# Re: PHYSICS: Getting knocked on your ass (was Re: TERRORISM: looking forsolutions)

From: Doug Jones (djones@xcor.com)
Date: Fri Sep 14 2001 - 19:59:42 MDT

Mike Lorrey wrote:
>
> Robert Coyote wrote:
> >
> > As an example in Momentum
> > Cartridge 44 Magnum
> > Caliber in Inches 0.43
> > Bullet Weight in grains 240
> > Muzzle Velocity in feet per second 1348
> > Muzzle Energy in foot-pounds 941
>
> Which means there is enough energy, leaving the muzzle, for the bullet
> to move 941 pounds one foot in distance. A person who is 157 pounds will
> be moved 6 feet: i.e. knocked on their asses.

As long as we keep this discussion to physics rather than politics, I
suppose this is reasonable, but at the first sign of acrimony I suggest
we take it to exi-freedom.

That said, I shudder at the mishmash of units- furlongs per fortnight,
anyone? Converting to slug-foot-second units, I get

Mass = 240gr / 7000 gr/lbm = .034 lbm = 1.06e-3 slug
V = 1348 ft/s

MV^2/2 = 967 ft-lb <note that lb is a unit of force, not mass

This is an energy, a measure of how much work the projectile can do.
This relates directly to wound damage, but does NOT say how much
velocity change can be produced by an impact. For that we need
momentum:

MV = 1.44 slug-ft/s = 46.2 lbm-ft/s (after multiplying by that pesky
factor of g for pounds mass)

Momentum is conserved, M1*V1 + M2*V2 = (M1 + M2)*V3

where object 1 is the bullet, object 2 is the target.

Since M2>>M1 and V2=0, this simplifies to

M1*V1 = M2*V3

so

V3 = M1*V1/M2

For our hypothetical 157 lbm target, the velocity is

V3 = 46.2/157 = .3 ft/s, hardly enough to make an adult stagger. If
you've seen live fire tests of body armor, you'll note that the person
being shot hardly moves with the impact... about as much as the shooter
did.

Projectile weapons do their damage via energy deposited in the target,
not momentum- since the momentum imparted to the gun is the same
magnitude as that sent downrange in the bullet, although of opposite
sign. This relates to the problem of rockets, in that to put a lot of
momentum into the exhaust gases, they must go very fast- which requires
tremendous energy. The gases from the engines I work with travel far
far faster than any bullet, typically 7000 ft/s or more.

```--
Doug Jones, Rocket Plumber
XCOR Aerospace
```

This archive was generated by hypermail 2b30 : Fri Oct 12 2001 - 14:40:46 MDT