 389 1.7 x 105 1274.65 65.26 1842.67

4.5 1550 5.8 193 219 8.3 x 104 1032.46 65.26 976.79

4 1550 5.8 193 131 4.1 x 104 815.77 65.26 553.57

5.1521 1500 5.93 193 377 1.8 x 105 1353.37 63.83 1832.5

5.1521 1340 62 193 3 1.3 x 103 1353.37 6.11 8.13

5.1521 2230 7 193 1256 5.9 x 105 1353.37 54.08 4483.26

∆V (%) Density (%) UTS (%) 𝑀𝑝 (%) 𝑀𝑅𝑡𝑝 (%) 𝑀𝑡 (%) L (%) 𝐴𝑡 (%) 𝐴0 (%)

3 0 0 0 17 21 6 0 19

13 0 0 0 53 63 24 0 57

22 0 0 0 72 82 40 0 76

0 3 -2 0 20 20 0 2 19

0 14 -969 0 99 99 0 91 100

0 -44 -21 0 -168 -168 0 17 -98

Table 1. Variation of Inputs and the corresponding outputs for tether slings on Luna.

Table 2. Convert table 1 data into the percentage form. A positive percentage represents the

decreased amount, and a negative number represents the increased amount.


𝑀𝑝: Payload Mass





UTS: Ultimate Tensile Strength

Appendix C: Equations

Appendix D: MATLAB Code








Natasha Yarlagadda - Backup Slides February 27, 2020

Propulsion Team - Mass Driver(Levitation Technology)

Backup Slide: EDS vs EMS Systems

Electromagnetic Suspension Electrodynamic Suspension

- Attraction system

- Electromagnet + ferromagnetic rail

- Open loop, unstable system

- Difficult to maintain gap at high speeds

- Inexpensive and simple

- Repulsion system

- Superconducting magnet + non-ferromagnetic rail

- Acts as open loop, stable system

- Very stable at high speeds

- Costly and complex

Backup Slide: Null Flux Coils and HTS Magnets

Null Flux Coil

- Figure 8 Null FLux coils can provide both levitation

and guidance with high lift/drag ratios (3)

- When center of magnet offset from center of coil,

lower loop generates more flux than upper and

induces a current

- The magnetic field generated as a result produces

repulsive force to move the magnet up to equilibrium

- Null Flux coils are affected by the type of wire and

number of loops

- Null Flux coils are also affected by the distance from

the upper to lower loop (cross sectional area)

High Temperature Superconducting Magnet

- REBCO superconducting coil

- Rare-Earth barium copper oxide

- Any rare Earth can be used (yttrium, lanthanides,

etc.)

- Need to be cooled with nitrogen and helium to begin

superconducting

- Require much less cooling than other types of

conductors

- Magnetomotive force of 700 kA and 5.2 T magnetic

flux when cooled to 35 K

Details and Considerations:

Backup Slide: Factors Affecting Levitation

Factor Increase (↑) or Decrease (↓) Effect on Flevitation

Vehicle Speed ↑ ↑*

Distance between upper/lower loop ↑ ↑

Offset between centerline of magnet/coil ↑ ↑*

Coil Sectional Area ↑ ↑

Air Gap between track/vehicle ↑ ↑*

*eventually the effect of increasing this factor levels out and does not increase Flevitation[3]

Backup Slide: Calculations/Plots

Backup Slide: Calculations/Plots

Backup Slide: References

[1] Guo, Li, and Zhou, “Study of a Null-Flux Coil Electrodynamic Suspension Structure for Evacuated Tube Transportation,”

Symmetry, vol. 11, Mar. 2019, p. 1239.

[2] Davey, K., “Designing with null flux coils,” IEEE Transactions on Magnetics, vol. 33, Sep. 1997, pp. 4327–4334.

[3] Ohsaki, H., “Review and update on MAGLEV,” European Cryogenics Day 2017 Available:

file:///C:/Users/Natasha/Downloads/OR3-1 Ohsaki Publication.pdf.

[4] He, J., Rote, D., and Coffey, H., “Survey of foreign maglev systems,” US Army Corps of Engineers, Jan. 1992.

[5] He, J., and Rote, D. M., “Computer Model Simulation of Null-Flux Magnetic Suspension and Guidance,” Center for

Transportation Research, Energy Systems Division, Argonne National Laboratory, Jun. 1992.

