Kerbal Space Program - The Missing Manual - Volume I.pdf

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Kerbal Space Program The Missing Manual (updated for version 0.24.2) Volume I Author: Anthony de Araujo

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Disclaimer The information in this book is for informational purposes only.

Kerbal Space Program is a product developed by Squad. It is currently in the alpha stage, but has been available for early access purchase for around 2 years. I am not a lawyer or a rocket scientist, nor am I affiliated with the producers of the Kerbal Space Program game. Any advice that I give in this publication is my opinion based on my own experience with the game and research I have done about the subject. The material in this book may include information, products or services by third parties. parties. Third Party Party Materials Materials are comprised comprised of the products and opinions expressed by their owners. As such, I do not assume responsibility or liability for any Third Party Material Material or opinions. opinions. The publication of such Third Party Materials does not constitute my guarantee of any information, instruction, opinion, products or services contained within the Third Party Material. Publication of such Third Party Material is simply a recommendation and an expression of my own opinion of that material. 3

4 No part of this publication shall be reproduced or transmitted, in whole or in part in any form, without the prior written consent of the author. All trademarks and registered trademarks appearing in this publication are the property of their respective owners. Readers of this book are advised to do their own due diligence when utilizing the information contained herein. By reading the information contained in this publication, you agree that the author is not responsible for the success or failure when utilizing any information presented.

Contents

1 About About the the Aut Autho horr

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2 Introd Introduct uction ion

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2.1 What What is Kerbal Kerbal Spa Space ce Prog Program ram?? . . . . . . . . . . . . . . . . . 11 2.2 2.2 Ab Abou outt this this book book . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 2.3 Co Conc ncep epts ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1

∆v (Delta-v) . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.2

I sp sp - Specific Impulse . . . . . . . . . . . . . . . . . . . 18

2.3.3 2.3.3

TWR - Thrus Thrustt to Weig Weight ht Ratio Ratio . . . . . . . . . . . . . 20

2.3. 2.3.44

Stag Stagin ingg . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3. 2.3.55

Attit ttitud udee . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3.6 2.3.6

Progra Prograde/ de/Ret Retrog rograd radee . . . . . . . . . . . . . . . . . . . 31

2.3.7 2.3.7

RCS RCS - React Reaction ion Con Contro troll Syste System m . . . . . . . . . . . . . 33

2.3.8

SAS - Stabili Stability ty Augmentat Augmentation ion System System . . . . . . . . . . 34 5

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CONTENTS

2.4 Orbita Orbitall Mechan Mechanics ics - The The ”Mathy ”Mathy”” part . . . . . . . . . . . . . 35 2.4. 2.4.11

What What is an Orbi Orbit? t? . . . . . . . . . . . . . . . . . . . . 35

2.4. 2.4.22

Peria eriaps psis is . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4. 2.4.33

Apoa Ap oaps psis is . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.4. 2.4.44

Semi Semimajo majorr Axis Axis . . . . . . . . . . . . . . . . . . . . . . 40

2.4.5 2.4.5

Eccen Eccentri tricit city y . . . . . . . . . . . . . . . . . . . . . . . . 43

2.4. 2.4.66

Incl Inclin inat atio ion n . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.4.7 2.4.7

LAN - Longi Longitud tudee of Ascend Ascending ing Node . . . . . . . . . . 47

2.4.8 2.4.8

Argume Argument nt of Peria Periapsi psiss (ω (ω ) . . . . . . . . . . . . . . . . 50

2.4. 2.4.99

Mean Mean An Anom omal aly y . . . . . . . . . . . . . . . . . . . . . . 50

2.4.10 Orbital Orbital Stabilit Stability y . . . . . . . . . . . . . . . . . . . . . 51 2.4.11 Lagrange Lagrange Point Pointss . . . . . . . . . . . . . . . . . . . . . . 54 2.4.12 Altitude Altitude vs. vs. Velocity elocity . . . . . . . . . . . . . . . . . . . 56 2.4.13 Oberth Effect Effect . . . . . . . . . . . . . . . . . . . . . . . 57

3 The The Na Navb vbal alll

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3.1 Navba Navball ll Indica Indicator torss . . . . . . . . . . . . . . . . . . . . . . . . 65 3.1. 3.1.11

Progr Prograd adee . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.1. 3.1.22

Retr Retrog ogra rade de . . . . . . . . . . . . . . . . . . . . . . . . 65

3.1.3 3.1.3

Target arget Progra Prograde de . . . . . . . . . . . . . . . . . . . . . . 66

3.1.4 3.1.4

Target arget Retrog Retrograd radee . . . . . . . . . . . . . . . . . . . . 67

3.1. 3.1.55

Mane Maneuv uver er Node Node . . . . . . . . . . . . . . . . . . . . . . 67

3.1.6 3.1.6

Level Level Indica Indicator tor . . . . . . . . . . . . . . . . . . . . . . 67

3.1.7 3.1.7

Other Other Navba Navball ll Indica Indicator torss . . . . . . . . . . . . . . . . . 68

3.1.8

Using the the Navball Navball To Change Change Your Your Attitu Attitude de . . . . . . 69

3.1. 3.1.99

Mane Maneuv uver er Nodes Nodes . . . . . . . . . . . . . . . . . . . . . 73

3.1.10 Executing Executing Maneuv Maneuvers ers . . . . . . . . . . . . . . . . . . . 81

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CONTENTS

4 Orb Orbita itall Maneuv Maneuvers ers

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4.1 Gravit Gravity y Turn . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.2 Circul Circulari arizin zingg your your Orbit Orbit . . . . . . . . . . . . . . . . . . . . . 87 4.2.1 4.2.1

Achie Achievin vingg Orbit Orbit . . . . . . . . . . . . . . . . . . . . . . 87

4.2.2 4.2.2

Circul Circulari arizat zation ion . . . . . . . . . . . . . . . . . . . . . . 88

4.3 Changing Changing your your Orbital Orbital Inclination Inclination . . . . . . . . . . . . . . . . 96 4.4 4.4 Aero Aerobr brak akin ingg . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 109 4.5 4.5 Rend Rendez ezv vous ous . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 122 4.6 4.6 Do Doccking king . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 155 4.7 Gravit Gravity y Assist Assist . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.8 4.8 Land Landin ingg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 178

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CONTENTS

Chapter 1 About the Author I am a software developer with 30+ years of experience. Over the course of my professional career, I have also been a big game enthusiast during my free time. I’ve played everything from Tetris, Breakout, Duke Nukem and Doom to Left 4 Dead, Portal, Space Engineers and, of course, Kerbal Space Program. I am not a rocket scienti scientist. st. I am simply simply an enthus enthusiast iast of the game with a knack for research. research. All the concepts and descriptions descriptions that I provide provide in this book are my own experiences with the game and are not guaranteed, in any way, to help you accomplish your own goals in the game. I strive to provide the technical content in a fashion that a layperson can easily understand. If you have suggestions about how I could better explain anything you see here in the book, I would appreciate it if you would drop me a note about it at [email protected]. For the real rocket scientists that might stumble upon this book, if I got anything anything wrong, wrong, please let me know so that I can fix it. I want to provide provide the most accurate information possible, but in trying to translate ”engineer-ese”, or ”rocket-scient-ese” to English I might have made some mistakes. Also bear in mind that some things I explain in this book might be ”wrong” in the real world, but may apply in the Kerbal universe, so be gentle. 9

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CHAPTE CHAPTER R 1. ABOUT ABOUT THE AUTHO AUTHOR R

I thoroughly enjoyed writing this book, and I hope that anyone who is reading it can glean some useful information from it and have a better, more enjoyable, experience in the game.

Chapter 2 Introduction 2.1 2.1

What What is is Kerb Kerbal al Spa Space ce Pro Progr gram am? ?

Kerbal Kerbal Space Program is an extremely extremely fun and educational educational game. Having Having always been interested in the space program, I thought I knew something about space. Turns out I was wrong. My firsts forays forays into space space in Kerbal Space Program ended in disaster, disaster, multiple disasters. disasters. If that is wha whatt you you are experie experienci ncing, ng, do not fret. fret. The learnin learningg curve curve is rather steep, but once you start to understand the concepts, that I describe scribe in detail detail in this this book, the game game beco b ecomes mes somethi something ng that is, well. well. . . indesc indescrib ribabl able. e. . . Without realizing it, you will be learning concepts about space travel that you never even imagined! The game comes with three distinct modes of play: play: sandbox, sandbox, science science and career. In sandbox mode, you have all of the parts available for use and can create some pretty impressive vehicles. 11

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CHAPTE CHAPTER R 2. INTROD INTRODUCTI UCTION ON

In science mode, you start with a few, basic parts, and you must do research to gain ”science points” which you use to unlock more advanced parts. parts. While science science mode might might seem intimidating, intimidating, it is a very good wa way y to start learning the game. Since you have access to a limited set of parts, you can use, and understand, those parts, naturally progressing to more advanced parts as they are unlocked. In care career er mode, mode, you you star startt with with a few, few, basi basicc part partss just just lik like in scie scienc ncee mode. mode. You still still must must do resear research ch to gain gain ”scien ”science ce poin p oints” ts” which which you you can use to unlock unlock more advanc advanced ed parts. parts. Beside Besidess the science science aspect aspect of career career mode, version version 0.24 introduce introduced d contrac contracts, ts, funds and reputation. reputation. These These three three resources must be acquired/used over the course of your career. Like science mode, it might seem intimidating but is also a very good way to start learning the game. The contract aspect of career mode forces you to use parts in some interesting ways that you might not have thought of otherwise. If you start playing in sandbox mode, the sheer number of parts can be a little overwhelming, which makes the game a little harder to learn.

2.2

Abou bout this book book

When I first started playing Kerbal Space Program, it was very difficult to find any type of refer referenc encee materi material al online. online. I follo followe wed d the advice advice of felfellow players (shout out to http://reddit.com/r/kerbalspaceprogram ) and watched all the mandatory videos (that mean’s YOU, Scott Manley! https: //www.youtube.com/user/szyzyg ) I still found it very hard to gain any real knowledge about the concepts that you need to understand to play the game effectively. So I decided I was going to figure this stuff out for myself, and publish what I had learned on a blog. So I created http://mykspcareer.com , hoping to share my ”knowledge”. The response to the blog was, well, underwhelming. So here I am again, trying to get this information out there. So I decided to write this book.

2.3. 2.3.

CONCEP CONCEPTS TS

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A lot of the content in this book can be found on the blog mentioned above, including some features that I, obviously, can’t include in the book, like .craft files. As I mentioned in the disclaimer above, I’m not a rocket scientist, just an enthusiast of the game with a knack for research, so I hope this book helps old and new players alike in accomplishing their goals within the game. If you happen to be a rocket scientist, or just someone smarter than me (probably not rare), and you see anything in this publication that is wrong, could be explained better or missing entirely, I would appreciate it if you dropped me a note at [email protected]. Any contributions made by third parties will be fully credited in subsequent editions of the book. The fact that you are even taking the time to read this book, makes me happy to have invested the time to produce it.

2.3

Conc nce epts pts

There are a myriad of concepts related to orbital mechanics, terminology, etc. that will help you immensely in learning the game. In this section I will go over SOME of the ones I think are more important.

2.3.1

∆v (Delta-v)

delta-v means, literally, change (∆) in velocity (v ( v ), and is simply short-hand used by personnel involved in astrodynamics. Think Think of your car: car: it has a gas tank tank of finite finite size; size; it has an engine engine of a specific power (in the case of cars, horsepower), and it has a certain ”drymass” (how much the car weighs, without fuel).

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The equivalent of your car’s ∆v ∆ v is not its MPG rating, nor is it the power of your engine. Imagine that your car doesn’t have an upper speed limit. So we put you in your car, car, with with a full full tank tank on the salt salt flats flats of Utah. You step on the gas, and hold it down, constantly accelerating, until you run out of fuel. If your speed, when you ran out of fuel was, let’s say, 2237 mph, then that is your ∆v . Your car has the capacity to change its speed, from a dead stop with a full tank, by 2237 mph until it runs out of fuel. I’ll take this opportunity to say that when dealing with astrodynamics, we use the metric system almost universal universally ly.. So instead of miles per hour, we use kilometers per hour, or even more frequently, meters per second. 2237 mph works out, in metric, to be almost exactly 1000 m/s. In your car above, the overwhelming majority of mass of the fully fueled vehicle is the vehicle itself, the mass of the fuel in your car, when compared to the total mass of the car is minuscule. minuscule. In the rocket rocket world, world, the ma jority jority of mass is the fuel. As an example, I’ll show you the specifications for the Space Shuttle: The Shuttle itself, just the orbiter, without the big orange tank or the solid boosters, has a gross liftoff mass of 110,000 kg (this includes payload, crew, crew, consum consumabl ables, es, fuel fuel for the shuttle shuttle to use in space, space, etc). To launc launch h the shuttle, we add the big orange external tank, and the two solid rocket boosters which weigh in, fueled, at 756,000 kg and 1,142,000 kg (each booster is 571,000 kg), respectively. 1,000 kg per ton is a fair approximation for our purposes, so let’s just call the entire shuttle assembly 2,000 tons. Bear in mind that we burn through the solid rocket boosters in the first 2 minutes of the flight and the external tank runs the shuttle’s main engines for a grand total of 8 minutes before being jettisoned, so we use 1,898 tons of hardware and fuel to launch 110 tons of spacecraft into space. So only 5.8% of our spacecraft is actual spacecraft, the remaining 94.2% of our spacecraft is launch hardware and fuel.

2.3. 2.3.

15

CONCEP CONCEPTS TS

In comparison, a 2010 Chevy Camaro weighs in at about 1720 kg and has a fuel tank capacity of about 20 gallons (19 actually, but 20 makes our calculations calculations easier). easier). Those 20 gallons of gas weigh eigh 55 kg. So our Cama Camaro ro,, at 1.8 tons, is 96.9% vehicle vehicle and only 3.1% fuel. But our Camaro can’t go straight straight up in the air either. This Camaro can also accelerate from 0 to 60 mph in 6 seconds, which gives us a very convenient 10 mph/s (4.5 mph/s (4.5 m/s m/s 2) of acceleration. ∼

Everyo Everyone ne knows that a heavier heavier vehicle vehicle gets worse gas mileage. But the 97/3 ratio for our Camaro is pretty negligible negligible.. In our example above, above, of 1000 m/s, the car was heavier when it started to accelerate than at the end when it was running out of gas. So of those 1000 m/s of ”∆v ”∆ v” slightly more of it came from the second half of the tank versus the first half of the tank. With our space shuttle, however, after 2 minutes of flight, the vehicle drops drops the two two solid solid boosters boosters which which accoun accounted ted for 1,142 1,142 tons: tons: more more than than HALF of the total mass of the vehicle when it was sitting on the launchpad. So in our example, 20 gallons of gas got us from 0 to 1000 m/s. m/s . And the mass of the vehicle only changed by 3%. In the case of the shuttle, at liftoff we are pushing 2,000 tons, the total burn time for the shuttle is 8 minutes. After 41 of the burn time (2 minutes), we shed more than half the mass of the vehicle vehicle.. So that last 43 of burn time, theoretically, we are accelerating more quickly than during the first 41 (not necessarily true, since during that first 41 we also have two additional engines - the two solid boosters - burning). The point I’m trying to make is that the mass of the shuttle changes VERY rapidly over the course of the launch (8 minutes). In the case of our Camaro, Camaro, you can use Newton’s Newton’s Second Second Law of Motion Motion to analyze the vehicle vehicle since, for all intents and purposes, we can consider the mass of the vehicle to be constant (it only varies by 3%, slowly decreasing as the fuel tank empties).

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When When it come comess to the the shut shuttl tle, e, we cann cannot ot use use Newton’s Newton’s Second Law of Motion Motion to analyze the system because the mass is not even close to constant (it varies by 94.2% over the course of 8 minutes!). Where the Space Shuttle’s Main Engines (SSMEs the three engines we see right below the vertical stabilizer) could not even budge the shuttle off the pad at its full 2,000 ton liftoff mass, once the shuttle is already moving at a good clip, and having dumped the extra 1,142 tons of solid booster mass, they are more than sufficient to propel the vehicle into orbit over those last 6 minutes of the launch burn. Due to this inability to analyze the shuttle system performance using Newton’s Second Law of Motion, we need a different mechanism. That mechanism is the ”Tsiolkovsky rocket equation”.

m0 ∆v = I sp g ln m ·

·

1

where: m0 is the total initial mass of the vehicle, including propellant; m1 is the total final mass of the vehicle (after burning all of the propellant) I sp is sp is the specific impulse for the engine(s) g is Standard Gravity (9.8 m/s 2 ) This equation takes into consideration the rapidly changing mass of the vehicle and allows us to calculate how much change in velocity the vehicle is capable of applying to itself. As you can see above, the equation needs the Isp of the engine to calculate I sp of the ∆v ∆v . For now, just accept that rocket rocket engines have have I sp values sp values (kind of

2.3. 2.3.

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CONCEP CONCEPTS TS

like the horsepower values you get for car engines, we’ll be discussing those next). Now we know what ∆v ∆ v is and how to calculate it, but why should we care? Every maneuver, performed by a rocket, has a specific amount of ∆v ∆v that that is require required d to perform perform the maneuv maneuver. er. For example: example: to launch, launch, from from the Kennedy Space Center and achieve a Low Earth Orbit (LEO), it takes anywhere from 9,300 to 10,000 m/s of ∆v . Once Once in an LEO, LEO, to transf transfer er to a Low Lunar Orbit (LLO), it takes an additional 4,000 m/s of ∆v. Sinc Sincee we don’t want to just leave our poor astronauts there, we need 1,300 m/s of m/s of ∆v to transfer from LLO back to LEO and then another minuscule amount of ∆v necessary to deorbit (since atmospheric drag does most of the work). So a vehicle, tasked with launching to LEO, then transferring to LLO, then transferring back to LEO and landing, would require a total of 15,300 m/s of ∆v . From

To

Low Low Earth Earth Orbit Orbit (LEO) (LEO) EarthEarth-Moon Moon Lagran Lagrange ge 1 (EML-1 (EML-1))

∆v req’d 3,770 3,770 m/s

Low Low Eart Earth h Orbi Orbitt (LEO (LEO))

Geosta Geostatio tionar nary y Eart Earth h Orbit Orbit (GEO) (GEO) 4,330 4,330 m/s

Low Earth Orbit (LEO)

Low Lunar Orbit (LLO)

4,040 m/s

Low Low Earth Earth Orbit Orbit (LEO) (LEO) EarthEarth-Moon Moon Lagran Lagrange ge 2 (EML-2 (EML-2))

3,430 3,430 m/s

Low Earth Orbit (LEO)

5,930 m/s

Mo on

Table listing approximate ∆v ∆v requirements within the Earth-Moon system

If you want to have an idea of how big of a rocket is needed to do that, thin think k Satur Saturn n V, the one that that went went to the the Moon: Moon: It was the lengt length h of a football field, at it’s base it was over half the width of a football field, and weighed, on the pad, ready to launch, 2,800 tons. Of that total, only 45 tons worth worth of spacecraf spacecraftt actually went went to the Moon. 1.6% worth of spacecraft spacecraft got

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to the Moon, the other 98.4% of the spacecraft was either burned (as fuel) or jettisoned (as spent stages). Thankfull Thankf ully y, the develo developers pers at Squad Squad realiz realized ed that that making making the Kerbal Kerbal Solar System an exact replica of our own Solar System would make the game WAY too difficult to be enjoyable. If you think you have it tough getting into Kerbin orbit, which only requires 4500 m/s of ∆v, imagine if our flimsy, wobbly rockets had to be 4 times as big as they are! ∼

2.3.2

I sp - Specific Impulse

I sp is, sp is, loosely, the rocket engine equivalent of an Earthbound car engine’s miles miles per p er gallon. gallon. It measures measures the efficien efficiency cy of the engine engine (each (each engine engine has its own I sp). have one engine, engine, with an I sp sp). If you have sp of 800, you might think that you could get more ∆v ∆ v if you add a second engine of the same I same I sp. sp. You won’t, you’ll get your ∆v ∆ v faster, but not more of it. ∆v you can, effectively, get out of a unit of fuel I sp sp defines how much ∆v (a kg, for exampl example). e). So if you you have have an engine engine with with an I sp of sp of 400 and 500 kg of propellant, in a 1,500 kg rocket (so 1,000 kg of rocket and engine, plus 500 kg of propellant) you would have a total ∆v ∆ v of 1,590 m/s. Let’ss say say m/s. Let’ that your rocket takes 4 minutes to burn through those 500 kg of propellant. So if I was moving at 1,000 m/s when m/s when I started burning, when I ran out of propellant (4 minutes later), I would be moving at 2,590 m/s, m/s , a change (∆) in velocity (v (v) of 1,590 m/s 1,590 m/s.. Too slow for me, I’m gonna add another engine on that rocket. So I put a second, identical, engine on the rocket. Do I get more ∆ v? No. My rocket now will burn through my propellant twice as fast, since I have two identical engine enginess suckin suckingg on the tank, tank, so my burn burn will will only only last 2 minute minutes. s. And to top it all off, my final speed, when the burn ends, is now only 2366 m/s!. m/s!. I got my ∆v ∆v faster (2 minutes versus 4 minutes), but I got less ∆ v than with the single engine. You LOSE a small amount of ∆v ∆v because the engine you added increased the overall mass of the vehicle (dead weight once it stops burning).

