Jed Rothwell wrote:
See:
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920005899_1992005899.pdf
http://en.wikipedia.org/wiki/Nuclear_thermal_rocket
It is interesting to think about how one might apply high temperature CF
for a rocket engine. I am rewriting my book, based on the Japanese
edition which I just finished writing. I am thinking about beefing up
the rocket propulsion section. My problem is that I know next to nothing
about rockets, so I better run this subject by the audience here,
especially Ed Storms who is an expert in nuclear propulsion.
I would like to know how much mass of propellant a rocket would require
to launch from earth to orbit, and from earth to Mars.
Single stage to orbit (stupid with conventional rockets but easy to
compute):
Rocket equation is V_f - V_i = V_e * log(M_i/M_f)
where V_f = final velocity, V_i = initial velocity, V_e = exhaust
velocity, M_i = initial mass, M_f = final mass, and log = natural log
Escape velocity is about 7 miles per second, IIRC, or about 11,000
meters/sec. Exhaust velocity with a kerosene rocket (like Saturn V) is
about 3000 meters/sec according to a random website. So
11,000 = 3,000 * log(M_i/M_f)
log(M_i/M_f) = 3.7
M_i/M_f = exp(3.7) = 39
and you need to use up about 97% of your mass to get to escape velocity.
Orbital speed is about half escape velocity but since it's a
logarithmic relationship it doesn't make much difference -- just getting
to orbit takes almost as much fuel as getting to escape velocity.
That's why nobody uses single-stage-to-orbit rockets fired by kerosene,
of course. Multiple stages improve the result dramatically. Different
fuel can help, too. H/O gives a higher exhaust velocity (I think) but
it's very bulky (witness the shuttle external tank).
With a chemical rocket, reaction temperature and mass of the molecules
most likely are the most important issues in determining the exhaust
velocity, though nozzle design plays a big part too. Ideally, I
suppose, you want a reaction which releases a great deal of energy and
has as its result nothing but hydrogen atoms.
Based on the Wiki
paper it seems fission rockets from earth to orbit did not have many
advantages over conventional ones,
And they pollute like the devil if you fire them in the atmosphere...
but the transit to Mars would be a
lot faster.
A 50 MW engine described in Ref. 1 consumed 2.36 kg/s of hydrogen
propellant (0.05 kg/MW), and a 5 GW NERVA rocket that was the planned
would have consumed 121 kg/s (0.02 kg/MW).
I don't understand this. It's not obvious to me how you give a power
rating to a rocket engine, save possibly by rating the energy released
by the fuel (most of which is typically lost as heat).
The actual power the engine gives to the vehicle is a function of the
velocity, and goes as velocity*thrust. At zero velocity the power is
zero (all the energy goes into heat). If you have enough fuel, the
power imparted can become arbitrarily large as the velocity increases.
This is not unlike the situation with an automobile engine, where power
= torque*rpm. The difference is that "rpm" is replaced with "velocity".
This 5 GW unit would have
been remarkably small. If I do my calculations right, it would produce
as much energy in one day (0.97 days) as a 100 kiloton nuclear bomb,
which is astounding.
For a deep space engine, people have been talking about using high ISP
Ion thrusters. According to Wiki and other sources, these have about an
order of magnitude better than liquid fuel rocket engines, but a very
poor power/weight ratio, and a very low propellant flow. Apparently you
cannot just increase the flow to any level you like. Perhaps with a CF
power supply you could generate 50 MW or even gigawatts continuously for
months.
http://en.wikipedia.org/wiki/Ion_thruster#Thrust
According to Wiki the best possible ion engine would be linear particle
accelerator for specific impulse of 30 million seconds (!) but you
cannot push much mass through one so the actual thrust is negligible.
As long as it's a rocket, the rocket equation dominates everything, and
you are stuck with delta-V being proportional to exhaust velocity. So,
you want as high an exhaust velocity as possible. Ion engines can
approach V_e=C, which is as good as it gets.
It
is not clear to me whether this is a design limitation or whether it is
because people do not have portable 5 GW electric power supplies.
I am not sure what kind of generator would work for this. Thermoelectric
generation might work; electrohydrodynamics would be great; but I was
thinking perhaps one could use water to drive a steam turbine, condense
and recycle some of the steam (with large cooling fins I suppose), and
then reheat some of the other waste steam for propellant.
Plan B might be a high temperature CF can be used to heat the propellent
(hydrogen or water) to high temperature gas, and perhaps something like
lasers with CF generated electricity then boosts the gas temperature far
above the melting point of the CF cell, kind of like an inertial
confinement hot fusion reactor. Of course converting heat to electricity
and using lasers would be energy inefficient but as I said the idea
would be to conserve propellant.
What we want are rockets that can achieve continuous 1 G thrust with a
payload of, say, 20,000 DWT (a small freight ship). Assuming the ratio
of ship to payload is the same as a Boeing 747, the empty ship would
weight about 30,000 tons. I have no idea how much the propellant would
weigh, or how much energy it would take. 1 G carries you to the moon in
~3 hours, which is about as long as I care to be crammed into a seat. I
am not sure how long it would take to get to Mars at kind of
acceleration (of course it depends on how far away Mars is at the
moment) . . .
NASA says Mars is usually about 78,300,000 km away
(http://aerospacescholars.jsc.nasa.gov/HAS/cirr/em/9/2.cfm) and it takes
about 6 months to get there, but they figure it can be reduced to 4
months (http://nssdc.gsfc.nasa.gov/planetary/mars/marsprof.html). With
constant 1 G acceleration I gather it would take around 3 days. That's
more like it! See:
http://www.cthreepo.com/cp_html/math1.htm
Enter 39 million for half the trip; ignore earth's gravity. This comes
out 2 days.
A more sophisticated calculator:
http://home.att.net/~srschmitt/script_starship.html
For Mars, enter 1.5 AU (from data shown below on this page), and 1 G. It
comes out 3.5 days. The longest trip in the solar system would be 17
days. Alpha Centuri is 3.5 years for the person on board, 5.9 years
earth time, taking into account special relativity.
20,000 DWT is fine for Mars, but for interstellar travel you want to
bring all your stuff. So let's Think Big. Even 30,000 tons is peanuts by
the standards of modern container ships. For interstellar travel done
right, I say take a fleet of 1,000 container ships, each with a 151,000
tons payload. Now that would take a lot of energy and a lot of propellant!
- Jed
