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From:	Marc Renouf renouf@********.com
Subject:	Ballistics (was: Two firearms at once)
Date:	Mon, 8 Mar 1999 10:35:49 -0500 (EST)

Message no. 1 Someone should mention this before things get out of hand. A
bullet does *not* drop 32 feet (9.8 meters) in the first second on flight.
It drops half that distance (approximately 16 feet or 4.9 meters).
Why? Because the bullet is being accelerated from rest in the
vertical reference frame. The equation that covers such motion is:

x = x0 + V0*t + 1/2 A*t^2

where x0 is the initial position, V0 is the initial velocity, and A is the
acceleration. Note the "1/2" term. For a bullet flying horizontally, V0
is zero in the vertical direction, and the only acceleration is gravity
(9.8 meters/second^2). Hence, the bullet drops 4.9 meters in the first
second. Yes, it's pedantic, but at least it's correct.
Finally, while others have pointed out that spinning bullets
actually do generate lift, it should also be pointed out that the
main reason that rifles and other long arms have longer ranges because
they can achieve much higher muzzle velocities than pistol rounds,
sometimes by as much as a factor of 2 or 3.

Marc

From:	Adam Getchell acgetchell@*******.edu
Subject:	Ballistics (was: Two firearms at once)
Date:	Mon, 8 Mar 1999 11:14:00 -0800

Message no. 2 > Finally, while others have pointed out that spinning bullets
>actually do generate lift, it should also be pointed out that the
>main reason that rifles and other long arms have longer ranges because
>they can achieve much higher muzzle velocities than pistol rounds,
>sometimes by as much as a factor of 2 or 3.

As I mentioned in my earlier post, aerodynamics plays an important role,
especially in the case of rifle bullets. Rifles have superior range in part
due to greater velocity, and in part due to the design of their bullets.

Drag force can be expressed by the equation F = 1/2 *Cd*rho*A*v^2

where Cd = Coefficient of drag
rho = density of medium (e.g. air)
A = cross sectional area
v = velocity of the object

Note: this law is not valid in all regimes (i.e. it is not fundamental).

The reason for going through this equation is one can immediately see that
the bullet shape of a rifle (ie pointy, boat-tailed) serves a number of
important functions in reducing area (note rifle bullets tend to be smaller
caliber than pistols) and the Cd (which can vary significantly between
blunt tip than a sharp nose/boattail).

Coefficient of drag is a catch-all term, that tends to incorporate effects
of boundary layers at different regimes of Reynolds' numbers. (For a golf
ball, for example, the area of interest is Re20,000 to 100,000.) That is to
say, the interactions can be complicated, which is why physicists call it
fluid mechanics and engineers call it aerodynamics.

As a practical note, regardless of initial velocity all bullets tend to
drop into the subsonic regime by around 900 meters, which degrades accuracy
at that point. Not saying it can't be done, but I would tend to think
sceptically of snipers making kills beyond that range. It would seem be one
reason why the OICW went for a bursting area-munition to achieve their .3 -
.5 hit probability at 1000 meters.

P.S. Note to Paul: I did mention that diameter of the round (i.e. wound
channel) is also important in determining volume of tissue damage. Body
tissues are elastic, and there is a minimum amount of energy that needs to
be imparted to cause trauma. Small, hard (compared to the body),
fast-moving pointy objects are rather good at doing so.

>Marc

--Adam

acgetchell@*******.edu
"Invincibility is in oneself, vulnerability in the opponent." --Sun Tzu

From:	hivemind hivemind@********.rr.com
Subject:	Ballistics (was: Two firearms at once)
Date:	Mon, 8 Mar 1999 15:34:13 -0600

Message no. 3 -From: Adam Getchell <acgetchell@*******.edu>
>> snip some physics<<
Adam,
Just a quick question, where does the spin generated by the rifling fit
into all this? I "know" from shooting both rifles and smoothbores, as well
as baseball and football, that spinning the projectile adds both range and
velocity. Why? And please, talk down for those of us who are physicsly
impaired;-]

hivemind

From:	Mongoose m0ng005e@*********.com
Subject:	Ballistics (was: Two firearms at once)
Date:	Mon, 8 Mar 1999 17:48:01 -0600

Message no. 4 :-From: Adam Getchell <acgetchell@*******.edu>
:>> snip some physics<<
:Adam,
: Just a quick question, where does the spin generated by the rifling
fit
:into all this? I "know" from shooting both rifles and smoothbores, as
well
:as baseball and football, that spinning the projectile adds both range
and
:velocity. Why? And please, talk down for those of us who are physicsly
:impaired;-]
:
:hivemind
:
:

Basically, spinning things keep spinning they way they were spun, and
that's good if you want to keep the bullet pointing the direction it was
fired.

