LESSON PLANS: SPRING SEMESTER OVERVIEW

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A NOTE FROM THE TEACHER


Narrative
These projects will take the student on a journey that begins in Low Earth Orbit (LEO) and winds up on the surface of the Moon. All the numbers involving spacecraft are real-world, which means that if the spacecraft could be built, it would actually fly!

Time Frame
One project divided into four parts over the course of one school year

Material List
A connection to the Internet

Mathematics Topics
Square Roots
Linear Equations
Natural Logarithms
Trigonometry

Science Topics
Physics, Astronautics

Grade
12th (Pre-Calculus)

Essential Questions

  • What is the relationship between the change in velocity and the spacecraft weight?
  • Why do I need to raise or lower my orbital altitude?
  • Who are are some of the pioneers in space exploration?
  • What previous learning needs to be activated to design a mission to land on the moon?
  • Where is the Environmental Control/Life Support System (EC/LSS) of a spacecraft located?
  • When are my S.T.E.M. projects due?
  • Why is the exact amount of propellant used in a space mission so critical?
  • How is the weight of a spacecraft related to the duration of a space mission?
  • How can I pay for a space mission and still make a profit?
  • Wait. I have to do science and technology and engineering and mathematics, all at the same time? Woah.
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Lesson Overview
Note: This website incorporates spreadsheets and slide-show presentations that are provided to teachers for use in the classroom.
  • Students first learn the basics of astronautics 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 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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Learning Objectives
Evaluation
  • Interpret data related to astronautics and rocketry.
  • Select an optimum design from many design options to solve technological problems.
Synthesis
  • Explain the principles of spaceflight in mathematical and physical terms.
  • Integrate mathematics and astronautics in the engineering design process.
Analysis
  • Analyze the physical principles of a change in orbital velocity (delta v) and the amount of propellant used, and relate these to a space mission design.
  • Use mathematics to calculate the change in orbital velocity, the spacecraft weight, and the amount of propellant used for a space mission.
  • Use financial analysis to determine if it is possible to make a profit from a space venture.
Application
  • Use the Engineering Design Process to construct a real-world space mission app that is constrained by certain astronautics factors.
Comprehension
  • Define constraints to the real-world model.
  • Explain how solutions to the problem address the specific requirement.
Knowledge
  • Explain the relationships of the principles of astronautics to the concept of delta v, weight, and propellant.
  • Demonstrate how their space mission design app addresses the requirements of the delta v, weight, and propellant.
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Science As Inquiry
  • Identify questions and concepts that guide scientific investigations.
  • Design and conduct scientific investigations.
  • Use technology and mathematics to improve investigations and communications.
  • Formulate and revise scientific explanations and models using logic and evidence.
  • Communicate and defend a scientific argument.
Physical Science
  • Use mathematics and logic to explain scientific principles.
  • Look up and use astronomical and astronautical constants.
Science and Technology
  • Identify a problem or design an opportunity.
  • Propose designs and choose between alternative solutions.
  • Implement a proposed solution.
  • Evaluate a solution and its consequences.
  • Communicate the problem, process, and solution.
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Time Frame