[6] Gupta, R., “Field Calculations and Computations,” School at CAT, Indore, India, Jan. 1998.

Rachel RothFebruary 27, 2020

Backup Slides

Backup Slides – Structure Sizing

Structural Component Mass (𝐌𝐠)Volume

(𝐦𝟑)

GEO/AREO

(3m x 3m x 3m)

External Structure 0.604 0.215

Internal Structure 0.610 0.217

Sun-Earth/Sun-Mars L4/L5

(4m x 4m x 2m)

External Structure 0.717 0.255

Internal Structure 0.691 0.246

Total GEO Satellite Structure 1.214 0.432

Total Sun-Earth L4/L5 Satellite Structure 1.408 0.501

Total Sun-Mars L4/L5 Satellite Structure 1.408 0.501

Total AREO Satellite Structure 1.214 0.432

5 cm

*Al 7075-T7351 [5]

Backup Slides – GEO Satellite Sizing

Component Mass (𝐌𝐠)*Volume (𝐦𝟑)

(internal)

Volume (𝐦𝟑)

(external)

StructuresExternal structure 0.604 0.215 -

Internal supports 0.610 0.217 -

Communications [1]

RF GEO to Earth 0.0075 - 0.125

RF GEO to GEO 0.030 - 8.0

LCS GEO to Sun-Earth L4/L5 0.085 - 36.0

Control [2] 0.089 0.003 -

Propulsion [3]

Propellant

0.165

22.06 -

Thrusters - 0.071

RCS - 0.36

Power & Thermal [4]

Solar panels0.028

- 0.027

Battery 0.0056 -

Thermal 0.108 - -

Total GEO Satellite* 1.757 22.501 44.583

*GEO Satellite: 1 RF Antenna for GEO to Earth

2 RF Antennas for GEO to GEO

1 LCS for GEO to Sun-Earth L4/L5

*Al 7075-T7351[1] AAE 450 Communications Team

[2] AAE 450 Control Team

[3] AAE 450 Propulsion Team

[4] AAE 450 Power & Thermal Team

*Sun-Earth L4/L5 Satellite:

1 LCS for GEO to Sun-Earth L4/L5

1 LCS for Sun-Earth L4/L5 to Sun-Mars L4/L5

*Al 7075-T7351


(internal)

Volume (𝐦𝟑)

(external)



Communications [1]

LCS GEO to Sun-Earth L4/L5 0.085 - 36.0

LCS Sun-Earth L4/L5 to

Sun-Mars L4/L50.201 - 88.0

Control [2] 0.089 0.003 -

Propulsion [3]

Propellant

0.099

11.88 -

Thrusters - 0.071

RCS - 0.36

Power & Thermal [4]

Solar panels0.037

- 0.053

Battery 0.003 -

Thermal 0.097 - -

Total Sun-Earth L4/L5 Satellite* 2.016 12.387 124.484

Backup Slides – Sun-Earth L4/L5 Satellite Sizing

[1] AAE 450 Communications Team




*Sun-Mars L4/L5 Satellite:

1 LCS for AREO to Sun-Mars L4/L5

1 LCS for Sun-Earth L4/L5 to Sun-Mars L4/L5

*Al 7075-T7351

Backup Slides – Sun-Mars L4/L5 Satellite Sizing


(internal)

Volume (𝐦𝟑)

(external)



Communications

[1]

LCS AREO to Sun-Mars L4/L5 0.050 - 18.75

LCS Sun-Earth L4/L5 to

Sun-Mars L4/L50.201 - 88.0

Control [2] 0.089 0.003 -

Propulsion [3]

Propellant

0.099

11.88 -

Thrusters - 0.071

RCS - 0.36

Power & Thermal

[4]

Solar panels0.037

- 0.053

Battery 0.003 -

Thermal 0.097 - -

Total Sun-Earth L4/L5 Satellite* 1.981 12.387 107.234





*AREO Satellite: 1 RF Antenna for AREO to Mars

2 RF Antennas for AREO to AREO

1 LCS for AREO to Sun-Mars L4/L5

*Al 7075-T7351

Backup Slides – AREO Satellite Sizing


(internal)

Volume (𝐦𝟑)

(external)



Communications [1]

