Tuesday, September 20, 2011

How To Build A Spaceship - Part 2

Okay, so the Ferrari Road Trip from Part 1 showed us that we needed to know a few things to figure out the time and cost of our trip. And Flying Cars, Jetpacks and Video Phones showed us that just because something hasn't been done, doesn't mean it can't be done. And, if in space, no one can hear you scream, then no one can charge your credit card, either, right? So we're going to almost forget about cost for now, except for two terms: "Realistic" and "Sci-Fi." I'll define those two terms:

  • "Realistic Cost" - If enough people in the right places want to do it, and it's based on something that somebody really smart really came up with, then it can be done eventually.
  • "Sci-Fi Cost" - If Old Ben can buy two 1-way tickets (Droids ride free) on the Millennium Falcon for 17,000 somethings, then that's all that matters.
So forget about cost for now, except to say that we'll use "Realistic Cost" and that any power plant or engine that we consider would be something our Rocketpunk characters would willingly spend lots of time and money to develop.

So much for cost. What we're most interested in is realistic time frames for our trips in space. So that means we'll have to figure out our power and fuel and propellant requirements. We'll also need to know the distances involved. Pretty much just like our little jaunt in the 250 GT from LA to NYC, right? Surprisingly, yes. Hey, it ain't rocket science!

Oh wait, it is rocket science. And there, dear reader, is the cool thing. There's a reason those Golden Age SF writers had Boy Scouts working out orbital mechanics on the back of an envelope. It's because they could! Once you know the right equations, it's pretty much plug and play. But wait, that's for a rough approximation. Those calculations might get you 9/10's of the way there, but that last 10% is going to look awfully important when you miss Mars by a few million kilometers and your shiny spaceship becomes a lifeless permanent fixture of the solar system. So that's where the real rocket science requiring really big brain cells comes in, to get all those extremely important little details exactly right. Lucky for us, we don't need to be that exact. Our rough approximation will work just fine for "realistic" space flight in our Mythik Universe.

Having said that, I do need to point out that on the Rough Rocket Science Approximation Scale, I am currently about half way through the Kindergarten level. So keep that in mind if my calculations send us to Mercury instead of Mars, or into the Sun, or anywhere but Mars. I know, we could fly right through a star or bounce too close to a supernova, and that would end our trip real quick, wouldn't it?

So here are the variables we need to know about to make our spaceship:
  • Distance
  • Mass
  • Propellant
  • Mass Ratio
  • Specific Impulse
  • Exhaust Velocity
  • Thrust
  • Ship Delta-V
  • Mission Delta-V
  • Transit Time
Distance - As I'm sure you're aware, space is really big. It's so big, in fact, that astronomers (and spaceship designers like us) use units called AU (Astronimical Unit) which is equal to the average distance from the Earth to the Sun (about 149 million kilometers.) Naturally, our Earth is 1 AU from the Sun. Here's a handy table:

Planet        Distance from Sun in AU
Mercury     0.39
Venus        0.72
Earth          1.0
Mars          1.5
Jupiter        5.2
Saturn        9.5
Uranus      19.2
Neptune    30.1
Pluto          39.5

So let's look at our destination, Mars. It is only .5 AU further from the Sun than Earth is. So that means we'll only have to travel about 74.5 million kilometers. Heh, yes, we are simplifying things a bit. But even so, you can see that any destination further than Mars will take a lot of effort to reach!
Mass - On Earth, we think of this as how much something weighs. But while weight will change based on the environment, mass is constant. So if you weigh 75kg on earth, your weight will be less on the Moon, but the mass will remain 75kg (kilograms.) Get used to kg and the metric system (Royal With Cheese - they call it that because of the metric system, right?) because we'll be using it a lot. We'll need to know how much total mass our ship has. That will enable us to determine our acceleration and our mass ratio.

Propellant - Rockets work by using Newton's Third Law. The rocket exhaust goes out the back at a high velocity. This makes the rocket go the other direction (forward.) That stuff that gets pushed out the exhaust is called propellant. In the Space Shuttle main engines for example, Liquid Hydrogen and Liquid Oxygen mix together and ignite and are both the fuel and the propellant. For some engines, like an Ion engine, propellant is not the same as fuel. Propellant (also called reaction mass) is just whatever you use to shoot out the back end of the rocket to make it accelerate the opposite direction. The units used are kg. Our Ferrari used its engine to turn the wheels which pushed against the road which caused the car to move forward. You could say the road (or the Earth) is the propellant. Our ship doesn't have a road, so it will need to carry its propellant.

Mass Ratio - The is the ratio of how much propellant you have compared to your ship's overall mass. If you have 10 tons of propellant and the total mass of the ship (propellant + everything else) is 15 tons, then the mass ratio is 3. The equation is Mass Ratio = Mass With Propellant / Mass Without Propellant. See, not too hard, right?

