Tutorial:Intermediate Rocket Design
Before we get into the details, a few physics facts. Namely, center of gravity, point of action and how they matter.
Center of gravity, point of action and how they demand symmetry in your rocket.
The center of gravity is the point in your rocket where it would be in total balance. It's the point where, if the rocket was resting on that point, you could give it a nudge and it would freely follow that nudge without gravity having a say, because left and right, up and down, front and back, they're all equally heavy and perfectly balanced on this single point. That is always one single point in space, and unless you have a very oddly shaped rocket, that point is somewhere inside your rocket. Sadly, this point is usually not the point of action, i.e. the point where your engines create thrust. If it was, that would be sweet, since we could push the rocket wherever and however we want (ignoring air resistance, of course).
So the next best thing we can do is to put that point of action "behind" the center of gravity and point its action vector towards the center of gravity. Or, simpler put, put the engine behind the mass and thrust in the other direction. What sounds obvious at first has some implications. First, your point of action, actually the vector sum of your thrust vectors, for you nitpickers, HAS to be lined up with your center of gravity. In other words, your rocket has to be symmetrical to be stable. You can try that for yourself. Get a broom. Put the endpoint of the handle on your hand, with the brush up, and you will notice that you can balance it. You will also notice two things: First, it's easy to balance it as long as you work hard on it, and it can very easily tilt to one side, and if it does it falls FAST. And second, it's surprisingly more easy to balance the broom with the brush up towards the ceiling rather than having it resing on your hand.
If you would now put a lot of pressure on that handle, you could thrust that broom upwards without it falling to the side (trust me, it would work). That's basically how our rocket works. Now attach something to the side of the broom and see how this works out for you. If you try to balance the broom the same way, it will fall to the side where you tacked something onto it. Unless you hold it at an angle to the side... looks stupid if it were a rocket, doesn't it? If you would thrust that broom upwards, it would not only fall to that one side, it would actually start to spin around the x-axis and do "loops"... or crash, which is more likely since gravity is playing in this game as well. So the first thing to keep in mind is to keep your rocket symmetrical, at least to the point where the center of gravity is always above the combined point of action (if you have more than one engine, you have more than one point of action, which can be summed up to a total point of action and an action vector). In physical terms, that point of action has to be lined up with the center of gravity, with its vector aligned with the hypothetical axis that exists between the cog and the poa. In simpler terms, the point where your rocket would be in balance has to be behind the point where the combined force of the engines pushes, and the engines have to push towards that center of gravity, i.e. their thrust exhaust has to point away from it.
That also means that "inwards" thrust stabilizes the rocket, as long as the thrust is equal from all sides. It forces the rocket to stay in its current direction, but it also means that you are wasting fuel since you have engines thrusting "against" each other. Think of it as the toe-in of your cars steering wheels.
Mass vs. weight
Your weight is directly related to your mass. Now, strictly speaking, weight is defined as the force on an object due to gravity. But gravity pulls every bit of mass in your rocket with the same force, making acceleration uniform throughout the ship. In space, not spinning and with engines off, there are no other forces actuating, so this is perceived as weightlessness. I'm not sure this is a good analogy, but think of being in a really quiet plane, flying level and at constant speed. You can't tell you're moving. Same thing with gravity, except there you can't tell you're being accelerated.
What we perceive as weight is caused by other forces, such as drag from an atmosphere, thrust from your engines or (usually) the normal force when landed. Assuming a flat landing area, the normal force matches gravity exactly but in reverse, so you stay at rest. Gravity pulls you down, the normal force is the ground pushing you up. But it doesn't act uniformly on every bit of mass like gravity does, it's just the ground pushing the bottom of the ship, so the force has to be distributed through the ship's structural elements, and that is perceived as weight. Same thing with thrust, or aerodynamic forces.
But even if you're (feeling) weightless, you're not without mass.
To cut the theoretical crap short, the more mass you have, the more energy you have to expend to change its speed and direction. The more massive your rocket is, the more fuel you have to spend to make it faster (or slower!). Usually, in this game as well as when you're overweight, physics works against you.
This also means, that a mass gets "heavier" if you accelerate it faster. More acceleration doesn't increase your mass (unless you're approaching light speed, let's ignore that for now), but the stress (perceived as weight) on the mass increases. That's called g-forces. On Kerbin, you experience 1g. (1g is defined as the acceleration equal to Kerbin's gravity at surface level which is about 9.81 m/s², not to be confused with gram).
How does this affect your rocket? Well, it affects it twofold. First, the more mass you have, the more fuel you have to spend to get that mass up into orbit. Hence "bigger" isn't always "better". We'll get to that in detail later. The other factor is that the faster you accelerate your rocket, the more stress you put on its parts. Some parts are able to sustain that stress. Some are not. It is, in general, easier to build a slowly climbing rocket than one that jumps into orbit at 9g or more, not only because our passengers don't really like having a truck sitting on their chest (which isn't as much an issue so far), mostly the problem now is that the acceleration you put into the rocket stresses the parts that keep it together past their breaking limit. Which means you have to add struts, which add to the mass, which cost you fuel.
