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.
::
6.1 Narrative
In this, the second of a four-part interconnected astronautics-based S.T.E.M. project, students will calculate the total weight of the Crew Module, the place where astronauts live while conducting a space mission. Students will also calculate the number of astronauts needed to conduct the space mission. The Crew Module weight and the Crew Size use the Mission Duration output from the previous chapter.
Time Frame
About 4 weeks
(about 22 days)
Astronautics Problems
Crew Module Static Weight (kg)
Crew Module Dynamic Weight (kg)
Crew Size (astronauts)
Mathematics Used
Linear Equations
Basic Algebra
Material List
A connection to the Internet
Google GMail account
Science Topics
Physics, Astronautics
Activating Previous Learning
Basic Mathematics
Scientific Calculator
Essential Questions
- What is the relationship between the time it takes to complete a mission and the number of astronauts?
- Why is it important to determine the weight of a spacecraft?
- How many astronauts can fit into a spacecraft?
- How does the duration of a mission effect the number of crew a spacecraft can carry?
- Who are are some of the pioneers in spacecraft design?
- Wait. I have to do science and technology and engineering and mathematics, all at the same time?
::
This lesson is powered by E^8:
1. Engage
Lesson Objectives
Lesson Goals
Lesson Organization
2. Explore
The Boeing Space Tug Study
The Crew Module (CM)
The CM Weight
The Crew Size
Additional Terms and Definitions
3. Explain
Basic Spacecraft Systems
The CM Static Weight
The CM Dynamic Weight
4. Elaborate
Other Crew Module Examples
5. Exercise
CM Weight and Crew Size Parameters
CM Weight and Crew Size Scenario
6. Engineer
The Engineering Design Process
SMDA Spacecraft CM Weight and Crew Size Plan
Designing a Prototype
SMDA Software
7. Express
Displaying the SMDA
Progress Report
8. Evaluate
Post Engineering Assessment
::
Lesson Overview
Students first learn the basics of crew module 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 S.T.E.M. projects, with each project dealing with different aspects of space mission design.
The assigned space mission will include four space vehicles or satellites that 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.
Constants
none
Input
Mission Duration (Days)
Spacecraft Systems Weight (lbs)
Output
Spacecraft Crew Systems Weight (kg)
Spacecraft EC/LSS Weight (kg)
Spacecraft Expendables Weight (kg)
Spacecraft Contingency Weight (kg)
Spacecraft Static Weight (kg)
Spacecraft Dynamic Weight (kg)
Spacecraft Total Weight (kg)
Crew Size (astronauts)
::
Visual Learning
Crew modules (sometimes called crew capsules) are still being designed today. The Boeing Company has one called the CST-100.
::
Continued...
6.2 Vocabulary
CM Communications CM Contingency CM Controls CM Crew Systems
CM Dynamic Weight CM EC/LSS CM Electrical Power CM Expendables
CM Instrumentation CM Misc. Equipment CM Static Weight CM Structure
CM Weight Crew Capsule Crew Module (CM) Crew Size
::
6.3 Analysis
The best thing for the students to construct for the Engineering part of S.T.E.M. is an actual spaceship. Obviously, students cannot build a real spaceship - not because they don't have the smarts to do it, but because they don't have the funding to do it! However, we can do the next best thing: simulate a space mission using a real spacecraft design using real spacecraft numbers.
The Apollo Command Module
And the Boeing Space Tug Study written in 1971 is that very spacecraft! The diameter of the vehicle was just under 15 ft. and would have fit perfectly in the Space Shuttle, which is what it was designed to do. The study was funded, but, alas, the spacecraft itself was not. Hence, it was never built. But we can take their misfortune (and ours, as a society) and make something good out of it: we get to design real space missions using a real spaceship!
This Space Tug was envisioned to have a Crew Module and an Engine Module, similar to the Apollo Command/Service Module (CSM).
We will extract information from the Boeing Study, and use it to create an equation that yields the CM weight, then the number of astronauts that can be safely carried on a space mission.