2.3. 2.3.

CONCEP CONCEPTS TS

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Our 1,500 kg rocket had 500 kg of propellant and I said 1,000 kg of rocket and engine. Consider that the engine was 200 kg (so 800 kg of other ”stuff” ”stuff” that that made made up the rocke rocket). t). I add added ed an add additi itiona onall 200 kg of mass to the vehicle, so my rocket’s total fueled mass is now 1,700 kg, and after all the fuel fuel is burned, burned, 1,200 1,200 kg. All the propella propellant nt that I burned burned during during my maneuver had to push 200 kg more of mass during the burn, therefore the ∆v produced was slightly less. From this we learn that if I want more ∆ v , I have to increase the mass of propellant available to the engine (assuming the engine remains the same) *OR* keep the mass of propellant I currently have and increase the I sp of the engine I am using to burn it (effectively taking the 40 mpg engine out of the car and replacing it with a 50 mpg engine). So why don’t they just use something like miles per gallon to indicate efficien efficiency? cy? Becaus Becausee rockets rockets aren’t aren’t cars. cars. The mpg rating rating on your car is a rating calculated under specific conditions (usually conditions that benefit the manufa manufactu cturer rer by maximizi maximizing ng said said rating rating). ). For example: example: the 30 mpg rating on your car might be at a constant speed, on level ground, with no wind. wind. Und Under er these these specific specific condition conditions, s, every every,, theore theoretic ticall ally y, 30 miles miles that that you you trave travel, l, your your engine engine consum consumes es one gallon gallon of gas. gas. If you then then turn turn your your engine engine off, your car, eventually eventually,, comes to a stop. THAT’S THAT’S the difference. difference. If I accelerate my rocket by burning, let’s say 200 kg of propellant, in space (outside of the atmosphere, with no gravity producing bodies nearby), from a standstill to 1,000 m/s, m/s, my speed will remain at 1000 m/s, m/s, theoretically, forever. So how far can I travel on 200 kg of propellant? An infinite distance (assum (assuming ing I don don’t ’t run into anythin anythingg that that exerts exerts force force on the vehicl vehicle)! e)! So there is no 1,000 miles/kg of propellant, or any other number related to a distance that we can use to indicate efficiency of the engine. What exists is velocity. With those 200 kg of propellant, I can accelerate my vessel by 1,000 m/s, m/s, and continue moving at that speed until I do another burn and change it (or run into something else that changes it). So in our example rocket, with 500 kg of propellant, if I double the amount of propellant, 1,000 kg, and leave the single engine, I double my ∆v ∆ v, right? Nope, Nope, wron wrongg agai again. n. Agai Again, n, it’s it’s clos close, e, bu butt not not quit quitee doub double le (2719 (2719 m/s), m/s), because at the start of the burn, the engine is pushing more mass (1,000 kg of fuel now versus the 500 kg it was pushing before), so it does it more slowly

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(while (while expendi expending ng the same amount amount of fuel). fuel). So after I burn burn the first half half of my propellant (the first 500 kg), I’ve only increased my velocity by 1,129 Thatt second second half of propell propellan antt (the (the origin original al 500 kg) will give give me the m/s. m/s. Tha same 1,590 m/s 1,590 m/s of of ∆v that it gave me before, which added to the 1,129 m/s comes out to the 2,719 m/s total ∆v for the vehicle (these calculations are m/s total ∆v ignoring the mass of the tanks for simplicity’s sake)! Increasing the mass of propellant of the vehicle when you want more ∆ v is a game of diminishing diminishing returns. Yes, more propellant propellant gives you more ∆v ∆ v. But every, let’s say, 1,000 kg of propellant that you add to your total, gives you less and less ∆v ∆v .

2.3.3 2.3.3

TWR TWR - Thru Thrust st to to Weig Weigh ht Ratio Ratio

One of the bigger issues when building vehicles in the game is finding out if you have enough engines/thrust to actually get your vehicle off the ground. The first thing we need to understand is that TWR is calculated by dividing the thrust of your vehicle by the weight of your vehicle. Both numbers should be in Newtons (N). Typically, engines have their thrust rated in kN (1000 N), but for the weight we need to do the conversion from kg to N. Contrary to popular belief, a kilogram (or a pound, for that matter) is unit of weigh weight. t. It is a unit of mass1 . Weight eight does not exist, unless NOT a unit there is gravity. So the weight of an object is its mass multiplied by the force of gravity gravity by which it is being affected. affected. On the surface of Kerbin, the force 2 of gravity is 9.81 m/s 9.81 m/s . 1,000 kg = 9,810 N on the surface of Kerbin. The main indicator of whether a vehicle will take off or not is the TWR. The TWR specifies a value, starting at 0, that indicates how much thrust you have have on your your vehicle, vehicle, compared compared to the weight weight of the vehicle vehicle.. So if your your engines provide 220,000 Newtons of thrust (220 kN) and your vehicle weighs 1

Actually, while there are multiple variations on them out there, in the traditional English system of units, a pound is the unit of weight/force (there being no notion of a distin distincti ction on between between weight weight and mass mass when when it was inve invent nted ed back in the day). day). The ft corresponding unit of mass is the slug - a mass that accelerates by 1 s when a force of one pound is exerted upon it - Contributed by Alistair Y. 2

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39,750 39,750 kg (389,9 (389,948 48 N), you’re you’re not going going anywh anywhere ere.. Your engines engines need to provide more thrust than the weight of your vehicle to get off the ground. Our example above has a TWR of 0.56 (220,000 N/389,948 N). The lesson here is that we need a TWR greater than 1.0 if we want to get off the ground. If you want to build this vehicle in the vehicle assembly building, it’s a Mk1 Cockpit, 2 Rockomax X200-32 Fuel Tanks (one on top of the other), and a Rockomax ”Poodle” Liquid Engine. What the TWR is specifying is, in reality, the amount of g-force that the vehicle is capable of generating. So if our vehicle is generating less gforce than what is being exerted by the planet it is sitting on, it’s not taking taking off. On Kerbin, Kerbin, the force force of gravity is the same as on earth, 1 G, or 9.81 m/s2 . If our vehic vehicle le cannot cannot overcome the force of gravity, it will not lift off the launch pad. If we modi modify fy our our vehicl hiclee, by adding more, or better, engines, to have 650,000 N of thrust, our TWR is now 1.61 (650,000 N/404,663 N). I replac replaced ed the ”P ”Poodle” oodle” engine engine Figure 2.1: Our non-flying vehicle with with a ”Mai ”Mains nsai ail” l” wh whic ich h weigh eighss slightly more. Since we only have to overcome 1 G of surface gravity, this tells us that the vehicle will ascend, off the launch pad, at 0.61 G or 5.98 m/s 2 .

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But, there are a couple of things that happen pen to a rock ocket as it launches. Firs Firstt off, off, as we disc discus usse sed d earearlier, lier, the vehicle vehicle loses mass mass VERY rapidly rapidly. As it loses mass, its weight weight goes down, as its weight goes down, its TWR goes UP ! Example: Example: We start with our vehicle that has 650,000 N of thrust and weighs 404,663 N. Let’s assume, for this example, that the vehicle is 90,473 N of hardware and 313,920 N (32, (32,00 0000 kg) kg) of fuel fuel (rem (remem embe berr that the shuttle was only 5.8% shuttle and 94.2% launch hardware and Figure 2.2: Our modified vehicle (that fuel). flies)

Our launch TWR is 1.61, so we lift off the launch pad at 5.98 m/s 2 . At 1 minute minute into the flight flight,, we’v we’vee burn bu rned ed 39.4 39.4% % of our our fuel fuel:: 123, 123,66 6655 N (12,60 (12,6066 kg). kg). So at the 1 minute minute mark our vehic vehicle le now weigh weighss 280,99 280,9988 N (28,644 (28,644 kg) but it still still has the same same thrust: thrust: 650,00 650,0000 N. Our TWR at 1 minute is: 2.31, so we are now accelerating a 1.31 Gs (12.85 m/s (12.85 m/s 2 ). At the 2 minute mark, we’ve burned 75.2% of our fuel and our vehicle now weighs 168,506 N (17,177 kg), giving us a TWR of 3.86, or 2.86 Gs of acceleration (28.06 m/s2 ). The vehicle runs out of fuel at the 2 minutes and 42 second mark. Right before it runs out of fuel, it weighs 90,752 N (9,251 kg), giving us a TWR of 7.16, or 6.16 Gs of acceleration (60.43 m/s 2 ) The second important thing about TWR that we need to understand is that, according to Newton’s Law of Universal Gravitation, masses attract

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Figure 2.3: This chart shows the change in the TWR of your vehicle over time for the example vehicle described above (a vehicle that consumes all of its fuel over the course of a 2 minutes and 42 seconds burn)

each other and that the attraction is proportional to the product of the two masses and inversely proportional to the square of the distance between them. What What does that mean to us? As our craft craft ascends ascends from Kerbin, Kerbin, it loses loses mass quickly, since gravity is proportional to the product of the two masses (the planet Kerbin and our ship), the force of gravity reduces as the mass of our ship reduces. reduces. We are also flying (at least for a part of our flight) flight) straight straight up, so we are increasing the distance between the two masses. Since the force of gravity is inversely proportional to the square of the distance between the two masses, it is reduced even more. Right above the previous chart, we discussed what the TWR was at the very end of our burn. burn. We came up with the value value of 7.16. I did this calculation so that you would understand the relationship between the weight of the vehicle vehicle and the TWR. But I slipped a white lie into those calculati calculations. ons. I was calculating the weight of the vehicle in N by always multiplying the mass in kg by the 9.81 m/s 9.81 m/s 2 gravitational constant. In reality, the force of gravity is changing as the vehicle ascends. In our example, by the time the vehicle ran out of fuel, it was actually packing a TWR of 9.45.

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Figure 2.4: As the vehicle increases its altitude the force of gravity diminishes. This graph shows the variation in gravity, by altitude, on Earth.)

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To obtain information like ∆v ∆ v , I sp and sp and TWR for your vehicles, you can either do the math, or use one of the various mods that provide that type of information. As of this writing the most popular mods that provide this type of information are: MechJeb and Kerbal Engineer Redux. More information about these mods will be discussed in the chapter on Mods in a future volume.

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2.3. 2.3.4 4


Stag Stagin ing g

As we saw above, mass is a big factor. The more mass we have to push with our engines (for a given I sp), ∆ v we get out of our propellant. The sp), the less ∆v problem here is that, in our day-to-day lives, we are not used to thinking of things in the scale necessary for astrodynamics. In the Camaro example discussed, we carry 20 gallons of fuel that masses 55 kg. What we didn’t mention was the mass of the fuel tank. I have no idea how much a fuel tank for a Camaro would actually weigh, so let’s say 10 kg. Our Camaro’s Camaro’s mass, fueled, fueled, in total, is 1,775 kg. Of that total, 55 kg (fuel) plus 10 kg (fuel tank) is for our propellant. Only 0.56% of our vehicle is fuel tank (fuel itself, if you remember, was 3.1%). If we want to give our Camaro greater range, we could add another fuel tank (+10 kg) and fill it with gas (+55 kg). So we add an additional 65 kg of propellant and hardware (the tank) bringing our total mass to 1,840 kg. This way we extend the range of our vehicle, at the cost of increasing its mass. That first tank of gas isn’t going to get us as far as it used to because now it is hauling the second, additional, additional, tank of gas with it. And even even after the first tank is empty, the second tank will not take us as far as the single-tanked version of our vehicle, because it is still hauling that extra 10 kg of empty (first) tank with it. Ideally, once the first tank is empty, we drop it on the road, giving the second tank its full range (since after we’ve burned the fuel in the first tank, and dropped the empty first tank, our Camaro now masses 1,775 kg again). That is what staging is all about, getting rid of mass that is no longer needed needed:: empty empty fuel fuel tanks, tanks, dead dead engines engines (i.e. (i.e. engine enginess that that have have no more more propellant propellant to burn), burn), continge contingency ncy hardware hardware (i.e. the Launch Escape System that sat on top of the Apollo command module in the Saturn V launch system), etc. We tend tend to think ”Empt ”Empty y tank? tank? Only Only 10 kg? Not worth worth the hardware hardware necessary necessary to detach detach and jettiso jettison n those 10 kg. . . ”, but that is car based thinkthinking. In the shuttle’s case, the empty big orange tank has a mass of 26 tons. Each one of the empty, solid-rocket boosters on the shuttle has a mass of 91

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tons. Remember that the shuttle itself (no external tank or boosters) has a mass of 110 tons. So the ”dead weight” on the shuttle, after all propellant is consum consumed, ed, is 208 tons (26 tons + 91 tons + 91 tons). tons). Almost Almost TWICE the mass of the orbiter itself! The faster your vehicle sheds its dead mass, the more ∆ v you will get from the engines and propellant that you still have, because there will be less mass to push. Your vehicle design can, theoretically, have as many stages as you see fit. Just remember remember that each stage requires requires additional additional hardware hardware (a decoupler decoupler or a separator, separator, at a minimum), minimum), which is more mass that you have have to push. Also remember that, at least in game, stage boundaries tend to be the weakest structural points of your vessel. This means that you have to, typically, use struts to strengthen the link so it can withstand the stresses of a launch and maneuvers. The shuttle is a 3 stage launch system: 1. At liftoff, liftoff, all three main engines on the orbiter are burning burning (being fed from the external tank) and the solid rocket boosters are also burning. Once the SRBs have exhausted their propellant, they are jettisoned. That is the first stage, the 2 minutes between ignition on the launch pad and the decoupling of the SRBs. 2. During the second stage, the orbiter orbiter continues continues burning its main engines using using fuel fuel from from the externa externall tank. tank. At this point (2 minute minutess into into the 1 flight), the external tank has only been 4 depleted. depleted. So the second stage stage will last, approximately, another 6 minutes. At this point, the external tank tank is empt empty y, so we get rid of it. it. Th That at is the the second second stage stage,, the the 6 minutes between SRB separation and external tank separation. 3. This is the final stage of the system and includes the orbiter alone. Its main engines are still attached to the vehicle, however they are no longer used in the mission. In the real world, it is not an economically sound proposition to jettison 3 $40 million pieces of hardware that would, wou ld, presumably presumably, be burned burned up and destroy destroyed ed upon reentry reentry.. So the shuttle hauls 10.5 tons (3.5 tons per engine) of hardware around space and brings it back when it lands.

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Fortunately for us, we don’t have (yet) congressional oversight oversight committees or politicians breathing down our necks in Kerbal Space Program, so feel free to drop your ”Mainsail”s in the ocean or leave them in a degrading orbit once you no longer need them. Just for completeness sake, I’m going to mention here the shuttle’s Orbital Maneuvering System (OMS). Since once the orbiter is in orbit, it can no longer use the main engines, it needs some type of engine to do orbital in jections, orbital corrections and deorbit burns. This is where the OM engines come in. Fairly lightwe lightweight ight (100 kg) engines, engines, that provide provide about 300 m/s of ∆v (it uses about 21.5 tons of propellant to provide that amount of ∆ v ). Bear in mind that this OM system is separate from the RCS system (that we know and love so much in Kerbal Space Program) used by the shuttle. We currently don’t have OM engines/tanks in KSP. The strangest part about doing staging is that, in Kerbal Space Program, we have have to build our vehicles from the top down. So if I were building a Saturn V equivalent, I would start with the Command Module (the capsule), would then add the Service Module, the third stage, the second stage and finally the first stage. The basics of staging are as follows: • To

separate a stage, you should use a stack decoupler or a stack separator. arator. A stack decoupler/ decoupler/separ separator ator is the type that was used in the Saturn V. Once the first stage is depleted it separates from the rest of the vehicle by ”dropping off” of the stack above it.

• In

Kerbal Space Program, fuel from tanks ”above” the stage boundary (above the decoupler/separator) will not feed ”through” the stage boundary to engines below the decoupler/separator.

• The

various stack decouplers, and stack separators, have different ”decoupling coupling forces”. forces”. This means that they will push the separated separated stage (the one being discarded), away from the rest of the vehicle, with a certain certain force. In most cases, this force is negligible negligible,, since it is a ”small” ”small” force, force, typically typically,, pushing pushing a large piece of hardware. hardware. But in some cases, people use stack decouplers to ”launch” satellites from their main vehicle and don’t take that force into consideration and the satellite ends up in an orbit different from what they expected.

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• It

does not matter if you have ”struts” crossing the stage boundary, since the struts will ”automagically” disappear when the stack decoupler/separ pler/separator ator is triggered triggered.. You don’t have have to worry about things not separating because they are strutted to other things. Obviously, this is only true in Kerbal Space Program. In real life, things would not work this way (actually they could, but it wouldn’t be a simple ”strut”).

• If

the part being separated (discarded) IS strutted across the stage boundary, the ”decoupling force” mentioned above, is affected by the struts struts.. Despit Despitee the fact that the struts struts DO ”break” upon triggering the decoupler/separator, it seems they absorb some of the force being exerted by the decoupler/separator, resulting in the part being pushed away from the vehicle with less force than if the part had NOT been strutted. strutted. This is true for both b oth stack decouplers/s decouplers/separa eparators tors and radial decouplers/separators (see below).

•

The difference difference between between a stack stack decoupler and a stack stack separator is that the decoupler only severs the connection on one side (the side that the ”arrow”, printed on the side of the decoupler, points to) and the decoup decoupler ler will remain remain attac attached hed to the part bein b eingg discar discarded ded.. A stack stack separator, on the other hand, severs the connection on both sides. This means that with a separator, you end up with one vehicle, one discarded stage and a third part, the separator, floating freely around in space on its own.

• Radial

Decouplers function just like stack decouplers, except they are used ”radially” (sideways/on (sideways/on the side). Think of the solid rocket rocket booster separation on the space shuttle: they are pushed off to the side as the shuttle (and external tank) continues to move forward.

2.3. 2.3.5 5

Attit ttitud ude e

From here on, you you will will start start seeing seeing the ”Attit ”Attitude ude”” a lot. lot. For those those of you you familiar with the aerospace industry, this isn’t a problem, but for those of us that are not familiar with it, I’m going to explain what is meant by ”Attitude”. From the Merriam-Webster, attitude is defined as:

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the position of an aircraft or spacecraft determined by the relationship between its axes and a reference datum (such as the horizon or a particular star) So? Did that help? Didn’t Didn’t thin think k so. . . Here’s Here’s the problem: problem: a spacec spacecraf raftt doesn’t doesn’t act like like any any other other terre terrestr strial ial vehicle with which you might be familiar. If you fire an engine in a spacecraft, that engine is going to push that spacecraf spacecraftt in a particular particular direction. direction. Once you turn the engine engine off, the spacecraft will continu continuee to move move in that direction, direction, at the same speed (i.e. (i.e. inertia), inertia), unless something else influences that movement. So. . . if you accelera accelerate te your your space spacecra craft ft in a certai certain n direct direction ion,, and then decide you want to stop moving in that direction, you have to ”turn around” and fire your engines again, to counteract the movement that you imparted on the vehicle when you fired them the first time. So it’s real easy for me to sit here and type ”turn around”, but in space how do you determine which way is forwards (and therefore, which ways is backwa backwards rds)? )? Compas Compasses ses don’t don’t wo work. rk. . . there’ there’ss no ”north” ”north” (magneti (magneticc or otherwise otherwise). ). . . I guess you could could use the stars for orien orientatio tation, n, but what if the particular celestial body you chose to use as guidance is no longer visible (on the other side of the planet, for example)? That’s That’s what attitude attitude is all about. . . rotating rotating your your vessel, vessel, using a myriad myriad of different actuators, so that it is pointing in the direction that you need to point to execute whatever maneuver you want. The two main methods of adjusting attitude are discussed a little further below: RCS and SAS (or CMG, as it should really be called). Those are the mechanisms that are used to change the attitude of you vessel, but how do we figure out where we should be pointing? The answer answer to that is the next section: section: Prograde/R Prograde/Retrog etrograde. rade. . .

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2.3.6 2.3.6

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Progra Prograde/ de/Ret Retrog rograd rade e

Prograde is nothing more than the current direction of travel for your vehicle. There is no magic involved. There are actual sensors on real spacecraft that can determine which direction your vehicle is moving. In the game, the navball automatically shows you the information about prograde and retrograde, but that information IS available available on real spacecraft. It might not be a pretty navball like the one we see in game (sometimes it is), but it’s there. But how does knowing what direction I am traveling help me in any way? Every Everythi thing ng in space space is about about motion motion.. If you want want to slow down, down, you you point in the direction opposite your direction of movement (retrograde) and fire your engines. engines. If you want to speed up, you point in the same direction direction as your current direction direction of movemen movementt (prograde) (prograde) and fire your your engines. engines. If you want to change the inclination of your orbit, you point in a particular direction, 90° from your current direction of movement, and fire your engines. And so on... But why would I want to do any of those things? Speed up? Slow down? You just said if I’m moving in a certain direction, I’ll keep moving in that direction, direction, at that speed. So what difference difference does it make if I’m going 1,000 mph or 2,000 mph? Or 500 mph? Because as we will see when we get to the Orbital Mechanics part of this book, how fast you are going (or not) determines exactly where you are, and will will stay stay (or not) in space. space. Remem Remember ber what I said said earlie earlier, r, or even better, better, let’s look at Newton’s first law of motion:

When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force .

