Section II PresentationsJanuary 30, 2020

Michael LagrangeJanuary 30, 2020

Assistant Project Manager,Road to PDR, Key Events, Looking Ahead

PDR Project State, Task Tracking

Task List

Task Description System Deadline

Responsible

Engineer Status Dependencies

Key Events Risk Analysis

version 1.0, Initial Key

events list and formatting APM 2/1/2020 Michael Lagrange In Progress

Event Risk Research, Mission

Completion Success Analysis,

Crew Loss Analysis

February 27 : PDR

• Expectations are needed for project design maturity at PDR so people can work backwards from

that point

• Road to PDR list of PDR deliverables in each vehicles master list, separated by sub-group

Road to PDR

Key Events – Risk Analysis 1.0

Taxi is supplied from Martian stockpiles

Crew and cargo secured, system checkout

Mass driver is activated craft begins to accelerate

Taxi travels length of mass driver successfully

Taxi reaches required ΔV

Taxi exits mass driver

Taxi exits Martian atmosphere

Excerpt from Mars to Phobos mission

Current Missions with Key Events:

• Leo to Luna

• Luna to Cycler

• Cycler to Mars

• Mars to Phobos

• Phobos to Cycler

• Cycler to Luna

• Cycler to Leo

Future Additions:

• Greater granularity as design

progresses

• Begin research into failure

percentages of events

Juliann MahonJanuary 30, 2020

Discipline: CAD TeamVehicle and System Group: Tether Sling on

Phobos

Designs

• Electromagnetic attachment of the tether and the

taxi (left)

• Magnet and counterweight for the tether.

Visualization of Process

Dylan Pranger January 30th, 2020

Discipline: CADGroup and System: Mass Driver

Mass Driver Design

Requirements:

• Launch the Taxi Vehicle to the Cycler

Assumptions/Constraints:

• Acc. Can’t exceed 5 g’s

• Length of driver not constrained

Need to Determine:

• Taxi Size

• Power Requirements/Sizing

• EM Spacing

EM Track

Loading Area/Control Room

Solar Array

Power Storage

Mass Driver Design

Going Forward:

• Update for Taxi sizing

• EM Spacing

• Track Length/”Bucket Design”

• Update Power System Sizing

William SandersJanuary 30, 2020

Discipline: CADVehicle System: Taxi

Preliminary Design

• Three Taxis, each with a passenger cabin and cargo hold

• Taxi meant to doc with the tether, launch from the mass driver, and land

• Will land vertically

Other Considerations

• Each Taxi holds up to 24 passengers

• Life support will be located below passengers’ feet

• Bathrooms and food prep/storage located in the rear of the cabin

Future Modifications

• Work with tether/cycler team to design

compatible Docking Couple

• Refine Dimensions Especially Engine

• Look into fail-safe/abort systems

• Add attitude control thrusters (where

necessary)

Aaron EngstromJanuary 29, 2020

CAD - Cycler (Preliminary Design)

The Problem

We need a fundamental structure with parameters that fit within the bounds of our

requirements:At least .34 Gs most of the trip

At least 2,100 m^3 of space

Protection from the space environment

Food supply, life support, anti-fire, and air purification systems last years

And it would be great if:

Max usable space w/ min weight

Exactly 1 G most of the trip

Simplify the control problem

The Solution

Sizing Analysis

Overall weight less than 945 tons

Cabin length 114 m

Cabin internal cross section is a 16 m^2

square (with curvature) that rotates

Rigid tether length is at least 75 m

Docking station internal radius is 1 m

Wall thickness is .3 m

Storage section provides a .75 m

walkway w/ 2 m height

To be determined:Accurate M and V of each component

Communications placement (on tether)

Life support placement

BREAKResume at 2:10

Nick Oetting January 30, 2020

CommunicationsCommunication Satellites

Communications

The Problem:

Require 24/7 line of sight from Earth to Moon, Mars, Phobos, and cycler vehicles

→ Communication constellation involving 8 satellites around Earth, the sun, and

Mars.

Two-way HD communication → Mix of RF and laser communication, capable of

data rates up to 1 Gbps.

Communications Architecture

Laser

communication

to L4 and L5

Earth & Moon / Mars & Phobos Sun Centered View

L5

L4

Eric SmithJanuary 30, 2020

CommunicationsCommunication Satellites

21

Optical System Link Budget

Problem: Communications Link must have sufficient power to support required

data rate.

Solution: A link budget analysis allows us to test if a communications link will

work and how much extra power is available.

22

Optical System Link BudgetParameter GEO <=> L4/L5 L4/L5 <=> Mars

Transmitted Power (PT ) 13.010 dBW 13.010 dBW

Transmit Gain (GT) 120.116 dB 130.219 dB

Free Space Loss (LFS) -361.676 dB -372.568 dB

Receive Gain (GR) 120.116 dB 130.219 dB

Other Losses -5.907 dB -5.907 dB

Required Power at

Receiver (PR)

-118.658 dBW -108.555 dBW

Link Margin 4.3168 dB 3.529 dB

23

Jacob LeetJanuary 30th, 2020

ControlsSimulation Development

Simulation of All Trajectories

Problem:

Models of Cycler/Taxi/Satellite trajectories needs to be developed for the

following reasons:

- Determine estimates for dV for trajectory correction due to external forces

(radiation, electromagnetic, etc.)

- Verify Mission Design dV estimates

Process:

- Create accurate model of

sun-planet-satellite system

- Introduce and overlay satellite trajectory

- Develop controller to maintain

satellite trajectory

MATLAB/SIMULINK Progress

Process:User enters in desired coordinates and velocities, and then

the program will numerically estimate each new position by

hour for about 1.5 years.

Polar coordinates instead of Cartesian will be implemented.

https://ssd.jpl.nasa.gov/horizons.cgi#top

Yash MishraJanuary 30th, 2020

Controls: SensorsRendezvous Maneuvers and Docking on the

Cycler

The Problem

Requirements:

• Taxi velocity control to avoid collision into Cycler

• Sense Cycler geometry to dock successfully

• Minimize fuel usage

• Minimize mass, power requirements of sensor while being effective

Assumptions:

• No space debris

• Cycler is of comparable size to the ISS

• No unexpected course adjustments required

The Solution: TriDAR Sensors

Limitations:

• Yet to account for unexpected external bodies

• Needs to pair with velocity/attitude control sensors for successful Rendezvous

Max Operating

Range

74 km

Imaging Frequency 5 Hz

Accuracy 1 cm/deg

Power 9 W

Mass 1.4 kg

Volume Asked Neptec

Pros Cons

Target-less More power

consumed due

to imaging

(assumption)

More

Information,

Less Data

Kevin HuangMonth Day, 2020

Human Factors - Artificial Gravity & Human Comfort in dealing with multiple G’s

Problem: How many G’s can a ‘normal’ human take?-

• Accelerating at more than 1G/sec can result in G-LOC; what was

recommended was 0.1G/sec [1], but it may be possible to go faster.

• Hard to find info how multiple G’s affect people, so used flight pilots as basis.

• Assumed amount of G’s linearly scaled with time before one blackout.

6Gs, 30 seconds info from [2].

Gs Time

before

blackout

1G 180 sec

2G 90 sec

3Gs 60

4Gs 45

5Gs 36

6Gs 30

Problem: Which Artificial Gravity System to use?

• Symptoms of microgravity

• Little is known on effects of 0-1Gs on humans; probably best to use 1G

Pros-Fire Baton [3] Pros-Stanford Toros

No rotating joints, etc. Design is simple

thrusters that spin/despin the

spacecraft can also be used for thrust

vectoring, BUT can also mess with AG-

generation

Simplest way to solve living/storage

space problem

lots of info on it already, BUT, NASA

design was for a small crew

More info in Backup Slides

BREAKResume at 2:44

Walter ManuelJanuary 30, 2020

Discipline: Human FactorsVehicles/Systems: Cycler

Topic: Radiation Shielding

34

Problem: Protecting Crew from Radiation

• Space radiation is a serious threat to extended human space exploration [1][2].

• Galactic Cosmic Rays• Low flux ionized particles from outside solar system, relatively steady rate

• Solar Particle Events• Large amount of particles discharged from sun, harder to predict

• Some long-term effects of radiation exposure:• Cataracts

• Increased risk of cancer

• Sterility

• Cardiovascular disease

• Current Exposure Limits [3]: • Average dose for a person = 0.0036 Sv/year.

• International Standards for those working with radioactive material = 0.05 Sv/year

• NASA limit for radiation exposure in low-Earth orbit = 0.50 Sv/year

35

Solution: Potential Methods of Radiation Shielding

● “Storm Shelter” – Can be formed by

reorganizing supplies or by having a

designated area [5]

● Protective vests [6]

● Early warning and detection systems [7]

Areal Density [0 g/cm2]

10 20 30

Dose Equivalent [mSv/year]

Liquid

Hydrogen

275 200 180

Boron

Nitride

Nanotube

600 440 360

Polyethlene 640 480 440

Water 660 500 450

Aluminum 875 730 620

Shielding Options for GCR [4]

Shielding Options for SPE

Notes on Materials

● Liquid Hydrogen – ideal, control condition.

● BNNT – Currently still a very new technology.

● Polyethlene – Concerns with strength, heat

resistance.

● Water – Can fluctuate based on crew needs.

● Aluminum – Commonly used for spacecraft.

36

Jordan MayerJanuary 30, 2020

Mission DesignCommunication Satellites

The Problem: Interplanetary Relay Visibility

Current Proposal: Two interplanetary relays at L4 and L5 Lagrange points (Sun-

Earth or Sun-Mars)

• Need to Determine:

• Can Sun block both relays?

• How often are both relays visible?

• Assumptions/Constraints:

• Assume coplanar orbits

• Only consider Sun blocking

• Define ‘blocked by Sun’ as ‘within 3 degrees of Sun from either Earth or Mars’

• Simulate for 15 years; geometry repeats after this (Byrnes, Longuski, & Aldrin)

• Ignore cyclers (for now)

The Solution: Sun-Mars Lagrange Points Preferable

• Conclusions

• At least one always visible

• Sun-Mars Lagrange points give more

consistent two-sat visibility

• Next Steps

• Assess distances

• Consider using cyclers as relays

• Consider placing relays at both pairs of

Lagrange points

Both relays visible (from

both planets) (% of time):

• Sun-Mars: 94.46%

• Sun-Earth: 89.78%

Colin MillerJanuary 30, 2020

Mission Design Group: Communication Satellites (Placement of satellites, worst case power scenarios, stability analysis research)

The Problem: Use Communication Relays to Talk to All Vehicles and Stations in MissionRequirements:

• At least two paths of communications with all

systems

• Constant communication available to all

stations and vehicles (including planets

and moons)

Assumptions:

• Worst case eclipse lengths at stationary orbits

• Perfectly stable orbits (for stationary orbits)

To-Do:

• Locations of all comm sats

• Major orbital perturbations for all comm sats

• Time in eclipse for geostationary and

areostationary

Results

Worst Case Eclipse Lengths of Stationary Orbits:

Body Semi-Major

Axis (km)

Orbital

Period

(s) [hr]

Eclipse

Length

(s) [hr]

Earth 4.2164×104 8.6164×104

[23.9345][1]

4.1686×103

[1.1579]

Mars 2.0428×104 8.8642×104

[24.6229][2]

4.7129×103

[1.3091]

Orbital Perturbations of Stationary Orbits:

• Mars:• Maximum change in longitude of 0.08

deg/day2 depending on target longitude[3]

• Perturbations 20 times stronger than that

of Earth from harmonics and SRP

• Earth:• Maximum change in longitude of 0.002

deg/day2 depending on target longitude[4]

• Moon interactions were accounted for in

this analysis

What’s Next

● Verify research done on orbital stability analysis

● Perform analysis to determine reliability of cycler vehicle as communications relay

● Verify Mars L4/L5 over Earth L4/L5

Grace Ness January 30, 2020

Mission Design - Phobos Tether Sling: End Tip Velocity, Tether Length, & Spin-up Time

Phobos Tether Sling Questions

★ What are the most important design

parameters?