Basically, it's the result of dividing your thrust (in newtons) by your weight (in kilograms times acceleration, i.e. kg*m/s², so... well, also in newtons). Thrust is what gets you up, weight is what keeps you down. And if thrust > weight, i.e. if your thrust-weight ratio is more than 1, you go up. If thrust < weight, you can put your engines into overdrive and you won't move an inch. For the record, the Saturn V first stage rocket engine had a TWR of 94.1. In other words, it could have lifted itself over 94 times. Beat that!
What does that mean for our space vehicle? Basically, it means that whatever we put as rockets behind our craft, it has to overcome the total weight of the craft. Which also means that, if you have multiple stages, the upper stages are just dead weight at start. Yes, yes, there are rockets in there and they might have a lot of punch, but they do not add to the thrust at start. Thrust is always only the thrust you ACTUALLY apply, not the thrust your rocket can eventually do in total.
Note that every rocket engine has a TWR of more than one. By definition. Engines below a TWR of 1 need some kind of aerodynamics on the craft to get it off the ground. The question is, though, whether the dead weight sitting on top of it STILL keeps that equation above 1. The F1's 94.1 TWR doesn't mean that the Apollo craft got shot into orbit at 100g. It means that there was a friggin' HUGE rocket sitting on top of that engine and hence it could barely get the whole behemoth up into an orbit!
My guess is that Kerbin has a gravity of about 10m/s² (much like earth), meaning that a rocket engine rated at 200 max thrust (like the non-gimballed stock engine) can lift 20 units of mass (or 8 stock liquid fuel tanks). Given that a rocket of 1 stock command center, 7 fuel tanks and 1 engine (totalling a mass of 20.5, 7*2.5+2+1) can't get off the ground but with 6 fuel tanks it can, I'd say that should be about right. So when building your rocket, always add up the mass of the parts you assembled, multiply by 10, then divide by the thrust of the engines, but ONLY the engines that actually thrust. The more you get out of that, the faster your rocket will climb. Considering that engines seem to overheat more readily if they're operated at the TWR limit, try to get to a TWR of at least 1.7 in your first stage. My Mun rocket has a first stage TWR of 2.2, which is plenty but not overdoing it to the point where the g-forces become unmanageable.
Also, keep in mind that you will use up fuel as you climb. Your fuel tanks will get emptier with every second your engine fires, making them lighter, meaning, less weight has to be lifted. Plus, gravity decreases with distance squared, which also makes the pull of Kerbin less and less with every inch you climb. Not as much as one would wish, though.
Staging, and when to do it
Staging usually means tossing dead weight. You jettison spent rocket parts to make your craft lighter. Less mass means less energy required to move the rest of the mass. The obvious choice would now be to stage as much as possible, to carry around as little dead weight as possible. This is not the best strategy, though.
Staging also means that you have to carry around the weight for the staging equipment and, in case of a liquid fuel set, another liquid engine. A spent stock booster weighs 0.36. The equipment to jettison it weighs 0.4. A spent liquid tank weighs 0.3. The additional engine and the staging equipment to toss it weighs 2.8.
A compromise has to be found. There is no hard limit to tell when to stage and when not to, what matters is how long you'd have to haul around the dead weight (if it's just a few seconds between the booster's end of life and until the other engine of this stage burns out, just keep the booster attached, it's not worth the extra weight for another set of staging couplers. If it's for the rest of the flight, tossing it pays off easily), whether the spent stage prevents you from firing the next (a lower stage burned up covering an upper stage has to be jettisoned, of course) and what the stage is used for (an upper stage is usually in use longer than a stage to reach orbit that is burning at max power constantly, i.e. a fuel tank in upper stages lasts much, much longer). I find the sweet spot for liquid tanks to be around 4-5 for lower stages and about 2 for upper stages.
Also easy to see, the more thrust you apply right from the start, the less dead weight you carry around. It's usually quite pointless to have a lot of thrust further up if you cannot get off the launch pad. On the other hand, as mentioned above, the more thrust you put behind your crate, the more g-force it has to endure and the more you stress your parts. Not to mention the air resistance which is of course worst lower in the atmosphere.
While we're at it, drag. I hope I got that one right, it's kinda hard to tell how that part really works. Basically, every part you add has air resistance. Doesn't matter once you're in orbit (and hence satellites rarely look streamlined), but it's a big issue until you hit that magical 70,000 meters. I still have very limited data on how drag really works and what affects what, so far all I can say is that it's there and that you should probably take it into account, i.e. creating insanely wide rockets to cram in a lot of boosters to fire at the same time might be a drag. Literally. Especially if you try to fly such a rocket at high speeds.