  • Each project is to be completed at or near the end of each quarter, (or half-semester).
  • This means Project 1 is due around Midterm Fall Semester, Project 2 around the end of the Fall Semester, Project 3 around Midterm Spring Semester, and Project 4 around the end of the school year.
  • This gives the students about 6 weeks to research, complete, and present each project. If students work 2 hours a week, that comes to a total of 12 hours devoted to the project every quarter. This should give them plenty of time to complete the calculations, update the spreadsheet, finish the website, finish the slide-show presentation, and practice.
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Vocabulary
  • Apoapsis: The highest point in an elliptical orbit.
  • Apoapsis Delta V Burn: The rocket firing at the highest point of a Transfer Orbit.
  • Circular Orbit: An orbit that takes the shape of a circle.
  • Communications: The CM TV, audio, antenna, etc.
  • Contingency: The CM emergency supplies.
  • Controls: The CM RCS, Expendables, controls, lines, etc.
  • Crew Module (CM): The part of the spacecraft where the astronauts live and work.
  • Crew Module Weight: The sum of the CM Static and CM Dynamic Weights.
  • Crew Module Dynamic Weight: The weight of the CM components that varies with the Mission Duration.
  • Crew Module Static Weight: The weight of the CM components that does not vary with the Mission Duration.
  • Crew Size: The number of astronauts aboard a spacecraft.
  • Crew Systems: The CM Bunks, seats, food, medical, etc.
  • Delta V: The change in velocity required to go from one orbital altitude to another.
  • Delta V Budget: The total amount of Delta V needed to accomplish a space mission.
  • EC/LSS: The CM Environmental Control/Life Support Systems. Cabin pressure, atmosphere, water, etc.
  • Electrical Power: The CM batteries, regulators, junction boxes, wires, cables, etc.
  • Elliptical Orbit: An orbit that takes the shape of an ellipse.
  • Empty Weight (M1): The weight of the spacecraft fully load excluding propellant.
  • Engine Module (EM): The part of a spacecraft that holds the propellant tanks and the rocket engine.
  • Exhaust Velocity: The velocity of the escaping gas exiting a rocket.
  • Expendables: The CM Reaction Control Systems propellant.
  • Gross Weight (M0): The weight of the spacecraft fully loaded including propellant.
  • Hohmann Transfer Orbit: The path taken to either raise or lower an orbital altitude.
  • Higher Orbital Altitude: The highest altitude above Mean Sea Level of an orbiting body.
  • Inert Weight: Weight of the EM.
  • Instrumentation: The CM displays, controls, wiring, lighting, etc.
  • Landing Kit: Includes the lunar landing legs, infrastructure, landing radar, etc.
  • Liquid Hydrogen (LH2): What a rocket engine uses as fuel.
  • Liquid Oxygen (LO2): What a rocket engine uses as an oxidizer.
  • Lower Orbital Altitude: The lowest altitude above Mean Sea Level of an orbiting body.
  • Lunar Investment: The amount of money needed to fully fund a mission to the Moon.
  • Lunar Material: The rocks and dirt that is brought back from the Moon and sold.
  • Miscellaneous Equipment: The CM manipulator arms, displays and controls, maintenance equipment, etc.
  • Mission Duration: The total time necessary to accomplish a space mission.
  • Nozzle: The bell-shaped protrusion at the tail end of a rocket that the exhaust of a rocket comes out of.
  • Nozzle (Extended): The rocket engine nozzle is elongated to provide approximately 3s more of Specific Impulse.
  • Nozzle (Retracted): The rocket engine nozzle is pulled back to its original shape.
  • On-Station Time: The duration spent at the mission destination.
  • Orbital Altitude: The altitude above mean sea-level that a spacecraft orbits a body.
  • Payload Tray: The tray that transports payload to and from the lunar surface.
  • Periapsis: The lowest point in an elliptical orbit.
  • Periapsis Delta V Burn: The rocket firing at the lowest point of a Transfer Orbit.
  • Powered Ascent Initiation (PAI): The lift off burn from the lunar surface to lunar orbit.
  • Powered Descent Initiation (PDI): The landing burn from lunar orbit to the lunar surface.
  • Propellant: Total weight of LO2 and LH2
  • Propellant Ratio: The ratio of LO2 to LH2 in a rocket engine.
  • Propellant Weight: The weight of both the fuel (LH2) and the oxidizer (LO2).
  • Radius of Higher Orbit: The higher circular orbital altitude of a spacecraft as measured from the center of an orbiting body.
  • Radius of Lower Orbit: The lower circular orbital altitude of a spacecraft as measured from the center of an orbiting body.
  • Reserve Percentage: The percent of the total propellant set aside as a reserve.
  • Reserve Propellant: The weight of the propellant used in case of an emergency.
  • RL10 Engine: The rocket engine used in the EM.
  • Standard Gravitational Parameter (mu): The product of the Gravitational Constant (M) and the mass of a body (M).
  • Standard Gravity (g0): The acceleration due to free fall.
  • Structure: The CM shell, micrometeoroid shielding, insulation, radiators, etc.
  • Specific Impulse (Isp): The force with respect to the amount of propellant used per unit of time.
  • Transfer Orbit #1: The elliptical orbit a spacecraft flies from periapsis to apoapsis.
  • Transfer Orbit #2: The elliptical orbit a spacecraft flies from apoapsis to periapsis.
  • Transfer Time: The time between apoapsis and periapsis Delta V rocket firings.
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Background for the Teacher
In these projects, students will examine the principles and the processes of science and engineering to understand how spacecraft travel in space. The teacher will use slide-show presentations to facilitate instruction, discussion, and demonstration. Students will be constructing real-world models based on real world parameters.

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 Boeing Space Tug Study written in 1971 is that spacecraft. The diameter of the vehicle was just under 15 ft, which 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, and so 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 CSM.

Boeing Space Tug Study Crew Module (CM) circa 1971

Boeing Space Tug Study Engine Module (EM) circa 1971

When the CM and the EM were attached, they would have formed one complete spacecraft. It had enough power to travel one-way from the Earth to the Moon.

Boeing Space Tug Study Vehicle circa 1971

In addition, this versatile spaceship even had a lunar landing kit that could be attached, complete with landing legs, landing radar, even an auxiliary power unit that would have been used for stays on the lunar surface.