RF AREO to Earth 0.0075 - 0.125

RF AREO to AREO 0.030 - 8.0

LCS AREO to Sun-Mars L4/L5 0.050 - 18.75

Control [2] 0.089 0.003 -

Propulsion [3]

Propellant

0.099

11.88 -

Thrusters - 0.071

RCS - 0.36

Power & Thermal

[4]

Solar panels0.033

- 0.051

Battery 0.0013 -

Thermal 0.108 - -

Total GEO Satellite* 1.629 12.316 27.357





Backup Slides – Material PropertiesAl 7075-T7351 [5]

Property Value

Density 2810 kg/m3

Tensile Strength, ultimate 505 MPa

Tensile Strength, yield 435 MPa

Modulus of Elasticity 72 GPa

Elongation at Break 13%

Fracture Toughness 20 – 32 MPa-m1

2

Melting Point 477 – 635 ℃

Thermal Conductivity 155 W/m-K

Backup Slides – References[5] Aluminum Association, Inc. (2001). Aluminum 7075-T73; 7075-T735x. Retrieved from

http://asm.matweb.com/search/GetReference.asp?bassnum=MA7075T73.

http://asm.matweb.com/search/GetReference.asp?bassnum=MA7075T73

Backup: ElectroDynamic Thrust calc VEZIN

• The Lorentz force is defined as follow:

𝐹𝐸𝐷 = Ԧ𝐽 × 𝐵 → cross product: F is perpendicular to B, always!

• The magnetic field is modele by the perfect, non titled dipole used in reference [1]:

𝐵 =𝐵0𝑅3

(3 Ԧ𝑟 ∙ 𝑛 Ԧ𝑟 − 𝑛)

with 𝑛 the orientation of the Dipole (vertical north−south)

Ԧ𝑟 the local radial vector in spherical coordinates

R3 the distance of the object from Earth’s center

B0 the specific intensity of Magnetic field (8x106 T.km3)

Method used: A matlab script is used to generate the 3D trajectory of the tether around

earth (LEO) for a duration of 1 circular orbit with a given inclination. For every point in the

trajectory, we compute the local orbital velocity and local vector for magnetic field and

measure the angle between the two. If the angle is 90°, prograde thrust is possible, if not,

thrust is not prograde and will affect the inclination and shape of the orbit.

• The formula used to compute the Nodal Precession rate is:

𝑑Ω

𝑑𝑡= −

3

2

𝑅𝐸2

𝑎 1 − 𝑒22 𝐽2

𝜇

𝑎3cos(𝑖)

with: - J2 = 1.083x10-3 the second dynamic form factor

- RE = 7368 km the orbit radius (equal to a, semi major axis)

- e=0 (circular orbit)

- 𝜇 = 398600 km3s-2

- i = 18-28° the inclination of Luna’s orbit wrt to the Equator

→ Precession rate ranges from -5.3 to -5.7 °/day which makes the orbit very unstable. The

alignment with the moon’s orbital plane won’t last more than a few hours without using very

expensive plane changing maneuver

Results are matching with Gmat propagation over a few days.

Backup: Nodal Precession

Backup: Matlab Code%% Orbital Parameters :

% assuming a perfectly circular orbit (very close to the actual orbit)

no = 2000; %number of points in discrete trajectory

inc = 28 * pi/180; %rad inclination

h_LEO = 1000; %km orbit altitude

r_earth = 6378; %km earth radius

r_LEO = r_earth + h_LEO; %km LEO radius

phi=linspace(0, 2*pi, no); %rad anomaly (range covering 360°)

% Trajectory in x,y,z coordinates :

position = [r_LEO*cos(phi); r_LEO*sin(phi).*cos(inc); r_LEO*sin(phi).*sin(inc)];

%% Earth Modeling (visual):

ne=1000; %number of points

nt = 50; %number of turns (spiral)

theta_earth=linspace(-pi/2, pi/2, ne); %latitude range

phi_earth = linspace(0,nt*2*pi, ne); %Longitude range

figure(1)

% Plot Earth 3D (simpified)

plot3(r_earth.*cos(theta_earth).*cos(phi_earth), r_earth*cos(theta_earth).*sin(phi_earth),

r_earth*sin(theta_earth), ':')

title('3D sketch of the problem')

hold on

% Plot Equatorial line

plot3(r_earth*cos(phi),r_earth*sin(phi),0*sin(phi), 'red', 'Linewidth', 0.1)

