Rocket exhaust: hot 'nuff for ya?
Kerbal Space Program has reignited (cough) my passion for rockets and space science, and it's also got me thinking about the basics again in non-mathematical terms. A great misconception is that "rocket science" is highly complex and abtruse. The basics, actually, are as simple as firecrackers; rocketry at its most rudimentary level is far simpler to explain than the internal combustion engines we see every day... it's the application of rocket science to real world solutions (particularly the engineering) that's brain-splitting.
In simplest terms, a rocket makes things move by transfering momentum to them. Momentum is a product (in the math sense) of velocity and mass. It's also conserved, which means that you can't summon momentum out of thin air; if you add momentum to something, you have to add an equal amount of momentum to something else in the exact opposite direction. In the case of a rocket, that's the exhaust out the back; you light up the rocket, a mass of hot gases comes out one end, the other end pushes on the payload (what we want to move) as a result. Unlike a car engine the exhaust is what we want, not a waste product to get rid of; everything depends upon the speed and mass of that exhaust.
Because momentum is a product of mass and speed, if you're trying to increase the amount of momentum transfered it doesn't much matter whether you increase the mass of the exhaust or the speed of the exhaust; increasing either will get the job done. You can increase the mass of exhaust by burning more fuel, which is the straight-forward and common sense approach... but for rockets, there's a catch. Rockets have to carry the fuel, and the unburnt fuel also has mass. Remember that momentum is a product of mass and speed; so, ironically, the more total fuel you carry the less speed you add to the payload by burning it because the fuel makes the whole rocket heavier. It is literally possible to create a rocket burdened with so much fuel that it can't lift itself off the ground. (A common failing among novice Kerbals.) Adding more engines would help create more exhaust, but they too add mass... and you can end up in a terrible spiral of diminishing returns.
(This is why the Apollo rockets started their voyages about as tall the Statue of Liberty, but ended the trip about the size of the flame on her torch. The vast majority of the fuel in a Saturn rocket was there to carry the rest of the fuel.)
The other way to increase the amount of momentum transfered is to increase the speed of the exhaust coming out. Exhaust (in the case of rockets) can be treated as a gas, and the average speed of the particles that make up that gas is something we measure every day; temperature. When we say something has a higher temperature than something else, in physics terms what we're saying is that the former's particles are on average moving faster than the particles in the latter. So if you take the same amount of fuel and make it burn hotter, it'll add more momentum but not encounter the same penalty for increasing the mass. For a rocket scientist, hotter fuel is better.
Again, though, there's a catch; there's a limit on how hot a particular fuel can burn. It's limited by the amount of energy produced by the fuel's burning; a chemical reaction produces a certain amount of energy per unit mass that can't be increased beyond a particular optimum for each fuel.* And by a cruel irony, energy too depends upon mass and velocity... but not as a product of the two, like momentum, but rather by the mass and the square of the velocity. So making the exhaust hotter is much tougher than simply making more exhaust, and gets increasingly tougher the hotter we try to make it.
Some rockets sidestep the limits of chemistry by heating up the fuel by different means; the current hot topic (cough) of research is ion engines, which use electricity to turn fuel into superheated plasma. It gets absurdly high temperatures**, making the oxyacetalyne torch in a metal shop look positively tepid by comparison, but the "mass times square of the velocity" problem still crops up because the fuel no longer provides its own energy so you have to provide an external source. Ion engines make the exhaust super-hot, but can only make tiny amounts of exhaust super-hot at a time because of limits on how fast their energy sources can create the electricity needed. You could put a bigger generator on, but generators too have mass and you soon end up in the same death spiral of needing more weight to move the added weight.
So with the current state of the art, energy limits mean we have to trade off between the mass of exhaust expelled and the speed of that exhaust. Near the surface of our gravity- and atmosphere-bound planet, it makes sense to trade speed for mass because we need to fight gravity and drag. Out in space, it makes more sense to trade mass for speed to make the craft lighter.
Is there a way around this problem? Well, sort-of. What we'd need is a lightweight source of tremendous power, so we could heat large quantities of fuel to extremely high temperatures. We have one, but, uh, let's say it has its own problems.
-- Steve'll probably revisit this subject later, but time alas requires he stop for now.
* In rocketry this limit is expressed by "specific impulse", which measures the amount of momentum transfered per unit of fuel. Think of I(sp) as the rocket version of "miles per gallon"; higher is better. The engines at the bottom of the Saturn V moon rocket had I(sp) of 263; the Space Shuttle main engines had I(sp) of 363. The highest I(sp) ever recorded for a chemical rocket came from burning lithium with fluorine (542) but no sane person would ever use it as a fuel; too tough to carry and store, and it's insanely toxic before and after burning.
** Ion engines are ridiculously fuel efficient, with I(sp) measured in the thousands. That's why they're such a hot topic.