Difference between revisions of "Tutorial:Whats with all the math?/ko"

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{{underlinked|July 2014}}
 
{{underlinked|July 2014}}
  
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=KSP math explained for the rest of us=
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=수포자를 위한 KSP 튜토리얼=
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I started playing KSP a few months ago. I tried to understand what everybody was talking about when they mentioned [[Thrust-to-weight ratio|TWR]], [[Specific impulse|ISP]], Δv, [[Orbit#Apoapsis|apoapsis]], [[Orbit#Eccentricity|eccentricity]], and a whole bunch of other terms from math and physics. The learning curve is high, but this tutorial will try to explain what all these different numbers mean and why they are important for people who do not have a mathematical background.
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저는 몇 달 전 부터 KSP를 플레이 하기 시작했습니다. 저는 다른사람들이 언급하는 [[Thrust-to-weight ratio|TWR]], [[Specific impulse|ISP]], Δv, [[Orbit#Apoapsis|apoapsis]], [[Orbit#Eccentricity|eccentricity]] 과 그 외 수많은 용어,공식,물리학을 이해하려고 노력했습니다. 진입장벽은 높지만 이 튜토리얼은 이 모든 서로다른 수치들이 무엇을 의미하는지, 그리고 왜 그것들이 수학적 사전지식이 없는 사람들에게 중요한 것 인지 설명 할 것입니다.  
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==A few words about physics==
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Many papartsrts of orbital mechanics can be counter-intuitive for people. Most of us have not been to space, so our intuition about how things should work is based  on how we experience them. Historically, this was actually a major sticking point in [[Wikipedia:physics|physics]] because we had to think in ways that were different from our intuition to really understand how planets moved. Here we will explain a few basic physics concepts, although interested readers are encouraged to research the work of [[Wikipedia:Isaac Newton|Isaac Newton]] and the development of these ideas. It should be noted that these explanations are not entirely rigorous, and simply meant to give people an intuitive understanding of how things work.
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==물리학에 관하여==
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===Velocity, Speed, Friction, and Acceleration===
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궤도 메카닉의 많은 부분들은 직관에 어긋납니다. 우리들 중 대부분은 우주에 가 본적이 없기에 '어떻게 작동하는가' 에 대한 우리의 직감은 우리가 어떻게 그것들을 경험하느냐에 바탕합니다. 역사적으로도 사실 이것이 물리학에서의 주된 난제였습니다. 행성들이 어떻게 움직이는지 실제로 이해하기 위해 직감과 다른 방식으로 생각해야만 하기 때문입니다.
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Say you are driving down the street at 70 miles per hour (about 113 kilometers per hour). If you were to turn put your car's engine in neutral, your car would slow to a stop. Our intuition says that if we want to keep moving the same speed, we need to keep pushing the gas pedal, or we will slow down. The reason we think this is that all our experiences involve [[Wikipedia:friction|friction]]. In the car example, there is air friction on the surface of the car and friction from the wheels on the ground. Friction can be thought of as pushing us backwards, while the gas pedal pushes us forwards. If we stop the engine, friction continues to push us backwards, which is why we stop.  
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여기서 우리는 몇가지 기본 물리학 개념에 대해 설명하겠습니다. 흥미가 있는 독자들은 [[Wikipedia:Isaac Newton|Isaac Newton]] 을 읽어보시기 바랍니다. 완벽한 설명은 아니지만, 요소들이 어떻게 작동하는지에 대한 직관적인 이해를 도울것입니다.  
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In space, there is no friction. Therefore, there is nothing pushing us backwards. Imagine you are in space, and there are no planets or stars or anything but you. If you are moving, you will keep moving in a straight line forever. This comes from one of [[Wikipedia:Newton's laws of motion|Newton's laws of motion]], that an object in motion stays in motion and an object at rest stays at rest unless acted upon by a [[Wikipedia:force|force]]. On earth, friction is a force that pushes us backwards, and the gas pedal applies a force that pushes us forwards. A force is basically just a 'push.'
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When we say velocity, we mean the speed you are moving in, and the direction you are moving in. Therefore, if your speed stays the same but you are turning, then your velocity is changing. Think about making a 90-degree turn in a car, you have to push the gas pedal down during the turn. Acceleration is nothing more than a change in velocity. Therefore in physics, when we say that something is accelerating, either it's speed is changing, the direction it is moving is changing, or both.
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===속도(Velocity), 속력(Speed), 마찰, 그리고 가속도===
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====Side-note for interested and advanced readers====
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달리는 자동차가 있습니다. 만약 가속페달에서 발을 때면 차는 점점 속력이 줄어 결국 멈추게 될것입니다. 우리는 차가 같은 속도를 유지하려면 가속페달을 계속 밟아야만 한다는 것을 직감적으로 알고있습니다. 우리가 이 이야기를 하는 이유는 우리의 생활에 마찰력이 포함되어 있기 때문입니다. 달리는 자동차의 경우, 자동차 표면의 공기저항과 타이어와 지면의 마찰이 있습니다. 마찰은 우리를 뒤쪽으로 미는것으로 생각 될 수 있습니다. 반면 가속페달은 우리를 앞쪽으로 밀어냅니다. 만약 엔진을 끄면 마찰은 우리를 계속 뒤로 밀기 때문에 차는 멈추게 됩니다.  
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우주에서는 마찰이 없습니다. 그러므로 우리를 뒤로 미는것은 아무것도 없습니다. 당신이 우주에 있고 거기에 행성이나 별같은것 없이 오직 당신만이 있다고 할 때, 만약 당신이 움직인다면 당신은 일직선으로 영원히 계속 움직이게 됩니다.  
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This comes from one of [[Wikipedia:Newton's laws of motion|Newton's laws of motion]], that an object in motion stays in motion and an object at rest stays at rest unless acted upon by a [[Wikipedia:force|force]].
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지구에서는 마찰은 우리를 뒤로 미는 힘이고 가속페달은 우리를 앞으로 미는 힘입니다. 힘(force)은 기본적으로 '미는' 것입니다.  
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속도는 당신이 움직이는 속력과 방향을 의미합니다. 따라서 만약 당신의 속력이 같지만 방향을 바꾼다면 당신의 속도는 달라집니다. 차에서 90도 회전하는것을 예로 들어 봅시다. 당신은 회전하는 도중에 가속페달을 밟아야만 합니다. 가속도는 속도의 변화일 뿐입니다. 그러므로 물리학에서는 무엇인가 가속한다는것은 그것의 속력이 변하거나, 움직이는 방향이 변하거나, 둘 다 변한다는 것을 의미합니다
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====흥미있거나 숙련된 독자를 위한 사이드 노트====
 
