```From: "Andrew Higgins" <higgins@mecheng.mcgill.ca>
Newsgroups: sci.space.policy
Subject: Re: Deep-undersea gas-gun launchers.
Date: Thu, 16 Dec 1999 22:39:21 GMT

----------
In article <83a84l\$jjt@crl3.crl.com>, gherbert@crl3.crl.com (George Herbert)
wrote:
>
> It's not the speed of sound, it's the gas expansion velocity of
> the propellant mix in question (which is roughly Ve or c* in rocket
> terms, if you're using the same propellant mix or have the same
> products of combustion).
>
> For example... max practical speed for tank guns is a shade under
> 2,000 m/s (typical is 1,500 to 1,700 m/s).  Isp for burning the
> propellants in question in a rocket, expanded to vaccum, is around
> 250s, or 2500 m/s.  If you take 1,650 m/s as typical main gun round
> muzzle velocity then the gun's operating at a hair under 2/3 of Ve.
> There are whole books on the details of internal ballistics leading
> to explaining what fraction of Ve a particular designed gun will get.
>

This is not quite right.

The maximum expansion velocity of gas in a gun is an *unsteady* expansion,
so the max velocity is different than the maximum expansion velocity in a
rocket nozzle.

For an unsteady expansion, the maximum velocity is:

Vmax = 2 a0 / (gamma-1)

Where "a0" is the *initial* speed of sound in the gas and "gamma" is the
ratio of specific heats (gamma = 1.4 for diatomic gases like nitrogen,
hydrogen, etc.).  So, the maximum velocity for a hydrogen gas gun is about 5
times the initial sound speed of the hydrogen propellant.  In practice, gas
guns can rarely reach these speeds; 2 or 3 a0 is a more realistic limit, due
to friction and other effects.

In steady expansions (such as rocket nozzles), the maximum velocity is:

Vmax = Sqrt[2/(gamma-1)] a0

Vmax = 2.24 a0 (for gamma = 1.4)

Thus, the maximum velocity is only about half the ideal maximum velocity for

This fact is why, for example, extremely high speed wind tunnels (hypersonic
tunnels) use an unsteady expansion to generate the high velocity flow, such
as shock tubes.  A steady, continuous flow wind tunnel would never be able
to simulate the aerodynamics of orbital re-entry.
--
Andrew J. Higgins            Department of Mechanical Eng.
Assistant Professor          McGill University
Shock Wave Physics Group     Montreal, Quebec CANADA
higgins@mecheng.mcgill.ca

```

```From: Bruce Dunn <bdunn@genastro.bc.ca>
Newsgroups: sci.space.policy
Subject: Re: Deep-undersea gas-gun launchers.
Date: Fri, 17 Dec 1999 01:41:43 GMT

George Herbert wrote:

> For example... max practical speed for tank guns is a shade under
> 2,000 m/s (typical is 1,500 to 1,700 m/s).

In the 1960s, using standard military gun propellant in a 16 inch naval
cannon, Gerald Bull indicated that:

normal naval shells in the 3000 lb class could be fired at 2800 fps (850
m/s)

sub-calibre shots weighing 400 lb could be fired at 6000 feet per second
(1830  m/s)

sub-calibre 400 lb shots in a redesigned cannon with a longer barrel and
chamber could be fired at 7000 fps (2130 m/s)

See my writeup at the following address which describes the contents of
some hard-to-get literature on Bull's HARP project:

http://www.islandone.org/Propulsion/GeraldBullInfo.html

--
Dr. Bruce Dunn
http://www.genastro.com/
Reliable, low-cost transportation to low Earth orbit and beyond

```

```From: "Andrew Higgins" <higgins@mecheng.mcgill.ca>
Newsgroups: sci.astro,sci.space.policy,sci.physics,sci.engr.mech
Subject: Re: Deep-undersea gas-gun launchers.
Date: Fri, 17 Dec 1999 18:43:44 GMT

In article <83cu8m\$li3\$1@nntp1.atl.mindspring.net>,
sbharris@ix.netcom.com(Steven B. Harris) wrote:
>
>     The speed of sound is dependent on gas temperature, and both
> pressure and density factor out if you write it in temperature terms.
> And since you can get the temperature pretty high, you can fire a
> projectile even from ordinary varmint rifle at almost 4 times the speed
> of sound. Air density is the limiting factor, however, as above Mach
> stresses.
>

Huh?  I have fired copper bullets to Mach 6 and there is no reason why they
cannot go much higher velocities.  Copper, in fact, is a decent coating
material to use at hypersonic velocities:  it does not burn (unlike
aluminum, titanium, etc.).

>
>    To get velocity as fast as gas of any energy you can make (including
> plasmas), it's merely necessary to have an evacuated barrel, and set
> off charges just behind the bullet as it travels along, so that it is
> always pushed by a column of expanding gas, without the pressure
> anywhere in the barrel exceeding stress limits.  (The Gerald Bull
> multistage cannon would have used this principle, but never got quite
> finished in Iraq before it was destroyed.)
>

Gerald Bull *never* designed or built a gun with charges distributed along
the barrel.  In fact, adding distributed charges along the barrel does
*nothing* to improve the muzzle velocity of guns.  I wrote a paper a few
years ago that proved this fact on gasdynamic/thermodynamic grounds:

Higgins, A.J., "A Comparison of Distributed Injection
Hypervelocity Accelerators", AIAA Paper 97-2897,
33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference
& Exhibit, Seattle, WA, July 6-9, 1997.

Send me e-mail if you would like a pdf version of this paper.

>
>     Aerodynamic drag is not absolutely a physical barrier to a gun that
> could get something above the atmosphere, with better than orbital
> energy.  But it would need to undergo enormous g stress from frictional
> deceleration at the beginning
>

The deceleration due to aerodynamic drag would be on the order of 100 g's.
While significant, this deceleration is nothing compared to the 10,000's of
g's that the projectile would experience during the gun-launch.

>
> and its initial energy would have to be
> enough to supply all that frictional heating.  Muzzle velocity would
> need to be much faster than orbital,
>

Detailed analysis of gun-launch-to-space concepts have concluded that, for a
1000 kg projectile with a muzzle velocity of 6-8 km/s, the projectile will
only loose 1-2 km/s due to aerodynamic drag.  This is hardly a show-stopper.
--
Andrew J. Higgins            Department of Mechanical Eng.
Assistant Professor          McGill University
Shock Wave Physics Group     Montreal, Quebec CANADA
higgins@mecheng.mcgill.ca

