Difference between revisions of "Tutorial:Intermediate Rocket Design/zh-cn"

Revision as of 02:58, 28 May 2013

物理学

在讨论火箭设计细节之前，先来了解一些必需的物理概念。亦即，重心、着力点，以及他们的关系。Namely, center of gravity, point of action and how they matter.

重心、着力点，以及它们对于火箭对称性的要求Center of gravity, point of action and how they demand symmetry in your rocket.

重心是火箭中各方向都能保持完全平衡的一个点。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. 重心是绝对存在的，除非你把火箭设计得过于奇葩，这个重心都会位于箭体的内部。不走运的是，通常火箭的作用力点，也就是火箭发动机的推力作用点，都无法与重心重合。如果能做到这样，实在会非常的完美，因为我们可以随心所欲的让火箭按照需要运动（当然，要忽略空气阻力的影响）。

所以我们退而求其次，把作用力点放在重心的“后”方，让推力矢量指向重心。简而言之，就是把发动机放在箭体重量的后方，然后向另一个方向推进。这种方法有几个明显的影响。首先，总推力矢量实际上是各个发动机推力的矢量和，那么就得吹毛求疵的要求其矢量方向与作用点和重心的连线重合。换句话说，你的火箭必须是对称形的才能保持稳定。你自己也可以做个实验。拿起一把笤帚，把它竖起来，手托着一端，你应该可以保持它的平衡。你也会发现这两点：首先，只要你尽力，你能一直保持它的平衡，不过它往一边倒过去无疑更容易；其次，只要把一头顶住天花板，相比单手托着它，你可以更容易保持住平衡。

如果你能在手持的一段施加足够大的压力，你肯定能用笤帚把天花板捅破而不让它倒向一边（相信我吧）。这其实就是火箭工作的原理。现在，找点东西拴在笤帚的一侧，再来看看。如果你还想用刚才一样的方法来保持平衡，它肯定会倒向你栓东西的方向。除非你换个角度握住的话……如果它是火箭的话看起来就有点蠢了，不是吗？如果你给笤帚加一个向上的推力，它不会倒向那一边，实际上它会绕 X 轴旋转，然后做个“回环”……或者直接“坠毁”，这一点估计可能性更大，因为重力也会在这里起很大的影响。

所以，首先必须记住的是，请保持火箭的对称性，至少要保证重心位于作用力的矢量方向（如果你安装了多台发动机，那么你就得注意多个作用力点，并利用总作用力点的合推力矢量）。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

As long as you're on Kerbin, they're interchangeable. Your mass is directly related to your weight. It's a bit different in space. Weight is the result of mass being accelerated, either by gravity or by movement. And while you're weightless in space (well, your outwards acceleration from your speed matches the inwards acceleration from gravity), 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 heavier your rocket is, the more fuel you have to spend to make it faster (or slower!), provided you do not have gravity to work for you. Usually, in this game as well as when you're overweight, gravity works against you.

This also means, that a mass gets "heavier" if you accelerate it faster. It doesn't increase its mass (unless you're approaching light speed, let's ignore that for now), but the stress weight puts on the mass increases. That's called g-forces. On Kerbin, you experience 1g. Which is equal to an acceleration equal to Kerbin's gravity at surface level.

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.

Thrust-weight ratio

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 weight 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.

As much thrust as possible to the bottom

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.

draaaaaaag

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.

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? And how that little service module that got them basically from orbit to moon also got them back? 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. Else it's dead weight we first have to haul upwards. If that gives you too much thrust and your rocket starts to fall apart due to excessive G forces, slap on another can of gas for that liquid fuel rocket, or take off some boosters (yeah, right...). It MAY be a good idea to not run that liquid engine at full power if you get so fast that your friction is killing most of the power you put behind it. Actually, I usually take off with full throttle, only to ease off a little as I climb to keep the speed from going overboard and being burned in friction. 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!

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 put only one of them into your rocket. 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, ASAS only works as well as YOU could, or, in other terms, if the rocket is uncontrollable, ASAS cannot control it either. If you have wings (and, IMO, you should have some at least as long as you're hauling a big ass rocket about), you might even be able to forgo the normal SAS modules. My Mun rocket only has one ASAS module and no SAS modules. Your rocket should get thinner as it progresses upwards. From afar, it should look like a very steep pyramide. At least IMO. 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 controlable stage for upper orbit that has rather little fuel compared to it. Try different designs here, it's all right to have zero control (aside of "keep it upright by ASAS") over the rocket for the first 20,000 or even 40,000 Meters of its trip.