Tutorial:How to Play

Introduction

Welcome to my tutorial of Kerbal Space Program. This guide is targeted at version 1.10.1, which is the latest version as of this writing. It assumes the availability of all expansions, but no mods. Obviously, those can change the game a lot.

So why do we need yet another tutorial? There is a lot of good information out there, including but not limited to elsewhere on this wiki. For one, a lot of it is outdated by now. While this guide will presumably also be outdated someday, there is always a need for new information to update the old that has become obsolete.

But there are two things that I wanted to focus on that most guides don't. First, the lengthy list of parts available to use can be rather bewildering to a new player. I go somewhat systematically through all of the major types of parts and explain what they are for.

Second, this guide has more of a focus on the underlying math and physics than most. Before you run away screaming, that does not mean lengthy algebraic derivations. I'll write down a handful of formulas, but not really do anything with them. But it does mean discussing the three great conservation laws of classical mechanics, explaining how some parts actually work in real life, and defining enough linear algebra terminology to at least give you the right way to think about what is going on.

Moving locally

One of the most basic activities in many games is moving around. Move up, down, left, right, or whatever in order to get where you're going. But as we'll see shortly, moving one direction now and then drifting in orbit could have you moving in a very different direction much later on. That's why this section is only about moving locally, with a separate section for moving globally coming later.

Law of conservation of momentum

Let's start with a few basic definitions. Your velocity is how fast you are moving. This is a three-dimensional vector, which incorporates both your speed and also which direction you are moving. Velocity is intrinsically relative to some frame of reference. If you're driving a car, for example, you might be moving pretty fast relative to the ground, but basically not moving relative to the car.

Loosely, the mass of an object is how much matter it consists of. More technically, mass is resistance to acceleration. The greater the mass of an object, the harder it is to move it very far.

When in an area with a fixed strength of gravity, mass can be interchangeable with weight. That's a good description of moving around on the surface of a planet, but a rather poor model of space travel. Weight is how much force gravity exerts on an object, which depends on the force of gravity in the area. And just to confuse you, gravity and acceleration are, in some weird sense, the same thing.

It turns out that mass in the sense of resistance to acceleration and mass in the sense of affected by gravity are actually the same thing. This conveniently means that your acceleration due to gravity doesn't depend on your mass.

Momentum is mass times velocity. In the mathematical sense, this is a scalar multiple of a vector. Momentum itself is a vector, with both a magnitude and a direction. As with velocity, your momentum depends on your frame of reference, as you could be moving very fast relative to one object and not moving at all (and thus zero momentum) relative to another.

The Law of Conservation of Momentum basically asserts that the sum of the momentum of everything in a system is constant, provided that nothing outside the system interacts with anything inside of it. Having a truly closed system that cannot interact with the rest of the universe at all isn't a common situation unless you consider the entire universe itself, and a model that must start by computing the sum of all momentum in the entire universe isn't likely to be useful.

But for a system to be isolated sometimes is a pretty good approximation on a small scale of time and space. And it's often a pretty good approximation if you allow an accelerating frame of reference where you consider everything in a system relative to what would have happened if the objects had just sat there and not interacted.

Conservation of momentum can be a problem for space travel. Sure, once you get going pretty fast, you keep going pretty fast, at least until gravity has its say. The problem is that if your rocket has to just sit there in space, it can't accelerate to speed up and get you where you want to go.

Specific impulse

The solution to this is that space rockets take stuff up into space so that they can throw it in the opposite direction of where they want to go. If you want to move to the right, then throw a piece of something to the left really hard, and that moves the entire rest of the rocket to the right. If you throw a small percentage of the rocket in one direction, though, the velocity gained in the opposite direction is much smaller in magnitude because it has much higher mass. The real solution is to do this repeatedly, or perhaps more to the point, continuously.

Rocket engines are basically giant bombs with a somewhat controlled explosion to throw burning fuel as hard as you can in the opposite of the direction that you want to go. The harder you can throw it, the more momentum it has, and the more momentum your rocket gains in the opposite direction. As you have to carry your future fuel along with you, firing your exhaust as hard as you can without losing control is very important. Hence the giant bomb approach.

The specific impulse of a rocket engine is basically a measure of its efficiency. The harder it can fire whatever it ejects as it explodes in one net direction, the harder it pushes your rocket in the opposite direction, and the more acceleration you can get from burning a given amount of fuel. Abbreviated as Isp, it is conventionally defined as the average velocity of the fuel ejected divided by 9.81 m/s^2. The latter quantity is the acceleration due to gravity at sea level on Earth, and also on Kerbin.

It should be obvious that if trying to accelerate in a vacuum, being able to eject mass harder in the opposite direction is an advantage. What may be less obvious is that breaking it into more, smaller chunks is also an advantage. Let's suppose, for example, that half of the mass of your rocket is fuel that you can burn and eject, and suppose that you can hurl it away at 3000 m/s, for a reasonably common Isp of a little over 300. If you do that all at once, then you get 1500 m/s of acceleration. Relative to where you started, the fuel will be traveling at 1500 m/s in one direction, and your rocket will be traveling at 1500 m/s in the opposite direction.

But suppose instead that you broke burning the fuel into two chunks. First, you throw back 1/4 of your mass, then you throw another 1/4, now 1/3 of what remains. The first explosion will fire the fuel at 2250 m/s relative to where you started, while accelerating the rocket by 750 m/s in the opposite direction. The second will throw the second batch of fuel at 2000 m/s relative to where the rocket was going, and the rocket another 1000 m/s in the opposite direction. On net, the rocket accelerates by 1750 m/s, which is a lot more than 1500 m/s.

Breaking this into more, smaller explosions yields further gains, though with diminishing returns. In the limiting case of a steady, continuous burn, the best possible acceleration that you can get is about 2079 m/s. The formula, in case you're wondering, is ln(start mass / end mass) * (velocity of ejected fuel), or more conventionally, ln(start mass / end mass) * Isp * 9.81 m/s^2. For those who know calculus, the logarithm naturally shows up by integrating 1/(mass) with respect to mass.

The delta-v approach

This leads to the delta-v way of thinking about what a rocket can do. That would be the Greek letter Delta (which isn't convenient for me to type here) as in "change in" and v for velocity. A given rocket with a given amount of fuel to burn and a given mass of other stuff besides fuel can do up to this amount of change in its velocity by burning fuel and no more.

Crucially, it doesn't have to be all at once. If a rocket has an available delta-V of 2000 m/s, there's no reason why it can't accelerate enough to change its velocity by 1000 m/s now, then wait some days or months, then use the other 1000 m/s later. For example, some now to get on a trajectory with the moon where it wants to land, then wait until it gets close, and some then to actually slow down and land safely.

In many situations, the proper way to think about how much fuel you have left is not in tons or units of liquid fuel. Rather, it is how much delta-v you have left. That's what dictates how far you can go and whether you can get to your intended destination. And back, if you want to come back.

Main rocket engines

Most of the rocket engines in the game rely on combustion to generate the force to fire something backward. You burn rocket fuel with oxidizer to get a good explosion, and that hurls the burnt mixture out the back of the rocket, thus propelling the rocket forward.

Normally, when things burn on Earth, it takes oxygen from Earth's atmosphere to burn with something else. There isn't a bunch of ambient oxygen in the middle of space, however. Thus, if you want to burn something, you've got to bring your own oxygen. There are some engines that don't take this approach and don't require oxidizer, but they all come with severe drawbacks. We'll cover them in a later section.

The game has many different rockets, in many different shapes and sizes. Some are wider than others. Some are longer than others. Some produce more thrust than others. Some cost more than others. In all four of those features, it tends to be the same rockets that are more in all ways. Some rockets are also more efficient than others, in the specific impulse metric explained earlier.

In most practical uses, you'll need to start by considering just how big of a rocket you need, and that will eliminate most of the rockets from contention for a particular use. This is most directly dictated by radial size, as you usually want a rocket to fit nicely on whatever you're attaching it to. There are six common radial sizes for many types of parts in the game: tiny (0.625 m), small (1.25 m), medium (1.875 m), large (2.5 m), extra large (3.75 m), and huge (5 m). For things that are placed in-line--which includes most rocket engines and fuel tanks--you usually want for both components that you're attaching to have the same radial size. This isn't absolutely required, and sometimes there are good reasons not to, but it's commonly more efficient if you do.

Just how much thrust you need to lift your payload plays a huge role. A spark, with its 20 kN of thrust and 0.13 t of mass is a fine engine. So is a rhino, with its 2000 kN of thrust and 9 t mass. But a spark isn't going to do much for you if you're trying to lift 1000 tons off the ground, as you'd need several hundred of them, which would be an incredibly awkward design. Meanwhile, a rhino would be ridiculous overkill for a 2 ton payload, as the weight of the engine alone would make it highly inefficient for the task.

Lower stage liquid engines

Using rockets for liftoff (and in some cases, landings) brings two additional complications. One is that gravity is pulling hard on you, and you don't have unlimited time. If the thrust from your engines is less than the force of gravity, then you don't get off the ground. If you're lucky, you don't move; if not, you fall over and blow up. But just having thrust slightly greater than gravity isn't enough, as then you use huge amounts of fuel to barely move.

This leads to the notion of a thrust to weight ratio. If you click the delta-v icon in the game, it will offer to show you a lot of computed values, including your current thrust to weight ratio. When taking off, you want this to be considerably greater than one, such as 1.3 or 1.5 or 1.7. You don't necessarily want it to be too large, as that means you're using too many or too heavy of rockets. Moving very fast in the lower atmosphere will also mean excessive drag, and can sometimes flip you over and make you lose control.

The other complication of taking off is that rocket engines don't work as well in an atmosphere. The air gets in the way, and so they just don't function as well. Some engines are affected by this far more than others. That's why for Isp and thrust, each engine gives two values, not one: one for performance in a vacuum, and another for 1 atmosphere of pressure, at sea level on Kerbin. In an atmosphere, you burn fuel at the same rate, but it produces less thrust.

Naturally, there are a lot of other amounts of atmospheric pressure besides 1 atmosphere or a vacuum. There are intermediate values, or in some places, pressures of greater than one atmosphere. At low pressures such as 0.01 atmospheres, the numbers for a vacuum are a pretty good approximation. Rocket engines get worse as the pressure increases, and produce no thrust at all at sufficiently high pressures. You can see the exact thrust and Isp for a given rocket engine in the vehicle assembly building by choosing a planet and altitude in the option on the lower right pane.

For taking off from Kerbin, or anywhere else with a thick atmosphere (Laythe, Eve, and the lower atmosphere of Jool), you pretty much have to discard any engines that have a large gap in efficiency between atmosphere and vacuum from consideration for your first stage. Engines with a small efficiency gap between a vacuum or one atmosphere of pressure are much better suited for the lower stages of a takeoff than those with a large gap. Such engines include a cub, vector, mainsail, or mammoth, among others.

Upper stage liquid engines

When out in deep space, you might want to adjust your trajectory by a given amount velocity, which consumes that amount of delta-v. It doesn't really matter how fast you do the maneuver, as you have plenty of time. What matters is how little fuel and cost you can use to do it. Some rockets are intended for the upper stages of an engine, and only intended to be used in a vacuum, or at most in a very thin atmosphere. These commonly focus more on efficiency, in the sense of high specific impulse.

Some engines sacrifice the ability to work well at high pressures in favor of the ability to be more efficient in a vacuum. These are the upper stage liquid engines. There isn't a formal demarcation between those suitable for upper stages versus lower stages, but good examples of upper stage engines include an ant, terrier, cheetah, poodle, wolfhound, or rhino.

With upper stages, you typically have a good idea of how much mass your payload is, and how big of a rocket you want, and how it needs to fit with other parts in your rocket. That will limit you to a handful of reasonable choices, and then you can pick one that seems efficient, in the sense that it can do the job while requiring the least fuel and cost to build.

You can use lower stage engines in deep space, but it's usually significantly less efficient than an upper stage engine. Meanwhile, using an upper stage engine at high pressures will give very poor performance.

Solid fuel boosters

Solid fuel booster rockets are a special type of rocket intended for the very first stage to get you off of the ground and moving upward. They won't get you very far, but they can be a good way to get started. While most liquid fuel rockets have the fuel as a separate component from the rocket proper, for a solid fuel engine, you get an integrated package with both fuel and the engine.

Solid fuel boosters do have some serious drawbacks, however. First of all, unlike liquid fuel engines that respond to the throttle and can be scaled up or down, solid fuel rockets can't be turned off. Once you ignite them, they burn until they are out of fuel, then stop entirely. The early fuel rockets can't gimbal at all, though some that were added to the game much more recently can. Their specific impulse is also pretty bad.

So why use solid fuel boosters at all? One reason is because they're dirt cheap. A kickback can provide about 600 kN of thrust in a lower atmosphere for 62.8 seconds, at a cost of only 2700 funds. There are few ways to get that amount of thrust from liquid fuel engines at double that cost for the engines alone, and that's not counting the additional cost of the fuel.

Solid fuel rockets also provide a lot of thrust in little space. That can also be helpful at liftoff, when you need a ton of thrust to get off of the ground, but want to keep your cross-sectional area small to reduce drag.

Solid fuel rockets are really only good for the first stage to get you off of the ground on Kerbin. Because of their poor efficiency, you don't want to carry all that weight up for use in the upper atmosphere or out in space. They're good for starting on a lot of rockets, but just use them, discard them, and move on. Once you get to launching larger rockets, you can expect to start attaching a bunch of clydesdales to nearly everything.

Specialized engines

It might seem like it's inefficient to have to bring a bunch of liquid oxygen with you so that you can burn it. Isn't there some other way to let you skip the oxygen? Well yes, there is. Several, in fact. But they all have major drawbacks. The specialty engines are the focus of this section.

Nerv atomic rocket

First is the nerv atomic rocket motor. The idea is that it has a nuclear reactor in the rocket that it can use to heat hydrogen to be very hot. As atoms get hotter, they move faster. Have a hole so that there's only one direction that goes out, heat it up, and let it go out the hole. Hydrogen is used for the fuel because it has the lowest molecular weight, and the lower the molecular weight of a molecule, the higher its velocity at a given temperature.

The advantage of the nerv is its enormous specific impulse of 800. For comparison, the highest for a normal rocket in the game is a wolfhound, at 380. So that's why you'd want to use a a nerv.

There are some enormous drawbacks, however. For starters, the thrust to weight ratio is awful, with a 3 ton engine for only 60 kN of thrust. Every single normal liquid or solid rocket in the game has a thrust to weight ratio of at least five times that, and many are more than ten times that. Throw in its poor performance in an atmosphere and at sea level on Kerbin, a nerv can't even lift half of its own weight off the ground, even without any fuel or payload.

They're also expensive, as they cost 10000 funds each. That makes a nerv the seventh most expensive engine in the game, and all of the more expensive engines are much larger with at least 1000 kN of thrust. You can sometimes compensate for a weak engine by just adding more, but that gets expensive with nervs.

The fuel ecosystem for nervs is also not very good. You can use normal fuel tanks and not include the oxidizer, but then your wet to dry mass ratio for your fuel tanks is only 4.6:1 rather than 9:1, which eats up much of their efficiency advantage. Otherwise, you have a handful of pure liquid fuel tanks that you can use, and mostly not of the sizes and shapes you'll want.

The low thrust means that you'll commonly have long burn times to get the change in velocity that you want. That's fine in deep space, but it's not fine in low orbit of a planet with strong gravity. If you try to do a 20 minute burn maneuver when your current orbit has a period of 30 minutes, you're not going to like the results. They are functional for getting you out of low orbit of a planet, but kind of a pain.

Even so, for long distance flights, a nerv is commonly worth using because of its efficiency. There's no sense in using them if you're only orbiting Kerbin or traveling to one of its moons, and they're not that great for going to Eve or Duna, either. But for faraway destinations such as Jool, Moho, or Eeloo, having a stage of Nervs in the middle for the deep space portion can considerably reduce the total mass at launch required to reach your destination.

Dawn engine

Another way to make a rocket engine that fires its exhaust at much higher speeds than normal rockets is the ion engine. The idea here is that you have some xenon gas in an electric field. Normally, as a noble gas, xenon is unreactive and electrically neutral. If you ionize a tiny fraction of the xenon atoms by ripping off an electron, then your electric field can push on that handful of ions with an enormous force while having no force on the rest of the xenon. That handful of ions zip out of the engine at enormous speeds while the rest stay put.

The result is a specific impulse of 4200 in a vacuum. That's more than five times that of a nerv, and more than 11 times that of any liquid or solid fuel rocket. That makes the dawn engine the best in the game at mass efficiency in a vacuum, and by an enormous margin.

Naturally, they come with some enormous drawbacks. First of all, they offer very little thrust, at only 2 kN. That's actually massively more powerful than the real-life versions, which tend to offer about 0.01% that much thrust--naturally measured in mN, not kN. While dawn engines are very efficient for deep space travel, you're either going to need a whole lot of them or else accept that your burns take a very long time.

