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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7.1 Narrative
In this, the third of a four-part interconnected astronautics-based S.T.E.M. project, students will calculate the weight of the rocket propellant (both the fuel and the oxidizer) needed to conduct a space mission. Students will also calculate the total weight of the Engine Module. The Crew Module is attached to the Engine Module to form a complete spacecraft. The propellant equations use the ΔV information from Chapter Five, and the Crew Module weight information from Chapter Six.
Time Frame
About 4 weeks
(about 22 days)
Astronautics Problems
Rocket Exhaust Velocity
Rocket Empty Weight
Rocket Gross Weight
Rocket Propellant Weight
Rocket Excess Propellant Weight
Mathematics Used
Exponential Equations
Basic Algebra
Material List
A connection to the Internet
Google GMail account
Science Topics
Physics, Astronautics
Activating Previous Learning
Periapsis Δv (mps)
Apoapsis Δv (mps)
Δv Budget (mps)
Round-Trip Δv Budget (mps)
Transfer Time (days)
Round-Trip Transfer Time (days)
Mission Duration (days)
Crew Size (people)
Crew Module Weight (lbs)
Essential Questions
- What is the Specific Impulse of rocket engine?
- Why is it important to determine the exhaust velocity of a rocket engine?
- How does the mass ratio of a rocket effect its final velocity?
- Who are some of the pioneers in rocket engine design?
- 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 Boeing Space Tug Study
The Engine Module (EM)
The EM Propellant
EM Fuel (LH2)
EM Oxidizer (LO2)
Additional Terms and Definitions
3. Explain
Basic Spacecraft Systems
The EM Specific Impulse
4. Elaborate
Other Engine Module Examples
5. Exercise
EM LH2 and LO2 Parameters
EM LH2 and LO2 Scenario
6. Engineer
The Engineering Design Process
SMDA Spacecraft EM Propellant 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 engine 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 (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 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
Standard Gravity (m/s2)
RL10 Rocket Engine Isp (sec)
Input
Rocket Inert Weight (lbs)
Propellant Mixture Ratio
Output
Rocket Exhaust Velocity (kps)
Rocket Empty Weight (kg)
Rocket Gross Weight (kg)
Total Amount of Propellant (kg)
Total Amount of LH2 (kg)
Total Amount of LO2 (kg)
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Visual Learning
The Apollo Command Service Module was the forst of the design to fly all the way to the Moon.
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Continued...
7.2 Vocabulary
EM Empty Weight (m1) EM Gross Weight (m0) EM Inert Weight Engine Module (EM)
Exhaust Velocity (VEXH) Liquid Hydrogen (LH2) Liquid Oxygen (LO2) Nozzle-Extended
Nozzle-Retracted Propellant Propellant Ratio Propellant Weight
Propellant Reserve RL10 Rocket Engine Specific Impulse (ISP)
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7.3 Analysis
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.
This project will use the un-piloted section, or Engine Module (EM) of the system, which is displayed below.
Boeing Space Tug Study Engine Module
Electrical power was to be derived from batteries, and the Reaction Control Systems (RCS) used gaseous hydrogen and oxygen, instead of an hypergolic propellant.
Combining the Engine Module with the Crew Module from Chapter Six, this is what the spacecraft looks like:
The Boeing Space Tug
This is also the spacecraft that would have flown as designed in 1971. Notice the similarity with the Apollo CSM space craft. Just like the former, this spaceship has a crew section and a rocket engine section.
This chapter will allow this great design to finally fly in space!
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We will be using the Rocket Equation to calculate the propellant needed to go from one orbit to another.
We will be using the Rocket Equation to calculate the propellant needed to go from one orbit to another.
Δv = vEXH * ln(m0/m1)
where
Δv = Change in orbital velocity
vEXH = Exhaust Velocity of the rocket engine
m0 = Gross Weight of the rocket
m1 = Empty Weight of the rocket, including propellant reserve
The rocket Exhaust Velocity (VEXH) is found by multiplying the Rocket Engine Specific Impulse (Isp) by the Standard Gravity (g0).
vEXH = ISP * g0
The Payload Weight is the weight of the cargo plus the weight of the Crew Module (see Chapter Six).
EMPAYLOAD = WeightCARGO + WeightCrewModule
The Empty Weight (m1) of the rocket includes the Inert Weight and the Payload weight.
m1 = EMINERT + EMRESERVE + EMPAYLOAD
The Space Tug diagram shows that the Inert Weight is 5,610 lbs, which equals to 2,545 kg.
So,
m1 = 2,545 + EMPAYLOAD
The Gross Weight (m0) of the rocket is the weight of the propellant plus m1. Referencing the diagram, the weight of the the propellant is 39,800 lbs which equals 18,053 kg. However, some missions will not require less than the capacity of the spacecraft, so the weight of the propellant will vary from mission to mission.
m0 = m1 + EMPROPELLANT
Solving the rocket equation for propellant, the amount of fuel and oxidizer needed for any space mission can be calculated.
Δv = vEXH * ln(m0/m1)
Δv / vEXH = ln(m0/m1)
Δv / vEXH = ln((m1 + EMPROPELLANT)/m1)
Δv / vEXH = ln(1 + (EMPROPELLANT/m1)
1 + EMPROPELLANT)/m1 = e^(V/VEXH)
EMPROPELLANT / m1 = e^(V/VEXH) - 1
EMPROPELLANT = m1 * (e^(V/VEXH) - 1)
ExcessPROPELLANT = Propellant - EMPROPELLANT
Finally, the EM propellant breakdown is the weight of the Liquid Hydrogen (LH2) fuel and the Liquid Oxygen (LO2) oxidizer.
