bulletproof wind

[Kragen]

In martial arts, when you "block" an oncoming blow, you almost never exert
a force opposite to the oncoming blow so as to make the attacker's body
part stop before reaching you.  Instead, you push against their arm or
leg at a right angle to its direction of motion, so their blow hits the
air instead of hitting you.

An even more recommended technique is to get out of the way, so your
attacker's blow hits the place where you were, but not you.

Bulletproof vests, bulletproof glass, etc., all take a different tack.
They just try to stop the oncoming bullet before it reaches whatever
they're trying to protect.

This involves absorbing a lot of energy and applying a lot of force; as
a result, such equipment is typically only useful once, and sometimes
only partly effective --- as anyone who's ever been shot wearing a
bulletproof vest can tell you.

The dodging technique could conceivably be used for many situations in
which a bullet is flying at you.  The trouble is that bullets are small
and relatively hard to see until it's too late.  The bullet described
below will travel 187 m in a normal person's reaction time, so manual
dodging (perhaps guided by HUD information on the bullet's estimated
trajectory) is likely to be ineffective in close-range circumstances.
Machine-controlled dodging (strapping a robot to your limbs that would
quickly remove you from the path of oncoming bullets) might be
more effective.

Suppose that, instead, a force was applied to the incoming bullet to
deflect it from its course, so that it would hit a tree or something.
How much force would it take?

http://www.geocities.com/CapitolHill/6856/fm23-35/FM23-_2.htm describes
the M9 pistol, a "9-mm semiautomatic, magazine-fed, recoil-operation,
double-action weapon chambered for the 9mm cartridge."  It has a muzzle
velocity of 375 meters per second and a muzzle energy of 569.5 newton
meters, according to this document.  (The document is rather confused
about the energies of several other weapons it describes, denominating
them in "foot-pounds" or even "per square inch" (no numerator).

But if we take these figures at face value, we know that v = 375 m/s and
mv^2/2 = 569.5 N m.  An N is a kg m^2/s^2.  v^2 we calculate to be
140625 m^2/s^2; this means that the bullet has mass .00405 kg, or 4.05
g.

For simplicity, I will assume no air resistance --- the bullet's
velocity will be assumed to be constant.  This is a very pessimistic
assumption.

Now, suppose a bullet is flying at the center of a broad-chested man's
chest.  Supposing he's a very wide man at 60 cm, we need to deflect the
bullet's path by 30 cm before it gets to where he is.  So we need to
move this 4-g mass by 30 cm, in a dimension it is initially at rest
within, in some very short time (and presumably short distance).

The distance an object moves from rest under constant acceleration is
\int_0^t ax dx, or a \int_0^t x dx, or at^2/2.  In this case, we want
0.3 m = at^2/2; 0.6 m = at^2; a = 0.6 m / t^2.

Suppose we only have a meter to deflect the bullet in.  In this case, t
= 1/375 of a second, and t^2 is 1/140625 s^2.  So a = 0.6 * 140625 m/s^2
= 84375 m/s^2.  Such an acceleration would require a force of 342
newtons, and such an acceleration is about 8500 G.  This might not be
practical to implement.

Suppose instead that we have 10 m to deflect the bullet in.  In this
case, the required acceleration is only 1/100 as great, at 844 m/s^2, or
about 85 G, and would require a force of 3.4 newtons.  This might be
slightly more practical, but would be rather difficult.

There are bullets that are several times faster.  These would be even
more difficult to deflect sufficiently.  For example,
http://www.diddybop.demon.co.uk/thear15.htm says that the AR-15 has a
muzzle velocity of almost 1000 m/s.

So you can't deflect bullets over any reasonable distance by using the
wind.  What about other methods?

One key problem is that deflecting the bullets with moving matter coming
from somewhere near the bullet's intended victim means that the matter
that hits the bullet has to be moving fairly quickly itself, in order to
get to the bullet before the bullet gets to its intended victim.  It is
difficult to accelerate significant masses to high velocities.

You could surround the person intended to be protected with a lot of
"smart material" that would respond to electrical impulses, which could
easily travel much faster than the bullet.  The "smart material" itself
wouldn't have to move very far; only the signals traveling through it
would have to move far.  With "Utility Fog", this could become a
practical reality.  Until then, it's a far-fetched fantasy.

More feasible kinds of "smart matter" clouds could be imagined.