There is an important mathematical relationship between position, velocity, and acceleration. In fact, the exploration of this relationship by [[Wikipedia:Isaac Newton|Isaac Newton]] and [[Wikipedia:Gottfried Leibniz|Gottfried Leibniz]] lead to the invention of what we math people now call [[Wikipedia:Calculus|Calculus]].
 
There is an important mathematical relationship between position, velocity, and acceleration. In fact, the exploration of this relationship by [[Wikipedia:Isaac Newton|Isaac Newton]] and [[Wikipedia:Gottfried Leibniz|Gottfried Leibniz]] lead to the invention of what we math people now call [[Wikipedia:Calculus|Calculus]].
  
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==Orbital Mechanics==
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==궤도 메카닉==
 
{{See also|Orbit}}
 
{{See also|Orbit}}
  
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Since we are trying to play Kerbal Space Program, we will spend a significant amount of time dealing with orbit. To help us think about being in orbit, we will first describe a 'thought experiment', although I would encourage anybody to go outside and give this a try. Imagine you tie a baseball to one end of a string. Now imagine you hold the other end of the string and spin around in a circle very quickly. The ball will 'orbit' around you. When your spacecraft orbits a planet or moon in KSP, the gravity pulls you in like the string keeps the ball near you.  
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KSP를 플레이 하려고 하면 우리는 상당한 시간을 궤도와 관련된 문제를 해결하는데 보내게 됩니다. 이해를 돕기위해 실으로 묶인 야구공을 상상해 봅시다. 실의 끝을 잡고 원으로 빠르게 돌립니다. 야구공은 당신 주변을 공전하게 됩니다. 만약 KSP에서 당신의 우주선이 행성이나 달에서 공전하게 되면 실이 야구공을 계속 당신 주변에 머무르게 하는것 처럼, 중력이 당신을 끌어당기게 됩니다.
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If you are in a circular orbit, your speed will not change (note that since you are always turning, you are actually always accelerating). The planet is pulling you straight down, but you are already moving fast enough away from the planet that you move in a circle. You are actually in free-fall, but you are moving so fast that you miss the planet every time. Readers are encouraged to convince themselves of this, it is easier to see in a highly eccentric orbit than in a circular orbit, more on that later.
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만약 당신이 원형궤도에 있다면, 당신의 속도는 변하지 않습니다 (항상 회전중이기 때문에 사실 항상 가속중입니다).
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In KSP, as long as you are in a well behaved orbit (not on an escape trajectory, not going to crash into the surface, completely above the atmosphere), your orbit will never change. You will keep moving in the same path forever. In the real world, it's not quite that simple, but that is outside the scope of this explanation.
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행성은 당신을 계속 당기지만 당신이 충분히 빠르게 움직인다면 행성주변을 돌게 됩니다. 당신은 사실 자유낙하중이지만 충분히 빠르게 움직이고 있기에 계속 행성에서 빗나가는 것입니다. 독자들은 원형궤도보다 타원형 궤도에서 이것이 보기 더 쉽다는것을 스스로 이해하길 바랍니다. KSP에서는, 궤도에 안착했다면(이탈궤적에 있거나 행성의 표면에 충돌하려 하지 않으면서 대기로부터 완벽히 벗어난) 당신의 궤도는 절대 변하지 않습니다. 현실에서는 이렇게 단순하지는 않습니다만 여기서는 다루지 않겠습니다.  
  