For this same reason a good (American) football throw has a "spiral"-
without the spin, the bullet tumbles randomly. Aerodynamic drag and lift
both figure in. If the bullet tumbles, its not point first, increasing
drag and decreasing velocity, which hurts range and damage.
Random tumble would add also a random "lift" in a random direction-
which affects accuracy. The bullets path would be like that of a baseball
pitchers Knuckle ball, which is thrown without spin- it is unpredictable.
This is actually the reason rifling was developed- muskets were quite
inaccurate past 20m, due to the balls random spin.

Mongoose

From:	Paul J. Adam Paul@********.demon.co.uk
Subject:	Ballistics (was: Two firearms at once)
Date:	Mon, 8 Mar 1999 23:13:37 +0000

Message no. 5 In article <v04011726b309c2e70083@[128.120.118.25]>, Adam Getchell
<acgetchell@*******.edu> writes
>As a practical note, regardless of initial velocity all bullets tend to
>drop into the subsonic regime by around 900 meters, which degrades accuracy
>at that point. Not saying it can't be done, but I would tend to think
>sceptically of snipers making kills beyond that range.

Just to nitpick, a few calibres remain usable for sniping past that
point: all are large, powerful specialist rounds, chambered in hefty
bolt-action rifles with semi-automatics very rare.

The best example offhand is .338 Lapua, which doesn't drop into
transonic instability until ~1400 metres or so. No idea when .50BMG goes
subsonic :)

For machine guns, of course, you either watch the tracers, or if the
tracers have burned out you look for strikes. We trained on the basis
that a tripod-mounted GPMG(SF) could be effective out to 1800 metres, if
you could observe the fall of shot and adjust it onto the target area.
Of course that wasn't for shooting at individuals, but for area fire.

>It would seem be one
>reason why the OICW went for a bursting area-munition to achieve their .3 -
>.5 hit probability at 1000 meters.

The only way you'd _ever_ achieve it with an infantryman's weapon... and
a pointless requirement, since when was the last time you ever expected
to _see_ a camouflaged infantryman at more than a few hundred metres?

'Tis a nice concept, but I'm unsure how useful it will be: shades of
SPIW and OICW, over which the simple, reliable, cheap and trusted M16
triumphed.

>P.S. Note to Paul: I did mention that diameter of the round (i.e. wound
>channel) is also important in determining volume of tissue damage. Body
>tissues are elastic, and there is a minimum amount of energy that needs to
>be imparted to cause trauma. Small, hard (compared to the body),
>fast-moving pointy objects are rather good at doing so.

And long spun projectiles, nutating their way through tissue like blunt
Cuisinart blades, are also much more efficient at causing incapacitating
injury than short relatively stable pistol bullets: hence the claimed
effectiveness of FN's 5.7mm round, which has a small but energy-dense
bullet to pierce armour, but a long spitzer bullet to cause severe
wounding.

--
Paul J. Adam

From:	dghost@**.com dghost@**.com
Subject:	Ballistics (was: Two firearms at once)
Date:	Mon, 8 Mar 1999 20:22:18 -0600

Message no. 6 On Mon, 8 Mar 1999 10:35:49 -0500 (EST) Marc Renouf <renouf@********.com>
writes:
>
>
> Someone should mention this before things get out of hand. A
>bullet does *not* drop 32 feet (9.8 meters) in the first second on
flight.
>It drops half that distance (approximately 16 feet or 4.9 meters).