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One of the trickier words in there is ”velocity”. We tend to think of velocity as ”speed”, but velocity is in reality a ”vector” quantity that represents both speed and direction. We might apply a force to an object, like a spacecraft, craft, that doesn’t modify it’s speed, but modifies it’s direction, direction, therefore therefore we ARE modifying it’s velocity. But your your questi question on still is: ”I’m ”I’m not firing my engines, engines, I’m out in space, space, so there’s no ’external force’ acting upon my ship, so who cares?” That’s where you are wrong. There ARE external forces acting on your ship. Dozens. Dozens. . . hun hundreds dreds.. . . thousands thousands of of externa externall forces forces acting acting on your your ship ship ALL THE TIME. Some to a great extent, some to a lesser extent. Every single body, from the Sun and Jupiter, to the smallest of the asteroids, are all exerting a gravitational force on your ship. Even stars light-years away are exerting, however minute, gravitational forces on your ship! Think about it, it is gravity that maintains the solar system in it’s current configuration, the same way that it is gravity that maintains the Milky Way galaxy in it’s current configuration! All those teeny, tiny little gravitational forces combine to affect your ship, and every other body in the universe. In most cases, we can ”ignore” a lot of these forces, because of how small they they are. are. Typic Typicall ally y, you you are under under the influence influence of a ”main” ”main” body, body, which which exerts exerts a significan significantt portion of the forces forces being applied applied to your your ship. In real life we can’t ignore ALL of the forces except the ”main” one, but because of limitations in the capability of your computer to process these hugely complex calculations, in Kerbal Space Program, only ONE body ever exerts force on your ship at a time. But back back to prograde/retr prograde/retrograd ograde. e. . . Knowing which direction you are moving (prograde) is EXTREMELY important, because knowing that one direction, you can figure out all of the other directions that you will need to know to perform any maneuver.

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2.3.7 2.3.7

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RCS RCS - Reacti Reaction on Contro Controll Syste System m

Now that we understand what attitude of the vehicle means, let’s see what we use to adjust attitude. There are two different systems to adjust attitude. The first of these systems is the Reaction Control System. Most liquid fueled engines, in real life, have very limited duty-cycles (how many times they can be ”fired” without requiring a rebuild/refurbishing). For example, the space shuttle main engines, the 3 big ones on the back of the shuttle, shuttle, are refurbishe refurbished d after every flight. flight. They light light up, once, during launc launch, h, and burn un until til their fuel is exhaus exhausted ted.. They They then then retur return n to Earth Earth with the shuttle and are refurbished before being fired again. The shuttle’s OMS (Orbital Maneuvering System) engines, on the other hand, are built to be fired multiple times between refurbishings. An interesting scene to watch, in the movie Apollo 13 , is the scene where the astronauts are tasked with firing the lunar module’s engine for a second time for a course correction. The representative, on screen, of the manufacturer of the engine (Grumman, I think) makes a comment along the lines of ”it wasn’t built to do this!” and the relief, after the successful firing is clearly clearly visible on his face! face! This is exactly because the engine was was designed to fire during the landing, and burn continuously until they reached the surface of the moon and stay behind when the ascent engine was used to return to orbit. It was never designed to be fired more than once. RCS thrusters, on the other hand are designed to be fired hundreds (if not thousands) thousands) of times, before needing to be rebuilt rebuilt or refurbish refurbished. ed. They provide very small amounts of thrust, compared to the SSME or even the OMS engines, but are more than sufficient to provide the necessary thrust for various arious types of maneuvers. maneuvers. These These maneuve maneuvers rs include, but are not limited limited to: • attitude • station

control during re-entry

keeping (small maneuvers performed by orbiting craft to maintain its position in space since most orbits degrade slightly over long periods of time)

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• docking

maneuvers, that require multiple, very small, adjustments to complete

• orientation,

pointing the vehicle in a specific direction

deorbitin ting, g, • deorbi

in extre extreme me situat situation ions, s, if the craft has lost its abilit ability y to deorbit due to a malfunction of the OMS engines or equivalent

In KSP, the RCS thrusters require a specific type of fuel, monopropellant, that you must provide for in your craft design. There There are also also two two differe different nt types types of RCS RCS thrust thrusters ers in game: game: the RCS block, which is a multi-directional thruster that can provide comprehensive maneuvering capability to a craft; and the Linear RCS thruster, which provides thrust in a single direction. The placement of the RCS thrusters on your vehicle is of paramount importance importance if you intend intend to do precise maneuver maneuverss such as docking. docking. Also, if your craft is very large, multiple banks of RCS thrusters might be necessary, otherwise the craft will be ”sluggish” to respond to your maneuvers (which may may be b e fine if you are the patient patient type). type). In the future future I will will go into more detail regarding RCS positioning and usage within the game.

2.3.8 2.3.8

SAS - Stab Stabili ilitty Augme Augmen ntation tation Syst System em

The actual definition of what is an SAS system is a system that uses devices to STABI STABILIZ LIZE E the flight flight of a vehic vehicle. le. The termin terminolo ology gy in Kerbal Kerbal Space Space Program gets confusing when they talk about capsules, cockpits and probes havin havingg SAS Torq Torque. ue. The SAS parts in Kerbal Kerbal Space Space Progra Program m do indeed indeed stabilize the vehicle, but the torque provided by the capsules/probes is NOT SAS torque. torque. The torque torque generate generated d by the capsul capsules/ es/pro probes bes is more more aptly aptly described as CMG (Control Moment Gyroscope) torque. SAS (Inline Advanced Stabilizer, Inline Reaction Wheel and Advanced SAS) can be used on your vehicles to reduce the vehicle’s tendency to ”wander” der” during during flight. flight. Most Most rocke rockets ts will have have some tendency tendency to ”pu ”pull” ll” to one

2.4. ORBITAL ORBITAL MECHANICS MECHANICS - THE ”MATHY” ”MATHY” PAR PART T

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side, or to rotate along it’s axis, etc., unless it is perfectly perfectly symmetrica symmetrical. l. Once atmospheric drag is implemented in the game in a proper fashion, this tendency will most likely increase since, even the positioning of a part, such as a strut, will affect how the vehicle reacts to the atmosphere. The dampening effect of an SAS unit can be increased by placing multiple units on your vehicles. Placement of the SAS units will determine how effective they are in dampening ening any any move movemen ment. t. An example example of this this wo would uld be a short, short, wide vehicle vehicle,, where a significant amount of mass is ”around” the center of mass, and not lined lined up with with the center center of thrust thrust (i.e. (i.e. asparag asparagus us staging). staging). If you were were to place place a single single SAS unit along along the center center of thrust thrust (i.e. (i.e. on the nose of the capsule), it would not be able to, efficiently, counter movement imparted by the mass ”outside” ”outside” of the center center of thrust. It will work, work, just not as well. well. A solution in a case like this would be to place additional SAS units, in our asparagus staging case, on top of each stack in the asparagus ”bunch”.

2.4 2.4 2.4. 2.4.1 1

Orbi Or bita tall Mec Mecha hani nics cs - The The ”Ma ”Math thy” y” part part What What is an Or Orbi bit? t?

An orbit is the ”gravitationally curved path of an object around a point in space”. This means that you are constantly constantly falling falling toward toward that poin p ointt in space, but you never reach it because your horizontal velocity pushes you away as you are falling. An example example:: a spacec spacecraf raftt in orbit orbit around around the Earth. Earth. The craft craft is conconstantly falling, however it is moving VERY fast horizontally, so as it falls it ”misses” the Earth, passing beyond the horizon and continues continues falling. falling. It is because of this ”falling” that astronauts astronauts experience experience weight weightlessn lessness. ess. They are not weightless, but in relation to the vehicle that they are in, they feel weightless. They are, in reality, free falling around the planet.

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When I say VERY fast above, I mean VERY FAST! Orbital velocity for Earth, in a low Earth orbit (200 - 2,000 km altitude) is somewhere between 15,400 and 17,400 mph! But what we are going to discuss here are some components of an orbit so you can understand the terminology that you will see in game, on the wiki, in the forums and other places where Kerbal Space Program is discussed.

Apsides An apsis (plural: apsides) is the point of greatest or least distance of a body from one of the foci of an elliptical orbit. In Kerbal Space Program, we are acquaint acquainted ed with two two of the apsides: periapsis periapsis and apoapsis. The referenc referencee focus, in our situation, is always the body that we are orbiting.

2.4. 2.4.2 2

Peria eriaps psis is

The periapsis of your orbit is the point in the orbit at which you will be at the least distance distance from the b ody you are orbiting. It is your your closest approach approach to the body being orbited. When we discuss orbital maneuvers, you will see why it is important to know know where this point p oint of your orbit is located. located. Certain Certain orbital maneuvers maneuvers work especially well when performed at specific points in your orbit. Another important use for the periapsis is that, since it is the lowest point in your orbit, you can tell whether your orbit will degrade due to atmospheric effects. If at the lowest point in your orbit you are still above the atmosphere of the body you are orbiting (for Kerbin: 70km), then you know that your orbit is ”stable” since you will not encounter any atmospheric effects at any point in your orbit. You could, theoretical theoretically ly,, leave leave your craft in that orbit, indefinitely, and it would never fall back to the body it is orbiting. ∼

Obviously, the previous paragraph only applies to bodies that have atmospheres. spheres. But even the bodies bo dies that don’t have atmosphere atmospheress have have a minimum minimum


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periaps periapsis is of which which you should should be mindfu mindful. l. For example, example, on the Mun the highest mountain peak is 3,340 meters; on Minmus, 5,725 meters; and on Gilly, 6,400 meters. If you are establishing an orbit around any body, make sure you verify the highest elevation of that planet/moon, unless you want to plow into the face of a mountain.

All elevations, including the periapsis and apoapsis, in game are expressed in relation to sea level of the reference body. According to Kepler’s Second Law of Planetary Motion:

”A line joining a planet and the Sun sweeps out equal areas during equal intervals of time”

If we substitute ”planet” with ”vessel” and ”Sun” with ”orbited body”, the law still applies, since physical laws are not exclusive to stars and planets. We now have:

”A line joining a vessel and the orbited body sweeps out equal areas during equal intervals of time”

What this implies is that the vessel’s velocity is higher when it is closer to the orbited body, hence lower when it is farther away. Since the periapsis is the closest the vessel can come to the orbited body (in a given orbit), it is also the point in the orbit where the vessel has it’s highest velocity. In Kerbal Space Program, the periapsis of your orbit is indicated, while in map view view,, by a litt little le blue blue mark marker er with with a ”P ”Pe” e” inside inside of it. it. Belo Below w is a picture of what that looks like:

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If you hold your mouse over the ”Pe” marker, it will show you the altitude of your periapsis:

Additionally, if you click on the little marker, it will stay showing the periapsis altitude even if you move your mouse elsewhere. It is kind of tricky to click on the marker and not on the orbit at the same time, because when you click on the orbit, you get the popup asking you if you want to ”Add Maneuver”.


2.4. 2.4.3 3

39

Apoa Apoaps psis is

Similar to periapsis, above, the apoapsis defines the point, in your orbit, where your vessel is at the greatest distance from the body begin orbited. Also, as discussed about the periapsis, it is important to know where, on your orbit, your apoapsis is located, because there are particular orbital maneuvers that work especially well, when executed at this point. According to Kepler’s Second Law of Planetary Motion, the apoapsis is the point, in your orbit, where your vessel has the lowest velocity. Just like the periapsis, the apoapsis is indicated, in map view, by a little blue marker with ”Ap” inside:

You can mouse over the marker like you can with the periapsis to see the altitude:

40


And you can click on it, to keep the apoapsis display showing regardless of whether you move the mouse or not. Another Another detail, that I didn’t mention mention in the periapsis explanation explanation above, above, is that below both of the markers, when they show you the altitude, they also show you how much time until you reach the marker. marker. This is important important because sometimes you need to plan a maneuver at exactly that point in the orbit. This countdown tells you how long you have until you reach that marker, so make sure to create the maneuver and leave sufficient time for ship positioning and burn time before you actually hit the marker.

2.4. 2.4.4 4

Semi Semimajo majorr Axis Axis

The longest diameter, of an ellipse (and remember that orbits are, typically, elliptical; a perfectly circular orbit is, for our purposes, considered an ellipse with eccentricity of 0), is called the major axis. The shorter diameter is, as you would would expect, the minor axis (just for completeness completeness sake). sake). The sum of your periapsis distance and your apoapsis distance is the major axis for your orbit. The semimajor axis is half of that. If you are in an orbit around Kerbin, and you have a periapsis of 281,969 meters and an apoapsis of 2,438,568 meters, the semimajor axis for your orbit is 1,960,268 meters


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(281, (281,969+600, 969+600,000)+(2, 000)+(2,438, 438,568+600, 568+600,000) 2 (The 600,000 in the equation above is the radius of the planet Kerbin. In calculating the semimajor axis, we count the distance to the center of the body being orbited. Since periapsis and apoapsis are both given as an altitude from sea level, we need to add the radius of the planet for our calculations.) The closer your orbit is to a perfect circle, the closer the semimajor axis will be to the radius of your orbit (in a perfect circle, the semimajor axis IS the radius). The semimajor axis is important to determine the orbital period of your orbit (how long it takes for your vessel to complete one orbit). The formula is:

   a3  T = 2π µ where:

•

a = the length of the semimajor axis of the orbit (in meters)

•

µ = the standard gravitational parameter of the body you are orbiting

When When perform performing ing the calcul calculati ation, on, if you you are so inclin inclined, ed, remem remember ber to use meters meters and not kilome kilometer terss for the semimajor semimajor axis. axis. The gravit gravitati ationa onall parameter for the various bodies in the Kerbol System can be found in the Kerbal Space Program Wiki. In the description of each body in the system, you can find the gravitational parameter listed as shown in the screenshot below:

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In our example above, the orbit with a semimajor axis of 1,960,268 meters (around Kerbin in this example), the orbital period would be: 9,176 seconds (a little over 2 12 hours) An impor importa tant nt thin thingg to un unde ders rsta tand nd from from this this is that that any any orbi orbits ts that that hav have the the same same semimajo semimajorr axis axis,, hav have the the same same orbita orbitall period period.. In our our exexample we used a semimajor axis of 1,960,268 meters (Pe=281,969 meters, Ap=2,438,568 meters), but any orbit that results in a semimajor axis of 1,960,268 meters (i.e. Pe=760,485 meters, Ap=760,051 meters) will have the same orbital period of 2 12 hours. ∼

Below is a picture of exactly the two orbits described above:


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The blue orbit is almost perfectly circular, with a periapsis of 760,051 meters and an apoapsis of 760,485 meters. The gray orbit has a periapsis of 281,969 meters and an apoapsis of 2,438,568 meters and is visibly elliptical. Both of these ships take the exact same time to complete one full orbit: the 2 12 hours I calculated above.

∼

2.4.5 2.4.5

Eccen Eccentri tricit city y

Eccentricity of an orbit describes how elliptic an orbit is, compared to a perfect circle. A perfectly circular orbit is an orbit where the vehicle is at a constant reference altitude, in every point of its orbit. Perfectly circular orbits are uncommon. Most orbits are, at least, slightly elliptical in nature.

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In Kerbal Space Program, Kerbin, and both of its moons, have perfectly circular orbits (the former around the Sun, the latter around Kerbin itself). Duna, on the other hand has an orbital eccentric eccentricity ity of 0.05. This indicates indicates that its orbit is slightly slightly elliptical. elliptical. Eeloo has an eccentr eccentricit icity y of 0.26, which means its orbit is much more elliptical than Duna’s. If you use the map mode in Kerbal Space Program and zoom WAY out, you will see how the shapes of the orbits of the different planets vary.

In real life, the eccentricity varies from 0.00677 (for Venus) on the low end, to 0.20563 (for Mercury) on the high end (for planets, not going into the realm of dwarf planets, comets, asteroids, etc.).

In the last picture shown in ”Semimajor Axis” above, I show two orbits. The blue one is an (almost) perfect circle, therefore it has an eccentricity of 0. The grey orbit is visibly elliptical (what us common folk call an oval) and has an eccentricity of 0.55.

2.4. 2.4.6 6

Incl In clin inat atio ion n

Inclin Inclinati ation on descri describes bes how how inclin inclined ed an orbit orbit is. To have have an inclin inclinati ation on (an angl anglee in degr degree ees) s),, you need need some some type of refe refere renc ncee poin point. In the the case case of orbital inclinations, we use what is called the ecliptic plane.

Draw the Sun on a sheet of paper, then draw the Earth’s orbit around the Sun. That gives gives you a roughly circular circular orbit. orbit. Now take take that page and look at it sideways, that is the ecliptic plane. So if another planet in the system has an inclination of 60 degrees (very unusual, but useful for our understanding), that means that if you were to draw its orbit on another sheet of paper, then you would combine the two sheets at an angle of 60 degrees.


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Most inclinations are given with relation to a specific body. In our solar system, Earth is the reference body, therefore Earth’s orbit has an inclination of zero degrees in relation to the ecliptic plane (since Earth’s orbit DEFINES the ecliptic plane, it couldn’t be any other way).

The planets of Earth’s solar system, do not all orbit on the same plane, they have have various different different inclinations inclinations.. The same is true of Kerbin’s Kerbin’s solar system system.. In Kerbin Kerbin’s ’s system system,, the planet planet that that has the closes closestt inclin inclinati ation on to Kerbin’s orbit is Duna, at 0.06 degrees.

Inclination is important because, when you are planning encounters, if the target is on a different plane, then you have to correct for the inclination of the target, otherwise you will pass the target’s orbit with the target ”above” or ”below” you.

This is a picture, picture, from in game, of two vessels vessels orbiting orbiting Kerbin. Both of these vessels are orbiting at an altitude of 100,000 meters:

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The orbit in blue is an equatorial orbit (it has an inclination of 0 °). The other vessel (the grey orbit) is NOT in an equatorial orbit; it’s in an orbit with an inclination of 25°. But what does that mean exactly? It helps to visualize the inclination by looking at the equatorial orbit on it’s edge:


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When looking at the equatorial orbit on its edge, it shows as a straight line. As an extra bonus, this shot also shows the ecliptic plane. As you can see, the other vessel’s orbit, when seen edge on, creates an angle between itself itself and the ecliptic ecliptic plane. plane. Tha Thatt angle angle is 25°, and that is why we say the orbit has an inclination inclination of 25°. In our example above, above, we happen to also have a vessel whose orbit is aligned with the ecliptic plane, but it’s the ecliptic plane reference reference that defines the inclination inclination angle.

2.4. 2.4.7 7

LAN LAN - Longi Longitu tude de of Asce Ascend ndin ing g Node Node

When an orbit is inclined to the ecliptic plane (has an inclination different than 0°), there will be two points, in that orbit, where the orbit crosses the ecliptic plane. At one of those points it will be below the ecliptic plane and will be crossing the plane to above the ecliptic plane. It will be ”ascending”. So that point will be the ascending node, the other point (where it’s crossing the ecliptic from above to below), is the descending node. So what’s this business with the longitude? The orbit orbit will will cross cross the eclip ecliptic tic plane plane at a specific specific point. point. Imagin Imaginee that that you were looking out from the ship at this point, and looking straight down at the planet you are orbiting. orbiting. You would be looking at a specific point on the planet (let’s say, in the case of the Earth, you happened to be looking down dow n at Tokyo) Tokyo).. Tokyo’s okyo’s longitude is approximate approximately ly 140 ° E. So the LAN (longitude of ascending node) would be 140 °. What this defines is the location of the p eriapsis eriapsis and apoapsis of the orbit in relation to the prime meridian (in our case, 140 ° is relative to the prime meridian of the Earth). The picture below shows an elliptical orbit (the same one from our previous topics), with an LAN of 0°:

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Notice Notice how the periapsis is on the dark side of Kerbin. The same orbit, below, with an LAN of 180 °:


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Notice Notice how, now, the periapsis is on the light side of Kerbin. The orbit is ”rotated” 180° in relation to the orbit that had an LAN of 0 °. All the other parameters of the orbit remain the same: periapsis, apoapsis, semimajor axis, eccentricity eccentricity,, inclination, etc. With an orbit that is elliptical, elliptical, we have have two main points: the periapsis and the apoapsis. The LAN defines, indirectly, where those two points are in the orbit, in relation to a longitude longitude system defined defined for the body it is orbiting. orbiting. Now you might say, ”but Mars (or Duna, for that matter) doesn’t have any ’defined’ longitude system!”. Well, you’re right, kinda. We, humans, self-centered creatures that we are, defined OUR longitude system system in relati relation on to the prime prime meridi meridian. an. Over Over the millen millennia nia,, the prime prime meridian has varied in location (the place we call longitude 0 °), until finally, in 1884, we as a species species,, decide decided d we needed needed one standa standard. rd. We electe elected d the Greenwich Meridian to be THE Prime Meridian and it has been ever since. Even so, that is not the prime meridian that we use when defining the LAN of orbits. The prime meridian for orbital parameters is called the origin of longitude. For Earth-based LANs (and any heliocentric orbits) we use the First Point of Aries. The First Point of Aries has been the origin of longitude for a very long time. It is still used as the origin even even though, due to the precession precession of the equinoxes, the point is no longer in the constellation of Aries. For bodies outside of the Earth solar system, another prime meridian is determined by a method WAY too complicated to explain here, and angles are measured from that meridian. For our purposes, the LAN has a reference meridian, in the Kerbol system, that is used to calculate the LAN. For orbits that have an inclination of 0 °, the orbit never actually crosses the reference plane (it is not inclined in reference to that plane, hence the inclination of 0°), it is established that the LAN is also placed at 0 ° longitude.

