The Big-Bertha was a semi-portable Howitzerdesign by Krupp in Germany prior to WorldWar I.It was used in World War I in Belgium andFrance against fortifications.It had a 420mm caliber (Yes! 420mm) andcould fire a semi-armor-piercing shell of1,160kg.The photo above is the portable version witha shorter barrel weighting 43 tons capable offiring a shell of 830kg.

BIG BERTHA - HISTORY

AIR GUN V2.0 - THE BIG BERTHA

• What is the best way to interest young kids in Physics? (Yes! I have two boys)

• They may not be that exited doing their lab work at school but these are experiments they will never forget.

• It is possible to run non-thermodynamic simulations in Excel and obtain a rough estimate of the performance of a gas gun.

• Thankfully, Hall consulting developed a FREE full thermodynamic simulator for gas guns. http://www.thehalls-in-bfe.com/GGDT

BANG! BAM! BOOOOM!

AIR GUN V2.0 BIG BERTHA – DESIGN HISTORY

BIG BERTHA

• The Big-Bertha is a wheeled gun with inter-changeable barrels of 2” caliber and 4” caliber. The 2” barrel is 8’ long, the 4” barrel is 6’ long.

• It uses two 4” diameter tanks with a total capacity of 17.3 liters. Max pressure is 150PSI

• It is triggered through a manifold of 6 x 1” Orbit sprinkler valves.

• It is currently fired electrically but will be modified to pneumatic triggering.

• Even fired electrically, it is absolutely lethal. We fired a big onion through 3 layers of 11-ply ¾” plywood!

BIG BERTHA

BIG BERTHA - DETAILS1” Orbit Sprinkler valves

Remote Fire Control

24VDC Power

Elevation Control

Air Tank

BIG BERTHA - DETAILS

Valve selector

Filling Manifold

Arming Switch

Flashing Lightsand Buzzer whenarmed

BIG BERTHA – PROJECTILE KINETIC ENERGY

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Projectile Energy - Big Bertha 2"Barrel @ 150PSI

BIG BERTHA – ENERGY EFFICIENCY (1)This needs to be researched further.

From WIKIPEDIA (http://en.wikipedia.org/wiki/Compressed_air_energy_storage), thetotal energy of a compressed gas in a volume Vb at a pressure Pb is:

𝐸 = −𝑃𝑏𝑉𝑏 ln(𝑃𝑎

𝑃𝑏) with Pa=atmospheric pressure=0.1MPa

For the BIG BERTHA, Vb=19.8liters=0.0198m3 and Pb=150PSI=1.02Mpa, thereforeE=46,856Joules

The kinetic energy of a 2kg projectile is 4,225Joules, therefore the efficiency of the

gun is η=9.0%

BIG BERTHA – ENERGY EFFICIENCY (2)

E(J/kg air) = -311 775*[(1/Pa)^0,286 -1)

However, from anther WIKIPEDIA page (lost the link), the total mechanical energy of1kg of compressed gas at a pressure Pa is:

E(J/kg air) = -311 775*[(1/Pa)^0,286 -1) with Pa=pressure in bar

For the BIG BERTHA, the tanks contain 0.252kg of air at a pressure of 150 PSI(10.2Bar). Therefore, the total mechanical energy is E=21,809Joules

The kinetic energy of a 2kg projectile is 4,225Joules, therefore the efficiency of the

gun is η=19.4%

BERT’S PROJECTS

2” PORTABLE CANNON

BERT’S PROJECTTWO-INCH PORTABLE CANNON

“PORTABLE” AIR CANNONThis gun is a compromise between performance andportability. The gun can be disassembled in smallerand portable components in minutes. The maincomponents are:

Base

Tanks and Valves Assembly

Barrel Assembly

“PORTABLE” AIR CANNON

Tanks Inlet Valve Pressure

Regulator

Pneumatic Elevation Compensator

Ammo Storage

Trigger

Pressure Gauge

Safety Valve Sprinkler valves x 4

2” Union Connector

Tactical Scope

For better flow and highvelocity performance, thegun uses an array of three 1”sprinkler valves. As theprojectile spends very littletime in the barrel, it is criticalto open the valves as quicklyas possible. The valves aremodified and triggeredpneumatically by dumpingthe pressure on top of thediaphragm. All 3 valves areconnected with ½” PVC to afourth valve. This valve is triggered pneumaticallywith a simple valve which in turn triggers the threemain valves providing enough flow for rapidresponse and fast opening.

“PORTABLE” AIR CANNON

1312

1922

2450

2888

3249

M16, 1,737

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Kinetic energy and projectile velocity for M=100, 200, 500, 1000 and 2000gr. These graphindicate that the gun is more efficient with heavier projectiles. Note, the 4.1gr, 5.56mm

NATO round used in the M16 at 1740 Joules at the muzzle. This gun perforated 12inches of solid wood!!! using a sub-caliber (sabot type) 1.5kg steel projectile.

“PORTABLE” AIR CANNON – FLOW LIMIT (1)In an ideal cannon (infinite tankcapacity and no flow losses), thekinetic energy of a projectile isINDEPENDENT of its mass.However, the previous slideclearly indicates that the kineticenergy of the projectile isstrongly dependent of its mass.WHY?The graph on the right showsthe tank and barrel pressures asthe projectile moves throughthe barrel with M=100, 500 and2000gr.

“PORTABLE” AIR CANNON – FLOW LIMIT (2)

If the flow of air between the tank and the base of theprojectile would be perfect, the pressures in the tankand the barrel should be equal.

