[FPSPACE] A question...what is an ICBM?

[robot at esper.com]

 Stefan Barensky <stefan at orbireport.com> wrote: 

>You can go into space with a MRBM (the name Thor comes to my mind).

You could go into space with a cheap Chinese bottle rocket ($1.99 per
gross at the fireworks store off the Interstate near my house), if
the payload was only a milligram. 

Well, I exaggerate, but not much.
What's the mass ratio of a single-stage-to-orbit blackpowder system?
(The Chinese invented blackpowder, didn't they?)
Assume blackpowder has a specific impulse of 100 [sec].
"g" is 9.8 [m/sec^2].
We'll take the "first cosmic velocity" (7.91 km/sec) for the mission
velocity, and add in a loss budget of ~2 km/sec. Let's just call it
10,000 m/sec.

The rocket equation sez:

mass ratio ("wet" mass:dry mass, or fuelled mass:burnout mass) 
           = e ^ [delta-vee / (Isp * g)] 
           = e ^ [10,000/(100*9.8)]
           = 2.718 ^ 10.2
           = 26,875:1 

which is rather high by current standards.

Payload = 1 mg, (say a microdot that proclaims, "We're here!") so
GLOW is 26,875 mg.

Plus the mass of the cardboard case, which I'm ignoring 'cuz I don't
want to do the calculation over again.

Now 27 thousand milligrams is just about an avoirdupois ounce, but
I've never seen a bottle rocket as big as an ounce, even counting the
little stick. So I did exaggerate, a bit. A skyrocket, maybe.

Also, there's another constraint sweeping in orthogonally, that is
the bottle rocket would have to burn the blackpowder so sparingly
that it couldn't even generate enough force at any one time to lift
itself off /terra firma/. In free space, OTOH, even a little thing
can build up an impressive burnout speed, but free space is not where
it's starting from.

Kidding aside, you can go into space with an MRBM like Stefan says.
The Chinese just did it, albeit not with their off-the-shelf DF-21,
but a heavily modified 4-stage variant, it would seem. See: 
 http://www.strategycenter.net/research/pubID.142/pub_detail.asp# ,
which is the best open-source analysis I've seen so far.

The question is, what size payload is to be orbited versus what
throwweight to another continent? 

My answer to Stefan's question is totally back-o'-the-envelope; I
haven't looked anything up, so the figures might be a little rough.

>Does anyone know the mass of an Iranian nuclear warhead with its
>thermal shield for high-speed reentry?

Well, thank goodness this question has no answer, because the
Iranians don't have any sort of nuclear device yet, let along a
weaponized design. If they did, they'd already be a war going on with
Persia.

Now, one might assume, based on the well-known Pakistani-North
Korean-Iranian blackmarket WMD triad (plus recent membership by Libya
and the Chicoms), that the Iranians would ultimately end up with
something similar to Pakistan's existing fission warhead, which has
been reputed to be based on uranium implosion (much more efficient
than gun-type assembly). This is roughly a 1000-kg package, yielding
~10-20 kilotons. 10-20 kt is enough to demolish a central business
district, thus eviscerating any major city in the world, which should
constitute a sufficient strategic deterrent. Add half again for the
RV wrapper. (Wasn't the mass of the reentry experiment which the
Indians just ran 300 kilos?)

But there's a wrinkle: The DPRK (whom I like to call the PeepReps)
have a device based on plutonium, not uranium. Crappy plute at that
(they cooked it too long), which was why their recent nuclear test
just about fizzled. The PeepReps don't have a uranium separation
cycle yet (thank goodness, or there'd be yet another war going on);
nor do the Iranians have one, though they're working on it, with
seemingly more success than the PeepReps. The PeepReps might not even
have a uranium weapon design (I hope); but that depends on just how
apallingly irresponsible the Chinese and the Paks have been at the
proliferation business. Based on this month's performance in LEO, I'm
not sanguine about the Chinese. The Paks, OTOH, who do have uranium
separation and a validated uranium design, are mostly Sunni (as are
the Libyans), whilst the Iranians of course are Shia. This wasn't a
consideration 4 years ago, but sure as heck is now, now that a
quasi-Reformation/Thirty Years War seems to be catching fire in the
Islamic world. So the Sunni majority (by headcount and financial
resources) might well intercede in the triad and outbid the Iranians
in order to keep a nuke out of Shiite hands. Or the Sunnis might use
stronger clandestine methods against the PeepReps directly to
forestall such a possibility permanently. (Has anyone thought of this
yet?) Wheels within wheels. So it looks like the "axis of evil" might
actually be a cracked axle, thus causing one of these wheels to come
off. Wouldn't that be nice.

But I digress. Again.