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2.4.8 2.4.8


Argum Argumen entt of Periaps eriapsis is ( ω )

The argument of periapsis, typically symbolized by ”ω ” ω”, is the angle between the longitude longitude of the ascending node and the periapsis periapsis of the orbit. Adding Adding the argument of periapsis to the longitude of the ascending node gives us another parameter: the longitude of periapsis. However, in many circles the terms ”longitude of periapsis” and ”longitude of periastron” are often used as synonyms to ”argument of periapsis”. So it is a parameter, in the strict sense, but probably nothing that we need to worry about in the game.

2.4. 2.4.9 9

Mean Mean Anom Anomal aly y

The mean anomaly of an orbit is a parameter relating position and time for a body in a Kepler orbit. Kepler’s law stipulates that the line connecting the orbiting body to the focus of its orbit sweeps equal areas in equal times during its orbit. The mean anomaly can vary from 0 to 2π 2 π radians. But it is not an angle. It is proportional to the area swept, by the line connecting the orbiting body and the focus of the orbit, since the last periapsis. It is kind of an indicator as to how far, past the periapsis, the orbiting body is in its journey around the orbit. Most of the parameters that we have seen up until this point have been parame parameter terss that that descri describe be the orbit orbit as a who whole: le: how how high high it is at differen differentt points (periapsis and apoapsis), how inclined it is in relation to the ecliptic plane (the inclination), how oval or round it is (the eccentricity), where the orbit crosses the plane when it is inclined (the longitude of ascending node) and where the periapsis is in relation to the LAN (the argument of periapsis). The one thing thing that that we have have not describe described d un until til now is: Where Where is the orbiting body, on this elliptic orbit that we so painstakingly defined, right now? That’s what the mean anomaly does. This This conclu concludes des the sectio section n about about orbita orbitall parame paramete ters. rs. Below Below is a graph graph that illustrates SOME of the concepts explained so far:


2.4.10 2.4.10

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Orbita Orb itall Stabi Stabilit lity y

I’ve mentioned ”stable” orbits a couple of times so far. But what is a stable orbit? A stable orbit is an orbit that will not degrade over long(ish) periods of time. In real life, a stable orbit is very hard to achieve. There are just too many factors that play into the stability of an orbit for it to be considered 100% stable. stable. The International Space Station (ISS), with an orbital periapsis of 330 km, is still subjected to drag from Earth’s upper atmosphere. atmosphere. This drag causes the station to slowly lose altitude, over time, which makes it necessary to

52


fire engines engines on the station to correct it’s altitude. altitude. But there are other factors factors that contribute to the lack of orbital stability for any body orbiting another. All All of the the bodies bodies in the the Sola Solarr Syst System em exer exertt some some influ influen ence ce,, how however ever minute minute,, on every every other other body. body. This This means means that even even if the ISS wa wass comcompletely free of the atmosphere, the gravitational pull of the Moon, the Sun, Jupiter, and even tiny little Mercury are all influencing it’s orbit. By far, the Earth, being the body that is closest to the ISS AND the body around which the ISS revolves, has the greatest influence on the ISS’s orbit. But it’s orbit will change, very slightly, over long periods of time, due to these other influences. But enough about real-life, it’s depressing. In Kerbal Space Program, things aren’t quite like that. This whole business of calculating all the little, teeny tiny influences of multiple bodies upon each other is what is known, in the astrophysics community, as the n-body proble problem. m. There There is no exact exact solutio solution n to the n-body n-body problem problem for n ¿ 2. For any system, that needs to be analyzed, that contains more than 2 bodies, the best we can do is an approximation, and even that takes A LOT of work. Much more than our measly little desktop computers are capable of in any realistic timeframe that would make the game still playable. So, we are limited, by the physics engine used in the game, to 2 bodies. So if a ship is orbiting Kerbin, Kerbin is one body and the ship is the other. The game’s physics engine doesn’t take into consideration any other bodies within within the system system that might might be influen influencin cingg the ship’s ship’s orbit. orbit. This This makes makes orbits orbits that we establish, establish, in game, more stable than they would be otherwise. otherwise. So in game we don’t have to worry about all the other bodies in the system influencing our vessels’ orbits. This howev however, er, has some drawbac drawbacks. ks. To be able to have transfers transfers from one body (i.e. (i.e. Kerbin Kerbin)) to anothe anotherr body (i.e. (i.e. the Mun), Mun), at some point the system has to stop considering Kerbin our first body and switch over to the Mun (our ship is the second body in both cases). This is resolved by what is called Spheres of Influence (usually abbreviated as SOI or SoI). Kerbin has a specific SOI that extends from Kerbin’s surface to a specific height. Every


53

other body in the system, system, similarly, similarly, have have their own SOIs defined. Once your vessel leaves Kerbin’s SOI it is shifted to another SOI. If your ship is not near enough to another body, to be within that body’s SOI, then the SOI of Kerbol (the game’s ”Sun”) is used. Below is a screenshot of a typical Mun transfer:

In this picture, the blue orbit is your orbit, within Kerbin’s SOI, the little circle at the point where the blue transitions to the yellowish line is what is called a ”Mun encounter”. Once we cross that point in the orbit, we are no longer within Kerbin’s SOI, we are then in the Mun’s SOI. The yellow orbit, further along, transitions to the purple orbit, the little circle circle on the threshold threshold identifies identifies it as ”Mun Escape”. Escape”. This means that left to

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its own devices, the ship will transition into the Mun’s SOI and continue on until until it leaves leaves the Mun’s SOI and transitions transitions back, in this particular particular case, to Kerbin’s SOI. If I let it go even further along this trajectory, it exits Kerbin’s SOI and transitions to Kerbol’s (the Sun’s) SOI and establishes itself in an orbit very similar to Kerbin’s own orbit around the Sun.

These spheres of influence are what allow the game’s physics engine to resolve resolve the 2 body problem. problem. Any given given vessel is only, only, ever, ever, in one sphere of influence at any given time.

But the 2 body ph physi ysics cs limitati limitation on also causes causes a proble problem m with. with. . .

2.4.11 2.4.11

Lagran Lagrange ge Points oints

Lagrange points are, in astrophysics, defined points, near two bodies, where a 3rd body (and herein lies the problem) can maintain a consistent position. The calculations calculations of these points requires some intense intense mathematics mathematics that the game’s physics engine is not capable of executing within a timeframe that would make the game playable.

Essentially, a body can position itself at one of these Lagrange points (there are five) and remain in a constant position, in relation to the other two bodies.

This graph indicates the position of the Lagrange points in the Earth-Sun system:


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At L1, the body is stable. The pull from the Sun’s gravity, and the pull from Earth’s gravity, ”drag” the body around the Sun in the same exact amount of time as the Earth takes to orbit the Sun (which is odd, as we’ll see in a bit). bit). L1 is the most most ”intui ”intuitiv tive” e” of the Lagran Lagrange ge points: points: it makes makes ”sense”; the body is being ”wrestled” by the other two bodies’ gravitational forces, therefore doesn’t quite react as it should. The other four Lagrange point are less ”intuitive”, but they exist nonetheless. less. An Any y objec ob jectt placed placed at those points, points, will remain remain in that exact exact same, same, relative spot (not so much a spot, in the case of L4 and L5, as an area). But why ”should” they react any differently?

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2.4.12 2.4.12


Altitu Altitude de vs. Veloc Velocit ity y

In any orbit, the semimajor axis (so indirectly, the periapsis and the apoapsis) defines the orbital period. An orbit with a semimajor axis of X has an orbital orbital period smaller smaller than an orbit with a semimajor axis of 2X. I’m not going to go into the mathematics and give you numbers, numbers, just accept accept that it is true. true. Crunch Crunch the numbers numbers if you don’t believe me. If I am orbiting Kerbin at 100 km, I am moving faster than another ship that is orbiting Kerbin at 200 km. If the ship at 200 km takes X amount of time to complete one full orbit, my ship will complete one full orbit in some fraction of X amount of time. So for every orbit that the 200 km ship makes I make make more more than than one orbit at 100 km. Effecti Effective vely ly,, I’m ”pulling ”pulling ahead” ahead” of the other ship. If I were to raise my orbit to 300 km, then I would be the one moving slower than the one at 200 km and it would pull ahead of me (or catch up, if it were already behind). The further the ships are from the center of mass they are orbiting, the slower they move to maintain that orbit (I’m assuming all circular orbits here, just for sanity’s sake). We discussed the same concept when we were discussing periapsis and eccen eccentri tricit city y. As I app approa roach ch my periaps periapsis is (in a non non-ci -circu rcular lar orbit), orbit), I gain velocity (because I’m closer to the planet). When I reach my periapsis, I am at the closest point I will ”ever” be to the planet, so I am also as fast as I’m going going to get in this this orbit. orbit. As I pass pass the periaps periapsis is and head head towa toward rd the apoapsis (gradually getting further from the planet), my velocity decreases until I reach the apoapsis (furthest point, lowest velocity) and start heading back to the periapsis again to begin the next cycle. This This is wha whatt is ”odd” ”odd” about bodies at Lagrange Lagrange points. points. If a body is at the L1 point, it is, by definition, closer to the Sun than the Earth is, so it should be moving faster than the Earth, pulling ahead of the Earth in its orbit. orbit. Howe Howeve ver, r, it doesn’t. doesn’t. Becaus Becausee of the inter interact action ion between between the Sun’s


57

gravity and the Earth’s gravity, the body moves as fast as the Earth does around the Sun, effectively maintaining its position with relation to both the Sun and the Earth. I think this information might come in handy later, in something called ”rendezvous”, so keep it in a safe place.

2.4. 2.4.13 13

Obert Oberth h Effec Effectt

As we learned in high school physics, objects in motion have kinetic energy. Kinetic energy is best described as the energy the object gained by being accelerated to its current speed. The Oberth Effect, after Austro-Hungarian-born physicist Hermann Oberth, describes how a vehicle employs it’s kinetic energy to generate more mechanical power, resulting in more usable energy, by the application of an impulse, usually provided by a rocket engine, while in close proximity to a gravitational body. If we skip all the math and get right down to the meat of the matter, what this means to us, in Kerbal Space Program, is that: The same amount of thrust expended (∆v (∆ v ), at a given point in our orbit will result in a final velocity (at distance) to be much larger than expected, depending on where in that orbit the burn occurs. In a previous section, I mentioned that knowing where the periapsis and the apoapsis apoapsis of your your orbit orbit is importan important, t, because because certa certain in maneuv maneuvers ers wo work rk especially well when executed at exactly those points. The Oberth maneuver is one of those maneuvers that works especially well when executed at the periapsis of your orbit. Imagine an elliptical orbit around Kerbin, with a periapsis of 100,000 meters and an apoapsis of 300,000 meters.

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Your vehicle is moving its fastest when it is at the periapsis and its slowest when at the apoapsis. Those speeds, for this orbit are: at your periapsis you are moving at 2,383 m/s. your apoapsis, apoapsis, you will will be movin movingg at 1,853 1,853 m/s. At your m/s. m/s.

If we now create a maneuver, at our periapsis, where we expend 100 m/s of ∆v , this is what our maneuver would look like:


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Our apoapsis was raised to 498,000 meters (an increase of 200,000 meters), and our periapsis remains remains the same. The velocitie velocitiess at both points are now: 2,483 m/s 2,483 m/s at the periapsis (what it was + 100 m/s 100 m/s), ), but our velocity at the apoapsis has changed to 1,581 m/s 1,581 m/s..

If we do the maneuver, the same 100 m/s increase, m/s increase, at the apoapsis, the maneuver looks like this:

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In this case, our apoapsis remains the same, and our periapsis increases to 251,00 251,0000 meters meters (an increa increase se of 150,000 150,000 meters) meters).. The velocit velocities ies at both points points are: 1,953 1,953 m/s at the apoapsis (what it was + 100 m/s), m/s), but our velocity at the periapsis is now 2,066 m/s. m/s. In the first case, we increased the semimajor axis of our orbit by 100,000 meters, but in the second case, we only increased it by 75,000 meters. Since the specific orbital energy is dependent on the semimajor axis of your orbit, the specific orbital energy, after the burn, was higher in the first case (burning at periapsis) than in the second, even though the total amount of ∆v ∆ v , and fuel, expended was the same. The reason reason for the gain in energy is as follows: follows: When the rocket rocket expels propellant, that propellant is expelled at a specific velocity. When compared with the velocity of the vehicle that is expelling the propellant, part of the energy expelled is lost in the mass that is expelled but part of it is kept by the vehicle. Example: If the velocity of your vehicle is 1,000 m/s, m/s, and propellant 1 is expelled at 2,000 m/s, of the energy of m/s, then your vehicle might retain 10 the propellant, the remaining 90% of the energy is lost with the propellant


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(not (not lost, lost, but stays stays with with the propellan propellantt expelle expelled). d). If the velocit velocity y of your vehicle is 5,000 m/s 5,000 m/s and propellant is expelled at the same 2,000 m/s, m/s , your vehicle might retain 40% of the energy of the propellant, only leaving the propellant propellant 60% of the original original energy energy.. The bottom line is that it is more efficient, energy-wise, for you to do burns of this type around your periapsis than it is anywhere else in your orbit.

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Chapter 3 The Navball

This is your Kerbal Space Program Navball:

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CHAPTE CHAPTER R 3. THE NAVBA NAVBALL LL

Right off the bat, couple of things: • If

you want to hide the navball, click on the little black arrow (right above where it says ”Orbit” in the above picture), or press the . (period) key ON THE NUMERIC KEYPAD.

• If

it’s not showing (like the default in map mode), same thing, either click on the little black arrow at the bottom of the screen, or press the (period) key on the numeric numeric keypad keypad.. .

The navball shows you, at different times, certain characteristics of your vehicle that are important: • which

direction your vehicle is pointing;

• which

direction your vehicle is moving;

• which

direction your target is located;

• how

much you have to fire your engines to accomplish a maneuver;

• which • how

direction you should fire your engines for a maneuver;

much throttle you are currently using;

• what

”mode” the navball is in;

• etc.

I’m going to explain each indicator on the navball separately. Where they are related to another indicator I will mention that. The first thing we have to understand about the navball, is that it works in differe different nt modes. In the picture picture above, above, our navball navball is showin showingg ”Orbit ”Orbit:” :” and ”335.6m/s”. This indicates indicates that our orbital orbital velocit velocity y is currentl currently y, 335.6 m/s. m/s. We can click on the word ”Orbit:” and it will change to ”Surface:” and, probably, show a different speed. The speed shown when in ”Surface” mode

3.1. NAVBALL NAVBALL INDICATORS INDICATORS

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is the speed in relation to the surface of the body we are orbiting, launching from or landing on. Additionally, if you have a target selected, and click on ”Surface” on the navball, it will switch to ”Target” and show another speed. The speed shown is the relative velocity between your vehicle and the target (how fast you are moving towards, or away from, your target). So, we basically have three modes that the navball can operate in: we’ll call call these these ”Orbit ”Orbit mode”, mode”, ”Su ”Surfa rface ce mode” mode” and ”T ”Targ arget et mode”, mode”, hopeful hopefully ly,, consistently, throughout the book.

3.1 3.1 3.1. 3.1.1 1

Navba Na vball ll In Indi dica cato tors rs Prog Progra rade de In Orbit mode, the prograde indicator tells you which direction you should point if you want to be facing the exact direction that your vehic vehicle le is movin moving. g. If you you wa want nt to increa increase se your your orbita orbitall veloci velocity ty,, point prograde, in Orbit mode, and thrust in that direction.

In Surface mode, the prograde indicator tells you which direction you should point if you want to be facing the direction that your vehicle is moving relative to the surface of the body you are orbiting/launching/landing. If you want to increase your surface velocity, point toward the prograde marker, in Surface mode, and thrust in that direction. In Target arget mode, mode, the progra prograde de indica indicator tor tells tells you you which which direc directio tion n you you should point if you want to be facing the direction that your vehicle is moving relative to your target. If you want to increase the relative velocity between your vehicle and your target, point toward the prograde marker, in Target mode, and thrust in that direction.

3.1. 3.1.2 2

Retr Retrog ogra rade de

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In Orbit mode, the retrograde indicator tells you which direction you should point if you want to be facing the direction exactly opposite of that which your vehicle is moving. If you want to decrease your orbital velocity, point retrograde, in Orbit mode, and thrust in that direction. In Surface mode, the retrograde indicator tells you which direction you should point if you want to be facing the direction exactly opposite of that which your vehicle is moving relative to the surface of the body you are orbiting/lau orbiting/launc nching/l hing/landing anding.. If you want to decrease decrease your surface surface velocit velocity y, point toward the retrograde marker, in Surface mode, and thrust in that direction. In Target mode, the retrograde indicator tells you which direction you should point if you want to be facing the direction exactly opposite of that which your vehicle is moving relative to your target. If you want to decrease the relative velocity between your vehicle and your target, point toward the retrograde retrograde marker, marker, in Target mode, and thrust thrust in that direction. direction. This maneuver is commonly referred to as canceling or zeroing your speed relative to the target.

3.1.3 3.1.3

Target arget Progr Prograde ade

This indicator is, in my opinion, erroneously called the Target Prograde indicator. indicator. I don’t like like that nomenclatur nomenclaturee becaus b ecausee it alludes alludes to the fact that this indicates indicates the prograde prograde direction direction that your target is moving. That is NOT the case. What this indicates is what vector you have to follow to get to your target. It indicates where your your target target is in relati relation on to your your ship. ship. If you you accele accelerat ratee direct directly ly towa towards rds your target by pointing at this indicator and engaging your engines, it will, indeed, become your target ”prograde” indicator, but not quite. Basically, this is the direction that you want to point your ship if you want to go towards your target. It is only HALF of the puzzle you will need to solve to do a rendezvous with a target. Obviously, this indicator will only show up on your navball if you have a target selected.


3.1.4 3.1.4

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Target arget Retrog Retrograd rade e

This indicator indicator is also, in my opinion, erroneously erroneously called the Target Retrograd Retrogradee indicator. indicator. I don’t like that nomenclature nomenclature because, like it’s brother, it alludes to the fact that this indicates the retrograde direction that your target is moving. That is NOT the case. What this indicates is what vector you would have to follow to move away from your target. Basically, this is opposite the direction that you would point your ship if you wanted to go towards your target. Obviously, this indicator will only show up on your navball if you have a target selected. Note that pro and retro are directions that are 180 ° from each other. Prograde is opposite (180°) from from retrog retrograd rade. e. Target arget prograde prograde is opposit oppositee (180°) from target retrograde.

3.1. 3.1.5 5

Mane Maneuv uver er Node Node This indicator tells you which direction to point your vehicle to execute the maneuver that you have created. You create maneuvers in the map screen and once you have adjusted the maneuver to your liking, this is the indicator that you should follow when executing the burn.

Please note that when you create a maneuver node, this indicator shows up immediately on your navball, but you should only execute the maneuver once the correct time arrives. If you do not currently have a maneuver established, then this indicator does not show up on the navball. navball. If you have multiple multiple maneuvers maneuvers planned, planned, then this indicator is for the ”next” maneuver.

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3.1. 3.1.6 6


Lev Level In Indi dica cato torr

This is the last indicator that shows up inside the navball. It indicates cates where the ”nose” of your vehicle vehicle is pointing. Note that this indica indicator tor does not move. move. As you you chang changee the attitud attitudee of your vehicle, the navball rotates underneath the level indicator to display your current attitude.