○ How does the velocity affect the

tether length?

■ What length is feasible?

■ Will the length need to

adjust?

○ How does the spin-up time affect

the power required?

■ How much power are we

capable of supplying?

■ How many days can we

allow for spin-up?

★ What is the maximum acceleration

allowed?

○ How many g’s are acceptable for

humans?

■ For how long?

Assumptions:

• Tapered tether

• Taxi Mass: 11.2 Mg

• Power per Area on Phobos: 26 W/m^2

Power Required:• Max = 11.92 GW

• Min = 0.0437 GW

Mass Ratio:• Max = 476.11

• Min = 3.489

Note: The Mass of Phobos is 1.0603E+13 Mg

Results

Dean Lontoc January 30, 2020

Power and ThermalTaxi Vehicle Power System

Taxi Vehicle Power Requirements

Total

Power:

22kW

Human

Factors[1]:

12 kW

Controls[2]:

< 1 kW

Communications[3]:

< 1 kW

Payload:

7 kW

Miscellaneous[4]:

2 kW

[1] AAE 450: Human Factors: Sarah Culp

[2] AAE 450: Controls: Brady Walter

[3] AAE 450: Communications: Adam Wooten

[4] AAE 450: Propulsion: Carly Kren

Taxi Vehicle Power SolutionProton Exchange Membrane Fuel Cell System

Mass (Mg) Power (kW) Volume (m^3)

1.0876 25 2.748

Component Mass (Mg) Volume

(m^3)

Hydrogen 0.3061 1.771

Oxygen 0.7665 0.736

Fuel Cells 0.0150 0.241

PEMFC

ModulesTaxi

PowerHydrogen

and

Oxygen

Tanks

Hydrogen and Oxygen

Water

Tanks

Water

5 PEMFC Modules,

each generating 5 kW

Mission lasting 14 days

BREAKResume at 3:20

Jacob Nunez-KearnyJanuary 30, 2020

Power & ThermalCycler: Power Generation & Storage

Cycler Power

Problem: Provide power to all systems on-board the cycler

Requirements:

• Cycler systems must have electrical power throughout a cycle

Assumptions:

• Initial sizing scaled from ISS

• Does not include additional propulsion requirements

Objectives:

• Determine metrics for spacecraft power generation and storage

• Initially size cycler arrays and batteries from existing systems

• Research low TRL power systems

Cycler Power Sizing Estimate

Solution:• Important metrics: W/kg, Wh/kg

• Scaled from ISS• Solar Panel Power: 2.893 GW

• Solar Panel Mass: 36.17 Mg

• Battery Capacity: 6.720 kA-hr

• Battery Mass: 8.064 Mg

• Total mass decreases with TRL

Next Steps:• Need backup power requirement and TRL designation

• Perform solar irradiance calculation during flight to size solar arrays

• Determine power draw of critical systems to size batteries

0

1

2

3

4

5

6

7

8

9

0

5

10

15

20

25

30

35

40

9 7 6 3

Batteries M

ass (

Mg)

Sola

r A

rray

Mass (

Mg)

Technology Readiness Level (TRL)

Cycler Power Mass Vs TRL

Solar Panels Batteries

Carly KrenJanuary 30, 2020

Propulsion TeamTaxi - Reaction Control Systems (RCS)

Slide: 1 of 8

The Problem: Determine the RCS systems to be utilized on taxi

Requirements:

• Rendezvous of taxi with cycler

• Orbit trajectory transfer (from cycler to Phobos/Mars orbit)

• Attitude adjustments • from LEO to Moon/Mars, from Moon to Mars/cycler,

from Mars to Phobos/cycler, from Phobos to cycler/Earth,

from cycler to Mars/Phobos

• Reusable

CG CG Example of attitude control on taxi:

= Thrust vector

= Rotation about axis

= Center of gravityCG

Slide: 2 of 8

The Solution: Orbital Maneuvering System & RCS

He N

Fuel Oxid-

izer

P&ID

He

FuelOxid-

izer

He

P&ID

Fuel Monomethyl Hydrazine

Oxidizer Dinitrogen Tetroxide

Wet Masstot* 6.37 Mg

Volumetank[1]

(propellant)

2.55 m3 (each)

Volumetank[1]

(He)

0.482 m3

Volumetank[1]

(N)

9.83E-4 m3

Thrust [3] 26700 N

Fuel Monomethyl Hydrazine

Oxidizer Dinitrogen Tetroxide

Wet Masstot*

(primary)

1.29 Mg (f), 1.29 Mg (a)

Wet Masstot*

(vernier)

1.27 Mg (f), 1.27 Mg (a)

Volumetank[2]

(propellant)

0.509 m3 (each)

Volumetank[2]

(He)

0.0497 m3 (each)

Thrust [4][5] 3870 N (p), 129 N (v)

Key:

(f) = forward

(a) = aft

(p) = primary

(v) = vernier

OMS RCS

Adapted from Shuttle OrbiterAdapted from Shuttle Orbiter

[1] Dumoulin, J., “Orbital Maneuvering System”, NSTS Shuttle Reference Manual, published online 31 Aug. 2000.

[2] Dumoulin, J., “Reaction Control Systems”, NSTS Shuttle Reference Manual, published online 31 Aug. 2000.

[3] Wade, M. “OME”, Astronautix.

[4] “LR-101 Vernier Engine”, Heroicrelics.

[5] “About: 11D428”, DBpedia.

* See Backup Slides pgs. 4-8 for calculations/codes

Slide: 3 of 8

For each OMS engine For each RCS engine

Griffin PfaffJanuary 30, 2020

Propulsion – CyclerMain Propulsion System

The Problem

• Thrust to weight ratio of cycler is .01 N/Mg

• Cannot add outrageous weight

• Long duration operation

• Assume one month of continual use before

refueling

• Accurately complete trajectory requirements

Solution

X3 Nested Hall

Thruster:• 5.4 N per thruster

• 100 kW

• Xenon propellant

• Will use 10 thrusters per

cycler

• Developed by University

of Michigan, NASA and

the Air Force

Figure based on Hall, Ref. [1].

Mass

(Mg)

Power

(MW)

Volume

(m^3)

Force (N)

5029 1 1708 54

Arch PleumpanyaJanuary 29, 2020

Propulsion TeamMass Driver

Mass Driver Fundamentals

Mass driver fundamentals:

- Coilgun

- Convert electric to kinetic energy using electromagnetic coils

- Coil switching is crucial at hypervelocities

- Efficiency can reach 90% [1]

Parameters to consider:

- Track length

- Acceleration

- Power consumption

- System mass

- Charge time per launch

[1] Davis, E., & Warp Drive Metrics LAS Vegas Nv. (2004). Advanced Propulsion Study.

Determine basic parameters

- Kinematic equations

- 94.34 Mg taxi vehicle

- Assuming 10% of vehicle mass for

suspension system

- Tentative parameters on Mars- 3g’s over 2.8 minutes

- 424 km track

- 3.05 MN magnetic force required

- Tentative parameters on the Moon- 2g’s over 2.0 minutes

- 144 km track

- 2.04 MN magnetic force required

Steven Lach January 30, 2020

StructuresTether Sling, ED Tether, and Mass Drivers

1

The Problem: Determine material and overall specifications for tethers

Requirements:

• Launch all taxis directly to all celestial

bodies

• Retain strength properties in a space

environment

Assumptions:

• Calculations are based on given

parameters

Goals:

• Set tether materials

• Determine length and mass of tethers

Given Parameters

Structure Tether Sling ED Tether

Max Delta V

(km/s)

4.314544 5

Taxi Mass (kg) 137,363.4 137,363.4

Max

Acceleration

6G 6G

2

Solution

Tether Sling on Phobos:

• Material: Dyneema fiber

• Length: 316.264 km

• Mass: 21,126 Mg

Electrodynamic Tether:

• Insulating Material:

Dyneema fiber with an

atomic oxygen resistant

coating

• Length: 424.737 km

• Mass: 90,580.7 Mg*

Tether Sling with Sunlight Exposure (8 Month Taxi)

Material Dyneema Zylon Kevlar Hexcel IM7

Effective

UTS (GPa)

3.325 2.03 2.044 4.82

Density

(kg/m3)

9701 1,5602 1,4502 1,5502

Tether

Mass (Mg)

21,126 17,206,000 7,668,500 32,851

Based on table by Jokic & Longuski2

ED Tether

Comparison

Cylcer/Mars Luna

Delta V (km/s) 5 3.06

Tether Length (km) 424.737 159.083

Tether Mass (Mg)* 90580.7 2163.4

*Not including conducting material mass

3

Nicki (Anna) LiuJanuary 30th, 2020

StructuresTaxi Vehicle - Layout / Moments of Inertia

Slide 1 of 3

Problem: Initial Sizing of the Vehicle

Requirements:

Human Factors:Customer: Mission Design:

• 70 passengers

• Reusable

• Able to Provide

Basic Human Needs

• Food and Water

for Cycler

Propulsion:

• Withstand Flight

Acceleration

• Withstand

Structural Loads

• Space for

Propellant

• Minimize Mass• Minimize Mass

• Useable with Tether

and Mass Driver

• Attach Point with

Tether• Safety Options

Slide 2 of 3

Vehicle Design

ComponentMass

(Mg)

Volume

(m3)

Available

Volume

(m3)

Needed

Support

Structure22.6 N/A N/A

Passenger

Bay [1] [2]

10.5

so far

78 (not all

useable)53 so far

Cargo Bay [1]

(6 months)

12.3

so far78

14.2 so

far

Prop [3] 45 234 19.8

Total 90.3 390 87

Material: Aluminum 2024-T4

Thickness: 2 cm*

[1] AAE 450: Human Factors: Emily Schott, Kait Hauber, Sarah Culp

[2] AAE 450: Power and Thermal: Dean Lontoc

[3] AAE 450: Propulsion: Carly Kren

Moments of Inertia

(Mg * m2)*

Principal Moments

of Inertia (Mg * m2)*

Ixx = 4.18 * 103 Px = 106.4

Iyy = 4.1811 * 103 Py = 1433

Izz = 1.0645 * 102 Pz = 1434

[4]

[4] “Boeing 777-300ER Seat map,” United Airlines, Inc. Available:

https://www.united.com/ual/en/us/fly/travel/inflight/aircraft/777-300.html.

