S.T.E.M. Project #2 Pulp Science Fiction Cover |

**Narrative**

In this, the second of a four-part interconnected space-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 Project 1.

**Due Date:**

End of Quarter 2

(End of Fall Semester)

**Mathematics Used**

Linear Equations

**Constants**

none

**Input**

Mission Duration (Days)

Spacecraft Systems Weight (lbs)

**Output**

Spacecraft Weight (kg)

Crew Size (people)

**Activating Previous Learning**

Project 1:

Mission Duration (people)

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**Analysis**

We discussed the Boeing Space Tug Study in the Overview. We will now extract information from the Boeing Study, and use it to create an equation that yields the CM weight and the number of astronauts that can be safely carried on a space mission.

This project will use the piloted section, or Crew Module (CM) of the system, which is displayed below.

Spacecraft system weight information is given in the upper right corner of the image below, and are described at the bottom part of the image.

Crew Module (CM) Diagram |

2 Day Mission = 15 Crew

50 Day Mission = 3 Crew

*Note that we make the Mission Duration (MD) the independent variable in the linear equation.*

This gives us two points, namely (2, 15) and (50, 3). We can use the formula for slope and the y-intercept to write the linear equation.

m = (y2 - y1) / (x2 - x1) = (3 - 15) / (50 - 2) = -12/48 = -0.25

b = y1 - m(x1) = 15 - (-0.25)(2) = 15 + 0.50 = 15.50 which rounds up to 16Therefore, we can find the crew size for a given MD by writing the linear equation (in slope-intercept form) that passes through these points.

y = f(x) = -0.25x + 16(Note: This calculation must be rounded

*down*to the nearest crew. It is impolite to have a partial crew member on a spaceflight)

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 StructureThe 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,

y = f(x) = 2,497Crew 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.

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. The choice of when to convert is left up to the student.

Note: The sample spreadsheet has the Project 2 and Project 3 information that is not needed for this project grayed-out. It is recommended that space is allowed for these future calculations.

Students that know how to use spreadsheet software should be encouraged to create their own Calculator (remember, Google Apps are free!)

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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.

The slides will guide the students as they run through the lesson powered by E^8:

The Student Workbook (below) accompanies the Teacher Lesson Plan.

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**Teacher Lesson Plan**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.

The slides will guide the students as they run through the lesson powered by E^8:

- Engage
- Lesson Objectives
- Lesson Goals
- Lesson Organization
- Explore
- The Rocket Equation
- Crew Module Components and Definitions
- Additional Terms and Definitions
- Explain
- y-mx+b: Basic Linear Equations
- Spacecraft Linear Equations
- Crew Module Equation
- Crew Module Components and Equations
- Elaborate
- Other Crew Modules
- Exercise
- Calculating Crew Module Weight
- Crew Module Mission Scenario 1
- Crew Module Mission Scenario 2
- Engineer
- The Engineering Design Process
- SMDC Spaceflight Plan
- Designing a Prototype
- SMDC Software
- Express
- Displaying the SMDC
- Progress Report
- Evaluate
- Post Engineering Assessment

The Student Workbook (below) accompanies the Teacher Lesson Plan.

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**Missions**

Spaceships are useless unless they have a place to go. These missions will add a sense of realism to the student project. Students will be placed into groups and asked to determine the total Crew Size and the total Spacecraft Weight for a given space mission:

Other missions can be created and modified to suit the interest of the students. For example, a group that is interested in dinosaurs could be given a mission to find fossils on Mars. Or a group that wants to start their own business one day could get a mission to make a profit on placing a satellite in orbit.

Encourage students to design their own missions. This project is very flexible in that regard.

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**Presentation**

Students will be asked to present their findings to the rest of the class. Parents are, of course, encouraged to attend (it is suggested that a pot luck would make things more interesting).

Each presentation will have slides that introduces the group, describes the mission, and displays the calculations. A short biography of the person named after the spacecraft should also be included.

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**Rubric**

Students will also create a website and embed their slide presentation and their S.T.E.M. Calculator in a webpage. Their journal will be kept on the webpage as well. If the class presentation is recorded to video, it can be uploaded to Youtube, then embedded in the webpage.

Therefore, each webpage (one for each project) should have the following items:

- Embedded View of S.T.E.M. Calculator
- Link to S.T.E.M. Calculator
- Link to working prototype of S.T.E.M. Calculator
- Embedded Slide Presentation
- Journal Entries
- Embedded Youtube Video of the presentation

EXAMPLE STUDENT WEBSITE

This is not a scoring rubric; rather it is a guide of what is expected for the project.

The presentation should take between 5 and 10 minutes, unless there are a lot of questions from the audience. For a class with 6 groups, this comes out to between 30 and 60 minutes.

Students should be encouraged to dress professionally, and to practice their presentations beforehand.

Scoring and grading these projects is left up to the professionalism of the teacher.

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**Conclusion**

The linear equations used in this project should be easy enough for the average high school Pre-Calculus student. The teacher may need to guide students through the setup of the equations and the calculations. As the semester progress, the concepts and the mathematics will become more challenging.

Using technology to do a high school math project should be easy and fun.

But above all, it should be free.

Both the spreadsheet and the presentation were built using Google Docs, a free application when you sign up for gmail through Google. Therefore, any student with an Internet access can use these tools for free, whether at the school, or at the library, or at the coffee shop, or at home, etc.

Students that do well on this project will learn many important skills that will help to succeed in whatever field they desire to choose.

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