 
===Orbital Velocity===
 
===Orbital Velocity===
 
[[File:Simple orbit diagram.svg|thumb|upright=3.0]]
 
[[File:Simple orbit diagram.svg|thumb|upright=3.0]]
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Given a fixed, stable orbit, your velocity (the speed you are moving and direction you are moving in) depends '''only''' on your position in that orbit. Understanding this is incredibly important, so here is some explanation. In the image to the right, look at any point on the bigger shape (the ellipse). If you don't burn your engines, your speed when you are at that point will be the same as when you return to that point after one orbital period (the amount of time your orbit takes to complete one full revolution).
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사실, 안정된 궤도에서, 당신의 속도는 (당신이 움직이는 속력과 방향) 오로지 궤도에서의 당신의 위치에 의해서만 영향을 받습니다. 이걸 이해하는것은 매우 중요하기때문에 예를 들겠습니다. 오른쪽 그림에서, 타원의 아무 지점을 보십시오. 당신이 엔진을 가동하지 않는다면, 그 지점에서의 당신의 속력은 한바퀴 궤도를 한바퀴 돌고나서도 같습니다.
  
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===Eccentricity===
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===이심률(Eccentricity,타원인 정도)===
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[[Orbit#Eccentricity|Eccentricity]] is a number to describe the 'shape' of our orbit. The closer our eccentricity is to 0, the more circular our orbit is. Elliptical orbits have eccentricity somewhere between 0 and 1. In the image to the right, the smaller, circular orbit would have an eccentricity of 0, and the larger orbit would have eccentricity around 1/2 (very rough number). Eccentricity of 1 or greater is what we call a parabolic or hyperbolic orbit. All that means is that you will not stay in orbit, you will escape the planet's sphere of influence and never come back without accelerating back towards it somehow.
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[[Orbit#Eccentricity|Eccentricity]] 은 궤도의 모양을 설명하는 숫자입니다. 이심률이 0에 가까울수록 궤도는 정원에 가깝습니다. 타원형 궤도의 이심률은 0과 1 사이입니다. 오른쪽 그림에서 더 작은, 원형 궤도는 0의 이심률을 가집니다. 나머지 하나(타원형)는 대략 1/2의 이심률을 가집니다. 이심률이 1이거나 1보다 더 클 경우 parabolic 또는 hyperbolic 궤도라고 부릅니다. 그것은 당신이 궤도상에 머무르지 않고 행성의 영향권 바깥으로 벗어나 추가적인 가속 없이는 절대 다시 돌아 올 수 없다는것을 의미합니다.
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====Side-note for interested and advanced readers====
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==== 흥미있거나 숙련된 독자를 위한 사이드 노트 ====
 
The circle, ellipse, parabola, and hyperbola are all [[Wikipedia:Conic section|conics]]. A troubling problem then becomes modeling [[Wikipedia:Precession#Perihelion precession| perihelion precessions]] whose orbits don't end and start at the same place.
 
The circle, ellipse, parabola, and hyperbola are all [[Wikipedia:Conic section|conics]]. A troubling problem then becomes modeling [[Wikipedia:Precession#Perihelion precession| perihelion precessions]] whose orbits don't end and start at the same place.
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===Maneuvers===
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===기동===
 
{{See also|Basic maneuvers}}
 
{{See also|Basic maneuvers}}
  
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Say we are at point A in the figure to the right, and we point the nose of our rocket in the direction of the arrow ([[prograde]], the direction we are moving) and burn our engines for a while. In reality, this burn takes a certain amount of time, and our position changes during that time. However, that is some much more complicated math, so we are going to pretend that the burn starts and ends instantly. Basically, we pretend that we '''accelerate''' by a certain amount at point A. Since we are still at point A, when we complete one orbital period, we will be back at point A. However, the opposite side of our orbit will move away from us, making our orbit more eccentric in this case. The important take-away here is that we '''accelerate''' at point A to change our '''velocity'''. This changes the shape of our orbit. Say our original velocity was 10,000 m/s (10 kilometers per second), and our new speed is 10,200 m/s. Our velocity changed by 200 m/s, and this is our Δv!  
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Say we are at point A in the figure to the right, and we point the nose of our rocket in the direction of the arrow ([[prograde]], the direction we are moving) and burn our engines for a while. In reality, this burn takes a certain amount of time, and our position changes during that time. However, that is some much more complicated math, so we are going to pretend that the burn starts and ends instantly. Basically, we pretend that we '''accelerate''' by a certain amount at point A. Since we are still at point A, when we complete one orbital period, we will be back at point A. However, the opposite side of our orbit will move away from us, making our orbit more eccentric in this case. The important take-away here is that we '''accelerate''' at point A to change our '''velocity'''. This changes the shape of our orbit. Say our original velocity was 10,000 m/s (10 kilometers per second), and our new speed is 10,200 m/s. Our velocity changed by 200 m/s, and this is our Δv!
  
