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Tuesday December 09, 2008 06:52 AM
Stardate: 210504.01
06:52
A Primer on the Physics of
Propulsion
Contributed by Eric Moore
This is a basic primer on the physics of conventional propulsion
systems. It assumes some knowledge of physics, but not much at all. I'll
try and keep everything as basic as possible, but this will be a
technical treatment of the subject.
The function of any propulsion system is to make something move forward.
Due to the conservation of momentum, this can only be accomplished by
making something else move backwards. (This article ignores
"reaction-less" drives, as none are known to exist, and postulating them
is difficult.) The heavier the stuff going backwards is, and the faster
it's going, the faster you go. Generally, in order to design a
spacecraft it's easiest to base your calculations off the force the
drive is capable of, so that's what we'll try and calculate.
The first drive we will work on is a standard reaction drive. This is a
drive where you take some material, and squirt it out the back of your
ship (a chemical drive, a fusion drive, ion drive, etc). The basic
relation we will use is the the one between change in momentum and
force:
F = dp/dt
In other words, the the force exerted by or on a body is equal to the
rate of change in it's momentum per unit time. This doesn't seem to help
us much, but it's often easier to calculate the change in momentum than
the force. Now all we need to know is how much stuff (mass) we're
pushing out the back of the ship, and how fast it's moving away from us.
p = mv
dp/dt = (dm/dt)*v
we'll take dm/dt as a parameter that describes the rate of reaction mass
usage ("reaction mass" is a technical term for the stuff we make move
backwards). We're assuming that we can use up stuff at any rate we want
(not really fair from an engineering standpoint, you need pipes and
stuff to get it into the drive, but that's irrelevant from a physics
standpoint. So the only thing we need is the velocity the reaction mass
is moving at relative to the vessel. Obviously for our spacecraft we're
going to want this to be as fast as possible, so that we get the maximum
amount of thrust out of each kilogram of reaction mass spent. How do we
know what velocity the reaction mass is traveling at? The easiest kind
of a drive to make is a rocket. Basically a rocket is where you make
your stuff hot, and use the heat to propel it out. In a gas (or any
other material, but we're working with gasses here) , the molecules are
in constant motion, and the speed at which they are traveling is
determined by the temperature. In a thermally based drive, we put the
reaction mass in a box that's open on only one side. Then any molecules
that are traveling in the direction of the hole will leave the box,
moving (relative to the box) at whatever velocity they're moving at due
to temperature. In a gas, the average velocity of the molecules is
determined by:
v = sqrt(kT/m)
where k is a constant (Boltzmanns constant = 1.38*10^-23) T is the
temperature, and m is the mass of the molecule. So in order to increase
the thrust we get out of each gram of reaction mass, we can do one of
two things, we can increase the temperature, or we can decrease the mass
of the molecule we're using. This makes Hydrogen (the lightest element)
an ideal choice for reaction mass (and is why the space shuttles main
engines carry more hydrogen than is needed to combust with the oxygen,
the extra hydrogen makes the exhaust lighter, and makes the engines more
efficient). Since it's pretty hard reduce the mass of the molecules
below that of hydrogen, all we can do to improve the efficiency of our
drive is to increase the temperature. The problem is that the specific
impulse (specific impulse is a technical term for how much force a given
amount of propellant can produce) of a drive is proportional to the
square root of the temperature, so if we want to double the specific
impulse, we need to quadruple the temperature. Quadrupling the
temperature requires quadrupling the energy input.
The reason we want a high specific impulse is
because we have to carry all of our reaction mass with us until we use
it. This means that in addition to accelerating the ship, our drive has
to accelerate the reaction mass we haven't used yet. In some drives this
isn't a problem (for example the ion drives on satellites), usually
because they aren't expected to do much accelerating, and therefore
carry a very small amount of reaction mass in comparison to their total
mass. For these drives getting the most amount of thrust out of a given
amount of energy is most important. So, if you give a particle a given
amount of energy (for example by accelerating it with an electric field)
it's energy is given by:
E = 1/2 mV^2
and it's momentum by:
p = mv
p = sqrt(2*E*m)
So, once again, doubling the specific impulse requires quadrupling the
energy, but you want as massive a particle as possible.
The limiting factor in interstellar travel is usually reaction mass. In
order to get anywhere in a reasonable amount of time, you need to
accelerate more or less all the way, however the longer you plan on
accelerating, the more reaction mass you need, and the more reaction
mass that you carry, the more massive your ship is, and the more
reaction mass you need to accelerate the reaction mass you haven't used
yet. It's a vicious cycle. So most interstellar starship propulsion
system designs use some method for getting around this. For example the
bussard ramjet collects interstellar hydrogen (which it did not have to
accelerate) along it's path, rather than carrying its reaction mass with
it. Another idea is to use light pressure to accelerate a remote vehicle
(eg the starwisp). With this design you do all the work at a stationary
power plant.
Human Factors Engineering Issues
There are many important Human Factors Engineering issues involved in
multi-generational starship design. One basic issue is Neutral Body
Posture, which is defined as the posture the human body naturally
assumes in microgravity and is similar to the fetal position. It is
important to note that in this position, each joint is at or near the
midpoint of its range of motion--the point at which each set of muscles
is able to exert the most force. If any portion of a long-term starship
will experience the effects of zero-gravity, tasks performed in that
part of the ship must take this posture into account. Proper Restraint
and Mobility Aids such as foot restraints and handholds assist the crew
members in maintaining this posture. It may seem like a minor detail in
the design of a multi-generational starship, and perhaps for generations
born on the ship, such considerations do indeed become minor, but for
older members of the first generation to become star travelers, this is
crucial.
Another piece of microgravity trivia is that the human spine stretches
two inches, making people two inches taller in microgravity. The
constant gravity load on the spine is removed; nifty, futuristic, lycra
uniform designers better remember this!
And of course, the psychological issues are many. I know they've been
bounced around in the newsletters, and everyone has their own opinions.
The basic, umbrella Human Factors concepts involved are workload and
personal space. Traditional workload issues include keeping the crew
member busy enough to feel valuable to the mission without overworking
and stressing him/her. I know the idea of having crew members who
perform multiple duties was pretty much agreed upon in earlier
newsletters. This would help keep everyone busy and feeling valuable.
Personal space is the other big issue. A multigenerational starship goes
way beyond the longest submarine tour of duty. People could easily go
batty, technically speaking :). Another idea bounced around in the
newsletters has been to tether two ships to each other with some sort of
tunnel and switch out crewmembers at a certain time. This makes sense to
me. If people know at a certain mission elapsed time they will be
switching ships, it gives them something to work toward and a major
change of scenery. Or the second ship could be storage and "vacation
space." There are many possibilities with that design; is it
technologically feasible? That's for the other engineering disciplines
to decide.
Andrea Berman
Human Factors Engineer
Lockheed Engineering and Sciences Company
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