a high school s.t.e.m. laboratory textbook
by Joe Maness
S.T.E.M. For the Classroom presents
ADVENTURES IN OUTER SPACE A High School S.T.E.M. Laboratory Textbook _____________ On the Front Cover: An image that encapsulates everything in this textbook. A Bigelow space station in Low Earth Orbit is seen here with two spaceships docked on either end. On the left end is the Space X Dragon crew capsule, and on the other end is a Boeing CST100 crew capsule. Behind the space station, an R.E.L. Skylon that had departed Spaceport America is now arriving to drop off cargo. In the background is the ultimate goal of any spacefaring civilization: the Moon. Image: NASA ::
Library of Congress Cataloging in Publication Data MANESS, JOE Adventures in Outer Space A High School S.T.E.M. Laboratory Textbook ISBN 9999999999
Adventures in Outer Space A High School S.T.E.M. Laboratory Textbook by Joe Maness Copyright © 2015 by ReNewSpace, LLC. Albuquerque, NM. All rights reserved. No part of this textbook may be reproduced, in any form or by any means, without permission in writing from the author. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN 9999999999 ReNewSpace, LLC. Albuquerque, NM http://www.stemfortheclassroom.org
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TABLE OF CONTENTS
PREFACE 1
SCIENCE TECHNOLOGY ENGINEERING MATHEMATICS 99
FALL SEMESTER AEROSPACE 99
UNIT 1: VEHICLES
Chapter 1: Suborbital Spaceflight 99 1.1 Narrative 99 1.2 Vocabulary 99 1.3 Analysis 99 1.4 Suborbital Space Mission Design App 99 1.5 Chapter Test 99
Chapter 2: Orbital Spaceflight 99 2.1 Narrative 99 2.2 Vocabulary 99 2.3 Analysis 99 2.4 Orbital Space Mission Design App 99 2.5 Chapter Test 99
UNIT 2: DESTINATIONS
Chapter 3: Space Station 99 3.1 Narrative 99 3.2 Vocabulary 99 3.3 Analysis 99 3.4 Space Station Design App 99 3.5 Chapter Test 99
Chapter 4: Space Port 99 4.1 Narrative 99 4.2 Vocabulary 99 4.3 Analysis 99 4.4 Unpowered Glide Landing App 99 4.5 Chapter Test 99
SPRING SEMESTER ASTRONAUTICS 99
UNIT 3: BASIC ASTRONAUTICS
Chapter 5: Delta V and Transfer Time 99 5.1 Narrative 99 5.2 Vocabulary 99 5.3 Analysis 99 5.4 Delta V Space Mission Design App 99 5.5 Chapter Test 99
Chapter 6: Spacecraft Weight 99 6.1 Narrative 99 6.2 Vocabulary 99 6.3 Analysis 99 6.4 Crew Module Space Mission Design App 99 6.5 Chapter Test 99
UNIT 4: ADVANCED ASTRONAUTICS
Chapter 7: The Rocket Equation 99 7.1 Narrative 99 7.2 Vocabulary 99 7.3 Analysis 99 7.4 Space Mission Design App 99 7.5 Chapter Test 99
Chapter 8: Lunar Landing 99 8.1 Narrative 99 8.2 Vocabulary 99 8.3 Analysis 99 8.4 Lunar Landing Mission Design App 99 8.5 Chapter Test 99
APPENDIX The App: Google Sheets Spreadsheet Design 99 Open Source Code 99 Layout 99
Admin: Google Blogger Website Design 99 Posts and Comments 99 Layout and Gadgets 99 Customizing 99
Express Yourself: Google YouTube Videos Creating a Video 99 Uploading a Video 99
Portfolio: Website Rubric 99 Introduction 99 Embedding Google Slides Presentations 99 Embedding Google Sheets Apps 99 Embedding Google Docs PDF Engineering Logs 99 Embedding Google Drawings 99 Embedding Google Forms 99 Embedding Google YouTube Videos 99
Stage Fright: Presentation of Student Website 99 Science Fair Setting 99 Videotaping and Uploading the Presentation 99
For the Educator: Lesson Plans 99 Teacher Presentations 99 Student Handouts 99
ANSWERS TO PROBLEM SETS 99
GLOSSARY 99
EQUATIONS AND CONSTANTS 99
INDEX 99 ::
The projects in this textbook feature the innovative technology of these aerospace/astronautics companies
S.T.E.M. For the Classroom
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S.T.E.M. For the Classroom: Adventures in Outer Space
PREFACE
In the beginning, Mathemagicians created aerospace and astronautics. But they were dull and lifeless and without form. The aerospace and astronautics, I mean. Not the Mathemagicians. Although, an argument could be made for that too. Now, where was I? And the Mathemagicians said, “Let there be realworld S.T.E.M. laboratories that students across all Socioeconomic Status (S.E.S.) levels can use to learn science and technology and engineering and mathematics at a deeper level,” and there was realworld S.T.E.M. labs that students across all S.E.S. levels could use to learn science and technology and engineering and mathematics at a deeper level. And the Mathemagicians looked at what they had wrought and saw that it was good... So begins the grand journey undertaken by this most, ahem, humble, high school teacher. :: Shortly after the creation of this S.T.E.M. ideal, a radical new thought began to emerge. The story goes something like this: ...you take a biology class, you get a biology lab. You take chemistry? Here’s your chemistry lab. Got S.T.E.M.? Then here you go with your S.T.E.M. lab. Got physics? Then you got a physics lab too. Got astronomy? well, then, here’s your astro... Wait. You mean to tell me that there is no such thing as a S.T.E.M. lab? What? Really? Wouldn’t modeling realworld data on realworld spacecraft get students to be a little more interested in learning S.T.E.M.? Why not? It’s not like there’s existing spacecraft designs that students can use to model the realworld, right? Go tell that to Virgin Galactic, Reaction Engines, Ltd., Bigelow Aerospace, Spaceport America, Boeing, SpaceX, et al. Of course, the choice of aerospace and astronautics for this lab textbook was purely arbitrary. Other textbooks focus on, say, an underwater adventure, complete with the science and technology and engineering and mathematics used for submarines and undersea habitats. The idea is that the student learns the same S.T.E.M. skill set no matter which class is taken. That being said, this class is the lab that accompanies all seniorlevel classes. It allows students to use S.T.E.M. in a fun and realworld fashion. The idea is that students learn the theory in their science and math classes and they apply the theory in a S.T.E.M. lab. It really is that simple and interesting! Given the above, students will learn basic aerospace and astronautics as a way to delve deeper into mathematics, as well as science and technology and engineering. They will demonstrate what they have learned by displaying their embedded slideshow presentations, embedded spreadsheet space mission apps, embedded PDF Engineering Reports, and embedded YouTube videos of their presentations on a website that they create. :: All of this sounds rather expensive. For instance, embedding frames in a website requires higher level HTML and PHP programming. So what’s the price of admission for all of this? It’s twofold: A) computers hooked to the Internet, and Page 1 of 129
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B) a free Google GMail account. That’s it! Since most high schools already have a computer lab, Part A is really no problemo. Since Google is free, well... All the software tools necessary to embed these slideshows, spreadsheets, PDF files, and streaming video come free from Google Technology. Therefore, the best part is that it is accessible to any student at any S.E.S. level, which means the affluent and the nonaffluent have equal access. Once the two parts have been met, students can then take virtual trips to any place their imaginations will allow. The best part is that their journey (of the imagination) will be realistic and doable, which makes things way more fun and interesting. With this textbook, and a little determination, it allows students to fly realistic space missions, from suborbital flights, all the way to a landing on the Moon! Another plus for this class is that the student has created a Portfolio of what they have learned in their final year of High School. Moreover, they can put the link to their website on their resume. There are probably more advantages that I have failed to list within these pages. Still, I think you get the point. Mathematics, especially higher math, like Algebra 2 and PreCalculus, can be daunting to a high school student. But tell them that they’re going to outer space, and here’s the science, technology, engineering, and the mathematics to get there, then watch what happens. You’ll see it in their eyes. So, there is no such thing as a S.T.E.M. lab, huh? Well, there is one now... ::
ACKNOWLEDGEMENTS This textbook would never have seen the light of day if it weren't for the tireless efforts of Dr. Rich Holzin, so any and all blame for this body of work must be shared by him. His devotion to the ideas presented in this textbook, and to the students that bravely ran it, made all the difference in the world. These ideas would have been nothing more than just another obscure technical paper if it wasn’t for his prodding (nagging?) me to publish it first as a website, then later as a textbook. I certainly would never have thought about presenting my ideas as something that can fit in a High School classroom (and I’m a teacher!), let alone writing a textbook on the thing. For my part, I worked on this textbook parttime while working my fulltime teaching job. We met on a fine morning in August 2012 when he was the substitute teacher for our school. He had noticed my flight jacket, and mentioned that he too was an enlisted AntiSubmarine Warfare (ASW) swabbie (Navy enlisted personnel) like me, and that he once flew commercial airplanes for a living. I told him my background (flying backseat ASW jets off of carriers), and the ultralight aircraft that I once owned and piloted. But the most intriguing of all our common interests were our love for human exploration of space and the society that it could spond, and our belief in education as the absolute backbone of our society. Another mutual advantage we shared was the fact that we weren’t in this for the money. Thus, it became a labor of love for both of us. The idea of students receiving this type of education at the high school level is what motivated us Page 2 of 129
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through the tough times. Indeed, here is proof that we could live in a Star Trek society where people work for growth and learning and not for personal wealth and gain. So it was the case that we would meet for breakfast on a Saturday or a Sunday, discussing the countless different aspects of the journey that we were on. One day, utterly exhausted from everything I had done up to that point, I quipped that if I had known back then how much work would have been involved in doing this adventure that I would have never started it in the first place. He just smiled knowingly (what do you know, Rich? Tell me!) and said that he understood. Rich always kept the process moving forward; always steering a true heading. I could never see the forest for the trees because he said that I was too close to it to see what was out there available to us. I hope he is right, and that this textbook opens doors that I would have never imagined. But even if it doesn’t, that’s still OK, because, I know deep in my own heart (where one cannot lie to oneself) that we have produced a fine piece of educational material. Thanks, Rich! :: Of course, this entire textbook could not have truly been called “realworld” unless it was flighttested first. So my eternal gratitude to the classes at The Learning Community Charter School Algebra 2 and PreCalculus classes. Without all of your courage and dedication in the face of everchanging space projects from your (slightly) deranged teacher, you endured and persevered. We salute you in this, your finest hour. Thanks, you wonderful test pilots er students! :: Finally, thanks to all my friends and family who had to endure my ups and downs during the course of developing this book (3 years!). I humbly apologize, and I hope that we’re all still cool. Thanks! Joe Maness ::
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WARNING: This textbook contains topics that may cause students to become excited about using the concepts they learn in the classroom on realworld space mission design, gaining a deeper understanding of mathematics. It is therefore advised that extreme caution be used when utilizing the contents of this textbook.
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SCIENCE TECHNOLOGY ENGINEERING MATHEMATICS
...but my friends call me S.T.E.M. Prerequisites There are only two conditions that must be met before a student is able to handle this lab. The student must: 1. be a High School Senior (HSS) 2. have passed or currently be enrolled in High School Algebra 2. Of course, it is always left up to the professionalism of the teacher to grant any waivers on a onetoone basis.
Students and their teacher taking the S.T.E.M. Lab waaaaaay too seriously...
