Calculated "base" dispersion of guns based on energy delivered

[Tony Williams]

An interesting report. It does emphasise the difficulty of shooting down even fighters (let alone bombers), even with 20mm Hispanos, as long as they were strongly made and well protected.

In view of the previous thread about whether or not bullets could be deflected from an aircraft's skin it's interesting to read that:

"The smaller calibre [i.e. .303 and .5] incendiary munitions will either be broken up or deflected away before reaching the fuel tanks"

and:  

"The angle of the fuselage with the line of attack is 6 degrees and this gives 0.303" B. Mk VII and 0.5" B. Mk.II no chance of causing a fire. These ammunition will be for the most part deflected or broken up on the 19 s.w.g. fuselage skin."

and:

"The angle of the engine cowlings and their material is such that all ammunitions will be deflected away without damage from this angle of attack."

Clearly, deflection off the skin was not such a rare event.

Tony Williams: Military gun and ammunition website and discussion
forum

[gripen]

Tony,
Do you have some kind of numbers how accurately the pilots could normally aim at ranges above 300m? I have been under impression that some amount of dispersion is a good feature and it actually improves probability of the hit at long range.

gripen

[Charge]

You didn't ask me but don't be offended if I tell you about my thoughts:

IMO there are two (or three) kinds of dispersion basically: pilot induced and platform/gun induced dispersion.

When fired from a jig the gun has its own dispersion depending on the ammo and barrel length etc.

In flight this is added to platform induced dispersion which is caused by mounting, vibration, a/c instability etc.

Then all this is added to pilot induced dispersion which is presenting the ability of the pilot to keep the hits in center of the target. So the resulting dispersion may be huge or small depending on these factors.

Considering ie. the dispersion of 8x50Cal in 300yds the combination of these factors added with a mediocre pilot would produce a considerably big dispersion pattern itself which would cause a high probability of a hit but a low probability of sufficient effect etc. So it is debatable if it would be advisable to add any convergence or elevation dispersion to guns.

The other example could be a 109F with 15mm cannon and two small caliber MGs on the cowling. I'd imagine that combination to be very accurate but in a hands of a mediocre shooter the large pilot induced dispersion would render the weapon platform to be very ineffective.

So there are many things that affect the effectiveness of a gun platform. For example, considering the 50Cal example above, on personal level the pilots could consider their weapon effect to be quite low but statistically the higher hit probability could be considered good considering the higher probability of damage caused to more a/c, than less enemy a/c that are verifiably destroyed immediately after firing.

Just a thought...



-C+

[Tony Williams]

Originally posted by gripen
Tony,
Do you have some kind of numbers how accurately the pilots could normally aim at ranges above 300m? I have been under impression that some amount of dispersion is a good feature and it actually improves probability of the hit at long range.

Not specifically - although the Luftwaffe reckoned that only between 2% and 5% of their shells hit the targets, which gives you some idea of the general accuracy of fire. And the Luftwaffe's targets were usually large bombers.

Whether dispersion is a good thing or not depends on how effective each individual hit would be. The less destructive the projectiles, the more important it is to concentrate their fire to gets lots of hits in one area. Which basically means: MGs = concentrate, cannon = disperse (to some extent).

TW

[Crumpp]

Not specifically - although the Luftwaffe reckoned that only between 2% and 5% of their shells hit the targets, which gives you some idea of the general accuracy of fire. And the Luftwaffe's targets were usually large bombers.

Combine the small percentage chance of hitting a fighter with the small chance your 20mm will do fatal damage and it's a wonder anyone was shot down in WWII.

"Filling the windscreen with enemy" certainly was sound advice and very practical advice.

Clearly, deflection off the skin was not such a rare event.

It seems to be a fairly common event.  It is interesting that the Fuel tanks on the FW-190 have no armour protection surrounding them.  

