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.

Start Date
Second Quarter
Spring Semester

Time Frame
About 4.5 weeks

Mathematics Used

Activating Previous Learning
Basic Mathematics
Scientific Calculator

Chapter 5:
Mission Duration (days)



Mission Duration (Days)
Spacecraft Systems Weight (lbs)

Spacecraft Weight (kg)
Crew Size (people)

Activating Previous Learning


Visual Learning
Here is a short (< 3 min) video of the Boeing CST-100, a Crew Module currently in the design stage. The video explains the docking sequence with an orbiting space station (see Chapter 3), and how the spacecraft returns to earth.

The Boeing CST-100 Crew Module in action (0:02:13)

The Boeing CST-100 is the leading contender in NASA's Commercial Crew Development (CCDev) program.


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 (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 are described at the bottom part of the image.
Crew Module (CM) Diagram
We can see from the data in the image above that
  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 16
Therefore, 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 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,
y = f(x) = 2,497
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.

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 3 and Project 4 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 app (remember, Google Apps are free!)


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:
  1. Engage
    • Lesson Objectives
    • Lesson Goals
    • Lesson Organization
  2. Explore
    • The Rocket Equation
    • Crew Module Components and Definitions
    • Additional Terms and Definitions
  3. Explain
    • y-mx+b: Basic Linear Equations
    • Spacecraft Linear Equations
    • Crew Module Equation
    • Crew Module Components and Equations
  4. Elaborate
    • Other Crew Modules
  5. Exercise
    • Calculating Crew Module Weight
    • Crew Module Mission Scenario 1
    • Crew Module Mission Scenario 2

  6. Engineer
    • The Engineering Design Process
    • SMDC Spaceflight Plan
    • Designing a Prototype
    • SMDC Software
  7. Express
    • Displaying the SMDC
    • Progress Report
  8. Evaluate
    • Post Engineering Assessment
This lesson can be delivered in one or two class periods, with students working on the project after school. It is recommended that a few minutes of a few class periods be set aside for student help.

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


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.


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.

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


Students will also create a website and embed their slide presentation and their S.T.E.M. app 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:
  1. Embedded Slide Presentation
  2. Embedded view of S.T.E.M. app
  3. Link to S.T.E.M. app
  4. Link to working prototype of S.T.E.M. app
  5. Journal Entries
  6. Embedded Youtube video of the presentation
(Link opens in a new window)

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.


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.


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