%Plot orbit

plot3(position(1,:), position(2,:), position(3,:), 'color', [0.93,0.69,0.13])

legend('Earth','Equator','Tether orbit')

%% Compute vectors to visualize several magnetic field lines

step = 100; %km integrator step --> correspond to the length of each infinitesimal

segment

j=1;

for initial_position = [7378:2000:20000]; % different initial condition (altitude)

for different lines

carabiner(:,1,j)=[0 initial_position 0];

i=2;

while norm(carabiner(:,i-1,j)) > r_earth/5

carabiner(:,i,j) = carabiner(:,i-1,j) + step * MagField(carabiner(:,i-1,j)) /

norm(MagField(carabiner(:,i-1,j)));

i=i+1;

end

j=j+1;

end

% Expand the Lines so that they go from North Pole to South Pole

c_opposite = carabiner;

c_opposite(3,:,:) = -carabiner(3,:,:);

% Plot the magnetic field lines on the 3D represetnation of Earth

for i=[1:1:length(carabiner(1,1,:))]

plot3(carabiner(1,:,i), carabiner(2,:,i), carabiner(3,:,i),'--r', 'HandleVisibility', 'off');

plot3(c_opposite(1,:,i), c_opposite(2,:,i), c_opposite(3,:,i), '--r', 'HandleVisibility', 'off');

end

hold off

%% Compute Prograde Vector at any point of traj (unit vector)

% these vector are obtained by position numerical differentiation

for i = [1:1:no-1]

prograde(:,i) = position(:,i+1) - position(:,i); % Numerical differentiation of position

prograde(:,i) = prograde(:,i)/norm(prograde(:,i)); % Make it a Unit vector

end

prograde(:,no) = prograde(:,no-1); % so that vector has same length as other

vectors

%% Magnetic Field Direction along the trajectory of the s/c

dipole_direction = [0; 0; -1]; %Earth magnetic field goes trough the poles and from north to

south (-z vector)

B0 = 8e6; %Tkm^3 Specific Intensity of Mag Field

for i = [1:1:no]

B(:,i) = MagField(position(:,i)); %Magnetic Field Vector (local)

B_unit(:,i) = B(:,i)./norm(B(:,i)); %Unit Vector assiciated with Magnetic field (local)

end

%% Compute angle between prograde vector and Magnetic field line

for i = [1:1:no]

angle(i)=acos(dot(prograde(:,i), B_unit(:,i)))*180/pi;

end

figure(2)

plot(phi*180/pi, angle,'blue', 90, 90,'ro', 270, 90,'ro')

title('Angle between Prograde Vector and Magnetic Field')

xlabel('Orbital Position (Anomaly) (°)');

ylabel('Angle between Mag. Field and Prograde');

%% Orbital stability (Nodal Precession) (If orbit is circular)

J2 = 1.08262668e-3;

GM_earth = 398600; %km^3/s^2 Earth Stand. Grav. Param

%compute nodal regression rate (°/day)

nodal_precession_rate = -3/2 * (r_earth/r_LEO)^2 * J2 * sqrt(GM_earth/r_LEO^3) * cos(inc) *

180/pi*3600*24

GMAT Tether.NAIFIdReferenceFrame = -9000001;GMAT Tether.OrbitColor = Red;GMAT Tether.TargetColor = Teal;GMAT Tether.OrbitErrorCovariance = [ 1e+070 0 0 0 0 0 ; 0 1e+070 0 0 0 0 ; 0 0 1e+070 0 0 0 ; 0 0 0 1e+070 0 0 ; 0 0 0 0 1e+070 0 ; 0 0 0 0 0 1e+070 ];GMAT Tether.CdSigma = 1e+070;GMAT Tether.CrSigma = 1e+070;GMAT Tether.Id = 'SatId';GMAT Tether.Attitude = CoordinateSystemFixed;GMAT Tether.SPADSRPScaleFactor = 1;GMAT Tether.ModelFile = 'aura.3ds';GMAT Tether.ModelOffsetX = 0;GMAT Tether.ModelOffsetY = 0;GMAT Tether.ModelOffsetZ = 0;GMAT Tether.ModelRotationX = 0;GMAT Tether.ModelRotationY = 0;GMAT Tether.ModelRotationZ = 0;GMAT Tether.ModelScale = 1;GMAT Tether.AttitudeDisplayStateType = 'Quaternion';GMAT Tether.AttitudeRateDisplayStateType = 'AngularVelocity';GMAT Tether.AttitudeCoordinateSystem = EarthMJ2000Eq;GMAT Tether.EulerAngleSequence = '321';

