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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.

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.

Longjocks
02-13-2005, 05:01 PM
Without going into physics equations and using simple lay observations, fire a simple 22 rifle and feel the recoil pushing into your shoulder. Now imagine 8 of them firing together. Now imagine them all as high calibre. Now imagine them all firing on automatic with high fire rates.

30mph is probably an exaggeration, but it's not for me to judge. The effect is modeled in the game though. Just sit on a runway and start firing... you'll move backwards.

prop-head
02-13-2005, 05:26 PM
There've probably been some dudes in the '40s who could more-or-less handle two .45 cal Tommyguns while keeping his feet firmly planted. If a 75 kg man can do that, a vehicle a good fifty times heavier should not recoil too greatly even with several times the firepower.

While we're at it, let's calculate a recoil velocity induced on the gun itself by firing single a .50 cal round.

Gun to bullet weight ratio = 20 kg (?) : .039 kg, or 513:1.

825 / 513 = 1.64 m/s, or 5.9 km/h.

So, place a .50 mg on a frictionless, weightless dolley, fire one round, and the gun/dolley will travel backward at nearly 6 km/h. A ten round burst will induce a velocity of nearly 60 km/h, assuming the gun is indeed transferring all recoil energy to the dolley. But on a one- two- or three-ton dolley (or aircraft) there is a lot of inertia to overcome, and the recoil velocity will be concomitantly smaller.

Longjocks
02-13-2005, 07:26 PM
Would the mass of the bullet be factored into the equation though? More important would be the force of the exploding gun powder escaping through the muzzle.

han freak solo
02-13-2005, 07:33 PM
"There've probably been some dudes in the '40s who could more-or-less handle two .45 cal Tommyguns while keeping his feet firmly planted. If a 75 kg man can do that, a vehicle a good fifty times heavier should not recoil too greatly even with several times the firepower."

I believe this. I fired a full auto Thompson sub-machine gun about one year ago and without taking your finger off the trigger, you can control and aim (by watching target strikes) for the full 2-3 seconds until the magazine is empty.

So, I believe that I could hold two, a struggle maybe, but probable. It is only pistol ammo after all. Could I aim two, doubtful.

han freak solo
02-13-2005, 07:45 PM
"Would the mass of the bullet be factored into the equation though? More important would be the force of the exploding gun powder escaping through the muzzle."

Absolutley. If you have the opportunity, shoot a firearm with a wide range of bullet weights for the same cartridge type, at least 100 grains difference. The felt recoil of the heavier bullet is definitely more. No scientific tests on my part, just experience.

As far as scientific testing, there are cartridges advertised as low recoil. The manufacturer reduces the bullet weight and sometimes a bit of the powder. I've only seen this in rifle cartridges though.

The focus has been mostly on reducing the bullet weight, though. Less recoil for the shooter and a flatter trajectory (because the amount of powder is the same), but less knock down power on the receiving end.

BBB_Hyperion
02-13-2005, 08:02 PM
Didnt check the calculation no time but dont forget that some guns use part of the recoil energy to reload .

prop-head
02-13-2005, 08:33 PM
BBB_Hyperion,
Exactly... that's one of the reasons why in my second example of the .50 mounted on a frictionless sled I added the caveat "...assuming the gun is indeed transferring all recoil energy to the dolley." But the effect of reduction of recoil by this process is probably not terribly significant, and for the sake of simplicity can (safely?) be ignored.


longjocks,
The powder's explosive gas is not by itself a really significant factor in the recoil velocity because:
1) its mass is rather less than the bullet, and to a lesser extent,
2) the gas can be considered to be somewhat "stationary" during the impulsive phase when both the bullet and gun are being accelerated in opposite directions, and there is loss of energy during the exiting gas's expansion and generation of a noisy shock. But yes, there must be some percentage of additional recoil velocity due to the expanding gas.

