Weasel Pilot said:

Wonder how much the aircraft slowed as these were being fired? If memory serves, we lost about 5 kt per second when firing the GPU-5 pods (30mm, same round as A-10's GAU-8) off our F-4Es.

No contest! A (probably over-) simplified, back-of-the-envelope calculation shows that:

Force = the time derivative of the impulse.

Impulse = mass X velocity

so

Force (recoil): mass X velocity X rate-of-fire

This ignores the recoil produced by the propellant gasses leaving the barrel together with the projectile (but I said it was simplified

).

So, for the GAU-13 in the GPU-5 pod:

Projectile mass: 15,1 oz (for the API) = 430 g = 0,430 kg

Muzzle velocity: 3.600 ft/sec = 1.030 m/s

rate of fire: 2.400 rds/min = 40 rds/sec

Recoil: 0,430 X 1.030 X 40 = 17.716 N

For 14 Browning M2 .50 cal's:

Projectile mass: 622,5 grains (for the M8 API) = 40,3 g = 0,0403 kg

Muzzle velocity: 3.050 ft/sec = 930 m/s

Rate of fire (per gun): 750 rds/min = 12,5 rds/sec

Rate of fire (combined): 14 X 12,5 = 175 rds/sec

Recoil: 0,0403 X 930 X 175 = 6.558 N

or roughly 1/3 that produced by the GAU-13.

The source for the above data is Wikipedia and Janes Infantry Weapons, 2009 edition.

The above calculation, as stated, ignores the recoil force produced by the propellant gasses (both the extra mass being ejected, as well as the propulsive "rocket" effect of the gas leaving the muzzle), and it tells you little about the "felt" recoil, since the mass of the gun itself is ignored. However, since 14 Browning M2's mass about 530 kg (38 kg pr. gun) and the GAU-13 comes in at 151 kg, "felt" recoil of the GAU-13 (1/3 the mass and 3 times the generated recoil force) should be significantly more than that of the 14 M2's.

There's probably a couple of 30mm-size holes in my calculations, so corrections are welcome (provided they are suitably polite :

).

Regards & all,

Thomas L. Nielsen

Denmark