:: Narrative This textbook deals with various aspects of space mission design. It is used as cover to expose HSS to applied mathematics disguised as fun projects they complete over the course of two semesters. Unwittingly, these students then become stronger in other fields of study as their selfconfidence grows. Students will be required to use the following software in this class (note the repetition of one name in particular): Page 5 of 129
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● ● ● ● ● ● ● ● ● ● ●
Research Email and Contacts: Time Management: Word Processor: Slideshow Presentation: Spreadsheet: Images: Information Collection: Streaming Video: Website Admin: Laptop Computer (optional):
Google Search Google GMail Google Calendar Google Docs converted to PDF format Google Slides Google Sheets Google Drawing Google Forms Google YouTube Google Blogger Google Chromebook
Since most, if not all, HSS already know the other version of these software tools, the learning curve should be fairly flat. Students will also use Social Media in their effort to show off what they have uploaded to the Internet. Organization and Pacing It is recommended that teachers follow a basic schedule as follows:
Chapter 1 Material: 4.25 weeks Chapter 1 Exit Exam: 0.25 weeks Chapter 2 Material: 4.25 weeks Chapter 2 Exit Exam: 0.25 weeks Unit 1: 9.00 weeks
Chapter 3 Material: 4.25 weeks Chapter 3 Exit Exam: 0.25 weeks Chapter 4 Material: 4.25 weeks Chapter 4 Exit Exam: 0.25 weeks Unit 2: 9.00 weeks
Chapter 5 Material: 4.25 weeks Chapter 5 Exit Exam: 0.25 weeks Chapter 6 Material: 4.25 weeks Chapter 6 Exit Exam: 0.25 weeks Unit 3: 9.00 weeks
Chapter 7 Material: 4.25 weeks Chapter 7 Exit Exam: 0.25 weeks Chapter 8 Material: 4.25 weeks Chapter 8 Exit Exam: 0.25 weeks Unit 4: 9.00 weeks Page 6 of 129
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Each unit is a separate entity and each unit exam is not cummulative. For example, the Fall Semester Final Exam assesses Spaceport America and the Bigelow space station, while the Spring Semester Midterm Exam covers the Hohmann equations and the Boeing Crew Module. :: Lesson Overview Students first learn the basics of aerospace and astronautics using pencil, paper, and scientific calculator. They then use what they have learned to create a space mission app designed according to the Engineering Design Process that will be used for realworld spacecraft. They will use spreadsheet software to create their apps. Eight apps will be developed over the course of eight S.T.E.M. projects, with each project dealing with different aspects of space mission design. The assigned space mission will include eight (8) space vehicles or satellites that are named after famous astronauts. Students will research and write a short biography (one slide) about these heroic individuals, one for each of the eight projects. Learning Objectives Evaluation ● Interpret data related to aerospace and astronautics. ● 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 various aspects for human spaceflight such as parabolic space flights, shuttle orbital payload capabilities, space station configurations, unpowered glide landing configurations, change in orbital velocity (delta v), weight of a crew capsule, and amount of propellant used, then relate these to a space mission design. ● Use mathematics to calculate parabolic space flights, shuttle orbital payload capabilities, space station configurations, unpowered glide landing configurations, change in orbital velocity (delta v), weight of a crew capsule, and 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 realworld space mission app that is constrained by certain astronautics factors. Comprehension ● Define constraints to the realworld model. ● Explain how solutions to the problem address the specific requirement. Page 7 of 129
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Knowledge ● Explain the relationships of the principles of aerospace and astronautics to the concept of parabolic spaceflight, orbital payload, space station configuration, landing configuration, delta v, weight, and propellant. ● Demonstrate how their space mission design app addresses the requirements of the parabolic spaceflight, orbital payload, space station configuration, landing configuration, delta v, weight, and propellant. 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. :: Time Frame Two chapters are to be completed every quarter, or halfsemester. This means that there will be four chapters covered per semester, or eight chapters in one school year. This curriculum gives the students about four weeks to research, complete, and present each mission design. During this time, students complete the calculations, update the spreadsheet, finish the website, finish the slideshow presentation, and practice their presentations. S.T.E.M. Scenario Each HSS is assigned different aerospace and astronautics missions that will be designed over the course of the school year. To make learning an adventure, even creative for a change, the student could create a callsign for themselves. Students pretend to be 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 to build space apps by an aerospace/astronautics company. Q: How many Cloud Engineers does it take to change a lightbulb? A: Zero. It's a hardware problem. For example, Virgin Galactic has announced a contract for an app that will calculate certain spaceflight milestones. Various companies compete for the contract by having their engineers (students) build a prototype Space Mission Design App (SMDA). The winning SMDA design will be “bought” by Virgin Galactic. Page 8 of 129
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The students will create and maintain a website to house the SMDA. A working prototype that anyone can use will also be included in the website. They will write a report of the design process for the Engineering PostDevelopment Analysis. They will present a progress slideshow report of their software prototype to the rest of the company during four quarterly company meetings. 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. The presentation takes on the form of a “Science Fair,” where each student stands at a separate table next to a computer that is displaying their website. As each guest walks up to student, they make their presentation. The HSS should be encouraged to dress professionally and to practice their presentations beforehand. The presentation should take between two and three minutes, unless there are a lot of questions from the guests. Students will navigate through the website, discussing the project development, displaying the SMDA, and demonstrating his or her working model. It is suggested that other classes be allowed to walk through the class, so that the young’uns can see what they get to do some day. Posters about this event can be made by the students and hung at various locations around the school. Make sure the students invite their parents too! Of course, the event is incomplete without the Principal being there as well. A call to the local press about a feelgood high school education story couldn't hurt either. All of this creates an atmosphere of a special event, which, by the way, it really is. Namely, students get to experience another way of correlating 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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FALL SEMESTER AEROSPACE Unit 1: Vehicles Chapter 1: Suborbital Spaceflight 13 Chapter 2: Orbital Spaceflight 25
Unit 2: Destinations Chapter 3: Space Station 39 Chapter 4: Space Port 51 ::
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Chapter 1: Suborbital Spaceflight 1.1 Narrative 14 1.2 Vocabulary 16 1.3 Analysis 16 1.4 Suborbital Space Mission Design App 30 1.5 Chapter Test 32 ::
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Suborbital Spaceflight
1.1 Narrative
In this, the first of four aerospacebased S.T.E.M. lessons, students will calculate various Virgin Galactic SpaceShipTwo (SS2) spaceflight parameters and milestones, create an app, and write a report about it. Time Frame About 4 weeks Aerospace Problems Maximum Altitude Time Weightless Time in Space Spaceflight Duration Mathematics Used Quadratic Equations The Quadratic Formula Material List A connection to the Internet Google GMail account Science Topics Physics, Aerospace Activating Previous Learning Basic Algebra Scientific Calculator Essential Questions ● Who are the pioneers of parabolic spaceflight? ● What is the altitude at rocket burnout of a parabolic spacecraft? ● What is the maximum height of a parabolic spacecraft? ● Where does space actually begin? ● When was the first COMMERCIAL parabolic spaceflight? ● Why do people want to go on a parabolic spaceflight? ● How can I be weightless if I am still increasing my altitude? ● Wait. I have to do science and technology and engineering and mathematics, all at the same time? :: Page 13 of 129
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This lesson is powered by E8: 1. Engage ○ Lesson Objectives ○ Lesson Goals ○ Lesson Organization 2. Explore ○ The Quadratic Equation ○ The Quadratic Formula ○ The Parabola and its Components and Definitions ○ Additional Terms and Definitions 3. Explain ○ The Vertex ○ The Vertex as a Maximum ○ Mission Duration Equation 4. Elaborate ○ Other Suborbital Spacecraft Examples 5. Exercise ○ Suborbital Space Mission Parameters ○ Suborbital Space Mission Design Scenario 6. Engineer ○ The Engineering Design Process ○ SMDA Spaceflight Plan ○ Designing a Prototype ○ SMDA Software 7. Express ○ Displaying the SMDC ○ Progress Report 8. Evaluate ○ Post Engineering Assessment :: Lesson Overview Students first learn the basics of parabolic spaceflight using pencil, paper, and scientific calculator. Students then use what they have learned to create a Space Mission Design App (SMDA), designed according to the Engineering Design Process, that will be used for realworld spacecraft. Students will use spreadsheet software to create the app. The app will accept input on the spacecraft flight data and display the space flight profile. Constants ● Standard Gravity (m/s2) Input ● Rocket Burnout Time (min MET) ● Rocket Burnout Altitude (ft MSL) ● Rocket Burnout Velocity (mph) Page 14 of 129
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Output ● Maximum Altitude (m MSL) ● Time Spent Weightless (min) ● Time Spent In Space (min) ● Spaceflight Duration (min) Weightless Phase 1. Begin Weightlessness 2. Begin Spaceflight 3. Maximum Altitude 4. End Spaceflight 5. End Weightlessness Spaceflight Duration 1. Carrier Phase 2. Boost Phase 3. Weightless Phase 4. Reentry Phase 5. Glide Phase SpaceShipTwo conducting a rocket test. Image: Virgin Galactic
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1.2 Vocabulary Boost Phase Carrier Phase End Spaceflight Maximum Altitude Reentry Interface Space Interface White Knight 2 ::
Begin Spaceflight Duration End Weightlessness Mean Sea Level (MSL) Reentry Phase SpaceShipTwo (SS2) Weightless Phase
Begin Weightlessness Drop Glide Phase Mission Elapsed Time (MET) Rocket Burnout Suborbital Spaceflight
1.3 Analysis A suborbital spacecraft, such as SS2, after a Drop from the White Knight 2 carrier aircraft, follows a flight profile that takes the shape of a parabola.. A parabola can be described with a quadratic equation, so that is what we will use. The SS2 follows a similar trajectory that a baseball thrown to another baseball player follows. As all baseball players are aware, a baseball is never thrown in a straight line; rather it is thrown slightly upward. As a result, the path the baseball follows is curved (parabolic). If the same baseball is thrown straight into the air, it will continue moving upward after it leaves the ball player's hand. The baseball at that point has an initial thrust to it, and the moment the ball is released it immediately begins to slow down. The ball will eventually reach a maximum height, where the speed becomes zero, and then drop back down to Page 15 of 129
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Earth (in this case, into the player's glove). The ball increased speed on the way down and arrived at the glove with the same energy that it left with. Note: the moment the player releases the ball, the ball is weightless. Weight returns when the ball is catched. That baseball (spacecraft) follows a nice parabolic curve and can be described by a quadratic equation. :: Virgin Galactic’s SpaceShipTwo is poised to go into space in the near future. Many people have already paid for their ticket, and will be flying into space as soon as the spaceship is ready. You are asked to build the prototype space mission app for your company. Given the initial conditions as input, the app should display the following: ● Rocket Burnout Time (TimeRBO) ● Initial Velocity (InitVel) ● Initial Height (InitHt) 1. How high into space you will go [Maximum Altitude (m)] 2. How long you will be weightless [Time Spent Weightless (min)] 3. How long you will be in space [Time Spent In Space (min)] 4. How long your space flight will be [Spaceflight Duration (hr:min)] 5. A graph of the weightless period [Time (min) vs. Altitude (m)] :: The graph represents a typical weightless period spaceflight profile for SpaceShipTwo. The horizontal axis of the graph represents time (in seconds), and the vertical axis represents height (in meters). Space is defined as beginning at 100,000 m. As you can see from the graph, the spaceflight takes the shape of an inverted parabola. This means that we can use a Quadratic Equation. To find the maximum height and the time spent weightless, first determine the time component of the vertex, a.k.a, the axis of symmetry. To find the time spent in space, find the time that the spacecraft entered space. Page 16 of 129
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But first, the Quadratic Equation is: h(t) =
2
1
+ v 0 t + h0
− 2 g0 t
where, ● g0 = Standard Gravity (9.80665 m/s2) ● t = time (s) ● v0 = initial velocity of the spacecraft (m/s) ● h0 = initial height of the spacecraft (m MSL) ● h(t) = height of the spacecraft at time t (m MSL) Therefore the time component of the vertex is: −v −v v vertext = 2(− 1 0g ) = −g0 = g0 0
2 0
0
The time spent weightless is twice vertext, taking advantage of the symmetry of a parabola. T imeweightless = 2(vertext ) To find the maximum height (vertexh), just plug vertext into the Quadratic Equation. vertexh = h(vertext ) = − 12 g 0 (vertext )2 + v 0 (vertext ) + h0 To find the time the spacecraft enters space, let h = 100,000, make the Quadratic Equation equal to zero, then use the Quadratic Formula: 2
1
100, 000 =
+ v 0 t + h0
− 2 g0 t
1
2
+ v 0 t + h0
1
2
+ v 0 t + h1
0 =
− 2 g0 t
0 =
− 2 g0 t
−
100, 000
where, ● h1 = height at space = h0 100,000 Now we use the Quadratic Formula to solve for the time you enter space: spacet =
−v 0
+
√v
1 2 o − 4(− 2 g 0 )(h1 ) 1 2(− 2 g 0 )
=
−v 0
+
√v
2 o
+ 2g 0 h1
−g 0
=
v0 −
√v
2 o
g0
+ 2g 0 h1
Once you have the time you enter space, subtract it from the vertext, double it (again, because of symmetry), and we Page 17 of 129
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have the Time Spent in Space. T imespace = 2(vertext − spacet ) To find the Mission Elapsed Time for the five milestones of the Weightless Phase use the following equations: W eightlessBegin = T imeRBO SpaceBegin = T imeRBO + spacet Altitudemax = T imeRBO + vertext SpaceEnd = T imeRBO + 2(spacet ) W eightlessEnd = T imeRBO + 2(vertext ) We can now tackle the spaceflight duration calculations. Given: ● Boost Phase = 70 s = 1.17 min ● Reentry Phase = 3.50 min ● Glide Phase = 25.00 min Then C arrier P hase = T imeRBO − Boost P hase and DurationSpacef light = Carrier + Boost + T imeW eightless + Reentry + Glide :: Example Suppose we have an input of ● TimeRBO = 110 min ● InitHt = 135,000 ft MSL ● InitVel = 2,600 mph What is the Time Spent Weightless, the Maximum Height achieved, the Time Spent In Space, and the Time Spent on Spaceflight aboard SpaceShipTwo? First, let’s convert the input into S.I. Units: 2,600 mi 1,609 m hr v0 = hr mi 3,600 s = 1, 162 mps Page 18 of 129
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h0 =
135,000 f t m 1 3.28 f t
= 41, 148 m M SL
So, v0 g0
vertext =
1162 9.80665
=
= 118.49 s
The Time Spent Weightless is: T imeweightless = 2(vertext )
= 2(118.49) = 236.98 s = 3.95 min
and the maximum altitude is: vertexh = f (vertext ) =
1
2
+ v 0 (vertext ) + h0 2 1 − 2 (9.80665)(118.49) + 1162(118.49)
− 2 g 0 (vertext )
=
+ 41148
= 110, 027 m M SL Finding h1, h1 = h0 − 100000 = − 58, 852 m we can use it to find the time you enter space: spacet =
v0 −
√v
2 o
+ 2g 0 h1
g0
=
1162 −
√(1162)
2
+ 2(9.80665)(−58852) 9.80665
= 73 s Once we know when we enter space we can calculate the Time Spent in Space: T imespace = 2(vertext − spacet ) = 2(118.49 − 73) s = 90.98 s = 1.52 min We now calculate the other mission milestones and the total mission duration: C arrier P hase = T imeRBO − Boost P hase = 110 min − 1.17 min = 108.83 min and Page 19 of 129
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DurationSpacef light = Carrier + Boost + T imeW eightless + Reentry + Glide = (108.83 + 1.17 + 3.95 + 3.50 + 25.00) min = 142.45 min = 2 hrs 22.45 min So, given an initial velocity at Rocket Burnout Time of 110 min going 2,600 mph, with an initial height of 135,000 ft MSL, we can make the following conclusions: 1. Time Spent Weightless is 3.95 min 2. Maximum Height achieved is 110,027 m MSL 3. Time Spent In Space is 1.51 min 4. Time Spent on Spaceflight aboard SpaceShipTwo is 2 hr 22.45 min Therefore, out of an almost two and a half hour flight, the passengers spend less than four minutes weightless, and less than two minutes in space. If each ticket costs $250,000, that comes out to about $2,747 for each second spent in space! The time spent in space is irrelevant anyway; that the passengers went into space is the real story.