This chapter will use the piloted section, or Crew Module (CM) of the system, which is displayed below (note the similarity with Boeing's current CST-100 design). Spacecraft system weight information is given in the upper right corner of the image below and described at the bottom part of the image.
A Boeing Crew Module circa 1971
We can see from the data in the image above that
15 Crew = 2 Day Mission
3 Crew = 50 Day Mission
Note that we make the Mission Duration (MD) the independent variable in the linear equation.
If we make the first number x and the second number y, we get two points, namely (2, 15) and (50, 3). We can use the formula for slope and the y-intercept to write the linear equation in slope-intercept (y=mx+b) form.
m = (y2 - y1) / (x2 - x1) = (3 - 15) / (50 - 2) = -1248 = -0.25
and
b = y1 - m * x1 = 15 - (-0.25)(2) = 15 + 0.5 = 15.5
Therefore, y = mx + b becomes
and
(Note: This calculation must be rounded down to the nearest crew. It is impolite to have a partial crew member on a spaceflight)
The CM habitable Volume-to-Crew ratio is simply the total volume of the CM divided by the Crew Size.
::
The other spacecraft component's linear equations can be found in the same manner. For example,
2 Day Mission = 2,497 lbs Structure
50 Day Mission = 2,497 lbs Structure
The points (2, 2497) and (50, 2497) yields a horizontal line, which means that this spacecraft component remains the same (i.e., constant) weight regardless of the MD.
Therefore,
Crew Systems yields (2, 3689) and (50, 1705), and so forth, until the entire list has been converted.
The Static Weight is the sum of all the spacecraft components that are constant, and the Dynamic Weight is the sum of all the spacecraft components that change when the MD changes. The total Weight of the CM is the sum of the two weights.
- WeightSTATIC = CMSTRUCTURE + CMELECTRIC + CMCOMM + CMINSTR + CMCONTROL + CMMISC
- WeightDYNAMIC = CMSYSTEMS + CMEC/LSS + CMEXP + CMCONTROL
- WeightCM = WeightSTATIC + WeightDYNAMIC
The weight needs to be converted to S.I. units; however, it is probably easier to keep the weight in pounds until the end, and then convert the units.
- WeightCrewModule = WeightCM / 2.2
::
Example
A wayward satellite requires repairs and to have some electronic parts replaced. The satellite is in a stable orbit and a repair vehicle is ready to go to the satellite. The same orbital parameters used in the previous chapter will be used here and it is estimated that the crew will need a total of 10 days to conduct all the necessary repairs and complete their mission. What is the size of the crew needed for this space mission and what is the weight of the Crew Module?
The number of astronauts needed is
CMCREW = -0.25MD + 15.5
= -0.25(10) + 15.5
= -2.5 + 15.5
= 13 Astronauts
Therefore, the Crew Volume Ratio is
CMVOLUME = 1260 / CMCREW
= 1260 / 13
= 96.92 ft3/Astronaut
That is, there is almost 100 cubic feet of space for each astronaut inside the Crew Module.
The Static Weight of the CM is constant, and so
CMSTATIC = CMSTRUCTURE + CMELECTRIC + CMCOMM + CMINSTR + CMCONTROL + CMMISC
= 2497 + 130 + 327 + 188 + 60 + 80
= 3,282 lbs
= 1,489 kg
The Dynamic Weight of the CM is found by plugging in 10 for MD in the following equations
CMSYSTEMS = -41.33MD + 3772
= -41.33(10) + 3772
= 3,358 lbs
CMEC/LSS = 27.81MD + 1211
= 27.81(10) + 1211
= 1,490 lbs
CMEXP = 20.50MD + 254
= 20.50(10) + 254
= 459 lbs
CMCONTINGENCY = 0.71MD + 852
= 0.71(10) + 852
= 859 lbs
and
WeightDYNAMIC = CMSYSTEMS + CMEC/LSS + CMEXP + CMCONTINGENCY
= 3358 + 1490 + 459 + 859
= 6,166 lbs
= 2,797 kg
The total weight of the Crew Module thus becomes
WeightCM = WeightSTATIC + WeightDYNAMIC
= 3282 + 6166
= 9,448 lbs
= 4,285 kg
::
R.A.F.T. Writing
Role: Teacher
Audience: Middle School students
Format: Five paragraph essay
Topic: The Apollo Crew Module (CM). Did any astronaut ever fly in the CM alone? Which CMs never traveled to the Moon? What was unique about the missions? What was in common with all the missions? How does an Apollo CM differ from the CM presented in this textbook? How are they the same? Why even bother to build a Crew Module anyway?