The tanks themselves are self-sealing.  The compartment they are mounted in is not armoured.  Once a bullet penetrated the skin of the A/C there would be very little metal past the compartment walls.  The tanks themselves are held in place by webbing straps.

Yet from the rear no .50 cal or .303 could damage the tanks even from 6 degrees off center.

Crumpp

[HoHun]

Hi Charge,

Good comments! :-)

>IMO there are two (or three) kinds of dispersion basically: pilot induced and platform/gun induced dispersion.

>When fired from a jig the gun has its own dispersion depending on the ammo and barrel length etc.

The dispersion values for the Luftwaffe guns at least are for the gun mounted in the airframe and the airframe jacked up on a ground range. (I assume the same is true for the US figures.)

German engineers pointed out that experience showed this gave a larger dispersion than shooting the same guns in flight.

I figure the jacked-up airframe was free to oscillate in the rigid mounting between the jack-up points, while the airborne airframe wasn't free to oscillate in the same manner because it was "suspended" by dynamic lift acting continously over the entire wing span.

>In flight this is added to platform induced dispersion which is caused by mounting, vibration, a/c instability etc.

>Then all this is added to pilot induced dispersion which is presenting the ability of the pilot to keep the hits in center of the target.

I'd combine both aircraft instability and pilot-induced dispersion into one factor because the instability can be considered an aspect of controllability.

At high speeds, most aircraft can be expected to be quite stable and well-controllable in level flight while at low speed inertia can overcome the damping forces more easily.

As an example for pilot-induced dispersion, an experienced USAAF pilot who had done countless test firing runs to determine the optimum damping factor for the LCOS pipper had an optimum aiming error of about 1 mil during a tracking run. (He was flying a P-38.)

>So there are many things that affect the effectiveness of a gun platform. For example, considering the 50Cal example above, on personal level the pilots could consider their weapon effect to be quite low but statistically the higher hit probability could be considered good considering the higher probability of damage caused to more a/c, than less enemy a/c that are verifiably destroyed immediately after firing.

After the first phase of WW2, the Luftwaffe analysed these factors, too, though with an eye on the MG vs. cannon question. They decided for cannon because they considered it much better to bring down an aircraft down immediately over the combat area. Damaged aircraft often made it home and could be repaired, or at least cannibalized, and even if the crew had to bail some time after receiving damage, they would often make it back into friendly territory before having to bail, meaning they would soon be back in the air and fighting against the Luftwaffe again.

Of course, this doesn't tell us anything about dispersion, but it suggests that it's better to hit a couple of aircraft decisively than to light or medium damage a larger number of planes.

Regards,

Henning (HoHun)

[gripen]

Originally posted by Tony Williams
Not specifically - although the Luftwaffe reckoned that only between 2% and 5% of their shells hit the targets, which gives you some idea of the general accuracy of fire. And the Luftwaffe's targets were usually large bombers.

Whether dispersion is a good thing or not depends on how effective each individual hit would be. The less destructive the projectiles, the more important it is to concentrate their fire to gets lots of hits in one area. Which basically means: MGs = concentrate, cannon = disperse (to some extent).

Well, if the accuracy of aiming was in that level, the LW would probably have benefitted from larger dispersion and higher velocity AC guns.

Regarding AH, a nice addition could be a film viewer which could calculate error of the aiming afterwards from the film and which could show a correct aiming point. I think such thing could improve players shooting abilities as well as it could give some data how accurately people can shoot in this game.

gripen

[HoHun]

Hi Tony,

>Not specifically - although the Luftwaffe reckoned that only between 2% and 5% of their shells hit the targets, which gives you some idea of the general accuracy of fire. And the Luftwaffe's targets were usually large bombers.