Assume the Iranians somehow manage to master the uranium separation
cycle and design and build a uranium-fuelled warhead. Figure
1300-1500 kg, all in, for an Iranian first-generation warhead (atomic
bomb + RV). Now there's no point in throwing a bomb if the CEP
exceeds the blast radius by very much, even for countervalue (i.e.
terror) targeting. (If anyone in the Mideast ever has a rational need
for counterforce targeting, the world will be in very bad shape
indeed; so I'm not going to think about that nightmare.) Most
residential structures are heavily damaged or demolished at 4 psi
overpressure. The 4 psi contours for a 10- to 20-kiloton blast are
just under to just over a nautical mile. So call the effective radius
of the Iranian weapon 2 kilometers. 

The Desert Storm-era Scud had an angular accuracy around a third to
half a percent, as I recall, i.e. a range:accuracy ratio of 300 to
200:1. Let's say the Iranians improve their missile guidance by an
order of magnitude. Say 2500:1. Then applying the 2-km CEP limit
would give them a maximum effective range of 5000 km for that
combination of warhead and launcher. Beyond that, they'd be wasting
their ammunition, else have to task two birds per target.

IIRC, the term "intercontinental" in ICBM means 10,000 km, since a
complete hemisphere can be covered from any one point with such a
range. (World's 40,000 km around.) Hitting Africa doesn't count,
because it's right next door. So what the Iranians would actually get
is better-called a "semi-ICBM". 

A 5000-km ballistic flight in half an hour would have to go at about
3 km/sec. Add a loss budget of 2 km/sec, and we have a total mission
velocity of 5 km/sec. For a 2-stage missile, we split the delta vee,
and run the rocket equation twice. (For a 3-stage missile, we'd
divide the delta vee into thirds, and run the equation three times;
but I think 2 stages is sufficient for a semi-ICBM.) I assume that
the dry weight of each stage is equivalent to the effective payload.

Let's say the SCUD-type hypergolics have an effective performance of
200 [sec].

So, applying the rocket equation for the upper stage, we get a mass
ratio (wet mass:dry mass) of:

M.R. = e ^ [ (5000/2) / (200 * 9.8) ]  
     ~ 2.718 ^ 1.25
     = 3.5

so the wet mass of the top stage is 3.5 x 1500 = 5250 kg,
plus the warhead (RV & A-bomb) itself, 1500 kg,
for a total of 6750 kg (which is pretty close to the gross mass of a
first-generation Soviet SS-1, or Scud).

The whole top stage is the effective payload of the bottom stage, so
again:

M.R. = 3.5

bottom wet mass is 3.5 x 6750 = 23,600 kg,
plus the "payload" (the top stage + warhead), 6750 kg,

for a total launcher mass of 30,300 kg, or ~30 tonnes.

Now, could a missile like this be a dual-capable space launcher as
well?

Consider replacing the warhead, 1500 kg, with a third-stage plus
bus-plus-satellite package of equal mass. Recall that the mission
velocity to just barely get into space is 10 km/sec, more or less.
Since the 2-stage missile has already developed 5 km/sec (inc. 2
km/sec for the loss budget already accounted for), the third stage
has to develop the difference, another 5 km/sec. Assuming the same
sort of propulsion, we get:

M.R. = e ^ [ (5000) / (200 * 9.8) ] = 3.5; 
add 1.0 for the dry mass of the structure, and we get an effective
payload of 1500 / (3.5 + 1) = 333 kg.

So, if the Iranians manage to put a 300+ kilogram satellite into
orbit soon, then yes, they will have demonstrated a /de facto/
semi-ICBM capability for their likely warhead.

How you independently calculate the mass of their bird is another
story, but I'll bet there's people on this list who can do that with
Kettering Group methods. If their bird is 300 kg or over, you'll have
your answer.

PS. If the Iranians:
- reduce their guidance error by half (or boost the warhead yield 10X
but that would be really hard), and
- reduce their dry mass structure by half, and
- reduce the mass of their warhead by a third, and
- increase the performance of their rocket engines by a tenth, 
then they'd have a /bona fide/ hemispherical-range, 7 km/sec, ICBM in
virtually the same liftoff envelope, ~30 tonnes.
But I believe the world won't let them get that far.

PPS. There's a lot of confusion on the Web, in connection with this
supposed impending Iranian space launch, concerning this German
report of Iran getting "18 sets of BM-25 missiles [sic] from the
North Koreans". For one thng, the BM-25 is a 250mm unguided multiple
rocket launch system, according to my handbook of Soviet weapons.
It's artillery. So I don't know what the German report is talking
about.

--
Robert G Kennedy III, PE
www.ultimax.com