KSP math explained for the rest of us
I started playing KSP a few months ago. I tried to understand what everybody was talking about when they mentioned TWR, ISP, Δv, apoapsis, 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.
- Length: 20-30 minutes
- Difficulty: Easy
- For version: Every version
A few words about physics
Many parts 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 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 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.
Velocity, Speed Friction, and Acceleration
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 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.
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 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. 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.'
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.
Note for the interested readers: 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.
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.
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.
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.
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. This is important, and counterintuitive for us, so here is a little explanation:
Tada! Now you've read a full tutorial. Congratulations!