*See Backup Slides for calculations

Slide 3 of 3

Backup SlidesJanuary 30, 2020

Backup Slides Juliann Mahon- Sketches

• Sketch for the tether

• Sketch for the approximate motion of the taxi, magnet,

and counterweight for the time when it attaches to

when it detaches

Backup Slides Juliann Mahon- Code Design

• Plotted out the motion of the taxi and

sling before coding.

• Points for each part

Backup Slide Juliann Mahon- Code

1. %% AAE 450 tether sling

2. clc

3. clear

4. n = 24;

5. m = 10;

6. tx= ones(1,n*2); %length 48

7. tx2 = linspace(-3,0,n*2); %length 48

8. Z = zeros(1,n);

9.10. X(1) = 1;

11. Y(1) = 0;

12. for f = 2:n*4

13. X(f) = cos(f*pi/n); %96

14. Y(f) = sin(f*pi/n); %96

15. end

16. magnet = [repmat(X,1,3);repmat(Y,1,3)]; % each repmatis 96 long

17. counterweight = [-repmat(X,1,3);-repmat(Y,1,3)]; %each is 96 long

18. taxi = [repmat(tx,1,1),repmat(X,1,1),X(1:2.5*n),-

linspace(0,2,3.5*n);repmat(tx2,1,1),

repmat(Y,1,1),Y(1:2.5*n),ones(1,3.5*n)];

19. tethercenter= [repmat(Z,n*m/2);repmat(Z,n*m/2)];

20.21. figure(1);

22. a4 = animatedline('Color','g','marker','o');

23. a5 = animatedline('Color','r','marker','x');

24. a6 = animatedline('Color','b','marker','*');

25. a7 = animatedline('Color','k','marker','+');

26. a8 = animatedline('Color','k');

27. mm = [-2 2];

28. count =1;

29. axis = [-2,2];

30. j=1;

31. for j = 1:length(magnet)

32. if j ~= 1

33. delete(c(j-count))

34. delete(p)

35. end

36. diffx=[magnet(1,j), counterweight(1,j)];

37. diffy= [magnet(2,j), counterweight(2,j)];

38. addpoints(a4,magnet(1,j),magnet(2,j));

39. if j <61

40. addpoints(a5,(j/60)*counterweight(1,j),(j/60)*counterweight(2,j));

41. else

42. addpoints(a5,counterweight(1,j),counterweight(2,j));

43. end

44. addpoints(a6,taxi(1,j),taxi(2,j));

45. addpoints(a7,tethercenter(1,j),tethercenter(2,j));

46. hold on

47. p = plot(diffx,diffy);

48. c(j) = plot(axis,mm,'Color',[0.35 0.35 0.35]);

49. drawnow

50. if j ~= linspace(0,n*m*m*2,(n*m*10))

51. if j == length(magnet)

52. return

53. end

54. clearpoints(a4);

55. clearpoints(a5);

56. clearpoints(a6);

57. clearpoints(a7);

58. delete(p);

59. end

60. legend('magnet','counterweight', 'taxi', 'tether center', 'tether cord')

61. end

William Sanders-Passenger Cabin Dimensions

Nick Oetting - Free Space Loss

System Distance Frequency FSPL

Ground Station

to GEO

35786 km [2] 30 GHz [3]

(K Band)

213.059 dB

GEO to L4/L5 1.496e+8 km [2] 193.545 THz [4] 361.676 dB

L4/L5 to Mars 5.242e+8 km [2]

(WORST CASE)

193.545 THz [4] 372.567 dB

GEO to Moon 348614 km [2] 30 GHz [3] 212.831 dB

Mars to Phobos 9378 km [2] 30 GHz [3] 181.426 dB

Nick Oetting -Backup Slides

The following equation is used to calculate free space loss across a distance with a certain frequency. It

was converted to decibels as that is more useful to the communications team.

Nick Oetting References

[1] - https://books.google.com/books?id=L-

ilDwAAQBAJ&pg=PT31&dq=%22free+space%22+%22path+loss%22#v=onepage&q=%22free%20spac

e%22%20%22path%20loss%22&f=false

[2] - https://nssdc.gsfc.nasa.gov/planetary/factsheet/

[3] - https://swfound.org/media/108538/swf_rfi_fact_sheet_2013.pdf

[4] - https://www.nasa.gov/sites/default/files/atoms/files/tglavich_dsoc.pdf

Eric Smith BACKUP: Required SNR

• 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) 0.1 nm = 2.998E+18 Hz

S/N 2.312E-10

76

Eric Smith BACKUP: Noise from Solar Irradiance

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

• Bandwidth = 0.1 nm

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

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

Telescope Diameter Noise Power, N

160 cm 0.060 W

50 cm 0.006 W

77

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”

Eric Smith BACKUP: Other LossesParameter 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”.

78

Eric Smith BACKUP: Code GEO_to_L4L5.m

%% Calculate the Link Budget for Optical Link between GEO Satellites

and L4/L5 Satellites

lambda = 1550e-9;% wavelength in m

d = 1.496e11; %distance between reciever and tranmitter in m

B_nm = 0.1; %Bandwidth in nm

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

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

Pt_Watts = 20;

Dt = .5; %transmit aperature diameter in m

Dr = .5; %recive aperature diameter in m

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

79

Eric Smith BACKUP: Code L4L5_to_Mars.m

%% Calculate the Link Budget for Optical Link between L4/L5 Satellites

and Mars

lambda = 1550e-9;% wavelength in m

d = 5.242e11; %distance between reciever and tranmitter in m

B_nm = 0.1; %Bandwidth in nm

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

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

Pt_Watts = 20;

Dt = 1.6; %transmit aperature diameter in m

Dr = 1.6; %recive aperature diameter in m

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

80

Eric Smith 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

81

Eric Smith 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

82

Eric Smith 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.

83

Yash Mishra Backup

January 30th, 2020

Controls: SensorsRendezvous Maneuvers and Docking on the

Cycler

Backup Slides

Other sensing techniques considered:

TCS – Trajectory Control System

SVS – Space Vision System

Other proximity sensors like LIDAR

Bibliography

• Ruel, S., Luu, T., & Berube, A. (2012). Space shuttle testing of the TriDAR 3D rendezvous and

docking sensor. Journal of Field robotics, 29(4), 535-553.

• English, C., Zhu, S., Smith, C., Ruel, S., & Christie, I. (2005, September). Tridar: A hybrid sensor for

exploiting the complimentary nature of triangulation and LIDAR technologies. In Proceedings of the

8th International Symposium on Artificial Intelligence, Robotics and Automation in Space (Vol. 1).

• Yaskevich, A. (2014). Real time math simulation of contact interaction during spacecraft docking and

berthing. J. Mech. Eng. Autom., 4, 1-15.

• Miele, A., Weeks, M. W., & Ciarcia, M. (2007). Optimal trajectories for spacecraft

rendezvous. Journal of optimization theory and applications, 132(3), 353-376.

Kevin HuangMonth Day, 2020

Backup SlidesHuman Factors - Artificial Gravity & Human

Comfort in dealing with multiple G’s

Sources[1] Wrick, B., and Brown, J.R., “Acceleration in Aviation: G-Force,” faa.gov

Available:

https://www.faa.gov/pilots/safety/pilotsafetybrochures/media/acceleration.pdf.

[2] Park, J. S., Choi, J., Kim, J. W., Jeon, S. Y., and Kang, S., “Effects of the

optimal flexor/extensor ratio on G-tolerance,” Journal of physical therapy science

Available: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5080197/.

[3] Joosten, B. Kent, “Artificial Gravity for Human Exploration Missions,”

history.nasa.gov Available: https://history.nasa.gov/DPT/Technology Priorities

Recommendations/Artificial Gravity Status and Options NExT Jul_02.pdf.

[4] Burton, R. R., Alexander, W. C., Davis, J. G., Crisman, R. P., Grissett, J. D.,

and Brady, J. A., “Physical Fitness Program To Enhance Aircrew G Tolerance,”

apps.dtic.mil Available: https://apps.dtic.mil/dtic/tr/fulltext/u2/a204689.pdf.

Sources (cont.)[5] Clément, G. R., Bukley, A. P., and Paloski, W. H., “Artificial gravity as a

countermeasure for mitigating physiological deconditioning during long-duration

space missions,” Frontiers in systems neuroscience Available:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4470275/.

Optimal Conditions for Experiencing Multiple G’s [4]

The following is a non-exhaustive list.

• Non-smoker

• Has not recently consumed alcohol

• Well-rested

• Well-hydrated

• On a healthy diet

• Preferably not on any medication, particularly self-medication

• Not afflicted with an illness

• Among others

Required dimensions of vehicle assuming 1G

Description Radius (m) Angular

Velocity

rpm

min radius 50.00 0.443 rad/s 4.228

1 rpm 893.7 0.105 rad/s 1.000

2 rpm 223.4 0.209 rad/s 2.000

3 rpm 99.29 0.314 rad/s 3.000

4 rpm 55.85 0.419 rad/s 4.000

Required dimensions of vehicle assuming 0.38G

Notes:

• rpm of 2.606 is infeasible as the required radius of the vehicle would then fall

under the previously decided minimum radius of the vehicle so as to prevent

psychological effects from differences in G’s between the head and legs

Description Radius (m) Angular

Velocity

rpm

min radius 50 0.2729 rad/s 2.606

1 rpm 339.6 0.1047 rad/s 1.000

2 rpm 84.90 0.2094 rad/s 2.000

3 rpm 37.73 0.3142 rad/s 3.000

4 rpm 21.22 0.4189 rad/s 4.000

Equations Used

Variables:

r: radius of spacecraft

G’s: amount of G’s experienced by spacecraft and its passengers

rpm: amount of full rotations the spacecraft does every minute

v: tangential velocity

ω: angular velocity

Coriolis Effect [5]

“the severity of side effects from Coriolis forces during head movements is gravitational

force-dependent, raising the possibility that an artificial gravity level less than 1 G would

reduce the motion sickness associated with a given rotation rate” (Lackner and DiZio,

2000)

The Coriolis Effect can be diminished by increasing the radius of the spacecraft

Optimal RPM of Spacecraft

Varying sources say that the max rpm for a spacecraft before dizziness occurs

should be somewhere between 6-10, so a conservative estimate would be 6rpm

at most. It should be noted that ample time must be given to passengers/civilians

before they are able to acclimate to high rpm speeds; in other words, the ramp up

to the final rpm should be done as slowly as possible.

