The GAU-8 Avenger Autocannon

This was written by me as a freshman undergrad at Case Western Reserve University in 2006 for PHYS 123, Physics I Honors. It is reprinted in full, original form, with no attempt made to make the conclusion more realistic. Some of my assumptions were silly and made the problem trivial, but these were never graded for strict accuracy.

Those with even a cursory knowledge of national air forces will know that there are several roles to fill- air superiority fighter, heavy bomber, stealth bomber, and close-in ground support.  The A-10, ugly and ungainly as it is, is a magnificent piece of work that fills the role of the last category.  With a low flying speed, “titanium bathtub” armor, immense endurance, and a phenomenally powerful main gun, the A-10 is a wonder of military technology and of physics.

Notice that autocannon in the nose?  This is the GAU-8 Avenger, a scaled-up version of the more familiar 7.62mm Minigun and 20mm Vulcan cannon.  It fires depleted uranium shells of 30 mm diameter at a rate of 4200 rounds per minute.  Here our cannon is shown to scale.

One of the most persistent claims by enthusiastic armchair strategists is that the Avenger is so powerful that its recoil is at least as powerful as the engines of the plane- thus, it is capable of slowing down and even stopping our A-10 in the air.  Is this true?  Let’s consider momentum and force.

(momentum) = (force)*(time)                            p = Ft

What is the momentum of our stream of fire?  Since we have a rate of fire and a mass, we can use dimensional analysis to determine momentum, and hence force.

momentum = (mass of shell)*(velocity)*(rate of fire)*(time)                   p = mrt

(mass of shell)*(rate of fire)*(velocity)*(time)/(time) = force                  (mrt)/t = F

(mass of shell)*(rate of fire)*(velocity) = force                                       F = mrv

Think of r as a frequency instead of rate of fire.  We are firing 4200rpm, which equates to 70 rounds per second or 70Hz.  Doing some additional research, we find that the mass of a round is 0.425kg and our muzzle velocity (highest velocity ever attained by the bullet) is 1036m/s.  In comparison, the makers of the A-10 claim that their two engines will produce 80kN of thrust.  Let’s see if we really have the power to stop a plane.

F = mrv

80.kN < (0.425kg)*(70.Hz)*(1036m/s)

80.kN </ 31kN

We can produce “only” thirty-one thousand newtons of force by our Avenger cannon.  This means that the plane will experience a possible deceleration if it is only using partial power, but this can be overcome by employing a steady, large amount of thrust, which is in practice what the pilots tend to do as they are well aware (and possibly fearful) of the myth of planes stopping in midair.

But the GAU-8 Avenger is still incredibly powerful.  Let’s say we mounted all 281kg of the gun on the Terminator’s back, gave him 1000 rounds of ammo and convinced him that he could fire the weapon from a standing position.  His hydraulic joints lock up (he will not drop the weapon and there will be no force lost to excess motion) and he prepares to fire at the full 4200rpm, perhaps too confident of his abilities after playing around with a 7.62mm Minigun in T2.  The Minigun is well beyond the range of a single soldier to carry and operate, but he manages it without difficulty.  However, this weapon can be mounted on a helicopter door, while the Avenger, as we have seen, generates nearly as much recoil as one the jet engines on the A-10.

The Terminator weighs 200.kg.  Of course, he manages to shoulder the behemothic weapon with a bit of effort, and starts firing at T-1000 who has found himself a nifty T-72 tank.  Arnold digs his heels into the muddy ground and achieves a coefficient of friction of 1.0.  How fast will the Terminator accelerate backwards, or can he actually stand in place?

frictional force = (coefficient of friction)(mass)(gravity)               Ff = μmg

Remember to add up all the weight that is now being held on the Terminator’s hyper-alloy legs.

Ff = (1.0)*(281kg + 425kg + 200.kg)*(9.81m/s^2)

Ff = 8.9kN

The friction force is massive, but it is less than a third of the GAU-8 recoil.  There is a net force and Arnold starts to slide immediately.  The net force, accounting for friction, on the Terminator and his gun is now 22kN.

F = ma

22kN = (281kg + 425kg + 200.kg)a

a = 2.4 m/s^2

Buh-bye Arnie. You'll be all over the place. Good luck aiming the thing.  Was the T-1000 terminated?

At 500m, the Avenger can pierce about 70mm of modern composite armor.  The armor of a T-72 is thicker than 70mm- but its armor is old-fashioned steel, meaning that it would take approximately twice as much armor to achieve the same strength.  Narrowing the range to near point-blank, the effect would be catastrophic to this pensionable commie tank.

At negligible range, the 30mm rounds would turn the tank into a hailstorm of steel confetti, and the pyrophoric depleted uranium rounds, upon piercing the frontal armor, would also set fire to the shrapnel within the tank.  They would have so much kinetic energy left that some of the rounds would indeed pierce the rear armor of the tank as well.