Boeing Space Tug  Study Vehicle with Lunar Lander Kit circa 1971

Using the Boeing design, students will use real-world data to design real world space missions. We feel that it is the creation of a hands-on, real-world project that will allow student to gain a deeper understanding of mathematics that they could never get on some test.

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Spaceport America
The REL Skylon spaceplane
Just like in the original Boeing study, our spacecraft will be "built" and transported into space aboard a space shuttle called the Skylon. The payload bay of the Skylon would be able to accommodate the Space Tug very easily (this particular space shuttle design is going through what the Boeing people had to go through decades earlier: dreaming about and designing something that may never get the funding needed to fly). The spaceplane will take off and land like any ordinary airliner, except this one can go into space! The Skylon will operate out of Spaceport America in NM, USA.

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Working in groups, students will use the Engineering Design Process to construct their space mission app.

Each group will be assigned two types of space missions: an orbital mission, and a lunar landing mission.

Note: It is left up to the professionalism of the teacher to differentiate the instruction to accommodate students that may have special needs.

Six examples of the orbital missions and mission parameters that students will conquer are listed in the following Google slide show:



Page 2 of 2 is listed only once, since it is the same information across for all the missions. This document can be download as a PDF file and printed, preferably with both pages on one paper. Page 1 is used for Projects 1 and 2, while Page 2 is used for Projects 3 and 4.

Each mission assures different answers for the different groups in the class, thus reducing the chance of cheating. However, since the astronautics concepts are similar, students are encouraged to assist other students with their projects, thus activating peer tutoring.
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The S.T.E.M. Project Scenario

1. The class is divided into groups of between 2 and 4. Each group is assigned a space orbital mission and a lunar landing mission that will be designed over the course of the school year. Each group will be assigned the following positions:
  • Project Leader
  • Website Administrator
  • Cloud Applications Engineer
  • Engineering Log
To make learning fun, each group could create a name for itself. Callsigns for the individual group members would add to the merriment.

2. Students are Space Mission Design Cloud Engineers that focuses on the "software as a service" aspect of cloud computing (others include "platform as a service", "infrastructure as a service", and "network as a service"). They are employed by Spacely Space Sprockets, a private New Space venture business. They are assigned to the Spaceflight Planning Division (SPD) within the company.

How many Cloud Engineers does it take to change a lightbulb?

Zero. It's a hardware problem.
3. The SPD is tasked with developing a prototype of an S.T.E.M. for the Classroom/Google Space Mission Design App (SMDA) for the company. The SMDA will be used by the Spaceflight Dynamics Team to simulate various space mission scenarios.





4. The SPD will be given two space mission scenarios to test their SMDA software design: an orbital mission and a lunar landing mission.

5. The SPD will create and maintain a website to house the SMDA. A working prototype that anyone can use will also be included in the website.

6. The SPD will keep a journal on the website of the design process for the Engineering Post-Development Analysis.

7. The SPD will present a progress report of their software prototype to the rest of the company during four quarterly company meetings.

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Rubric
Students can use the Example Student Website as a rubric for these S.T.E.M. projects. Scoring and grading these projects is left up to the professionalism of the teacher.

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

But above all, it should be free.

The spreadsheets, presentations, websites, and videos were built or uploaded using Google Drive, Blog Spot, and YouTube, which are all free applications 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 home.

Therefore, students can create their SMDA using Google sheets. They can present their findings to the rest of the class using a Blogger website that they create that includes an embedded Google slides. Finally, the video of all of their presentations can be embedded into the website.

Google technology truly is a remarkable set of tools for any student that happens to go to a school that has limited resources.

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The Presentation
As the due date of the presentations draws near, the entire class will have the opportunity to learn the final lesson of these projects: dealing with a deadline, and its corollary, time management. Students will certainly get to experience the pressure of the presentation, in the same way an actor gets the jitters before going on stage.

Students should be encouraged to dress professionally, and to practice their presentations beforehand. The presentation should take between 5 and 10 minutes, unless there are a lot of questions from the audience. They will navigate through the website, discussing the project development, displaying the SMDA, and demonstrating a working model.

It is suggested that students bring snacks and drinks to help foster a more festive mood; a pot luck would be even better. Make sure the students invite their parents too! Of course, the event is incomplete without the Principal being there as well. And a call to the local press about a feel-good high school education story couldn't hurt either. All of this creates an atmosphere of a special event, which, by the way, it is.

The students get to experience another way of tying together learning with doing something fun, the parents get to beam at their child's brilliance, and the class gets to look good on the 6 o'clock news. It's a winning situation for everyone.

Now that's the way to learn science and technology and engineering and mathematics!


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