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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3.1 Narrative
In this, the third of four aerospace-based S.T.E.M. project, students will use the Bigelow Aerospace BA-330 and BA-2100 space station pressurized modules to launch and assemble a space station in Low Earth Orbit (LEO). Students will calculate the total pressurized volume, the total weight, the crew size, and the total cost of launching into space and setting up their own space station.
Time Frame
About 4.5 weeks
(22 days)
Aerospace Problems
Space Station Cost
Space Station Weight
Space Station Volume
Space Station Crew
Mathematics Used
Matrices
Material List
A connection to the Internet
Google GMail account
Science Topics
Physics, Aerospace
Activating Previous Learning
Basic Mathematics
Scientific Calculator
Essential Questions
- Who are the many space station pioneers?
- What is a space station?
- Where can a Bigelow space station be spotted in the night sky?
- When will the first commercial Bigelow space station be flown?
- Why do people want to live on a space stations in orbit
- How many people can live on a space station?
- 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 BA-330 Habitat Specifications
The BA-2100 Habitiat Specifications
The Bigelow Space Station and its Components and Definitions
Additional Terms and Definitions
3. Explain
Launch Constraints
4. Elaborate
Other Space Station Examples
5. Exercise
Space Station Parameters
Space Station Design Scenario
6. Engineer
The Engineering Design Process
SMDA Space Station 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 space station design using pencil, paper, and scientific calculator. Students then use what they have learned to create a Space Mission Design App (SMDA), designed according to the Engineering Design Process, that will be used for real-world spacecraft.
We will be using the products from Bigelow Aerospace, which makes inflatable habitat modules that once placed into orbit, well, inflate. This allows for a greater volume of space inside for the crew. It has solar panels for electrical power and radiators to dispose of waste heat. It even has windows!
Students will use spreadsheet software to create the app and will use slide-show software for their presentations. They will also create a document of their experiences engineering the SMDA and presenting their findings to the rest of the class.
Constants
(None)
Input
Total BA 2100 Modules
Total BA 330 Modules
Total PB/DN Modules
Output
Total BA 2100 Stacks
Total BA 330 Stacks
Total PB/DN Stacks
Total SpaceX Falcon Heavy
Total NASA SLS Block I
Total Weight of the space station
Total Crew Size
Total Cost of the space station
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Visual Learning
Bigelow Aerospace has a promotional video showing the Genesis of their Genesis (sorry) and highlighting their BA-330 inflatable space station module.
Bigelow has built and placed into Low Earth Orbit (LEO) two flight test articles called Genesis I and Genesis II. They are still in orbit, and you can track them in real-time at the following links:
Bigelow Genesis I
(NORAD Tracking ID Number: 29252)
Bigelow Genesis II
(NORAD Tracking ID Number: 31789)
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Continued...
3.2 Vocabulary
BA-330 Module BA-300 Stack BA-2100 Module BA-2100 Stack
Crew Size Crew Volume Docking Node (DN) Expendable Launch Vehicle
Falcon Heavy PB-DN PB-DN Stack Pressurized Volume
Propulsion Bus (PB) SLS Block IA (SLS-IA) Space Station
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3.3 Analysis
To launch these excellent habitat modules into space, we obviously need a launch vehicle. Shopping around for what’s available to use to launch our city, we find two Expendable Launch Vehicles (ELV). These rockets haven’t been built yet, but so long as funding continues they will be... one day. The two ELVs are the SLS I-A and the Falcon Heavy.
Since the SLS I-A ELV can carry 105,000 kg into Low Earth Orbit (LEO), and one BA-2100 weighs 100,000 kg, it can carry only one unit at a time. We will call this the “BA-2100 Stack.”
The Falcon Heavy ELV can lift 53,000 kg to LEO. Each BA-330 weighs 25,000 kg, so it can carry 2 units at a time (assuming, of course, that it could fit in a payload shroud). We will call this the “BA-330 Stack.”
The PB-DNs each weigh 17,000 kg, so 3 units will fly on the Falcon Heavy ELV to LEO. This will be called the “PB-DN Stack.”