Who knows -- perhaps the energy sink of the reloading mechanism and energy supply from the exiting gas may to some extent cancel each other out??? http://forums.ubi.com/images/smilies/16x16_smiley-wink.gif

Akronnick
02-13-2005, 08:40 PM
I took a few minutes to check your calculations and I believe your formula works out right. Now, it's more likely a plane may seem to slow down when firing guns is because it's manuevering violently and bleeding its energy. In a dogfight, I seriously doubt that the pilot is watching the airspeed indicator to see how much velocity he loses when he pulls the trigger. it's more likely that he checks his guage when he begins his firing pass, and then again afterwards. He sees that his plane has slowed down 30 mph, and he may think it was because of the three second burst of his guns, but it's more likely that it's from the three G's he was pulling during the burst.

But if you tie a rope to the bullets and hold onto it with frictionless gloves...

reisen52
02-13-2005, 09:21 PM
How many 180lb .50 cal machine gunners have you seen sliding along the ground at 30mph when they fire the weapon? http://forums.ubi.com/groupee_common/emoticons/icon_eek.gif

Does a B-17 move sideways at 30 mph when all the available guns fire at a 3'oclock target?

Does a A-10 stop in the air when the 30mm avenger is fired as 6,000rpm?

Does a B-25H gunship fly backwards when 10X.50 fire forward along with the 75mm cannon?

Do you really believe a 12,000lbs plane will slow 30mph when 6X.50 are fired?

Zeke

indylavi
02-13-2005, 10:20 PM
An A-10 does in fact loose speed when it fires due to recoil. That could be the 30 mph drop you might have heard about. I'm not going to act like I know exactly why or that I'm good in physics. So this is my idea of why it slows down.

A man firing a gun and a plane are different. A man has a steady platform to shoot from. The energy from the gun goes into his shoulder, then through his body and to the ground. He has a steady platform to transfer energy. This is why MG's are fired either prone or on a bipod. A plane is a like a boat in water. I can move my boat in water quite easily if I'm steady. I can push it away from the dock with some ease. However, on land I could hardly push my boat as it's heavy.

Now a plane will absorb the energy of a weapon that is fired. Force makes an object heavier. On land your weight is transferred to the lowest point of your body. Usually your feet. So the ground absorbs the added weight. Now if your suspsended in water or air the weight has nowhere to transfer to. So your body would have to absorb all of the added weight. This is why a plane slows down. The added weight of the recoil. This added weight is also focused weight. Usually making the aircraft jerk slightly. This jerk also cuts airflow and provides more drag to the airframe. So if you don't increase throttle your plane will slow down momentarily

VF-3Thunderboy
02-13-2005, 11:28 PM
<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>Without hesitating the Zero rolled into a steep climbing left turn, then leveled off in a wide, sweeping, flat turn to the right. I was momentarily spellbound watching the fighter's clean, seemingly effortless maneuvers. Within seconds it was in position to make a run on the last plane on the formation's right flank. Nosing down slightly the pilot continued his curving approach, five hundred feet above and slightly to my right, as though I had not yet been seen. I moved my engine controls into combat power range, and pushed the throttle to the forward stop. Easing back on the control stick until the F4F was hanging on the prop, I brought the gun sight pip to an almost full deflection lead on the Zero's nose. The index finger of my right hand squeezed down on the gun trigger set in the molded grip of the control stick. The six, 50 caliber, wing guns rumbled. I held the trigger down just long enough to see the red stream of tracers converge into the Zero's engine and start to drift back into the fuselage. The thought flashed through my mind, right down the target sleeve's throat. But this was no target sleeve. The Zero's nose bucked up momentarily, dropped back, then the plane came diving down in my direction.

At the moment my guns were firing and the tracers were curving up and into their target, I was literally hanging in air. The muzzle blast and recoil of the six fifties was all that was needed to push my overloaded, under powered, F4F over the edge into a control sloppy stall. As I let my fighter's nose drop and started a recovery rolling to the left, the Zero swept past on my right, black smoke and flames spewing from the engine, a river of fire trailing back along its belly.