Second, their fuel tanks are inefficient with a full to empty mass ratio of only about 4:1, as compared to 9:1 for liquid fuel tanks, which implicitly eats up some of that mass efficiency advantage.

Third, they're expensive. A cost of 8000 funds for an engine isn't outlandish, until you realize that you're only getting 2 kN of thrust. Their fuel tanks are even more expensive, as xenon doesn't exactly grow on trees. Xenon costs more than 40000 funds per ton. For comparison, liquid rocket fuel costs less than 100 funds per ton.

Fourth, they use a lot of electricity to maintain a strong electric field. Each dawn engine consumes 8.741 electricity per second while in operation. The mass in electrical equipment that it takes to generate that much electricity that fast can easily make them seem like they're not that efficient anymore.

Fifth, that very weak thrust means very long burn times. For a single dawn engine to drain a single PB-X750 Xenon Container takes more than three hours. You can't time warp while accelerating, either, though you can do up to 4x physics warp. That still requires waiting more than 45 minutes. And remember that even that speed is because they made the engines far more powerful than their real-life counterparts. The real-life ion engines can burn for days or weeks.

Sixth, their xenon fuel cannot be refilled by mining. All other engines in the game allow you to land on some arbitrary planet or moon, use some mining equipment, and completely refill your fuel. But you can't expect to find xenon gas in arbitrary places. On many planets and moons, if they even had xenon in the first place, it would just float off into space and be gone.

Dawn engines are pretty much unusable for lower stages because of their high cost and low thrust. Where they really shine is for bringing a very small payload back to Kerbin, such as a command pod with few Kerbals, an experiment storage unit with valuable data, or some part that you were asked to bring home for a contract. They're great for coming home from Moho. They're less great for faraway planets such as Jool or Eeloo, as solar panels are far less effective there. Dawn engines are also nearly mandatory if you want to put something in low orbit about the Sun.

Jet engines

Another way to provide thrust is to not use rockets at all. Jet engines as used on airplanes are massively more efficient than rocket engines, as they have two huge advantages. First, they only need to carry fuel and not oxygen, as they can grab oxygen out of the air to burn. Second, they don't have to implicitly carry something to hurl off into space, as turbines can push against the air to provide thrust. This results in specific impulse ratings for jet engines ranging from 3200 to 12600. That's competitive with a dawn engine at the low end, and massively more efficient at the high end.

However, jet engines have some enormous drawbacks, too. Their key weakness is a need for oxygen. Thus, they only work in the lower atmosphere, and even then, only if there is oxygen present. So that limits you to Kerbin and Laythe. The problem with this is that if you're in the lower atmosphere of a planet, the first thing you want to do is to get out of the lower atmosphere--either up into space or down on the ground. For most missions, jet engines would be functional for such a short amount of time that their fuel efficiency doesn't matter.

Second, their thrust to weight ratio is awful by the standards of rocket engines, so they provide little thrust for the weight that they bring. It doesn't work to have one engine pointing its exhaust at another, as that would screw up your aerodynamics, so the number of jet engines you can use is sharply limited by your cross-sectional area. You generally need a vehicle to be longer than it is wide or else aerodynamics will try to flip you out of control, so this limits you to small vehicles at launch.

Third, take-offs and landings are a problem. In real-life, there are many airports with runways, and planes generally fly from one to another. Kerbin has only three runways, and Laythe has none at all, which makes take-offs and landings a problem. It is possible to do a vertical take off and landing so as not to need a runway, but this is difficult to construct.

Fourth, jets force you to deal intricately with finicky aerodynamics, which is just plain hard. It's hard in real-life, too, but there, aerospace engineers have much more precise tools available. You can mostly manage rockets by rotational symmetry, which prevents things being slightly off from breaking everything for you. For jets, you can use mirror symmetry for one dimension, but still have to balance things in another dimension with tools that are just too imprecise for the job.

If you look around, you can find a lot of people saying that they did this or that with jets. Most of it is very old and dates to before aerodynamics was redone in version 1.0, so that what they did then won't still work today. You can perhaps make a small jet with no meaningful payload and fly it around, but I haven't found any practical situation where that's not markedly worse than using a rocket. It's best to regard jet engines as being a toy with no practical use in the game.

Rotors

In addition to using the built-in jet engines, it's also possible to roll your own using rotors. Rotors don't use fuel, but rather, rely on electricity. A rotor has two main components, and forces one to spin relative to the other. This can be used to spin propeller blades, helicopter blades, or structural panels to provide a modest amount of thrust.

You can be creative with your use of rotors, but do keep in mind that they're tricky to use well. You can make them into propellers for planes, rather than using jet engines. You can also make helicopters. These don't rely on atmospheric oxygen, so they can also work on Eve or Jool. Indeed, helicopters are the only thing that work far into Jool's lower atmosphere.

Another alternative that lets you avoid the finicky aerodynamics is to use rotors to make a boat engine. That way, if you land in the water while out of fuel, you fire up the boat engine and slowly get back to shore, where you can switch to rover wheels or mine for more rocket fuel. So long as you move slowly enough, aerodynamics won't flip you over and blow you up.

RCS thrusters

One other specialized type of engines is RCS thrusters. These are intended for small, precise movements, especially in deep space. RCS thrusters won't get you into orbit and won't land you, but they might help you line up something just right to have two vehicles dock in space.

Personally, I don't find them useful. They work, but you can also make things precise enough for docking by other means, without needing an additional type of fuel and additional engines.

Rotating

For most purposes, it isn't enough to just provide a lot of force. You need to provide it in the right direction in order to get where you want to go. With rockets, that typically means rotating the rocket such that it is pointing away from the direction in which you want to travel. To do that, you'll need to be able to rotate your vehicle. That's what this section is about.

Law of conservation of angular momentum

Linear velocity has an angular version, too. We'll talk more about coordinate systems in a subsequent section, but your angular velocity is the rate at which your angle about something is changing. Just as there is linear momentum, there is also angular momentum. The angular momentum of an object about a point is the vector cross product of the distance from the point to the object and the momentum of the object. The cross product is algebraically messy and unintuitive, so I won't define it here.

What is important about angular momentum is that it is conserved. So long as there aren't any external torques applied, the sum of the angular momenta of a system about a fixed point is constant. No external torques is a weaker condition than there being no external forces applied to the system; I'll explain the concept of torque shortly. While conservation of momentum explains how rockets work and not much else of consequence in the game, conservation of angular momentum is an extremely important principle with broad consequences.

Conservation of angular momentum works with any object and any point. In the limit as the point that you are rotating about becomes infinitely far away, it becomes equivalent to ordinary conservation of momentum. Most combinations of an object and a point really aren't very illuminating--in part because there are external torques on the system.

There are two types of situations in the game where conservation of angular momentum is extremely consequential. The more complicated and profound one is that of your rocket orbiting some celestial body, such as a planet or moon. The object whose angular momentum we track is your rocket, and the point is the center of the planet or whatever it is that you're orbiting. We'll need more terminology before we can make sense of that, so we'll get to it a little later.

The other situation where angular momentum is important is your rocket rotating about its center of mass. The center of mass of an object is loosely the average position of mass in the object. For a collection of point masses, it is computed as the (sum of (mass times position)) / (sum of masses). For continuous, solid objects, you would technically want integrals instead of sums.

Some objects have a center of mass that is pretty simple by symmetry. For example, the center of mass of a ball is at the center of the ball. When building rockets, if you place everything with mirror symmetry in the spaceplane hangar, you're guaranteed that the center of mass will be somewhere in the plane that the mirror symmetry is symmetric about. If you place everything with rotational symmetry in the vehicle assembly building, the center of mass will be somewhere on the vertical line through the center of the rocket. Both buildings have an option to show you where your center of mass is.

One important thing to understand about the center of mass of an object is that when the object rotates while not being touched by anything else, it rotates about its center of mass. Thus, in order to rotate your rocket at all, you're usually going to rotate it about the center of mass.

Reaction wheels

Reaction wheels probably look like magic if you don't know how they work. The idea is that you're in deep space and not touching anything. You want to rotate your rocket in a particular direction. So you fire up the reaction wheels and rotate the entire rocket to exactly the direction you want. And then you stop, and stay pointing in exactly the direction you wanted. And it didn't require firing any rockets, but only using some electricity. And that is actually a real thing.

The first reaction wheels were discovered accidentally. Some space program had launched a satellite, and it was going along just as they expected. Then when it started to transmit data back to Earth, it started rotating. That was a nuisance, so they had to stop it and rotate it back to the intended direction, which wasted fuel. Then when it started transmitting data again, it started rotating again. This was rather baffling at first.

Eventually, they figured out what was happening. When the satellite transmitted data, it rotated some tapes internally as part of the tape drives where it stored data. In an appropriate reference frame, the satellite had zero net angular momentum before it started transmitting. When rotating the tape wheels, those wheels had some angular momentum in some direction. In order for the net angular momentum of the entire satellite to remain zero (as angular momentum is conserved), that caused the entire rest of the satellite to rotate slowly in the opposite direction.

Figuring that out was a huge advance for space rockets. Instead of needing a bunch of small thrusters all over the place to make it possible to rotate your rocket in arbitrary directions, all that they needed was a few internal wheels. Want to rotate the rocket in one direction? Just rotate the wheels in the opposite direction. Stop the wheels to stop the rocket from rotating.

There are three dedicated reaction wheels objects in the game, with three different radial sizes. The game simplifies this for you somewhat by allowing all reaction wheels to rotate you in arbitrary directions, and much faster than real-life reaction wheels would tend to. Furthermore, the game doesn't limit the cumulative torque that reaction wheels can provide, unlike the real-life versions that can only spin so fast. But reaction wheels are a real thing, not just magic to make the game easier for you.

In addition to the dedicated reaction wheels, most of the pods in the game have some built-in reaction wheels. These tend to be lower torque than dedicated reaction wheels, so other than for some very small vehicles, you'll typically want to add one or more dedicated reaction wheels.

Torque

Torque is basically the angular version of force. Technically, the torque on an object about a particular point is the vector cross product of (the distance from the point about which you rotate to the point where the force is applied) with the force. Thus, the torque depends not only on the force, but also on the point that you're computing the torque around.

For our purposes, there are again two useful choices for the point that you compute the torque about. One is the center of mass of your rocket. The other is the celestial body that you're orbiting. We'll come back to the latter in a later section. The torque about the center of mass of your rocket will rotate your rocket.

There are two important cases where the cross product is zero. One is that cross product of zero with any other vector is always zero. This means that zero force causes zero torque. It also means that any force applied to the center of mass of an object applies zero torque to the object.

The other, broader situation is that the cross product of two parallel vectors is zero. Thus, if the force applied is pointed right at the center of mass of an object, it causes zero net torque, and does not rotate the object.

There are five major sources of torque in the game other than reaction wheels. They can be intentional or undesirable, but they will cause the rocket to rotate, so it's important to understand them.

Asymmetric rocket placement

First is if your rockets are placed asymmetrically. A rocket engine that isn't pointed right at your center of mass will have some torque. If you have another engine on the opposite side, it will cause the opposite torque. These cancel out, for a net sum of zero torque. That's usually what you want, so that you can avoid extra torque when you don't want it.

The vehicle assembly building and spaceplane hangar will both draw this for you. You can show the sum of the forces, as well as the center of mass. If the former is pointed right at the latter, you're fine, at least for a rocket. Making everything use rotational symmetry will accomplish this for you. For a plane, you want the sum of the forces to be pointed right at the center of mass in the horizontal direction, but possibly not quite in the vertical.

There are two ways to screw up the net force here. One is if the rockets firing at a given time are placed asymmetrically. This can happen because of the way that the rocket is built, with one engine not having others to balance it. Even if the initial design is correct, it can happen if one engine is firing while the other(s) to balance it are not. It can also happen if something goes awry and blows up some but not all of your engines.

The other way to mess this up is if your center of mass is off-center. For example, if you stick one extra fuel tank off to one side without a counterpart on the other side, you can end up with a center of mass that is off to the side. Then even if you properly pair all of your engines, the net force isn't pointing at the center of mass, and so the rocket still rotates. To avoid this, you need all of your parts to be either paired with other, identical parts using the rotational symmetry tool, or else a single part actually on the center line of the rocket.

Engine gimbal

In addition to pointing their exhaust in the exact direction that they're facing, some engines can angle the nozzle off to the side. This is something that can be adjusted from moment to moment, so that you can have the nozzle pointed to the side one moment when you want to turn and centered again a second later when you want to go straight.

Each engine has a maximum amount of gimbal. Some engines can't gimbal at all, and the maximum angle for most of those that can is very small, such as two or three degrees. A few engines have a very large gimbal angle, such as 10.5 degrees for the vector or 22.5 degrees for the cub--though the cub can only angle in one axis, not two.

Large gimbal can be handy sometimes, but excessively large gimbal can mean a lot of torque. With SAS on, this can cause it to overshoot back and forth on angles until the entire ship shakes violently or even flies apart. Fortunately, you can reduce the maximum gimbal of any rocket engine. Sometimes it is handy to have a stage that mixes some engines with high gimbal with others with no gimbal at all so that you can still rotate at a decent rate.

Aerodynamics

Air resistance when in the lower atmosphere is another source of torque. For planes, this is essential to make the plane fly at all. For rockets, it's generally undesirable at take-off, but can be helpful to slow you down before landing.

While air resistance mostly slows you down in whatever direction you were going, it can also provide some torque. Because it pushes so hard, a slight angular tilt can offer considerable torque. In some cases, it can cause a rocket to flip over shortly after launch.

For a rocket of a fixed size and shape, there will be some amount of force applied to the rocket as it moves in any particular direction. The force generally varies with the direction, and often by quite a lot. A pancake moving with its wide face catching the wind will draw a lot of air resistance, for example, but the same shape will get much less if it moves in the direction of an edge.

The most stable direction for a rocket is whichever direction offers the least resistance. For a long, narrow rocket, this will usually be either retrograde or prograde. For a short, wide rocket, it can be moving on an edge. If you're near the direction of minimum wind resistance, aerodynamics will often push you toward it.

There can be multiple local minima that are stable if you're near them. Additionally, so long as the torque applied by aerodynamics is less than what you can apply with other sources (typically engine gimbal or reaction wheels), you can keep the rocket stable in the direction you want it to be facing.

Ultimately, aerodynamics is very complicated. New players commonly have to figure out why their rocket is flipping over shortly after launch, and aerodynamics is the culprit. It often helps to make your rocket have less drag when traveling in the direction you want to go, such as by using aerodynamic nose cones. Sometimes you need more torque from other sources. Occasionally, you just have to make the rocket go slower when in the lower atmosphere to keep it stable.

Collisions

If one object directly pushes on another, it can apply some torque to the other object. Actually, both objects can apply some amount of torque to each other. In one sense, this is obvious, and also the simplest example of torque. But in another sense, it's fairly rare, as you typically don't collide with other objects when deep in space.

The main issue where collisions will spin your rocket around is when landing. If the ground is uneven and one side of your rocket touches before the other, the ground will apply some torque to spin the rocket away from the side that touched first. You can reduce this force considerably by touching down at a lower velocity. It also helps a lot if you can find a level place to land, though this isn't always practical.

Rotors

The basic goal of a rotor is to apply some torque to rotate some small portion of the ship in one direction, such as helicopter blades. But as angular momentum is conserved, this rotates the entire rest of your ship in the opposite direction, albeit usually much more slowly. Even so, if you're reckless with rotors, they can easily cause you to spin out of control.

The solution to this is usually to have an even number of rotors, and spin them in opposite directions. Thus, when some of them apply torque in one direction, others apply an equal amount of torque in the opposite direction. The net effect is zero torque on the rest of your ship.

Inertia

Just mass is resistance to acceleration, so inertia is resistance to rotation. The amount of angular acceleration of an object is the amount of torque divided by the moment of inertia about the axis that the torque is trying to rotate the object. Importantly, the moment of inertia is not a single, fixed constant for a single object, but varies with the axis. The axis of rotation always goes through the center of mass of the object.

Technically, the moment of inertia is the integral over space of the mass density of the object times the square of the distance from the axis of rotation. You can think of it intuitively as the mass of the object times the square of the "average" distance of parts of the object from the axis of rotation. It would be more proper to use the root mean square (which is greater than the average) rather than the average, but using the average is probably more intuitive and usually won't lead you too far astray.

One thing that is important to understand is that an object of fixed shape gets larger in all directions, the moment of inertia grows much faster than the mass. Meanwhile, the aerodynamic forces on it grow proportionally to the cross-sectional surface area, and thus more slowly than the mass. If you increase the size of the rocket in all dimensions by a factor of n, the aerodynamic forces (including torque) increase by a factor of n^2, the mass by a factor of n^3, and the moment of inertia by a factor of n^5. That last one is n^3 for the mass times n^2 because the distance from the axis of rotation increases by a factor of n.

Thus, the angular acceleration due to aerodynamic forces decreases by a factor of n^3. For example, make the rocket twice as big in all dimensions, and the angular acceleration due to aerodynamics will only be 1/8 as big as before. This is why small rockets are prone to flipping, but a similar shape with a much larger rocket allows you to nearly ignore aerodynamics when taking off.

