| From: | Paul Jonathan Adam <Paul@********.DEMON.CO.UK> |
|---|---|
| Subject: | Re: Knock Back |
| Date: | Wed, 12 Apr 1995 01:21:47 GMT |
> All the energy is transfered directly to the shooter in a single lump;
> there's no bolt, no slide to absorb and disperse the recoil energy.
Which is why revolvers kick harder than automatics :-)
> Paul> About 550 Joules for my .45... so that's going to give you a velocity
> Paul> of about four metres a second backwards if it all hits you. That is
> Paul> pretty fast and I think you'd have trouble staying on your feet.
>
> >> Divide by the mass of your target (call it 80- 100Kg for simplicity's
> >> sake) over the time of energy transfer (call it 1/10 second, again for
> >> simplicity) to get an approximate distance the round will move the
> >> target.
>
> SO your 550 Joules, assuming 100% energy transfer in 1/10 second, will
> accelerate me, at... call it 70Kg, 7.8 meters/second squared. My velocity
> after 1/10th of a second, due to the impulse of the slug, is .78 meters per
> second. That means I'm going to be moved at best, 8 centimeters for a full
> second. Because my acceleration isn't constant, and there are many other
> forces at work trying to slow me down, it's unlikely that I'm going to move
> much further than that.
Um, no. Not even slightly. <sigh>. Look, sorry to flaunt it, but as a B.Eng
(Hons) in mechanical engineering this is my *job* as well as my hobby here.
Assuming the bullet stops on your armour, it has to go from 270 to 0 metres
a second almost instantaneously. 1/10 of a second is *WAY* too long. If we
use an unarmoured man hit in the chest with a hollowpoint (because I can
put numbers on that), his chest is 0.3 metres deep and the bullet enters at
270 and comes to rest at the back. So it decelerates in 0.3 of a metre. Its
mean speed over that distance is 135 metres a second: so it takes 2 milliseconds
to come to rest. 0.002 seconds... Less if you're wearing armour.
You have to exert an acceleration of 135 000 metres/s/s on it to slow it down
in that time: the force exerted is (135 000 x 0.013) for f=ma and that comes
to 1755 Newtons, or the weight of two burly men. That force smacks you in the
chest for a short impulse and knocks you back.
Over your whole body you have a backwards velocity of about 3.4 metres a second
now. But because you're flexibly jointed, your legs and arms haven't really
started to move yet: it's just your torso going back for the moment, so the
velocity of your chest is higher and you have to slow it down with the rest of
your body. Somehow.
> Paul> Sadly a 5.56mm bullet (say 55 grains at 915 metres/sec) has an energy
> Paul> of about 1500 joules...
>
> Ok, so far that's two very different values for muzzle energy there :).
The previous was for my .45 automatic, this is the 5.56mm from a M-16 or
similar. Pay attention in class! :-)
> Paul> so assuming a 100% transfer (it mashed flat on your armour) you're
> Paul> suddenly going backwards at 6 or 7 metres a second.
>
> You're forgetting something: 100% energy transfer over a what period of
> time? I use 1/10 second because it's reasonable and easy to work with. Ok,
> assuming 100% energy transfer using your numbers, over .1 second (which
> doesn't happen, even with body armor with the 5.56, BTW), that's 2 meters
> per second acceleration over the .1 second, for a whopping 20 centimeters
> after 1 second. Yeah, that's pretty close to what would happen under those
> conditions.
Again, your assumptions are severely flawed. If the bullet takes 1/10 of a
second to come to rest, it's travelled 45 metres or so! How deep is your
torso anyway?
A rifle bullet tends to overpenetrate and only deposit about 50% of energy
(Dr Marvin Fackler, US Army) so it comes in at 900 and comes out at about 600
to lose half its KE. For the same chest shot that gives you 0.0004 - 0.4 of
a millisecond - to transfer the energy. The math works out to an applied
force in that interval of 2700 Newtons. You overall have a backwards vector
of about 3.8 metres a second, but again your chest has the bulk of that
and the rest of you is playing catchup.
Oh, and you now have a tunnel drilled clean through your chest, still
cavitating wildly from the passage of the bullet. You are definitely not
going to get up and dance the tango. If you want to stop the bullet, you
are going to have to absorb *all* the energy in your armour, which means
even more force.
> Paul> A three round burst? You're flying backwards at forty miles an hour!
Actually more like thirty when I do the math in more detail :-) Of course,
if you're well braced and ready, this is no worse tham taking the impact
of a running man crashing into you. Try the experiment: find a friend and
run into him, fast but not sprinting, and he'll stagger but stay upright.
He braced himself, was ready, and dissipated the energy. Now blindfold him and
put a Walkman on him so he can't hear you coming and try it again, and he'll
go over most of the time, especially if he doesn't even know the direction.
> Only in comic books. Remember, energy transfer must occour over a span of
> time. 300 Joules in .1 second is going to hurt a hell of a lot more than
> 3,000 Joules in 1 second.
My mathematics tells me I'm depositing 300-8000 joules in 0.001 second... If
you have a different set of theories, feel free, but this is the physics/math/
terminal ballistics approach. This shouldn't pick a man up and throw him,
but it makes standing upright through it a challenging proposition. Especially
if the footing is uncertain, for instance.
--
When you have shot and killed a man, you have defined your attitude towards
him. You have offered a definite answer to a definite problem. For better or
for worse, you have acted decisively.
In fact, the next move is up to him.
Paul J. Adam paul@********.demon.co.uk