Grah! I can't believe I mucked that up! :) Well, that's what I get for
doing that in my head (I actually don't know the position formula ... I
know the acceleration and integrate twice. :)

--
D. Ghost
(aka Pixel, Tantrum, RuPixel)
"You, you're like a spoonful of whoopass." --Grace
"A magician is always 'touching' himself" --Page 123, Grimoire (2nd
Edition)

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From:	Adam Getchell acgetchell@*******.edu
Subject:	Ballistics (was: Two firearms at once)
Date:	Tue, 9 Mar 1999 18:05:02 -0800

Message no. 7 There's not a quick answer to this, but here goes ....

If you've ever watched a volleyball game, you might notice that the best
serves are hit with top spin. This is called the Magnus effect.

When a spinning object such as a volleyball travels through the air, the
top spin produces different flow velocities between surfaces. In the case
of a volleyball serve, the top spin subtracts airflow velocity along the
top of the ball and adds velocity to the bottom of the ball. Bernoulli's
equation equates high velocity with low pressure, and vice versa. (An
amusing analogy can be seen in traffic. The average velocity of motorists
decreases as the number of cars rise, and vice versa. In fact, traffic
engineering often uses fluid flow equations.) The result is a pressure
differential which forces the volleyball downward, and hence, a wicked
serve.

In bullets, the Magnus effect produces a downward Magnus force.

However, the Magnus effect is very important for stability.

All bullets, when fired, have yaw. Yaw is the angle between the axis of
symmetry (rotational) of the bullet and the velocity vector (ie. which way
the bullet is flying). Simply put, yaw is the discrepancy between where the
nose is pointed and where the round is headed.

The dominant aerodynamic force on a bullet is termed the wind force, which
applies at the center of pressure. For a spin stabilized bullet, the CP is
located in front of the center of gravity (fin stabilized bullets have CP
behind CG). Because of the discrepancy between the CP and CG (due to
spinning of the bullet), an overturning moment arises which attempts to
rotate the bullet on an axis perpendicular to its axis of symmetry. A
cross-wind force is produced which will drift a bullet sideways. A
right-handed bullet (ie one spinning clockwise) will drift to the right; a
left-handed bullet will drift to the left. This drift can be quite
significant at range; up to 100 yards or more [references below].

Wind force can be split into drag (which I mentioned before in an earlier
post) and cross wind force. Note that due to reduction of spin rate, the CP
can change. This is generally termed dynamic stability, and can be lost in
flight (or even at the muzzle, in which case the bullet is dynamically
instable). Loss of dynamic stability generally results in tumbling.

The most important effect of spinning is gyroscopic effect, which is a
result of angular momentum (curl your right hand in the direction of spin;
your thumb points in the direction of angular momentum). A basic law of
physics is that angular momentum is conserved, which is to say, it doesn't
like to change.

When the bullet attempts to tumble due to overturning moment, angular
momentum converts this into a slow precession around the bullets spin axis.
There are actually at least two precession rates; one for the tip of the
bullet and another for the base. The details on this are complicated.

The summary of all of these factors (and more) is that there are 3
criterion for good bullet design:

Static stability: If the gyroscopic effect converts the overturning moment
into a precession, the bullet is statically stable. If the bullet is not
spun, or spun at too low a rate, it will tumble.

Dynamic stability: If the angle of yaw of a bullet is reduced with time,
the bullet is dynamically stable. Most military rounds are dynamically
stable.

Tractable: It is possible to be over-stabilized (many handguns are) with
the result that a discrepancy between axis of rotation and velocity causes
the bullet to hit base first at range. A bullet that is not over-stabilized
is considered tractable.

There is an excellent article entitled "How do bullets fly?" by Ruprecht
Nennstiel which I used for much of this information. It is available at:
http://www.povn.com/~4n6/index.htm and is a very good read if you are
interested in such things. Physics understanding is necessary, but the
author has done a good job of making equations and graphs illustrate his
point. The formulae are not necessary to understanding his explanations
(and are interesting to derive).

>-From: Adam Getchell <acgetchell@*******.edu>
>>> snip some physics<<
>Adam,
> Just a quick question, where does the spin generated by the rifling fit
>into all this? I "know" from shooting both rifles and smoothbores, as well
>as baseball and football, that spinning the projectile adds both range and
>velocity. Why? And please, talk down for those of us who are physicsly
>impaired;-]
>
>hivemind

--Adam

acgetchell@*******.edu
"Invincibility is in oneself, vulnerability in the opponent." --Sun Tzu

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