3.1.7 3.1.7

Other Other Na Navba vball ll In Indic dicato ators rs

There are a few more items that we need to discuss on the navball and then we will discuss maneuvers. Below the ”artificial horizon” (the blue/brown ”bally” part of your navball), is your heading: ”HDG”. Your heading is indicated in degrees and is counted, clockwise, from whatever is considered ”North” on the navball (indicated by the solid red line going up and down the navball, assuming you are level). On the left side of the navball (between 6:30 and 10 o’clock, if the navba navball ll were were a clock clock face) face) is your your throttle throttle indicato indicator. r. It has a little white arrow indicator that tells you where your throttle is positioned. The very bottom of the scale, your engines are off, the very very top of the scale, your engines are at full thrust. thrust. The scale also has a red area that currently is not used by the game. I’m assuming that this will be used in the future when it is possible to throttle your engines over their rated thrust. On the right side of the navball, similar to the throttle indicator on the left, is the G-force G-force meter. meter. This meter meter indicates indicates how many Gs of force force your craft is undergoing. undergoing. This indicator, indicator, in the real world, is used to assess the stress being imposed upon the vehicle and the occupants.


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Notice that the G force scale starts at -5 Gs and goes all the way wa y up to 15 Gs. The ”dange ”dangerr zone” starts starts at 9 Gs (the (the red area on the dial) and should be avoided whenever possible. G forces must be kept within tolerable levels both for the airframe and for the crew. Excessive G force on the airframe can cause rapid unplanned disassembly and excessive G forces on the crew can cause everything from lightheadedness and loss of consciousness to death. In Kerbal Space Program, G forces are not taken into consideration (yet) in the stock game. I believe there are mods in the community that implement some excessive G force consequences. On the left side of the navball, right above the throttle indicator, is the RCS indicator. This is simply an on/off indicator to tell you whet wh ethe herr RCS is turn turned ed on or not. not. If it is lit up gree green n and and says says ”RCS” ”RCS”,, then then your RCS RCS is on. If it is black black,, RCS RCS is off. To turn RCS on or off, press the r key (default key). On the right side of the navball, right above the G force meter, is the SAS indicator. Like Like the RCS indicator, indicator, it is simply an on/off indicator to tell you whether SAS is turned on or not. If it is lit up white, and says ”SAS”, then your SAS is on. If it is black, SAS is off. To turn SAS on or off, press the t key (default key). These are all of the characteristics of the navball itself. Let’s talk about navigating with the navball.

3.1.8

Using the the Navbal Navballl To To Change Change Your Your Attit Attitude ude

or ”What is all this talk about prograde and retrograde?” First First let’s clarify clarify what attitude attitude is. I’ve I’ve mention mentioned ed it a few times before before so I want to make sure we understand what I mean. The attitude of an aircraft (or a spacecraft) is the orientation of that craft relative to its direction of travel.

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In space (and even in the air), you can turn completely around from your direction of travel and still continue in that direction of travel, rear-first indefinitely (not indefinitely indefinitely in the air, obviously). obviously). You can turn your your vessel up, down, sideways, in any direction that you want and your direction of travel (or speed, for that matter) is not changed changed at all, until until you fire your engines. This is unfamiliar ground for people only exposed to terrestrial modes of transportation and therein lies the problem. In astrodynamics we use the attitude to describe the orientation of the vessel in relation relation to it’s directi direction on of trave travel. l. So if I launc launch h a rocke rockett in a straig straight ht line at the Moon (let’s assume that both the Earth and Moon are stationary objects for this example) and I’m going 1,000 m/s. m/s. If the nose of my rocket rocket is still pointing pointing at the Moon, we say that that the rocke rockett is pointing pointing ”progra ”prograde” de”.. So if I were were to tell tell you ”point prograde”, that means point your rocket in the exact direction that it is moving, in our example, straight at the Moon. If I were to tell you ”point retrograde”, that means point your rocket in the direction exactly opposite of the direction that you are moving (i.e. point the tail of your rocket in the exact direction you are moving), in our example, straight back at the Earth. The main reason why these two directions are important is that in space there are no other reference reference points to which which you can really point. I can’t say stuff like ”turn 15° north-northeast once you pass the mountain range” because ”northnortheast” has no meaning in space, nor are there any mountains up there (unless you count the asteroids). We need some reference reference points to plan maneuvers. maneuvers. Prograde Prograde and retrograde retrograde are two of them. Radial and anti-radial are another two, normal and anti-normal are another two. You’re thinking ”Oh crap! What is that all about?”. Simple. You’re in another another ship, orbiting Earth (or Kerbin, Kerbin, it doesn’t matter), countercounterclockwise (as seen from the North pole), at a constant altitude, let’s say 1,000 km, traveling at a constant speed. Your orbit is (unnaturally) perfectly circular. Your ship is pointin pointingg straigh straightt in the direct direction ion that it is moving. moving. You are standing standing in the cockpit, looking out the ”windshield ”windshield”, ”, straight ahead. Your head is pointed in the same direction as the planet’s North pole, and your feet are pointing in the same direction as the planet’s South pole.


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Where you are looking is prograde.

Right behind your head (180° from prograde) is retrograde.

Straight up, from the top of your head in the direction of the ceiling, is normal.

From the bottom of your feet, straight down (180° from normal), is anti-normal.

Now raise both of your arms straight out from your body (like a ”+”).

Where your left hand is pointing, straight at the center of the planet you are orbiting, is radial (or radial in).

Where your right hand is pointing, away from the center of the planet you are orbiting (180° from radial), is anti-radial or (radial out).

If I now need to give you directions like ”point 30° anti-radial from prograde and 15° normal normal from from progra prograde” de”,, you you know know that, that, assumi assuming ng you you where where pointin pointingg straight at prograde to start, that you have to rotate your ship 30° to the right and 15° up. My entire direction direction system is now based on prograde, prograde, since knowing knowing that, I can derive all the other 5 ”cardinal” points.

Even if your ship is rotated 180° on it’s long axis and you are, from an external observers point of view (your head is now pointing in the direction of the planet’s South pole), standing on the ceiling, you know that normal is ”above your head” only if your left arm is pointing ”radial in”. If you’re upside down like I said, your left arm will be pointing away from the planet (radial out) and your head will be pointing anti-normal, so you know that the directions I just gave you should now be: 30° to the left and 15° down from your frame of reference.

So let’s take a look at the first picture in this article again:

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Right above the ”HDG” indicator at the bottom, you see a little vertical yellow line. line. That’s That’s the very tip of the prograd progradee indica indicator tor.. If your ship’s ship’s attitude attitude were were the one pictured here, and I told you ”turn prograde”, what would you do on your keyboard/joystick to get there? You would press the w key to push push the nose of your vessel vessel (shown (shown by by the fixed level indicator in the middle of the navball) ”down” towards the prograde vector which is ”below” your nose in this picture. You can also think of the w key key as being ”up”, as in the direction direction I want want the navball to ”rotate”. So the level indicator stays put (it never moves), the navball rotates ”up” (the line that divides the blue from the brown in the navball, moves vertically up your screen), bringing the prograde indicator with it, until it is lined up with the nose of my vessel. It depends on how you see things. The ”pushing up/forward means nose down” paradigm comes from aviation (from where most astronauts were recruited) where to push the nose of a plane down, down, you push the control control yoke forward. forward. I’m not here to say whether one interpretation or the other is ”right”, there is no ”right”, it’s


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anti-radial, remember? It’s all a matter of interpretation and whatever works for you is the best. I only explain this here because throughout this book I will say (and have alread already y said, said, above above)) ”up” ”up” and ”down” ”down”.. When When I say say ”up” ”up” I mea mean n press press the s key to move your nose up; when I say ”down” I mean press the w key to move move your your nose down. down. I want want to avoid avoid the confus confusion ion of ”you ”you said down, so I presse pressed d even though though s is below w on the keyboard, keyboard, s is up, w is down. down. s ” even That’s what works for me, so that’s how I use them. If you understand them the opposite, that’s great, it works for you, but then you have to translate what I say into your terminology. Now that we understand the basic ”directions” involved in maneuvering in space our next section will cover maneuver nodes.

3.1. 3.1.9 9

Mane Maneuv uver er Nodes Nodes

To create a maneuver node, you have to switch to map view ( m key). key). If you you now now click anywhere on your orbit (the blue line in map mode), a popup will appear with a button button ”Add Maneuve Maneuver”. r”. If you click on that that button button,, a maneuv maneuver er node is created. created. When When create created, d, the maneuv maneuver er node doesn’t doesn’t do anyth anything ing,, it’s just a placeholder. placeholder. When you start playing playing with the little handles handles (6 of them, attached attached to the maneuver node along the 6 different ”cardinal” directions we just discussed) the maneuver node starts to have meaning. One of the ”golden ”golden rules” of orbital orbital maneuvers maneuvers is this: any change change you make to your orbit, orbit, affe affects cts the opposite opposite side of your your orbit. orbit. Exampl Example: e: If I ”speed ”speed up”, by thrusting thrusting prograde, prograde, at my apoapsis, I raise my periapsis. If I thrust thrust prograde at my periaps periapsis, is, I raise raise my apoapsis apoapsis.. Simila Similarly rly,, if I ”slow ”slow down”, down”, by thrusti thrusting ng retrog retrograd rade, e, at my apoapsi apoapsis, s, I lower lower my periaps periapsis. is. If I thrust thrust retrogr retrograde ade at my periapsis, I lower my apoapsis. So a very common orbital maneuver, that we will discuss in more detail later, is circularization. Typically, when you launch a craft, you’re launching it ”upwards” from the planet. I’m not going to say straight up, because that’s a bad idea, but it is in a generally upwards direction. If you look in map mode, as your launching, you will see a parabola forming. The very top of your parabola, your highest point, is your apoapsis, and should

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have have a little little blue ”Ap” indicat indicator or on it. What What that parabola parabola is showing showing you is that, if you leave your ship on it’s current trajectory, it will, eventually fall back to Kerbin. Kerbin. We have an apoapsis in our trajectory, trajectory, but no periapsis. periapsis. Actually Actually there IS a periapsis, it’s ZERO, so the game doesn’t show it. But it’s there. If I want to get into orbit, I need to make both my apoapsis and my periapsis higher higher than 70,000 meters meters (for (for a Low Low Kerbin Kerbin Orbit). Orbit). Let’s Let’s assume assume my apoapsi apoapsiss is at 80,000 meters already, my engines are turned off and my current altitude is 50,000 meters. meters. I’m essentially essentially ”coasting” ”coasting” towards towards my apoapsis. apoapsis. What do I do to get into orbit? What am I trying to accomplish? Low Kerbin Orbit is a trajectory where both apoapsis and periapsis is above 70,000 meters. meters. Ok. . . chec checkli klist st time: time:

• Apoapsis

above 70,000 meters: check

• Periapsis

above 70,000 meters: not so much

But wait wait a minute, minute, didn’t we just just talk about ”raising ”raising periapsis”? periapsis”? Oh yeah. yeah. . . ”If I ’speed up’, by thrusting prograde, at my apoapsis, I raise my periapsis.” Let’s do that... I line my ship up, pointing prograde. Wait for the apoapsis, and fire my engines. Nothin Nothingg seems seems to happen happen initially initially,, but my orbit’s orbit’s getting getting ”wider ”wider”. ”. No, wait! wait! A periaps periapsis is just showe showed d up on the other side side of the planet. planet. 5,00 5,000 0 meters. meters. . . 10,0 10,000 00 meters meters.. . . 50,0 50,000 00 meters. meters. . . 80, 80,000 000 meters meters!! Quick Quick,, shut down down the engine engine ( x key). My orbit orbit is now now ”circul ”circulari arized zed”” (hopefu (hopefully lly it’s roughly roughly circular circular). ). That’s That’s called called ”winging ”winging it”. Let’s try that in a less stressful, more planned, way. We’re e’re back back at 50,000 meters. meters. Apoapsi Apoapsiss is at 80,0 80,000 00 meters. meters. Engine Enginess are off. We’re coasting towards our apoapsis.


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In map mode. Create a maneuver node AT your apoapsis:

Click on the little blue ”Ap” indicator (notice the little blue dot on the orbit near the apopasis indicator)

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and select ”Add Maneuver”.


This creates a maneuver node

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Now what we did before was to thrust prograde, so we’re going to plan this maneuver in the same fashion. So grab the little prograde marker on the maneuver node (it looks the same as the prograde marker on the navball) and pull it slowly away from the center of the maneuver node. An orange-ish line appears on the map. That’s the new orbit you will have, if you execute the maneuver node. There’s also an orange-ish ”Ap” and ”Pe” indicator that tells you what your apoapsis and periapsis will be in this new orbit. If your periapsis isn’t high enough (or hasn’t shown up at all yet), keep ”stretching” that prograde marker handle. The process here is: adjust maneuver by dragging prograde handle; release mouse; mouse over (orange) periapsis to see height; and keep keep doing doing that until until the periapsis periapsis is high enough. enough. Made Made it too high? Ad just maneuver by dragging retrograde handle; release mouse; mouse over (orange)


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periapsis to see height; and keep doing that until the periapsis is where you want it.

Once you’ve adjusted your maneuver properly, you should have a roughly circular orange-ish orbit around Kerbin with both an apoapsis and periapsis of, roughly, 80,000 meters. meters.

Let’s check out our apoapsis and periapsis for the new orbit:

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Not perfect perfect,, but close close enough enough.. Both Both apoapsi apoapsiss and periaps periapsis is are out of the atmosphere. So let’s switch back out of map mode. Press m again.


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There’s There’s something new here now. Some kind of meter along the right right side of the navball navball that wasn’ wasn’tt there there before. before. That That meter meter tells you how how much much thrust thrust is required to complete the maneuver the way you set it up. So it will say something like ”1128.2 m/s”. Below Below the meter is an estimated estimated burn time, ”Est. Burn”, Burn”, that indicates, indicates, based on the capacity of your engines, how long the computer thinks it will take, at full thrust, to generate that ”1128.2 m/s” worth of thrust, in our case, ”47 s”. Below Below the estimated burn time is another line of text that says: ”Node in T48s” and is counting counting down. What this indicates is that you are 48 seconds away away from reaching the maneuver node you created. Now we have Now have a maneuv maneuver er node all set up the way way we want want it. Let’s Let’s execute execute that maneuver.

3.1.10 3.1.10

Execut Executing ing Maneu Maneuve vers rs

The orbit that you saw in map mode:

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is calculated as if the maneuver were executed in an instant. This means that for your orbit to end up exactly as projected, you would have to change your velocit velocity y by 1,128.s 1,128.s m/s instant instantly ly,, the moment moment you you hit the node. node. Since Since that is physically impossible, because your engines don’t work that way, it is an estimate.

Since it is an estimate, we’re going to do our best to estimate how to execute the maneuver as well.

Remember that any change you make in your orbit, affects the opposite side of your orbit (i.e. burning prograde at apoapsis, raises your periapsis and vice-versa). Therefore we are executing our burn at our apoapsis (to raise our periapsis from zero, in this case). But if my burn is going to take 47 seconds and I start it exactly at the node, per the countdown clock, I will be executing the burn, effectively, AFTER having passed my apoapsis.

A good rule of thumb, to execute a burn, is to ”split” the burn evenly around your your node. So if the burn burn is 47 second seconds, s, cut that that in half, 23.5 seconds, seconds, and start executing executing the burn 23.5 seconds seconds BEFORE hitting the node; and continue burning an additional 23.5 seconds, after the node. That way the ”error” in your maneuver is distributed evenly at both sides of the node.

This technique does not work very efficiently if your burn time is very long (i.e. more than a minute). This is because the longer the burn, the more ”off” the prediction of the resulting orbit is going to be (because the prediction assumes 0 seconds of burn time for the maneuver).

An even better approach is to execute the maneuver in steps. In this particular case, we cannot execute the maneuver maneuver in steps. steps. Because Because this is a circularization circularization maneuver, you don’t have the luxury of executing a smaller maneuver now, and executing another small maneuver on your next orbit. There will be no next orbit unless you circularize your orbit.

An example of a maneuver that can be executed in steps is one where you wish to change your inclination by 90°. Let’s assume that you are in a circular orbit, at 80,000 meters. meters.


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The ∆v ∆v for a 90° inclination inclination change change is enormous. enormous. 3,188 m/s. m/s. The estim estimated ated burn time is 1 minute and 56 seconds. A burn that long will result in your orbit not being even remotely close to the target you set, because the burn will be executed almost 1 minute before the node and last until about 1 minute after the node. In a case case like like this, this, you you would would be better better off execut executing ing a smalle smallerr inclina inclinatio tion n chang change, e, for example, example, 20°; on your your next next orbi orbit, t, exec execut utee anot anothe herr 20° inclination chang change; e; and so on until until you you have have achiev achieved ed the desire desired d orbit. orbit. Please Please note that doing it this way does not make the maneuver ”cheaper” in any way. You will still expend the same 3,188 m/s 3,188 m/s of of ∆v to make the full 90° inclination change, but you will have have more control over over the resulting final orbit by doing it in steps. In fact, the multiple maneuvers might cost you a little more in terms of ∆v ∆v , because of the inevitable errors in piloting. But enough enough about the economics economics of maneuvers. maneuvers. . . To execute any maneuver, your want to adjust the attitude of your vehicle, to point to the maneuver node indicator on the navball.

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Once you are pointing directly at the maneuver node indicator, you should wait until the appropriate time to start your maneuver. The discussion above, on when to execute a maneuver, is simply a suggestion that I follow when executing maneuv maneuvers ers.. You are free to execut executee the maneuve maneuvers rs in the fashion fashion that you you see best. As you fire your engines, you will notice the ∆v ∆ v meter on the right side of the navball start to decrease. Once it reaches ”0”, you should stop your engines. Also note that during the maneuver, you should try to keep your vessel pointed in the right direction, towards the maneuver node indicator. If you go ”off” course slightly, you do not have to worry, because both the maneuver node indicator and the ∆v ∆v meter are recalculated, in real time, as you execut executee the maneuve maneuver. r. The system system does it’s best to mak makee sure sure that, that, when when you you are done executing the maneuver, you end up with an orbit as close as possible to what was projected when you created the maneuver node. A tip for executing maneuvers: As you approach the end of your burn (when the ∆v ∆v meter is almost ”empty”), you might want to throttle down your engines slowly. That way you have more control over the cut off, as close to zero as possible, for your maneuver. maneuver. If you have a very powerful powerful engine, or set of engines, it will eat through the required ∆v ∆v pretty fast, and that will make it harder for your to cut the engines at the appropriate time, most likely ”overshooting” your maneuver. Just Just remem remember ber that the burn time was was calcul calculate ated d at full full thrust thrust,, so if you you throttle back the end of the burn, it is going to take longer, so take that into consideratio consideration n when ”splitting” ”splitting” your burn around the node. Give yourself yourself an extra few seconds of total burn time for a controlled shut down of your engines. Now that Now that we’re we’re ”expert ”experts” s” in maneuv maneuvers ers,, let’s let’s start start discus discussin singg the differe different nt types of maneuvers that are typically executed in game.

Chapter 4 Orbital Maneuvers 4.1 4.1

Gra Gr avit vity Tur urn n

A gravity turn is a maneuver that is used to optimize the trajectory of the vehicle during during launch launch (or landing). landing). It’s It’s mai main n purpose purpose is the utilizat utilization ion of the body’s gravity to assist in steering the vehicle to its desired trajectory. It has two advantages over using solely thrust in controlling the vehicle:

1. We don’t use the thrust to steer the vehicle, vehicle, therefore more thrust is available available to accelerate. 2. During During ascent, ascent, the vehicle vehicle can maintain maintain a low angle of attack (or zero). zero). This minimizes the stress put on the vehicle from aerodynamic forces, allowing for a less robust, therefore lighter vehicle.

Why use a gravity turn?

During launch, the vehicle goes straight up, gaining vertical speed and altitude. Gravity, at this point, is acting directly against the thrust of the vehicle, lowering its vertical vertical acceleration. acceleration. The losses that occur during this phase of the flight flight are known as gravity drag.

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CHAPTER CHAPTER 4.

ORBITAL ORBITAL MANEUVERS MANEUVERS

The sooner the vehicle pitches over its ascent, the sooner the effects of gravity drag drag can be minimiz minimized. ed. The earlier earlier this this pitch pitch over over happens, happens, the better. better. If the vertical velocity of the vehicle is high when the pitch over maneuver is executed, the aerodynamic aerodynamic loads on the vehicle vehicle can be very very high. This is the general general rule, in real life. In Kerbal Space Program, the general rule of thumb is to initiate the pitch over maneuver anywhere between 7,000 meters and 15,000 meters of altitude. In real life, the angle (not the heading, how much we pitch the vehicle over; the heading is entirely up to the desired trajectory, though in most cases in the game we are aiming for an equatorial orbit, therefore the heading is 90°) into which we turn the vehicle, during the pitch over maneuver, varies with the vehicle. An important part of an ideal gravity turn is that the gimbaling of the engines is only used during the initial pitching over maneuver. From that point forward the vehicle’s engines should always be pointing straight down the axis of the rocket. Gravity will slowly turn the rocket further and further towards the horizon as the rocket accelerates accelerates.. By no longer actively actively turning the rocket in one direction or another, we minimize the aerodynamic stress that the rocket incurs as a result of such such maneuvers. maneuvers. The intent intent of a gravity gravity turn is to, by the time the rocket rocket levels off (is flying parallel parallel to the ground), ground), have gained sufficient sufficient altitude altitude and velocity to be in a stable orbit. With vehicles that are launching from a planet with a dense atmosphere, the smaller the angle of the initial pitch over, the better, since our main goal in this scenar scenario io is to get out of the thicke thickerr part part of the atmosph atmosphere ere more quickly quickly.. The faster we get out of the thicker part of the atmosphere, the more we reduce the aerodynamic drag and aerodynamic stress that the vehicle will suffer during launch. Maximum dynamic pressure is another concern during launch. In Kerbal Space Program, Program, as of this writing, it is not yet a concern. concern. Once aerodynamic aerodynamic calculations calculations are included in the KSP universe, it might need to be addressed. Maximum dynamic pressure, sometimes referred to as ”max Q”, is due to the build up of dynamic pressure due to the acceleration against the thicker part of the atmosphere. Again, similar to the turn early or turn late for the gravity turn, it is a tradeoff between gaining more speed while in the lower part of the atmosphere and making the vehicle heavier, since it needs to withstand greater pressure, or a lighter vehicle and gaining less speed while in the lower atmosphere.