Specific Impulse - This often abbreviated as Isp. This is sort of the equivalent of a car's gas mileage. For our ship, it means how long until we run out of propellant. The units used are seconds. The Space Shuttle's main engines have about 453 seconds of Isp. That's not enough to get to Mars. Isp is dependent on engine type. Some engines have high Isp, some have low Isp. If you have a high Isp, you can use less propellant, which saves weight, or you can go further and do more things (like maneuver and decelerate) with the same amount of propellant.

Exhaust Velocity - The units used are meters per second, or m/s. We can determine the Exhaust Velocity by multiplying the specific Impulse by the gravitational constant or 1G, which is 9.81 m/s. So the equation is: Ve = Isp * 9.81. The Exhaust Velocity (Ve) of the Space Shuttle Engine is 453 * 9.81 = 4443 m/s. Since we just multiplied our Specific Impulse by a constant, you can see that Exhaust Velocity is just another way of expressing our Specific Impulse. To put it another way, a certain Isp will always have the same Ve. Right? Yep.

Thrust - This is how much acceleration our engine can generate. The units used are (N) Newtons. Naturally, different engines make different amounts of thrust. Using our Space Shuttle example, one of the three main engines makes 1,750 kN (kilo Newtons) of thrust. So that's 1,750,000 Newtons. Our ship will have, um, a lot less thrust. But our Isp will be much higher, so we'll be able to slowly accelerate for a much longer time than the Space Shuttle. It'll sort of be like a tortoise vs. hare scenario.

Delta-V - This is the really fun one. Delta-V is determined by the Rocket Equation, which is over 100 years old. Delta-V means change in velocity, and shows how much our ship can change its speed, which is important when accelerating to distant planets and then slowing down to orbit and sightsee. Delta-V = Exhaust Velocity * ln[Mass Ratio] The unit used is m/s. I'll explain the ln thingy later. This is really the true analog to a car's gas mileage. Any maneuver in space requires some amount of Delta-V. From a hard SF writer's standpoint, you could use Delta-V as a sort of Technology Currency. You gotta pay to play, and if you want to play in the outer planets or (even more so) nearby stars, you better be able to afford lots of Delta-V. If you don't have enough Delta-V required for a mission in your propellant tanks, then you can't do that mission. All the cool missions, of course, take lots of Delta-V. Which brings us to the next item...

Mission Delta-V - This is how much Delta-V it requires to get to a certain place in space. It depends on gravity and orbits and whatnot. You know, rocket science stuff. We'll deal with it later, but just know that our ship Delta-V needs to be equal to or greater than the Mission Delta-V (and double the Mission Delta-V for a round trip.)

Transit Time - The units are in days, months or years. Very roughly speaking (Kindergarten level rocket science, remember?) there are three ways to get some place in our Solar System. 1. Use something called a Hohmann Transfer Orbit. This is also known as as a minimum Delta-V, maximum transfer time orbit. It gets you where you want to go and doesn't require sci-fi unrealistic drives to get there. But it takes a long time. If your ship can come up with enough Delta-V (even the minimum amounts are hard,) then it will take 8.5 months to get to Mars. You turn on your rockets at the beginning, then coast. Then when you get close to the destination, you do another rocket "burn" and match orbit with the lovely red planet. Oh, and it also only works like this when the planets are lined up correctly. So if you miss your "launch window" for the Hohmann Earth to Mars orbit, you need to wait over a year and a half before the next window. That also means that once you get to Mars, you need to be able to stay alive long enough for the next window to open up. That's pretty annoying. 2. The other extreme is a Brachistochrone Orbit. The cool thing about this is that you can come and go whenever you feel like it. You fire up your engines and accelerate till you are half way to Mars. Then you flip around and fire the engines the opposite direction to decelerate the last half of the trip. The drawback to this is that it uses (pardon the pun) astronomical amounts of Delta-V. Yep, that's the problem with trying to be anywhere close to "realistic." Anything fun takes really large amounts of Delta-V. 3. The last way is Semi-Brachistochrone, which is somewhere in between the first two. It involves more "burning" that Hohmann, and more "coasting" than Brachistochrone.

And, just by sprinkling a few of these terms in a few strategic places, a story will at least have a more hard SF feel to it. "We don't have enough Delta-V to catch the space pirate, Captain!" It's better than complete technobabble, right?

Anyway, with just these 10 simple things you can conquer the universe! Or at least the inner Solar System. On paper. And that's exactly what we'll do in Part 3 when I show you how to build the Mythik Magnetoplasmadynamic Artificial Gravity Mark VII Mars Expedition Spaceship!

Other parts of this series:
How To Build A Spaceship

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