Another consequence of this is that big rockets are much harder to turn than small ones. Small probes that only weigh a few tons can commonly spin very fast from the minor reaction wheels inside of a pod or probe core. Giant stations with a mass of thousands of tons can take minutes to rotate to the direction you wanted, even with a number of dedicated reaction wheels.

Moving globally

Your intuition is likely that if you want to move from point A to point B, you start moving directly toward point B. Keep moving in that direction for a while, and eventually, you'll get there. For moving small distances, that works pretty well, with some fake forces that we'll discuss near the end as the only real impediments.

For moving from one celestial body to another, however, just pointing in the direction you want to go will fail spectacularly. Constantly firing rockets to counteract the force of gravity will drain your fuel in a hurry. Rather, you need to apply minimal thrust at carefully chosen places, and then rely on gravity to take you where you want to go.

This section is by far the most math-intensive in the entire guide. As before, I promise not to give you lengthy algebraic derivations. I will, however, introduce some linear algebra terminology, to at least give you the proper nomenclature for what is going on.

Coordinate systems

If you want to describe the location of a point in space, there are a variety of ways to do it. The three that will generally be introduced in a fairly introductory physics or multivariable calculus course are rectangular, cylindrical, and spherical coordinates. There are plenty of others, and we'll get to some that are useful for describing orbital mechanics shortly. Cylindrical coordinates aren't important in this game, but I'd like to explain rectangular and spherical coordinates before moving on.

Rectangular coordinates

To describe a point on a line, you can use a single number. Pick a point on the line as your zero point. You can then specify any other point by saying how far from the zero point it is, and in which direction. One side of the point is positive, and the other side is negative.

You can do about the same in two dimensions, but you'll need two numbers. For example, to specify a point on your monitor, you could have one number that describes the position in the horizontal direction, and another that describes it in the vertical direction. Each spot on the screen corresponds to a unique pair of numbers.

You can do the same in any other number of dimensions, too. As space is three-dimensional, we commonly want three dimensions. In this case, it takes three numbers, that is, three coordinates, to describe the position. The three coordinates are customarily called x, y, and z.

It's important to understand that there is not a canonical origin (zero) point. Nor are there canonical directions of which way is x, which way is y, and which way is z. Rather, you're allowed to pick whatever is most convenient. It's common to use z as "up", but out in the middle of space, there isn't a clear "up" direction.

Spherical coordinates

Another way to describe a point in space is with spherical coordinates. As with rectangular coordinates, you start by picking one particular point as your origin. Your three coordinates are the Greek letters rho, theta, and phi. I'll call them r, t, and p, respectively, simply because it's hard to type Greek letters here.

The r coordinate is your distance from the origin, regardless of the direction. The t coordinate is your angle in some particular plane through the origin that you pick. The p coordinate is your angle with that plane. The t and p coordinates together specify a direction. Physicists sometimes reverse the roles of theta and phi, but I'm going to stay with the convention I've just described.

One notable feature of spherical coordinates is that the three coordinates aren't allowed to be arbitrary numbers. As r is a distance, it must not be negative. As t and p are angles, they would repeat if allowed to become arbitrarily large. By convention, t is allowed to be in [0, 2 * pi), while p is allowed to be in [-pi/2, pi/2], where pi = 3.14159...

There's one important use of spherical coordinates built into the game that you're probably already familiar with. The zero point is the center of a planet or moon. r is essentially your altitude, though it is commonly displayed as (distance from the center of the planet) - (distance from sea level to the center of the planet). t is your longitude, that is, how far east or west you are. p is your latitude, which is how far north or south you are.

Some linear algebra

If using a rectangular coordinate system, you can choose the directions almost arbitrarily. But some choices are often better than others. To explain why, we're going to need some terminology.

When using rectangular coordinates, we said that we had x, y, and z coordinates. We commonly write a point (or a vector) by listing the three coordinates. For example, we might write (2, 5, -3) to mean that we're at the location where x = 2, y = 5, and z = -3. We can add two vectors algebraically by adding their coordinates. For example, (2, 5, -3) + (7, 1, 3) = (9, 6, 0). In the x-coordinate, we get 2 + 7 = 9, and so forth.

Geometrically, we can write a vector by drawing an arrow from the origin to the point. We can add two vectors geometrically by moving the tail point of one to the head of the other, and then drawing a vector from the other tail to the other head.

We can also take scalar multiples of vectors. Algebraically, this is just multiplying each coefficient by the same number. For example 3 * (2, 5, -3) = (6, 15, -9). Geometrically, this corresponds to making the vector longer or shorter (or pointing in the opposite direction if negative) without changing the direction that the vector is pointing.

Orthonormal bases

The span of a set of vectors is the set of all linear combinations of them. That is, pick a scalar multiple of each vector in the set, then add them all together. The span of a set of vectors is a subspace of the original vector space, that is, the space in which our vectors live.

A set of vectors spans a vector space if the span of the set of vectors is the whole space. A good coordinate system should span the whole space, so that you have a way to describe all of the points in it. For example, the set of vectors (1, 0, 0), (0, 1, 0), and (0, 0, 1) spans the whole three-dimensional space. If we want to write a point (a, b, c), we can write it as a * (1, 0, 0) + b * (0, 1, 0) + c * (0, 0, 1). The set of vectors (1, 0, 0) and (0, 1, 0) does not span the whole space, as it gives us no way to make the z-coordinate not be zero. Similarly, the set of vectors (1, 0, 0), (1, 1, 0), (2, 1, 0), and (0, 1, 0) does not span the whole space.

A set of vectors is linearly independent if the only linear combination of the vectors to give zero is the zero combination. For example, the set (1, 0, 0), (0, 1, 0), and (0, 0, 1) is linearly independent. The set (0, 1, 0) and (1, 0, 1) is also linearly independent. The set (1, 0, 0) and (2, 0, 0) is not linearly independent, as we could compute 2 * (1, 0, 0) + (-1) * (2, 0, 0) = (0, 0, 0). A good choice of a rectangular coordinate system should have its coordinate vectors be linearly independent, as otherwise, more than one set of coordinates will give the same point.

A set of vectors is a basis for a vector space if it is both linearly independent and a spanning set. This requires that every point in the space can be written as a linear combination of the basis vectors in exactly one way.

The dot product of two vectors is obtained by multiplying the components, then adding the products. For example (1, 2, 3) dot (4, 5, 6) = 1 * 4 + 2 * 5 + 3 * 6 = 32. Two vectors are orthogonal to each other if their dot product is zero. In other contexts, this is sometimes called perpendicular or normal, but I'll generally stick with orthogonal.

We usually want for the coordinate vectors in a coordinate system to be orthogonal to each other, as otherwise, we could get some peculiar effects. For example, the set of vectors (2, 1, 1), (1, 2, 1), and (1, 1, 2) forms a basis for three-dimensional space. But it's kind of an awkward basis to use, as we can get the vector (4, 4, 4) by using +1 as the coefficient for all three basis vectors. We can get the vector (2, -1, -1) by using +2 for the first coordinate and -1 for each of the other two. But this makes the vector (2, -1, -1) look "larger" than (4, 4, 4), which seems intuitively wrong.

The length of a vector is the square root of the dot product of the vector with itself. This does geometrically give the length if you measure it. An orthogonal set of vectors is called orthonormal if each of its vectors has length 1.

We typically want a good coordinate system to have its coordinate vectors form an orthonormal basis. We could use (1, 0, 0), (0, 2, 0), (0, 0, 2398) as a basis for a space. But that would make the z-coordinates tend to be much smaller than the x and y coordinates, which would seem weird.

Dimension and degrees of freedom

All bases for a vector space have exactly the same number of vectors. It isn't a coincidence that rectangular coordinates and spherical coordinates for the same space each have three coordinates. The number of vectors in such a basis is the dimension of the space.

It might be surprising that most ways of picking vectors randomly will form a basis, if you pick the right number of them. It's kind of like observing that most ways of picking three points at random won't happen to accidentally place them on the same line. Most sets of vectors will not happen to form an orthonormal basis, however.

Spherical coordinates don't technically define a basis for a space globally. They do provide a valid coordinate system for treating the space as a smooth manifold, except along the axis through the poles, but that's far beyond the scope of this guide.

When you get to non-rectangular coordinate systems, the number of degrees of freedom is basically the dimension that you're dealing with. That's the number of coordinates that you'll need.

Maneuver nodes

To help you plan your journey, maneuver nodes let you specify to specify how much thrust you want to apply in which places. They will map out your future trajectory after that thrust so that you can see if you need to thrust more or less or in a different direction or whatever. Changing maneuver nodes doesn't use any fuel, as it's only planning, not actually firing rockets.

Just as your position has three coordinates, so does your velocity. Thus, if we want to describe the direction in which you're moving, it will take three coordinates. It may be tempting to make them just the change in the three coordinates to describe your position. That works, after all. But it's usually a rather bad choice, and especially terrible if you're using spherical coordinates.

Rather, the game has a built-in orthonormal basis that it will show you that is very useful. One of the coordinates is the direction you're going. That's the "prograde" direction, and the opposite direction from it is "retrograde". For reasons that we'll get to shortly, much of the time, when you want to thrust at all, it is best to do it in either the prograde or retrograde direction.

Another coordinate is kind of away from the celestial body that you're orbiting, but not quite. This is the "radial out" coordinate, and its opposite direction is "radial in". There are two reasons why it is only "kind of". One is that you're not necessarily orbiting anything; we'll get to spheres of influence in a bit.

The larger reason is that directly toward some celestial body usually isn't orthogonal to the direction you're moving. We want the basis to be orthonormal, as otherwise, it will do weird things, so it needs to be orthogonal to the prograde direction. What they actually do is to pick the direction nearest to pointing away from the celestial body from among those directions orthogonal to the prograde direction. For those who know linear algebra, they're using the Gram-Schmidt process under the hood.

The third coordinate is the normal direction, which basically means, whatever direction is orthogonal to the first two axes. Its opposite direction is the anti-normal direction. This is the normal direction to the plane in which your trajectory lies.

When you specify how much thrust to apply at a given maneuver node, the you specify numbers in each of the prograde, radial out, and normal directions. Those directions are as you will be traveling at the node itself. This makes it fairly easy to do a purely prograde burn, or purely retrograde, or whatever.

Law of conservation of energy

The first thing to know about energy is that there is no such thing as energy. It simply isn't a real, physical thing. Rather, it's a made-up quantity that is designed to make computations easier. It can also help with your intuition about how things work.

What has happened over the centuries is that there are various situations in which scientists have noted that some computed quantity is constant, even as various components of it change. In a number of intuitively related situations, they decided to call this quantity energy. Most such situations don't matter to us, but converting between a rocket's speed and its height above an object is hugely important.

I promised that there wouldn't be any lengthy algebraic derivations, so I'll just give you the formula. If you're in orbit about some celestial body, let your speed relative to the body be v and your distance from the center of the body be r. Then there is some constant k such that v^2 - k/r is constant, even though both v and r will probably change as you move through your orbit. The constant k varies by celestial body. For those who are previously familiar with conservation of energy in a gravitational sense, I've factored out some terms and folded some constants into each other.

Furthermore, your total energy gives you information about the status of your orbit. If it is positive (i.e., v^2 > k/r), then you're on an escape trajectory and not coming back. If negative (i.e., v^2 < k/r), then you're either in orbit or else going to fall and crash.

If you are in a circular orbit, then v and r will be constant. A circular orbit implies constant distance from the planet, after all, which is what makes r constant. Furthermore, in a circular orbit, you will always have k/r = 2v^2, and your total energy will be -v^2 = -k/2r. This gives you a fairly easy way to compute k: get to a circular orbit and compute k = 2rv^2. This works regardless of the height of the circular orbit, so long as it's a stable orbit. You'll have to add the radius of the body you're orbiting to the altitude above sea level that the game displays for you to compute r. For v, you want the speed relative to orbit, not relative to the surface.

Remember that if you're in orbit and not on an escape trajectory, your energy is negative. A higher orbit (greater altitude) corresponds to higher (less negative) energy, even though you're moving slower.

Describing orbits

To describe your trajectory, we'd like an appropriate coordinate system. One could specify your current position and velocity as vectors, with three coordinates for each. But this is awfully inconvenient, as you'll have six coordinates, all of which are constantly changing in seemingly weird ways.

What we really want is a different coordinate system that is better suited to describing orbits. We'll need six coordinates, but we'd like one of those six to be your position on the orbit. Furthermore, we'd like for the other five coordinates to not be changing as you drift along in space on your orbit.

Those who don't have a strong math background may be surprised to learn that not only is it possible to devise such a coordinate system, but there are a lot of ways to do it. The game has one such coordinate system built-in that it will display for you. I'll present an alternative that is sometimes more illuminating than the one that the game gives you.

In-game coordinates: apoapsis, periapsis, argument of periapsis, inclination, longitude of ascending node

Let's start with the game's coordinate system for describing an orbit. One coordinate is the altitude of your apoapsis, which is the highest point in your orbit. Another is the altitude of the periapsis, which is the lowest point in your orbit. The third coordinate is the argument of your periapsis, which is what would change if you rotate the orbit while leaving it in the same plane. The fourth argument is your inclination, which is the angle between the plane that contains your orbit and the equator of the body you're orbiting. THe fifth coordinate is the longitude of the ascending node, which is where along the equator of the body you're orbiting your orbit passes from below the equator to above it.

The game displays the apoapsis and periapsis prominently for you. Inclination is somewhat prominent on the map, though the numerical display shoves it off into the advanced orbital info tab. Longitude of ascending node (LAN) and argument of periapsis (LAN PE) are displayed numerically in the advanced orbital info tab. They're implicit in the drawing of your orbit on a map, but not displayed numerically there. The math is a little complicated, but those five coordinates uniquely determine your orbit.

You may find it puzzling that the game sometimes displays your apoapsis as negative. It does this when you are on an escape trajectory, rather than in orbit. There is a sound mathematical reason for it, and it is meaningful information about an escape trajectory. After all, you don't have a highest point when you're going to go off to infinity. I'll get to this in a later section.

Alternative coordinate system: energy, angular momentum (vector), argument of periapsis

The alternative coordinate system that I would propose keeps the argument of periapsis from above, but replaces the other four coordinates. The other four coordinates are your energy and your angular momentum, both divided by your mass. Your angular momentum is a vector, so it encompasses three coordinates. We'll effectively use spherical coordinates to describe your angular momentum, with one coordinate for the magnitude of it and two for the direction.

The direction of your angular momentum is basically equivalent to the inclination and longitude of ascending node as the game displays for you. Indeed, it can be explicitly written that way, with the longitude of the ascending node as the theta angle and the inclination as phi, at least up to a sign issue where the coordinates remain the same if you traverse the orbit in the opposite direction. Because you usually don't want to change the direction of your angular momentum other than to make it the same as that of your target, I find it easier to think if the two coordinates as just a direction on a sphere rather than two separate things.

Your energy and the magnitude of your angular momentum (both divided by your mass) are equivalent to your apoapsis and periapsis in the game's built-in coordinate system. You can compute either pair of coordinates from the other. If your energy is E, your angular momentum L, your apoapsis altitude A, your periapsis altitude P, and the radius of the body you're orbiting R, then you can compute L = sqrt(k(A+R)(P+R)/(A+P+2R)) and E = -k/(A+P+2R). In the other direction, A = (-sqrt(k^2+4EL^2)-k)/(2E) - R and P = (sqrt(k^2+4EL^2)-k)/(2E) - R. The exact formulas don't particularly matter, but that there are formulas to convert proves that the coordinates are equivalent.

At this point, you may be wondering why I'm pushing energy and angular momentum as coordinates rather than apoapsis and periapsis. The latter pair is graphically intuitive, after all, while the former is definitely not. The answer is that when you thrust, how it changes your apoapsis and periapsis is weird and unintuitive. How a thrust changes your energy and angular momentum is much easier to understand. I'll come back to this in a future section.

Conic sections

The shape of the path of one object as it passes by another while affected by the gravity of the latter object has some nice structure. Algebraically, it is a quadratic equation in the two variables for the plane in which the object's path lies. Geometrically, it is a conic section, that is, the intersection of a plane with a cone.

There are two main cases. If your energy is negative, so that you're in a stable orbit, the path will be an ellipse. Geometrically, an ellipse has two foci, one of which is at the center of the object you're orbiting. The ellipse itself is the collection of all points whose sum of the distances from the two foci is some fixed value. So basically, there is some point in space such that at any point on your orbit, the sum of the your distances from that point plus the center of the body you're orbiting is constant. The other point is geometrically intuitive, as the two foci are symmetric about the center of the ellipse.

If your energy is positive, so that you're on an escape trajectory, the path will be a hyperbola, or perhaps more properly, one arc of it. A hyperbola also has two foci, but the arc is the collection of points such that the difference between the distances to the two foci is constant. So basically, when you're on an escape trajectory, the distance to the object you're flying by minus that of some other point in space is constant.