Walter Manuel – Backup SlideJanuary 30, 2020

Discipline: Human FactorsVehicles/Systems: Cycler

Topic: Radiation Shielding

96

References

• [1]https://www.nasa.gov/feature/goddard/2019/how-nasa-protects-astronauts-from-space-

radiation-at-moon-mars-solar-cosmic-rays

• [2]https://www.nasa.gov/feature/goddard/real-martians-how-to-protect-astronauts-from-space-

radiation-on-mars

• [3]https://www.nasa.gov/pdf/284273main_Radiation_HS_Mod1.pdf

• [4]https://www.nasa.gov/sites/default/files/atoms/files/niac_2011_phasei_thibeault_radiationshi

eldingmaterials_tagged.pdf

• [5]https://www.popsci.com/this-is-how-orion-astronauts-might-protect-themselves-from-

radiation-storms/

• [6]https://www.lockheedmartin.com/en-us/news/features/2016/stemrad-vest-space.html

• [7]https://three.jsc.nasa.gov/articles/Shielding81109.pdf

97

Jordan MayerJanuary 30, 2020

Mission DesignCommunication Satellites

Backup Slides

Appendix A: References

1. Byrnes, D. V., Longuski, J. M., & Aldrin, B. (1993). Cycler Orbit

Between Earth and Mars. Journal of Spacecraft and Rockets, 30(3),

334-336.

2. Simon, J., Bretagnon, P., Chapront, J., Chapront-Touze, M.,

Francou, G., & Laskar, J. (1994). Numerical expressions for

precession formulae and mean elements for the Moon and the

planets. Astronomy and Astrophysics, 282, 663-683.

NOTE: Bretagnon et al. not referenced in slides, but used to obtain Earth

and Mars longitude of ascending node and longitude of perihelion (used

in MATLAB code to obtain results)

Appendix B: NASA JPL Horizons Data

The following data was obtained via the NASA JPL HORIZONS Web-

Interface (https://ssd.jpl.nasa.gov/horizons.cgi#top) and was used to

determine important characteristics of Earth, Mars, and the Sun,

including initial mean anomaly values for orbit simulation. Input

parameters were as follows:

• Ephemeris type: ELEMENTS

• Target Body:

• Earth [Geocenter] [399]

• Mars [499]

• Center: Sun (body center) [500@10]

• Time Span: Start=2005-01-27, Stop=2005-01-28

• Table Settings: output units=KM-S; CSV format=YES

• Display/Output: plain text

Appendix B: NASA JPL Horizons Data*******************************************************************************

Revised: July 31, 2013 Earth 399

GEOPHYSICAL PROPERTIES (revised Aug 15, 2018):

Vol. Mean Radius (km) = 6371.01+-0.02 Mass x10^24 (kg)= 5.97219+-0.0006

Equ. radius, km = 6378.137 Mass layers:

Polar axis, km = 6356.752 Atmos = 5.1 x 10^18 kg

Flattening = 1/298.257223563 oceans = 1.4 x 10^21 kg

Density, g/cm^3 = 5.51 crust = 2.6 x 10^22 kg

J2 (IERS 2010) = 0.00108262545 mantle = 4.043 x 10^24 kg

g_p, m/s^2 (polar) = 9.8321863685 outer core = 1.835 x 10^24 kg

g_e, m/s^2 (equatorial) = 9.7803267715 inner core = 9.675 x 10^22 kg

g_o, m/s^2 = 9.82022 Fluid core rad = 3480 km

GM, km^3/s^2 = 398600.435436 Inner core rad = 1215 km

GM 1-sigma, km^3/s^2 = 0.0014 Escape velocity = 11.186 km/s

Rot. Rate (rad/s) = 0.00007292115 Surface area:

Mean sidereal day, hr = 23.9344695944 land = 1.48 x 10^8 km

Mean solar day 2000.0, s = 86400.002 sea = 3.62 x 10^8 km

Mean solar day 1820.0, s = 86400.0 Love no., k2 = 0.299

Moment of inertia = 0.3308 Atm. pressure = 1.0 bar

Mean temperature, K = 270 Volume, km^3 = 1.08321 x 10^12

Mean effect. IR temp, K = 255 Magnetic moment = 0.61 gauss Rp^3

Geometric albedo = 0.367 Vis. mag. V(1,0)= -3.86

Solar Constant (W/m^2) = 1367.6 (mean), 1414 (perihelion), 1322 (aphelion)

HELIOCENTRIC ORBIT CHARACTERISTICS:

Obliquity to orbit, deg = 23.4392911 Sidereal orb period = 1.0000174 y

Orbital speed, km/s = 29.79 Sidereal orb period = 365.25636 d

Mean daily motion, deg/d = 0.9856474 Hill's sphere radius = 234.9

*******************************************************************************

Appendix B: NASA JPL Horizons Data

*******************************************************************************

Ephemeris / WWW_USER Wed Jan 29 11:03:32 2020 Pasadena, USA / Horizons

*******************************************************************************

Target body name: Earth (399) {source: DE431mx}

Center body name: Sun (10) {source: DE431mx}

Center-site name: BODY CENTER

*******************************************************************************

Start time : A.D. 2005-Jan-27 00:00:00.0000 TDB

Stop time : A.D. 2005-Jan-28 00:00:00.0000 TDB

Step-size : 1440 minutes

*******************************************************************************

Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}

Center cylindric: 0.00000000,0.00000000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}

Center radii : 696000.0 x 696000.0 x 696000.0 k{Equator, meridian, pole}

Keplerian GM : 1.3271283864237474E+11 km^3/s^2

Output units : KM-S, deg, Julian Day Number (Tp)

Output type : GEOMETRIC osculating elements

Output format : 10

Reference frame : ICRF/J2000.0

Coordinate systm: Ecliptic and Mean Equinox of Reference Epoch

Appendix B: NASA JPL Horizons Data*******************************************************************************

JDTDB, Calendar Date (TDB), EC,

QR, IN, OM, W,

Tp, N, MA, TA,

A, AD, PR,

**************************************************************************************

**************************************************************************************

**************************************************************************************

********************************************************************************

$$SOE

2453397.500000000, A.D. 2005-Jan-27 00:00:00.0000, 1.601485446006504E-02,

1.470778413129797E+08, 1.525882844459133E-03, 1.525936412678601E+02,

3.087479127041030E+02, 2.453372217113541E+06, 1.142197077338493E-05,

2.495062571346842E+01, 2.573904212862790E+01, 1.494716073506118E+08,

1.518653733882438E+08, 3.151820356946273E+07,

2453398.500000000, A.D. 2005-Jan-28 00:00:00.0000, 1.611134192723532E-02,

1.470736727225537E+08, 1.856346178777592E-03, 1.479177191477421E+02,

3.132716955654213E+02, 2.453372069503432E+06, 1.142077633460141E-05,

2.608042663135691E+01, 2.690699854299472E+01, 1.494820288005360E+08,

1.518903848785183E+08, 3.152149989220187E+07,

$$EOE

**************************************************************************************

**************************************************************************************

**************************************************************************************

********************************************************************************

Appendix B: NASA JPL Horizons DataCoordinate system description:

Ecliptic and Mean Equinox of Reference Epoch

Reference epoch: J2000.0

XY-plane: plane of the Earth's orbit at the reference epoch

Note: obliquity of 84381.448 arcseconds wrt ICRF equator

(IAU76)

X-axis : out along ascending node of instantaneous plane of the Earth's

orbit and the Earth's mean equator at the reference epoch

Z-axis : perpendicular to the xy-plane in the directional (+ or -) sense

of Earth's north pole at the reference epoch.

Symbol meaning:

JDTDB Julian Day Number, Barycentric Dynamical Time

EC Eccentricity, e

QR Periapsis distance, q (km)

IN Inclination w.r.t XY-plane, i (degrees)

OM Longitude of Ascending Node, OMEGA, (degrees)

W Argument of Perifocus, w (degrees)

Tp Time of periapsis (Julian Day Number)

N Mean motion, n (degrees/sec)

Appendix B: NASA JPL Horizons Data

MA Mean anomaly, M (degrees)

TA True anomaly, nu (degrees)

A Semi-major axis, a (km)

AD Apoapsis distance (km)

PR Sidereal orbit period (sec)

Geometric states/elements have no aberrations applied.

Computations by ...

Solar System Dynamics Group, Horizons On-Line Ephemeris System

4800 Oak Grove Drive, Jet Propulsion Laboratory

Pasadena, CA 91109 USA

Information: http://ssd.jpl.nasa.gov/

Connect : telnet://ssd.jpl.nasa.gov:6775 (via browser)

http://ssd.jpl.nasa.gov/?horizons

telnet ssd.jpl.nasa.gov 6775 (via command-line)

Author : Jon.D.Giorgini@jpl.nasa.gov

******************************************************************************

*

Appendix B: NASA JPL Horizons Data*******************************************************************************

Revised: June 21, 2016 Mars 499 / 4

PHYSICAL DATA (updated 2019-Oct-29):

Vol. mean radius (km) = 3389.92+-0.04 Density (g/cm^3) = 3.933(5+-4)

Mass x10^23 (kg) = 6.4171 Flattening, f = 1/169.779

Volume (x10^10 km^3) = 16.318 Equatorial radius (km)= 3396.19

Sidereal rot. period = 24.622962 hr Sid. rot. rate, rad/s = 0.0000708822

Mean solar day (sol) = 88775.24415 s Polar gravity m/s^2 = 3.758

Core radius (km) = ~1700 Equ. gravity m/s^2 = 3.71

Geometric Albedo = 0.150

GM (km^3/s^2) = 42828.375214 Mass ratio (Sun/Mars) = 3098703.59

GM 1-sigma (km^3/s^2) = +- 0.00028 Mass of atmosphere, kg= ~ 2.5 x 10^16

Mean temperature (K) = 210 Atmos. pressure (bar) = 0.0056

Obliquity to orbit = 25.19 deg Max. angular diam. = 17.9"

Mean sidereal orb per = 1.88081578 y Visual mag. V(1,0) = -1.52

Mean sidereal orb per = 686.98 d Orbital speed, km/s = 24.13

Hill's sphere rad. Rp = 319.8 Escape speed, km/s = 5.027

Perihelion Aphelion Mean

Solar Constant (W/m^2) 717 493 589

Maximum Planetary IR (W/m^2) 470 315 390

Minimum Planetary IR (W/m^2) 30 30 30

*******************************************************************************

Appendix B: NASA JPL Horizons Data

*******************************************************************************

Ephemeris / WWW_USER Wed Jan 29 11:09:00 2020 Pasadena, USA / Horizons

*******************************************************************************

Target body name: Mars (499) {source: mar097}

Center body name: Sun (10) {source: mar097}

Center-site name: BODY CENTER

*******************************************************************************

Start time : A.D. 2005-Jan-27 00:00:00.0000 TDB

Stop time : A.D. 2005-Jan-28 00:00:00.0000 TDB

Step-size : 1440 minutes

*******************************************************************************

Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}

Center cylindric: 0.00000000,0.00000000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}