:: R.A.F.T. Writing ● Role: Teacher ● Audience: Middle School students ● Format: Five paragraph essay ● Topic: The X15. Who were some of the astronauts that flew the missions? Did any of the pilots fly into space? What was unique about their missions? What was in common with all the missions? How does an X15 suborbital space mission differ from the space mission presented in this textbook? How are they the same? Why even bother to fly a suborbital spaceflight anyway? ::
1.4 Suborbital 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. Page 20 of 129
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Sample Open Source Code Once the cells have been named referencing cells is easy. ● CALCULATIONS ○ VertexTime=v0/g0 ○ TimeWeightless=2*VertexTime ○ MaxAlt=0.5*g0*VertexTime^2+v0*VertexTime+h0 ○ h1=h0Space ○ SpaceTime=(v0SQRT(v0^2+2*g0*h1))/g0 ○ TimeInSpace=2*(VertexTime SpaceTime) ● GRAPHING ○ BeginWt=RBO ○ BeginSpace=RBO+TimeSpace ○ MaxAlt=RBO+VertexTime ○ EndSpace=RBO+2*TimeSpace ○ EndWt=RBO+2*VertexTime INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE Page 21 of 129
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INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE
::
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Sample App Interface Design
::
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1.5 Chapter Test I. VOCABULARY Match the aerospace term with its definition. 1. End Spaceflight
A. The moment a rocket engine shuts itself off, where the spacecraft continues upward on its own momentum.
2. Mission Elapsed Time
B. The spacecraft that is dropped from White Knight 2. After rocket burnout, the spacecraft coasts up to space and back.
3. Rocket Burnout
C. The third of six phases in a parabolic spaceflight, where the spacecraft and its occupants experience weightlessness.
4. SpaceShipTwo
D. The moment a spacecraft exits from space. The spacecraft returns to the atmospheric environment.
5. Weightless Phase
E. Time since the beginning of the spaceflight.
II. MULTIPLE CHOICE Circle the correct answer. 6. The Quadratic Equation describing the parabolic flight profile of a Virgin Galactic suborbital spaceflight has a leading coefficient that is less than zero. A. True B. False 7. After reaching maximum altitude, weight returns and the Virgin Galactic passengers are no longer weightless. A. True B. False 8. If Vertext = 1.75 min, then the Time Spent Weightless is A. 1.75 min B. 3.50 min C. 5.25 min D. None 9. You reach the maximum altitude 30 seconds after crossing into space. How long will you be in space? A. 30 sec B. 60 sec C. 90 sec D. None. 10. A Virgin Galactic suborbital spacecraft is going 1,100 mps at the moment of Rocket Burnout. How long will it take to coast up to the maximum altitude? A. 56.12 sec B. 112.24 sec C. 224.48 sec D. 336.72 sec Page 24 of 129
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III. CALCULATIONS A Virgin Galactic suborbital spacecraft has an initial velocity at Rocket Burnout Time of 108 minutes, going 2,550 mph, with an initial height of 140,000 feet MSL. 11. How long does it take to reach maximum altitude after rocket burnout? 12. What is the maximum altitude of this spaceflight? 13. How long does it take to reach space after rocket burnout? 14. How long were the Virgin Galactic passengers weightless? 15. How long were the Virgin Galactic passengers in space? 16. How long was the Carrier Phase of the suborbital spaceflight? 17. How long was the spaceflight? 18. What percent of the suborbital spaceflight was spent during the Weightless Phase? 19. What percent of the suborbital spaceflight was spent in space? 20. What percent of the suborbital spaceflight was not spent in space or during the Weightless Phase? IV. WRITING Write a one paragraph essay on the topics below. 21. Explain why the leading coefficient of the quadratic equation describing the parabolic spaceflight profile of a Virgin Galactic suborbital spacecraft is negative. 22. Explain why the total time weightless can be calculated by doubling the time it takes to reach the vertex of the parabola of a Virgin Galactic suborbital spaceflight. 23. Explain why passengers feel weightless even though the spacecraft is coasting to a maximum altitude in the UP direction. 24. Describe the stepbystep procedure to calculating the maximum altitude reached by a Virgin Galactic suborbital spacecraft given the time that the maximum altitude occurred. 25. Write a short story about what it would feel like to float weightlessly inside of SpaceShipTwo while gazing at the curvature of the Earth as it flies a parabolic spaceflight profile. ::
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Chapter 2: Orbital Spaceflight 2.1 Narrative 26 2.2 Vocabulary 28 2.3 Analysis 28 2.4 Student Worksheets 99 2.5 Orbital Space Mission Design App 33 2.6 Chapter Test 34 ::
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Orbital Spaceflight
2.1 Narrative
In this, the second of four aerospacebased S.T.E.M. projects, students will calculate the payload capacity of the R.E.L. Skylon spaceplane. Students will use the launch site latitude to determine the weight of an orbiting payload. Time Frame About 4 weeks Aerospace Problems Launch Latitude Orbital Inclination Orbital Altitude Payload Weight Mathematics Used Quadratic Equations Linear Equations Material List A connection to the Internet Google GMail account Science Topics Physics, Aerospace Activating Previous Learning Basic Algebra Scientific Calculator Essential Questions ● Who are the pioneers of spaceplane technology? ● What is the Orbital Inclination of a spacecraft? ● Where is the payload bay of the R.E.L. Skylon located? ● When will be the first flight of the Skylon spaceplane? ● Why do people want to fly payload into orbit on a spaceplane? ● How does the latitude of the Launch Site effect an orbital payload? ● How does the desired orbital altitude effect an orbital payload? ● Wait. I have to do science and technology and engineering and mathematics, all at the same time? :: Page 27 of 129
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This lesson is powered by E8: 1. Engage ○ Lesson Objectives ○ Lesson Goals ○ Lesson Organization 2. Explore ○ The Quadratic Equation ○ The Linear Equation ○ The AltitudePayload Line and its Components and Definitions ○ Additional Terms and Definitions 3. Explain ○ Orbital Inclination ○ Orbital Altitude vs. Payload Weight ○ Payload Weight vs. Orbital Altitude 4. Elaborate ○ Other Orbital Spacecraft Examples 5. Exercise ○ Orbital Space Mission Parameters ○ Orbital Space Mission Design Scenario 6. Engineer ○ The Engineering Design Process ○ SMDA Spaceflight Plan ○ Designing a Prototype ○ SMDA Software 7. Express ○ Displaying the SMDC ○ Progress Report 8. Evaluate ○ Post Engineering Assessment :: Lesson Overview Students first learn the basics of spaceflight launch payload using pencil, paper, and scientific calculator. They then use what they have learned to create a Space Mission Design App (SMDA), designed according to the Engineering Design Process that will be used for realworld spacecraft. Students will use spreadsheet software to create the app and will use slideshow software for their presentations. They will also create a document of their experiences engineering the SMDA and presenting their findings to the rest of the class. Constants ● (none) Page 28 of 129
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Input ● ● ● Output ●
Launch Site Latitude (deg) Payload Weight (lbs) Orbital Altitude (mi)
Payload Weight (kg) ○ At Latitude (km) ○ To I.S.S. (km) ○ To Polar Orbit (km) ● Orbital Altitude (km) ○ At Latitude (kg) ○ To I.S.S. (kg) ○ To Polar Orbit (kg) :: The R.E.L. Sylon in Low Earth Orbit. Image: R.E.L.
2.2 Vocabulary International Space Station Latitude Orbital Altitude Polar Orbit ::
Latitude Launch Site Orbital Inclination Payload
Launch Site Latitude Payload Weight
2.3 Analysis To determine the weight and orbital altitude of a spacecraft climbing into earth orbit, we need information on the space plane's capabilities at various launch latitudes. Fortunately, R.E.L. provides us with exactly what we need.
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PayloadAltitude Graph for an Equatorial Launch Site
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Using these graphs, we can determine the general formula for each of these lines. So, let's make a couple of tables, shall we? We will concentrate on the Launch Site Latitude equal to the Orbital Inclination. For the Launch Site Latitude of 0o, we will look for the graph at 250 km for the Orbital Inclination of 0o. For the 15o graph, we will look at the 250 km point on the 15o Orbital Inclination line. This process continues for each graph: 250 KM
800 KM
0o 15,500 kg
0o 11,000 kg
15o 15,250 kg
15o 10,750 kg
30o 14,500 kg
30o 10,000 kg
45o 13,250 kg
45o 8,750 kg
60o 11,750 kg
60o 7,000 kg
Now we can analyse the tables to see what kind of equation that we have. We can use the old trick of subtracting the dependent variables (absolute value) to determine the degree of the polynomial equation. If all the subtractions keep coming up with the same number it is a linear (degree 1) polynomial. If after 2 subtractions we get a constant, then it is a quadratic (degree 2) polynomial. If 3, then a cubic (degree 3), etc. Let's see what we get for the first table: 15,500 15,250 => |15,500 15,250| = 250 14,500 => |15,250 14,500| = 750 => |250 750| = 500 13,250 => |14,500 13,250| = 1,250 => |750 1,250| = 500 11,750 => |13,250 11,750| = 1,750 => |1,250 1,750| = 500 So we get a constant after two iterations. Therefore, we are dealing with a second degree polynomial, or a quadratic equation. y = ax2 + bx + c Writing the quadratic in aerospace form, the general equation becomes: AtLatitudeP ayloadALT = aDEG 2 + bDEG + P ayload0 where ● AtLAtitudePayloadALT = Weight of the orbital cargo headed to a certain altitude in space ● a = Constant ● DEG = Orbital Inclination of Payload ● b = Constant ● Payload0 = Initial Payload Page 32 of 129
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Since the initial weight of the payload is irrelevant, we can zero out b: AtLatitudeP ayloadALT = aDEG 2 + P ayload0 Using the table of data for a 250 km orbital altitude, we can calculate Payload0 by plugging in DEG = 0o and Payload250 = 15,500: AtLatitudeP ayload250 = aDEG 2 + 15, 500 We can then easily calculate a by using the table (again) and plugging DEG = 15o and Payload0 = 15,250: AtLatitudeP ayload250 = − 0.0011DEG 2 + 15, 500 We now have the equation that we need to determine the payload capability (PayloadALT) depending on the latitude of the launch site (DEG) for a 250 km Orbital Altitude. The other polynomial equation can be determined using the same technique on the 800 km table: AtLatitudeP ayload800 = − 0.0011DEG 2 + 11, 000 We now have the equation that we need to determine the payload capability (PayloadALT) depending on the latitude of the launch site (DEG), this time for an 800 km Orbital Altitude. We can now determine the two points needed to draw the linear equation for the payload. :: Example An R.E.L. Skylon is conducting spaceflight operations from Spaceport America. A customer has a satellite that needs to be placed in an orbital altitude of 490 miles. The Orbital Inclination is irrelevant. What is the maximum weight that the satellite can be? Spaceport America has a location in New Mexico of 32.9980 North Latitude, so we will set our independent variable DEG to 33. AtLatitudeP ayload250 = − 0.0011(33) 2 + 15, 500 = 14, 290 kg and AtLatitudeP ayload800 = − 0.0011(33) 2 + 11, 000 = 9, 790 kg So, the endpoints to to our linear equation are (250, 14,290) and (800, 9,790). We can finally write the linear equation in slopeintercept (y=mx+b) form by finding the slope (m) and the yintercept (b). The slope is the change in y divided by the change in x. Plugging one of the points back into the equation yields the yintercept. 9,790 − 14,290 S lope = m = 800 − 250 = − 8.18 Page 33 of 129
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and y − int = b = y 1 − mx1 = 14, 250 − (− 8.18)(250) = 16, 335 km Therefore, the linear equation for the Skylon operating out of Spaceport America given a desired orbital altitude of between 250 km and 800 km is: S paceport − to − AtLatitude ALT = − 8.18ALT + 16, 335 Converting 490 miles to 789 kilometers, and plugging that into our formula, we get: S paceport − to − AtLatitude 789 = − 8.18(789) + 16, 335 = 9, 883 kg Therefore, the satellite can have a maximum weight of almost ten thousand kilograms. The same technique described above can be used to determine the equations to reach the NASA’s International Space Station (I.S.S.) and for a polar orbit from Spaceport America. These will be exercises left up to the student. S paceport − to − I SS ALT = − 7.73ALT + 13, 982 S paceport − to − P olar ALT = − 7.27ALT + 8, 118 :: R.A.F.T. Writing ● Role: Teacher ● Audience: Middle School students ● Format: Five paragraph essay ● Topic: The Space Transportation System (Space Shuttle). Who were some of the astronauts that flew the missions? What payload did they deposit in orbit? What was unique about their missions? What was in common with all the missions? How does the Space Shuttle differ from the spaceplane presented in this textbook? How are they the same? Why even bother to build a spaceplane anyway? ::
2.4 Orbital 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 Page 34 of 129
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4. Calculations The App can now be developed. Sample Open Source Code Once the cells have been named referencing cells is easy. ● CALCULATIONS ○ AtLatitudePayload250=0.0011* DEG^2+15500 ○ AtLatitudePayload800=0.0011* DEG^2+11000 ● GRAPHING ○ m=(AtLatitudePayload800AtLatitudePayload250)/550 ○ b=AtLatitudePayload250 m*250 ○ AtLatitudePayload=m*ALT+b Sample App Interface
::
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2.5 Chapter Test I. VOCABULARY Match the aerospace term with its definition. 1. Launch Site Latitude
