See also parts I, III, IV, V, and VI.
The most common sort of rocket and the ones we're all familiar with from seeing them on TV are the ones that work by burning stuff. That is, they work by combining two different chemicals that react to produce the energy that propels the byproduct of the reaction out the back of the rocket. Since the fuel that provides the energy and the propellant that is ejected for the momentum are the same thing this means that you're always using more or less the same amount of energy for the same amount of propellant. This means that the ve, the velocity of the exhaust, is always going to be more or less constant depending on sort of chemicals you're using with some variation depending on inefficiencies in the engine.
Many chemical rockets use cryogenic fuels - substances that are normally gasses but which have been cooled down enough that they liquefy and can be put in reasonably sized fuel tanks. Take the fuel used by the Space Shuttle, liquid hydrogen and liquid oxygen. When you combine H2 and O2 to make H2O you liberate 232 kJ (kilojoules) of energy per mol of water. A mol of water weights 18 grams. Plug that into you your standard equation for kinetic energy (½mv2) and we find that if everything goes well we'll be getting steam coming out the back of the rocket at 5077 m/s. If you go look up the Space Shuttle's main engines you'll see that their exhaust goes out at 4436 m/s in a vacuum. Clearly there are a lot of sources of inefficiency that I'm not including, as you would expect. Still, first principles give you a fairly decent ballpark estimate.
However they also list the ve for when they start firing at sea level as only 3590 m/s. The atmosphere sort of gets in the way of stuff exiting out the back without interruption. Oh well.
Out of the various chemical fuels you could put into a rocket hydrogen is the best in terms of ve but it's got some drawbacks. For instance even after you liquefy it hydrogen isn't really very dense. Also, it takes a lot of work to liquefy hydrogen in the first place. Oxygen turns to a liquid at 90 degrees Kelvin which is admittedly rather chilly but still warmer than liquid nitrogen. Hydrogen by contrast will only stay liquid below 20 K. So you need big bulky tanks to store your liquid hydrogen propellant and even with lots of insulation some will boil off during the countdown and need to be continually replaced. If you've ever watched a rocket launch and wondered what that gas was coming out of the rocket before liftoff or why it has those tubes connected, well, now you know.
Some rockets use other fuels. You can combine liquid methane with oxygen for a ve of up to 3700 m/s. Liquid methane is much denser than hydrogen and liquefies at a relatively reasonable 112 K. Purified kerosene is even denser and doesn't have to be cooled at all but at the cost of a ve of only 3500 m/s.
There are also the hypergolic propellants. When you mix your fuel together with, say, oxygen and methane you have to do something to ignite it. Otherwise it will just build up in the combustion chamber and if it accidentally gets ignited after having built up it can explode. Hypergolic propellant doesn't have to be mixed - it will ignite all by itself when you bring the two chemicals together. Even better both halves are liquid at room temperature meaning you don't have any cooling or boiloff concerns at all! Why do we bother with this liquid oxygen stuff then? Well its ve is generally around 3300 m/s and more importantly it's toxic as all hell. Still, if you've got something like a maneuvering thruster that's going to be turning on and off repeatedly it's hard to avoid using.
Oh, and finally there are solid rocket propellants. They have the lowest ve of the bunch but they're pretty tough for rockets and since they aren't particularly toxic and don't have to be kept cold they tend to be cheaper than the other kind. Because they don't mind being shaken a bit they're the sort of rocket that is used in most military weapons.
So there you have the basic types of chemical rockets. I'll talk about electric rockets next post.
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