The algebraic equation for a hyperbola actually gives something with two separate arcs, not just one. One arc is for points closer to one of the foci, and the other arc is for points closer to the other. When on an escape trajectory, if you regard the nearest point in the other arc to the body you're escaping as being the apoapsis, the negative of that height will be the apoapsis that the game reports for you. It also matches the formula that I gave in the previous section to compute the apoapsis from your energy and angular momentum. This probably isn't helpful, but a negative apoapsis does have actual meaning and isn't just a bug in the game.

The degenerate cases also give you a conic section. If your energy is exactly zero, your path is a parabola, which is another conic section. If you are traveling directly toward (or away from) the center of the body you're orbiting, your path is a line, or rather, half of one, as if you don't escape to infinity, you're going to go splat and stop. Geometrically, a half-line is also a conic section, obtained when the plane is tangent to the cone.

Modifying orbits

In order to get to where you want to go, it isn't enough to just know where you're going on your current trajectory. You need to know how to change your orbit so that it goes where you want. That's what this section is about.

When near a planet, thrust to go up, down, or sideways is intuitive enough. When off in space, it really isn't. Thrust in one direction at one point can have you going in a very different direction much later in the orbit. The best way to understand this is by understanding the results of thrusting in each possible direction. We'll break down what thrusting in the coordinate axes presented by the game does for you.

In order to rendezvous with some distant body, whether a moon, another rocket, or whatever, you basically need to make all of the coordinates of your orbit match those of the other object. If you use the game's built-in coordinates with the apoapsis and periapsis, how this works is simple enough if you only thrust at those two spots. Thrusting at apoapsis changes your periapsis and vice versa. Burning prograde increases the altitude of the other end and retrograde decreases it. Burning normal or anti-normal doesn't change your apoapsis or periapsis.

One problem with this is that burning inradius or outradius does weird things. Another problem is that it gives you no intuition at all about what happens if you thrust anywhere else. And sometimes, you'll want to thrust somewhere else, so that you can time where you cross paths to get there at the same time as your target. It is possible to make all prograde or retrograde thrusts off in space either from a circular orbit or else at periapsis or apoapsis, often to circularize an orbit. But that's rather limiting.

Burning prograde/retrograde

Burning prograde increases your velocity and angular momentum. Burning retrograde decreases both of them. The amount by which it changes your energy is proportional to your speed. A slight thrust when you are moving at 2000 m/s thus increases your energy by 10 times as much as if you were only moving 200 m/s. Here, it is critical to use your velocity relative to orbit, not relative to the surface. Thus, a given amount of delta V changes your energy the most when you were already moving very fast.

In order to see what this does to your angular momentum, a different coordinate system would be more natural. Earlier, we said that we wanted two coordinates for the plane in which your orbit lies to be the direction you're going and the direction away from the body you're orbiting, or more colloquially, "up". But usually, those aren't orthogonal to each other, so the outradius direction is as close to "up" as we can get while still being orthogonal to the prograde direction.

To see angular momentum, what you'd really like is for "up" to be one of the coordinate axes, and another one to be as close to it as we can get while still being orthogonal to it. This basically means taking the same basic vectors that you started with, but swapping their order before doing Gram-Schmidt. In this new coordinate system, thrusting in the modified "prograde" direction that is orthogonal to "up" increases your angular momentum by an amount proportional to your distance from the center of the object you're orbiting. Thrusting up or down does not affect your angular momentum.

Burning prograde or retrograde does not affect the direction of your angular momentum. Thus, it does not affect the equivalent coordinates of the inclination and longitude of the ascending node.

Note that the effect of burning prograde on your energy depends on your current speed but not your position, while the effect on your angular momentum depends on your position but not your speed. When you do the burn at periapsis, this makes the largest possible change to your energy, but the smallest change to your angular momentum. At apoapsis, it is the other way around.

Burning inradius/outradius

Burning inradius or outradius changes the shape of your orbit. It will typically change both your apoapsis and periapsis in peculiar ways, unless the burn is done at one of the two apses. It does not change your energy at all, however. Its effect on the magnitude of your angular momentum is as explained in the previous section. Burning inradius or outradius does not affect the direction of your angular momentum.

Burning normal/anti-normal

Burning normal or anti-normal does not affect your energy or the magnitude of your angular momentum. As such, it does not affect your apoapsis or periapsis. It likewise does not affect the argument of your periapsis.

You may have noticed that a large burn in the normal direction at a maneuver node makes your orbit end up higher than it was initially. I just said it wouldn't do that. The reason is that as you do the burn, you change which direction is your normal direction. The start of the burn could be exactly in the normal direction, but as the burn goes along, your direction is partially prograde or inradius or something else that isn't purely normal or anti-normal. You can avoid this effect by using SAS to point in the normal or anti-normal direction and turning as you go. For small burns in the normal direction, this doesn't matter much, but you may wish to compensate for it somehow if you need to change your inclination by something large like 50 degrees.

Burning normal or anti-normal modifies the direction of your angular momentum. I think it is pretty intuitive about what direction it turns your orbit in if you think of angular momentum as a direction rather than your inclination and longitude of ascending node as two completely independent coordinates. The rate at which it changes the direction of your angular momentum is inversely proportional to your speed relative to orbit.

Thus, you can make a given change in your inclination or whatever using much less delta-v when you are high above the body rather than close to it. For small adjustments, this doesn't matter much, but if you need to make large changes, or in the most extreme case, turn around to orbit in the other direction, it is more efficient to do this at a whichever of your ascending and descending nodes has greater altitude.

It can sometimes even save a lot of delta-v to first burn prograde so that your orbit reaches a very high apoapsis, then do a small burn at apoapsis to change your angular momentum, and then do a retrograde burn at periapsis to return your orbit to its previous shape. If you need to turn around to orbit in the opposite direction, this will use less than half as much delta-v as the brute force approach of a very long normal or anti-normal burn.

Hohmann transfers

Above, I said that the optimal directions to change your energy and angular momentum using as little delta-v as possible tend to be different directions. At apoapsis and periapsis, however, they coincide. Thus, it is more efficient to do your burns at these two locations when possible. You do a burn at apoapsis by however much you want to change your periapsis, and then the other way around. Or you can do them in the other order. This is called a Hohmann transfer.

It isn't always possible to do a Hohmann transfer. For one thing, if you're trying to land on a planet or dock with another rocket or whatever, it might get you there at the wrong time. If you're not already in a circular orbit, to first circularize the orbit so that you can have a second burn happen at the right time may take more delta-v than just changing your orbit in a single burn.

Another problem with Hohmann transfers is that as an ideal case, it basically assumes an instantaneous thrust, rather than one spread over a long period of time. If your angle in your orbit changes very little over the course of a burn, this is a very good approximation. It's not a good approximation to a five minute burn at periapsis when you start out orbiting on a forty minute period. That doesn't make Hohmann transfers into a bad idea so much as that it sometimes makes them impractical.

Bielliptical transfers

Pop quiz time: you're orbiting the Sun in a circular orbit with a speed of 10000 m/s. There are no planets in this system, so there isn't anything that you can use for a gravity assist. You want to crash head-on into the very center of the sun, or perhaps rather, burn up as you get close while traveling directly toward the center of the sun. How much delta-v does it take to do this?

There's an obvious answer: 10000 m/s. That's what it would take to stop so that you can go directly toward the sun. That's what it would take for the first step of a Hohmann transfer to a very low orbit. But that's not the correct answer.

Rather, you can do it in under 4200 m/s of delta-v. Instead of thrusting retrograde to stop, you thrust prograde to bring your rocket to just shy of an escape velocity. For a circular orbit of 10000 m/s, the minimum escape velocity would be 10000 * sqrt(2) ~ 14142 m/s. So you thrust by perhaps 4140 m/s, then wait a very long time until you reach apoapsis. If you reach apoapsis at, say, 1000 times your periapsis, then by conservation of angular momentum, you'll have 1/1000 times the speed. At that point, you're traveling about 14 m/s, and it only takes 14 m/s of delta-v to come to a dead stop. Then you wait a very long time and crash into the center of the Sun.

This is an extreme case, of course, but this sort of bielliptical transfer is the optimal way to make very large changes to your orbital height. The idea is that you first thrust prograde to get just shy of an escape velocity. Then you wait until apoapsis, where you're barely moving, so it costs very little to dramatically change your periapsis. Then you thrust retrograde at your new periapsis to circularize the orbit. One downside of this is that it takes a very long time to get to a very high apoapsis, however.

What is going on here is that at a very high apoapsis, it takes very little delta-v to change your angular momentum to whatever you want. If you want to change the direction of your angular momentum, this can be a relatively cheap way to do it. For example, if you're in a low equatorial orbit of a planet and want to shift to a low polar orbit, this approach is much cheaper than just burning normal for a long time.

A bielliptical transfer intrinsically costs a lot of delta-v. From a circular orbit, it takes sqrt(2)-1 times your current speed to get up to the very high apoapsis, plus sqrt(2)-1 times your final speed to get back down to your new orbit. Thus, it is a very bad choice for making small changes to your orbit. Still, it's good to understand for when you need to make very large changes to a low orbit.

Spheres of Influence

The way that gravity is believed to work is that everything in the universe has some force on everything else in the universe. One could quibble about what counts as part of "everything", but it certainly includes everything with mass. I say the way that gravity is believed to work because it really isn't well understood. The best known formulas are measurably wrong, not just the classical mechanics approach that dates to Newton, but also the adjustments suggested by relativity.

Gravity is hard to study because it is such a weak force. For example, two electrons repel each other because they have the same charge, and also attract each other due to gravity. The former effect is on the order of a tredecillion times as large as the latter. This is why after Newton wrote down his law of gravity (force = GMm/r^2, where M and m are the two masses, r is the distance between them, and G is some constant), it took about a century before Cavendish made the first effort at calculating the constant G.

One of the problems with implementing this model of gravity in a game is that the collection of all pairs of objects in the entire game is quite a lot. That's going to be computationally expensive. It also doesn't lend itself to nice simplifications such as orbits being known ellipses or hyperbolas.

Another problem with it is that it would make the game a pain to play, as there would be no such thing as a truly stable orbit. You'd put your satellite in some position and it would seem to stay there for months or years, then sometimes wander off and crash or blow up. Real-life space programs have to deal with this, but the game would be a lot easier if players didn't.

For example, you might think of Earth as being in a stable orbit about the Sun, but it's a lot less stable than you might think. That doesn't mean we're in imminent danger of crashing into the Sun. Rather, consider the length of a year. That's one orbit about the Sun, right?

But what counts as an orbit? If two observers are rotating relative to each other, they might disagree. For example, if an observer is slowly rotating at a rate of one rotation per year, he might think that the Earth is always on the same side of the Sun. The idea of a sidereal year is that we take how long it would look like it takes for the Earth to revolve about the Sun once, as viewed from very distant stars. A tropical year doesn't want to rely on some distant points, but is the time between two consecutive summer solstices. An anomalistic year tries to measure purely based on the orbit itself, and is the time between two consecutive times that the Earth is at its periapsis.

These are all reasonable definitions of a year, but they all give different year lengths. An anomalistic year is currently more than 20 minutes longer than a tropical year. And all three of these definitions of a year also have the length of a year change with time due to the effect of other objects pulling on Earth and the Sun besides each other.

The game's approach to simplifying this is to use spheres of influence. The celestial bodies (the Sun, the planets, and their moons) operate on fixed orbits. Everything else is affected by gravity of a celestial body, but does not exert any force due to gravity on anything else. For example, two rockets don't affect each other due to gravity, even though they would in real life.

Furthermore, an object is only directly affected by the gravity of one celestial body at a time. For all others, the effect of gravity on you is assumed to be the same as the effect of gravity on that one particular object. For example, your rocket could be affected by gravity properly measured from Kerbin or Minmus, but not both at once. Which one affects you depends on where you are. Loosely, the game ignores all but the strongest gravitational effect, but that isn't quite right.

More properly, each celestial body has a sphere of influence. If you are outside of its sphere of influence, then it has no effect on you. If you are inside the sphere of influence of multiple bodies, then you are directly affected only by whichever has the smallest sphere of influence, as being in that small sphere ensures that you are much closer to it than to the others. You are also implicitly affected by the bodies with a larger sphere of influence, but the effects of their gravity on you is presumed to be the same as that of the body in your sphere of influence.

For example, if you are not in the sphere of influence of any planet, then the game will compute the effect of the Sun's gravity on you, but no planets will affect you at all. If you are in the sphere of influence of Kerbin but not Mun or Minmus, then the game will compute the effect of Kerbin's gravity on you directly. It will not compute the effect of the Sun's gravity directly, but will assume that it is the same as the effect of the Sun's gravity on Kerbin. If you are in Minmus's sphere of influence, then the effect of Kerbin's gravity is assumed on you is assumed to be the same as on Minmus. The effect of the Sun's gravity on you is assumed to be the same as its effect on Minmus, which is itself assumed to be the same as its effect on Kerbin.

This is a hack that is not true at all of real life. It's the price of making a game playable. It usually isn't that far off from real-life gravity, at least on short time scales. But it does have some weird effects when you transfer from one sphere of influence to another.

One thing that you absolutely should consider when switching spheres of influence is what your velocity will be when escaping. Recall that v^2 - k/r is constant by conservation of energy. If you have just barely enough velocity to escape a sphere of influence, your speed will be basically zero when you leave. But adding a little bit of thrust long before you reach the boundary can give you a lot of speed upon leaving. If you were barely at an escape velocity before, so that v = sqrt(k/r), and then you burn prograde to increase your speed by t, then new velocity upon leaving the sphere of influence is sqrt(2vt + t^2). This will be greater than t, and for large planets like Eve, Jool, or even Kerbin, can be massively larger.

For example, if you're barely on an escape velocity from Kerbin at v = 3000 m/s, and then you add a mere 15 m/s, your speed upon leaving the sphere of influence will now be over 300 m/s. Add 60 m/s and your speed upon leaving will be over 600 m/s. That's an extremely efficient use of delta-v, and unless you're traveling to another planet with a fairly nearby orbit (e.g., from Kerbin to Eve or Duna), you nearly always want to leave the sphere of influence of a big planet with a lot of speed.

Vehicle controls

In order for a ship to go where you want, you have to have some way to control it. There are two basic approaches: manned and unmanned. In this section, we'll consider both.

Manned pods

There are a variety of pods that can hold kerbals and that you can use to control a ship. These only work to control a ship if there is a kerbal inside. Any kerbal can control the ship, but pilots can do it better than scientists or engineers.

The pods differ in a lot of ways, including size, shape, mass, and the number of kerbals that they can hold. Many pods have some degree of built-in batteries, reaction wheels, or monopropellant storage, though these tend to be pretty meager and not a viable replacement for dedicated units in any but the smallest of cases.

The cockpits are not radially symmetric, and are intended for planes, not rockets. As a consequence, they're pretty terrible as a way to control rockets.

The Mk1 Command Pod, Mk2 Command Pod, and Mk1-3 Command Pod command pods have good aerodynamic properties for launch, and are intended to go at the top of a rocket. They vary in radial size and number of kerbals. Their aerodynamics are not so great for landing, however, as they'll try to flip the rocket prograde and then you don't slow down as quickly as you might want. They're also relatively heavy for their number of kerbals.

The KV line of reentry modules have aerodynamics optimized for an atmospheric landing. So long as your lander is just a the pod on top of a stack of things with a radial size of small, you just need to get into the atmosphere at a low enough velocity as to not burn up and then aerodynamics will force you retrograde for a nice landing, at least if you have enough parachutes. Their aerodynamics are bad for launching a small rocket, however, and can easily flip you over.

The Mk1 Lander Can and Mk2 Lander Can are optimized to get kerbals into a lightweight module so as not to waste fuel. Their aerodynamics are terrible, and they're really only intended for use in a vacuum. Most planets and moons have no atmosphere, though, and the lander cans have the lowest mass of any command pods for their number of kerbals.

The PPD-12 Cupola Module is a dumb part whose only real use is contracts that require a base to have a cupola module.

The EAS-1 External Command Seat gives you a very lightweight way for a kerbal to control a ship. It's needlessly dangerous in most situations, but if you absolutely need to get your mass as low as possible for some purpose, this is a way to do it. Be warned that it cannot run crew reports.

Probe cores

In addition to the manned pods, there are unmanned pods that allow you to control a vehicle without needing to have a kerbal on board. This can be useful for a variety of purposes. They don't allow you to reset experiments like a scientist, repack parachutes or repair wheels like a parachute, gather a surface sample, or anything else that you need a kerbal for. But they can be perfectly appropriate for missions that aren't going to do any of those things, such as leaving a relay or telescope in space indefinitely. Unmanned command modules can also be useful for vehicles that will only sometimes have a kerbal present, so that you can control the vehicle without the kerbal.

By far the most important feature of an unmanned module is its SAS level. We'll get to what that means in the next section. But you'll want to get to the SAS level 3 modules as quickly as possible, and then completely ignore all of the ones with a lower SAS level, with rare exceptions. Because probe cores can offer high SAS levels, they can often make having a pilot unnecessary even on manned missions.

