From: emory!ke4zv!gary@gatech.edu (Gary Coffman)
Newsgroups: rec.guns
Subject: Re: Stupid question time, again...
Date: 26 Dec 92 00:17:34 GMT
Organization: Destructive Testing Systems

In article <1992Dec22.184105.19382@cbfsb.cb.att.com> osan@cbnewsb.cb.att.com (Mr. X) writes:
#Hi Folks!
#
#I have a question that has been nagging at me for quite some time.  Why is it
#that large artillery guns can toss projectiles out the muzzle at velocities
#so much higher than a shoulder arm?  Is there any absolute reason why you could
#not build a .30 rifle that spits a projectile down range at 10K fps, muzz. ?

Well artillery doesn't approach 10K fps either. Most of it is sub-3000 fps,
some of the heavier guns very much sub-3000. You can watch the shells pass over
in flight. Now the APDS anti-armor round of the 120mm Rhinemetal smoothbore
used on the M1A1 does sing right along at about 1,500 meters/sec, or about
5,000 fps. The penetrator is quite slender, however, and the large base
area of the 120 mm sabot gives a large area to push against for the projectile
mass, so the pressures can remain reasonable. Note the Remington Accelerators 
in 30-06 use this same technique with a .30 sabot carrying a .224 penetrator. 
They get 4,000 fps from that out of a rifled barrel. Fired in a smoothbore 
.30 cal, it should do better.

There are two limitations to hyper-velocity rounds. First is chamber
pressure, and second is the speed of sound in the propellant medium.
There are two ways to get more pounds of push against the back of a
bullet, use higher gas pressure, or give the PSIs more square inches
to push against. Now artillery does both. The guns are very heavy,
2.5 ton breeches are common, that allows high chamber pressure, and 
the shells have a fairly big base area, 70 sq inches in the case 
of the M1A1 main gun. The pounds of force pushing a projectile is the
product of the pressure and the base area. for the Rhinemetal cannon
that's about 4.9 million pounds. Compare that to the 11,309 pounds of
force behind a 30-06. Now the mass of the projectile matters, with
the Accelerator massing 55 gr and the APDS massing 100 pounds. If you
divide the mass of the projectile into the pounds force, you get a
figure of merit, a dimensionless number, showing the relative potential
velocity differences. For the APDS it's 49,000. For the Accelerator it's
791,630. So why is the APDS faster?

This brings up the second constraint on velocity, the speed of sound
in the propellant gases. No projectile can go faster than the pressure
wave generated by the burning propellant. If it did, it would trail
a vacuum behind it and get no push. Now the speed of sound is faster
in a hot dense gas than it is in ordinary air or no bullet could exceed
1,100 fps. The molecular weight of the gas matters too. Light molecules
can give higher speeds than heavy ones, and you have more light molecules
for a given weight of gas than you do heavy ones which increases pressure
by Boyle's Law. As the barrel lengthens, gas pressure decreases with the 
larger expansion volume. Eventually the pressure falls enough that the 
speed of sound in the gas drops to the speed of the projectile and you can't 
go any faster. In big bore artillery the volume increases less for a given
distance down the barrel vis the chamber volume than it does in the slender 
barrel of small arms. So the artillery piece can achieve a higher velocity 
before the speed of sound falls too much.

Gary

-- 
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