Center radii : 696000.0 x 696000.0 x 696000.0 k{Equator, meridian, pole}

Keplerian GM : 1.3271248287031293E+11 km^3/s^2

Output units : KM-S, deg, Julian Day Number (Tp)

Output type : GEOMETRIC osculating elements

Output format : 10

Reference frame : ICRF/J2000.0

Coordinate systm: Ecliptic and Mean Equinox of Reference Epoch

*******************************************************************************

Appendix B: NASA JPL Horizons Data JDTDB, Calendar Date (TDB), EC,

QR, IN, OM, W,

Tp, N, MA, TA,

A, AD, PR,

**************************************************************************************

**************************************************************************************

**************************************************************************************

********************************************************************************

$$SOE

2453397.500000000, A.D. 2005-Jan-27 00:00:00.0000, 9.341686346997068E-02,

2.066474110927086E+08, 1.849361710600804E+00, 4.953879429753077E+01,

2.866068045070586E+02, 2.453569131659152E+06, 6.065198530558276E-06,

2.700593204934113E+02, 2.594147985828359E+02, 2.279409386365347E+08,

2.492344661803608E+08, 5.935502328344452E+07,

2453398.500000000, A.D. 2005-Jan-28 00:00:00.0000, 9.341707518067797E-02,

2.066472305106390E+08, 1.849361473014427E+00, 4.953879348114902E+01,

2.866071986450913E+02, 2.453569132214481E+06, 6.065204356245016E-06,

2.705829767494479E+02, 2.599277361816943E+02, 2.279407926768783E+08,

2.492343548431175E+08, 5.935496627237750E+07,

$$EOE

********************************************************************************************************

********************************************************************************************************

********************************************************************************************************

**************************

Appendix B: NASA JPL Horizons Data

Coordinate system description:

Ecliptic and Mean Equinox of Reference Epoch

Reference epoch: J2000.0

XY-plane: plane of the Earth's orbit at the reference epoch

Note: obliquity of 84381.448 arcseconds wrt ICRF equator (IAU76)

X-axis : out along ascending node of instantaneous plane of the Earth's

orbit and the Earth's mean equator at the reference epoch

Z-axis : perpendicular to the xy-plane in the directional (+ or -) sense

of Earth's north pole at the reference epoch.

Symbol meaning:

JDTDB Julian Day Number, Barycentric Dynamical Time

EC Eccentricity, e

QR Periapsis distance, q (km)

IN Inclination w.r.t XY-plane, i (degrees)

OM Longitude of Ascending Node, OMEGA, (degrees)

W Argument of Perifocus, w (degrees)

Tp Time of periapsis (Julian Day Number)

N Mean motion, n (degrees/sec)

Appendix B: NASA JPL Horizons Data

MA Mean anomaly, M (degrees)

TA True anomaly, nu (degrees)

A Semi-major axis, a (km)

AD Apoapsis distance (km)

PR Sidereal orbit period (sec)

Geometric states/elements have no aberrations applied.

Computations by ...

Solar System Dynamics Group, Horizons On-Line Ephemeris System

4800 Oak Grove Drive, Jet Propulsion Laboratory

Pasadena, CA 91109 USA

Information: http://ssd.jpl.nasa.gov/

Connect : telnet://ssd.jpl.nasa.gov:6775 (via browser)

http://ssd.jpl.nasa.gov/?horizons

telnet ssd.jpl.nasa.gov 6775 (via command-line)

Author : Jon.D.Giorgini@jpl.nasa.gov

*******************************************************************************

Appendix C: MATLAB Code

The following slides contain MATLAB code used to generate the plots and results

in this presentation. Note that the function “kep2car.m” was written by Prof.

Carolin Frueh of Purdue University’s Department of Aeronautical and

Astronautical Engineering. All other scripts and functions were written by Jordan

Mayer.

Appendix C: MATLAB Code%%%%%

% AAE 450: Spacecraft Design

%

% Determine during which periods the Sun may interfere

with optical

% communications between Earth, Mars, and the Sun-Mars L4

and L5 Lagrange

% points.

%

% Author: Jordan Mayer (Mission Design)

% Created: 01/27/2020

% Last Modified: 01/27/2020

%%%%%

%% Preliminary setup

clear all; close all; format compact;

AU_to_km = 149597870.7; % astronomical unit

% Set constants from NASA JPL HORIZONS Web-Interface for

January 27, 2005

% Gravitational parameters (GM), km^3/s^2

mu_Sun = 1.3271283864237474e11;

mu_Earth = 398600.435436;

mu_Mars = 42828.375214;

Appendix C: MATLAB Code

% True anomalies on 01/27/2005, deg

nu_0_Earth = 2.573904212862790*10;

nu_0_Mars = 2.594147985828359*10^2;

% Mean anomalies on 01/27/2005, deg

M_0_Earth = 2.495062571346842*10;

M_0_Mars = 2.700593204934113*10^2;

% Semimajor axes, km (assume constant)

a_Earth = 1.494716073506118e8;

a_Mars = 2.279409386365347e8;

% Eccentricities, dimensionless

e_Earth = 1.611134192723532e-2;

e_Mars = 9.341686346997068e-2;

% Mean motions, rad/s

n_Earth = sqrt(mu_Sun/a_Earth^3);

n_Mars = sqrt(mu_Sun/a_Mars^3);

Appendix C: MATLAB Code% Set values from Simon et. al

% Longitudes of ascending nodes, deg

OMEGA_Earth = 174.87317577;

OMEGA_Mars = 49.55809321;

% Longitudes of perihelion, deg

omega_bar_Earth = 102.93734808;

omega_bar_Mars = 336.06023395;

% Arguments of perihelion, deg

omega_Earth = omega_bar_Earth - OMEGA_Earth;

omega_Mars = omega_bar_Mars - OMEGA_Mars;

%% Generate position data

% Set up time steps

yr_to_day = 365;

day_to_hr = 24;

hr_to_sec = 60*60;

yr_to_sec = yr_to_day*day_to_hr*hr_to_sec;

t_f = 15*yr_to_sec;

% simulate for 15 years (from Byrnes, Longuski, and Aldrin: "The inertial

Appendix C: MATLAB Code% geometry repeats every 15 years")

n_data = 10000; % number of data points

t_list = linspace(0.0,t_f,n_data).'; % all times, sec

% Allocate data arrays

% 2-D position arrays

r_list_Earth = zeros(n_data, 2);

r_list_Mars = zeros(n_data, 2);

r_list_ML4 = zeros(n_data, 2);

r_list_ML5 = zeros(n_data, 2);

r_list_EL4 = zeros(n_data, 2);

r_list_EL5 = zeros(n_data, 2);

% Visibility arrays (0 if visible, 1 if not)

% ML: Mars-Sun Lagrange point

% EL: Earth-Sun Lagrange point

ML4_block_list = zeros(n_data, 1);

ML5_block_list = zeros(n_data, 1);

Mars_block_list = zeros(n_data, 1);

EL4_block_list = zeros(n_data, 1);

EL5_block_list = zeros(n_data, 1);

Appendix C: MATLAB Code

% Minimum distance arrays

min_dist_Earth_ML = zeros(n_data, 1); % Earth to closest ML4/ML5

min_dist_Mars_EL = zeros(n_data, 1); % Mars to closest EL4/EL5

min_dist_EL_ML = zeros(n_data, 1);

% Shortest distance between EL4/EL5 and ML4/ML5

% Prepare Keplerian element arrays

% [semimajor axis (km), eccentricity, inclination (deg), longitude of

% ascending node (deg), argument of periapsis (deg), mean anomaly (deg)]

kep_Earth = [a_Earth, e_Earth, 0.0, OMEGA_Earth, omega_Earth, M_0_Earth];

kep_Mars = [a_Mars, e_Mars, 0.0, OMEGA_Mars, omega_Mars, M_0_Mars];

% Compute position data

for k = 1:n_data

delta_t = t_list(k);

Appendix C: MATLAB Code% Compute mean anomalies, deg

M_Earth = update_M(M_0_Earth, n_Earth, delta_t);

M_Mars = update_M(M_0_Mars, n_Mars, delta_t);

% Update Keplerian element arrays

kep_Earth(6) = M_Earth;

kep_Mars(6) = M_Mars;

% Compute Cartesian vectors [position (km), velocity (km)]

car_Earth = kep2car(kep_Earth, mu_Sun, 'deg');

car_Mars = kep2car(kep_Mars, mu_Sun, 'deg');

if car_Earth(3) > 0 || car_Mars(3) > 0

error('3-D?');

end

% Get 3-D position vectors

r_Earth = car_Earth(1:3);

r_Mars = car_Mars(1:3);

r_ML4 = rot_mat_3(deg2rad(60)) * r_Mars;

r_ML5 = rot_mat_3(deg2rad(-60)) * r_Mars;

r_EL4 = rot_mat_3(deg2rad(60)) * r_Earth;

r_EL5 = rot_mat_3(deg2rad(-60)) * r_Earth;

Appendix C: MATLAB Code

% Compute angles to Sun, as viewed from Earth

r_Earth_Sun = -r_Earth;

r_Earth_ML4 = r_ML4 - r_Earth;

r_Earth_Mars = r_Mars - r_Earth;

r_Earth_ML5 = r_ML5 - r_Earth;

r_Earth_EL4 = r_EL4 - r_Earth;

r_Earth_EL5 = r_EL5 - r_Earth;

theta_ML4_Earth = angle_between(r_Earth_Sun, r_Earth_ML4);

theta_ML5_Earth = angle_between(r_Earth_Sun, r_Earth_ML5);

theta_Mars = angle_between(r_Earth_Sun, r_Earth_Mars);

theta_EL4_Earth = angle_between(r_Earth_Sun, r_Earth_EL4);

theta_EL5_Earth = angle_between(r_Earth_Sun, r_Earth_EL5);

% Compute angles to Sun, as viewed from Mars

r_Mars_Sun = -r_Mars;

r_Mars_ML4 = r_ML4 - r_Mars;

r_Mars_Earth = -r_Earth_Mars;

Appendix C: MATLAB Code

r_Mars_ML5 = r_ML5 - r_Mars;

r_Mars_EL4 = r_EL4 - r_Mars;

r_Mars_EL5 = r_EL5 - r_Mars;

theta_ML4_Mars = angle_between(r_Mars_Sun, r_Mars_ML4);

theta_ML5_Mars = angle_between(r_Mars_Sun, r_Mars_ML5);

theta_Earth = angle_between(r_Mars_Sun, r_Mars_Earth);

theta_EL4_Mars = angle_between(r_Mars_Sun, r_Mars_EL4);

theta_EL5_Mars = angle_between(r_Mars_Sun, r_Mars_EL5);

% Store 2-D positions

r_list_Earth(k,:) = r_Earth(1:2);

r_list_Mars(k,:) = r_Mars(1:2);

r_list_ML4(k,:) = r_ML4(1:2);

r_list_ML5(k,:) = r_ML5(1:2);

r_list_EL4(k,:) = r_EL4(1:2);

r_list_EL5(k,:) = r_EL5(1:2);

