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수포자를 위한 KSP 튜토리얼

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

물리학에 관하여

궤도 메카닉의 많은 부분들은 직관에 어긋난다. 우리들 중 대부분은 우주에 가 본적이 없기에 '어떻게 작동하는가' 에 대한 우리의 직감은 우리가 어떻게 그것들을 경험하느냐에 바탕한다. 역사적으로도 사실 이것이 물리학에서의 주된 난제였다. 행성들이 어떻게 움직이는지 실제로 이해하기 위해 직감과 다른 방식으로 생각해야만 하기 때문이다. 여기서 우리는 몇가지 기본 물리학 개념에 대해 설명하겠다. 흥미있는 독자들은 Isaac Newton 을 읽어보고 이 아이디어들을 발전 시켜보길 바란다. 완벽히 철저한 설명은 아니지만, 어떻게 동작하는지에 대한 직관적 이해를 돕는다

속도(Velocity), 속력(Speed), 마찰, 그리고 가속도

당신이 차를타고 시속 113킬로미터로 달리고 있다고 하자. 만약 당신이 기어를 중립에 놓으면 차는 점점 속력이 줄어 결국 멈추게 될것이다. 우리는 차가 같은 속도를 유지하려면 가속페달을 계속 밟아야만 한다는 것을 직감적으로 안다. 우리가 이걸 생각하는 이유는 우리의 경험에 마찰이 포함되어 있기 때문이다. 자동차를 예로들면, 자동차 표면의 공기저항과 타이어와 지면의 마찰이 있다. 마찰은 우리를 뒤쪽으로 미는것으로 생각 될 수 있다. 반면 가속페달은 우리를 앞쪽으로 민다. 만약 엔진을 끄면 마찰은 우리를 계속 뒤로 밀기 때문에 차는 멈추게 된다. 우주에서는 마찰이 없다. 그러므로 우리를 뒤로 미는것은 아무것도 없다. 당신이 우주에 있고 거기에 행성이나 별같은것 없이 오직 당신만이 있다고 하자. 만약 당신이 움직인다면 당신은 일직선으로 영원히 계속 움직이게 된다.

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 뒤고 미는 힘이고 가속페달은 우리를 앞으로 미는 힘이다. 힘(force)은 기본적으로 '미는' 것이다. 속도는 당신이 움직이는 속력과 방향을 의미한다. 따라서 만약 당신의 속력이 같지만 방향을 바꾼다면 당신의 속도는 달라진다. 차에서 90도 회전하는것을 생각해보자. 당신은 회전하는 도중에 가속페달을 밟아야만 한다. 가속도는 속도의 변화일 뿐이다. 그러므로 물리학에서는 무엇인가 가속한다는것은 그것의 속력이 변하거나, 움직이는 방향이 변하거나, 둘 다 변한다는 것을 의미한다

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 된다. 이해를 돕기위해 실으로 묶인 야구공을 상상해 보자. 실의 끝을 잡고 원으로 빠르게 돌린다. 야구공은 당신 주변을 공전하게 된다. 만약 KSP에서 당신의 우주선이 행성이나 달에서 공전하개 되면 실이 야구공을 계속 당신 주변에 머무르게 하는것 처럼, 중력이 당신을 끌어당기게 된다. 만약 당신이 원형궤도에 있다면, 당신의 속도는 변하지 않는다 (항상 회전중이기 때문에 사실 항상 가속중이다).

행성은 당신을 계속 당기지만 당신이 충분히 빠르게 움직인다면 행성주변을 돌게 된다. 당신은 사실 자유낙하중이지만 충분히 빠르게 움직이고 있기에 계속 행성에서 빗나가는 것이다. 독자들은 원형궤도보다 편심성 궤도에서 이것이 보기 더 쉽다는것을 스스로 납득하길 바란다.  KSP에서는, 궤도에 안착했다면(이탈궤적에 있거나 표면에 충돌하려 하거나 하지 않으면서 대기로부터 완벽히 벗어난) 당신의 궤도는 절대 변하지 않는다. 다만 현실에서는 이렇게 단순하지 않으나 여기서는 설명하지 않는다. 

Orbital Velocity

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

이심률(Eccentricity,타원인 정도)

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.

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.

Determining 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 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.

Thrust and Thrust-to-Weight Ratio(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.

What about SRBs?

→ 참고하기: SRB

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 struts when we have trouble reaching orbit.

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.

마치며

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.