prop-head

02-13-2005, 04:36 PM

I recall reading a couple of years back in a book (don't remember which) an account by a WWII pilot (Hurricane??) which stated that firing the fighter's guns would decrease the aircraft's speed by something like 30 mph. And a recent post somewhere here said that the IL2 sim line models this kind of speed drop.

Hmmmm... In the first instance, this just doesn't seem to be possible to me. And in the second instance, I haven't myself noted in PF any speed decreases induced by firing guns. If this kind of thing occurred in reality, wouldn't pulling the trigger while in a low 'n slow turn fight likely be a career-ending move? To examine the problem analytically I did a "first order analysis on the back of an envelope."

I proceded with Newton's old saw which states that for every action there is an equal and opposite reaction. Imagine a freely rolling sled which, with it's rubber band-powered launcher, weighs a total of 1 kg. Suppose we put in the launcher a ball which also weighs 1 kg -- sled and launcher together would weigh 2 kg. Once launched, the ball would travel at velocity X, but because the sled and ball weigh the same, the sled would recoil also at velocity X, and the speed of each with respect to the other would of course be 2X. Make the sled heavier and its recoil velocity will decrease proportionately. Make sense so far?

Now let's look at the problem in hand. The numbers I use here are not necessarily accurate, as some are taken from memory. Moreover, because of the large mass difference between plane and bullet we can slightly simplify the formula to the form given below, and at the same time neglect the proportionately small mass decrease which results from the expenditure of ammo

Aircraft weight = 6,000 kg.

.50 cal round = 39g, or 0.039 kg.

Aircraft to bullet weight ratio = 154,000 : 1.

Bullet muzzle velocity = 825 m/s.

Aircraft recoils at 0.00536 m/s per bullet fired (825 / 154,000 = 0.00536).

6 x .50 cal at 750 rpm each = 75 rounds/sec.

So, for a 1 second burst of 6 x .50 guns, the aircraft slows by 0.402 m/s (75 x 0.00536 = 0.402), or 1.45 km/h. For a similarly-gunned 3,000 kg fighter, the speed drop would be nearly 3 km/h.

Here's the formula:

V_recoil = (V_bul/(M_ac/M_bul)) x N_gun x (ROF/60) x DOF

where;

V_recoil = aircraft recoil velocity (m/s),

V_bul = bullet muzzle velocity (m/s),

M_ac = mass of aircraft (kg),

M_bul = mass of bullet (kg),

N_gun = number of guns firing,

ROF = rate of fire per gun (rpm) and

DOF = total duration of firing (sec).

To convert m/s to km/h, multiply by 3.6.

If a plane sports a variety of guns, perform the calculations for each weapon type separately and add the results.

The bottom line, given the small mass of a bullet as compared to an aircraft, recoil velocity (slowing of the plane) is not very significant over typical firing durations.

And this leads to a final comment. In the movies I have to cringe when the effect of a single gunshot (pistol, shotgun, etc.) is represented by a body hurtling through the air! Why, even a machine gun burst would not come close to doing that, especially if the rounds pass through and hence do not dissipate all energy in the body. If a bullet could pitch the body of the victim through the air, why wouldn't the shooter's arm/shoulder shatter? Remember the action/reaction rule.... you don't get something for nothing.

Hmmmm... In the first instance, this just doesn't seem to be possible to me. And in the second instance, I haven't myself noted in PF any speed decreases induced by firing guns. If this kind of thing occurred in reality, wouldn't pulling the trigger while in a low 'n slow turn fight likely be a career-ending move? To examine the problem analytically I did a "first order analysis on the back of an envelope."

I proceded with Newton's old saw which states that for every action there is an equal and opposite reaction. Imagine a freely rolling sled which, with it's rubber band-powered launcher, weighs a total of 1 kg. Suppose we put in the launcher a ball which also weighs 1 kg -- sled and launcher together would weigh 2 kg. Once launched, the ball would travel at velocity X, but because the sled and ball weigh the same, the sled would recoil also at velocity X, and the speed of each with respect to the other would of course be 2X. Make the sled heavier and its recoil velocity will decrease proportionately. Make sense so far?

Now let's look at the problem in hand. The numbers I use here are not necessarily accurate, as some are taken from memory. Moreover, because of the large mass difference between plane and bullet we can slightly simplify the formula to the form given below, and at the same time neglect the proportionately small mass decrease which results from the expenditure of ammo

Aircraft weight = 6,000 kg.

.50 cal round = 39g, or 0.039 kg.

Aircraft to bullet weight ratio = 154,000 : 1.

Bullet muzzle velocity = 825 m/s.

Aircraft recoils at 0.00536 m/s per bullet fired (825 / 154,000 = 0.00536).

6 x .50 cal at 750 rpm each = 75 rounds/sec.

So, for a 1 second burst of 6 x .50 guns, the aircraft slows by 0.402 m/s (75 x 0.00536 = 0.402), or 1.45 km/h. For a similarly-gunned 3,000 kg fighter, the speed drop would be nearly 3 km/h.

Here's the formula:

V_recoil = (V_bul/(M_ac/M_bul)) x N_gun x (ROF/60) x DOF

where;

V_recoil = aircraft recoil velocity (m/s),

V_bul = bullet muzzle velocity (m/s),

M_ac = mass of aircraft (kg),

M_bul = mass of bullet (kg),

N_gun = number of guns firing,

ROF = rate of fire per gun (rpm) and

DOF = total duration of firing (sec).

To convert m/s to km/h, multiply by 3.6.

If a plane sports a variety of guns, perform the calculations for each weapon type separately and add the results.

The bottom line, given the small mass of a bullet as compared to an aircraft, recoil velocity (slowing of the plane) is not very significant over typical firing durations.

And this leads to a final comment. In the movies I have to cringe when the effect of a single gunshot (pistol, shotgun, etc.) is represented by a body hurtling through the air! Why, even a machine gun burst would not come close to doing that, especially if the rounds pass through and hence do not dissipate all energy in the body. If a bullet could pitch the body of the victim through the air, why wouldn't the shooter's arm/shoulder shatter? Remember the action/reaction rule.... you don't get something for nothing.