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=What does all this mean?=
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=이것들이 다 뭘 의미하는가?=
 
Okay, by now if you are still reading, you are probably starting to think "How does all this stuff help me go to space!?" Well, we are going to start talking about that right now!
 
Okay, by now if you are still reading, you are probably starting to think "How does all this stuff help me go to space!?" Well, we are going to start talking about that right now!
  
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==Why is Δv so important?==
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==왜 Δv 가 그렇게 중요한가?==
 
Note that above, when we talked about how fast our rocket was moving, or how it's orbit changed, we said nothing about the mass of the rocket. We don't know if we are talking about a tiny satellite, a spaceplane, or a huge rocket, but we know that how our orbit changes is only dependent on how our velocity changes! This is why we talk about Δv so much, because no matter what rocket you build, it takes the same amount of Δv to go from point A to point B in space. Furthermore, we know it takes about 4600 Δv to get into orbit around Kerbin, so if we know the Δv our ascent stage generates, we know if it will get us to space! This is why Δv is probably the most important thing to understand.
 
Note that above, when we talked about how fast our rocket was moving, or how it's orbit changed, we said nothing about the mass of the rocket. We don't know if we are talking about a tiny satellite, a spaceplane, or a huge rocket, but we know that how our orbit changes is only dependent on how our velocity changes! This is why we talk about Δv so much, because no matter what rocket you build, it takes the same amount of Δv to go from point A to point B in space. Furthermore, we know it takes about 4600 Δv to get into orbit around Kerbin, so if we know the Δv our ascent stage generates, we know if it will get us to space! This is why Δv is probably the most important thing to understand.
  
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==Determining Δv==
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==Δv를 결정==
 
Since this is an article for people without mathematical backgrounds, we are not going to look at the formula for calculating Δv. There are great [[Tutorial:Advanced_Rocket_Design|tutorials]] explaining the [[Tutorial:_Basic_Orbiting_(Math)|equations]] for all of this, and readers are encouraged to consult them for a more rigorous understanding. However, most people see big, complicated equations and they stop reading, whether it comes from some post-traumatic stress left over from school, or being generally uninterested in mathematics, and that is okay. Here, we are going to simply look at what Δv depends on, that is, what effect does building a rocket in one way or another impact Δv?
 
Since this is an article for people without mathematical backgrounds, we are not going to look at the formula for calculating Δv. There are great [[Tutorial:Advanced_Rocket_Design|tutorials]] explaining the [[Tutorial:_Basic_Orbiting_(Math)|equations]] for all of this, and readers are encouraged to consult them for a more rigorous understanding. However, most people see big, complicated equations and they stop reading, whether it comes from some post-traumatic stress left over from school, or being generally uninterested in mathematics, and that is okay. Here, we are going to simply look at what Δv depends on, that is, what effect does building a rocket in one way or another impact Δv?
  
 
There are mods that will tell you what your stage's Δv is, and I personally use one of them, but since this article is about vanilla KSP we will leave them out of this discussion. There are also mods that will do your entire take-off, gravity turn, and all your orbital maneuvers for you. While these can be fun, I personally do not believe in using them outside of sandbox mode for experimental purposes, since the point of playing the game is learning for me.
 
There are mods that will tell you what your stage's Δv is, and I personally use one of them, but since this article is about vanilla KSP we will leave them out of this discussion. There are also mods that will do your entire take-off, gravity turn, and all your orbital maneuvers for you. While these can be fun, I personally do not believe in using them outside of sandbox mode for experimental purposes, since the point of playing the game is learning for me.
  
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===Thrust and Thrust-to-Weight Ratio(TWR)===
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===추진력과 추진력대 중량비(TWR)===
 
{{See also|Thrust-to-weight ratio}}
 
{{See also|Thrust-to-weight ratio}}
  
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TWR changes during the flight of a rocket. As you burn more fuel, you lose mass, and your TWR increases since your weight decreases. TWR also depends on what planet/moon you are on since each celestial body has different gravity. Therefore, the same rocket with the same amount of fuel as a lower TWR on Eve than it does on Kerbin.
 
TWR changes during the flight of a rocket. As you burn more fuel, you lose mass, and your TWR increases since your weight decreases. TWR also depends on what planet/moon you are on since each celestial body has different gravity. Therefore, the same rocket with the same amount of fuel as a lower TWR on Eve than it does on Kerbin.
  