The probe cores that offer SAS level 3 can also store science experiment data, in addition to the normal probe core functions. Less advanced probe cores cannot do that.

SAS levels

SAS, or Stability Assist System, allows you to automatically rotate your ship in a particular direction. Rather than having to manually adjust the pitch, yaw, and roll, it can do this for you to get your ship pointing in the desired direction and keep it there. SAS can use both reaction wheels and engine gimbal to point you in the intended direction. This is very useful, and you'll want to get to SAS level 3 quickly. Higher levels of SAS give you more directional options of which way you want to point.

Your SAS level is determined by the highest SAS level of any unmanned command pod or pilot kerbal in a manned command pod on the ship. The possible SAS levels range from 0 to 3. For an unmanned probe core, the SAS level is determined by the module. For a pilot, it is his experience level, at least up to level 3. Only pilots offer SAS; engineers and scientists do not. It is also possible to have a vehicle that offers no SAS, not even level 0.

SAS level 0 offers only simple stability assist. Whatever direction you're pointing, keep you pointing in that direction. If this doesn't sound useful, its utility becomes immediately obvious when you try to fly a ship using only a scientist or engineer and no SAS. Without it, your ship will constantly rotate a little in one direction or another. When in a vacuum, you can make the ship stop rotating by briefly turning on time warp, but you can't do that in an atmosphere.

SAS level 1 adds prograde and retrograde as options. Retrograde is very, very useful for landing. Prograde is useful in a lot of situations.

SAS level 2 adds inradius, outradius, normal, and anti-normal as options. These are occasionally useful, but not very. The difference between SAS level 1 and 2 isn't important.

SAS level 3 adds pointing toward your target, away from your target, and in the direction of a maneuver node as options. The maneuver node option is extremely useful, and makes it much easier to use maneuver nodes. The target and anti-target options are only occasionally useful, but are so valuable for docking in space that I'd hold off on even attempting to dock until you have SAS level 3.

Passenger modules

Sometimes you want to take a lot of kerbals on a single mission. There could be a lot of reasons for this, such as having a lot of tourists to transport. You could load up your ship with a lot of manned command modules, and get the kerbal capacity you need that way. But that is inefficient.

A better approach is to use the passenger modules from the utility section. These don't offer any SAS, and don't give you any way to control the ship. You'll still need either a manned module or an unmanned command core, in addition to the passenger modules. But the passenger modules can carry more kerbals per ton than any command module other than the EAS-1 external command seat. They're also built to be in-line rather than designed to go on the top of a rocket, which makes it much easier to stack them and thus pack a lot of them in.

Coupling

It is possible and commonly even necessary to disconnect a ship into multiple pieces, or connect separate pieces into a larger ship. What you build on Kerbin usually isn't the shape that your rocket will keep for long.

Staging

In most cases, you'll need to stage rockets to get very far. That is, you have some big rockets that provide a ton of thrust to get you off the ground and take you well into Kerbin's atmosphere. After a while, those rockets run out of fuel, so you disconnect them, and have a smaller ship with smaller rockets that can take off from there. Depending on what you're trying to do, you may need to stage like this several times in a single journey.

As an example, suppose that we have a payload of 5 tons for command pods, science equipment, or whatever. We want to get that 5 ton payload to its destination. For simplicity, suppose that we start in a vacuum. Suppose that our last stage has a 4.5 ton fuel tank (which has 4 tons of fuel, counting both the oxidizer and liquid fuel, as well as the tank itself weighing half a ton) and a terrier engine, which ways 0.5 tons. That is good for a delta-v of 1729 m/s, with acceleration that starts at 6 m/s and increases to 10 m/s as the fuel tank empties.

Now suppose that we treat that 10 ton rocket as a payload and add another stage. The next stage will have 9 tons of fuel tanks and two terrier engines. That adds delta-v of another 1729 m/s, and also starts at 6 m/s of acceleration, increasing to 10 m/s as this stage's fuel tanks empty. I'm ignoring the mass of a decoupler for simplicity, but that wouldn't change the values much. After that, another stage that has 18 tons of fuel tanks and four terrier engines would add another 1729 m/s of delta-v with the same acceleration as before to get the 20 ton payload started. Another stage with 36 tons and eight terrier engines would do likewise. The net result of this four-stage rocket is that we have an 80 ton rocket that ends with a 5 ton payload, and has about 6915 m/s of delta-v and always has acceleration of at least 6 m/s available. That won't get you off the ground on Kerbin, but if it starts from orbit, that will get you pretty far.

One might ask, why do we need to make this several stages? Why not have the 80 ton rocket as a single stage with a ton of fuel? If we have just a single terrier engine, and have the other 74.5 tons as fuel tanks, that only gets you 5953 delta-v, which is less than before. Worse, your initial acceleration will only be 0.75 m/s, which won't even get you off the ground on the Mun. If you have eight terrier engines like in the previous example for the same initial acceleration, that reduces your delta-v to 5264 m/s. Having multiple stages works better. And that's even before we consider that later stages give you a smaller, lighter, more maneuverable rocket, which is a major advantage except when trying to take off in a dense atmosphere.

So why? Why does staging work? Without staging, when we finish a fuel tank, we have to carry that empty fuel tank around with us forever. Staging lets us discard the fuel tank and be rid of its extra mass. That allows the same remaining thrust to offer more acceleration than before. Discarding engines, too, is sometimes a drawback, but staging is still a net win if done properly. It is sometimes possible to discard empty fuel tanks without also discarding engines, but the mechanics of doing this properly and still having a decently shaped rocket are tricky. We'll come back to that in a bit.

Vertical decouplers

Perhaps the simplest method of staging is using the vertical decouplers. The TD-12 Decoupler, and about the same thing with other numbers, gives you a way to split two stages vertically. You can put the later stage on top of the earlier one, then disconnect them when you please. There are six such decouplers, and they correspond to the six radial sizes that the game offers.

The vertical decouplers all have arrows on them. When you fire a decoupler, it will disconnect the piece that the arrows point toward, but stick to the other side. You usually want the arrows to point up, as you discard the lower piece while letting the upper piece ignite its engines and take off. There are less common reasons to disconnect in a different direction, and the ability to rotate the decoupler before attaching it gives you this capability when you need it.

Usually the way that decouplers are used are as part of the game's staging sequence. Rocket engines, decouplers, and some other things can be grouped into stages. When you press the space bar (or whatever you reassign it to), it starts all of the parts on a single stage. The simplest, most common example of this is whatever decouplers are needed to discard empty fuel tanks and unwanted engines from your previous stage, while also enabling the engines that you'll fire for your next stage. You don't want to fire the engines for later stages too soon, or else they'll blow up the decoupler and whatever it is immediately attached to from the previous stage. Rather, you fire them when you decouple whatever they were attached to.

Radial decouplers

Using exclusively vertical decouplers tends to lead to some very tall, narrow rockets. That's fine for two or three stages, but once it gets too tall, this can make your rocket not be mechanically stable, so that it falls apart as you try to fly it. It's much like how if you hold a relatively short length of wire, it can seem plenty rigid, but a much longer wire of the same gauge will be bent downward by gravity.

The solution to this is radial decouplers. Rather than having all of the stages stacked vertically on top of each other, you attach some of them horizontally. This allows for a wider, shorter rocket. It also allows connecting pieces more rigidly, so that the rocket doesn't fall apart as you try to launch it.

There are three radial decouplers: the TT-38K Radial Decoupler, the TT-70 Radial Decoupler, and the Hydraulic Detachment Manifold. The TT-38K is the basic one, and the best choice for small, cheap projects. The hydraulic detachment manifold detaches the discarded portion with more force, but has such a high mass for the coupler itself that I've never seen a reasonable use for it. The TT-70 barely detaches with more force than the TT-38K, but it does stand off further, which reduces the chances of the detached piece immediately smashing into remaining parts of your rocket.

For large projects, I like the TT-70 best, as the extra force of the hydraulic detachment manifold barely matters when detaching debris weighing tens of tons, but the extra space that you start with can help. Additionally, the TT-70 makes it easiest to see exactly how things are lined up, so that if you need to separately attached multiple decouplers at almost exactly the same height, you can.

It is probable that one or more of your early attempts at using radial decouplers will fail spectacularly. Basically, you'll decouple something to toss it aside, then the next stage of your rocket will immediately accelerate into it. This causes a high-speed collision of the sort that causes parts to explode. Once you lose some of the rockets that you had counted on having, and might no longer have a symmetric center of mass, you're doomed.

The solution to this is that, if you use a radial decoupler in an atmosphere, make you're that you're accelerating prograde relative to the surface when you do it. Prograde relative to orbit or any direction that isn't particularly close to prograde is no good, as the air is likely to throw the debris that you rejected right back at you. Prograde relative to the surface means that you're acceleration is parallel to the direction in which the air will push debris, and so you don't get an unwanted collision. In a vacuum, this usually isn't a problem unless you have a really dumb design.

Stack separators

Sometimes you want to detach two sections of your ship but keep both. This can be the case if you want to take several small probes to the same area, so you make them various parts of one larger ship for simplicity to get them there. With normal decouplers, the decoupler itself will stick to one piece or another when you try to separate them.

The solution to this is stack separators. These work like vertical decouplers, except that they disconnect from the parts on both sides. As with the vertical decouplers, there is a stack separator for all of the radial sizes of rockets in the game. Stack separators cost a little more than vertical decouplers and add a little more mass, making them an inferior option if one of the pieces that you disconnect is debris that you want to be rid of, as it usually is. But anything that can be done with vertical decouplers could, in principle, be done with stack separators.

While the game has dedicated stack separators available, it is often better to build your own out of vertical decouplers. The reason for this is that while making an implicit stack separator just out of two vertical decouplers is dumb, you can put other things between the vertical decouplers. For example, you could put some batteries or reaction wheels, then attach I-beams to them. From there, you could have a lot of struts that use the "stack separator" as their base point, so that they won't be tied to either of your real vehicles when you separate them. I'll discuss this more when I get to struts later.

Engine plates

It is common for rockets to have a fuel tank with one rocket engine immediately below it. Or sometimes you have a rocket engine immediately below a stack of two or three fuel tanks. When you do that, you generally want the rocket engine centered on the fuel tank, and then vertical decouplers will disconnect the way you want.

Sometimes, though, you want to have a big fuel tank with several rocket engines attached below it. A ring of six nerv engines pushing a Mk3 Liquid Fuel Fuselage Long is my most common case of this. Sometimes you may want to have several dart or vector engines under an S3 or S4 fuel tank. I've had reasons to load up with a bunch of spark engines. The normal vertical decouplers don't work very well if you have several engines like this, as a vertical decoupler must attach to exactly one piece.

The solution is engine plates. So long you don't have an engine at the center of the piece it is attached to, you can attach an engine plate instead. This functions like a vertical decoupler, but has structure to allow you to attach the next stage to the fuel tank or whatever the engines are attached to, rather than having to pick an engine. For example, you could have a Kerbodyne S3-14400 Tank with six dart engines attached to it, then an EP-37 Engine Plate, and then another Kerbodyne S3-14400 fuel tank for the next stage. The engine plate will be attached to both fuel tanks, with the dart engines covered up under the engine plate but not required for structural strength.

If you use engine plates, make sure that you see the option to choose a length. You can adjust to any one of five lengths in the vehicle assembly building. You usually want to pick the shortest length that will fit the engines or whatever else you're hiding under there without clipping into the previous stage.

FTX-2 External Fuel Duct and asparagus staging

When you discard previous stages, you might sometimes wish to only discard the empty fuel tanks while keeping the engines. This is possible, though sometimes it makes the rocket so awkwardly shaped as to be a bad idea. What you can do is to have several fuel tanks that are all there to feed the same engine. You use FTX-2 external fuel ducts to connect the fuel tanks to each other, so that fuel can flow from one to another. You wait until the first tank(s) are empty, then discard them by staging, while keeping the others.

An alternative version of this is to have several fuel tanks each of which have a rocket attached, and fire them all simultaneously to get enough acceleration for what you need. You route the fuel ducts such that all of the engines draw their fuel from one or a few of the fuel tanks, and then when that first round of tanks is empty, you discard them, as well as the attached engines. Meanwhile, you keep the rest of the engines firing into the next stage, then all drawing fuel from a different set of fuel tanks.

Taken to its extreme, this is called asparagus staging, as you end up with rockets that look like a handful of asparagus. This was more common before the aerodynamics model was redone in version 1.0. The problem is that a handful of asparagus is not known for its good aerodynamic properties, so you end up with rockets that would be fine in space, but struggle to get out of Kerbin's atmosphere without flipping over, falling apart, or other things that ultimately cause rockets to blow up. Rather than having a large amount of asparagus staging, it's usually better to just use bigger fuel tanks and bigger rockets for better aerodynamics and better structural stability.

That said, a modest amount of asparagus staging can sometimes be useful. Just don't get carried away with it.

It is also important to realize that if two fuel tanks are connected by a coupler or stack separator, you don't need a fuel duct to pass fuel from one to the other. While couplers disable fuel crossfeed by default (to prevent an engine from an earlier stage from consuming the fuel intended for a later one), you can enable it if you want to.

Docking

Suppose that you design your dream space station. It has some of this, some of that, and a bunch of some other things. Space for 72 kerbals. 50 tons of monopropellant. Four science labs. In all, the space station has a mass of about 1300 tons. And you want to put it into a low polar orbit of Jool.

So you design a magnificent rocket to deliver your station to Jool. With all of the staging needed, your gigantic rocket weighs over 40,000 tons. You press the launch button to take it to the launchpad. Then you see that you've got boosters hanging far off of all sides of the launchpad. So far off that the lack of structural support beneath them makes the rocket unstable. It falls apart and blows up on the launchpad before you get a chance to launch. Oops. Does this mean that your dream is dead? Hardly!

In the previous section, we talked about starting with big rockets and splitting them into smaller pieces, commonly to discard empty fuel tanks or other debris. It's also possible to do the reverse of this. You can launch multiple pieces, then connect them to create a larger ship.

There are a variety of reasons why you might want to do this. One is as a way to create larger bases or space stations than it is practical to launch all in one go. Another is to temporarily connect two ships so that you can transfer kerbals, fuel, scientific data, or whatever else you want to transfer from one to another. A vehicle may run out of fuel and become stranded, and you may want to send a rescue ship to pick it up and bring it home. You can have a base or rocket with a bunch of detachable modules, so that you can have that science lab or mining gear when you want it, and not have to carry it around with you when you don't.

Docking ports

One way to connect ships is with docking ports. There are three radial sizes of docking ports available (tiny, small, and large), with multiple form factors for the small radial size. If you want to connect two ships in the future, you give them both a docking port of the same radial size in the places where you will want to connect them. Later, you can have the two docking ports touch, and they will stick together. We'll talk about how to actually dock in a much later section, as it is tricky to do.

One advantage of docking ports is that you can pick exactly where the two ships will dock. They could be rotated a little differently from how you planned if you don't have some way to control that axis when you dock. But other than that one rotational degree of freedom, they'll end up attached exactly how you planned.

In addition to docking, you can also undock. Click on a docking port that is linked to another and you can undock to disconnect them. Thus, the connection from a docking port can be only temporary if you want it. You can dock, transfer fuel, data or whatever, and then undock and carry on.

Advanced grabbing unit

The other option for docking is the Advanced Grabbing Unit, or its recently added smaller cousin. The idea is that one component doesn't have to have any docking equipment, but the other ship can latch on using an advanced grabbing unit. This is the only option when you don't get to design one of the ships, such as if you want to grab an asteroid. It is also an option for grabbing other ships.

The advanced grabbing unit generally doesn't give you nearly as precise of an assembly as the docking ports. You get to pick the precise point on your own ship that has the advanced grabbing unit, but you don't get to pick the precise point that it will latch on to on the other vehicle. Rather, it's probably going to be off somewhat from what you had planned. In addition to being rotated wrong, the point that you latch on to can be off in two dimensions.

When using an advanced grabbing unit, the resulting, combined ship isn't likely to still be radially symmetric. Sometimes your center of mass can be significantly off from your center of thrust, which makes it very hard to control. You can adjust how you've grabbed it after making the initial grab, but realistically, you're never going to get it exactly perfect.

Connecting two ships via an advanced grabbing unit allows you to transfer scientific data and kerbals between them. It does not allow you to transfer fuel, however. When you only want to transfer data or kerbals, using an advanced grabbing unit is easier than needing to line up two docking ports perfectly.

Landing gear

You don't actually need any of the equipment in this section. When you want to land, you can burn retrograde to slow to a near stop, then touch down gently, landing on your engines or whatever the lowest point of your rocket is. So long as you positioned equipment correctly, you can have kerbals get out, plant a flag, reset science equipment, or whatever else you need, and then get back into the vehicle. All that said, a lot of the gear in this section sure does make landing a lot easier.

Lander legs

When landing, there are two basic problems. One is that you could hit the ground too hard, causing parts to explode as part of the collision. The other is that you could land in area so uneven that your ship falls over. The latter is sometimes okay if you're landing on Kerbin at the end of a mission and just going to recover the vessel anyway, but usually means that you're stuck and can't take off. Lander legs can help with both problems.