4.2. 4.2.

CIRCUL CIRCULARI ARIZIN ZING G YOUR ORBIT ORBIT

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The space space shutt shuttle, le, for exampl example, e, throttl throttles es back back its main engines engines during during the initial phase of the ascent as it approaches max Q to reduce stress on the airframe. Once it passes through the thicker part of the atmosphere, it accelerates again to maximum thrust to gain speed as fast as possible.

4.2 4.2

Circ Circul ulari arizi zing ng your our Or Orbi bitt

4.2. 4.2.1 1

Achi Achiev evin ing g Or Orbi bitt

Achieving orbit, for the first time, is one of the most gratifying experiences that you you will will encoun encounter ter in gam game. e. A lot of beginne beginners rs in the game tend to launc launch h their their rockets rockets straight straight up. Launching Launching a vehicle vehicle straight straight up will not put your rocket rocket in orbit. A lot of times, even going up at all can be a challenge. For our purposes, we will consider an orbit as a trajectory that your vessel follows in such a way that it will never ”fall” back down to the body it is orbiting. If we take Kerbin as an example, for the vessel to not fall back to the planet, we need to satisfy a single condition:

• The

trajectory has to be high enough, at all points, that the vessel is no longer being affected by the atmosphere (which causes drag and makes the vessel lose speed)

The paramete parameters rs of such such an orbit orbit are fairly fairly simple simple:: At no point, point, in our orbit, orbit, should our vessel go below 70,000 meters. ∼

Orbiting is not so much about vertical velocity, as it is about horizontal velocity. For an object to ”orbit” another object, it needs to have a horizontal velocity, in relation to the object it wishes to orbit, high enough that it will constantly ”miss” the object as it continuously ”falls” towards it. What that velocity needs to be varies according to the altitude of the orbit: the closer the orbiting object is to the body it is orbiting, the higher the required velocity velocity to maintain maintain that orbit. The previous statement statement assumes assumes that the physical physical chara characte cteris ristic ticss of the two bodies are the same same in all cases. cases. Also Also note that that the

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CHAPTER CHAPTER 4.


orbital velocities listed in the table below are velocities assumed to be parallel to the surfac surfacee of the body being being orbite orbited. d. It is entir entirely ely possible possible to achie achieve ve the velocities stated below, but if that velocity is not in the right direction, it will not result in an orbit. A few examples: Altitu Altitude de 70,000 m 100,000 m Orbital Velocity around Kerbin 200,000 m 400,000 m 1,000,000 m

Orbital Orbital Velocit elocity y 2,296 m/s 2,246 m/s 2,100 m/s 1,879 m/s 1,486 m/s

What this table shows us is that to establish an orbit at, for example, 100,000 meters, we need to be moving, horizontally, at 2,246 m/s. m/s. While it is possible to go straight up until we reach 100,000 meters and then turn and accelerate to the necessary 2,246 m/s, m/s, it is not, from the standpoint of energy expended, efficient to do that. that. This This is why why we typically typically use a ”gravity ”gravity turn” turn” during during launch. launch. The purpose of the gravity turn is to impart as much horizontal velocity during our launch phase as we possibly can. That leaves us less velocity that we need to add, once we get ”out into space”, to establish the orbit. A typical launch, whose purpose is to establish an orbit, will involve getting our apoapsis above 70,000 meters and imparting some degree of horizontal velocity (by means of a gravity gravity turn), turn), before reaching reaching the apoapsis. apoapsis. An important important thing to remember is that when you are launching a rocket, it does not behave like a common terrestrial vehicle, you might be at 50,000 meters of altitude, but if your apoapsis is already at 70,000 meters, or more, you can shut down your engines and coast the rest of the way way. Once we reach reach the apoapsis, we have to execute a maneuv maneuver er that is called. called. . .

4.2.2 4.2.2

Circul Circulari arizat zation ion

The circularization burn is the maneuver where we take our parabolic trajectory and transform it into an actual (somewhat) circular orbit. In a typical launch, we might reach our apoapsis with an orbital velocity of 2,030 m/s. m/s. Since Since orbit orbital al velocity velocity (at 100,000 meters) meters) is 2,246 m/s 2,246 m/s,, that means that we need to add another 220 m/s 220 m/s of velocity to establish an orbit. ∼

∼

4.2. 4.2.


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There are a couple of different schools of thought on how the circularization burn is supposed to be done:

• Point

prograde at your apoapsis and burn

• Point

at the horizon at your apoapsis and burn

Technically speaking, these two methods are essentially the same. The difference lies in interpretation of ”prograde” and ”horizon”. In a perfect system, where I could impart changes in velocity instantaneously, both of these scenarios would be identical. identical. Howeve However, r, that is not the case. I cannot instantly instantly increase my velocity velocity by 220 m/s 220 m/s..

When you are EXACTLY at your apoapsis, prograde IS exactly at the horizon. The The prob proble lem m is that that you are are only only AT your our apoap apoapsi siss for for a split split second second.. Your our trajecto trajectory ry,, before before the circular circularizat ization ion burn, is a parabola parabola.. This This mea means ns that that you you reach the peak of that parabola at some point in time and IMMEDIATELY start the downward leg of that parabola. Since prograde means ”the direction that you are moving”, your prograde vector is pointing slightly ”upwards” before reaching the apoapsis, it is perfectly horizontal AT your apoapsis, then immediately shifts to point slightly ”downwards” as you start the ”descending” leg of your trajectory.

The result of this inability to instantaneously accelerate means that whichever of the two methods described above you choose, will result in an approximation to the ”ideal” circularization burn. Feel free to use whichever method suits your play style. style. For the purposes of this tutorial, tutorial, I am going to discuss the circularization circularization method using a maneuver node at our apoapsis.

Switch to Map Mode ( m key) and create create a maneuver node at your apoapsis, by clicking on your orbit as close to your apoapsis as possible. You might want to zoom way in so that you have better control over where, exactly, the maneuver is created.

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Drag the prograde vector away from the center of the maneuver node. As you do so, you should see the orange-ish colored line that represents what your orbit will be after executing the maneuver.

4.2. 4.2.


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Once your periapsis is (about) the same height as your apoapsis, your maneuver plan is complete.

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Look at the ”Est. Burn” time and the time to Node, next to the navball.

4.2. 4.2.

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This particular maneuver that I performed came up with a little bug that is important important to discuss. discuss. The computer calculates calculates your Estimated Estimated Burn based on the engines that you have on your craft. However, when I was establishing this orbit, I was throttled way down, because I was trying to adjust my apoapsis as close to 100,000 100,000 meters meters as possible. possible. When When the game goes to calcul calculate ate the burn time, instead of it using the total thrust of the engine, it uses the last thrust that was actually actually used on the engine(s). engine(s). So it came up with this great 2 hour and 12 minute estimate. Not very useful, but I assume that it will be fixed at some point by the developers. The actual burn time for this maneuver was 10 seconds seconds.. Let’s Let’s just make make believe the computer did it right to illustrate my point. ∼

Take the estimated burn time and divide it by two. You are going to start your burn burn at around around T- 5 s. This This is because, because, since the burn will be an approxim approximati ation on (because I can’t change my velocity instantly), I want to split the ”error” that I am introducing to the burn, evenly, on both sides of the point where the computer expects the burn to happen. The net result of doing it this way is that the deviation from optimal that I introduce before the node is reached is cancelled out by the deviati deviation on I introd introduce uce after after the node is reached reached.. This This is not optimal, optimal, but it’s the best our poor Kerbals can do with the tools at hand, maybe someone will come up with some some type type of autopilot autopilot that that can do this this better. better. But. But. . . mo movin vingg on. . . Change the attitude of your vessel to point at the blue maneuver node indicator on the navball.

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When the time arrives, fire your engines

Notice Notice how when I starte started d the burn, burn, the estimate estimate got more more realist realistic. ic. This This is one of the characteristics of both the ∆v ∆v meter and the maneuver node indicator on your navball. For the duration of the burn, they will constantly update for the same target trajectory. This means that if you deviate from either the path or the burn profile (you’re not burning full throttle, or worse, your stage runs out midburn and you have to switch to another stage) both the meter and the indicator will update for the new total ∆v ∆v that still needs to be expended and the vector you should should follow. All so that your final trajectory ends up where you projected with the maneuver node (or as close as possible).

Watch the ∆v ∆v meter next to the navball, it will slowly countdown the required ∆v for the burn

4.2. 4.2.


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When you are close to the end of the burn, throttle down a bit. This gives you more control over engine shutdown, so you can cut the engines at the right time and not ”overshoot” your goal.

Cut engines ( x key) key) as soon as the ∆v meter reaches 0.0 (or as close as you can get without without oversh overshooting). ooting).

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Notice Notice that the countdo countdown wn reads T + 11s. 11s. If I starte started d the burn burn at T - 5s, that means I burned for about 16 seconds total. But wasn’t it 10 seconds? The 10 second second estimate is based on full throttle throttle until shut down. Since I throttled down a little at the end of the burn to better control engine shut down, I spent about 3-4 seconds extra burning those last 5-6 m/s 5-6 m/s off the clock, hence the difference. Also throw in a second or two before I took the screen shot ∼

4.3 4.3

Chang Changin ing g you yourr Orbi Orbita tall Incl Inclin inat atio ion n

There are a number of different reasons why you might want to change your inclination:

• You You

want want to rendez rendezvo vous us with another another vesse vessel, l, that that is in an orbit orbit with a different inclination

• You

have some particular inclination that will work better for your vessel (i.e. a communication satelite, a mapping satelite, etc.)

• You

want to transfer to another planet that is on an orbit with a different inclination than the planet you are currently orbiting

• You

just want things to be organized

4.3. CHANGING CHANGING YOUR ORBITAL ORBITAL INCLINA INCLINATION

97

Depending on the inclination change that you need, there are a number of different different ways ways that you can proceed. proceed. Some of them are expensive expensive (in terms if ∆v ∆v ), others are cheap (or cheaper, at least). As an example, look at the inclination change that we discussed in ”Executing ˙ Maneuvers”. That was an inclination change of 90°You were in an equatorial orbit, and wanted wanted to change change to a polar p olar orbit. That is a hugely ”expensive ”expensive” ” maneuver, maneuver, executed executed as was described. described. There are other ways ways to execute execute inclination changes changes that are more ”economical”. Here is our current orbit:

As you can see, we are in an equatorial orbit at approximately 100,000 meters. What we want to do is change this orbit so it is still at 100,000 meters but is at an inclination of 90° (a polar orbit). The maneuver maneuver described below will save save you ∆v ∆v by changing your orbit into a highly elliptical orbit before attempting the inclination change. The main steps of the process are: • Burn

prograde at the periapsis of your current orbit to raise your apoapsis until until your orbit orbit is highly highly elliptica elliptical. l. You burn at your your periapsis periapsis to take take advantage of the Oberth effect.

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• When


at your your apoapsis, apoapsis, burn to adjust adjust your your inclin inclinatio ation n as desired. desired. This This should require much less ∆v ∆ v than the maneuv maneuver er as origina originally lly descri described. bed. Furthermore, we do the inclination change in steps. With our first burn we will make the orbit 30° inclined to the ecliptic plane ∼


• Notice

99

how we kept the periapsis where it was. Next we’ll do another burn, also at our apoapsis, and change the inclination to 45° ∼

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• One


last burn, to 90° (we could do smaller increments and save even more ∆v , but this demonstrates what I want to communicate well enough)


• After

101

your inclination is adjusted, burn retrograde at your periapsis to circularize your orbit once again.

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And now we have a polar (90° inclination) orbit.



103

Let’s look at the ”cost” of this maneuver:

• Initial • First

apoapsis change: 504.8 m/s 504.8 m/s

inclination change (to

• Second • Final

∼

inclination change (to

30°): 407.6 m/s 407.6 m/s 45°): 307.7 m/s

∼

inclination change (to 90°): 701.9 m/s 701.9 m/s

• Recircularization

at original altitude ( 100,000 m): 504.9 m/s 504.9 m/s ∼

Total cost of the maneuver: 2,426.9 m/s of m/s of ∆v

If we try to execute this maneuver in one step, without the raised apoapsis, this is what we get:

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A maneuver that costs 3,176.5 m/s. m/s. Doing Doing it our way way, we save saved d 750 m/s of ∆v ! This works because when you do the inclination change, far away from the orbited body, you can make a much smaller adjustment, and that adjustment is ”amplified” by the increased distance from the orbited body. But why? Imagine you are holding a laser pointer and point at a wall from 1 foot away. For you to move the projected dot on the wall 1 foot to the right, you need to rotate your your hand a certain certain amount. Now back back away away from the wall 10 feet. Point Point at the same same initial initial spot on the wall. wall. Mo Move ve the projected projected dot 1 foot to the right. right. Notice how much less you had to rotate your hand to achieve the same amount of ”movement”. This This is true of pretty pretty much much all maneuve maneuvers rs you make in the game. game. The earlier you can make an adjustment to your final target trajectory, the easier (and cheaper) cheaper) it is to do so. An example: example: You create a maneuver maneuver for a Mun intercept intercept and you have have a Mun periapsi periapsiss of 20,000 meters. meters. While While you are still still in Kerbin Kerbin’s ’s sphere of influence, you can make a very small change to your course (typically,


105

using any engine the change will be TOO LARGE to manage effectively, so you usually use RCS for these kinds of changes), on the order of ¡ 3 m/s 3 m/s,, and you can affect your final periapsis around the Mun by tens of thousands of meters. If you wait until you are halfway to the Mun to adjust, you will have to expend more ∆v ∆v . The The closer closer you you get to the the Mun, Mun, the the more ∆v ∆v you have to expend to perform the same adjustment. So always adjust early, as early as you possibly can! But But the the abov above expl explan anat ation ion was an alte altern rnat ativ ivee to a radi radica call 90° inclination chang change. e. Typic Typically ally you you are not going to be doing doing changes changes of that that magnitu magnitude de in your your inclina inclination tion.. A typic typical al inclin inclinatio ation n chang changee is of a few degrees, degrees, just just ”twe ”tweakaking” your orbit really. really. To perfor p erform m a maneuver maneuver like that is much much easier than the maneuver described above. Let’s take a typical equatorial orbit. We have an inclination of 0°.

If we want to transfer to Minmus, an equatorial orbit is not the greatest because of Minmus’ 6° of orbital orbital inclination. inclination. Before Before trying trying a transfer transfer maneuver, maneuver, we should ”align planes” planes” with Minmus. Minmus. That means we are going to make our orbit have have the same inclination as Minmus’ orbit. In Map Mode ( m key), key), zoom out until you can see Minmus Minmus,, and click on it. This will bring up a dialog, click ”Set as Target”.

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Minmus and it’s orbit will now be yellow in your map view.

Zoom back back in to your orbit orbit around around Kerbin Kerbin.. Create Create a maneuv maneuver er node at the ”ascending node” on your orbit. It is marked by a little yellow marker with ”AN” in it.


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Adjust your camera-view so that you see your orbit and Minmus’ orbit ”edge on”, so that they both appear as lines to you. Also make sure that you are looking from an angle that the ascending node marker and the descending node marker are right on top of each other

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Drag the anti-normal maneuver ”handle” away from the center of the maneuver node until your orbit is lined up with Minmus’ orbit

Execute Execute the node: Point Point your vessel at the blue maneuver maneuver node indicator indicator on the navball; Calculate your burn start time (T - half the burn time); and burn until your ∆v ∆v meter reaches 0.0.

Your orbit is now at the same inclination as Minmus, making any transfer you want to do there, that much easier.

4.4. 4.4.

4.4 4.4

AEROBR AEROBRAKI AKING NG

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Aero Aerobr brak akin ing g

If you have ever reentered the atmosphere of Kerbin with a ship, you know that you lose velocity velocity VERY VERY fast as you hit the lowers lowers levels of the atmosphere atmosphere.. It is that loss of velocity that we are trying to exploit when we perform an aerobraking maneuver.

Most approaches to a planet involve a hyberbolic trajectory (one that doesn’t orbit the planet, as much as swing by it). This means that typically you approach a planet at a high velocity in such a fashion that your trajectory is changed by the influence of the planet’s gravity on your vessel, but not changed enough to put you in an orbit around that planet.

Typic Typically ally,, we resolv resolvee this this issue issue by firing firing retrog retrograd radee at our point point of closes closestt approach to the planet and establishing an orbit around it. An alternative to this method, when the target planet has an atmosphere, is to use aerobraking.

So I’m coming into Duna’s sphere of influence FAST!

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WAAAYYYY before I get there, I adjusted my trajectory so that my periapsis around around Duna, on arrival, arrival, is in the atmosphere atmosphere.. Duna’s atmosphere atmosphere extends extends 41,447 mete me ters rs from the surf surfac ace. e. As you can see see in the the pict pictur uree below below,, even even thou though gh I am 29+ DAYS away from reaching Duna, I’ve already established a periapsis of 24,000 meters. meters. I’m going to adjust this further to be around around 12,000 meters for maximum aerobraking effect. ∼

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As soon as I reach Duna’s sphere of influence (SoI), I now see that my periapsis is 89,569 meters. This is because the estimate that I was shown, shown, before actually getting there, was slightly off.

One last final adjustment to my periapsis using RCS, because the engine would be WAY too powerful for this minute adjustment.

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Look at my trajectory from another another angle. According According to the computer’s computer’s pro jection, I will swing by Duna and escape on a hyperbolic trajectory. What the computer computer is not taking into consideration consideration is the aerobraking aerobraking that is going to occur.

Now if we wanted to enter orbit around Duna, and get off that hyperbolic trajectory, typically what we would do would be wait until we reach our periapsis, burn retrograde to lose velocity and make our trajectory elliptical and eventually (somewhat circular). Problem with that is that uses fuel. This is where aerobraking comes in, so let’s do this!

I’m coming in FAST, and gaining velocity as I approach my periapsis (I’m currently currently at 670,000 meters)

4.4. 4.4.


50,000 meters, going 1500+ m/s. m/s. Hang on cuz here we go!

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I hit the dense part of the atmosphere at mosphere HARD, my vessel loses velocity QUICKLY. QUICKLY.

4.4. 4.4.


Enough so that my hyberbolic trajectory

is now transformed into a highly elliptical orbit around Duna.

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And still losing speed, lowering my apoapsis even more

I zip through Duna’s atmosphere, losing a lot of my velocity, but not enough to actually land, and come out the other side of the atmosphere still moving at a good clip.

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My apoapsis is now high above Duna

When I hit it my apoapsis, I can thrust prograde, very little, just to lift my periapsis out of the denser part of the atmosphere, but still leave it inside the

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atmosphere. atmosphere. We don’t want want to do another hardcore hardcore aerobraking aerobraking session session like the last one, but we still want to use the atmosphere to lower our apoapsis some more.

I come around to my periapsis a second time and my apoapsis drops some more due to the aerobraking.

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I can repeat this process, as many times as I want, each pass lowering my apoapsis some more, until I have an apoapsis at the height that I want. After my third pass through the atmosphere

After my fourth pass

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And I can continue orbiting Duna for as long as I want, each pass, in this case, lowering lowering my apoapsis by only 500 meters. That’s pretty pretty precise control. control. If I wanted to lower it faster, just dip my periapsis further into the atmosphere; if I want to lower it slower, lift my periapsis a little bit more up in the atmosphere. Once I’m at the height that I want, I can thrust prograde at my apoapsis to bring my periapsis completely out of the atmosphere and circularize into a stable orbit.

Or I can even let it go all the way until my apoapsis also falls into the atmosphere, making my trajectory sub-orbital, and I can then (try to) land.