A. The height above Mean Sea Level (MSL) of a spacecraft.
2. Orbital Altitude
B. The mass of a payload that is effected by Earth’s gravity.
3. Orbital Inclination
C. An orbit that flies above the North and South poles; it has an Orbital Inclination of 98 degrees.
4. Payload Weight
D. The latitude (measured in degrees) of the launch site.
5. Polar Orbit
E. The number of degrees that an orbit subtends relative to the equator.
II. MULTIPLE CHOICE Circle the correct answer. 6. The R.E.L. Skylon Payload Equation when graphed forms a parabola which can be describe using a quadratic equation. A. True B. False 7. The R.E.L. Skylon Payload Equation when graphed forms a straight line which can be describe using a linear equation. A. True B. False 8. The further north the R.E.L. Skylon launches from, the ____________ payload weight it can carry into Low Earth Orbit. A. More B. Less C. Neither D. Cannot be determined 9. The higher the orbital altitude of the R.E.L. Skylon, the ____________ payload weight it can carry into Low Earth Orbit. A. More B. Less C. Neither D. Cannot be determined 10. The more the R.E.L. Skylon carries into Low Earth Orbit, the ____________ the final orbital altitude of the spaceplane. A. More B. Less C. Neither D. Cannot be determined Page 36 of 129
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III. CALCULATIONS An orbital spacecraft launches from Baikonur Cosmodrome to the International Space Station (I.S.S.). 11. What is the Launch Site Latitude of the cosmodrome? 12. What is the orbital inclination that the spacecraft needs to attain? 13. What is the Orbital Altitude of the International Space Station? 14. What is the Baikonur CosmodromeI.S.S. general Quadratic Equation? 15. What is the Baikonur CosmodromeI.S.S. 250 km general Quadratic Equation? 16. What is the Baikonur CosmodromeI.S.S. 800 km general Quadratic Equation? 17. What is the slope of the Baikonur CosmodromeI.S.S. general Linear Equation? 18. What is the yintercept of the Baikonur CosmodromeI.S.S. general Linear Equation? 19. What is the Baikonur CosmodromeI.S.S. general Linear Equation? 20. What is the maximum weight that the R.E.L. Skylon can lift to the International Space Station from the Baikonur Cosmodrome? IV. WRITING Write a one paragraph essay on the topics below. 21. Explain how to find the leading coefficient of the R.E.L. Skylon payload Quadratic Equation. 22. Explain why the further north a launch site is located, the less payload that can be carried into space. 23. Explain why the higher the orbital altitude needed, the less the amount of payload that can be carried. 24. Explain why the more the amount of payload is needed to be carried into space, the less the orbital altitude that the R.E.L. Skylon can attain. 25. Write a short story about what it would feel like to float weightlessly inside of an R.E.L. Skylon spaceplane while gazing at the curvature of the Earth as it flies an orbital spaceflight profile. ::
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Chapter 3: Space Station 3.1 Narrative 40 3.2 Vocabulary 42 3.3 Analysis 42 3.4 Space Station Design App 44 3.5 Chapter Test 47 ::
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Space Station
3.1 Narrative
In this, the third of four aerospacebased S.T.E.M. project, students will use the Bigelow Aerospace BA330 and BA2100 space station pressurized modules to launch and assemble a space station in Low Earth Orbit (LEO). Students will calculate the total pressurized volume, the total weight, the crew size, and the total cost of launching into space and setting up their own space station. Time Frame About 4 weeks Aerospace Problems Space Station Cost Space Station Weight Space Station Volume Space Station Crew Mathematics Used Matrices Material List A connection to the Internet Google GMail account Science Topics Physics, Aerospace Activating Previous Learning Basic Mathematics Scientific Calculator Essential Questions ● Who are the many space station pioneers? ● What is a space station? ● Where can a Bigelow space station be spotted in the night sky? ● When will the first commercial Bigelow space station be flown? ● Why do people want to live on a space stations in orbit ● How many people can live on a space station? ● Wait. I have to do science and technology and engineering and mathematics, all at the same time? Page 39 of 129
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:: This lesson is powered by E8: 1. Engage ○ Lesson Objectives ○ Lesson Goals ○ Lesson Organization 2. Explore ○ The BA330 Habitat Specifications ○ The BA2100 Habitiat Specifications ○ The Bigelow Space Station and its Components and Definitions ○ Additional Terms and Definitions 3. Explain ○ Launch Constraints 4. Elaborate ○ Other Space Station Examples 5. Exercise ○ Space Station Parameters ○ Space Station Design Scenario 6. Engineer ○ The Engineering Design Process ○ SMDA Space Station 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 space station design using pencil, paper, and scientific calculator. Students then use what they have learned to create a Space Mission Design App (SMDA), designed according to the Engineering Design Process, that will be used for realworld spacecraft. We will be using the products from Bigelow Aerospace, which makes inflatable habitat modules that once placed into orbit, well, inflate. This allows for a greater volume of space inside for the crew. It has solar panels for electrical power and radiators to dispose of waste heat. It even has windows! Students will use spreadsheet software to create the app and will use slideshow software for their presentations. They will also create a document of their experiences engineering the SMDA and presenting their findings to the rest of the class. Page 40 of 129
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Constants ● None Input ● Total BA 2100 Modules ● Total BA 330 Modules ● Total PB/DN Modules Output ● Total BA 2100 Stacks ● Total BA 330 Stacks ● Total PB/DN Stacks ● Total SpaceX Falcon Heavy ● Total NASA SLS Block I ● Total Weight of the space station ● Total Crew Size ● Total Cost of the space station ::
Interior view of the BA330 module. Image: Bigelow Aerospace
3.2 Vocabulary BA330 Module Crew Size Falcon Heavy Propulsion Bus (PB) ::
BA300 Stack Crew Volume PB/DN SLS Block IA (SLSIA)
BA2100 Module Docking Node (DN) PB/DN Stack Space Station
BA2100 Stack Expendable Launch Vehicle Pressurized Volume
3.3 Analysis To launch these excellent habitat modules into space, we obviously need a launch vehicle. Shopping around for what’s available to use to launch our city, we find two Expendable Launch Vehicles (ELV). These rockets haven’t been built yet, but so long as funding continues they will be... one day. The two ELVs are the SLS IA and the Falcon Heavy. Since the SLS IA ELV can carry 105,000 kg into Low Earth Orbit (LEO), and one BA2100 weighs 100,000 kg, it can carry only one unit at a time. We will call this the “BA2100 Stack.” The Falcon Heavy ELV can lift 53,000 kg to LEO. Each BA330 weighs 25,000 kg, so it can carry 2 units at a time (assuming, of course, that it could fit in a payload shroud). We will call this the “BA330 Stack.” The PB/DNs each weigh 17,000 kg, so 3 units will fly on the Falcon Heavy ELV to LEO. This will be called the “PB/DN Stack.” BA2100 Stack: ● Cost: (1) SLS IA + (1) BA2100 = $750M + $500M = $1,250M ● Weight: (1) BA2100 = (1) 100,000 kg = 100,000 kg ● Volume: (1) 2,100 m3 = 2,100 m3 Page 41 of 129
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● Crew: (1) 16 = 16 Astronauts BA330 Stack: ● Cost: (1) Falcon Heavy + (2) BA2100 = $150M + (2) $125M = $400M ● Weight: (2) BA330 = (2) 25,000 kg = 50,000 kg ● Volume: (2) 330 m3 = 660 m3 ● Crew: (2) 6 = 12 Astronauts PB/DN Stack: ● Cost: (1) Falcon Heavy + (3) PB/DN = $150M + (3) $75M = $375M ● Weight: (3) 17,000 kg = 51,000 kg It now becomes an easy matter to compute the specifications of any space station design that we choose. If a design calls for using four BA330 modules, then two BA300 Stacks are needed. Note, however, that the space station design does have constraints. For instance, the number of BA300 habitat modules must be even, and the number of PB/DNs must be a multiple of 3. To summarize, BA2100 Stack ● $1,250M ● 100,000 kg ● 2,100 m3 ● 16 Astronauts BA330 Stack ● $400M ● 50,000 kg ● 660 m3 ● 12 Astronauts PB/DN Stack ● $375M ● 51,000 kg Everything can be put into a matrix: Stack Information = The number of each stack that is needed can also be written as a matrix: Number of Stacks = [BA − 2100 Stacks BA − 330 Stacks P B /DN Stacks]
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However, the Number of Stacks will have to first be calculated, since the number of BA330s and PB/DNs must be multiples of 2 and 3 respectfully. Therefore, given: ● Number of BA2100s ● Number of BA300s ● Number of PB/DNs N umber of Stacks =
[N umber of BA
−
2100
N umber of BA−300 2
N umber of P B /DN 3
]
Since the Number of Stacks is a [1 x 3] matrix, and the Stack Information is a [3 x 4] matrix, we can perform the dot product of the 2 matrices, which is represented as: [1 x 3] X [3 x 4] = [1 x 4] Number of Stacks X Stack Information = Total where Total is represented as: T otal = [Cost W eight V olume Crew] So let’s build us a city in space, shall we? :: Example The folks at Bigelow Aerospace have made it easy for us: they’ve already designed a very nice space station! It’s called the “Hercules Resupply Depot,” but we’ll just call it “Home.” Thanks, Bigelow! As you can see from the poster, we’ll need three BA2100s, six BA330s, and three PB/DNs to complete the design. We can therefore calculate how many “stacks” we’ll need: (3) BA2100 = (3) BA2100 Stacks ● (3) $1,250M = $3,750M ● (3) 100,000 kg = 300,000 kg ● (3) 2,100 m3 = 6,300 m3 ● (3) 16 Crew = 48 Crew (6) BA330 = (3) BA330 Stacks ● (3) $400M = $1,200M ● (6) 25,000 kg = 150,000 kg The Hercules space station. Image: Bigelow Aerospace Page 43 of 129
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● ●
(6) 330 m3 = 1,980 m3 (6) 6 Crew = 36 Crew
(3) PB/DN = (1) PB/DN Stack ● (1) $375M ● (3) 17,000 kg = 51,000 kg Adding everything up we get: ● Total Cost: $5,325M ● Total Weight: 501,000 kg ● Total Volume: 8,280 m3 ● Total Crew: 84 Astronauts Top view of the Hercules space station. Image: S.T.E.M. For the Classroom The calculations, however, are waaaaaay easier to handle using Matrix Notation: 6 3 N umber of Stacks = [ 3 3 1] 2 3 ] = [3 and [3 3 1] X = [$5,325M 501mt 8,280m3 84Crew] Notice that our volume is close to the 8,300 cubic meters advertised in the Hercules image. The amount of space that each astronaut gets can now be calculated. V olume C rew V olume = TTotal otal Crew =
8280 84
= 98.59m3 per astronaut. As we can see, the Resupply Depot “Hercules” has the following specifications: ● Total Cost: $5,325M ● Total Weight: 501,000 kg ● Total Volume: 8,280 m3 ● Total Crew: 84 Astronauts ● Total Crew Volume: 99 m3 So this is a space station that weighs half a million kilograms, has over eight thousand cubic meters of habitable space, can house 84 people, with almost one hundred cubic meters of elbow room for each person, can reboost its orbit, and costs a little over five billion dollars. :: Page 44 of 129
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R.A.F.T. Writing ● Role: Teacher ● Audience: Middle School students ● Format: Five paragraph essay ● Topic: The Apollo Skylab. Who were the astronauts that flew the missions? How many days did each crew stay? What was unique about their missions? What was in common with all the missions? How does the Skylab differ from the space station presented in this textbook? How are they the same? Why even bother to build a space station anyway? ::
3.4 Space Station 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 ○ TotBA2100Wt=InputNumBA2100*BA2100Wt ○ TotBA2100Vol=InputNumBA2100*BA2100Vol ○ TotBA2100Crew=InputNumBA2100*BA2100Crew ○ TotBA2100Cost=InputNumBA2100*BA2100Cost ○ TotBA330Wt=InputNumBA330*BA330Wt ○ TotBA330Vol=InputNumBA330*BA330Vol ○ TotBA330Crew=InputNumBA330*BA330Crew ○ TotBA330Cost=InputNumBA330*BA330Cost ○ SpaceStationVol=TotBA2100Vol+TotBA330Vol ○ SpaceStationCrew=TotBA2100Crew+TotBA330Crew ○ SpaceStationCrewVol=SpaceStationVol/SpaceStationCrew INSERT CODE HERE Page 45 of 129
S.T.E.M. For the Classroom: Adventures in Outer Space
INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE Page 46 of 129
S.T.E.M. For the Classroom: Adventures in Outer Space
Sample App Interface Design
::
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3.5 Chapter Test I. VOCABULARY Match the aerospace term with its definition. 1. BA330 Module
