Note to readers: This lesson plan, as well as all the other similar articles we've written, may appear, to some folks, like the next thing to Greek language (the math stuff), but bear in mind these S.T.E.M. lessons are really all about the students. Ergo, preparing high school students for the real rocketry world using real math. That being said, we invite you into their world, their minds, and let's support them in this heroic endeavor, because these students are truly going where no high school student has ever gone before.
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8.1 Narrative
In this, the fourth and final part of a four-part interconnected astronautics-based S.T.E.M. project, students will design a mission that will land on the moon! Students will also calculate the total weight of the Engine Module. The Crew Module is attached to the Engine Module to form a complete spacecraft. Finally, a Landing Kit is attached to form the Lunar Lander. The ΔV information from Chapter 5, the Crew Module weight information from Chapter 6, and the Propellant information in Chapter 7 will be used in this project.
Time Frame
About 4 weeks
Astronautics Problems
Lunar Lander Exhaust Velocity
Lunar Lander Empty Weight
Lunar Lander Gross Weight
Lunar Lander Propellant Weight
Return On Investment (R.O.I.)
Mathematics Used
Finance, Basic Algebra
Material List
A connection to the Internet
Google GMail account
Science Topics
Physics, Astronautics
Activating Previous Learning
Periapsis ΔV (mps)
Apoapsis ΔV (mps)
ΔV Budget (mps)
Round-Trip ΔV Budget (mps)
Transfer Time (days)
Round-Trip Transfer Time (days)
Mission Duration (days)
Crew Size (people)
Crew Module Weight (lbs)
Essential Questions
- What is the ΔV requirement for a landing on the lunar surface from lunar orbit?
- What is the ΔV requirement for a taking off from the lunar surface back to lunar orbit?
- Why is it important to have a Return On Investment (R.O.I.)?
- How does the the amount of lunar material available for sale on the open market effect the selling price of the lunar material?
- Who are are some of the pioneers in lunar landing design?
- Wait. I have to do science and technology and engineering and mathematics, all at the same time?
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This lesson is powered by E^8:
1. Engage
Lesson Objectives
Lesson Goals
Lesson Organization
2. Explore
The Boeing Space Tug Study
The Lunar Lander Kit
Landing Legs
Payload Tray
Additional Terms and Definitions
3. Explain
Basic Spacecraft Systems
The Rocket Nozzle
Extended
Retracted
4. Elaborate
Other Lunar Lander Examples
5. Exercise
Lander Lander Payload and Payback Example
Lander Lander Payload and Payback Scenario
6. Engineer
The Engineering Design Process
SMDA Spacecraft EM Propellant Plan
Designing a Prototype
SMDA Software
7. Express
Displaying the SMDA
Progress Report
8. Evaluate
Post Engineering Assessment
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Lesson Overview
Students first learn the basics of lunar landing mission design using pencil, paper, and scientific calculator. Students then use what they have learned to create a space mission app designed according to the Engineering Design Process, that will be used for real-world spacecraft. They will use spreadsheet software to create the app.
The spreadsheet will be developed over the course of four (4) S.T.E.M. projects, with each project dealing with different aspects of space mission design.
The assigned space mission will include four (4) space vehicles or satellites that are named after famous astronauts. Students will research and write a very short biography (one slide) about these heroic individuals, one for each of the 4 projects.
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Constants
Unit Conversion (carats/lbs)
Lunar Investment (USD)
PDI delta V (kps)
PAI delta V (kps)
Weight of Lander Kit (lbs)
Weight of Lunar Tray (lbs)
Input
TEI Orbital Altitude (km)
EOI Orbital Altitude (km)
Average Selling Price (USD)
Output
Lander Gross Weight (lbs)
Propellant Weight (lbs)
Excess Propellant (lbs)
LH2 Weight (lbs)
LO2 Weight (lbs)
Weight of Lunar Material (lbs)
Gross Income (USD)
Net Income (USD)
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Visual Learning
Back in the late 1960s, human walked on a celestial body other than Earth. We have not been able to to replicate the feat since.
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Continued...