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And there you have it, I successfully established an orbit around Duna (or landed on Duna, depending on which scenario you followed above), while expending very little (or no) ∆v ∆v . The amount expended would be typically less than any minor minor orbital orbital correct correction ion that you you might might mak makee on a typic typical al missio mission. n. All thanks thanks to aerobraking. Unfortunately, this maneuver only works on planets that have an atmosphere, but the ”larger” and denser the atmosphere, the better it works! Let’s do the math for the above above maneuver: maneuver: When I first entered entered Duna’s SoI, I used RCS (about 2.2 m/s m/s worth) to readjust my periapsis; after my first trip through the atmosphere, I burn 9.2 m/s worth m/s worth of ∆v ∆v to lift my periapsis almost out of the atmosphere; after A LOT of orbits, I finally used 56.5 m/s of ∆v to circularize my final orbit. If I went for the landing scenario, don’t count that last 56.5 m/s. m/s. To summarize:

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• Establish


150,000 meter orbit around Duna using aerobraking: 67.9 m/s of

∆v • To

land on Duna, using aerobraking: 11.4 m/s 11.4 m/s of ∆v

With those kinds of budget, you don’t even need an engine! You could do the whole thing with RCS!

4.5 4.5

Rend Rendez ezv vous ous

Here’s Here’s the setup. setup. . . I have have one ship orbiting orbiting Kerbin Kerbin at an altitude altitude of 1,0 1,000,0 00,000 00 meters. It has an orbital inclination of 45°. The second ship is in a 500,000 meter equatorial orbit (inclination of 0°). The blue orbit in the picture below is the ship at 500,000 meters. The yellow orbit is the ship with which I want to rendezvous. This is going to make this section longer, but I did it for two reasons:

4.5. 4.5.

RENDEZ RENDEZVO VOUS US

123

• With

this inclination and altitude, I avoid falling behind Kerbin’s shadow, so the screenshots should be better.

•

This will give me the opportunity to show how how you incorporate an inclination change into your rendezvous process.

Make sure you click on your target ship and select ”Set as Target” (this is what makes the orbit yellow, and shows you the ascending and descending nodes).

The first thing we want want to do is match planes. At the Ascending Ascending Node in my orbit

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I create a maneuver node and adjust by pulling the anti-normal indicator (pink triangle with ”spikes”) down until I have about half the plane change done.

4.5. 4.5.


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If I look at my proposed orbit from another another angle, you’ll notice that the apoapsis raised significantly

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I can pull the retrograde marker a little to bring that back, if I want, but we’re going to need to do something like that anyway (since it’s almost exactly at the 1,000,000 meter mark) so I’ll just leave it.

Let’s execute this node:

4.5. 4.5.


Our orbit looks like we expected.

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Now we do anothe Now anotherr inclin inclinatio ation n chang change. e. Same Same thing: thing: create create maneuve maneuverr at ascending node; adjust anti-normal again

4.5. 4.5.


Inclination looks good, but apoapsis got way out of hand now

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So let’s adjust the retrograde marker of the maneuver node and bring that back

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We execute this second maneuver

Then we time accelerate. accelerate. Do a couple of orbits, until the intersect intersect markers markers are somewhat somewhat close (couple of hundred hundred kilometers) kilometers)

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Now create a maneuver node about 41 of an orbit BEFORE the intersect

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Drag the prograde marker on your maneuver node, until the 2 purple intersect markers are REALLY close

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And there we have an intersect of 4.8 km (not the closest in the world, but it will do for us). us). Couple Couple of things we can do here here if we can’t can’t get a close close enough enough intersect: •

Tweak Tweak the other attributes attributes of the maneuver maneuver node like radial-in radial-in or radial-out to see if we can get a better intercept (least effective)

• Click

and hold on the middle of the maneuver node (it turns white) and ”drag” it around your orbit to find a better spot to execute the node (most effective)

• Or

delete the maneuver node altogether and create a new one (more work, but also effective)

•

Also remember that you can try for the intersect at either the purple intersect (2nd intersect) intersect) markers markers OR the orange intersect intersect (1st intersect) intersect) markers. markers. Whichever one you can get to be close first, better for you.

Execute the node

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We now have a pretty decent intersect. Now we need to get there and ”establish an orbit” orbit” ident identica icall to the target target ship. ship. To do this, what we want want to do is get to the intersect and zero our velocity in relation to the target. If we are (practically) in the same orbit as our target and we are moving at the same speed, we will be stationary in relation to each other. So if we want to have a zero velocity in relation to the target, we need to put our navball in ”Target mode”. Click on the navball where it says ”Orbit” until it says ”Target”. If you were paying attention when you clicked, you’ll have noticed that the prograde/retrograde markers on the navball ”jumped around” when you click clicked. ed. If you didn’t, didn’t, do it aga again, in, I’ll wait wait here. . .

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The reason they jumped is that the prograde and retrograde markers on the navball are now indicating your velocity vector in relation to the target. And the velocit velocity y being being shown shown is also also in relation relation to the target. target. Our objectiv objectivee here here is that once we reach the intersect, we want to make our velocity 0 m/s (or m/s (or as close as we can get it to zero). Like Like I mentioned mentioned above, above, if we have have no velocity velocity in relation to each other, we are stationary in relation to each other. That’s what we want!

Time Time warp to the inters intersect ect.. Don’t Don’t get too crazy with the time warp warp or you you will overshoot the intersect, and you can’t just come around for the next try, it doesn’t work that way.

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Notice that as we pass the orange intersect markers (1 st intersect) on the orbit, the purple ones (2 nd intersect) turn orange, since what was our 2nd intersect now became our 1st intersect.

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Once we are near the intersect (notice how I’m intersect)

1 minute away from the

∼

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139

Point retrograde on your navball and turn on SAS ( t key). key). Time your your burn so that you have enough time to bleed off the speed that you have in relation to the target (in my case, 223.4 m/s). m/s). Let’s Let’s call it 25 second seconds. s. So when I’m 25 seconds seconds from the intersect I will activate my engines.

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I cancelled (almost) all of my velocity in relation to my target and am now sitting at 5.9 km from the target and our relative velocity is almost zero. So we’re pretty much stationary. My original intersect said 4.8 km and I’m at 5.9 km. The discre discrepan pancy cy is because because of how how I execut executed ed the ”zero your velocit velocity” y” maneuv maneuver. er. I didn’t wait until the very last minute and burn full thrust, I slowly burned off the speed speed in a con controll trolled ed fashi fashion on,, so yeah, yeah, it won’t won’t be exac exact. t. But But 5.9 5.9 km is stil stilll a respectable intersect, and don’t let any of the 0.1 km and 0.2 km intersect pilots tell you any different. Using RCS (since my velocity is so low now), I point retrograde again and bring our relative velocity to zero.

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Now we need Now need to get closer closer.. . . point point at your target target prograde prograde indicat indicator or in the navball (pink circle) and thrust to about 10 m/s. m/s. You’r ou’ree goin goingg to see people people sayin sayingg ”that’s ”that’s WA WAY too slow slow if you’re you’re at 6 km!”. km!”. Whatev Whatever. er. . . this this whole whole thing took me 15 minutes of real time to do, I’m not in that much of a hurry! Let them go thrusting about at 60 m/s and m/s and we’ll see who ends up with solar panels still attached and who ends up without.

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Notice how the prograde marker popped up in front of us on the navball, because that’s the direction I’m moving. But also notice how it is not EXACTLY on top of the target prograde indicator. That means we are not moving EXACTLY in the direction direction of the target, target, but a little little off. What What we want want to do is ”pull” ”pull” that that yellow prograde marker into the middle of the target prograde indicator. To do that, there are two different methods that we can use. The first method is:

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143

• point

to the spot that is almost exactly opposite of the yellow prograde marker on the other side of the target prograde marker

See how I’m pointed to almost the exact opposite position, compared to the yellow yellow prograde, prograde, except on the other side of the target prograde prograde marker? Use RCS

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forward ( h key) key) to thrust in that direction direction A LITTLE LITTLE BIT to pull the yellow yellow prograde prograde marker where you want it. Wherever Wherever you are point p ointing ing when you thrust is where the prograde marker is going to move towards.

I screw screwed ed that one up, on purpose purpose.. See how my prograde prograde is now now to the right right of my target? Point to the left of the target and thrust there

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Now we’re Now we’re all lined lined up, heading heading toward toward the target target.. But all this thrusti thrusting ng to adjust the markers has brought our speed up to 53.9 m/s 53.9 m/s.. . . let’ let’ss slow slow that down down,, we don’t want to plow into the other ship. Point Point yellow retrograde retrograde,, and fire your

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engines (since it’s a pretty decent amount of velocity, RCS will take too long), but use a slow slow burn, you don’t don’t want want to overs overshoot. hoot. . . bring bring it down down to the 10 m/s we wanted.

Notice how retrograde and target retrograde are also lined up. The second way to adjust you’re prograde when closing on the target is:

4.5. 4.5.

147


• use

the RCS keys ( i

, j

, k

So. . . if you you were were in this situat situation: ion:

and l

to adjust adjust your your trajectory trajectory

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you would press the i the target indicator


key to ”push” the prograde indicator ”down” ”down” toward toward

if you were in this situation:

4.5. 4.5.


you would use the j target indicator.

149 key to ”push” the prograde indicator ”left” toward the

One of the big advantages of the second method is that you will not end up with your closing speed as high as the first method (53.9 m/s (53.9 m/s), ), which can be very importa important nt if you you are closing closing from from a smalle smallerr distan distance. ce. At smaller smaller distanc distances, es, you you don’t want to end up accelerating too much toward your target, or bad things will happen.

So. . . whatev whatever er method you use, eveythi eveything ng should should be lined lined up and you should should be approaching approaching your your target at a reasonable speed. speed. . .

If it’s taking too long to get to the target, DO NOT ACCELER ACCELERA ATE warp. I’m not saying saying you have have to only do rendez rendezvo vous us at 10 MORE! Use time warp. m/s, m/s, what I’m saying is: find a velocity you are comfortable with and stay there. Don’t adjust adjust your velocity velocity to speed things up. Use time warp, because once you are REALLY close, you can instantly leave time warp. If you accelerated to make things go faster, when you are REALLY close, you CAN’T instantly slow down (gotta point in the right direction, fire engines or RCS, be careful not to overshoot, etc.). It’s a lot harder harder to do that ”on-the-fly” ”on-the-fly” when you are 20 meters from your your target and going too fast!

Depending on how well aligned you managed to get those two markers, they will tend to drift as you get close to your target (I did pretty good actually, they only only drifte drifted d a tiny tiny bit and I’m alre alread ady y at 196 196 m). m). If they drift drift,, use use the the same same process you used to align them initially, to realign them.

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I’m moving WAY too fast fast (see (see?? I told you you!) !).. . . gotta gotta slow slow down. down. . . Bill Bill jams jams on the brakes

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Now align your prograde vector again, using either of the two methods described above

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A little bit of time warping and here we are, up close and personal, with our target target ship. 12 meters meters is not bad to start start a dockin dockingg procedu procedure, re, but we’ll do that that in the next section.

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Before wrapping up, some other tips to discuss: • When

trying to adjust your velocity, if the change is small (less than 5-10 m/s), m/s), use RCS.

• Using

RCS forward ( h key) key) is the same as using your your engines engines to thrust thrust very slowly in the direction you are pointing. This is sometimes exactly what you want/need: very fine adjustments. Likewise, RCS backwards ( n key) is very useful for reducing your velocity without having to do ”space-flips” (see below).

• If

you are pointing prograde and want to reduce your velocity, it is more efficient to STAY pointing prograde, and thrust RCS backwards ( n key) than to flip 180° and thrust forward and then have to flip 180° again again.. It will save RCS monopropellant and even if you are only using torque to turn around, it’s still a lot faster to thrust backwards than to flip around.

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Obviously, this doesn’t apply if you have to make a significant change in your velocity (requiring engines), since engines don’t thrust backwards (unless you mount a set facing forward on your craft, there’s nothing to say you can’t!). • Ditto

if you are pointing retrograde, but need to increase your velocity. Just thrust backwards, same concept.

• Another

adjustment you can make, similar to the two above. If we want to ”pull” the yellow prograde we thrust forward after pointing in the appropriate direction. But if we overshoot our target prograde indicator (we ”pulled” it too much), you don’t have to turn and adjust again. Just thrust backwards (assuming you are using RCS), if thrusting forwards ”pulls” the prograde, thrusting backwards ”pushes” it away from wherever you are pointing!

•

Always Always try to be as precise precise as possible when positioning positioning the yellow yellow prograde prograde vector over your target prograde vector. The more precise you are, the less adjustments you will have to make to your trajectory as you get closer.

• In

my example above, I was only pointing a little off the target indicator, to illustrate the point, but you can point further away and use less thrust to achieve achieve the same correction. correction. I only did not do that because if I pointed 90° away from the target prograde indicator, it wouldn’t have been visible on my navba navball ll and my explana explanation tion would would be vague. ague. Just Just mak makee sure sure that that the vector you are pointing is correct (if yellow prograde is to the left, you point to the right; if yellow prograde is above, you point below; etc) for the adjustment you want to make.

•

And finally, finally, keep your velocity velocity in check. check. Those darn solar panels are attached with bubble gum and will fall off at the slightest slightest nudge! Use time warping warping liberally during rendezvous. Use it a lot, but not high time warps otherwise debris will happen!

Just Just so you have have an idea of how how hard hard this this was: Even Even with making making sure to take all the screenshots at the right times, actual play time from the very first screenshot to the very last screenshot in this section, was about 15 minutes real time. time. Game time was a lot more than that due to the time warpin warpingg (especi (especially ally when I was waiting for that 200 km intersect intersect). ). All maneuver maneuver nodes were created manually manually,, no MechJebbin MechJebbingg any of them. I did Hyperedit Hyperedit both of those ships into their their initial initial positions positions,, but that was was it. Infinit Infinitee fuel fuel was was on (but (but probab probably ly didn’t didn’t need to be). ∼

4.6. 4.6. DOCK DOCKIN ING G

155

I did dock both of those ships together after completing this section so I can use the same two ships in the next section ”Docking”. I’ll undock them and move them about 50 meters apart before starting that one. This was a very fun section to write and I hope you enjoyed it!

4.6

Dock ocking

Our Starting Point We’re going to continue where we left off in the rendezvous section. At the end of that section, we were 12 meters from our target. Since I know that it is sometimes difficult difficult to achieve achieve an approach approach that close, I’m going to back away away from our target vessel and start the docking procedure from around 50 meters. So our starting point will be our two vessels, with 0 m/s relative velocity between them, and about 50 meters apart.

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Pre-Docking Checklist Make sure Make sure your your navball navball is still still set to Targe Targett mode. mode. If it’s not, click click on where where it says ”Orbit” or ”Surface”, and the speed right underneath, until it says ”Target” Typic Typicall ally y, at this this point point in the maneuv maneuver, er, you will not be using using engines. engines. We are way too close to our target and we don’t want to ram into it, so if you haven’t already, start using RCS. Turn on RCS by pressing the r key. Another thing that we have to do to prepare for the docking procedure is to select the port, on our ship, that we are going to use to dock. Right click on the port, and select ”Control From Here”.

This is VERY important if you have ports that are not lined up with your pod/probe pod/probe (like (like on my ship). ship). When When you you are using using dockin dockingg contro controls ls (like (like the IJKL/HN keys, or WASD/Shift-Ctrl keys in docking mode), the direction that your ship is going to move when you press a key is in relation to whatever port on which you said ”Control From Here”. So in the case of my ship, which has it’s docking port mounted on the side of the main body of the craft, if I don’t ”Control From Here” on the correct port, my controls will be crazy to understand.


157

If done properly, on my ship, for example, when I press h to move forward, the RCS is going to thrust in such a fashion that the docking port I am controlling from moves forward (which means the ship, as a whole, will be moving sideways). Another thing that you should do is decide which port, on the target ship, you wish to dock TO. Right click on that port and select ”Set As Target”.

If you still can’t pick out the target docking port on the target ship to be able to right click on it, you’re not close enough. Setting the target to the specific port makes the game now show you the distance between YOUR docking port and the target docking docking port. When you you set a ship as a target (like you did in Map mode for the rendezvous), the system is actually targeting the ship’s center of mass. Since, typically, the docking ports are not located at the center of mass, the distance indicator to that center of mass doesn’t really help us for the docking procedure. So once you are close enough, target the specific port with which you want to dock. Before trying to do any close-up-and-personal maneuvering near your target, switch your camera to CHASE mode (press v a few times, until it says says ”Camera: CHASE”).

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Once your camera is in Chase Mode, rotate your camera (by holding the right button and moving the mouse) until you are looking straight at the backside of your docking port. In the case of the ship being used for this tutorial, since I have two docking ports on opposite sides of the ship, I want to be looking straight down at the docking port opposite the one from where I am controlling.


159

Another tip is that if you are using RCS, you can point at your where you want to go (prograde/target) and press h to thrust forward. When you want to brake, instead of flipping your ship around and pressing h , just point point prograde prograde and press n (RCS (RCS thrust backwar backwards). ds). That way way you don’t waste waste time turning your ship around dozens of times, which also uses RCS. Now that you have positioned your camera properly, in Chase Mode, the IJKL keys make sense: i = down, down, k = up, j = left left and l = right, right, just like your WASD WASD keys. While WASD WASD will rotate your vessel vessel in the correspondin correspondingg direction, IJKL will ”translate” your vessel in that direction. What is translation? Imagin Ima ginee you you are standing standing up straigh straight: t: to rotate rotate left, you turn turn your your entire entire body left to face left; to translate left, you would continue facing the same direction and

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you would ”side-step” left. It is also called ”sliding” or ”strafing” in some games. It’s NOT changing your orientation but still moving. The next thing we want to do is position our target ship so that our docking process process is easier. easier. If you are in a ship ship in orbit, orbit, pointing pointing prograde prograde,, as you circle circle the planet you are orbiting, your ship’s orientation doesn’t change (the prograde slowly moves away from the nose of your vehicle and loops around a complete 360° for every every orbit you you com comple plete) te).. The net result result of this this is that if you you are in a separate vehicle, stationary in relation to that first ship, it looks as if that ship is ”tumbling” in front of you. In real life, there are usually pilots in both ships and they can maintain a certain attitude to avoid the ship tumbling out from under you as you are trying to dock with it, but in Kerbal Space Program, where we can only control one ship at a time, these attitude changes of the target ship, along the course of it’s orbit are unavoidabl unavoidable. e. There is, howeve however, r, a ”trick” ”trick” to minimize this problem. problem. If you orient the docking port of the target ship to point EXACTLY in the normal, or anti-normal direction, the ship will still ”tumble”, but in such a fashion that the docking port, for your purposes, is stationary (because the ship is tumbling ”around” the docking port). To accomplish this, switch to your target ship (pressing the [ or ] keys), and select the port you were going to dock with and ”Control From Here” on the docking docking port you you want want to use. use. No Now w on your navball navball,, point point in the ”norma ”normal” l” direction. direction. In an equatorial equatorial orbit, if you were pointing prograde prograde to start, turn 90° ”towards” ”towards” the planet planet (radial-in), (radial-in), then 90° ”up” (in the direction of the north pole of the planet). In an equatorial orbit, my navball should look like this:


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Because my ships are not in an equatorial orbit, my navball, for this maneuver, will look like this:

Once you have positioned your target ship’s docking port pointing ”normal”, turn on SAS ( t key). key). Good!

Switch back to your original ship (pressing the [ or ] keys). keys). Since we switched vessels, we lost our target designation, so right click on the target docking port on the target ship again and select ”Set As Target” Target”.. Just to make sure, select the port you want to use for docking on your ship, right click and select ”Control From Here”. If we want these docking ports to connect, they have to meet as ”flat” as possible. Since we oriented the target ship’s docking port in the normal direction, we have to orient the docking port, on the ship we are docking from, in the antinormal direction. For an equatorial orbit, anti-normal on the navball, will look like this:

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In my case, my antinormal direction looks like this on my navball:

We do the same thing we did on the target ship and lock in SAS ( t key) on our docking docking ship. If we’ve we’ve done this properly, properly, we can now use the translation translation controls on our docking ship and the orientation of our docking port will not change (if it does, SAS will bring it back to where we want it). Now it’s just a matter of getting the two docking ports in front of each other and then closing the distance between them.


163

Before we move on to docking these two ships I want to discuss the orienting of the ports ports to normal normal and anti-n anti-norm ormal. al. If you are not in an equatori equatorial al orbit, it might be difficult to figure out where those two points are on the navball. An easy way to figure that out is to create a ”dummy” maneuver node, and adjust as if you were were performing a burn in the desired desired direction. direction. Doesn’t matter how ”long” of a burn since you won’t be actually executing it. Once you’ve created the node, there will be a maneuver node indicator on your navball in the exact position that you need it. Orient your ship in that direction, engage SAS ( t key), key), and then you you can delete delete the maneuve maneuverr node. This is where we currently stand, docking ports are aligned (orientation-wise) properly. and we’re still about 50 meters from our target. (I know this screenshot is horrible, but it was the best I could do. Trust me, they’re aligned in this picture).

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Docking Before we actually start the docking process, let’s look at some tips on using RCS: •

Use RCS sparingly sparingly.. . . if you are holding holding any given RCS RCS thrust key key for more than than 1 second second,, you’r you’ree doing doing it wrong! wrong! The closer closer you get, the shorter shorter the bursts should be (really just quick taps on the keys).