A. The number of astronauts aboard a spacecraft or space station.
2. Crew Size
B. A Bigelow habitat module that has a pressurized volume of 330 cubic meters, weighs 25,000 kg, and can hold 6 crew.
3. Crew Volume
C. The unit used to reboost the space station due to orbital decay.
4. Falcon Heavy
D. The total pressurized volume for each crew member.
5. Propulsion Bus (PB)
E. An ELV from SpaceX that can lift 53,000 kg into Low Earth Orbit.
II. MULTIPLE CHOICE Circle the correct answer. 6. The name of the Bigelow habitat module is also the volume (in cubic feet) of the habitable interior of the module. A. TRUE B. FALSE 7. Bigelow habitat modules come complete with docking ports, solar panels, radiators, and a breathable atmosphere. A. TRUE B. FALSE 8. What is the habitable volume of a space station design that consists of one BA2100 module and two BA330 modules? A. 2,760 in3 B. 2,760 ft3 C. 2,760 m3 D. Cannot be determined 9. A space station design calls for eight BA330 habitat modules. How many BA330 Stacks will be needed? A. Two B. Four C. Six D. Cannot be determined 10. The Crew Volume can be found by dividing the space station ______________ into the total number of space station crew A. Volume B. Weight C. Crew Size D. Cannot be determined Page 48 of 129
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III. CALCULATIONS A space station design calls for 6 BA330 modules and 3 PB/DNs. 11. How many SLS IA ELVs will be required? 12. How many Falcon Heavy ELVs will be required? 13. How many BA2100 Stacks will be required? 14. How many BA330 Stacks will be required? 15. How many PB/DN Stacks will be required? 16. What is the weight of this space station? 17. What is the habitable volume of this space station? 18. What is the number of crew of this space station? 19. What is the Crew Volume of this space station? 20. What is the total cost of this space station? IV. WRITING Write a one paragraph essay on the topics below. 21. Explain how to find the total habitable volume of a Bigelow space station simply by knowing how many of each module it has. 22. Explain why (or why not) three PB/DNs can be launched using a Falcon Heavy ELV. 23. Explain why (or why not) two BA2100 habitat modules can be launched using the SLS IA ELV. 24. Explain how to calculate the total pressurized volume for each crew member (Crew Volume). 25. Write a short story about what it would feel like to float weightlessly inside of an R.E.L. Skylon spaceplane, while gazing at the curvature of the Earth as it flies an orbital spaceflight profile. ::
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Chapter 4: Space Port 4.1 Narrative 52 4.2 Vocabulary 54 4.3 Analysis 54 4.4 Spacecraft Landing App 57 4.5 Chapter Test 59 ::
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Space Port
4.1 Narrative
In this, the fourth and final aerospacebased S.T.E.M. project, students will track the position and speed of a spacecraft that is landing at Spaceport America. Students will also determine the spacecraft descent rate, ground speed, and time until touchdown. Time Frame About 4 weeks Aerospace Problems Glide Slope Altitude Distance from Spaceport Descent Rate Ground Speed Mathematics Used Trigonometry Vector Analysis Material List A connection to the Internet Google GMail account Science Topics Physics, Aerospace Activating Previous Learning Basic Mathematics Scientific Calculator Essential Questions ● Who are the pioneers of spaceports? ● What is the Complement of an angle? ● Where can a spaceport be located? ● When was Spaceport America open for business? ● Why would people prefer to land at a spaceport as opposed to an airport? ● How do I use Trigonometry to calculate the distance and altitude of a spacecraft? ● Wait. I have to do science and technology and engineering and mathematics, all at the same time? Page 51 of 129
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:: This lesson is powered by E8: Engage ○ Lesson Objectives ○ Lesson Goals ○ Lesson Organization Explore ○ The Right Triangle ○ The Trigonometric Identities ○ Basic Vector Analysis ○ Additional Terms and Definitions Explain ○ Glide Slope Elaborate ○ Other Spaceport Examples Exercise ○ Spacecraft landing Parameters ○ Spacecraft landing Scenario Engineer ○ The Engineering Design Process ○ SMDA Spacecraft Landing Plan ○ Designing a Prototype ○ SMDA Software Express ○ Displaying the SMDA ○ Progress Report Evaluate ○ Post Engineering Assessment :: Lesson Overview Students first learn the basics of spaceflight unpowered glide landing using pencil, paper, and scientific calculator. Students then use what they have learned to create a Space Mission Design App (SMDA), designed according to the Engineering Design Process, that will be used for realworld spacecraft. We will be using Spaceport America (33o N, 107o W), located just north of Las Cruces, NM. Typical spacecraft that could land at this facility are the Virgin Galactic SpaceShipTwo and the R.E.L. Skylon. Students will use spreadsheet software to create the app, and will use slideshow software for their presentations. They will also create a document of their experiences engineering the SMDA and presenting their findings to the rest of the class. Page 52 of 129
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Constants ● None Input ● Glide Angle (deg) ● Glide Distance 1 (ft) ● Glide Distance 2 (ft) Output ● Altitude (m AGL) ● Distance from Spaceport (m) ● Glide Slope (deg) ● Glide Speed (mps) ● Descent Rate (mps) ● Ground Speed (mps) ● Time to Touchdown (min) ::
A facility that services spacecraft. Image: Spaceport America
4.2 Vocabulary Adjacent Side Distance From Spaceport Glide Speed Landing Profile Time To Touchdown ::
Altitude Glide Angle Ground Speed LineOfSight Touchdown
Above Ground Level (AGL) Glide Distance Hypotenuse Opposite Side
Descent Rate Glide Slope Landing Laser Right Triangle
4.3 Analysis Any spacecraft returning from space is always out of propellant. This is because all the propellant is used during the trip into space. Consequently, there is none available for the return trip. All machines that have wings can glide, that is, fly with the engine turned off. Some glide better than others, but still, they all glide. This is why spacecraft come in with their nose down; they are maintaining required airspeed. As they cross over the edge of the runway, the nose is pulled up and the spacecraft flattens out its glide as air is packed underneath the wings. It’s then just a simple matter of letting the spacecraft sink to a gentle touchdown. Once on the ground the nose is kept in the air “wheelie” fashion, so that speed can be bled off without using brakes, because they can get very hot extremely quickly. After the nose comes down on its own the brakes can then be (sparingly) applied. Eventually, the spacecraft rolls to a full stop. Back home once again! Page 53 of 129
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Glide path of a vehicle returning from space. Image: S.T.E.M. For the Classroom
We will be tracking a hypothetical spacecraft returning from space (such as the Virgin Galactic SpaceShipTwo) as the pilots on board perform an unpowered glide landing back to the Spaceport. A Landing Laser located at the edge of the Spaceport runway will be used to track the landing spacecraft. The laser will determine the Glide Angle and the Glide Distance:
Diagram of Landing Configuration. Image: S.T.E.M. For the Classroom
This laser will measure the Glide Angle from the vertical, since the ground may or may not be level. The laser itself when triggered will perform two bursts over a one second period. This gives us Glide Distance 1 and Glide Distance 2. Note: Ideally, the laser would be firing every second so that a more accurate plot of the spacecraft can be made as it comes in for the landing. This constraint to the project means that we are basically taking a snapshot of the position and speed of the spacecraft with each laser firing. Page 54 of 129
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The resulting Landing Profile can be represented as a Right Triangle, and can then be labeled appropriately. The Glide Slope is simply the Complement of the Glide Angle. Glide Slope = Complement(Glide Angle) = 90o − Glide Angle
Pythagorean Triangle used to calculate spacecraft landing data. Image: S.T.E.M. For the Classroom
The Right Triangle can be solved by using the Trigonometric functions of Sine and Cosine. For the purposes of this exercise, the angles will not have to first be converted to radians. Adjacent Side cos(θ) = Hypotenuse sin(θ) =
Opposite Side Hypotenuse
Writing the trigonometry in aerospace form, the general equation becomes: Distance T o Spaceport cos(Glide Slope) = Line−Of −Sight Distance sin(Glide Slope) =
Altitude Line−Of −Sight− Distance
Rearranging the equation, we get, Distance T o Spaceport = Line − Of − S ight Distance ∙ cos(Glide Slope) Altitude (AGL) = Line − Of − S ight Distance ∙ sin(Glide Slope) To graph the Landing Profile, simply graph the two points: (0, 0) & (Distance to Spaceport, Altitude) The linear equation can easily be derived from these two points. :: Page 55 of 129
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The two laser bursts one second apart gives us two distances with t=1. Thus we get two different distances, LineOfSight Distance 1 and LineOfSight Distance 2. Using d = rt and rearranging, we get, Glide Speed = Line − Of − S ight Distance 2 − Line − Of − S ight Distance 1 Using the same trigonometric functions as before, the other rates can be calculated. Ground Speed = Glide Speed ∙ cos(Glide Slope) Descent Rate = Glide Speed ∙ sin(Glide Slope) and Line−Of −Sight Distance T ime T o T ouchdown = Glide Speed Example An R.E.L. Skylon is returning to Spaceport America from space after dropping off some passengers and picking up more that are homeward bound. The Landing Laser bounces a laser off of the spaceplane to determining the following information: ● Glide Angle = 55 degrees ● Glide Distance 1 = 19.80 mi ● Glide Distance 2 = 19.75 mi Find the following information about the landing spacecraft at this moment in time. ● Altitude AGL ● Distance to Spaceport ● Glide Slope ● Glide Speed ● Descent Rate ● Ground Speed ● Time To Touchdown First, we must change our inputs to S.I. units: Distance 1 Line − Of − S ight Distance 1 = Glide 1609 = 31, 865 m Line − Of
−
S ight Distance 2 =
Glide Distance 2 1609
= 31, 785 m
So, Glide Slope = 90o − 55o = 35o Altitude (AGL) = Line − Of
−
S ight Distance 2
∙
sin(Glide Slope) Page 56 of 129
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= 31785(0.57) = 18, 277 m
Distance T o Spaceport = Line − Of − S ight Distance 2 = 31785(0.82) = 26, 102 m
∙
Glide Speed = Line − Of − S ight Distance 1 − Line − Of = 31865 − 31785 = 81 mps Descent Rate = Glide Speed ∙ sin(Glide Slope) = 81(0.57) = 46 mps
cos(Glide Slope)
−
S ight Distance 2
Ground Speed = Glide Speed ∙ cos(Glide Slope) = 81(0.82) = 46 mps T ime T o T ouchdown =
Line−Of −Sight Distance 2 Glide Speed
= 690 s = 11.5 min
S.T.E.M. Education. Don’t come home without it... :: R.A.F.T. Writing ● Role: Teacher ● Audience: Middle School students ● Format: Five paragraph essay ● Topic: The Kennedy Space Center (KSC). What spacecraft were launched from there? Did any of the space launches go to the Moon? What was unique about their missions? What was in common with all the missions? How does KSC differ from the spaceport presented in this textbook? How are they the same? Why even bother to build a spaceport anyway? ::
4.4 Unpowered Glide Landing 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. Page 57 of 129
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Sample Open Source Code Once the cells have been named referencing cells is easy. ● CALCULATIONS ○ LOSDist1=GlideDist1/1609 ○ LOSDist2=GlideDist2/1609 ○ GlideSlope=90GlideAngle ○ Alt=LOSDist2*sin(GlideSlope) ○ DistToSpaceport=LOSDist2*cos(GlideSlope) INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE Page 58 of 129
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Sample App Interface Design
::
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4.5 Chapter Test I. VOCABULARY Match the aerospace term with its definition. 1. Adjacent Side of a Right Triangle
A. A triangle with one of the angles equal to exactly 90 degrees.
2. Descent Rate
B. The side next to the given angle (not the Hypotenuse).
3. Glide Slope
C. The distance a spacecraft descends over a certain period of time.
4. Hypotenuse
D. The angle a spacecraft makes to the horizontal.
5. Right Triangle
E. The longest side of a right triangle.
II. MULTIPLE CHOICE Circle the correct answer. 6. A spacecraft is returning from space for a landing back at Spaceport America. It is required for the spacecraft to have the engines turned on in order to land safely. A. TRUE B. FALSE 7. Given a Right Triangle, the sine of an angle (that is not the Right Angle) is defined as the Hypotenuse divided by the Adjacent side. A. TRUE B. FALSE 8. What is the Glide Slope of a landing spacecraft if the Glide Angle is 60o? A. 60o B. 30o C. 15o D. Cannot be determined 9. The Landing Laser is malfunctioning and is giving the Glide Angle of a landing spacecraft. What is the distance to the Spaceport of the spacecraft? A. 8.3 km B. 16.6 km C. 33.2 km D. Cannot be determined 10. If the Adjacent Side of an angle is increased, then the measurement of that angle ____________. A. Increases B. Decreases C. Unchanged D. Cannot be determined Page 60 of 129
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III. CALCULATIONS An R.E.L. Skylon is in an unpowered glide landing returning to Spaceport America. The Landing Laser paints the spacecraft with a 61o Glide Angle and a 19.70 miles Glide Distance. Exactly one second later, the spacecraft is holding steady at 61o, but is now at 19.65 miles. 11. What is Glide Distance 1? Glide Distance 2? 12. What is LineofSight Distance 1? 13. What is LineofSight Distance 2? 14. What is the Glide Slope? 15. What is the Distance to the Spaceport? 16. What is the Altitude (AGL)? 17. What is the Glide Speed? 18. What is the Ground Speed? 19. What is the Descent Rate? 20. What is the Time To Touchdown? IV. WRITING Write a one paragraph essay on the topics below. 21. Explain why a triangle can never have two right angles. 22. Explain why if in a Right Triangle, increasing the Opposite Side of an angle increases the measurement of that angle. 23. Explain how to convert Glide Distance into LineOfSight Distance, that is, convert Glide Distance to S.I. units. 24. Explain how to find the Descent Rate of a spacecraft returning from space. 25. Write a short story about what it would be like to feel the adrenaline after an unpowered glide back to Spaceport America from Low Earth Orbit aboard any spacecraft that you desire. ::
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END FALL SEMESTER ::
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SPRING SEMESTER ASTRONAUTICS Unit 3: Basic Astronautics Chapter 5: Delta V and Transfer Time 99 Chapter 6: Spacecraft Weight 99
Spring Semester Basic Astronautics Final Exam 99
Unit 4: Advanced Astronautics Chapter 7: The Rocket Equation 99 Chapter 8: Lunar Landing 99
Spring Semester Advanced Astronautics Final Exam 99 ::
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Chapter 5: Delta V and Transfer Time 5.1 Narrative 65 5.2 Vocabulary 99 5.3 Analysis 99 5.4 Space Mission Design App 99 5.5 Chapter Test 99 ::
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Delta V and Transfer Time
5.1 Narrative
In
this, the first of a fourpart interconnected
astronauticsbased S.T.E.M. project, students will calculate the change in orbital velocity Delta V (Δv) needed to change the orbital altitude of a spacecraft. Students will also calculate the total roundtrip time to transfer between orbits and use that information to determine the duration of their space mission. Time Frame About 4 weeks Aerospace Problems Periapsis Δv Apoapsis Δv Δv Budget Transfer Time Mission Duration Mathematics Used Square Root 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 change in velocity and the orbital altitude? Why do I need to raise or lower my orbital altitude? How long does it take to reach my destination? How long can I stay at my destination? How does the radius of the earth determine Δv? Who are are some of the pioneers in space exploration? Wait. I have to do science and technology and engineering and mathematics, all at the same time? Page 65 of 129
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:: This lesson is powered by E8: Engage ○ Lesson Objectives ○ Lesson Goals ○ Lesson Organization Explore ○ The Circular Orbit ○ The Elliptical Orbit ○ Delta V (Δv) ○ Additional Terms and Definitions Explain ○ Change in Velocity Elaborate ○ Other Orbital Examples Exercise ○ Δv and Transfer Time Parameters ○ Δv and Transfer Time Scenario Engineer ○ The Engineering Design Process ○ SMDA Spacecraft ΔV Plan ○ Designing a Prototype ○ SMDA Software Express ○ Displaying the SMDA ○ Progress Report Evaluate ○ Post Engineering Assessment :: Lesson Overview Students first learn the basics of astronautics involving the Hohmann Transfer Orbit Equations using pencil, paper, and scientific calculator. Students then use what they have learned to create a Space Mission Design App (SMDA), designed according to the Engineering Design Process, that will be used for realworld spacecraft. Students will learn about circular and elliptical orbits and how orbital altitude can be changed using rocket burns. Students will be using the Periapsis and Apoapsis Δv equations, as well as the Transfer Time equation. Students will use spreadsheet software to create the app and will use slideshow software for their presentations. They will also create a document of their experiences engineering the SMDA and presenting their findings to the rest of the class. Page 66 of 129
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Constants Standard Gravitational Parameter μ (m3/s2) Earth Radius (equatorial) (m) Input Lower Orbital Altitude (m) Higher Orbital Altitude (m) OnStation Time (days) Output Periapsis Δv Burn (mps) Apoapsis Δv Burn (mps) Δv Budget (mps) Transfer Time (days) RoundTrip Time (days) Mission Duration (days) ::
5.2 Vocabulary
Apoapsis Δv Budget Higher Orbital Altitude Orbital Altitude Radius of Lower Orbit Transfer Orbit #1 ::
Orbital Mechanics Diagram. Image: Wikipedia
Apoapsis Δv Burn Elliptical Orbit Lower Orbital Altitude Periapsis RoundTrip Time Transfer Orbit #2
Circular Orbit Gravity Parameter (μ) Mission Duration Periapsis Δv Burn RoundTrip Δv Transfer Time
Delta V (Δv) Hohmann Transfer Orbit OnStation Time Radius of Higher Orbit Standard Gravity (g0)
5.3 Analysis In order to raise or lower a spacecraft that is in orbit around a body, such as the Earth, the Hohmann equations are used. These equations determine the change in orbital velocity (Δv) needed to go to different orbital altitudes. Δv P ERIAP SIS =
√
Δv AP OAP SIS =
√
μ R1
μ R2
√
(
(1
−
2R2 R1 + R2 −
√
1)
2R1 R1 + R2
)
where ● μ = Standard Gravitational Parameter, equal to 398,600.44189 km3/s2 ● R1 = Radius of the inner (smaller) orbit ● R2 = Radius of the outer (larger) orbit The Δv Budget is simply the two Δv rocket burns added together. Page 67 of 129
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Δv BU DGET = Δv P ERIAP SIS + Δv AP OAP SIS Using the principle of Reversibility of Orbits, the total Δv needed to get to the destination and back is Δv ROU N D−T RIP = 2(Δv BU DGET ) The transfer time is calculated in seconds. T ransf er T imeSECON DS = π
√
(R1 + R2 )3 8μ
There are 86,400 seconds per day, so the number of days it takes to change the orbital altitude of a spacecraft becomes: T ransf er T imeSECON DS T ransf er T imeDAY S = 86400 And the RoundTrip Time is double the Transfer Time: Round − T ripDAY S = 2(T ransf er T imeDAY S ) The Mission Duration is the RoundTrip Time added to the OnStation Time. M ission Duration = On − S tationDAY S + Round − T ripDAY S Orbits are circular and the transfer orbit is an ellipse:
Hohmann Transfer Orbit Diagram. Image: Wikipedia Page 68 of 129
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In the diagram above, green represents the lower circular orbital altitude and red represents the higher circular orbital altitude. Yellow represents the elliptical transfer orbit from green to red (or dashed yellow representing from red to green). The first Δv rocket engine firing is done at the lowest point in the elliptical transfer orbit (periapsis). This puts the spacecraft on the path in yellow. At the highest point in the elliptical orbit (apoapsis), another rocket engine firing occurs, this time circularizing the orbit (in red). To go home, simply reverse the procedure, using the principle of reversibility of orbits. We will use as inputs the lower and higher orbital altitudes, as well as the OnStation Time, which is the number of days the astronauts spend at the mission destination. To review, the Δv Budget is found by adding the two Δv numbers together. The RoundTrip Time is twice the Transfer time, and the Mission Duration is the OnStation Time plus the RoundTrip Time. Example You are the Captain of a spacecraft that is currently in a Low Earth Orbit (LEO) at an orbital altitude of 200 km. You need to increase your orbital altitude to 8,500 km so that you can deposit a new satellite and bring back the old one. Your OnStation Time is 5 days. Find the change in velocity, transfer time, RoundTrip Time, and the Mission Duration for this space mission. AltitudeLOW ER = 200 km AltitudeHIGHER = 8, 500 km First, we need to calculate R1 and R2. R1 = AltitudeLOW ER + RadiusEART H = 200 + 6378 = 6, 578 m R2 = AltitudeHIGHER + RadiusEART H = 8500 + 6378 = 14, 878 m Therefore, Δv P ERIAP SIS =
√
398600 6578
√
(
2(14878) 21456 −
1)
= 1, 383 mps Δv AP OAP SIS =
√
398600 14878
(1
−
√
2(6578) 21456
)
= 1, 123 mps Δv BU DGET = 1383 + 1123 Page 69 of 129
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= 2, 506 mps Δv ROU N D−T RIP = 2(2506) = 5, 011 mps T ransf er T imeSECON DS = π
√
(6578 + 14878)3 8(398600)
= 5, 529 s T ransf er T imeDAY S =
T ransf er T imeSECON DS 86400
=
5529 86400
= 0.064 days
Round − T ripDAY S = 2(T ransf er T imeDAY S )
= 2(0.064) = 0.128 days M ission Duration = On − S tationDAY S + Round − T ripDAY S
= 5 + 0.128 = 5.13 days :: R.A.F.T. Writing ● Role: Teacher ● Audience: Middle School students ● Format: Five paragraph essay ● Topic: The Gemini spacecraft. Who were the astronauts that flew the mission? What spacecraft was used to boost the Gemini to a higher orbit? What was unique about the missions? What was in common with all the missions? How does a Gemini change in orbital altitude differ from the one presented in this textbook? How are they the same? Why even bother to change an orbit anyway? ::
5.4 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: Page 70 of 129
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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 ○ TotBA INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE Page 71 of 129
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INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE ::
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Sample App Interface Design
::
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S.T.E.M. For the Classroom: Adventures in Outer Space