%General Mission Analysis Tool(GMAT) Script

%Created: 2020-02-18 15:10:08

%----------------------------------------

%---------- Spacecraft

%----------------------------------------

Create Spacecraft Tether;

GMAT Tether.DateFormat = TAIModJulian;

GMAT Tether.Epoch = '21545';

GMAT Tether.CoordinateSystem = EarthMJ2000Eq;

GMAT Tether.DisplayStateType = Keplerian;

GMAT Tether.SMA = 7367.999999999998;

GMAT Tether.ECC = 2.626830445736181e-016;

GMAT Tether.INC = 28.00000000000001;

GMAT Tether.RAAN = 0;

GMAT Tether.AOP = 0;

GMAT Tether.TA = 0;

GMAT Tether.DryMass = 15000;

GMAT Tether.Cd = 2.2;

GMAT Tether.Cr = 1.8;

GMAT Tether.DragArea = 15;

GMAT Tether.SRPArea = 1;

GMAT Tether.NAIFId = -10000001;

%----------------------------------------

%---------- ForceModels

%----------------------------------------

Create ForceModel TetherLEOprop_ForceModel;

GMAT TetherLEOprop_ForceModel.CentralBody = Earth;

GMAT TetherLEOprop_ForceModel.PrimaryBodies = {Earth};

GMAT TetherLEOprop_ForceModel.PointMasses = {Luna};

GMAT TetherLEOprop_ForceModel.Drag = None;

GMAT TetherLEOprop_ForceModel.SRP = Off;

GMAT TetherLEOprop_ForceModel.RelativisticCorrection = Off;

GMAT TetherLEOprop_ForceModel.ErrorControl = RSSStep;

GMAT TetherLEOprop_ForceModel.GravityField.Earth.Degree = 10;

GMAT TetherLEOprop_ForceModel.GravityField.Earth.Order = 10;

GMAT TetherLEOprop_ForceModel.GravityField.Earth.StmLimit = 100;

GMAT TetherLEOprop_ForceModel.GravityField.Earth.PotentialFile =

'JGM2.cof';

GMAT TetherLEOprop_ForceModel.GravityField.Earth.TideModel =

'None';

%----------------------------------------

%---------- Propagators

%----------------------------------------

Create Propagator TetherLEOprop;

GMAT TetherLEOprop.FM = TetherLEOprop_ForceModel;

GMAT TetherLEOprop.Type = RungeKutta89;

GMAT TetherLEOprop.InitialStepSize = 60;

GMAT TetherLEOprop.Accuracy = 9.999999999999999e-012;

GMAT TetherLEOprop.MinStep = 0.001;

GMAT TetherLEOprop.MaxStep = 2700;

GMAT TetherLEOprop.MaxStepAttempts = 50;

GMAT TetherLEOprop.StopIfAccuracyIsViolated = true;

%----------------------------------------

%---------- Subscribers

%----------------------------------------

Create OrbitView DefaultOrbitView;

GMAT DefaultOrbitView.SolverIterations = Current;

GMAT DefaultOrbitView.UpperLeft = [ -0.00123304562268804 -

0.004629629629629629 ];

GMAT DefaultOrbitView.Size = [ 0.9858199753390875

0.9745370370370371 ];

GMAT DefaultOrbitView.RelativeZOrder = 229;

GMAT DefaultOrbitView.Maximized = false;

GMAT DefaultOrbitView.Add = {Tether, Earth};

GMAT DefaultOrbitView.CoordinateSystem = EarthMJ2000Eq;

GMAT DefaultOrbitView.DrawObject = [ true true ];

GMAT DefaultOrbitView.DataCollectFrequency = 1;

GMAT DefaultOrbitView.UpdatePlotFrequency = 50;

GMAT DefaultOrbitView.NumPointsToRedraw = 0;

GMAT DefaultOrbitView.ShowPlot = true;