Note: Shape does not matter, only adding drag values (Unless you use Ferram Aerospace Research). This is why asparagus works. (I can't wait for a thousand years into the future, when people will see this and believe it's how asparagus works. Real asparagus)
Where do you need the most power?
That's a simple one again: From ground to orbit. You will NEVER in your flight have to spend as much energy as in that part of your flight. Getting from orbit to the Mun, landing on the Mun, getting back off the moon, flying back to Kerbin and landing there? Easily done with about 1/6th of the fuel spent to get into orbit. I am NOT kidding or exaggerating here. Remember that Saturn V rocket that sent Apollo to the moon? Remember how friggin' huge that thing was? And what a tiny little bit of it actually went to the moon, with the rest being tossed somewhere along the way? Of the total mass of the Saturn V on 2,800,000 kg, most of which was fuel, only 120,000 kg was used for TLI. It's the same here. You will spend a good 80% of fuel and dump about as much of your rocket before you reach the Mun.
Long or wide?
Preferably neither. Making your rocket longer is about as bad as making it wider. For various reasons. Wide rockets tend to be bottom-heavy (because, usually, they are wide at the bottom, to maximize thrust at liftoff), making them harder to control because they sway easily, and they are prone to out of control rolling if the thrusters on the outer edges are not PERFECTLY aligned (which they are, well, never), due to leverage. Also, I'd expect them to be very susceptible to drag, meaning a lot of power is lost due to air resistance. Wide rockets usually need quite a bit of SAS to keep from spinning out of control. And they are prone to "flipping", i.e. uncontrollably going upside down because they are easy to tilt and bank. Think of the broom example at the beginning.
Long rockets are very hard to tilt and bank, making them hard to steer and very sluggish. They also usually suffer from top-heaviness, especially after a good deal of their lower stage fuel is spent, which can result in rockets that are very hard to control and to keep from going "keel-up", i.e. nose-down without a lot of RCS thrust. Long rockets usually need quite a few wings to keep them manageable and responsive. And even then they are very slow to react and need foresightful piloting. They usually keep their direction pretty well as long as they are balanced and there's a lot of thrust applied, but once you bank and tilt them, they can very easily oversteer, especially in horizontal flight with a center of mass that's very close to the top (as it is usually just before your ascent stage is burned up, with a lot of empty and near empty fuel tanks hanging on your tail). Still, I prefer long over wide rockets.
So, with all that, what IS now the best design?
From these tidbits we can puzzle together a few cornerstones that give us a good idea what a GOOD design would be, and what would be a BAD one.
It's a good idea to put every engine that can actually thrust at launch to work right at launch. Otherwise, they're dead weight that must be hauled upwards before it can be used. If that gives you too much thrust and your rocket starts to fall apart due to excessive G forces, consider putting the throttle to 75% or so. Remember, it is highly inefficient to go faster than 200 meters per second below 10,000 meters. Once your rocket has cleared the thickest portion of the atmosphere you can try bringing the throttle up to full. But if you have a big rocket, it CAN be a very good idea to make the first stage(s) only of solid boosters, they're very light for their push and even with a coupler on them they have a better TWR than liquid engines. Their main drawback, the inability to control their thrust output, doesn't matter for the first 20,000 Meters since you actually just want to get the hell up there. Do not expect too much from that, a full complement of two solid-only stages underneath every single engine of my actual first stage only got me about half a fuel tank. Yes, half a stock fuel tank is all you get for slapping two rows of solid stages under your rocket. The diminishing returns are stunning!
While solid boosters can be appealing, they prevent you from using the highly efficient "asparagus" stage design. The idea behind the asparagus design is that instead of burning through multiple fuel tanks simultaneously, two fuel tanks stacks are drained at a time. This saves weight because it greatly reduces the fuel mass to tank mass ratio after you have dropped your first two tank stacks. See the thumbnail for details.
With bigger rockets, you'll run into the need to add SAS to keep them manageable. Only one ASAS module gives you any benefits, so placing more does nothing but weigh down your rocket unnecessarily. The key difference between SAS and ASAS is, as the description says, that ASAS is more like an autopilot, SAS is more like a gyroscope. In other words, if the rocket is uncontrollable, ASAS cannot control it either. If you have wings (recommended on large rockets), you might even be able to forgo the normal SAS modules.
Your rocket should get thinner as it progresses upwards. From afar, it should look like a teardrop or a very steep pyramid, with multiple radial stages around the bottom stage thinning out to a single top stage. Top-heavy rockets are usually very hard to control, since their center of gravity is far from the point of action. The further away, the bigger the lever, the more wings and other control tidbits you need to keep it upright.
You need most of your fuel on your way up. Once you're in orbit, even the trans-lunar shot is peanuts compared to the expense to get into an orbit. It's quite ok to create an unwieldy, but powerful lower stage and create a very manageable and precisely controllable stage for upper orbit that has rather little fuel compared to it. Try different designs here, it's alright to have zero control beyond keeping the nose pointed upwards for the first 20,000 or even 40,000 Meters of its trip.