5.5 Chapter Test I. VOCABULARY Match the astronautics term with its definition. 1. Apoapsis
A. The lower circular orbital altitude of a spacecraft as measured from the center of an orbiting body.
2. Δv Budget
B. The rocket firing at the lowest point of a Transfer Orbit.
3. Mission Duration
C. The highest point in an elliptical orbit.
4. Periapsis Δv Burn
D. The total time necessary to accomplish a space mission.
5. Radius of Lower Orbit
E. The total amount of Delta V needed to accomplish a space mission.
II. MULTIPLE CHOICE Circle the correct answer. 6. The Apoapsis Δv rocket burn occurs at the highest point of the Hohmann transfer orbit. A. TRUE B. FALSE 7. The Δv Budget is the total change in velocity needed to conduct a roundtrip space mission. A. TRUE B. FALSE 8. A spacecraft is orbiting the Earth at an orbital altitude of 1,000 km. What is the orbital radius of the spacecraft? A. 5,371 km B. 6,371 km C. 7,371 km D. Cannot be determined 9. What is the Hohmann transfer time of a spacecraft headed for the apoapsis ΔV rocket burn if the RoundTrip Transfer Time is 7 hrs? A. 3.5 hrs B. 7.0 hrs C. 10.5 hrs D. Cannot be determined 10. There are always two Δv rocket burns whenever a spacecraft needs to raise or lower its orbital altitude. The second Δv rocket burn is used to change the shape of an orbiting spacecraft into a ____________. A. Ellipse B. CircleC. Parabola D. Cannot be determined Page 74 of 129
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III. CALCULATIONS A wayward satellite is need of repairs and to have some electronic parts replaced. The satellite is in a stable orbit 1,250 km above the Earth. A crew inside a repair vehicle is also in a stable orbit, but at an orbital altitude of 400 km below the satellite. It is estimated that the crew will need 3 days to conduct all the necessary repairs. 11. What is the Lower Orbital Radius? 12. What is the Higher Orbital Radius? 13. What is the OnStation Time? 14. What is the Periapsis Δv Rocket Burn? 15. What is the Apoapsis Δv Rocket Burn? 16. What is the Δv Budget? 17. What is the Round Trip Δv Budget? 18. What is The Transfer Time? 19. What is Round Trip Transfer Time? 20. What is the Mission Duration? IV. WRITING Write a one paragraph essay on the topics below. 21. Explain why a spacecraft must first push off and then stop when it wants to go from one point in space to another, such as a higher (or lower) orbital altitude. 22. Explain how the OnStation Time effects the Mission Duration. 23. Explain how a spacecraft would return back to its original orbital altitude if the Apoapsis ΔV rocket burn was not performed. 24. Explain why a spacecraft must have a larger Round Trip Δv Budget if it needs to go to a higher orbital altitude. 25. Write a short story about what it would feel like to float weightlessly in space, while gazing at the curvature of the Earth as it transfers from a lower orbital altitude to a higher orbital altitude. ::
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Chapter 6: Spacecraft Weight Analysis 6.1 Narrative 65 6.2 Vocabulary 99 6.3 Analysis 99 6.4 Space Mission Design App 99 6.5 Chapter Test 99 ::
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Spacecraft Weight Analysis
6.1 Narrative
In
this, the second of a fourpart interconnected
astronauticsbased 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 Aerospace 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? :: Page 77 of 129
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This lesson is powered by E8: Engage ○ Lesson Objectives ○ Lesson Goals ○ Lesson Organization Explore ○ The Boeing Space Tug Study ○ The Crew Module (CM) ○ The CM Weight ○ The Crew Size ○ Additional Terms and Definitions Explain ○ Basic Spacecraft Systems ○ The CM Static Weight ○ The CM Dynamic Weight Elaborate ○ Other Crew Module Examples Exercise ○ CM Weight and Crew Size Parameters ○ CM Weight and Crew Size Scenario Engineer ○ The Engineering Design Process ○ SMDA Spacecraft CM Weight and Crew Size Plan ○ Designing a Prototype ○ SMDA Software Express ○ Displaying the SMDA ○ Progress Report 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 realworld 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. Page 78 of 129
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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) ::
6.2 Vocabulary CM Communications CM Dynamic Weight CM Instrumentation CM Weight ::
The Apollo Command Module. Image: NASA. CM Contingency CM EC/LSS CM Misc. Equipment Crew Capsule
CM Controls CM Electrical Power CM Static Weight Crew Module (CM)
CM Crew Systems CM Expendables CM Structure 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. 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. Page 79 of 129
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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 CST100 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.
Boeing Space Tug Study Crew Module (CM). Image: Boeing 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 yintercept to write the linear equation in slopeintercept (y=mx+b) form. m =
y2 − y1 x2 − x1
=
3 − 15 50 − 2
=
12
− 48
=
−
0.25
and b = y 1 − mx1 = 15 − (− 0.25)(2) = 15 + 0.5 = 15.5 Therefore, y = mx + b becomes Page 80 of 129
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CM CREW = mM D + b and CM CREW = − 0.25M D + 15.5 (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 VolumetoCrew ratio is simply the total volume of the CM divided by the Crew Size. CM V OLU M E = CM1260 CREW
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, CM ST RU CT U RE = 2497 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. W eightST AT IC = CM ST RU CT U RE + CM ELECT RIC + CM COM M + CM IN ST R + CM CON T ROL + CM M ISC W eightDY N AM IC = CM SY ST EM S + CM EC /LSS + CM EXP + CM CON T ROL W eightCM = W eightST AT IC + W eightDY N AM IC 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. W eight W eightCrewM odule = 2.2 CM :: 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? Page 81 of 129
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The number of astronauts needed is CM CREW = − 0.25M D + 15.5 = − 0.25(10) + 15.5 = − 2.5 + 15.5 = 13 Astronauts Therefore, the Crew Volume Ratio is CM V OLU M E = CM1260 CREW
=
1260 13
= 96.92 f t3 /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 CM ST AT IC = CM ST RU CT U RE + CM ELECT RIC + CM COM M + CM IN ST R + CM CON T ROL + CM M ISC = 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 CM SY ST EM S = − 41.33M D + 3772 = − 41.33(10) + 3772 = 3, 358 lbs CM EC /LSS = 27.81M D + 1211 = 27.81(10) + 1211 = 1, 490 lbs CM EXP = 20.50M D + 254 = 20.50(10) + 254 = 459 lbs CM CON T IN GEN CY = 0.71M D + 852 = 0.71(10) + 852 = 859 lbs and W eightDY N AM IC = CM SY ST EM S + CM EC /LSS + CM EXP + CM CON T ROL = 3358 + 1490 + 459 + 859 = 6, 166 lbs = 2, 797 kg Page 82 of 129
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The total weight of the Crew Module thus becomes W eightCM = W eightST AT IC + W eightDY N AM IC = 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: 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 ○ TotBA INSERT CODE HERE Page 83 of 129
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INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE INSERT CODE HERE ::
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Sample App Interface Design
::
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6.5 Chapter Test I. VOCABULARY Match the astronautics term with its definition. 1. CM EC/LSS
A. The number of astronauts aboard a spacecraft or space station.
2. CM Static Weight
B. A spacecraft, such as the Boeing CST100, that is used to ferry crew to and from a space station.
3. CM Structure
C. The CM shell, micrometeoroid shielding, insulation, radiators, etc.
4. Crew Capsule
D. The weight of the CM components that does not vary with the Mission Duration.
5. Crew Size
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 Page 86 of 129
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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. ::
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Chapter 7: The Rocket Equation 7.1 Narrative 65 7.2 Vocabulary 99 7.3 Analysis 99 7.4 Space Mission Design App 99 7.5 Chapter Test 99 ::
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The Rocket Equation
7.1 Narrative
In
this, the third of a fourpart interconnected
astronauticsbased 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 Aerospace Problems Rocket Exhaust Velocity Rocket Empty Weight Rocket Gross Weight Rocket 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) RoundTrip Δv Budget (mps) Transfer Time (days) RoundTrip Transfer Time (days) Mission Duration (days) Crew Size (people) Crew Module Weight (lbs) Page 89 of 129
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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? :: This lesson is powered by E8: Engage ○ Lesson Objectives ○ Lesson Goals ○ Lesson Organization Explore ○ The Boeing Space Tug Study ○ The Engine Module (EM) ○ The EM Propellant ■ EM Fuel (LH2) ■ EM Oxidizer (LO2) ○ Additional Terms and Definitions Explain ○ Basic Spacecraft Systems ○ The EM Specific Impulse ○ The CM Dynamic Weight Elaborate ○ Other Engine Module Examples Exercise ○ EM LH2 and LO2 Parameters ○ EM LH2 and LO2 Scenario Engineer ○ The Engineering Design Process ○ SMDA Spacecraft EM Propellant Plan ○ Designing a Prototype ○ SMDA Software Express ○ Displaying the SMDA ○ Progress Report Evaluate ○ Post Engineering Assessment :: Lesson Overview Students first learn the basics of engine module design using pencil, paper, and scientific calculator. Page 90 of 129
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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 realworld 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) ::
7.2 Vocabulary EM Empty Weight (m1) Exhaust Velocity (VEXH) NozzleRetracted Propellant Reserve ::
The Apollo 15 CSM in lunar orbit. Image: NASA EM Gross Weight (m0) Liquid Hydrogen (LH2) Propellant RL10 Rocket Engine
EM Inert Weight Liquid Oxygen (LO2) Propellant Ratio Specific Impulse (ISP)
Engine Module (EM) NozzleExtended Propellant Weight
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 unpiloted version of the rocket system would have carried satellites and other sensors to higher earth orbits. This project will use the unpiloted section, or Engine Module (EM) of the system, which is displayed below. Page 91 of 129
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Boeing Space Tug Study Engine Module. Image: The Boeing Co. 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. Image: Mark Wade 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! :: We will be using the Rocket Equation to calculate the propellant needed to go from one orbit to another. Page 92 of 129
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Δv = v EXH 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). v EXH = I SP ∙ g 0 The Payload Weight is the weight of the cargo plus the weight of the Crew Module (see Chapter Six). EM P AY LOAD = W eightCARGO + W eightCrewM odule The Empty Weight (m1) of the rocket includes the Inert Weight and the Payload weight. m1 = EM IN ERT + EM RESERV E + EM P AY LOAD The Space Tug diagram shows that the Inert Weight is 5,610 lbs, which equals to 2,545 kg. So, m1 = 2, 545 + EM P AY LOAD 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 + EM P ROP ELLAN T Solving the rocket equation for propellant, the amount of fuel and oxidizer needed for any space mission can be calculated. Δv = v EXH ln
( ) m0 m1
Δv v EXH
= ln
( )
Δv v EXH
= ln
(
Δv v EXH
= ln 1 +
m0 m1
(
m1 + EM P ROP ELLAN T m1
)
EM P ROP ELLAN T m1
)
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1 +
EM P ROP ELLAN T m1
ΔV
= e V EXH
EM P ROP ELLAN T m1
ΔV
= e V EXH
−
(
1 ΔV
EM P ROP ELLAN T = m1 e V EXH
−
)
1
ExcessP ROP ELLAN T = P ropellant
−
EM P ROP ELLAN T
Finally, the EM propellant breakdown is the weight of the Liquid Hydrogen (LH2) fuel and the Liquid Oxygen (LO2) oxidizer. EM P ROP ELLAN T LH 2 = M ixureRatio +1 LO2 = LH 2 ∙ M ixureRatio The excess propellant is the capacity of the rocket minus what we actually carry. :: 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. v EXH = I SP ∙ g 0 = (460)(9.80665) = 4, 511 mps EM P AY LOAD = W eightCARGO + CM = 4761 + 4345 = 9, 106 kg m1 = 2545 + EM P AY LOAD = 2545 + 9106 = 11, 650 kg
(
ΔV
EM P ROP ELLAN T = m1 e V EXH
−
)
1 Page 94 of 129
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4133
= (11650)(e 4511 = 17, 475 kg
−
1)
The excess propellant becomes: ExcessP ROP ELLAN T = P ropellant − EM P ROP ELLAN T = 18053 − 17475 = 578 kg The propellant breakdown is: EM P ROP ELLAN T LH 2 = M ixureRatio +1 =
17457 6.85
= 2, 551 kg LO2 = LH 2 ∙ M ixureRatio = 2485 ∙ 5.85 = 14, 924 kg Finally, the Gross Weight of the spacecraft is, m0 = m1 + EM P ROP ELLAN T = 11, 650 + 17, 475 = 29, 126 kg :: 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? ::
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 Page 95 of 129
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Graph Constants Calculations The App can now be developed. Sample Open Source Code Once the cells have been named referencing cells is easy. ● CALCULATIONS ○ TotBA INSERT CODE HERE INSERT CODE HERE ::
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Sample App Interface Design
::
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7.5 Chapter Test I. VOCABULARY Match the astronautics term with its definition. 1. EM Inert Weight