8.2 Vocabulary
Lunar Lander Kit Lunar Investment Lunar Material
Lunar Payload Tray Powered Ascent Initiation (PAI) Powered Descent Initiation (PDI)
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8.3 Analysis
We will be using data from a spacecraft design that was completed but never constructed. The Boeing Space Tug study was finished in 1971. It called for a piloted rocket system that would operate in Low Earth Orbit (LEO). An un-piloted version of the rocket system would have carried satellites and other sensors to higher earth orbits.
A CM/EM is brought up to the space station and a Lunar Lander Kit is attached to it.
The Boeing Space Tug with a Lunar Lander Kit and a Lunar Payload Tray
The Lunar Lander Kit contains the following items:
Landing Legs Kit
Landing RADAR Kit
Auxiliary Power Supply Kit
RCS Booster Kit
Extra Insulation
Extra Micrometeoroid Shielding
Total Weight (estimated): 896 lbs.
In addition, a tray resembling a doughnut is attached around the bottom part of the vehicle below the landing legs. Total Weight: 1,500 lbs.
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We will again be using the Rocket Equation (Chapter 6), solved for propellant, to calculate the rocket fuel and oxidizer needed to go from one orbit to another.
EM-PROPELLANT = m1(e^(ΔV/VEXH) - 1)
Instead of going from one orbit to another, we will be going from lunar orbit down to the lunar surface.
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We will be using the Reaction Engines, Ltd., Skylon spacecraft (Chapter 2) to shuttle back and forth between Earth and Space Station Alpha (Chapter 3) in Low Earth Orbit LEO. The Skylon spaceliners are operated out of Spaceport America (Chapter 4) in New Mexico, USA.
The lander is transported to the Moon, where it proceeds down to the lunar surface. The crew fills the Tray with lunar material. After the containers have been filled, the crew lifts off from the lunar surface and connects to another transport. The Lander with its lunar material combination heads home.
The Stack
Once the crew returns to Space Station Alpha, a Skylon transports the containers back to Earth. A passenger Skylon returns the triumphant lunar crew home.
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Example
A consortium of astronautics companies have raised $27.14B USD to invest in a space mission comprising of a Lunar Lander that is tasked to bring back Lunar Material from the surface of the Moon.
You are the Mission Commander.
Your vehicle is a Boeing Space Tug, outfitted with a Lunar Lander Kit and a Payload Tray. The Command Module (CM) weighs in at 4,345 kg, and the science mission payload is 4,761 kg, including the Payload Tray. The science payload will be left on the lunar surface, and the equivalent weight in lunar material will be brought back. This material has an estimated value at $1,500 USD per carat.
Calculate the propellant needed to land on the Moon and lift-off back into lunar orbit, the excess propellant, the amount of Lunar Material brought back, the Gross Weight of the Lander, the Gross Income after all the Lunar Material has been sold, the taxable income from the sale, and finally, the Return on Investment.
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Using the the equations from Chapter 7, we see that we need to use the Rocket Equation to calculate the needed propellant. Also, since the rocket nozzle needs to be retracted in order to make room for the landing, the Specific Impulse of the rocket drops by 3 seconds.