BA-2100 Stack:
Cost: (1) SLS IA + (1) BA-2100 = $750M + $500M = $1,250M
Weight: (1) BA-2100 = (1) 100,000 kg = 100,000 kg
Volume: (1) 2,100 m3 = 2,100 m3
Crew: (1) 16 = 16 Astronauts
BA-330 Stack:
Cost: (1) Falcon Heavy + (2) BA-2100 = $150M + (2) $125M = $400M
Weight: (2) BA-330 = (2) 25,000 kg = 50,000 kg
Volume: (2) 330 m3 = 660 m3
Crew: (2) 6 = 12 Astronauts
PB-DN Stack:
Cost: (1) Falcon Heavy + (3) PB-DN = $150M + (3) $75M = $375M
Weight: (3) 17,000 kg = 51,000 kg
It now becomes an easy matter to compute the specifications of any space station design that we choose. If a design calls for using four BA-330 modules, then two BA-300 Stacks are needed. Note, however, that the space station design does have constraints. For instance, the number of BA-300 habitat modules must be even, and the number of PB-DNs must be a multiple of 3.
To summarize,
Interior view of the BA-330 module.
BA-2100 Stack
- $1,250M USD
- 100,000 kg
- 2,100 m^3
- 16 Astronauts
BA-330 Stack
- $400M
- 50,000 kg
- 660 m^3
- 12 Astronauts
PB-DN Stack
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Everything can be put into a matrix:
The number of each stack that is needed can also be written as a matrix:
- Number of Stacks = [BA-2100 Stacks BA-330 Stacks PB-DN Stacks]
However, the Number of Stacks will have to first be calculated, since the number of BA-330s and PB-DNs must be multiples of 2 and 3 respectfully.
Therefore, given:
- Number of BA-2100s
- Number of BA-300s
- Number of PB-DNs
So,
- Number of Stacks = [Number of BA-2100 Number of BA-300/2 Number of PB-DN/3]
Since the Number of Stacks is a [1 x 3] matrix, and the Stack Information is a [3 x 4] matrix, we can perform the dot product of the 2 matrices, which is represented as:
- [1 x 3] X [3 x 4] = [1 x 4]
Number of Stacks X Stack Information = Total
where Total is represented as:
- Total = [Cost Weight Volume Crew]
So let’s build us a city in space, shall we?
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Example
The folks at Bigelow Aerospace have made it easy for us: they’ve already designed a very nice space station! It’s called the “Hercules Resupply Depot,” but we’ll just call it “Home.” Thanks, Bigelow!
As you can see from the poster, we’ll need three BA-2100s, six BA-330s, and three PB-DNs to complete the design. We can therefore calculate how many “stacks” we’ll need:
The Hercules space station.
(3) BA-2100 = (3) BA-2100 Stacks
- (3) $1,250M = $3,750M
- (3) 100,000 kg = 300,000 kg
- (3) 2,100 m3 = 6,300 m^3
- (3) 16 Crew = 48 Crew
(6) BA-330 = (3) BA-330 Stacks
- (3) $400M = $1,200M
- (6) 25,000 kg = 150,000 kg
- (6) 330 m3 = 1,980 m^3
- (6) 6 Crew = 36 Crew
(3) PB-DN = (1) PB/DN Stack
- (1) $375M
- (3) 17,000 kg = 51,000 kg
Adding everything up we get:
- Total Cost: $5,325M
- Total Weight: 501,000 kg
- Total Volume: 8,280 m^3
- Total Crew: 84 Astronauts
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The calculations, however, are waaaaaay easier to handle using Matrix Notation:
Notice that our volume is close to the 8,300 cubic meters advertised in the Hercules image.
The amount of space that each astronaut gets can now be calculated.
Crew Volume =Total Volume/Total Crew
= 8280/84
= 98.59m^3 per astronaut.
As we can see, the Resupply Depot “Hercules” has the following specifications:
- Total Cost: $5,325M USD
- Total Weight: 501,000 kg
- Total Volume: 8,280 m^3
- Total Crew: 84 Astronauts
- Total Crew Volume: 99 m^3
So this is a space station that weighs half a million kilograms, has over eight thousand cubic meters of habitable space, can house 84 people, with almost one hundred cubic meters of elbow room for each person, can re-boost its orbit, and costs a little over five billion dollars.