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===So, what engine should my rocket use, and what is engine ISP?===
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===어떤 엔진을 써야하는가?, engine ISP는 무었인가?===
 
{{See also|Specific impulse}}
 
{{See also|Specific impulse}}
 
Let's start with engine ISP. Basically, it tells you how fuel-efficient your engine is. An engine with a higher ISP will give you more Δv for the same amount of fuel as an engine with lower ISP. However, it is important to keep in mind the thrust different engines generate and strike a balance between ISP, which determines Δv, and thrust, which effects TWR. Put in different terms, the choice is between how much your spacecraft accelerates and how fast your spacecraft accelerates.
 
Let's start with engine ISP. Basically, it tells you how fuel-efficient your engine is. An engine with a higher ISP will give you more Δv for the same amount of fuel as an engine with lower ISP. However, it is important to keep in mind the thrust different engines generate and strike a balance between ISP, which determines Δv, and thrust, which effects TWR. Put in different terms, the choice is between how much your spacecraft accelerates and how fast your spacecraft accelerates.
  
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====Example====
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====예시====
 
The [[LV-909 Liquid Fuel Engine]] engine has ISP of 300 in atmosphere or 390 in space. The [[Rockomax "Mainsail" Liquid Engine]] has ISP of 320 in atmosphere or 360 in space. This doesn't seem like much of a difference. However, the mainsail can generate a thrust of 1500, while the LV-909 can only generate a thrust of 50. Therefore, the LV-909 will accelerate your rocket more slowly. Sometimes, you need to generate a lot of thrust very quickly (like when you are trying to go from the ground to orbit), so an engine with lower ISP but higher thrust may be better.
 
The [[LV-909 Liquid Fuel Engine]] engine has ISP of 300 in atmosphere or 390 in space. The [[Rockomax "Mainsail" Liquid Engine]] has ISP of 320 in atmosphere or 360 in space. This doesn't seem like much of a difference. However, the mainsail can generate a thrust of 1500, while the LV-909 can only generate a thrust of 50. Therefore, the LV-909 will accelerate your rocket more slowly. Sometimes, you need to generate a lot of thrust very quickly (like when you are trying to go from the ground to orbit), so an engine with lower ISP but higher thrust may be better.
  
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==What about SRBs?==
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==SRB(고체연료 부스터)==
 
{{See also|SRB}}
 
{{See also|SRB}}
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My first ship to successfully orbit [[Minmus]] had around 50 SRB's on it. I do not recommend this approach. First off, as of .24, we have to pay for parts, so efficiency is important. Second, it was very difficult to get enough struts on the ship to get it to stay in one piece. Third, it was very difficult to steer, so my [[gravity turn]] was very inefficient. I only mention this because a common part of the learning curve for new players is to add more SRB's and more [[strut]]s when we have trouble reaching orbit.
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제 첫번째 우주선은 [[Minmus]]궤도에 오르는데 성공했는데 대략 50여개의 고체연료 부스터를 달고 있었습니다. 저는 이런 방식을 추천하지 않습니다. 첫째로, 우리는 부품들에 대한 비용을 지불해야 합니다. 때문에 효율성은 중요합니다. 둘째로, 우주선이 한 조각으로 유지되기 위한 충분한 스트럿트들을 가지기가 매우 힘들었습니다 세번째로, 매우 조종하기 어려웠습니다. 그래서 제 [[gravity turn]] 은 매우 비효율적 이었습니다. 제가 이것을 언급하는 이유는 새 플레이들이 궤도에 도달하는데 어려움을 겪을때 흔히들 더 많은 고체연료 부스터와 스트러트를 추가하기 때문입니다.
  
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SRB's add a good amount of thrust, but also add weight. Therefore, the more you add, the less of a benefit you are getting. Also, since they only have one setting, which is to burn until empty, they are best used for ascent stages only, since we need more control when we are in space. Therefore, my recommendation is that if you are having trouble getting into orbit, putting a few SRB's on the side of your rocket as a first stage may help. As you unlock more parts in career mode, and get a better feel for getting into orbit, you may or may not continue to use them.
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고체연료 부스터는 많은 추진력을 주지만 동시에 무겁습니다. 그러므로 우주선에 더 달수록 얻는 이득은 줄어듭니다. 또한 가용한 유일한 셋팅이 연료를 다쓸때까지 계속 태우는것 밖에 없기때문에 상승 단계에서만 쓰는것이 좋습니다. 우주에 나가고 나서부터는 좀 더 통제력이 필요하기 때문입니다. 그러므로 저는 당신이 궤도에 도달하는데 어려움을 겪는다면 로켓의 측면에 첫 스테이지로써 고체 연료 부스터를 다는것을 추천합니다. 커리어 모드라면 더 많은 부품들이 언락되고 더 쉽게 궤도에 오를 수 있기 때문에 당신은 더이상 고체연료 부스터를 쓰지 않게 될 지도 모릅니다.  
  