For M=2000gr, the velocity of the projectile inside thebarrel is “slow”. There is sufficient flow through the 3valves to almost “keep up” with the motion of theprojectile and the drop in pressure in the barrel issmall.

For M=100gr, the velocity of the projectile inside the barrel is fast (up to 2000G’sacceleration). As the projectile accelerate quickly inside the barrel, there is insufficientair flow through the 3 valves to “keep up” with the rapid motion of the projectile andthe pressure drops dramatically resulting in limited kinetic energy.

2” AIR CANNON – AMMUNITION

Some example of sub-caliber ammunitionfor the 2” cannon. These are similar toAPFSDS (Armor Piercing Fin StabilizedDiscarding Sabot) KE Penetrators used asanti-tank projectiles in modernsmoothbore guns of main battle tanks.However, since the distance between thecannon and the target is short, fins areunnecessary and the distance is notsufficient for effective sabot separation,resulting in simpler projectile design.

These projectiles can penetrate 12” of solid wood

With projectile in the 3kJ+range, it is critical to build atarget capable of stoppingthe projectile. Failure to doso would be catastrophicwhen shooting in ourbackyard. Hitting theneighbors house with one ofour sub-caliber projectilewould result in severedamages (on the right anglethe projectile could gostraight through…. …to the

other side), risk of injury or DEATH. Thetarget is 18” square, made of 2 layers of2x4 pressed together with ½” threaded

rods. This modular construction allows us to quickly recondition the targetafter a shooting session. In addition, 2 layers of 2x10 (1.5” thickness) and 2layers of ¾” 11-ply plywood are positioned behind the 2x4s, resulting in atotal thickness of 11.5”.

BERT’S PROJECTAIR RIFLES

105CAL RIFLEThe 105CAL rifle is a light weight air rifle with a 1” PVC pipe barrel using a single 1” sprinkler valve. The valve is triggered by a solenoid powered by 3x9volts batteries.Sprinkler valves are not designed to open quickly. On the contrary, in a sprinkler system it is preferable that the valves open smoothly to prevent damage to the pipes.

The valves are rated at 100PSI (water). However, they can withstand 150PSI with good reliability. In a gun application, it is better to modify the valves to be triggered pneumatically by dumping the air over the diaphragm for faster response and much improved performance. (For a 20gr projectile, the time spent in the barrel is only 13ms (200gr, 34ms). Therefore, valve speed is critical)

105CAL RIFLE

Air Hose Fitting for filling tank

Tank (2” PVC)TriggerBatteries Compartment

Orbit 1” Sprinkler Valve

Quick Connector for Breech Loading

50mm Scope, Laser, Flashlight

1” PVC Barrel (110cm)Sliding Barrel for Breech Loading)

105CAL RIFLE ELECTRICALLY TRIGGERED

AIR RIFLES

105 CAL RIFLE THERMODYNAMIC MODELING PROJECTILE MASS=20GR

Muzzle velocity = 158m/s (565km/h or 353mph)Kinetic Energy = 249J

The barrel pressure drops WAY BELOW the reservoirpressure. The PERFORMANCE IS LIMITED by POOR AIRFLOWthrough the valve as the projectile velocity increases

105 CAL RIFLE THERMODYNAMIC MODELING PROJECTILE MASS=200GR

Muzzle velocity = 63.5m/s (229km/h or 143mph)Kinetic Energy = 404J

The barrel pressure tracks the reservoir pressure. The Rifle almost reaches its maximum performance E=435JNo airflow restriction as the projectile moves slower in thebarrel.

161CAL RIFLE

Air Hose Fitting for filling tank

Tank (2” PVC)Trigger

2 X MODIFIED Orbit 1” Sprinkler Valve

1” PVC Barrel (110cm)

½” PVC for pneumatic triggering

Pressure Gauge

1 ½ “ Union Coupling

Sliding Barrel (Breech or Muzzle Loading)

Fake Suppressor

Gun Sight

Gun Sight

161CAL RIFLE - AMMUNITIONS

161CAL THERMODYNAMIC MODELING - 100GR PROJECTILE

Muzzle velocity = 133.7m/s (371km/h or 232mph)Kinetic Energy = 894J

The barrel pressure drops significantly BELOW the reservoirpressure. The PERFORMANCE IS LIMITED by AIRFLOWthrough the valves.

Muzzle velocity = 53m/s (191km/h or 120mph)Kinetic Energy = 1405J *An M16 firing a 5.56 NATO round delivers 1600J

The barrel pressure tracks the reservoir pressure. The gunreaches its maximum kinetic energy potential.

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161CAL RIFLE – AIRFLOW AT 60PSI

60PSI

A projectile traveling through the barrel ata velocity V displaces a volume equal tothe surface area of the barrel multipliedby the velocity and the relative pressure.

F (m3/s)= 𝜋𝑑2VP/4d = diameter of barrel in mV = velocity in m/sP = Pressure (PSI)/14.7

A 161CAL projectile at 100m/s and 60PSIdisplaces 536 liters/s (0.53 m3/s)

161CAL THERMODYNAMIC MODELING

*The kinetic energy of a projectile fired by an M16 atpoint blank range is 1600J. On a human target, only afraction on this energy is absorbed by the body asthe projectile exits the body at high velocity. On theother hand, the effects of a 1.6” diameter, 1kgprojectile, at 53m/s on a human body would beabsolutely horrific as most of the kinetic energywould be converted into massive organ damage. Adirect hit to the torso or head would result in instantdeath. A direct hit to the arms or legs would most

likely result in limb loss. THIS IS NOT A TOY.