Top view of the Hercules space station.
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R.A.F.T. Writing
Role: Teacher
Audience: Middle School students
Format: Five paragraph essay
Topic: The Apollo Skylab. Who were the astronauts that flew the missions? How many days did each crew stay? What was unique about their missions? What was in common with all the missions? How does the Skylab differ from the space station presented in this textbook? How are they the same? Why even bother to build a space station anyway?
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3.4 Space Station 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
TotBA2100Wt=InputNumBA2100*BA2100Wt
TotBA2100Vol=InputNumBA2100*BA2100Vol
TotBA2100Crew=InputNumBA2100*BA2100Crew
TotBA2100Cost=InputNumBA2100*BA2100Cost
TotBA330Wt=InputNumBA330*BA330Wt
TotBA330Vol=InputNumBA330*BA330Vol
TotBA330Crew=InputNumBA330*BA330Crew
TotBA330Cost=InputNumBA330*BA330Cost
SpaceStationVol=TotBA2100Vol+TotBA330Vol
SpaceStationCrew=TotBA2100Crew+TotBA330Crew
SpaceStationCrewVol=SpaceStationVol/SpaceStationCrew
Space Station Design App
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3.5 Chapter Test
I. VOCABULARY
Match the aerospace term with its definition.
1. BA-330 Module
2. Crew Size
3. Crew Volume
4. Falcon Heavy
5. Propulsion Bus (PB)
A. The number of astronauts aboard a spacecraft or space station.
B. A Bigelow habitat module that has a pressurized volume of 330 cubic meters, weighs 25,000 kg, and can hold 6 crew.
C. The unit used to reboost the space station due to orbital decay.
D. The total pressurized volume for each crew member.
E. An ELV from SpaceX that can lift 53,000 kg into Low Earth Orbit.
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II. MULTIPLE CHOICE
Circle the correct answer.
6. The name of the Bigelow habitat module is also the volume (in cubic feet) of the habitable interior of the module.
A. TRUE B. FALSE
7. Bigelow habitat modules come complete with docking ports, solar panels, radiators, and a breathable atmosphere.
A. TRUE B. FALSE
8. What is the habitable volume of a space station design that consists of one BA-2100 module and two BA-330 modules?
A. 2,760 in3 B. 2,760 ft3 C. 2,760 m3 D. Cannot be determined
9. A space station design calls for eight BA-330 habitat modules. How many BA-330 Stacks will be needed?
A. Two B. Four C. Six D. Cannot be determined
10. The Crew Volume can be found by dividing the space station ______ into the total number of space station crew
A. Volume B. Weight C. Crew Size D. Cannot be determined
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III. CALCULATIONS
A space station design calls for 6 BA-330 modules and 3 PB/DNs.
11. How many SLS IA ELVs will be required?
12. How many Falcon Heavy ELVs will be required?
13. How many BA-2100 Stacks will be required?
14. How many BA-330 Stacks will be required?
15. How many PB/DN Stacks will be required?
16. What is the weight of this space station?
17. What is the habitable volume of this space station?
18. What is the number of crew of this space station?
19. What is the Crew Volume of this space station?
20. What is the total cost of this space station?
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IV. WRITING
Write a one paragraph essay on the topics below.
21. Explain how to find the total habitable volume of a Bigelow space station simply by knowing how many of each module it has.
22. Explain why (or why not) three PB/DNs can be launched using a Falcon Heavy ELV.
23. Explain why (or why not) two BA-2100 habitat modules can be launched using the SLS IA ELV.
24. Explain how to calculate the total pressurized volume for each crew member (Crew Volume).
25. Write a short story about what it would feel like to float weightlessly inside of a Bigelow space station, while gazing at the curvature of the Earth as it flies around the world.
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CLICK HERE TO OPERATE THE SPACE STATION DESIGN APP
CLICK HERE FOR THE TEACHER SLIDE SHOW
(coming soon)
CLICK HERE FOR THE STUDENT HANDOUT
(coming soon)
CLICK HERE FOR THE SPACE STATION DESIGN PARAMETERS HANDOUT
(coming soon)
CLICK HERE TO GO TO THE EXAMPLE RUBRIC STUDENT WEBSITE
(coming soon)
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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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