::
6.4 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...
The Boeing Space Tug Crew Module App
::
6.5 Chapter Test
I. VOCABULARY
Match the astronautics term with its definition.
1. CM EC/LSS
2. CM Static Weight
3. CM Structure
4. Crew Capsule
5. Crew Size
A. The number of astronauts aboard a spacecraft or space station.
B. A spacecraft, such as the Boeing CST-100, that is used to ferry crew to and from a space station.
C. The CM shell, micrometeoroid shielding, insulation, radiators, etc.
D. The weight of the CM components that does not vary with the Mission Duration.
E. The CM Environmental Control/Life Support Systems. Cabin pressure, atmosphere, water, etc.
::
II. MULTIPLE CHOICE
Circle the correct answer.
6. The Dynamic Weight of a spacecraft Crew Module changes depending upon the number of days needed for astronauts to perform a space mission.
A. TRUE B. FALSE
7. The number of astronauts that a mission can carry for a space mission is determined by the Static Weight of the Crew Module.
A. TRUE B. FALSE
8. What is the maximum number of astronauts that can fit into the Boeing Space Tug Study CM?
A. 3 B. 10 C. 15 D. Cannot be determined
9. The weight of the Electrical Power component of the Crew Module will ____ as the Mission duration increases.
A. Increase B. Decrease C. Stay the Same D. Cannot be determined
10. The weight of the Environmental Control/Life Support System component of the Crew Module will ____ as the Mission duration increases.
A. Increase B. Decrease C. Stay the Same D. Cannot be determined
::
III. CALCULATIONS
A wayward satellite is need of repairs and to have some electronic parts replaced. The satellite is in a stable orbit, and a repair vehicle is ready to go to the satellite. It is estimated that the crew will need a total of nine days to conduct all the necessary repairs and complete their mission.
11. What is number of Astronauts needed?
12. What is the habitable volume for one astronaut?
13. What is the weight of the Crew Systems component?
14. What is the weight of the EC/LSS component?
15. What is the weight of the Expendables component?
16. What is the weight of the Contingency component?
17. What is Dynamic Weight of the CM?
18. What is Static Weight of the CM?
19. What is the Total Weight of the CM?
20. What is the Total Weight of the CM in kilograms?
::
IV. WRITING
Write a one paragraph essay on the topics below.
21. Explain why the weight of some Crew Module components, such as Instrumentation and Control, do not depend on the duration of the space mission.
22. Explain why the weight of some Crew Module components, such as Environmental Control and Life Support, depend on the duration of the space mission.
23. Explain why taking more astronauts than what was calculated for the Crew Size decreases the Mission Duration for the space mission.
24. Explain why taking less astronauts than what was calculated for the Crew Size increases the Mission Duration for the space mission.
25. Write a short story about what it would feel like to float weightlessly inside a Crew Capsule as it orbits the Earth.
::
CLICK HERE TO OPERATE THE CREW MODULE SPACE MISSION APP
CLICK HERE FOR THE TEACHER SLIDE SHOW
(coming soon)
CLICK HERE FOR THE STUDENT HANDOUT
(coming soon)
CLICK HERE FOR THE CREW MODULE SPACE MISSION DESIGN PARAMETERS HANDOUT
(coming soon)
CLICK HERE TO GO TO THE EXAMPLE RUBRIC STUDENT WEBSITE
::
END OF DIARY
::
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...
::