Assigning labels to the inputs, and converting everything to S.I. units, we get:
Lunar Investment = $24,000,000,000 USD
Propellant = 39,800 lbs = 18,053 kg
CM = 4,327 kg
PDI = 2,181 mps
PAI = 1,890 mps
g0 = 9.80665 m/s2
Science Payload = 4,761 kg
Payload Tray = 1,500 lbs = 680 kg
Lander Kit = 896 lbs = 406 kg
Selling Price = $1,500/carat = $7,500,000/kg
The output becomes:
Rocket Engine:
Lander ISP = (ISP - 3) s
= 460 - 3
= 457 s
Landing vEXH = Landing ISP g0
= (457)(9.806650
= 4,482 mps
Landing v Budget = PDI + PAI
= 2181 + 1890
= 4,071 mps
Landing Reserve v = 0.75% Landing v Budget
= 0.0075(4071)
= 31 mps
Landing v = Landing v Budget + Landing Reserve v
= 4071 + 31
= 4,102 mps
Lunar Material:
Lunar Material = Science Payload - Payload Tray
= 4761 - 680
= 4,081 kg
Propellant:
m1 = 2,545 + CM + Lunar Material + Payload Tray + Lander Kit
= 2545 + 4327 + 4081 + 680 + 406
= 12,057 kg
LanderPROPELLANT = m1*(e^(Landing Δv/Landing vEXH) - 1)
= (12057)(e^41024482 - 1)
= 18,052 kg
Excess Landing Propellant = Propellant - LanderPROPELLANT
= 18053 - 18052
= 1 kg
Gross Weight:
m0 = m1 + Landing Propellant
= 12057 + 18052
= 30,108 kg
Financial:
Gross Income = Lunar Material * Selling Price
= 4081 * 7500000
= $30,604,579,769 USD
Taxable Income = Gross Income - Lunar Investment
= 30604579796 - 27140000000
= $3,464,579,796 USD
R.O.I. = (Taxable IncomeLunar / Investment x 100)%
= 3464579796 / 27140000000 x 100
= 12.77%
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So, in conclusion,
Propellant Needed: 18,052 kg
Lunar Material: 4,081 kg
Lunar Lander Gross Weight: 30,108 kg
Gross Income: $30,604,579,976 USD
Taxable Income: $3,464,579,976 USD
R.O.I: 12.77%
The Apollo 17 Lunar Module on the surface of the Moon.
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R.A.F.T. Writing
Role: Teacher
Audience: Middle School students
Format: Five paragraph essay
Topic: The Apollo Lunar Module (LM). Who were the astronauts that flew the missions? Where on the Moon did they land? What was unique about their missions? What was in common with all the missions? How does an Apollo space mission differ from the space mission presented in this textbook? How are they the same? Why even bother to explore the Moon anyway?
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8.4 Space Mission Design App
Given the above information, we can use a spreadsheet to enter equations and data to create a Space Mission Design App (SMDA).
The S.T.E.M. for the Classroom/Google App is broken down into four (4) parts:
1. Input/Output Interface
2. Graph
3. Constants
4. Calculations
The App can now be developed.
Sample Open Source Code
Once the cells have been named referencing cells is easy.
CALCULATIONS
Coming Soon...
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Sample App Interface Design
The Lunar Lander Space Mission App
8.5 Chapter Test
I. VOCABULARY
Match the astronautics term with its definition.
1. Lunar Investment
2. Lunar Lander Kit
3. Lunar Payload Tray
4. Powered Ascent Initiation
5. Powered Descent Initiation
A. The amount of money needed to fully fund a mission to the Moon.
B. Includes the lunar landing legs, infrastructure, landing radar, etc.
C. The tray that transports payload to and from the lunar surface.
D. The lift off burn from the lunar surface to lunar orbit.
E. The landing burn from lunar orbit to the lunar surface.
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II. MULTIPLE CHOICE
Circle the correct answer.
6. The propellant needed to land on the Moon is equal to the propellant needed to take off again.
A. TRUE B. FALSE
7. The ΔV Budget for a landing on the moon is just as much as going from the Earth to the Moon.
A. TRUE B. FALSE
8. Collectors can purchase Lunar Material in the form of ______ that has fallen to Earth.
A. Meteors B. Meteorites C. Regolith D. Cannot be determined
9. Lunar Material that has been brought back to Earth and sold for $1,000/carat has the equivalent price of ______ per gram.
A. $1,000 B. $5,000 C. 10,000 D. Cannot be determined
10. By retracting the nozzle of the RL10 rocket engine, the Specific Impulse (ISP) of the engine decreases by approximately ______ seconds.
A. Two (2) B. Three (3) C. Zero (0) D. Cannot be determined
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III. CALCULATIONS
You have invested $22.35B (USD) in a trip to the Moon. A Boeing Space Tug with a Lunar Lander Kit and Lunar Payload Tray has been selected to be used to deposit geologic sensors on its surface, and to load the equivalent weight of the sensors in Lunar Material to be sold to pay for the trip. The PDI ΔV is 2,181 mps and the PAI ΔV is 1,890 mps. The payload for this mission is a standard 10-Crew Boeing Space Tug Crew Module, which weighs 9,540 lbs, and a standard Lunar Sensor Package, which weighs 9,500 lbs. Assume a Propellant Reserve of 1% of the Round-Trip ΔV Budget, and that the Lunar Material has an average selling price of $1,500/carat.