% Determine if any communications are blocked by the Sun

if theta_ML4_Earth <= 3 || theta_ML4_Mars <= 3

ML4_block_list(k) = 1;

end

Appendix C: MATLAB Codeif theta_ML5_Earth <= 3 || theta_ML5_Mars <= 3

ML5_block_list(k) = 2;

end

if theta_Mars <= 3 || theta_Earth <= 3

Mars_block_list(k) = 3;

end

if theta_EL4_Earth <= 3 || theta_EL4_Mars <= 3

EL4_block_list(k) = 1;

end

if theta_EL5_Earth <= 3 || theta_EL5_Mars <= 3

EL5_block_list(k) = 2;

end

if (ML4_block_list(k) == 1) && (ML5_block_list(k) == 2)

fprintf('Uh oh! Both Mars Lagrange points blocked!');

end

if (EL4_block_list(k) == 1) && (EL5_block_list(k) == 2)

fprintf('Uh oh! Both Earth Lagrange points blocked!');

end

% Compute and store closest distances

dist_Earth_ML4 = norm(r_Earth_ML4);

dist_Earth_ML5 = norm(r_Earth_ML5);

Appendix C: MATLAB Codedist_Mars_EL4 = norm(r_Mars_EL4);

dist_Mars_EL5 = norm(r_Mars_EL5);

dist_EL4_ML4 = norm(r_ML4 - r_EL4);

dist_EL4_ML5 = norm(r_ML5 - r_EL4);

dist_EL5_ML4 = norm(r_ML4 - r_EL5);

dist_EL5_ML5 = norm(r_ML5 - r_EL5);

min_dist_Earth_ML(k) = min([dist_Earth_ML4, dist_Earth_ML5]);

min_dist_Mars_EL(k) = min([dist_Mars_EL4, dist_Mars_EL5]);

min_dist_EL_ML(k) = min([dist_EL4_ML4, dist_EL4_ML5, ...

dist_EL5_ML4, dist_EL5_ML5]);

end

%% Plot results

close all;

yr_list = t_list ./ yr_to_sec;

% Plot visibility of Lagrange points

figure(2);

subplot(2,1,1);

msize = 4;

Appendix C: MATLAB Codefunction [car] = kep2car(kep,GM,atype)

% Name: kep2car.m

% Author: C. Frueh

% Purpose

% To compute the Cartesian position/velocity given Keplerian elements.

% Inputs

% kep - Keplerian elements, (6 x 1) vector with order semi-major axis,

% eccentricity, inclination, right-ascension of the ascending

% node, argument of periapse, mean anomaly

% mu - value of the gravitational parameter of the central body

% atype - units of the angles in the Keplerian elements, 'rad' or 'deg'

% Outputs

% car - Cartesian position/velocity

% Dependencies

% None

sma = kep(1);

ecc = kep(2);

inc = kep(3);

raan = kep(4);

argp = kep(5);

manm = kep(6);

Appendix C: MATLAB Codeif(strcmp(atype,'deg'))

inc = inc*(pi/180.0);

raan = raan*(pi/180.0);

argp = argp*(pi/180.0);

manm = manm*(pi/180.0);

end

itermax = 10;

toler = 1.0D-12;

delta = 1.0;

eanm = manm;

iter = 0;

while((iter < itermax) && (abs(delta) > toler))

iter = iter + 1;

delta = ((eanm - ecc*sin(eanm) - manm)/(1.0 - ecc*cos(eanm)));

eanm = eanm - delta;

end

tanm = 2.0*atan(sqrt((1.0+ecc)/(1.0-ecc))*tan(0.5*eanm));

% if ~isreal(tanm)

% keyboard

% end

Appendix C: MATLAB Coder = sma*(1.0-ecc*cos(eanm));

slr = sma*(1.0-ecc*ecc);

angm = sqrt(GM*slr);

vr = (angm/slr)*ecc*sin(tanm);

vf = (angm/slr)*(1.0+ecc*cos(tanm));

argl = argp + tanm;

cos_s = cos(argl);

sin_s = sin(argl);

cos_i = cos(inc);

sin_i = sin(inc);

cos_W = cos(raan);

sin_W = sin(raan);

R3s = [cos_s,sin_s,0.0;-sin_s,cos_s,0.0;0.0,0.0,1.0];

R1i = [1.0,0.0,0.0;0.0,cos_i,sin_i;0.0,-sin_i,cos_i];

R3W = [cos_W,sin_W,0.0;-sin_W,cos_W,0.0;0.0,0.0,1.0];

T = R3s*R1i*R3W;

x = T(1,1)*r;

y = T(1,2)*r;

z = T(1,3)*r;

xd = T(1,1)*vr + T(2,1)*vf;

yd = T(1,2)*vr + T(2,2)*vf;

zd = T(1,3)*vr + T(2,3)*vf;

Appendix C: MATLAB Codecar = [x;y;z;xd;yd;zd];

end

Appendix C: MATLAB Code%%%%%

% Generate rotation matrix for rotation about 3rd (z) axis.

%

% Inputs:

% theta: rotation angle, rad

%

% Outputs:

% R3: rotation matrix, to be used in the format of

% r_prime = R3*r, where r is a 3-element column vector

%

% Author: Jordan Mayer

% Created: 10/01/2019

% Last Modified: 01/29/2020

%%%%%

function R3 = rot_mat_3(theta)

R3 = [cos(theta), -sin(theta), 0; sin(theta), cos(theta), 0; 0, 0, 1];

end

Appendix C: MATLAB Code%%%%%

% Determine angle between two vectors, with quadrant checks!

%

% Inputs:

% r1, r2: two 3-element vectors (column or row, but must be consistent)

%

% Outputs:

% theta: angle between r1 and r2 vectors, deg

%%%%%

function [theta] = angle_between(r1, r2)

r1_dot_r2 = dot(r1, r2);

r1_r2 = norm(r1)*norm(r2);

r1_cross_r2 = norm(cross(r1, r2));

theta1 = acosd(r1_dot_r2/r1_r2);

theta2 = -theta1; % cos(x) = cos(-x)

theta3 = asind(r1_cross_r2/r1_r2);

theta4 = 180 - theta3; % sin(x) = sin(180 - x)

theta1 = bound_180(theta1);

theta2 = bound_180(theta2);

theta3 = bound_180(theta3);

theta4 = bound_180(theta4);

Appendix C: MATLAB Codewiggle = 0.00001;

if abs(theta1 - theta3) < wiggle || abs(theta1 - theta4) < wiggle

theta = theta1;

elseif abs(theta2 - theta3) < wiggle || abs(theta2 - theta4) < wiggle

theta = theta2;

else

fprintf('\ntheta1 = %.4f\n', theta1);

fprintf('theta2 = %.4f\n', theta2);

fprintf('theta3 = %.4f\n', theta3);

fprintf('theta4 = %.4f\n', theta4);

error('no consistent theta');

end

end

Grace Ness

Backup Slides - 1

Grace Ness

Backup Slides - 2

Grace Ness

Backup Slides - 3

Grace Ness

Backup Slides - 4

Grace Ness

Backup Slides - 5

Dean Lontoc January 30, 2020

Backup Slides

Assumptions

• Tank sizing and weight is linearly scaled

• Assume flight computer is the same as Orion: IBM PowerPC 750 flight computer

• Each takes 7 watts to power, three flight computers totals 21 watts for controls

• Hydrogen and Oxygen flow rate of PEMFC the same as space shuttle fuel cells. Commercial

PEMFC’s do not give flow rates because they assume fuel cells run in atmosphere

• Mission lasts 14 days

• Cargo will have 7 kW available for use: same as the space shuttle

Oxygen and Hydrogen Requirements

14 days = 336 hours

Hydrogen flow rate: 0.6 pounds per hour

Oxygen flow rate: 4 pounds per hour

Hydrogen requirement = 0.6 * 336 = 201.6 pounds = 91.44 kg

Oxygen requirement = 4*336 = 1344 pounds = 609.62 kg

Tank sizing

92 H2 weight/ 216 tank dry weight = 201.6 H2/X

X = 473.32 pounds

X = 214.69 kg

781 O2 weight/ 201 tank dry weight = 1344 O2/X

X = 345.89 pounds

X = 156.87 kg

26094.09 O2 tank dimensions /781 = X/1344

X = 67356.83 in^3

X = 1.104 m^3

49321.11/92 = X/201.6

X = 108077.56 in^3

X = 1.771 m^3

Total mass calculated by adding empty tank mass, fuel and catalyst mass, and the mass of the fuel cell

modules.

Proton Exchange Membrane Fuel Cell

• Special type of hydrogen fuel cell

• Basing fuel cell performance off of Horizon 5000 Watt Fuel Cell

• Mass: Each stack is 30 kg so 5 stacks will be 150 kg

• Volume: 0.350 x 0.212 x 0.650 meters per stack

• Most commercial fuel cell manufacturers focus on the automobile industry, so they do not provide

numbers for oxygen flow rate because they assume fuel cell operates in atmosphere

How PEM Fuel Cells Work

Simply put, the PEM generates power by having hydrogen protons pass through a membrane while the

electrons travel in an external circuit which generates electricity. The hydrogen bonds to the oxygen

catalyst which then produces water as a byproduct.

Water Production

Water is a byproduct of the reaction within the fuel cell

Moles = mass of substance/ molar mass

Molar mass oxygen: 15.999 g/mol

Mass of oxygen: 609620 g

Moles: 38103.63 mol

Molar mass hydrogen: 1.00784 g/mol

Mass of hydrogen: 91440 g

Moles: 90728.69 mol

Oxygen is limiting factor therefore mass of H2O = 38103.63 moles * 18 g/mol = 685.865 kg

Why PEMFC?

• No moving parts

• Lower weight and volume compared to regular other types of fuel cells

• The proton exchange membrane allows for lower operating temperatures because it allows protons

to pass through smoothly while blocking electrons that can build up and create excess heat

• Fast startup time in case of emergencies, under 30 seconds

• More consistent power generation compared to solar panels

• Less mass and volume than nuclear reactors

• More efficient power generation compared to alkaline fuel cells used in space shuttle

SourcesA Basic Overview of Fuel Cell Technology Available: https://americanhistory.si.edu/fuelcells/basics.htm.

Aggarwal, V., “Solar Panel Efficiency: What Panels Are Most Efficient?: EnergySage,” Solar News Available:

https://news.energysage.com/what-are-the-most-efficient-solar-panels-on-the-market/.

Dunbar, B., “Fuel Cell Use in the Space Shuttle,” NASA Available:

https://www.nasa.gov/topics/technology/hydrogen/fc_shuttle.html.

“ELECTRICAL POWER SYSTEM,” NASA Available: https://science.ksc.nasa.gov/shuttle/technology/sts-newsref/sts-

eps.html.