LH2 = EMPROPELLANT / (MixureRatio + 1)
LO2 = LH2 * MixureRatio
The excess propellant is the capacity of the rocket minus what we actually carry.
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Example
You are the Mission Commander of a spacecraft that is tasked to repair a satellite in Low Earth Orbit. Your vehicle is a Boeing Space Tug outfitted with a Crew Module (CM) that weighs in at 4,345 kg, and a repair kit that weighs 4,761 kg. The Δv Budget + Reserve is 4,133 mps.
Calculate the amount of propellant needed, the propellant, the propellant breakdown, the excess propellant, and the Gross Weight of your spacecraft.
vEXH = ISP g0
= (460)(9.80665)
= 4,511 mps
EMPAYLOAD = WeightCARGO + CM
= 4761 + 4345
= 9,106 kg
m1 = 2545 + EMPAYLOAD
= 2545 + 9106
= 11,650 kg
EMPROPELLANT = m1eVVEXH - 1
= (11650)(e41334511 - 1)
= 17,475 kg
The excess propellant becomes:
ExcessPROPELLANT = Propellant - EMPROPELLANT
= 18053 - 17475
= 578 kg
The propellant breakdown is:
LH2 = EMPROPELLANTMixureRatio + 1
= 174576.85
= 2,551 kg
LO2 = LH2 MixureRatio
= 2485 5.85
= 14,924 kg
Finally, the Gross Weight of the spacecraft is,
m0 = m1 + EMPROPELLANT
= 11,650 + 17,475
= 29,126 kg
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R.A.F.T. Writing
Role: Teacher
Audience: Middle School students
Format: Five paragraph essay
Topic: The Apollo Service Module (SM). What Launch Vehicles were used? Which SM traveled to the Moon? What was unique about the missions? What was in common with all the missions? How does an Apollo SM differ from the EM presented in this textbook? How are they the same? Why even bother to build a Service Module anyway?
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7.4 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:
Input/Output Interface
Graph
Constants
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 Orbital Spaceflight App
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7.5 Chapter Test
I. VOCABULARY
Match the astronautics term with its definition.
1. EM Inert Weight
2. Liquid Oxygen (LO2)
3. Nozzle-Retracted
4. Propellant Ratio
5. Specific Impulse (ISP)
A. The force with respect to the amount of propellant used per unit of time.
B. The weight of the Engine Module without propellant and payload.
C. The rocket engine nozzle which is pulled back to its original shape.
D. What a rocket engine uses as an oxidizer.
E. The rocket engine nozzle which is pulled back to its original shape.
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II. MULTIPLE CHOICE
Circle the correct answer.
6. The propellant of a rocket is the rocket fuel needed to make the rocket fly.
A. TRUE B. FALSE
7. The more a rocket carries, the more ΔV the rocket can generate.
A. TRUE B. FALSE
8. A propellant ratio of 5:1 means that there is five times as much ___ as there is rocket fuel.
A. LH2 B. LO2 C. Propellant D. Cannot be determined
9. As the Specific Impulse (ISP) of a rocket engine _____, the ΔV capability of the rocket engine increases.
A. Increases B. Decreases C. Stay the the Same D. Cannot be determined
10. By extending the nozzle of the RL10 rocket engine, the Specific Impulse (ISP) of the engine increase by approximately ____ seconds.
A. Two (2) B. Three (3) C. Stay the Same D. Cannot be determined
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III. CALCULATIONS
A Boeing Space Tug has been selected to be used on a satellite repair mission in Earth orbit. The Round-Trip ΔV Budget is calculated at 5,216 mps. The Specific Impulse of the rocket engine is 460 s, and the Inert Weight is 5,610 lbs. The payload for this mission is a standard 10-Crew Boeing Space Tug Crew Module, which weighs 9,540 lbs, and a standard satellite repair kit, which weighs 12,000 lbs. Assume a Propellant Reserve of 1% of the Round-Trip ΔV Budget.
11. What is the Exhaust Velocity (VEXH) of the rocket engine?
12. What is the Crew Module (CM) weight in S.I. units?
13. What is the weight of the Propellant Reserve in S.I. units?
14. What is the mission payload in S.I. units?
15. What is the Empty Weight (m1) of the rocket?
16. What is the Gross Weight (m0) of the rocket?
17. What is the amount of propellant needed for this space mission?
18. What is the amount of LH2 fuel needed for the space mission?
19. What is the amount of LO2 oxidizer needed for the space mission?
20. What is the amount of propellant that will be left over at the end of the space mission?
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IV. WRITING
Write a one paragraph essay on the topics below.
21. Explain why one of the most common misconceptions in rocketry is that the propellant of a rocket is not just the rocket fuel only.
22. Explain why the payload weight of space mission is critical to the performance (i.e., the ΔV requirements) of a rocket engine.
23. Explain why the greater the rocket engine Specific Impulse (ISP), the greater the rocket Exhaust Velocity.
24. Explain why the greater the rocket Exhaust Velocity, the greater the change in velocity that the rocket engine can perform.
25. Write a short story about what it would be like to feel the power of a rocket engine as it accelerates you up to a destination in space.
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<<>>
CLICK HERE TO OPERATE THE ORBITAL SPACEFLIGHT APP
CLICK HERE FOR THE TEACHER SLIDE SHOW
(coming soon)
CLICK HERE FOR THE STUDENT HANDOUT
(coming soon)
CLICK HERE FOR THE ORBITAL SPACE MISSION DESIGN PARAMETERS HANDOUT
(coming soon)
CLICK HERE TO GO TO THE EXAMPLE RUBRIC STUDENT WEBSITE
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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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