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==Final Notes==
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==마치며==
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Hopefully this tutorial has given you a decent primer on what all the math really means. I highly recommend experimenting with different rocket designs, reading more rigorous mathematical explanations, and continuing to learn, since this is just a baseline to get you started.
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이 튜토리얼이 여러분에게 수많은 수학적 요소들이 실제로 뭘 의미하는지에 대한 개괄적인 이해에 도움이 되었기를 바랍니다. 이 글은 그저 시작일 뿐이니 앞으로 다양한 로켓 디자인을 시도해보고 더 상세한 수학적 설명을 읽어보며 계속해서 배워나가기 바랍니다.

Latest revision as of 03:31, 23 July 2015

This page needs more links to other articles to help integrate it into the Kerbal Space Program Wiki

수포자를 위한 KSP 튜토리얼

저는 몇 달 전 부터 KSP를 플레이 하기 시작했습니다. 저는 다른사람들이 언급하는 TWR, ISP, Δv, apoapsis, eccentricity 과 그 외 수많은 용어,공식,물리학을 이해하려고 노력했습니다. 진입장벽은 높지만 이 튜토리얼은 이 모든 서로다른 수치들이 무엇을 의미하는지, 그리고 왜 그것들이 수학적 사전지식이 없는 사람들에게 중요한 것 인지 설명 할 것입니다.

물리학에 관하여

궤도 메카닉의 많은 부분들은 직관에 어긋납니다. 우리들 중 대부분은 우주에 가 본적이 없기에 '어떻게 작동하는가' 에 대한 우리의 직감은 우리가 어떻게 그것들을 경험하느냐에 바탕합니다. 역사적으로도 사실 이것이 물리학에서의 주된 난제였습니다. 행성들이 어떻게 움직이는지 실제로 이해하기 위해 직감과 다른 방식으로 생각해야만 하기 때문입니다. 여기서 우리는 몇가지 기본 물리학 개념에 대해 설명하겠습니다. 흥미가 있는 독자들은 Isaac Newton 을 읽어보시기 바랍니다. 완벽한 설명은 아니지만, 요소들이 어떻게 작동하는지에 대한 직관적인 이해를 도울것입니다.

속도(Velocity), 속력(Speed), 마찰, 그리고 가속도

달리는 자동차가 있습니다. 만약 가속페달에서 발을 때면 차는 점점 속력이 줄어 결국 멈추게 될것입니다. 우리는 차가 같은 속도를 유지하려면 가속페달을 계속 밟아야만 한다는 것을 직감적으로 알고있습니다. 우리가 이 이야기를 하는 이유는 우리의 생활에 마찰력이 포함되어 있기 때문입니다. 달리는 자동차의 경우, 자동차 표면의 공기저항과 타이어와 지면의 마찰이 있습니다. 마찰은 우리를 뒤쪽으로 미는것으로 생각 될 수 있습니다. 반면 가속페달은 우리를 앞쪽으로 밀어냅니다. 만약 엔진을 끄면 마찰은 우리를 계속 뒤로 밀기 때문에 차는 멈추게 됩니다. 우주에서는 마찰이 없습니다. 그러므로 우리를 뒤로 미는것은 아무것도 없습니다. 당신이 우주에 있고 거기에 행성이나 별같은것 없이 오직 당신만이 있다고 할 때, 만약 당신이 움직인다면 당신은 일직선으로 영원히 계속 움직이게 됩니다. 

This comes from one of Newton's laws of motion, that an object in motion stays in motion and an object at rest stays at rest unless acted upon by a force.

지구에서는 마찰은 우리를 뒤로 미는 힘이고 가속페달은 우리를 앞으로 미는 힘입니다. 힘(force)은 기본적으로 '미는' 것입니다. 속도는 당신이 움직이는 속력과 방향을 의미합니다. 따라서 만약 당신의 속력이 같지만 방향을 바꾼다면 당신의 속도는 달라집니다. 차에서 90도 회전하는것을 예로 들어 봅시다. 당신은 회전하는 도중에 가속페달을 밟아야만 합니다. 가속도는 속도의 변화일 뿐입니다. 그러므로 물리학에서는 무엇인가 가속한다는것은 그것의 속력이 변하거나, 움직이는 방향이 변하거나, 둘 다 변한다는 것을 의미합니다

흥미있거나 숙련된 독자를 위한 사이드 노트

There is an important mathematical relationship between position, velocity, and acceleration. In fact, the exploration of this relationship by Isaac Newton and Gottfried Leibniz lead to the invention of what we math people now call Calculus.