```

```From: "Andrew Higgins" <higgins@mecheng.mcgill.ca>
Newsgroups: sci.astro,sci.space.policy,sci.physics,sci.engr.mech
Subject: Re: Deep-undersea gas-gun launchers.
Date: Fri, 17 Dec 1999 18:25:02 GMT

In article <83chk5\$632\$1@bgtnsc02.worldnet.att.net>, "Paul Colby"
<Paul.Colby@worldnet.att.net> wrote:

>
> A factor of ten is a long way to go seeing as the speed of sound
> goes like the square root of the density.
>

Sound speed of a gas (which is the working propellant in all guns) is nearly
independent of density.  It depends on the the square root of temperature
and the inverse square root of molecular weight.  For a high sound speed,
you want a light, hot gas.  Hence, "light gas guns."

>
> There is no doubt one
> can achieve a large muzzle velocity. It's just unclear though
> that escape velocity can be achieved. All web pages aside, the
> only reliable source I have is recollections of conversations
> with my father about gas guns.
>

Engineering libraries are a good source, too.  Especially textbooks on
gasdynamics and compressible fluid flow.

>
> Dad spent his career designing
> military weaponry and knew a great deal about the state of the
> art including gas guns. His opinion, after he finished laughing,
> was such things couldn't reach orbit. My opinion this is just
> another incredibly stupid boondoggle, one that comes up over and
> over. Why don't these guys use a rail gun. At least they are not
> limited by matters of principle.
>

Maybe because gas guns have demonstrated velocities of greater than 10 km/s,
while railguns have only demonstrated 6 km/s, and even those railguns
basically vaporized the rails and part of the projectile in the launch
process.

Also, work out the size of capacitor you would need to send a 1000 kg
projectile to orbital velocity using a rail gun.

Of course, the LLNL designs for a orbital-launching light gas gun had a 6 m
diameter by 0.5 km long pump tube and a breach block that was an
office-building-size cube of steel.  You can debate which one is more
improbable if you want.

The most promising hypervelocity launcher for gun-launch-to-space is the ram
accelerator:

Although I have a bias here, since I did my Master's and PhD on this
concept.
--
Andrew J. Higgins            Department of Mechanical Eng.
Assistant Professor          McGill University
Shock Wave Physics Group     Montreal, Quebec CANADA
higgins@mecheng.mcgill.ca

```

```From: "Andrew Higgins" <higgins@mecheng.mcgill.ca>
Newsgroups: sci.astro,sci.space.policy,sci.physics,sci.engr.mech
Subject: Re: Deep-undersea gas-gun launchers.
Date: Fri, 17 Dec 1999 21:27:27 GMT

----------
In article <83e64h\$8ac\$1@iceman.tac.net>, "Paul Skoczylas"
<pauls@cfertech.com> wrote:

> Andrew Higgins <higgins@mecheng.mcgill.ca> wrote:
>
>>
>> Sound speed of a gas (which is the working propellant in all guns) is
>> nearly independent of density.  It depends on the the square root of
>> temperature and the inverse square root of molecular weight
>
> Please explain to me why when I look up values for nitrogen, I see that if
> we have a constant temperature of 20°C, and increase the pressure from 1 MPa
> to 101 MPa, the speed of sound changes from 350 m/s to 851 m/s.  That's a
> big difference for being independent of pressure/density.  (100x increase in
> pressure--> 2.5x increase in sound speed --> c is proportionate to P^0.2,
> approximately)
>

Because the ideal gas law no longer applies at 100 MPa.  That's 1000 times
atmospheric pressure, at which point nitrogen's density is close to that of
water and it is not even a proper gas anymore.  It's supercritical at this
pressure, meaning the distinction between gas and liquid becomes fuzzy.  In
condensed matter (a liquid or solid), of course, sound speed does depend on
density.

However, you are unlikely to encounter supercritical gases (100 MPa and room
temperature) in light gas guns, which is the topic of this thread.

>
> Hence, I would concur with your square root of temperature statement, but I
> think that 5th root pressure dependence still needs to be considered,
> depending of course, on how big the pressures will get...
>

We are discussing the propellant gas in light gas guns.

While light gas guns can and do produce pressures of 100 MPa, they do so by
dynamically compressing the gas, so that the temperature is also very high
(T can be greater than 10,000 K in a light gas gun).  At these extremely
high pressures, the ideal gas law is still (somewhat) applicable, and sound
speed is still pretty much independent of density and depends on the square
root of temperature.
--
Andrew J. Higgins            Department of Mechanical Eng.
Assistant Professor          McGill University
Shock Wave Physics Group     Montreal, Quebec CANADA
higgins@mecheng.mcgill.ca
```