GMAT DefaultOrbitView.MaxPlotPoints = 20000;

GMAT DefaultOrbitView.ShowLabels = true;

GMAT DefaultOrbitView.ViewPointReference = Earth;

GMAT DefaultOrbitView.ViewPointVector = [ 30000 0 0 ];

GMAT DefaultOrbitView.ViewDirection = Earth;

GMAT DefaultOrbitView.ViewScaleFactor = 1;

GMAT DefaultOrbitView.ViewUpCoordinateSystem =

EarthMJ2000Eq;

GMAT DefaultOrbitView.ViewUpAxis = Z;

GMAT DefaultOrbitView.EclipticPlane = Off;

GMAT DefaultOrbitView.XYPlane = On;

GMAT DefaultOrbitView.WireFrame = Off;

GMAT DefaultOrbitView.Axes = On;

GMAT DefaultOrbitView.Grid = Off;

GMAT DefaultOrbitView.SunLine = Off;

GMAT DefaultOrbitView.UseInitialView = On;

GMAT DefaultOrbitView.StarCount = 7000;

GMAT DefaultOrbitView.EnableStars = On;

GMAT DefaultOrbitView.EnableConstellations = On;

Create GroundTrackPlot DefaultGroundTrackPlot;

GMAT DefaultGroundTrackPlot.SolverIterations = Current;

GMAT DefaultGroundTrackPlot.UpperLeft = [ 0 0.1875 ];

GMAT DefaultGroundTrackPlot.Size = [

0.1726263871763255 0.1898148148148148 ];

GMAT DefaultGroundTrackPlot.RelativeZOrder = 233;

GMAT DefaultGroundTrackPlot.Maximized = false;

GMAT DefaultGroundTrackPlot.Add = {Tether};

GMAT DefaultGroundTrackPlot.DataCollectFrequency = 1;

GMAT DefaultGroundTrackPlot.UpdatePlotFrequency = 50;

GMAT DefaultGroundTrackPlot.NumPointsToRedraw = 0;

GMAT DefaultGroundTrackPlot.ShowPlot = true;

GMAT DefaultGroundTrackPlot.MaxPlotPoints = 20000;

GMAT DefaultGroundTrackPlot.CentralBody = Earth;

GMAT DefaultGroundTrackPlot.TextureMap = 'ModifiedBlueMarble.jpg';

Create XYPlot XYPlot1;

GMAT XYPlot1.SolverIterations = Current;

GMAT XYPlot1.UpperLeft = [ 0.3199753390875462

0.2476851851851852 ];

GMAT XYPlot1.Size = [ 0.499383477188656 0.6643518518518519 ];

GMAT XYPlot1.RelativeZOrder = 225;

GMAT XYPlot1.Maximized = false;

GMAT XYPlot1.XVariable = Tether.ElapsedDays;

GMAT XYPlot1.YVariables = {Tether.EarthMJ2000Eq.RAAN};

GMAT XYPlot1.ShowGrid = true;

GMAT XYPlot1.ShowPlot = true;

%----------------------------------------

%---------- Mission Sequence

%----------------------------------------

BeginMissionSequence;

Propagate TetherLEOprop(Tether) {Tether.ElapsedDays = 2};

Gmat output: Right ascension of Asc. Node over time

348

350

352

354

356

358

360

362

0.0 0.5 1.0 1.5 2.0 2.5R

igh

t A

sce

nsio

n o

f A

sce

nd

ing

No

de

(°

)Time (days)

Right Ascension ofAscending Node (18°)

Linear (RightAscension ofAscending Node (18°))

For 28 degrees inclination we get a

precession rate of -5.3°/days as well

Backup: References

[1] Moon Orbital Parameters

https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html

[2] Earth Magnetic Field Model:

Journal Article: M.J. Mueterthies and J.M. Longuski,“Modeling and Analysis of the Electrodynamic

Tether” AIAA/AAS Astrodynamics Specialist Conference, August 2012.

[3] Lorentz Force

https://www.britannica.com/science/Lorentz-force

[4] Nodal Precession

Book: Charles D. Brown, « Elements of Spacecraft Design », AIAA Education Series, january 2002,

page 89

https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html

https://www.britannica.com/science/Lorentz-force

Documents

Section III Presentation - Purdue University