Missiles

Bertil writes:
>Archive-Message-Number: 5567
>From: Bertil Jonell [email removed]
>Subject: Re: solid fuel missiles
>Date: Fri, 4 Jun 1993 21:42:23 +0200 (MET DST)

>> 	For a 150Kg dry mass (warhead, electronics, structure, NO fuel), a
>> missile with ONE G-hour delta-V requires 70,936,947Kg of the best solid
>> fuel we make today.

>  Ok, but what are the equivalent numbers for hydrogen/oxygen or NERVA-type
>nuclear fission rockets?
>
>  And (nasty question) what are the equivalent numbers for a fusion rocket
>powered missile? :)

Well, let me give you a quick basic rocketry tour.
Delta-V (change in velocity) can be found in any rocket
by looking at the following formula:
DelV=g*Isp*ln(Mr)

DelV is change in velocity in m/s
g is gravity, 9.81 (say 10)
Isp is specific impulse, the measure of how long the fuel can provide
	a given thrust
Mr is the mass ratio (initial mass plus fuel mass over initial mass) of the
	stage as a whole.

Say we have a vehicle whose mass ratio is e (2.78ish), so ln(Mr) is about 1 .
That means that the delta-V in m/s is about 10 times the specific impulse.
(To be realistic, the limiting maximum delta-V is about 1.5 times this without
staging, and tends to be about 1.2 times that much).

Hydrogen/Oxygen current day engines max out at Isp of 454 (Space SHuttle
Main ENgines).  THat gives you about 4.5 km/sec per stage, max maybe
7 km/sec per stage.  (A LOX/LH2 Single Stage to Orbit is _just_ possible
on the earth).

One G-hour is 3600 sec * 10 m/s is 36 km/sec.  You'd need roughly an
eight stage rocket using LOX/LH2 to make a g-hour (which equals a mass
ratio from start to finish of about 4^8 or 65,500ish.  Or 9.8 million kg
for the 150kg payload.  A bit bigger than a Saturn V (ten times as large).

NERVA motors have perhaps Isp of 1000, up to 1100 in really far out
designs.  Assuming 1000, that gives you per-stage a delta-V or 10 km/sec,
so you need 3 or 4 stages to reach 1 g-hour.  Maybe a beginning to end
ratio of 100, or 15,000 kg for your 150 kg payload.

Known fusion rocket technologies are around Isp 5,000.  This gives you
a stage delta-V of 50 km/sec, or a little over one g-hour.  This means
a 10-G hour rocket (360 km/sec) needs a seven-stage rocket.  Again,
that's about 2 million kg initial mass.  About the mass of a Frigate
on the sea today.  I guess TNE presumes they get better as technology
marches on 8-)

The hottest rocket around (literally) is the Nuclear Salt Water Rocket
(proposed by Dr. Robert Zubrin of Martin Marietta Aerospace).
Basically, you disolve uranium or plutonium salts in water,
store them in a heavily-internally-shielded tank, and spray them
into a nozzle where the amount of fuel finally reaches critical
mass and they go FIZZ!.  Specific impulse is about 10,000 for
Uranium, or 15,000 for Plutonium.  That gives for a one-stage
rocket about 100 km/sec to 150 km/sec, or 3 to 5 g-hours.
So you can build a two or three stage nuclear salt water rocket
that will reach 10 to 12 g-hours and is compatable with the
missiles given in TNE.  That missile will mass about 200*150 or
30000 kg, or 30 tons.  More than TNE posits.

I don't know what TNE posits their motors have as specific impulse.
I'll try to work it out over the weekend.

sigh.  *shakes head*  I'm all done now.  Back to work...

- -george william herbert
Retro Aerospace

[yes, as a matter of fact, I _AM_ a rocket scientist.  8-) published, even]