A. The force with respect to the amount of propellant used per unit of time.
2. Liquid Oxygen (LO2)
B. The weight of the Engine Module without propellant and payload.
3. NozzleRetracted
C. The rocket engine nozzle which is pulled back to its original shape.
4. Propellant Ratio
D. What a rocket engine uses as an oxidizer.
5. Specific Impulse (ISP)
E. The rocket engine nozzle which is pulled back to its original shape.
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 Page 98 of 129
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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 RoundTrip 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 10Crew 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 RoundTrip 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? 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. :: Page 99 of 129
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Chapter 8: Lunar Landing 8.1 Narrative 65 8.2 Vocabulary 99 8.3 Analysis 99 8.4 Space Mission Design App 99 8.5 Chapter Test 99 ::
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Lunar Landing
8.1 Narrative
In
this, the fourth and final part of a fourpart
interconnected astronauticsbased S.T.E.M. project, students will design a mission that will land on the moon! 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. Finally, a Landing Kit is attached to form the Lunar Lander. The ΔV information from Chapter 5, the Crew Module weight information from Chapter 6, and the Propellant information in Chapter 7 will be used in this project. Time Frame About 4 weeks Aerospace Problems Lunar Lander Exhaust Velocity Lunar Lander Empty Weight Lunar Lander Gross Weight Lunar Lander Propellant Weight Return On Investment (R.O.I.) Mathematics Used Finance, 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) RoundTrip ΔV Budget (mps) Transfer Time (days) RoundTrip Transfer Time (days) Mission Duration (days) Crew Size (people) Crew Module Weight (lbs) Page 101 of 129
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Essential Questions What is the ΔV requirement for a landing on the lunar surface from lunar orbit? What is the ΔV requirement for a taking off from the lunar surface back to lunar orbit? Why is it important to have a Return On Investment (R.O.I.)? How does the the amount of lunar material available for sale on the open market effect the selling price of the lunar material? Who are are some of the pioneers in lunar landing design? Wait. I have to do science and technology and engineering and mathematics, all at the same time? :: This lesson is powered by E8: Engage ○ Lesson Objectives ○ Lesson Goals ○ Lesson Organization Explore ○ The Boeing Space Tug Study ○ The Lunar Lander Kit ■ Landing Legs ■ Payload Tray ○ Additional Terms and Definitions Explain ○ Basic Spacecraft Systems ○ The Rocket Nozzle ■ Extended ■ Retracted Elaborate ○ Other Lunar Lander Examples Exercise ○ Lander Lander Payload and Payback Example ○ Lander Lander Payload and Payback Scenario Engineer ○ The Engineering Design Process ○ SMDA Spacecraft EM Propellant Plan ○ Designing a Prototype ○ SMDA Software Express ○ Displaying the SMDA ○ Progress Report Evaluate ○ Post Engineering Assessment :: Page 102 of 129
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Lesson Overview Students first learn the basics of lunar landing mission 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 realworld 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 Unit Conversion (carats/lbs) Lunar Investment (USD) PDI delta V (kps) PAI delta V (kps) Weight of Lander Kit (lbs) Weight of Lunar Tray (lbs) Input TEI Orbital Altitude (km) EOI Orbital Altitude (km) Average Selling Price (USD) Output Lander Gross Weight (lbs) Propellant Weight (lbs) Excess Propellant (lbs) LH2 Weight (lbs) LO2 Weight (lbs) Weight of Lunar Material (lbs) Gross Income (USD) Net Income (USD) ::
The Apollo 17 LM on the lunar surface. Image: NASA
8.2 Vocabulary Lunar Lander Kit Lunar Payload Tray ::
Lunar Investment Powered Ascent Initiation (PAI)
Lunar Material Powered Descent Initiation (PDI)
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8.3 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 unpiloted version of the rocket system would have carried satellites and other sensors to higher earth orbits. A CM/EM is brought up to the space station and a Lunar Lander Kit is attached to it.
The Boeing Space Tug with Lunar Lander Kit and Lunar Payload Tray. Image: Mark Wade
The Lunar Lander Kit contains the following items: ● Landing Legs Kit ● Landing RADAR Kit ● Auxiliary Power Supply Kit ● RCS Booster Kit ● Extra Insulation ● Extra Micrometeoroid Shielding Total Weight (estimated): 896 lbs. In addition, a tray resembling a doughnut is attached around the bottom part of the vehicle below the landing legs. Total Weight: 1,500 lbs. :: We will again be using the Rocket Equation (Chapter 6), solved for propellant, to calculate the rocket fuel and oxidizer needed to go from one orbit to another.
(
ΔV
EM P ROP ELLAN T = m1 e V EXH
−
)
1
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Instead of going from one orbit to another, we will be going from lunar orbit down to the lunar surface. :: We will be using the Reaction Engines, Ltd., Skylon spacecraft (Chapter 2) to shuttle back and forth between Earth and Space Station Alpha (Chapter 3) in Low Earth Orbit LEO. The Skylons are operated out of Spaceport America (Chapter 4) in New Mexico, USA. The lander is transported to the Moon, where it proceeds down to the lunar surface. The crew fills the Tray with lunar material. After the containers have been filled, the crew lifts off from the lunar surface and connects to another transport. The Lander with its lunar material combination heads home.
Image: Mark Wade and S.T.E.M. For the Classroom
Once the crew returns to Space Station Alpha, a Skylon transports the containers back to Earth. A passenger Skylon returns the triumphant lunar crew home. :: Example A consortium of astronautics companies have raised $27.14B USD to invest in a space mission comprising of a Lunar Lander that is tasked to bring back Lunar Material from the surface of the Moon. You are the Mission Commander. Your vehicle is a Boeing Space Tug, outfitted with a Lunar Lander Kit and a Payload Tray. The Command Module (CM) weighs in at 4,345 kg, and the science mission payload is 4,761 kg, including the Payload Tray. The science payload will be left on the lunar surface, and the equivalent weight in lunar material will be brought back. This material has an estimated value at $1,500 USD per carat. Calculate the propellant needed to land on the Moon and liftoff back into lunar orbit, the excess propellant, the amount of Lunar Material brought back, the Gross Weight of the Lander, the Gross Income after all the Lunar Material has been sold, the taxable income from the sale, and finally, the Return on Investment. :: Page 105 of 129
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Using the the equations from Chapter 7, we see that we need to use the Rocket Equation to calculate the needed propellant. Also, since the rocket nozzle needs to be retracted in order to make room for the landing, the Specific Impulse of the rocket drops by 3 seconds. Assigning labels to the inputs, and converting everything to S.I. units, we get: Lunar Investment = $24, 000, 000, 000 U SD P ropellant = 39, 800 lbs = 18, 053 kg C M = 4, 327 kg P DI = 2, 181 mps P AI = 1, 890 mps g 0 = 9.80665 m/s2 S cience P ayload = 4, 761 kg P ayload T ray = 1, 500 lbs = 680 kg Lander Kit = 896 lbs = 406 kg S elling P rice = $1, 500/carat = $7, 500, 000/kg The output becomes: Rocket Engine: Lander I SP = (I SP − 3) s = 460 − 3 = 457 s Landing v EXH = Landing I SP ∙ g 0 = (457)(9.806650 = 4, 482 mps Landing Δv Budget = P DI + P AI = 2181 + 1890 = 4, 071 mps Landing Reserve Δv = 0.75% ∙ Landing Δv Budget = 0.0075(4071) = 31 mps Page 106 of 129
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Landing Δv = Landing Δv Budget + Landing Reserve Δv = 4071 + 31 = 4, 102 mps Lunar Material: Lunar M aterial = Science P ayload − P ayload T ray = 4761 − 680 = 4, 081 kg Propellant: m1 = 2, 545 + CM + Lunar M aterial + P ayload T ray + Lander Kit = 2545 + 4327 + 4081 + 680 + 406 = 12, 057 kg Landing Δv
LanderP ROP ELLAN T = m1 ( e Landing vEXH − 1) 4102 = (12057)(e 4482 − 1) = 18, 052 kg E xcess Landing P ropellant = P ropellant − LanderP ROP ELLAN T = 18053 − 18052 = 1 kg Gross Weight: m0 = m1 + Landing P ropellant = 12057 + 18052 = 30, 108 kg Financial: Gross Income = Lunar M aterial ∙ Selling P rice = 4081 ∙ 7500000 = $30, 604, 579, 769 U SD T axable Income = Gross Income − Lunar Investment = 30604579796 − 27140000000 = $3, 464, 579, 796 U SD T axable Income R.O.I. = ( Lunar Investment x 100)% =
3464579796 27140000000
x 100
= 12.77% :: Page 107 of 129
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So, in conclusion, ● Propellant Needed: 18,052 kg ● Lunar Material: 4,081 kg ● Lunar Lander Gross Weight: 30,108 kg ● Gross Income: $30,604,579,976 USD ● Taxable Income: $3,464,579,976 USD ● R.O.I: 12.77% :: R.A.F.T. Writing ● Role: Teacher ● Audience: Middle School students ● Format: Five paragraph essay ● Topic: The Apollo Lunar Module (LM). Who were the astronauts that flew the missions? Where on the Moon did they land? What was unique about their missions? What was in common with all the missions? How does an Apollo space mission differ from the space mission presented in this textbook? How are they the same? Why even bother to explore the Moon anyway? ::
8.4 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 ○ TotBA :: Page 108 of 129
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Sample App Interface Design
::
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8.5 Chapter Test I. VOCABULARY Match the astronautics term with its definition. 1. Lunar Investment