All parts in the game have some maximum velocity at which they can hit the ground without breaking. Deployed solar panels will generally shatter at the slightest direct touch, but so long as you're not landing on the solar panel itself, everything can handle touching down at 4 m/s, and just about everything can handle up to 6 m/s. Depending on how you build your rocket, you may be able to handle a little higher than that.

So what happens if you hit the ground at a little over 6 m/s? If whatever touches the ground first can't handle that speed, it explodes. If the lowest part can handle that speed, but is a rigid part connected to something above it that can't, the part above it can explode. If what touches the ground first is lander legs, then their springs can absorb a lot of the shock of landing, so that other parts further up the rocket don't explode. This won't always make it safe to touch down at 12 m/s, but it might make it safe to hit at 8 m/s. Ultimately, you'd like to land at under 6 m/s, but lander legs can bail you out if you go slightly over that.

Lander legs are springy, and they explode not by whether they touch the ground at higher than their rated speed, but whether that provides enough force to crush the leg and destroy it. For example, a LT-2 Landing Strut is officially rated at 12 m/s impact tolerance, but I've had a vehicle land at over 35 m/s on LT-2 lander legs with no damage.

The springs in lander legs don't help you if you land in water, however. They just submerge right into the water, and whatever you were try to protect by putting lander legs under it then smacks into the water, and may explode.

The other advantage of lander legs is that they stick out further from your vehicle. A given position of the rocket touching the ground is stable if the line through your center of mass and the center of the planet or moon you land on passes through the convex hull of the collection of places where your vehicle touches the ground. You may not be familiar with the mathematical concept of the convex hull of a set, but it's a pretty simple concept and easy to look up. Lander legs stick some points that hit the ground further out from your rocket, giving you a significantly larger convex hull, and allowing you to land on a steeper slope without tipping over.

Another use of lander legs is that you can adjust the spring in them after landing to raise or lower your entire vehicle slightly. I've used that to line up pieces for docking. Be warned that if you don't revert the spring strength to automatic before switching away from the base, it is likely to explode when you switch back. I'm pretty sure that that is a bug.

That said, lander legs are hardly indestructible. Too much force on them will cause them to explode themselves. This can happen because you hit the ground too hard, or because you have too few to hold up your rocket. The game says that engineers can repair broken lander legs, but I've never seen them break in a repairable manner. Rather, they explode and are gone.

There are three models of lander legs in the game. The largest, the LT-2 Landing Strut, is usually what you want to use. Only for landing very small vessels does it really make any sense to save some mass by using the others.

Rover wheels

If you want to land in a particular spot, you can aim carefully and land right there exactly. Depending on the precision needed, that can sometimes be very difficult. For scanning surface features, you need to be within 4 m, and that sort of precision can be very difficult to achieve when landing from space. One solution to this is to put your vehicle on wheels and then roll around on the ground. Get kind of close, such as within 1 km, then drive over to the surface feature and stop right next to it.

Rover wheels can also give you a lesser degree of the same benefits as lander legs. They can't support as much mass as lander legs, and they don't stick out as far, so you should prefer lander legs to wheels if you don't actually want to roll around.

Rover wheels are also prone to breaking, and will not roll after they break. A level 3 or higher engineer can fix wheels if they break. They can also explode, but the threshold that it takes for them to explode is much higher than for them to merely break.

Rover wheels vary in their size, how much weight they can support, how fast they can go, and how much torque they can apply to brake or push up hills. I generally prefer the TR-2L Ruggedized Vehicular Wheel, as it can support more weight and move faster than the smaller wheels. The RoveMax Model XL3 is the largest rover wheel by far, but it cannot steer, so a vehicle based on them cannot turn.

Ladders

Sometimes, you need a kerbal to go outside and do something. It is nice to be able to get back into the craft without needing the awkwardness of firing up the jetpack. For a simple EVA report or surface sample, you can stay holding the door. If you need to plant a flag, repack parachutes, repair wheels, or reset certain science equipment, ladders can often make it so that you just climb up or down at your leisure to get to where you need to go. On Kerbin, Eve, Tylo, and Laythe, gravity is stronger than your jetpack, so you can't go up at all unless you have something to climb.

There are three types of ladders in the game, all placed in the utility section. For the most part, the Kelus-LV Bay Mobility Enhancer is the best of them, as it is the longest, and they all have the same mass.

Ladders other than the Pegasus I Mobility Enhancer can be deployed and retracted as needed. That allows you to get them out of the way when they aren't needed, land safely, and then deploy your ladders and have them exactly where you need them.

Airplane wheels

In addition to rover wheels, there are also airplane landing gears. They are built to allow you to take off and land, which means they have to function while rolling on the ground at very high speeds. They are also built to keep the rest of your plane well off of the ground, so that you don't crash due to a slight bump.

The problem with all of this is that it assumes that you're building a plane, which you probably aren't. If you are, then yes, do look at the airplane wheels. If not, then ignore them.

Parachutes

The final type of gear intended for landing is parachutes. As with ladders, these are found in the utility section, not the ground section.

As you pass through an atmosphere, drag from the air will slow you down relative to the surface. It is important here that your speed is relative to the surface, not relative to orbit. The idea of a parachute is to have a large surface area that will catch the air to slow you down a lot more than just ordinary air resistance would. Depending on your design, this can sometimes slow you down enough that once you enter the atmosphere, you don't need any further thrust to land safely. Other times, it just slows you down most of the way, so that you only need a little bit of thrust at the very end to land.

Parachutes only work at all in an atmosphere. That means that you are restricted to Kerbin, Eve, Laythe, Duna, and Jool. Parachutes are completely useless everywhere else, and merely a waste of mass.

Furthermore, parachutes will slow you down more in a denser atmosphere. They would provide so little force in a thin, upper atmosphere that they won't even deploy. Rather, they wait until there is some substantial amount of air before they deploy. That means that parachutes aren't that effective on Duna, but are extremely effective on Eve. Parachutes are generally ineffective on Jool because they won't fully deploy until you get near sea level, by which point, the pressure is so high that rocket engines won't work at all.

Parachutes effectively harness the air to exert force to pull your ship in a retrograde direction. But they can only exert so much force without tearing off. By default, parachutes won't deploy until you're traveling slowly enough for it to be safe. In some cases, you can rely on simple drag with the air before parachutes are deployed to slow you down enough to reach this threshold.

On Eve or Jool, you can't just rely on a bunch of parachutes as the only way to slow you down. Those planets are large enough that you'll burn up in the atmosphere before you slow down enough for parachutes to deploy unless you either burn retrograde or use a heat shield. That can happen on Kerbin, Laythe, or Duna, too, if you come in too fast, but parachutes alone are enough from a low orbit.

There are two types of parachutes: drogue and main. Drogue parachutes are smaller and tougher, so they can safely deploy at higher speeds. They don't offer as much drag once deployed as main parachutes, however. Ultimately, you probably want some of each type.

Parachutes also partially deploy at one stage, then fully deploy at another, lower stage. If they fully deployed too soon, the huge amount of force to slow you from high speeds could tear your ship apart. The partial deployment is based on atmospheric pressure, while full deployment is based on altitude. Normally, the order of parachute deployment is that drogues partially deploy, then main parachutes partially deploy, then drogues fully deploy, and then your main parachutes fully deploy. Breaking this into four stages makes it easier to have progressively increasing drag without too big of a spike all at once that tears your ship apart.

That said, you do have to be smart about parachute placement. You generally want to place them high up on your craft. They'll pull you retrograde from wherever they are placed. If they are placed up high, this pulls your ship right-side up, so that you can land in the direction you want. If placed too low, they could flip you upside-down.

Still, that doesn't mean that you want to put a lot of parachutes all on the highest point. For a heavy vehicle, that much force applied to a single part can sometimes yank it off entirely. Rather, you want to spread them out quite a bit to apply their force somewhat evenly, while keeping the center of parachute force substantially above your center of mass.

If landing is the end of a mission, such as to recover a vehicle on Kerbin or leave a probe permanently located on another planet, then parachutes can be single use. If you have an engineer of level 1 or higher, you can repack parachutes to use them again. This allows you to use parachutes to land once, then repack them, then deploy them again the next time you land. The engineer has to be able to get close to a parachute to repack it, so you may need to have a lot of ladders available. This can also restrict parachute placement to places you can reach.

The game has five particular models of parachutes, but other than the extremely early game when the Mk16 Parachute is the only one available, the Mk2-R Radial-Mount Parachute and Mk12-R Radial-Mount Drogue Chute are really the only ones that are useful. In particular, the larger Mk16-XL Parachute and Mk25 Parachute are completely useless. Using two of the analogous radial parachute (and an aerodynamic nose cone where the larger parachute would have gone) instead will get you more deployed drag for less mass and less non-deployed drag.

Communications

There are two basic reasons why you'll want to have your ships be able to communicate with the home base on Kerbin. One is sending information from Kerbin to the ship to tell it what to do. If you have a pilot on board, you always have full control of the ship, as the pilot can do whatever he needs to. But probe cores don't know what to do, so they won't be fully functional unless you can contact them from Kerbin to tell them what to do.

The other reason is sending information from the ship back to Kerbin. When you run some science experiment, you can recover the data by flying the ship all the way back to Kerbin and landing. But you can also get some science immediately by transmitting the data back. The latter often gives you less science than returning the vessel, but you can also transmit the data, immediately rerun the experiment, and get the rest of the science that way. That gives you some science now and some later, rather than all of it having to wait for later.

Controlling probes

If you have a pilot on board, you'll always have full control of the vessel with whatever SAS capabilities the pilot can offer, even without any communications link back to Kerbin. But without a pilot, you'll either have only very limited controls (no SAS) from a scientist or engineer, or only what controls a probe core can give you. And if you can't contact the probe core, you can't make it do what you want.

Exactly what you can make a probe core do while you cannot contact it depends on your difficulty settings. The default is that it will not let you create maneuver nodes, and will not let you do any amount of thrust beyond maximum or nothing. You can also set it to give you no control of the ship at all. Or you can make things easier on yourself and always have full control of a probe even without a communications link.

Communications gear

There are two types of communications gear: antennas and relays. They work just as well for transmitting data, but relays can receive data, as well. Relays allow a spacecraft to act as an intermediate node when some other ship wants to transmit data, while antennas cannot do this. As such, if you're going to bring a relay, there is scarcely any point to bringing an antenna, too.

That might lead you to ask why use antennas at all. The answer is that antennas are smaller, cheaper, lighter, and can be deployed to avoid aerodynamic issues. You generally need to ask whether you need a vessel to relay communications from other vessels. If not, then make things simpler and bring an antenna instead of a relay. Ground-based relays aren't very useful, as the planet they're on blocks them at least half of the time, so you likely don't want a relay for vessels that are going to land somewhere and stay there.

There are six strengths of antennas for you to use. The weakest is built into command pods, but other than doing experiments around Kerbin (or Mun, once you upgrade the tracking station), is really only intended to let you contact some other relay. The next two are really only intended to connect to another vessel in the same planetary system, and likely the same planet or moon within the system.

If you're using an antenna, you might as well use the most powerful one you have access to, with exceptions for very small and light vessels. Even the top end Communotron 88-88 is smaller, cheaper, and lighter than the RA-2 Relay Antenna that is only 2% as powerful as it. For a relay, it can depend on just how much of a problem the bulk and awkward aerodynamics of an RA-100 are. Regardless, it is pretty much always better to use one of a larger relay than to combine multiples of a smaller one.

While weak, the Communotron 16-S can be handy for flying in an atmosphere. Unlike all other antennas, it is surface mounted, rather than deployed, so wind won't snap it off. Unlike the surface mounted relays, it is very lightweight and does not cause aerodynamic problems.

CommNet

In order to be able to communicate with a vessel out in space, you don't necessary need a direct signal from Kerbin to the ship. Indeed, sometimes that is impossible because there is some planet or moon in the way--often the one you're landed on. Rather, you can have the ship connect to one satellite, that satellite connects to another satellite, and the second satellite connects back to Kerbin. Or however many hops you want.

Your network of satellites that can act as intermediate hops to connect any spaceship to Kerbin is called CommNet. Only vessels that have a relay rather than an antenna can act as intermediate hops. Larger, more powerful relays allow connecting over longer distances. You can also put several relays on a satellite, and they will partially combine to further increase distances.

A communications link isn't necessarily just there or not there. There can be intermediate amounts of strength. For purposes of controlling a probe, any weak connection is good enough. For transmitting science, a stronger connection will get you more science. This is unrealistic, as what they would do in real life is to still get all of the data back, but just take longer to do it. For example, transmit every bit 5 times instead of 1, then do a majority vote to determine what the real bit is.

Exactly how many relays you need to send out depends on your communications needs and how reliable you need the link to be. For example, if you have one powerful relay near a planet, any other craft near that planet only needs to connect to that one relay, which can send the data back to Kerbin. And that might work fine most of the time, but occasionally, you'll be on the opposite side of the planet from that relay and lose the connection. Or if you're going to land, then "occasionally" might mean about half of the time.

That is solvable by having a bunch of relays about the planet. It is generally better for them to be in a relatively high orbit, so that the planet only infrequently blocks one relay from seeing another. You can have one satellite with a bunch of relays on it for the main jump back to Kerbin, and the rest be much weaker. That way, if your vessel can see any one of the relays, it can connect to it, which will connect to other relays to get to the big, powerful one, and from there, send the data back to Kerbin.

The transmission strength matters for both ends of the link for a connection. The strength of the link is basically the geometric mean of the strength at the two ends. You can also put a satellite with a bunch of relays in orbit about Kerbin, to have a far stronger connection to it from deep space than any of the ground-based satellites offer.

Transmitting science

Any part that is capable of storing science experiments results can ask to transmit the results back to Kerbin. It will actually use any antenna or relay to do the transmission. Transmitting data back uses electricity, and if you run out of electricity before you finish the transmission, it fails. If this happens, you still have the data on your ship, but don't get any science for it.

The amount of science that you get by transmitting data depends on the strength of your connection back to Kerbin and the particular experiment. An EVA report or crew report will give you the full science value by transmitting it. Other experiments will only give you a fraction of the science value from transmitting it, and you'll have to go land back in Kerbin to get the rest of the science value. To a scientist on Kerbin, someone telling you about a moon rock just isn't as good as actually having the moon rock in your hands.

Heat

When traveling through space, it is quite possible for a spacecraft to overheat and explode. This section is about what causes that and how to avoid it. While rocket engines put out considerable heat, I'll ignore them for the rest of this section, as they don't put out enough heat to cause any parts to overheat and fail unless you botch your design by having a rocket engine pointed right at some other part of your ship.

Atmospheric entry

The main source of overheating and burning up is moving too fast inside of an atmosphere. It is sometimes called re-entry, as the most natural place for it to occur is when a ship returns to Kerbin. It is also possible to overheat and explode before you get out of the atmosphere in the first place, though doing so on Kerbin takes a sufficiently botched design that it's unlikely that you'll ever do so by accident.

The reason why atmospheric entry causes overheating is mysterious to a lot of people. Some think it is due to friction with the air, but this is completely wrong. Traveling at 2500 m/s at a height of 40 km above Kerbin can cause serious heat issues, even though it results in far less friction with the air than traveling at 100 m/s at sea level. You can readily verify this by looking at how quickly your velocity changes due to air resistance. And traveling only 100 m/s at sea level causes no heat problems at all.

It is sometimes said that the heating of atmospheric entry is caused by compressing air, as in the ideal gas law, PV = nRT. This is kind of true, but not very helpful. It's not at all obvious what to use for the volume, and whatever you use, air is rushing in and out. Having P, V, n, and T all changing wildly makes it difficult to glean any insight. (R ~ 8.314 J/K-mol is a constant and does not change.)

A better model is that of gas molecules bouncing around randomly. The kinetic energy of a molecule is .5mv^2, where m is the mass of the molecule and v is its speed. An atmosphere may be composed of a mix of numerous gases, but a single molecule isn't going to cause your ship to overheat, so we may simplify this by assuming that all of the molecules in an atmosphere are average in some sense (but not velocity, where the average velocity vector is 0). Thus, the temperature of a molecule is proportional to the square of its speed.

The key insight here is, speed in which reference frame? Oxygen molecules on Earth typically have a speed of around 500 m/s relative to the nearby surface of the Earth. But if you're in a spaceship and moving at 2000 m/s relative to the surface, those oxygen molecules aren't moving at 500 m/s relative to you. They're probably moving at around 2000 m/s relative to you. And that means that, to you, they seem many times hotter.

If an air molecule is moving at v m/s relative to the planet it is near, and you are moving at w m/s relative to that planet, then the molecule is moving at somewhere between w-v m/s and w+v m/s relative to you. For complicated reasons (you can derive this with a double integral over a sphere if so inclined), if the direction of the molecule relative to the planet is uniformly random, then the root mean square (not average when doing kinetic energy computations) speed of the molecule relative to you is sqrt(w^2 + v^2). If you're traveling fast enough for atmospheric entry to be an overheating problem, then w is going to be much greater than v, so this will be a little greater than w.