Clearly visible, the pilot sat rigidly facing straight ahead. He's dead, flashed across my mind. Alive he would have been watching me; looking for any movement of my control surfaces; anticipating my next move. This night, Teruo Kawamata, P O 3c, Imperial Japanese Navy, would be listed as missing in action. Rolling into level flight, the throttle still fire walled, I tried to bring my guns to bear on two Zeros diving in on the formation's left quarter. The Wildcat's straining engine could not build up maneuvering speed fast enough. With the pipper of the gun sight at a point well ahead of the pair, I snapped off a short burst. As the tracers crossed their diving path the Zeros abruptly zoomed skyward. Their climbing ability was stunning to watch, they were out of sight, and mind, in seconds as I rolled to the right reversing course. <HR></BLOCKQUOTE>


A 50 calibure shell has a force of X. When you fire 6 of them within a few seconds, you get 90 X, this may have some noticeable effects when near stall speed, or climbing. Not going strait down. So yes it probably effects the plane at low speeds, dependingon how many/size of guns also.

One thing you dont see are as described above, the guns "shaking" the planes.

jarink
02-14-2005, 12:13 AM
<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>Originally posted by prop-head:
Who knows -- perhaps the energy sink of the reloading mechanism and energy supply from the exiting gas may to some extent cancel each other out??? http://forums.ubi.com/images/smilies/16x16_smiley-wink.gif <HR></BLOCKQUOTE>

Not really. The recoil springs only serve to lengthen the recoil impulse; they do not absorb it. Think of a trampoline. If you fell from 10 ft in the air on a solid surface, it would hurt. The same fall onto a trampoline doesn't since your energy is gradually transferred, but it's still the same amount on kinetic energy.

What backwards energy the spring has absorbed will be mostly be expended again when it returns the bolt to battery also.

There were truly recolless guns used in A/C as early as WWI. They were simple tubes firing a round forwards and a counterweight to the rear. The Germans experimented with several such contraptions during WWII using both counterweights and jet efflux (mass times velocity; gas at very high velocity can have the same kinetic energy as a solid at a slower speed) The most impressive being the Geraet 104 35cm aircraft gun which was slung below a DO-217, which fired a 1400-lb projectile. Needless to say, it was a single-shot weapon!

UKPsycho
02-14-2005, 01:41 AM
<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>Originally posted by VF-3Thunderboy:
One thing you dont see are as described above, the guns "shaking" the planes. <HR></BLOCKQUOTE>

Get yourself into a 109, 190, 262, ju-87G etc. and fire your cannon, if you have a force feedback joystick, you'll shake all over the sky!!!

Longjocks
02-14-2005, 03:41 AM
I found a couple of interesting pages on the matter;

The math...
http://www.loadammo.com/Topics/August01.htm

A take on powder type and bullet weight (make of it what you will)...
http://www.robleatham.com/answers040227.htm

TgD Thunderbolt56
02-14-2005, 07:35 AM
The book was Duel of Eagles by Peter Townsend and it IS modeled in the sim. Sit on the tarmac and fire your guns without brakes. You'll scoot backwards.

I have enough letters after my name to say that without getting into BC (ballistic coefficient) and the effects of recoil-operated vs gas-operated reloading mechanisms, this sim is fun regardless.


TB

han freak solo
02-14-2005, 07:37 AM
"If you do NOT have a comp, you want this pressure to be as low as possible and have as little of it as you can. A heavy bullet, such as a 230 grain in a .45, will reduce your powder charge over a lighter projectile, like a 200 grain bullet. The smaller powder charge generally creates less pressure and volume than a larger charge."

Rob is saying that in this cartridge that the heavier bullet apparently displaces the room for the powder charge, making it smaller or less.

What I had written, was meaning that bullet weight was greater and the powder charge stayed the same.