• Learn

the translation controls IJKL/HN as opposed to WASD/QE. That way you can leave the WASD keys to adjust orientation with your left hand (or just let SAS take care of rotation, if you set it as described above), while still translating using IJKL with your right hand.

• For

the beginners (people who don’t have experience docking), only adjust one one axis axis at a time. time. Exam Exampl ple: e: use use the the I/K I/K keys eys to adjust adjust your your ”up” ”up” and ”down” position until your docking port is at the same height as the target docking docking port. Once you are done that part of the maneuver, maneuver, your velocity velocity in relation relation to the target target should should be 0 m/s (or as close as possible) possible).. THEN THEN start using the J/L keys to adjust your ”left” and ”right” position until your dockin dockingg port is aligned aligned properly properly with the target target docking docking port. When When you you are done with that part of the maneuver, again, your velocity in relation to the the targ target et shou should ld be 0 m/s. m/s. While While this this proce process ss consum consumes es mo more re RCS monopropellant (instead of making a bee-line straight for the docking port), it is much easier to accomplish this way.

•

Use time warping warping to accele accelerat ratee the process. process. Don’t Don’t increa increase se your speed to much much over over 0.1-0.3 m/s during during the final final approac approach. h. Exampl Example: e: you’r you’ree too ”high” in relation to the target port: quick quick burst of RCS using the i key; your ship will start to slowly move down; If you’ve got 10-20 meters that you need to go down, time warp; once you are near perfect position, exit time warp; quick burst of RCS using the k key (to cancel cancel out out the initial burst when you pressed the i key); key); you you should should now now be stationary stationary again; again;

The objective of our docking procedure is to make the two ports come into contact as ”flat” as possible. We already know that the ports are currently ”flat” in relation to each other because of the pre-docking steps we took above. Since we did the ”Control From Here” on the docking port we are using, the navball is now oriented as if we were ”inside” the docking port, looking straight out. This is where our problem currently is:


165

The target indicator indicator is nowhere nowhere near, where it needs to be. For us to be able to dock, the target indicator needs to be ”dead-center” on our navball. Let’s deal with the ”up”/”down” position first. I can see in the navball picture right above that my target is ”below” me. So I thrust with RCS down ( i key). key). The target target indicat indicator or slowly slowly move movess up. When the target indicator is almost centered, vertically, in the navball (about halfway up)

166 I thrust RCS up ( k 0.0 m/s again. m/s again.

CHAPTER CHAPTER 4.


key) key) to cancel my downwar downward d movemen movement, t, until I’m at

Now let’s deal with ”left”/”right”. As you can see in the last navball picture, target is far to the left, so I thrust RCS left ( j key). The target indicator slowly moves right towards the center of the navball

As the target indicator gets close to the center, we see that our vertical alignment ment is not great. great. I stop stop the sideway sidewayss mo move vemen mentt by thrusti thrusting ng RCS RCS right right ( l key) back to 0.0 m/s 0.0 m/s.. Let’s readjust that vertical. I thrust RCS down again ( i key).


167

After a few more small adjustments, I stop my movement and it looks like I’m perfect perfectly ly aligned. aligned. No Now w we move move in for the docking. docking. Thrust Thrust RCS forwa forward rd ( h key).

As we start to move forward, we notice how the target indicator drifts away from center pretty quickly. This means we weren’t as perfectly aligned as it looked. The closer you get the bigger the tiny discrepancies will show. So we stop, thrusting RCS backwards ( n key).

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And readjus readjustt the centeri centering ng of the target target indicat indicator or in the navba navball. ll. Nice Nice and centered again.

Up until until this point, point, I only only showe showed d you you screen screensho shots ts of the navbal navball. l. I did this for a reason. When you are maneuve maneuvering ring in to dock do ck,, that’s where you should be looking. The directions on the navball (up, down, left and right) don’t change. If you look at the ships, depending on the position that your camera is in, they could


169

be completely backwar backwards. ds. Howeve However, r, once you get really close (like the 5 meters meters I’m at now), you are pretty much docked and it’s just a matter of nudging them together, so at this point watch the ships. Let’s Let’s try movin moving g in again. . . h key...

As we move move in, we very lightly lightly contro controll position position using IJKL. TINY, TINY bursts bursts.. We’re e’re at 3 meters. meters. This This might might work! work! But I’m in the dark dark again, again, let me rotate that camera so we can actually see this docking.

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2.7m...

171

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2.5m. . . This 2.5m. This is where where the magnets magnets on the dockin docking g ports kick kick in and start start to pull pull your your two ships togethe together. r. . .

2.4m...


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And we’re docked!

Docking Docking is a very very delicate and complex complex maneuver. maneuver. Your biggest enemy when docking docking is velocity velocity.. Mak Makee sure you keep the velocity as low as you possibly possibly can. Use time warping warping to get through the long boring parts. The more gentle you you are on the RCS controls, especially during those last few meters, the more successful you will be. The ships ships used used in this this tutori tutorial al have have docking docking ports mounted mounted radially radially.. I do not suggest suggest you do that. It is much much simpler simpler when the docking docking port is orien oriented ted forwa forward rd from from the normal normal position position your ship flies. flies. Ho Howe weve ver, r, design design constr constrain aints ts sometimes force you to do things like mounting them radially. Once you have a lot of experience with docking, you can probably mount them anywhere you want and not notice the difference. difference. For starters, stick with mounting mounting them forward forward (unless you can’t for design reasons). There are some very important things to know about docking and docking ports:

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1. Dockin Docking g ports must be the same size size to dock dock to each each other. other. You cannot cannot dock a Clampotron Jr, to a regular sized Clampotron, or a regular sized Clampotron to a Clampotron Sr. 2. A very common common mistake is putting putting the docking ports on backwards. backwards. This is especially true of the Clampotron Srs. Whichever side is ”up” (in the VAB), or ”front” (in the SPH), when first picking the docking port from the parts list, is the side that actually docks. docks. If you are not sure which which side is up, grab the part and press space in the VAB/SP VAB/SPH H and that will reset the part’s orientation to as if you had just picked it from the parts list. 3. When docking docking ports are close enough together together to dock, there is a magnetic magnetic force force that that they they exert exert on each each other other to com comple plete te the dockin docking, g, someti sometimes mes having SAS on when trying to dock, causes it to not dock. You can still use SAS during the docking maneuver, just make sure to turn it off for that last half meter or so of approach. 4. When you undock two two docki do cking ng ports, the magnetic force mentioned mentioned above above ”turns off” to allow you to separate the two vessels without pulling them back back togethe together. r. The magnets magnets only ”reset” ”reset” if you you mo move ve the dockin dockingg ports ports a certain certain distanc distancee from from each each other other (somethin (somethingg like like 5-1 5-100 meters meters). ). So if you you just undocked (usually to adjust a docking position) and can’t redock, try backing backing away away about 5-10 meters and THEN redocking. redocking. Some people have said that quick saving and quick loading also resets the magnets, I have not confirmed this. 5. The ”Rockomax ”Rockomax HubMax Multi-Point Multi-Point Connector” Connector” DOES DOES NOT HA HAVE VE want to dock to it, you HAVE HAVE to DOCKING PORTS ON IT!. If you want add the docking port to it. Ditto for the ”BZ-52 Radial Radial Attachmen Attachmentt Point”. 6. The ”Inline Clamp-O-Tron” Clamp-O-Tron” and the ”Clamp-O-Tron ”Clamp-O-Tron Shielded Docking Port”, Port”, on the other hand DO HAVE docking ports built into them. You have to right click the part to ”open” and expose the docking port once you have launched (can’t do the right clicking part during assembly). I sincerely hope that this section helped you learn the fine art of docking!

4.7 4.7

Gra Gr avit vity Assi Assist st

A gravity assist, also known as: gravitational slingshot or swing-by, is a maneuver where a spacecraft approaches a planet, moon or other celestial body, and uses it’s

4.7. 4.7.

GRAVITY ASSIST ASSIST

175

gravity to alter it’s course and/or change it’s velocity. The strange part of a gravity gravity assist is that it looks like it shouldn’t work. work. Take a look at the diagram below:

In the diagram above, the length of the arrows represent the magnitude of the velocity velocity. The longer the arrow, the higher the velocity velocity.. Looking at the above above diagram we see that the vehicle approaches Jupiter at a specific velocity, gains velocity, due to Jupiter’s gravitational influence, reaching it’s highest velocity at the closest approach to Jupiter, and then slowly loses velocity as it leaves the influence influence of Jupiter’s gravitatio gravitational nal field. It’s velocity velocity is the same as it leaves leaves as when it entered. If you were standing on Jupiter watching this maneuver, you saw a craft approaching Jupiter at, let’s say, 1,000 m/s. m/s. As it fell into Jupiter’s Jupiter’s gravity gravity well, well, it picked up speed, until at it’s closest approach it was moving at, let’s say, 1,500 m/s. m/s. Then Then it starte started d to lose lose velocity velocity,, at the same rate that it gained gained it, until until once it leaves Jupiter’s gravity well, it is moving at the same 1,000 m/s that m/s that you observed when you first saw it approaching. So, what’s the point?

The point is that all the velocities discussed in the previous two paragraphs, and shown in the diagram are in relation to Jupiter (or to you standing on Jupiter). Jupite Jupiterr is not a station stationary ary object. object. It is mo movin vingg around around the Sun at a pretty pretty good clip. When you you perform a gravity assist, assist, you ”steal” some of that velocity velocity from Jupiter and add it to your vehicle’s velocity. Look at this diagram that includes a vector for Jupiter’s movement around the Sun:

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When you add in Jupiter’s movement vector (the red vectors above), you can see that both the V in in and V out out (blue) vectors are larger than the simple vehicle’s velocity vectors (black). Let’s put this in context: If you were standin standingg on the Sun (bring (bring sun block!) block!) and were were watc watchin hingg this this maneuver, you would see that the vehicle is traveling at a velocity of, let’s say, 2,000 m/s, m/s, in relation to you, around the Sun. It is approaching Jupiter at 1,000 m/s, m/s, just like before. From your standpoint, Jupiter is also traveling at a velocity of, let’s say, 1,000 m/s, m/s, in relation to you, around the Sun. You see the spacecraft gain velocity as it approaches Jupiter, and you see it lose velocity as it moves away from Jupiter, but from THIS standpoint, outside of Jupiter’s Jupiter’s frame of reference, reference, the gain and loss are not equal. equal. As it approach approaches es Jupiter you see it gain way more than the 500 m/s that m/s that the observer on Jupiter saw, because you also see it gain the angular momentum of Jupiter’s orbit, so you see, for example, a gain of 1,300 m/s. m/s. The vehic vehicle le is now moving moving at 3,30 3,3000 m/s in relation relation to the Sun. As it depart departss Jupiter Jupiter’s ’s gravity gravity well, well, it loses loses those same 500 m/s 500 m/s that the observer on Jupiter saw it lose, but it keeps that 800 m/s, m/s, that it gained from Jupiter’s orbital velocity, ending up, to you, looking like it is now moving at 2,800 m/s and m/s and on a different trajectory than what it was on before. The important part of this whole thing, is that it was accomplished without expending any fuel. All using gravity. You can adjust your approach to the body that you want to use for a gravity assist so that the angle, and the amount of speed you gain, when you leave their gravity well, is the one you want.

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177

This This entir entiree process process also works works to reduce reduce your your velocit velocity y. The only thing thing that that changes is the direction in which you approach the body you want to use for the gravity assist. If you perform the maneuver as below, you will lose orbital velocity, proport proportion ional al to Jupiter Jupiter’s ’s orbital orbital velocit velocity y. If we use the same numbe numbers rs we used above, your resultant orbital velocity, in relation to the Sun would be, after the maneuver, 1,200 m/s; m/s; instead of gaining 800 m/s, m/s, your vehicle would lose 800 m/s. m/s.

Disclaimer: All the numbers used in the two examples above are completely

random and used for example purposes only. Jupiter’s true orbital velocity is more like 13,000 m/s. m/s. The proportion of velocity velocity gained/lost gained/lost in the two maneuvers maneuvers is also completely completely random. The numbers numbers were chosen to illustrate illustrate the point that you gain/lose some fraction of the body’s orbital velocity, but not all of it. The actual result of a gravity assist maneuver, be it to gain velocity or lose velocity, will vary in accordance to the angle at which you approach the body and the distance of your closest approach to the body. A gravity assist is not really a maneuver that I can simulate ”on demand”, especially if you consider that I would have to show you multiple maneuvers, very similar in nature, with small variations so that you could evaluate the different end result of each maneuver based on the variations. I will leave you here with this information and hope that it helps you executing this type of maneuver.

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CHAPTER CHAPTER 4.


Land ndiing

Landing sounds like a fairly simple maneuver, however it is one of the more complex maneuvers that you will execute in the game.

The reason it is difficult is that for you to land successfully (without exploding or otherwise destroying your vehicle), you must do so at a very low velocity, typically less than about 5 m/s. m/s. The problem is that for you to maintain proper attitude when you are moving this slowly and being pulled by gravity, all at the same same time, time, is very very difficul difficultt because because your your ship is very very unstable unstable.. Using Using SAS to control your attitude at this phase of the maneuver is HIGHLY recommended.

Another point that sometimes people overlook, is that for you to land successfully, your velocity, in relation to the surface that your are trying to land on, should be as close to 0.0 m/s 0.0 m/s as as possible. Howeve Howeverr in game, there is no indicator of your horizontal velocity. You have to gauge, based on the vertical speed indicator (next to the altimeter), and the speed indicator (above the navball) and kind of deduce deduce what your your horizontal horizontal velocity might might be. b e. Usually Usually it’s easier easier just to view the terrain and see if you are moving in relation to it.

Disclaimer: I don’t claim that this is the best or most efficient way to perform a landing. I’m sure there are people that can do this WAY better than I can, but this WORKS (not that any other method doesn’t). If you like my method, enjoy, if you don’t like my method, write a thorough description on how to perform this better and I will be happy to include it in the next edition of this book.

But let’s try to do this. Our startin startingg point point is a circul circular, ar, equator equatorial ial orbit at 30,000 meters, around the Mun. Our intention is to land somewhere north of the big crater that sits right below the equator of the Mun.

4.8. 4.8. LAND LANDIN ING G

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Our first step in landing is to do a deorbit burn. What that means is we want to transform our now, ”perfectly”, circular orbit, into a suborbital trajectory. To do this, we wait until we are about 41 of the way around the Mun, BEFORE our desired landing site, and burn retrograde.

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We want to burn retrograde enough so that our blue trajectory line ends up sligh slightly tly AFTER AFTER where where we want want to land land.. The The reas reason on for this this is that that the the blue blue trajectory line is a perfect parabola and we don’t want to perform a parabolic landing landing maneuver maneuver (they are possible, possible, but extremely extremely difficult). What we want to do is make our trajectory ”overshoot” our target landing site by a little bit, this means we will still be ”in the air” as we pass over our desired landing site.


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It is at this point that we want to burn retrograde again to lower our velocity to virtually 0.0 m/s 0.0 m/s.. This will allow us to descend straight to our desired landing site.

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If you do this correctly, and follow your retrograde vector as you burn, you will end up with your retrograde vector pointing straight up to the middle of the blue part of the navball (which means your prograde vector is straight down, which is what we want!).


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When we turn off our engines at this point, we will start to gain velocity again. This is the Mun’s gravity pulling us down. This is where things get complicated. We don’t know how high up we are because the altimeter on the main flight screen is showing showing altitude altitude to sea level. level. The actual actual surface surface of the Mun is going going to show up WAY before that reaches anything close to 0. The only way, without mods, to know your true altitude in relation to the surface is to check the radar altimeter in the cockpit. Press c .

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As you can see, the radar altimeter is showing that we are about 800 meters above the surface. Quick switch back to regular flight screen ( c again)

Our dumb altimeter is telling us we are 3,600 meters off the surface. We do the math and figure that we should reach the surface when the flight altimeter reads somewhere around 2,800 meters. Don’t cut it too close or ground will show up faster than you think. But we’ll double check that anyway. ∼

We continue continue to fall. We’re expecting expecting surface around around 2,800 m. So what I like to do is wait for a nice round number (3,000 m, in this case) and double check our math. So I wait until 3,000 rolls around on the altimeter. ∼


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Once I’m there, I press c to switch switch back back to the cockpi cockpit. t. If our math math is right, right, our radar altimeter in the cockpit should be showing about 200 meters

Bingo! It looks like it’s a little below 200 meters, so let’s readjust our estimate of surface from 2,800 meters to 2,850 meters just to be on the safe side.

Time to slow down big time

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This This is where where things things get hairy. hairy. The slower slower you are goi going, ng, the harder harder it is to keep keep that retrograde retrograde vector vector at the top of the navball navball (pointing straight straight up). But you have to chase it! Make sure it stays at the top! Throttle up and down to keep a reasonable reasonable velocity velocity (something betw b etween een 3-10 3-10 m/s m/s). ).

We’re still descending


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We’re at 2,919 meters. Our radar altimeter should be marking around 75-100 meters if our math is right. Let’s see.

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Looks like almost 100 meters exactly (it’ll be nice when we have a digital radar altimeter). altimeter). So let’s assume we’re we’re gonna be reaching reaching the surface at about 2,820 meters. Nice and slow ∼

We can see our shadow! Altimeter is reading 2,823 meters (don’t know why I cut that out of the screenshot). Still controlling throttle up and down to maintain a low vertical velocity.

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And we’re down! Cut thrust ( x And your landing is complete!

key) key) so it doesn’t hop back back up in in the ”air”. ”air”.

And it looks like we ended up where we wanted!

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A brief recap: • Burn

retrograde about 41 of an orbit before your desired landing site

• Burn

until your trajectory ends slightly beyond your desired landing site

• Once

you are over your landing site, burn retrograde to 0.0 m/s. are m/s. You are now falling straight down

• Control

descent (throttle up/down) to maintain both a reasonable velocity and a good attitude for the vehicle

• Check Check

true distance distance to surfac surfacee via radar altimete altimeterr in cockpi cockpit. t. Estimat Estimatee regular altimeter surface altitude.

•

Rechec Recheck k true altitude/altimete altitude/altimeterr reading reading often during descent. descent. Adjust Adjust estimate accordingly.

• Below • Watch

100 meters true altitude, keep speed low (less than 5 m/s 5 m/s). ).

for shadow (day landing) or use lights on your vehicle (night landing) to gauge visual distance to surface


• Try •

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to land with less than 5 m/s 5 m/s of of velocity (less than 3 m/s 3 m/s is is even better)

Cut engines immediately upon touchdo touchdown wn

• Call

Mission Control and say ”The Eagle has landed!” or some other memorable phrase.

Suicide Burn or How I learned to live dangerously! A suicide burn is a very aptly named maneuver because in many instances it will result in pieces of ships and/or kerbals strewn across the landscape. My above landing procedure, while ”easy”, is not even close to an efficient landin landing. g. I used used more more than than half half of the fuel in the two two stage stage lander lander to accomplis accomplish h that landing. landing. The most efficient way to land is to wait until the last possible moment, and burn retrograde at full thrust in such a fashion that as you reach the ground, you velocity is exactly 0.0 m/s m/s (or low enough that things don’t fall apart upon touchdown). I have two problems with suicide burns:

1. I don’t don’t know, know, with with any any degree degree of certai certaint nty y, my exact altitude altitude above above the surface. This information is crucial to know exactly when to start a suicide burn (remember, you start it at the last possible moment) 2. I don’t know, with any degree degree of certaint certainty y, how fast my vehicle vehicle can deceldecelerate. erate. This This can be mitigate mitigated d if I’ve I’ve flown flown the same same vehic vehicle le variou variouss times times and know how it ”responds”. But remember remember that the vehicle vehicle will perform differently depending on it’s mass. If I have full tanks, it will be sluggish, if I’ve already burned off have my fuel, it will be more responsive.

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So, So, a suic suicid idee burn burn to me soun sounds ds like, like, well. well. . . just just plain plain suici suicide de (I gues guesss the the burn part comes in when the explosion happens). But we can work work with this. . . instead instead of being super cautious (like (like I was above) above) and decelerating to 10 10 m/s m/s at at 200 meters of altitude, you can ”semi-suicide” and let it ride until about 100 or even 50 meters, then burn full thrust to cancel all that vertical vertical velocity velocity, and just be cautious cautious those last 25-50 meters. meters. It’s really up to you. ∼

A suicide burn is nothing more than a launch in reverse and is truly the most efficien efficientt (fuel(fuel-wis wise) e) method method of perform performing ing a landin landing. g. I think think an unassi unassiste sted d (i.e. (i.e. manual) suicide burn is just crazy. No one in real life would even attempt to perform such a maneuver without the assistance of a computer (MechJeb, anyone?), but to each his own. It would be like giving the astronauts on the shuttle manual control of engine gimbals to maintain the attitude of the craft during launch (yeah, that would end well!). I hope this information will help you on your way to planting flags on various celestial bodies in the Kerbol system!

Thank You! Thank you for reading this book! It was a joy to write and I anticipate the other volumes will be the same. Stay tuned for news on the next volume!

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Kerbal Space Program - The Missing Manual - Volume I.pdf

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