“Horizon 5000W PEM Fuel Cell SKU: FCS-C5000. Categories: Education, Fuel Cell Stacks, Fuel Cells, Kits. Brands:

Horizon. Price: $19,141.00,” fuelcellearth.com Available: https://www.fuelcellearth.com/fuel-cell-products/horizon-5000w-

pem-fuel-cell/.

“HSF - The Shuttle,” NASA Available: https://spaceflight.nasa.gov/shuttle/reference/shutref/orbiter/eps/pwrplants.html.

“NASA's Orion spacecraft runs on a 12 year-old single-core processor from the iBook G3,” Geek.com Available:

https://www.geek.com/chips/nasas-orion-spacecraft-runs-on-a-12-year-old-single-core-processor-from-the-ibook-g3-

1611132/.

“Types of Fuel Cells,” Energy.gov Available: https://www.energy.gov/eere/fuelcells/types-fuel-cells.

YouTube Available: https://www.youtube.com/watch?v=_MsG9REFN3s.

Jacob Nunez-Kearny - BackupJanuary 30, 2020

Power & ThermalCycler: Power Generation & Storage

Cycler Power Sizing Data

Data for solar panel and space battery systems based on existing spacecraft and

upcoming technologies.

Solar Panels ISS Dawn Cycler

Power(kW) 248[2] 10[2] 2893

Specific Power (W/kg) 27[2] 80[2] 80

Mass (Mg) 6696 800 36.167

Batteries ISS Ni-H ISS Li-Ion Cycler

Capacity (Amp-hr) 24[1] 48[1] 6720

Specific Energy (Wh/kg) 40[1] 100[1] 100

Mass (Mg) 2400 2364 8.064

TRL Sizing 9 7 6 3

Panels-Specific Power

(W/kg) 80 150[3] 150[3] 300[3]

Panels-Mass (Mg) 36.1666667 19.2888889 19.2888889 9.644444

Batteries-Specific Energy

(Wh/kg) 100 140 200 350

Batteries-Mass (Mg) 8.064 5.76 4.032 2.304

References

[1] Surampudi, S. (2011). Overview of the Space Power Conversion and Energy Storage Technologies.

Jet Propulsion Laboratory, Pasadena.

[2] Beauchamp, P. (2015). Solar Power and Energy Storage for Planetary Missions. Jet Propulsion

Laboratory, Pasadena.

[3] Surampudi, S., et al. (2017). Solar Power Technologies for Future Planetary Science Missions. Jet

Propulsion Laboratory, Pasadena.

Carly Kren – Backup SlidesJanuary 30, 2020

Propulsion TeamTaxi - Reaction Control Systems (RCS)

Slide: 4 of 8

Mass calculations: Hand calcs

Slide: 5 of 8

Mass calculations: Hand calcs (continued)

Slide: 6 of 8

Mass calculations: MATLAB code

Slide: 7 of 8

Delta V calculations: MATLAB code

Slide: 8 of 8

Griffin Pfaff – Backup SlidesJanuary 30, 2020

Propulsion – CyclerMain Propulsion System

Codecyclermass = 5039; %Mg

taximass = 60; %Mg

totalmass = cyclermass + 3*taximass; %Mg

forceneed = totalmass * .01; %N

x3thrust = 5.4; %N

numx3 = 10;

fullthrust = x3thrust * numx3; %N

excessthrust = fullthrust - forceneed %N

x3power = 100; %kw

fullpower = x3power * numx3 %kw

proptime = 1/12; %year

propflow = 3900; %cm/min

propvolume = propflow * 525600 * proptime * numx3 / 1000000 %m^3

propmass = propvolume * 2.942; %Mg

x3mass = .23; %Mg

totalmass = propmass + x3mass*10 %Mg

excessthrust =

1.8100

fullpower =

1000

propvolume =

1.7082e+03

propmass =

5.0255e+03

totalmass =

5.0278e+03

Output:

References

[1] http://pepl.engin.umich.edu/pdf/2017_Hall_thesis.pdf

[2] http://pepl.engin.umich.edu/pdf/IEPC-2017-228.pdf

[3] http://pepl.engin.umich.edu/pdf/AIAA-2018-4418.pdf

Arch PleumpanyaBackup Slides

January 29, 2020

Propulsion TeamMass Driver

Kinematics

clear

clc

close all

set(0,'DefaultLineLineWidth',1.5);

%

%% Kinematic equations on mass driver

g = 9.81; % Earth's gravitational acceleration [m/s2]

V_esc_mars = 5000; % Mars' escape velocity [m/s]

V_esc_moon = 2380; % Moon's escape velocity [m/s]

x_track_moon = linspace(50000,200000); % possible range of driver length on the Moon

[m]

acc_moon = V_esc_moon^2/2./x_track_moon; % vehicle acceleration on the Moon [m/s2]

delta_t_moon = V_esc_moon./acc_moon; % launch duration on the Moon [s]

x_track_mars = linspace(100000,500000); % possible range of driver length on Mars [m]

acc_mars = V_esc_mars^2/2./x_track_mars; % vehicle acceleration on Mars [m/s2]

delta_t_mars = V_esc_mars./acc_mars; % launch duration on Mars [s]

%

%% Calculate force required at chose acceleration

m_taxi = 94.34e3; % estimated vehicle mass [kg]

F_req_moon = 1.1*m_taxi*acc_g_moon*g; % force required on the Moon [N]

acc_g_mars = 3; % chosen acceleration limit on Mars [9.81 m/s2]

F_req_mars = 1.1*m_taxi*acc_g_mars*g; % force required on Mars [N]

acc_g_moon = 2; % chosen acceleration limit on the Moon [9.81 m/s2]

%

% Plots

figure(1)

subplot(211)

yyaxis left

plot(x_track_mars/1000,acc_mars/9.81)

ylabel('acceleration [g]','fontsize',12)

yyaxis right

plot(x_track_mars/1000,delta_t_mars/60,'--')

ylabel('duration [min]','fontsize',12)

title('G-Force and Duration on Taxi Vehicle on the Moon','fontsize',16)

xlabel('track distance [km]','fontsize',12)

legend('acceleration','duration','Location','best')

grid on

subplot(212)

yyaxis left

plot(x_track_moon/1000,acc_moon/9.81)

ylabel('acceleration [g]','fontsize',12)

yyaxis right

plot(x_track_moon/1000,delta_t_moon/60,'--')

ylabel('duration [min]','fontsize',12)

title('G-Force and Duration on Taxi Vehicle on Mars','fontsize',16)

xlabel('track distance [km]','fontsize',12)

legend('acceleration','duration','Location','best')

grid on

%

% end

Steven Lach Slide 2 Table

• Max Delta V: Given from mission design team

• Taxi Mass: Given from taxi team

• Max Acceleration: Given from Human Factors team

4

Steven Lach Slide 3 Table

• Effective UTS: Calculated by factoring in environmental strength

loss. Kevlar3, Zylon4, IM75, Dyneema was estimated to have a

strength loss of 5% because specific information could not be found

• Tether Mass and Length: Tether Code attached on back.

Mathematical models used in code2

• Delta V given by Mission Design Team

5

Steven Lach Code

6

Steven Lach References

1. “Ultra High molecular Weight Polyethylene fiber from DSM

Dyneema,” eurofibers, CIS YA100, January 2010

2. Jokic, M.D., Longuski, J.M., “Design of Tether Sling for Human

Transportation Systems Between Earth and Mars,” Journal of

Spacecraft and Rockets, Vol. 41, No. 6, November-December 2004,

pp. 1010-1015

3. Finckenor, M.M., “Comparison of High-Performance Fiber Materials

Properties in Simulated and Actual Space Environments,”

NASA/TM-2017-219634, January 2017

4. “Zylon®(PBO fiber) Technical Information (2005),” Toyobo Co.,

LTD., F0739K, 2005

5. Kumar, B.G., Singh, R.P., Nakamura, T., “Degradation of Carbon

Fiber-Reinforced Epoxy Composites by Ultraviolet Radiation and

Condensation,” Journal of Composite Materials, Vol. 36, No. 24,

2002, pp. 2713-2733

7

Nicki Liu Backup – Solidworks

Our Moments of Inertia:

• Ixx = 4.1801 * 106 kg/m2

• Iyy = 4.1811 * 106 kg/m2

• Izz = 1.0645 * 105 kg/m2

• Center of Mass is located 11.02m out of a 25m body

Space Shuttle Moments of Inertia for comparison: [Chyu, Cavin, & Erickson]

• Ixx = 1.1829 * 108 kg/m2

• Iyy = 8.8239 * 108 kg/m2

• Izz = 9.0297 * 108 kg/m2

• Ixz = 2.8748 * 107 kg/m2

• Center of Mass is located at 22m out of 33m body

• Aluminum 2024 – T4 [“Aluminum 2024-T4”]

• Composite Materials [“Applied Nanostructured Solutions PC/ABS - Carbon NanoStructure Chopped Fiber Composite”]

Nicki Liu Backup – Material Properties

Mechanical Properties Metric English Comments

Ultimate Tensile Strength >= 395 MPa >= 57300 psi Wire, rod, bar and shapes

Yield Tensile Strength >= 260 MPa >= 37700 psi Wire, rod, bar and shapes

Elongation at Break >= 10 % >= 10 % Wire, rod, and bar (rolled or

cold finished)

Modulus of Elasticity 73.1 GPa 10600 ksi

Fatigue Strength 138 MPa 20000 psi completely reversed stress

Melting Point 502 - 638 °C 935 - 1180 °F

Thermal Conductivity 121 W/m-K 840 BTU-in/hr-ft²-°F

Mechanical Properties Metric English Comments

Bulk Density 0.150 g/cc 0.00542 lb/in³

Ultimate Tensile Strength 100 MPa 14500 psi ASTM D638

Tensile Modulus 8.96 GPa 1300 ksi ASTM D638

Flexural Strength 140 MPa 20300 psi ASTM D790

Flexural Modulus 8.76 GPa 1270 ksi ASTM D790

Nicki Liu Backup – Thickness [8]

Additional thickness

requirements due to

asteroid and space

debris protection.

Additional thickness

requirements also due

to a safety factor of 2 or

higher, which is

generally used for

pressure vessels. [7]

Nicki Liu Backup – Works Sited[1] Aluminum Association, Inc. (n.d.). Aluminum 2024-T4. Retrieved January 29, 2020, from

http://www.matweb.com/search/DataSheet.aspx?MatGUID=67d8cd7c00a04ba29b618484f7ff7524&ckck=1

[2] Applied Nanostructured Solutions. (n.d.). Applied Nanostructured Solutions PC/ABS - Carbon NanoStructure

Chopped Fiber Composite. Retrieved January 29, 2020, from

http://www.matweb.com/search/DataSheet.aspx?MatGUID=ad234c236a8a4424af3b3ad164120167

[3] Boeing. (n.d.). Boeing 777-300ER Seat map. Retrieved January 29, 2020, from

https://www.united.com/ual/en/us/fly/travel/inflight/aircraft/777-300.html

[4] Chyu, W. J., Cavin, R. K., & Erickson, L. L. (1978). Static and Dynamic Stability Analysis of the Space Shuttle

Vehicle-Orbiter . NASA Technical Paper 1179. Retrieved from

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19780012233.pdf

[5] Khan, A., Subhan, M., & Ali, W. (2020, January). Retrieved from https://www.slideshare.net/subhan90/skin-

stringersinanaircraft-56785765

[6] Steeve, B. (2012). STS-133 Space Shuttle External Tank Intertank Stringer Crack Investigation Stress Analysis.