A. The amount of money needed to fully fund a mission to the Moon.
2. Lunar Lander Kit
B. Includes the lunar landing legs, infrastructure, landing radar, etc.
3. Lunar Payload Tray
C. The tray that transports payload to and from the lunar surface.
4. Powered Ascent Initiation
D. The lift off burn from the lunar surface to lunar orbit.
5. Powered Descent Initiation
E. The landing burn from lunar orbit to the lunar surface.
II. MULTIPLE CHOICE Circle the correct answer. 6. The propellant needed to land on the Moon is equal to the propellant needed to take off again. A. TRUE B. FALSE 7. The ΔV Budget for a landing on the moon is just as much as going from the Earth to the Moon. A. TRUE B. FALSE 8. Collectors can purchase Lunar Material in the form of ________________ that has fallen to Earth. A. Meteors B. Meteorites C. Regolith D. Cannot be determined 9. Lunar Material that has been brought back to Earth and sold for $1,000/carat has the equivalent price of ___________ /gram. A. $1,000 B. $5,000 C. 10,000 D. Cannot be determined 10. By retracting the nozzle of the RL10 rocket engine, the Specific Impulse (ISP) of the engine decreases by approximately _________ seconds. A. Two (2) B. Three (3) C. Zero (0) D. Cannot be determined Page 110 of 129
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III. CALCULATIONS You have invested $22.35B (USD) in a trip to the Moon. A Boeing Space Tug with a Lunar Lander Kit and Lunar Payload Tray has been selected to be used to deposit geologic sensors on its surface, and to load the equivalent weight of the sensors in Lunar Material to be sold to pay for the trip. The PDI ΔV is 2,181 mps and the PAI ΔV is 1,890 mps. The payload for this mission is a standard 10Crew Boeing Space Tug Crew Module, which weighs 9,540 lbs, and a standard Lunar Sensor Package, which weighs 9,500 lbs. Assume a Propellant Reserve of 1% of the RoundTrip ΔV Budget, and that the Lunar Material has an average selling price of $1,500/carat. 11. What is the new Specific Impulse of the rocket engine with the rocket nozzle retracted? 12. What is the Exhaust Velocity (VEXH) of the rocket engine? 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 lunar lander? 16. What is the Gross Weight (m0) of the lunar lander? 17. What is the amount of propellant needed for this Moon landing mission? 18. What is the amount of Lunar Material in carats? 19. What is the Gross Income from the Lunar Investment? 20. What is the Taxable Income from the Lunar Investment? IV. WRITING Write a one paragraph essay on the topics below. 21. Explain why it is as difficult to get into and out of the Moon’s gravity well as it is to fly to the Moon from Low Earth Orbit. 22. Explain why creating a Lunar lander Kit to be attached to a Boeing Space Tug is easier and more cost effective than designing and building a separate landing vehicle. 23. Explain why Lunar Material would be a rare commodity if mined and transported back to Earth and sold on the open market. 24. Explain how to calculate how much an object would weigh on the lunar surface. 25. Write a short story about what it would feel like to land on the Moon and walk on its surface, experiencing the onesixth gravity of the lunar environment. :: Page 111 of 129
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END SPRING SEMESTER ::
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APPENDIX COMING SOON ... Page 113 of 129
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COMING SOON... ::
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ANSWERS TO PROBLEM SETS COMING SOON... Page 115 of 129
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COMING SOON... ::
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GLOSSARY Above Ground Level (AGL): The distance a spacecraft is above the ground. Adjacent Side of a Right Triangle: The side next to the given angle (not the Hypotenuse). Altitude: The distance a spacecraft is above a given point. Apoapsis: The highest point in an elliptical orbit. Apoapsis ΔV Burn: The rocket firing at the highest point of a Transfer Orbit. BA330 Module: A Bigelow habitat module that has a pressurized volume of 330 cubic meters, weighs 25 tonnes, and can hold 6 crew. BA330 Stack: Two BA300s attached to a Falcon Heavy that is on the Launch Pad. BA2100 Module: A Bigelow habitat module that has a pressurized volume of 2,100 cubic meters, weighs 100 tonnes, and can hold 16 crew. BA2100 Stack: A BA2100 attached to a SLSI that is on the Launch Pad. Begin Spaceflight: The moment a spacecraft crosses into space. Until this moment the spacecraft has been travelling in the atmosphere. Begin Weightlessness: The moment after Rocket Burnout, when forces due to acceleration cease. Boost Phase: The second of six phases in a parabolic spaceflight, where the rocket engine is turned on for maximum velocity. Carrier Phase: The first of six phases in a parabolic spaceflight, where the parabolic spacecraft is carried to launch altitude. Circular Orbit: An orbit that takes the shape of a circle. CM Communications: The CM TV, audio, antenna, etc. CM Contingency: The CM emergency supplies. CM Controls: The CM RCS, Expendables, controls, lines, etc. CM Crew Systems: The CM Bunks, seats, food, medical, etc. CM Dynamic Weight: The weight of the CM components that varies with the Mission Duration. CM EC/LSS: The CM Environmental Control/Life Support Systems. Cabin pressure, atmosphere, water, etc. Page 117 of 129
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CM Electrical Power: The CM batteries, regulators, junction boxes, wires, cables, etc. CM Expendables: The CM Reaction Control Systems propellant. CM Instrumentation: The CM displays, controls, wiring, lighting, etc. CM Miscellaneous Equipment: The CM manipulator arms, displays and controls, maintenance equipment, etc. CM Static Weight: The weight of the CM components that does not vary with the Mission Duration. CM Structure: The CM shell, micrometeoroid shielding, insulation, radiators, etc. CM Crew/Volume Ratio: The volume that one astronaut occupies during a space mission. CM Weight: The sum of the CM Static and CM Dynamic Weights. Crew Capsule: A spacecraft, such as the Boeing CST100, that is used to ferry crew to and from a space station. Crew Module (CM): The part of the spacecraft where the astronauts live and work. Crew Size: The number of astronauts aboard a spacecraft or space station. Crew Volume: The total pressurized volume for each crew member. Delta V (Δv): The change in velocity required to go from one orbital altitude to another. Δv Budget: The total amount of Delta V (ΔV) needed to accomplish a space mission. Descent Rate: The distance a spacecraft descends over a certain period of time. Distance From Spaceport: The ground distance from the edge of the runway to the spacecraft. Docking Node (DN): A module that allows Crew Capsules and Bigelow modules to be attached together. Drop: Releasing SpaceShipTwo from the mother ship. SpaceShipTwo then falls away to a safe distance before igniting its rocket engine. Elliptical Orbit: An orbit that takes the shape of an ellipse. EM Empty Weight (M1): The weight of the spacecraft fully load excluding propellant. EM Gross Weight (M0): The weight of the spacecraft fully loaded including propellant. EM Inert Weight: The weight of the Engine Module without propellant and payload. Page 118 of 129
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End Spaceflight: The moment a spacecraft exits from space. The spacecraft returns to the atmospheric environment. End Weightlessness: The moment at Reentry Interface, where the spacecraft begins to slow down and gravity returns. Engine Module (EM): The part of a spacecraft that holds the propellant tanks and the rocket engine. Exhaust Velocity (vexh): The velocity of the escaping gas exiting a rocket. Expendable Launch Vehicle (ELV): A vehicle that carries its payload into space and is then thrown away, never to be used again. Falcon Heavy: An ELV from SpaceX that can lift 53 mT into Low Earth Orbit. Glide Angle: The angle from the vertical that a Landing Laser points. Glide Distance: The distance the Landing Laser measures. Glide Phase: The fifth of six phases in a parabolic spaceflight, where the spacecraft returns to the launch site in an unpowered landing. Glide Slope: The angle a spacecraft makes to the horizontal. Glide Speed: The speed of the spacecraft during the unpowered glide landing. Ground Speed: The speed of the spacecraft as related to the ground. Higher Orbital Altitude: The highest altitude above Mean Sea Level of an orbiting body. Hohmann Transfer Orbit: The path taken to either raise or lower an orbital altitude. Hypotenuse of a Right Triangle: The longest side of a right triangle. International Space Station (I.S.S): The space station currently orbiting the earth; it is at an average orbital altitude of 382 km (237 mi) with an Orbital Inclination of 52 degrees. Landing Laser: The laser used to determine the Glide Distance to a spacecraft. Landing Profile: The graph of a landing spacecraft. Latitude: The number of degrees above (or below) the equator. Launch Pad: Where a rocket takes off. Launch Site: The spaceport where the Skylon spaceplane launches and recovers. Launch Site Latitude: The latitude (measured in degrees) of the launch site. Page 119 of 129
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LineOfSight Distance: The Glide Distance converted to S.I. units. Liquid Hydrogen (LH2): What a rocket engine uses as fuel. Liquid Oxygen (LO2): What a rocket engine uses as an oxidizer. Low Earth Orbit (LEO): A body circling the Earth at a minimum orbital altitude of 185 km (115 mi). 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 Lander Kit: Includes the lunar landing legs, infrastructure, landing radar, etc. Lunar Material: The rocks and dirt that is brought back from the Moon and sold. Lunar Payload Tray: The tray that transports payload to and from the lunar surface. Maximum Altitude: The highest point that a spacecraft reaches during a parabolic spaceflight. Mean Sea Level (MSL): The distance above the average of Earth's oceans. Mission Duration: The total time necessary to accomplish a space mission. Mission Elapsed Time (MET): Time since the beginning of the spaceflight. Nozzle: The bellshaped protrusion at the tail end of a rocket where the exhaust of a rocket comes out. NozzleExtended: The rocket engine nozzle which is elongated to provide approximately 3 seconds more of Specific Impulse. NozzleRetracted: The rocket engine nozzle which is pulled back to its original shape. OnStation Time: The duration of time spent at the mission destination. Opposite Side of a Right Triangle: The side opposite the given angle. Orbital Altitude: The height above Mean Sea Level (MSL) of a spacecraft. Orbital Inclination: The number of degrees that an orbit subtends relative to the equator. Payload: The useful load carried into space or to the surface of an astronomical body. Payload Shroud: The covering that protects the cargo from the atmosphere on its way into space. Payload Weight: The mass of a payload that is effected by Earth’s gravity. PB/DN: Combination of a Propulsion Bus attached to a Docking Node and weighs 17 tonnes. Page 120 of 129
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PB/DN Stack: Three PB/DNs attached to a Falcon Heavy that is on the Launch Pad. Periapsis: The lowest point in an elliptical orbit. Periapsis ΔV Burn: The rocket firing at the lowest point of a Transfer Orbit. Polar Orbit: An orbit that flies above the North and South poles; it has an Orbital Inclination of 98 degrees. Powered Ascent Initiation (PAI): The lift off rocket burn from the lunar surface to lunar orbit. Powered Descent Initiation (PDI): The landing rocket burn from lunar orbit to the lunar surface. Pressurized Volume: The volume of sealevel pressure air that is in a Bigelow module. 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). Propellant Reserve: The percent of the total propellant that is set aside in case of emergency. Propulsion Bus (PB): The unit used to reboost the space station due to orbital decay. 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. Reentry Interface: The moment a spacecraft encounters Earth's atmosphere, which is used to slow the spacecraft down for a safe landing. Reentry Phase: The fourth of six phases in a parabolic spaceflight, where the spacecraft comes back down into the atmosphere. Reserve Propellant: The weight of the propellant used in case of an emergency. Right Triangle: A triangle with one of the angles equal to exactly 90 degrees. RL10 Engine: The rocket engine used in the EM. Rocket Burnout: The moment a rocket engine shuts itself off, where the spacecraft continues upward on its own momentum. Round Trip Δv Budget: The total Δv a space mission needs to go to a destination and come back home. It is found by doubling the Δv Budget. Page 121 of 129
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RoundTrip Time: The time it takes for a spacecraft to reach its destination and to return. It is found by doubling the Transfer Time. Space Interface: The height where space "officially" begins, which is set at the internationally agreed upon altitude of 100,000 m (62 mi) MSL. Space Launch System Block IA (SLSIA): An expendable vertical launch vehicle that can lift 105 mT into orbit. SpaceShipTwo: The spacecraft that is dropped from White Knight 2. After rocket burnout, the spacecraft coasts up to space and back. Space Station: A place where scientists, engineers, and tourists can gather to explore the many wonders of space. Specific Impulse (Isp): The force with respect to the amount of propellant used per unit of time. Standard Gravitational Parameter (mu): The product of the Gravitational Constant (G) and the mass of a body (M). Standard Gravity (g0): The acceleration due to free fall. Suborbital Spaceflight: A spacecraft that coasts into space after rocket burnout that has a flight profile in the shape of a parabola. Time To Touchdown: The time the spacecraft will take to glide to a landing. Touchdown: The moment the spacecraft makes contact with the runway during a landing. 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. Weightless Phase: The third of six phases in a parabolic spaceflight, where the spacecraft and its occupants experience weightlessness. White Knight 2: The mother ship that carries SpaceShipTwo to launch altitude. ::
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EQUATIONS AND CONSTANTS Altitude (AGL) Altitude (AGL) = Line − Of − S ight Distance CM Communications CM COM M = 327 CM Contingency CM CON T IN GEN CY = 0.71M D + 852 CM Control CM CON T ROL = 60 CM Crew Size CM CREW = − 0.25M D + 15.5 CM Crew Systems CM SY ST EM S = − 41.33M D + 3772 CM Crew Volume Ratio CM V OLU M E = CM1260
∙
sin(Glide Slope)
CREW
CM Dynamic Weight W eightDynamic = CM SY ST EM S + CM EC /LSS + CM EXP + CM CON T ROL CM EC/LSS CM EC /LSS = 27.81M D + 1211 CM Electrical CM ELECT RIC = 130 CM Expendables CM EXP = 20.50M D + 254 CM Instrumentation CM IN ST R = 188 Page 123 of 129
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CM Miscellaneous CM M ISC = 80 CM Static Weight CM ST AT IC = CM ELECT RIC + CM COM M + CM IN ST R + CM CON T ROL + CM M ISC CM Structure CM ST RU CT U RE = 2497 CM Weight (lbs) W eightCM = W eightStatic + W eightDynamic CM Weight (kg) W eight W eightCM = 2.2 CM Cosine of an Angle Adjacent Side cos(θ) = Hypotenuse Δv Apoapsis Δv AP OAP SIS =
√
μ R2
(1
−
√
2R1 R1 + R2
)
Δv Budget Δv BU DGET = ΔV P ERIAP SIS + ΔV AP OAP SIS Δv Periapsis Δv P ERIAP SIS =
√
μ R1
√
(
2R2 R1 + R2 −
1)
Descent Rate Descent Rate = Glide Speed ∙ sin(Glide Slope) Distance to Spaceport Distance T o Spaceport = Line − Of − S ight Distance ∙ cos(Glide Slope) Glide Slope Glide Slope = Complement(Glide Angle) = 90o − Glide Angle Page 124 of 129
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Glide Speed Glide Speed = Line − Of − S ight Distance 2 − Line − Of Ground Speed Ground Speed = Glide Speed ∙ cos(Glide Slope) Height S.I. Conversion h0 = I nitial Height/3.28 Maximum Height 2 vertexh = − 12 g o (vertext ) + v 0 (vertext ) + h0
−
S ight Distance 1
Mission Duration M D = On − S tationDAY S + Round − T ripDAY S OnStation Time On − S tationDAY S = M ission Duration − Round − T ripDAY S Radius of Lower Orbit R1 = AltitudeLOW ER + RadiusEART H Radius of Higher Orbit R2 = AltitudeHIGHER + RadiusEART H RoundTrip Transfer Time Round − T ripDAY S = 2(T ransf er T imeDAY S ) Sine of an Angle Adjacent Side cos(θ) = Hypotenuse Space Height h1 = h0 − 100, 000 Space Interface 100, 000 km Spaceport America At Latitude Payload S paceport − to − AtLatitude ALT = − 8.18ALT + 16, 335 Page 125 of 129
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Spaceport America I.S.S. Payload S paceport − to − I SS ALT = − 7.73ALT + 13, 982 Spaceport America Polar Payload S paceport − to − P olar ALT = − 7.27ALT + 8, 118 Standard Gravity g 0 = 9.8 m/s2 Standard Gravitational Parameter μ = 398, 600.4419 km3 /s2 Time at Maximum Height v vertext = g0 0
Time at Space Interface spacet =
v0 −
√v
2 o
g0
+ 2g 0 h1
Time Spent in Space T imespace = 2(vertext − spacet ) Time Spent Weightless T imeweightless = 2(vertext ) Time To Touchdown Line−Of −Sight Distance T ime T o T ouchdown = Glide Speed Transfer Time T ransf er T imeDAY S = π
√
3
(R1 + R2 ) 8μ
Velocity S.I. Conversion v 0 = I nitial V elocity(1609)/3600 :: Page 126 of 129
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INDEX This book is provided in the form of a free PDF download. Please use your PDF reader to find any words or phrases that you wish to look up. ::
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::
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ADVENTURES IN OUTER SPACE A High School S.T.E.M. Laboratory Textbook © 2015 by ReNewSpace, LLC. Albuquerque, NM. All rights reserved. No part of this textbook may be reproduced, in any form or by any means, without permission in writing from the author. ISBN 9999999999 ::
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ADVENTURES IN OUTER SPACE A High School S.T.E.M. Lab Textbook by Joe Maness
This textbook is the lab for High School Senior mathematics. Students that have passed or are currently enrolled in Algebra 2 (or equivalent) should take this class. The textbook is based on a technical paper he had written earlier about a commercial space program.
ABOUT THE AUTHOR Shortly after High School graduation, Joe enlisted in the U. S. Navy. He flew backseat in S-3A Viking jet aircraft, accumulating over one hundred carrier landing or â&#x20AC;&#x153;traps.â&#x20AC;? Joe rose to the rank of Petty Officer, 2nd Class. Joe then went to college after the Navy, earning his Bachelor of Science degree in Applied Mathematics from the University of New Mexico. Joe was a member of Kappa Mu Epsilon National Mathematics Honor Society. Joe eventually became a Microsoft Certified Trainer, which in turn lead to a job as a High School Math Teacher. During this time, Joe put together the website version of this textbook. Joe is currently a Level 2 Secondary Education Teacher endorsed in Mathematics with over 14 years of experience in the classroom. He resides in Albuquerque, NM, USA.