궤도 메카닉

→ 참고하기: Orbit

KSP를 플레이 하려고 하면 우리는 상당한 시간을 궤도와 관련된 문제를 해결하는데 보내게 됩니다. 이해를 돕기위해 실으로 묶인 야구공을 상상해 봅시다. 실의 끝을 잡고 원으로 빠르게 돌립니다. 야구공은 당신 주변을 공전하게 됩니다. 만약 KSP에서 당신의 우주선이 행성이나 달에서 공전하게 되면 실이 야구공을 계속 당신 주변에 머무르게 하는것 처럼, 중력이 당신을 끌어당기게 됩니다. 만약 당신이 원형궤도에 있다면, 당신의 속도는 변하지 않습니다 (항상 회전중이기 때문에 사실 항상 가속중입니다). 행성은 당신을 계속 당기지만 당신이 충분히 빠르게 움직인다면 행성주변을 돌게 됩니다. 당신은 사실 자유낙하중이지만 충분히 빠르게 움직이고 있기에 계속 행성에서 빗나가는 것입니다. 독자들은 원형궤도보다 타원형 궤도에서 이것이 보기 더 쉽다는것을 스스로 이해하길 바랍니다. KSP에서는, 궤도에 안착했다면(이탈궤적에 있거나 행성의 표면에 충돌하려 하지 않으면서 대기로부터 완벽히 벗어난) 당신의 궤도는 절대 변하지 않습니다. 현실에서는 이렇게 단순하지는 않습니다만 여기서는 다루지 않겠습니다.

Orbital Velocity

Simple orbit diagram.svg

사실, 안정된 궤도에서, 당신의 속도는 (당신이 움직이는 속력과 방향) 오로지 궤도에서의 당신의 위치에 의해서만 영향을 받습니다. 이걸 이해하는것은 매우 중요하기때문에 예를 들겠습니다. 오른쪽 그림에서, 타원의 아무 지점을 보십시오. 당신이 엔진을 가동하지 않는다면, 그 지점에서의 당신의 속력은 한바퀴 궤도를 한바퀴 돌고나서도 같습니다.

이심률(Eccentricity,타원인 정도)

Eccentricity 은 궤도의 모양을 설명하는 숫자입니다. 이심률이 0에 가까울수록 궤도는 정원에 가깝습니다. 타원형 궤도의 이심률은 0과 1 사이입니다. 오른쪽 그림에서 더 작은, 원형 궤도는 0의 이심률을 가집니다. 나머지 하나(타원형)는 대략 1/2의 이심률을 가집니다. 이심률이 1이거나 1보다 더 클 경우 parabolic 또는 hyperbolic 궤도라고 부릅니다. 그것은 당신이 궤도상에 머무르지 않고 행성의 영향권 바깥으로 벗어나 추가적인 가속 없이는 절대 다시 돌아 올 수 없다는것을 의미합니다.

흥미있거나 숙련된 독자를 위한 사이드 노트

The circle, ellipse, parabola, and hyperbola are all conics. A troubling problem then becomes modeling perihelion precessions whose orbits don't end and start at the same place.

기동

→ 참고하기: Basic maneuvers

Say we are at point A in the figure to the right, and we point the nose of our rocket in the direction of the arrow (prograde, the direction we are moving) and burn our engines for a while. In reality, this burn takes a certain amount of time, and our position changes during that time. However, that is some much more complicated math, so we are going to pretend that the burn starts and ends instantly. Basically, we pretend that we accelerate by a certain amount at point A. Since we are still at point A, when we complete one orbital period, we will be back at point A. However, the opposite side of our orbit will move away from us, making our orbit more eccentric in this case. The important take-away here is that we accelerate at point A to change our velocity. This changes the shape of our orbit. Say our original velocity was 10,000 m/s (10 kilometers per second), and our new speed is 10,200 m/s. Our velocity changed by 200 m/s, and this is our Δv!

이것들이 다 뭘 의미하는가?

Okay, by now if you are still reading, you are probably starting to think "How does all this stuff help me go to space!?" Well, we are going to start talking about that right now!

왜 Δv 가 그렇게 중요한가?

Note that above, when we talked about how fast our rocket was moving, or how it's orbit changed, we said nothing about the mass of the rocket. We don't know if we are talking about a tiny satellite, a spaceplane, or a huge rocket, but we know that how our orbit changes is only dependent on how our velocity changes! This is why we talk about Δv so much, because no matter what rocket you build, it takes the same amount of Δv to go from point A to point B in space. Furthermore, we know it takes about 4600 Δv to get into orbit around Kerbin, so if we know the Δv our ascent stage generates, we know if it will get us to space! This is why Δv is probably the most important thing to understand.

Δv를 결정

Since this is an article for people without mathematical backgrounds, we are not going to look at the formula for calculating Δv. There are great tutorials explaining the equations for all of this, and readers are encouraged to consult them for a more rigorous understanding. However, most people see big, complicated equations and they stop reading, whether it comes from some post-traumatic stress left over from school, or being generally uninterested in mathematics, and that is okay. Here, we are going to simply look at what Δv depends on, that is, what effect does building a rocket in one way or another impact Δv?