The upshot of this is that, when you're approaching an atmosphere at high speeds, the apparent temperature of that atmosphere will be approximately proportional to the square of your speed relative to the surface of that planet. And yes, it's relative to the surface, not orbit, though in the game, that doesn't make a very big difference other than on Jool. Still, a given orbital speed will be a smaller speed relative to the surface if you're traveling east near the equator.

The rate at which the atmosphere will heat your ship is proportional to (the difference between the atmosphere's apparent temperature and your ship's temperature) times (the density of the atmosphere). The first component of temperature difference is just how thermal transfer works. The second is because heat is transferred by collisions with individual molecules, and the more of them that are there for you to hit, the more heat can be transferred.

Or at least, that's what it would be if you weren't moving. The front part of the ship will hit many more molecules as it cuts a path for the rest of your ship to follow. The exact term is complicated, but at high velocities, you roughly have to multiply by (your speed relative to the atmosphere) / (average speed of an air molecule). This means that the front part that is hitting the brunt of the atmosphere will heat up much faster than side parts, even if both see the same apparent temperature of the atmosphere.

The upshot is that the temperature to which the atmosphere will heat your ship is roughly proportional to your speed squared, and the rate at which it will push the front parts of your ship toward that temperature is roughly proportional to your speed cubed. That 100 m/s at sea level ship doesn't cause overheating because the equilibrium temperature is cool enough to not be a problem. But if you enter an atmosphere at 3000 m/s, that's likely to cause enough heating to cause your ship to explode, at least once you get to denser portions of it. Still, the very top of an atmosphere is so thin that even very high velocities are okay.

Still, it is not the case that the effective temperature of air depends only on your speed. The effective speed of individual molecules will be roughly your own speed when you are traveling fast enough, but different gases will have different root-mean-square speeds even at the same temperature. At a given temperature, all gases will have about the same kinetic energy per molecule, but that means that those with lower masses will tend to have higher speeds. While I haven't done precise measurements, it is fairly obvious that Jool's atmosphere causes much less heating than would be expected from your speed as compared to other atmospheres, while Eve's seems to cause more of it.

The Sun

The other major source of heat that can cause your ship to explode is the Sun. Basically, if you get too close to the Sun, you die. Technically, this could add to atmospheric entry heating, but no atmospheres are close enough to the Sun to be a real problem. Thus, other than when trying to get into a low orbit about the Sun, you can generally ignore the Sun's heating.

For science purposes, the boundary between a low and high orbit about the Sun is one million km, or one thousand Mm, as the game will display it when you approach that threshold from above. So long as you're either in a high orbit about the sun or barely in a low orbit, you can largely ignore such solar heating. You'll get warnings that your ship is hot while near the edge of a low orbit, but it won't actually blow things up. If you want to get much closer to the sun, you absolutely can cause your ship to explode.

Blackbody radiation

The main source of cooling in the game is blackbody radiation. All normal matter emits electromagnetic radiation unless it is already at absolute zero. That's just how the universe works.

To explain the name, an ideal blackbody is an object for which radiation reflected is negligible as compared to radiation emitted. There are basically two ways this could happen. One is that very little radiation reaches the object, so that radiation reflected will be neglible regardless of whether it is reflected or absorbed. The Sun is a good example of this. The other is an object that absorbs nearly all radiation rather than reflecting it. An object that does this for the visible light spectrum will visibly appear black, which is the source of the name. Other portions of the electromagnetic spectrum matter, too, especially infrared if dealing with objects near room temperature.

According to the Stefan-Boltzmann Law, the intensity of blackbody radiation that an object emits is proportional to the temperature to the fourth power. The temperature here has to be a distance from absolute zero, so it is customary to use Kelvins (not Celsius or Fahrenheit!). There are some complications, in that some objects will radiate more heat at a given temperature than others. In particular, those that reflect more energy (so as to absorb less) also emit less. But for a given spaceship, the rate at which you cool down via blackbody radiation is proportional to temperature to the fourth power. Which is to say, it scales up very quickly as you get hotter.

This allows you travel in an atmosphere at a high enough speed for it to have an apparent temperature of 3000 K without your ship ever exceeding 2000 K, at least so long as the atmosphere is thin enough not to heat you up too quickly. So long as the rate of heating from the atmosphere (or from the sun) is less than the rate that you'll shed that heat via blackbody radiation at a temperature just shy of what will cause you to explode, you'll be fine.

The spectrum of blackbody radiation emitted also depends on the temperature. At room temperature, it is almost entirely in the infrared range, but as an object heats up enough, it can start emitting a lot of visible light. That's what causes very hot objects to start glowing red. Or orange or yellow if they get hot enough. The game doesn't modify the color changing as objects heat up, though, other than by making things turn red.

Thermal control systems

Most of your cooling will come from blackbody radiation, but you can also use thermal control systems to transfer heat within your ship. This is mainly used to cool mining parts, but you can also use it to transfer heat from the front portion of your ship that is heating up tremendously to a radiator that isn't, and then the radiator can dissipate that heat off into space. That's typically not a great idea for handling atmospheric entry, as the good thermal control systems will break off from drag with the air. It can help if you want to go unreasonably close to the sun, however.

Part fragility

All parts have some maximum temperature for safe operation. If they go above this, they are liable to explode. Many parts have a maximum temperature of 2000 K. It is often handy to think of your entire ship as having a maximum safe temperature of 2000 K. So long as the ship stays below that, you're fine.

Some parts have a lower maximum temperature, however, most commonly 1200 K. That's true of all science equipment and rover wheels, for example. Such equipment largely needs to be protected from overheating. In some cases, this means putting them inside of a service bay, so that they won't get hot during atmospheric entry. In others, it can mean leaving them out of the mission entirely. You really don't need rover wheels to go diving into Jool's atmosphere or low orbit about the sun. If you can't protect them, such as when trying to land a large rover on Eve, you'll just need a much more robust retrograde burn than normal to protect them from atmospheric entry.

There are also some parts with a maximum temperature greater than 2000 K. Most of the time, this doesn't offer any benefit as compared to a maximum temperature of 2000 K, as if something else reaches 2000 K and blows up, your mission probably still fails. The key exception is for the front parts that take the brunt of the heating during situations where parts are likely to overheat.

Heat shields

One strategy to protect your ship from death by overheating is to put some parts that can handle very high temperatures in the front of the ship, so that the brunt of the heating is borne by parts that can handle it. While there are some parts that could be reappropriated for this use, heat shields are specifically designed for it. All heat shields have a maximum temperature of at least 3300 K. Furthermore, most of them have some ablator that can boil off to absorb heat and protect the heat shield even against heating loads that would otherwise have caused it to exceed 3300 K and explode.

Heat shields aren't really intended for getting closer to the sun. They're unnecessary if you just want to get to low orbit for science purposes. They can help if you want to get closer than necessary for science reasons, but even heat shields will overheat and explode if you get too close.

Rather, the real intended use of heat shields is for heating from atmospheric entry. That's obviously useless for bodies that don't have an atmosphere. It's also pretty easy to land on Kerbin, Laythe, or Duna without a heat shield. If you're in a low orbit just outside of the atmosphere, then slow down a little to get your periapsis into the atmosphere and wait, you'll reach the ground without overheating, at least provided that the atmospheric entry heating is mostly hitting parts that can handle 2000 K.

Rather, the real use of heat shields is if you need to hit an atmosphere at higher speeds. If you want to land on Eve or reach Jool's lower atmosphere, then expect to overheat and explode unless you either have a heat shield or use a lot of fuel to burn retrograde and slow down.

Alternatively, a heat shield can allow you to approach a planet at a higher velocity without having to burn fuel to get into a low orbit first. For example, if properly shielded, you could set your Kerbin orbit to a periapsis of about 30 km while orbiting one of Kerbin's moons, enter Kerbin's atmosphere at around 3000 m/s, have the heat shield take the brunt of the atmospheric entry heating, and survive. If you wanted to first return to a low orbit about Kerbin before entering its atmosphere, you'd need about another 1000 delta-v of fuel to burn retrograde. That sort of aerobraking can save you a lot of fuel.

Still, heat shields can only do so much for you. If you want to enter an atmosphere at 20000 m/s, your heat shields will overheat and explode, and then so will the rest of your spacecraft. So while they increase the speed at which you can enter an atmosphere, they hardly make it infinite.

Additionally, while it usually isn't that hard to use heat shields to protect a small craft that only needs to land to finish its mission, it's much harder to properly shield larger vehicles that will have additional stages and need to subsequently move around. Heat shields are unaerodynamic, which makes it easy for drag to cause your ship to flip over, have something else besides the heat shield take the brunt of the heating, and still explode. Heat shields having a lot of drag is an intentional and necessary feature of their design, as otherwise, they wouldn't slow you down to survive landing. Try leading with aerodynamic nose cones and watch your ship crash into the ground at speeds too high for the parachutes to safely deploy, which would be the alternative if heat shields were more aerodynamic.

Mining and refueling

One challenge to any mission is that you only have so much delta-v. Once you've used up your fuel, you can't thrust anymore, and you're done. Hope you've made it back to Kerbin, or at least reached your intended destination.

Except that the universe is made out of rocket fuel. All that you have to do is land somewhere, pick up some dirt, and fill up. That's not how real-life works, of course, but it is how the universe of Kerbal Space Program works.

In order to refuel, there are three things that you need: mining drills to dig up ore, tanks to hold the ore, and converters to process the ore and turn it into your needed fuel. You can't create xenon, but you can convert ore into all of the other types of fuel: liquid fuel, oxidizer, and monopropellant.

You can refuel on planets or moons. You must be landed, however; splashed down doesn't count. And you can't drill for fuel on Jool or the sun, since you can't land there. You can also refuel on asteroids or comets, though asteroids have a limited amount of ore that you can drill up. Planets and moons have unlimited ore.

Excavators

There are two excavators in the game: the 'Drill-O-Matic Junior' Mining Excavator and the 'Drill-O-Matic' Mining Excavator. As you might guess, the latter has higher cost, mass, size, and output.

The critical difference is that the full excavator can dig up ore anywhere that there is ore at all. The junior version can't get any ore at all if the concentration is too low. At default ore concentrations, the larger excavator can get ore absolutely anywhere that you're landed, while the junior one won't be able to find anything in some places. If you reduce the ore concentration of the universe, there will also be places that the larger excavator can't pick up any more, but still fewer of them than where the junior one will fail.

It can be quite a nasty surprise to land somewhere in a mission that requires you to refuel, and then learn that there is no ore to be had. Mission failed. Because of that, I don't recommend using the junior drill at all unless you absolutely have to.

Both drills are radially mounted, so if you only have one, your center of mass will be off center. As such, if you're going to use mining drills at all, you probably want two, placed in a radially symmetric manner.

Ore

The game regards ore tanks as a type of fuel tanks. There are three, in different sizes: radial, small, and large. They all helpfully give their size in their name. Unlike most fuel tanks, ore tanks can jettison their contents without needing a drain.

You have to have at least one ore tank or else mining drills won't have anywhere to place their ore. They can't pass ore directly to a converter. But even the smallest ore tank as a small buffer is plenty for most purposes. If using radial ore tanks, you might want two, so that you can make them symmetric. But if you're only ever going to run a converter while you're on the ground mining, two radial tanks or one small (whichever is easier to fit into your design) is plenty for a lot of purposes.

There are some non-obvious reasons why you might want more ore holding capacity, however. One is that in career mode, there are missions to drill up a particular amount of ore on a particular body, generally less than 3000 ore. If you have two large holding tanks, and dump their contents just before leaving a base to return to the space station, but leave the drills running, they'll fill up with 3000 ore while you're away, at least if you're away for long enough. If you later pick up a mission to mine some amount of ore on that particular planet, you can switch back to the base, instantly complete the mission (as it credits you with acquiring the ore when you switch to the base), and dump the ore again in preparation for the next mission.

Full ore tanks have a very high density, as they have far more mass than a rocket fuel container of the same volume. Most rockets will float if they splash down in the water. If you have some full ore tanks around, you can make your ship heavy enough to sink. If you sink to the bottom of an ocean, you can perform science experiments while landed in the ocean, rather than merely splashed down. That gives you separate science rewards--including some on Laythe that are otherwise unobtainable. You can also return to the surface if so inclined by jettisoning your ore tank contents.

A third reason to consider having a lot of ore tanks is that they have a better ratio of wet mass to dry mass than liquid fuel tanks (without oxidizer), as well as offering a different and often more convenient form factor than the jet fuel tanks. By packing ore instead of liquid fuel, then converting it to liquid fuel while in flight, you can get more delta-v for nerv rockets from less mass and much less space than if you had instead packed jet fuel directly. You do need at least one jet fuel container as a buffer for conversion, however. This only works for very long flights that have plenty of time to convert the ore into jet fuel, and really only lets you burn as much at a time as you have space to store jet fuel. But nerv rockets tend to be targeted at very long distances, especially interplanetary, so this fits their typical use case perfectly.

Converters

There are two converters: the Convert-O-Tron 125 and the Convert-O-Tron 250. As you would probably guess, the latter has higher cost, mass, size, and output. But while the large converter will give double the output per unit time of the small converter, it actually burns only one fifth as much ore. As such, the larger converter gives you ten times the ore efficiency of the smaller one.

The two converters use the same amount of electricity while running. Both converters and excavators use a lot of electricity, so you'll likely want some pretty robust electricity generation methods to power them. Alternatively, you could use the trick of waiting for your batteries to fill, starting both the converters and excavators, and then switching back to the space center. Your electric charge level only changes while you're watching a base, so the converters can keep running without needing more electricity while you're elsewhere.

Unlike with excavators, the smaller converter does fundamentally work, however, at least when landed on planets and moons. It just takes ten times as long to refuel as the larger one would. The smaller converter is basically unusable on asteroids, where you can only recover a finite amount of ore before the asteroid runs out. But elsewhere, it's really just a question of how long you're willing to wait.

Thermal efficiency

Excavators and converters burn a lot of electricity, and that mostly gets turned into heat. If not cooled properly they can overheat. They do need to get fairly hot, as they work better once they've heated up, but overheating reduces their efficiency.

You can make excavators and converters work by strobing them off and on. Turn them on, let them heat up, then turn them back off and let them cool down. But the faster solution to let them run continuously is to use thermal control systems. Those will automatically cool excavators and converters down to their optimal running temperature if they had been running long enough to exceed that. Thermal control systems have a finite cooling capacity, so make sure that you bring enough to handle however many converters and excavators you want to run at once.

Scanners

The ore concentration varies by biome, and is rolled randomly when you create a new game. Rather than just landing somewhere and finding out how much ore is there (possibly none, depending on your settings), you can also use a scanner to find out before you land.

There are three scanners. The M700 Survey Scanner must be used first. The idea is that you put a satellite in a polar orbit of moderate height, and then run a survey. What would happen if this were realistic is that a survey would take place over an extended period of time, as you pass over every portion of the planet over the course of many revolutions. The polar orbit allows that, while a non-polar orbit does not, as it does not take you over the poles. But that would be a pain, so instead, the game just gives you the results of the scan almost immediately.

The game uses your antennas or relays to transmit the results of the survey back to Kerbin. As with transmitting science, this takes electricity, and if you run out, the transmission can abort. For most bodies, this doesn't take very much, but it takes quite a lot for Jool, which is huge. As such, you'd better bring either a lot of batteries or some very robust electricity generation, which that far away from the sun, probably means fuel cells. You cannot do a survey of the Sun.

The other two scanners are intended to get you a higher resolution of the ore concentration in particular locations. As the ore varies by biome, you can largely figure out where to go by comparing the survey scanner results to a biome map from any device that gives you KerbNet access. As such, I don't personally find the smaller scanners useful.

Electricity

A number of pieces of equipment use electricity. As such, you need to have sufficient electricity available to power them. The game doesn't have any restrictions on voltage or current, but only on how much electrical charge you have. If you're generating electrical charge faster than you're using it, your stored electrical charge goes up until all of your batteries are at maximum capacity. In the reverse scenario, it goes down until it reaches zero, at which point, some things that are using electricity must shut down. We'll break this into three sections, to cover generating electricity, storing it, and using it.

Consuming electricity

First up is the things that consume electricity. Deciding how to handle electricity for a given ship generally starts with determining how much you need. That's driven by your mission, and what equipment you need to run. Only after you know how much you need does it make sense to choose how to store and generate it.

Probe cores

Unmanned probe cores use a very modest amount of electricity, ranging from 1.2 to 4.8 charge per minute. For many purposes, that is negligible. If you have no means of generating electricity at all, however, that is very much not negligible. Slowly drain electricity for days and eventually you run out. That forces the probe core to shut down, which leaves you with absolutely no control of the satellite. Often, this means that a satellite is dead and useless, though it can be recoverable if you have solar panels that eventually pick up some sunlight. Remember that once a probe is out of electricity, you cannot give it any commands, so forgetting to deploy solar panels before you run out of electricity can sometimes cause a mission to fail. Having a nuclear generator on board will mean that you always have far more than enough to power a probe core.