You could conceivably deflect the bullet with high-velocity proton
beams.  These could easily deflect the bullet sufficiently to make it
miss the person it was aimed at.  They have the major disadvantages that
they would probably kill whoever was on the other side of the bullet at
the time, cost a lot of money, are huge, and produce significant random
radiation in their immediate vicinity.

You could conceivably hit the bullet with a high-velocity water stream.
I understand there are water-stream machine tools that (using a water
stream laced with fine grit) can easily cut through big hunks of marble.
http://www.jetpoint.com/process.htm explains:

   Abrasive waterjet cutting is a process for cutting materials using a
   stream of high pressure water, sometimes adding an entrained stream
   of abrasive particles to aid with the cut. Almost any material can be
   cut with this technology; metal, untempered glass, stone, wood; you
   name it, it can be cut with high pressure water. A special pump
   raises the pressure of the water from about 60 psi (pounds per square
   inch) to between 15,000 and 55,000 psi, depending on the raw material
   of the workpiece. The nozzle is moved in X and Y axes under computer
   control and can cut shapes difficult or impossible to make using
   other processes. The diameter of the "directed beam" of water will be
   about .040 inches in diameter, with some variation as components
   wear.

That diameter, by the way, is about 1 mm.

I'm not sure how fast water in a 55,000 psi jet moves, nor how to
calculate it.  But, according to this data, it's .00126 square inches,
and thus exerts a force of 69 pounds or so on whatever object it hits.
2.2 pounds is a kg G; a G is 9.8 m/s^2.  So a pound is about 4.45
newtons, so a 55,000 psi water stream exerts a force of about 307
newtons on whatever it strikes.  (OTOH,
http://www.composiflex.com/factsheet.html claims that it exerts a force
of "less than 1 pound" on the workpiece.) So it might conceivably be
able to deflect an M9 bullet if it had a couple of meters to do it in,
and if the force did not fall off too quickly with distance.  It would
need several meters to deflect a faster or heavier bullet.

Another possibility is to deflect the bullet with another projectile.
Doing this with a projectile comparable in size to the original bullet
could be rather dangerous, as great accuracy would be needed in
positioning the point of impact to bounce both projectiles in safe
directions.  Doing it with a projectile much larger than the original
bullet could safely avoid this problem, but might prove injurious to
those on the other side of the original bullet --- as well as being
either slow to do or rather bulky.  Doing it with several projectiles
much smaller than the original bullet might be effective --- these
projectiles could travel much faster than the original bullet.  However,
this would also create a hazard to other people in the area.

Another possible kind of 'smart matter' might take the form of thin
strands of fiber distributed through the air around the person to be
protected.  If they could stick sufficiently well to the flying bullet,
they could easily pull it off-course.

The forces and energies required in deflecting the moving bullet are
relatively small --- the energy can be arbitrarily small (since the
force is, ideally, at right angles to the bullet's trajectory) or even
negative (since the bullet has a lot of kinetic energy ripe for the
picking) and the force is just a few pounds.

Another possibility: small movable non-projectile metal objects.  If you
could move one of these into the path of the bullet, you would have no
trouble exerting enough force to deflect it from its path.  You'd have
to exert some pretty major forces on the small objects to move them into
the path of the bullet in time, though.


I've taken as given that it is possible to automatically detect that a
bullet is flying and begin to take action before it flies very far.
Obviously, this implies that this action be taken automatically,
accurately, and expeditiously.  There are great risks involved in
operating any of the systems suggested above --- if a high-energy proton
beam, high-velocity projectile, or high-pressure water jet were to
accidentally strike a person, it could easily kill them.  Utility Fog
carries major dangers of its own, but they are both more hideous and
more complex.

Detection of the bullet itself might be difficult to do with radar ---
the bullet is of a size comparable to the radio waves used.  Laser
scanning systems might work; they could detect the velocity of the
bullet rather accurately with the Doppler effect.

Ordinary high-speed cameras (cameras are currently available that can
deliver a frame every 5 ns) could possibly also work, although a great
deal of computer processing would be required in a very short time to
detect the bullet.

Kragen

-- 
<kragen@pobox.com>       Kragen Sitaker     <http://www.pobox.com/~kragen/>
Irony and sarcasm deflate seriousness, and when your seriousness becomes detum-
escent, you're not held responsible for your thoughts. Irony beats thinking like
rock beats scissors. -- http://www.hyperorg.com/backissues/joho-june2-98.html