There are mods that will tell you what your stage's Δv is, and I personally use one of them, but since this article is about vanilla KSP we will leave them out of this discussion. There are also mods that will do your entire take-off, gravity turn, and all your orbital maneuvers for you. While these can be fun, I personally do not believe in using them outside of sandbox mode for experimental purposes, since the point of playing the game is learning for me.

추진력과 추진력대 중량비(TWR)

→ 참고하기: Thrust-to-weight ratio

Thrust is the amount of force (how much 'push') your engine is generating. Recall the car metaphor where the car is going down the road, the engine pushes the car forward, and friction pushes the car backwards. Thrust is basically how hard the rocket is being pushed up from the surface of Kerbin.

We all know that heavy things are harder to pick up than lighter things. If you don't believe me, go lift a piece of paper off the ground over your head, and then do the same with a piece of furniture, like a couch. The couch is much harder to pick up. The same thing is true in rocket science, heavier rockets are harder to pick up (lift off) than lighter rockets! This is why TWR is so important, the rocket's engines are pushing the rocket up, and gravity is pushing the rocket back down. If you have ever arm-wrestled, you know that the person who pushes harder is going to win. The rocket's weight is how hard gravity is pushing down. Therefore, the rocket's thrust must push harder than gravity, or you are not going to space. A TWR less than one means that gravity is going to win. A TWR over one means the rocket is going to win, and a TWR of exactly one means the rocket will hover in place. However, once you are in a stable obit, you no longer need a TWR over one to change your velocity.

Side-note for interested and advanced readers

TWR changes during the flight of a rocket. As you burn more fuel, you lose mass, and your TWR increases since your weight decreases. TWR also depends on what planet/moon you are on since each celestial body has different gravity. Therefore, the same rocket with the same amount of fuel as a lower TWR on Eve than it does on Kerbin.

어떤 엔진을 써야하는가?, engine ISP는 무었인가?

→ 참고하기: Specific impulse

Let's start with engine ISP. Basically, it tells you how fuel-efficient your engine is. An engine with a higher ISP will give you more Δv for the same amount of fuel as an engine with lower ISP. However, it is important to keep in mind the thrust different engines generate and strike a balance between ISP, which determines Δv, and thrust, which effects TWR. Put in different terms, the choice is between how much your spacecraft accelerates and how fast your spacecraft accelerates.

예시

The LV-909 Liquid Fuel Engine engine has ISP of 300 in atmosphere or 390 in space. The Rockomax "Mainsail" Liquid Engine has ISP of 320 in atmosphere or 360 in space. This doesn't seem like much of a difference. However, the mainsail can generate a thrust of 1500, while the LV-909 can only generate a thrust of 50. Therefore, the LV-909 will accelerate your rocket more slowly. Sometimes, you need to generate a lot of thrust very quickly (like when you are trying to go from the ground to orbit), so an engine with lower ISP but higher thrust may be better.

SRB(고체연료 부스터)

→ 참고하기: SRB

제 첫번째 우주선은 Minmus궤도에 오르는데 성공했는데 대략 50여개의 고체연료 부스터를 달고 있었습니다. 저는 이런 방식을 추천하지 않습니다. 첫째로, 우리는 부품들에 대한 비용을 지불해야 합니다. 때문에 효율성은 중요합니다. 둘째로, 우주선이 한 조각으로 유지되기 위한 충분한 스트럿트들을 가지기가 매우 힘들었습니다 세번째로, 매우 조종하기 어려웠습니다. 그래서 제 gravity turn 은 매우 비효율적 이었습니다. 제가 이것을 언급하는 이유는 새 플레이들이 궤도에 도달하는데 어려움을 겪을때 흔히들 더 많은 고체연료 부스터와 스트러트를 추가하기 때문입니다.

고체연료 부스터는 많은 추진력을 주지만 동시에 무겁습니다. 그러므로 우주선에 더 달수록 얻는 이득은 줄어듭니다. 또한 가용한 유일한 셋팅이 연료를 다쓸때까지 계속 태우는것 밖에 없기때문에 상승 단계에서만 쓰는것이 좋습니다. 우주에 나가고 나서부터는 좀 더 통제력이 필요하기 때문입니다. 그러므로 저는 당신이 궤도에 도달하는데 어려움을 겪는다면 로켓의 측면에 첫 스테이지로써 고체 연료 부스터를 다는것을 추천합니다. 커리어 모드라면 더 많은 부품들이 언락되고 더 쉽게 궤도에 오를 수 있기 때문에 당신은 더이상 고체연료 부스터를 쓰지 않게 될 지도 모릅니다.

마치며

이 튜토리얼이 여러분에게 수많은 수학적 요소들이 실제로 뭘 의미하는지에 대한 개괄적인 이해에 도움이 되었기를 바랍니다. 이 글은 그저 시작일 뿐이니 앞으로 다양한 로켓 디자인을 시도해보고 더 상세한 수학적 설명을 읽어보며 계속해서 배워나가기 바랍니다.

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