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference≪BR≫20th

AIAA/ASME/AHS Adaptive Structures Conference≪BR≫14th AIAA. doi: 10.2514/6.2012-1777

[7] “Technical Standard for High Pressure Gas Equipment for Space Use,” Japan Aerospace Exploration Agency,

Mar. 2016.

[8] Tsutsui, W. (n.d.). Failure Criterion. AAE 3500. West Lafayette.

BACKUP SLIDES Jacob Leet

MATLAB CODE (acceleration function)function [accel] = forcefunc(m,G,pos)

%% SETUP

DoF = 3;

index = 1:length(pos)/DoF;

F = zeros(length(pos),1);

accel = zeros(length(pos),1);

%% FORCE CALCULATION

for i = index

for j = index

% Doesn't calculate force on itself

if i == j

continue

end

% CALCULATES DISTANCE BETWEEN BODIES

% fprintf('x coordinate %d %d | y coordinate %d %d\n',pos(2*j-1),pos(2*i-1),pos(2*j),pos(2*i))

dx = pos(DoF*i-2) - pos(DoF*j-2);

dy = pos(DoF*i-1) - pos(DoF*j-1);

dz = pos(DoF*i) - pos(DoF*j);

r = sqrt(dx^2+dy^2 + dz^2);

% DETERMINE DIRECTION OF FORCE

dirx = -dx/r;

diry = -dy/r;

dirz = -dz/r;

% DETERMINE NET FORCE

Fnet = G*m(i)*m(j)/r^2;

% SEPARATES FORCE INTO COMPONENTS

Fx = Fnet*dirx;

Fy = Fnet*diry;

Fz = Fnet*dirz;

% fprintf('%d %d | %d %d\n',i,j,Fx,Fy)

% SUMS FORCES

F(DoF*i-2) = F(DoF*i-2) + Fx;

F(DoF*i-1) = F(DoF*i-1) + Fy;

F(DoF*i) = F(DoF*i) + Fz;

end

end

%% ACCELERATION CALCULATION

for i = index

for j = 0:(DoF-1)

accel(DoF*i-1 + j-1) = F(DoF*i-1 + j-1) / m(i);

end

end

MATLAB CODE (setup menu)function ParameterSetup()

%% GENERAL INITIAL CONDITIONS

% INITIAL VALUES

bodies = {'SUN', 'EARTH', 'MOON', 'MARS', 'PHOBOS', 'SATELLITE'};

mass = {'1.9885e30', '5.9736e24', '7.346e22', '6.41710e23', '1.06590e16', '5000'};

radius = {'696340000', '6378100', '1738100', '3396200', '11100', '10'};

init_pos = {'0','0','0', '147090000000','0','0', '147451836243','0','32579494', '206512303194','0','6670309540', '206516452294','0','6678717532',

'1000000000','0','0'};

init_vel = {'0','0','0', '0','30290','0', '0','30290','1082', '0','26500','0', '0','26500','2139', '0','2e5','0'};

%% WINDOW DIMENSIONS

close all

box_height = 350;

box_width = 1000;

xbox = 110;

ybox = 180;

%% WINDOW GENERATION

h.f = figure('units','pixels','position',[xbox,ybox,box_width,box_height],...

'toolbar','none','menu','none');

%% TITLE CREATION

% TITLE DIMENSIONS

th = 28;

tw = 485;

tx =(box_width-tw)/2;

ty = box_height - th;

% TITLE DISPLAY

uicontrol('style','text','units','pixels', ...

'position',[tx,ty,tw,th],'string', ...

'TRAJECTORY SIMULATION MENU',...

'FontWeight','Bold','FontSize',20,'FontAngle','italic');

%% GENERATE EDIT BOXES

% BOX SET UP

th = 30;

tw = 105;

tx = 110;

ty = 275;

for i = 1:6

% MASS

h.m(i) = uicontrol('style','edit','units','pixels', ...

'position',[tx,ty - th*i,tw,th],'string', ...

mass{i}, ...

'FontSize',10);

% GEOMETRY

h.r(i) = uicontrol('style','edit','units','pixels', ...

'position',[tx+1*tw,ty - th*i,tw,th],'string', ...

radius{i}, ...

'FontSize',10);

% INITIAL POSITIONS

h.pos(3*i-2) = uicontrol('style','edit','units','pixels', ...

'position',[tx+2*tw,ty - th*i,tw,th],'string', ...

init_pos{3*i-2}, ...

'FontSize',10);

h.pos(3*i-1) = uicontrol('style','edit','units','pixels', ...

'position',[tx+3*tw,ty - th*i,tw,th],'string', ...

init_pos{3*i-1}, ...

'FontSize',10);

h.pos(3*i) = uicontrol('style','edit','units','pixels', ...

'position',[tx+4*tw,ty - th*i,tw,th],'string', ...

init_pos{3*i}, ...

'FontSize',10);

% INITIAL VELOCITIES

h.vel(3*i-2) = uicontrol('style','edit','units','pixels', ...

'position',[tx+5*tw,ty - th*i,tw,th],'string', ...

init_vel{3*i-2}, ...

'FontSize',10);

h.vel(3*i-1) = uicontrol('style','edit','units','pixels', ...

'position',[tx+6*tw,ty - th*i,tw,th],'string', ...

init_vel{3*i-1}, ...

'FontSize',10);

h.vel(3*i) = uicontrol('style','edit','units','pixels', ...

'position',[tx+7*tw,ty - th*i,tw,th],'string', ...

init_vel{3*i}, ...

'FontSize',10);

end

%% HEADER SETUP

fsize = 13;

ty = 278;

th = 20;

uicontrol('style','text','units','pixels', ...

'position',[tx,ty,tw,th],'string', ...

'MASS',...

'FontWeight','Bold','FontSize',fsize,'FontAngle','italic')

uicontrol('style','text','units','pixels', ...

'position',[tx+1*tw,ty,tw,th],'string', ...

'RADIUS',...

'FontWeight','Bold','FontSize',fsize,'FontAngle','italic')

uicontrol('style','text','units','pixels', ...

'position',[tx+2*tw,ty,tw,th],'string', ...

'X-POS',...

'FontWeight','Bold','FontSize',fsize,'FontAngle','italic')

uicontrol('style','text','units','pixels', ...

'position',[tx+3*tw,ty,tw,th],'string', ...

'Y-POS',...

'FontWeight','Bold','FontSize',fsize,'FontAngle','italic')

MATLAB CODE (setup menu)uicontrol('style','text','units','pixels', ...

'position',[tx+4*tw,ty,tw,th],'string', ...

'Z-POS',...

'FontWeight','Bold','FontSize',fsize,'FontAngle','italic')

uicontrol('style','text','units','pixels', ...

'position',[tx+5*tw,ty,tw,th],'string', ...

'X-VEL',...

'FontWeight','Bold','FontSize',fsize,'FontAngle','italic')

uicontrol('style','text','units','pixels', ...

'position',[tx+6*tw,ty,tw,th],'string', ...

'Y-VEL',...

'FontWeight','Bold','FontSize',fsize,'FontAngle','italic')

uicontrol('style','text','units','pixels', ...

'position',[tx+7*tw,ty,tw,th],'string', ...

'Z-VEL',...

'FontWeight','Bold','FontSize',fsize,'FontAngle','italic')

%% COLUMN SETUP

th = 30;

for i = 1:6

uicontrol('style','text','units','pixels', ...

'position',[tx-tw,-8+ty-i*th,tw,th],'string', ...

bodies(i),...

'FontWeight','Bold','FontSize',12,'FontAngle','italic')

end

%% NOTE

th = 58;

tw = 315;

tx =(box_width-tw)/5-30;

ty = 25;

h.p = uicontrol('style','text','units','pixels',...

'position',[tx,ty,tw,th],'string','Units for mass are in kilogram. Units for position & radius are in meters.

Units for velocity are in meters per second.',...

'callback',@s_call,'FontWeight','Bold','FontSize',12);

%% BUTTON CREATION

th = 28;

tw = 365;

tx =(box_width-tw)/4*3;

ty = 35;

h.p = uicontrol('style','pushbutton','units','pixels',...

'position',[tx,ty,tw,th],'string','RUN SIMULATION',...

'callback',@s_call,'FontWeight','Bold','FontSize',12);

uiwait(h.f)

%% BUTTON FUNCTION

function s_call(varargin)

m = str2double(get(h.m,'String'));

assignin('base','m',m)

pos = str2double(get(h.pos,'String'));

assignin('base','x0',pos)

vel = str2double(get(h.vel,'String'));

assignin('base','v0',vel)

assignin('base','G',6.67408e-11)

assignin('base','bodies',bodies)

radius = str2double(radius);

assignin('base','radius',radius)

close

end

end

Colin Miller -BackupJanuary 30, 2020

Mission Design Group: Communication Satellites (Placement of satellites, worst case power scenarios, stability analysis research)

Eclipse Code

function [time] = AAE450_EclipseLengthStat(r, mu, day);

% takes in radius of body, gravitational parameter of body and length of

% day of body and returns time in eclipse

% code written with km, s, kg, and radians

a = (mu*day^2/(4*pi^2))^(1/3) % semi-major axis

halftheta = asin(r/a); % angles in radians

theta = 2*halftheta;

orbvel = sqrt(mu/a); % orbital velocity

arclength = a*theta; % length of curve in eclipse

time = arclength/orbvel;

Eclipse Code Background

• Eclipse code assumes the planetary body to be a perfect sphere, assumes the shadow cast by the

body to be a cylinder of radius equal to that of the body, and assumes the orbit of the satellite to be

perfectly stationary (e=0, i=0, a=constant, Period = day)

• Code finds angle swept by shadow (eclipse) of planet on stationary orbit (Θ)

• Angular velocity of satellite is constant (⍵=constant)

• Time in eclipse is therefore t = Θ/⍵

References

[1] “Earth Fact Sheet.” NASA, NASA, nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html.

[2] “Mars Fact Sheet.” NASA, NASA, nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html.

[3] Silva, Juan J., and Pilar Romero. “Optimal Longitudes Determination for the Station Keeping of

Areostationary Satellites.” Planetary and Space Science, Pergamon, 17 Feb. 2013,

www.sciencedirect.com/science/article/pii/S0032063313000044#bbib11.

[4] Romero, Pilar, and Jose M. Gambi. “Optimal Control in the East/West Station-Keeping Manoeuvres

for Geostationary Satellites.” Aerospace Science and Technology, Elsevier Masson, 1 Oct. 2004,

www.sciencedirect.com/science/article/pii/S1270963804000987.