11. What is the new Specific Impulse of the rocket engine with the rocket nozzle retracted?
12. What is the Exhaust Velocity (VEXH) of the rocket engine?
13. What is the weight of the Propellant Reserve in S.I. units?
14. What is the mission payload in S.I. units?
15. What is the Empty Weight (m1) of the lunar lander?
16. What is the Gross Weight (m0) of the lunar lander?
17. What is the amount of propellant needed for this Moon landing mission?
18. What is the amount of Lunar Material in carats?
19. What is the Gross Income from the Lunar Investment?
20. What is the Taxable Income from the Lunar Investment?
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IV. WRITING
Write a one paragraph essay on the topics below.
21. Explain why it is as difficult to get into and out of the Moon’s gravity well as it is to fly to the Moon from Low Earth Orbit.
22. Explain why creating a Lunar lander Kit to be attached to a Boeing Space Tug is easier and more cost effective than designing and building a separate landing vehicle.
23. Explain why Lunar Material would be a rare commodity if mined and transported back to Earth and sold on the open market.
24. Explain how to calculate how much an object would weigh on the lunar surface.
25. Write a short story about what it would feel like to land on the Moon and walk on its surface, experiencing the one-sixth gravity of the lunar environment.
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CLICK HERE TO OPERATE THE ORBITAL PAYLOAD SPACEFLIGHT APP
CLICK HERE FOR THE TEACHER SLIDE SHOW
(coming soon)
CLICK HERE FOR THE STUDENT HANDOUT
(coming soon)
CLICK HERE FOR THE ORBITAL PAYLOAD SPACE MISSION DESIGN PARAMETERS HANDOUT
(coming soon)
CLICK HERE TO GO TO THE EXAMPLE RUBRIC STUDENT WEBSITE
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END OF DIARY
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A (partial) list of future topics in the series:
- S.T.E.M. Education For the 21st Century and Beyond
An Introduction to S.T.E.M. For the Classroom
- Go Where No Student Has Gone Before
A more indepth discussion of what we’re trying to accomplish.
- Suborbital Spaceflight - Quadratic Equations
Students calculate the height that SpaceShipTwo reaches space.
- Orbital Payload - Quadratic and Linear Equations
Students calculate the payload that the R.E.L. Skylon can place into Low Earth Orbit (LEO).
- A City in the Sky - Matrices
Students design a space station, and find the cost to place it into orbit. They also find the total volume and the number of crew that can safely occupy the station.
- Landing is the Hardest Thing to Do - Trigonometry
Students calculate the ground speed and altitude of a spacecraft returning from space.
- Delta V and Transfer Time - Square Root Equations
Students calculate the change in orbital velocity needed to go from a lower orbital altitude to a higher orbital altitude and find the time it takes for the maneuver.
- Spacecraft Weight Analysis - Linear Equations
Students find the weight of a real crew capsule that was designed in 1971 and determine the mission duration and the number of crew that can fly the mission.
- The Rocket Equation - Exponential Equations
Students determine the amount of cryogenic propellant needed to fly a space mission using an engine module designed in 1971.
- Fly Me to the Moon - Finance
Students calculate the amount of cryogenic propellant needed to land on the Moon and find the amount of profit you can make by selling moon rocks.
- Delta V and the Gravity of the Situation - Square Root Equations
Where we ask the question: does the mathematics add up to what the astronauts are depicted doing?
- The Thrill(e) in the Rille - Trigonometry
Students calculate the amount of rope needed for Apollo astronauts to safely descend into a lunar canyon.
- The Bone of Contention - Proportions
Students determine the identities of fictitious astronauts who have perished on a lunar landing mission using their recovered femur bones.
- TBA - Mathematics Topic is also TBA
Lesson plans that are still in the works...
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