You can greatly reduce the electricity consumption of a probe core by putting it in hibernation mode. That limits your control of the probe, but that's fine if it only hibernates while doing a time warp. That can help with short missions that have no electricity generation, or for missions that have very limited power generation, such as relying on solar panels near Jool or Eeloo.

Reaction wheels

Reaction wheels also use electricity, though typically not very much. Even the largest of them only uses 0.6 charge per second, and you usually don't run reaction wheels for very long. As such the electricity usage of reaction wheels is usually negligible. The main exception is if you have a manned spacecraft with no means of generating electricity. If your mission is too long, you can run out of electricity and then be unable to turn. This can also be a problem if you were relying on solar panels and then have to operate in the dark for too long.

Rover wheels

Rover wheels also use electricity to power the rover. They range from 1 to 5 electric charge per wheel per second. The TR-2L Ruggedized Vehicular Wheels that I usually recommend use 3.5 charge per second per wheel. Multiplied by several wheels, this can easily cost you tens of charge per second.

Even so, rover wheels only use electricity when accelerating. Even moving fast while not accelerating doesn't use charge. As such, it can work to bring plenty of battery capacity and only modest electricity generation, then stop and park for a while when you need to recharge.

Rover wheels are only used when landed, and when landed, whatever you've landed on will block the sun about half of the time. Or more, if you're in a crater. As such, you may not wish to rely on solar panels to power a rover, as that will make the rover only usable in the daytime.

Antenna transmissions

Having antennas transmit science can burn electricity quickly. Antennas range from 20 to 200 charge per second, with the larger relays all using 68.6 charge per second. That's quite a lot, but the transmissions tend to be in short bursts. If you start a transmission and then run out of charge, the transmission fails. You'll still have the data, but have to start over on transmitting it. The usual solution to this is to have sufficient battery capacity to handle an entire transmission, and then let the batteries recharge over a potentially longer period of time.

Dawn engine

Each dawn engine uses 8.741 charge per second at maximum thrust. As that maximum thrust is only good for 2 kN, they're really only good for very small spacecraft, and even then, you might want several. As such, dawn engines can burn through electricity in a hurry.

Furthermore, the nature of dawn engines greatly restricts how you can reasonably power them. If you use fuel cells to generate their electricity, then the mass of rocket fuel burned to generate the electricity will be about 2.25 the mass of the xenon fuel used. If you count the fuel in addition to the xenon when computing the specific impulse, then you basically divide the specific impulse by 3.25. A specific impulse of 1293 would still be the highest in the game, but it's not that far superior to nerv engines, and with a lot more drawbacks.

Relying on nuclear generators can be a problem because of their mass. You'd need nearly a ton of generators per dawn engine, and all that added mass would greatly decrease the delta-v. If you have too few nuclear generators to power the dawn engines continuously, then you can run them at lower power. That can work, but it's something of a nuisance, as it can turn a one hour burn into a five hour burn. And you have to be there watching that spacecraft the whole time. And remember that you can't time warp while burning, though you can physics warp, but only up to x4 speed.

That really leaves solar panels as the ideal way to power a dawn engine. But that only works if you have access to plenty of solar power, which you won't if in the shadow of some planet. And even solar panels don't generate very much energy if too far away from the sun. If near Jool, they generate much less electricity per mass than a nuclear generator. Near Dres, they're close to even with a nuclear generator, and even that assumes that the angle is optimal. You probably don't need dawn engines to go to Eve or Duna, leaving trips to Moho or a low orbit about the sun as the places where they work well. But they do work really well in a low orbit about the sun.

Mining gear

The 'Drill-O-Matic' Mining Excavator uses 15 charge per second, and the Convert-O-Tron 250 uses 30. As you probably want to run multiple excavators and the converter all at once for long periods of time, this can burn quite a lot of electricity.

One approach is to effectively cheat by starting up the mining gear, then switching to a different ship. So long as you switch before you run out, the mining gear will keep running, but the stored electric charge won't change while you aren't watching the ship.

The other approach that makes it easy to run continuously is to use however many fuel cell arrays (plural!) you need, typically packing one per excavator and two for a converter. Yes, this burns fuel, and the point of mining is to replenish your fuel. But apart from an extremely low ore concentration, mining will tend to replenish your fuel much faster than the fuel cells burn it. On net, you're still gaining fuel, but only a little slower than before. That can often be worth it for the convenience.

Robotics

Robotic arms use electricity to run. For servos and cylinders that only move briefly, this can often be negligible. For rotors that are intended to run for long periods of time, this can use a lot of electricity quickly. If trying to power a helicopter, using fuel cells is nearly mandatory.

Generating electricity

There are several basic methods of generating electricity, and they all have their uses.

Solar panels

One way to generate electricity is with solar panels. Basically, if a solar panel is pointed in the right direction to pick up sunlight, then it will convert that sunlight to electric charge.

There are two basic types of solar panels: static and deployable. The OX-STAT and OX-STAT-XL Photovoltaic Panels are fixed in place and cannot be moved or rotated. The other solar panels can rotate on one axis to point in a better direction and pick up more sunlight. One drawback of deployable panels is that they're far more fragile, and will break off if traveling very quickly through an atmosphere. They also tend to shatter if you so much as touch them. Static panels are far more durable.

Deployable panels do have some advantages, in that they can pick up more sunlight by changing their angle. A static panel pointed in a random direction will on average only pick up 1/4 as much sunlight as if it were pointed right at the sun, while a deployable one will on average pick up 1/2 as much sunlight. Or at least it would if it weren't blocked by other parts of your spaceship, which tends to happen more to deployed panels than static ones. If you're smart, you place a static solar panel in a location where it won't be blocked by the rest of your ship.

The amount of sunlight that reaches a panel also varies with your distance to the sun. Sunlight intensity is proportional to distance to the negative second power. This means that when near Moho, you tend to generate five times as much power as when near Kerbin. Near Eve is a little less than double Kerbin, while Duna is less than half. Dres gets you about a tenth of the power of Kerbin, and Jool about 4%.

How far away is far enough that solar panels don't make sense anymore is a judgment call. Even near Moho, nuclear generators always work and solar panels only when not blocked by Moho. Meanwhile, solar panels can be competitive with nuclear on an electricity per mass ratio as far out as Dres if aimed properly, and on an electricity per funds basis all the way out to Eeloo.

Nuclear generators

The game only has one nuclear generator for general use, the PB-NUK Radioisotope Thermoelectric Generator. It generates 0.75 electric charge per second at all times, and without requiring fuel. The key drawback is that they cost 23300 funds each, which is quite a lot for career mode. And if you want to generate a lot of electric charge using them, that will take a lot of generators. In some cases, a ship can cost several hundred thousand funds just for the generators alone.

Still, depending on a spacecraft's electrical needs, sometimes it is very convenient to be able to just put a single nuclear generator on the ship, have all the electricity you need, and be done with it.

Rocket alternators

Some rockets have an alternator that will generate electricity while the rocket is running. This is a very inefficient way to generate electricity, but it is a free bonus if you were going to use the rocket anyway.

Fuel cells

If you want to burn fuel to generate electricity, the way to do it is fuel cells. Fuel cells burn liquid fuel and oxidizer in the usual ratio, and will generate electricity at a rate of 80000 electric charge per ton of fuel. That can be a problem if you're relying on fuel cells to generate electricity for long periods of time when in deep space. When landed and readily able to mine for replacement fuel, the fuel consumption of the cells usually isn't a problem. As such, fuel cells are largely a way to power whatever you need when on the ground, as opposed to in orbit or in deep space. Fuel cells can also readily provide the power for short missions.

Storing electricity

You can store electric charge in batteries. Adding more batteries increases the maximum electric charge that the spacecraft can store. Command pods and probe cores generally have some modest electrical storage capability. For most missions other than putting a simple relay into its intended orbit, you'll want to add some batteries for additional electrical storage capacity.

There are in-line batteries of the tiny, small, and large radial sizes that can be placed in a spacecraft in much the same way that you'd place a fuel tank. There are also radial attached batteries that can be placed anywhere on the side of something. Both conveniently have their charge storage capacity in their name. For all batteries, the mass is proportional to the storage capacity, at 20000 charge per ton.

Radial batteries are less robust than in-line batteries, with a max temperature tolerance of only 1200 K, as compared to 2000 K for the in-line batteries. Radial batteries are often intended to be placed inside of a service bay, which will protect them during atmospheric entry.

Radial batteries can be packed very densely inside of a service bay. To place them, turn off the snap to grid option, and turn on the rotational symmetry option to place however many you want--likely eight. You can place batteries partially on top of each other, and it's pretty easy to fit three rings of Z-400 batteries on the bottom of a 2.5m service bay. You can then fit three more rings on the top if so inclined, for up to 48 batteries and a total charge of 19600 in a single 2.5m service bay. Or you can have fewer batteries and leave space for other equipment such as generators or science gear.

Aerodynamics

Aerodynamics is basically for what happens when you're in an atmosphere surrounding a planet or moon. Some planets and most moons don't have an atmosphere, which makes aerodynamics irrelevant. But the atmosphere is quite important when you're in it.

Atmospheres have several effects in the game. The cause parts to blow up if you travel to fast through them, as covered in the heat section. They slow you down when trying to take off, so that it takes more fuel to escape. They also slow you down when you approach for landing, so that the act of landing can take far less fuel than it would otherwise. And they also threaten to flip you over if you do something wrong.

Atmosphere density

The amount of drag due to air resistance for a given shape moving at a given velocity is proportional to the density of the air through which you're traveling. That drops off roughly exponentially as you get higher. Because it is zero on some planets and most moons, there is zero drag there.

You can compute drag as (some constant for the shape of the vehicle) * (density of the atmosphere) * (the square of your current speed relative to the surface). The vehicle shape constant can and probably will vary as your vehicle rotates. When relying on parachutes to land, those parachutes will typically provide nearly all of your drag, so it's basically your number of parachutes, at least if weighted properly due to some parachutes being larger than others.

It's important to understand that drag is proportional to the density of the atmosphere where you are, which is not the same thing as atmospheric pressure. For those who know calculus, if we ignore the fact that gravity varies with height, the atmospheric density is basically the first derivative of atmospheric pressure as a function of height, or possibly the negative of it, depending on how you orient your axes.

For those who don't know calculus, the force that the atmosphere exerts on a given patch of ground is the total weight of the air that is above that patch of ground. On level ground, we can compute that the force is equal to the air pressure at that altitude times the area of the patch of ground. If we make an arbitrary rectangular box with axes pointed in the appropriate directions to have top and bottom sides, the amount of air above the bottom of the box is equal to the amount of air above the top of the box plus the amount of air inside the box. You can see this by examining what happens to a particular molecule: if it is above the bottom of the box, it is either also above the top, or else below the top and hence inside the box. Thus, the difference between the force on the bottom of the box and the force on the top is the weight of the air inside the box. With a bit of arithmetic, the average density of air inside the box is ((pressure at the bottom of the box) - (pressure at the top of the box)) / (height of the box). By normalizing the box height, you can get that the atmospheric density at an altitude of between k and k+1 km on a given planet or moon is roughly proportional to (pressure at altitude k) - (pressure at altitude k+1).

Drag is proportional to speed squared, so when traveling at high speeds, you'll have a lot of drag even in a relatively thin atmosphere. Even so, if you're pointed in a direction where your ship is too good aerodynamically, it is possible to crash all the way into the surface while still going too fast for parachutes to deploy. Approaching a planet at a wide angle so that you have to pass through a lot more atmosphere before you touch down can often fix that problem. For example, when coming to land on Kerbin, you might pick an orbit with a periapsis of about 30 km, then let air resistance slow you down enough to land safely.

Of the objects that have an atmosphere, Duna has the thinnest. At sea level, it is 1/15 of the pressure of that of Kerbin, and about 1/20 of the density. That's not quite thin enough to ignore it, but it won't give you that much trouble unless you have egregiously awful aerodynamics. Laythe's atmosphere has 3/5 of the pressure of Kerbin's at sea level, and about 1/3 of the density. Eve's atmosphere is five times the pressure of Kerbin's at sea level, and about three times the density. Jool's atmosphere at sea level has 50 times the pressure of Kerbin's, though once you get deep enough into Jool's lower atmosphere that rockets don't work at all, is scarcely matters exactly how thick it is.

In real life, provided that an atmosphere isn't so dense that there isn't very much space to pack in more air, each gas component of the atmosphere has its concentration drop off exponentially with height. For example, every 5 km of altitude could drop the concentration by half. But how fast it drops off with altitude depends on the temperature, the force of gravity, and the molecular weight of the particular gas. The temperature and force of gravity at a given altitude are the same for all gases, but the molecular weight is not. Heavier molecules drop off faster with altitude. For example, the concentration of carbon dioxide will decrease with altitude faster than that of water vapor, which in turn, drops off faster than helium. This is why the Earth's upper atmosphere consists almost entirely of hydrogen and helium, even though for the entire atmosphere, they are present in far smaller amounts than nitrogen, oxygen, or argon.

The game does not explicitly model having different gases in an atmosphere like this, as demonstrated by there being portions of the atmosphere of Laythe and Eve where density goes up as altitude does. For game purposes, you can just think of the density of an atmosphere as something that drops off pretty quickly with altitude.

Cross-section area

Most of the time, you'll want to reduce the effects of the atmosphere. Drag basically acts on the cross-sectional area that gets hit as you travel. If you view your rocket from far away with the camera oriented such that the rocket is traveling directly at you, what you can see is roughly the part that the atmosphere acts on. Making your rocket wider will cause more drag, but making it longer will not. Thus, to reduce drag, it is ideal for a rocket to be very long and narrow. That is, of course, the opposite of what you want it to be in order to land.

It's also important that your rocket be symmetric. If it is pressing a part of the rocket on one side to slow you down, you want it to also have an equal force on the opposite side. Otherwise, drag could provide a potentially strong net torque and flip you around in a direction that you don't want.

Aiming rockets

A rocket that is built to be rotationally symmetric only has drag provide no net torque if it is rotationally symmetric around the direction that the rocket is traveling. If it is going sideways, the portion that the atmosphere acts on is not symmetric at all, so it can provide a strong net torque, and that could flip you in a direction that you do not want.

If your rocket is rotationally symmetric and pointed directly prograde relative to the surface (since the atmosphere gets dragged along with a planet's surface), then there will be no net torque, and you don't flip over. Directly retrograde also works for the same reason. Usually you want to be prograde when taking off and retrograde when landing. Importantly, these are relative to the surface, not orbit.

Usually at launch, you want to point straight up initially. If your rocket landed on some planet and is taking off from wherever it landed, then you probably won't be directly vertical at launch, but you want to get pointed that way quickly. You have a little bit of time, as you'll initially be moving slowly enough for there to be minimal drag.

You may wish to tilt a little to one side to start your gravity turn early on. But you're going to have to point directly prograde for a while, which will allow gravity to move your prograde direction more and more horizontal as you go. If you tilt too far to the side, too soon, you don't get out of the atmosphere.

Once you pick up some speed in the lower atmosphere, you need to stay exactly prograde, or at least very close to it. Otherwise, you'll flip over. Perhaps not on Duna, but certainly on any of the other places with an atmosphere. Once you get to a high enough altitude for the air to be very thin, you can then change your direction to adjust your gravity turn without further fear of flipping over.

Nose cones

Some shapes naturally allow air to flow by them much more easily than others. Most of the functional parts in the game such as fuel tanks and rover wheels really aren't very aerodynamic. The game offers aerodynamic nose cones that are designed specifically to reduce drag. The idea is that you put them on the top of your rocket so that most of the portion of the rocket that is cutting through the air is nose cones that are designed to have minimal drag. This can greatly reduce your drag at takeoff, and thus allow you to reach orbit with less fuel.

Nose cones don't do much to prevent you from flipping over, though. If you're turned to the side, the atmosphere is acting strongly on other portions of the rocket besides the nose cones, and that's what flips you over.

Service bays

One way to prevent awkwardly shaped parts from causing a lot of drag is to hide them so that they don't hit the air at all. Service bays allow you to do this with small equipment such as batteries or science gear. They don't just protect the gear from blowing up, but also prevent it from causing undesirable drag.

Fairing

Sometimes, you need to put something that is awkwardly shaped on the top of a rocket, and it just can't be covered with nose cones. Trying to carry a rover to some distant planet is a common situation. Needing to put a large relay on your satellite is another. You can build fairing to go around whatever your awkwardly shaped object is, and reduce drag in a manner similar to nose cones.

The idea of fairing is that there are several fairings of different radial sizes, and you can place one in-line in your rocket, like a fuel tank. You can then build the fairing by having several slices at chosen radii and lengths to cover whatever comes above it. That will give you a more aerodynamic shape when taking off from Kerbin. Once you leave Kerbin's atmosphere, you can discard the fairing.

Be warned that the act of removing fairing is explosive, and discarded portions of fairing can hit other parts of your rocket and destroy them. It's really only safe to have one fairing on a rocket, and only at the very top of the rocket, above all other portions.