According to the documents I have seen, the numbers were either 5% as a rule of thumb (against bombers), or more specifically:

At 500 m against a four-engined bomber:

MG151/20:  9,1%
MG213:    10,0%
MK108:     8,3%
MK103:    10,0%
MK412:    10,0%
MK214:    10,5%

Regards,

Henning (HoHun)

[HoHun]

Hi Tony,

>Not specifically - although the Luftwaffe reckoned that only between 2% and 5% of their shells hit the targets, which gives you some idea of the general accuracy of fire. And the Luftwaffe's targets were usually large bombers.

To get 10% hits at 500 m against a B-17 as the Luftwaffe expected, you'd need about 14 mil aiming dispersion.

To get 5% hits, you'd need 22 mil aiming dispersion.

The B-17 wingspan at 500 m equals 63 mil.

My conclusion is that the Luftwaffe based its figures for attacks on bomber formations on a more difficult firing solution than found in a straight six approach :-)

>Whether dispersion is a good thing or not depends on how effective each individual hit would be.

Actually, dispersion is as likely to make a correctly aimed shot miss the target as it is to make an incorrectly aimed one hit the target. It would only help against systematic aiming mistakes, such as always aiming high, because some projectiles would scatter low and hit. Still, even more would scatter left, right and up and miss.

Regards,

Henning (HoHun)

[Tony Williams]

Originally posted by HoHun
Actually, dispersion is as likely to make a correctly aimed shot miss the target as it is to make an incorrectly aimed one hit the target. It would only help against systematic aiming mistakes, such as always aiming high, because some projectiles would scatter low and hit. Still, even more would scatter left, right and up and miss.

Hi Henning,

Well, it's rather like the shotgun principle - you stand more chance of scoring hits with a wide dispersion shotgun than you do with a rifle. They crucial question is the amount of damage a single hit can do.

At one point the RAF was certainly interested in setting their wing-mounted Hispanos to diverge slightly, as the cone of dispersion for the guns would still have overlapped to ensure hits with accurate shooting.

Tony Williams: Military gun and ammunition website and Discussion forum

[HoHun]

Hi Tony,

>Well, it's rather like the shotgun principle - you stand more chance of scoring hits with a wide dispersion shotgun than you do with a rifle.

The shotgun comparison is misleading here because the shotgun fires multiple projectiles while the rifle fires a single one.

Comparing two rapid-fire weapons, though, both fire multiple projectiles.

Assuming that we have two different rapid-fire weapons of different gun-inherent dispersion and gun-inherent as well as aiming dispersion being Gaussian, that means that the gun with higher gun-inherent dispersion will always have a higher total dispersion, though less than the sum because the random factors involved will compensate each other to some amount.

So, an inaccurate weapon will make inaccurate aiming only worse. With regard to random aiming errors, nothing is gained from having a higher dispersion weapon.

Regards,

Henning (HoHun)

[gripen]

Actually the shotgun comparison is fully valid. The AC weapon actually sends bursts of projectiles and these disperse around aimed point depending on dispersion. Therefore the weapon with larger dispersion has better probability to hit.

HoHun's logic assumes that the every projectile is aimed individually.

gripen

[Wotan]

Butch made this post on his AAW II forum.

Here are the results of a lenghty research into dispersion data, which is quite hard to come by...
The data is based on 100% diameter dispersion with 1 mil = 1/1000th of rad, the kind of mount is precised next to the weapon. 75% dispersion diameter is supposed to be half the 100% diameter which seems quite true for most weapons, this value is provided when quoted in the source (M2 data for instance).

We can clearly see the impact of the wing mounting compared to engine mounting, the later seems to have absorbed recoil and vibration much better... indeed dispersion is at least 2 times greater with wing mounted weapons.

Engine mount are the most efficient but nose mounting or cowling mounting does not provide the same amount of precision the mount being much more prone to vibration it seems.

Note that US data on the M2 is confusing since the reference data comes from a P-38 nose mounted M2, but the US manuals use the same dispersion data for wing mounted weapons. Either the P-38 mounts are really up to no good or the manuals make a wrong assumption when it comes to wing dispersion. I tend to believe the later, i think the wing mounted M2 would have had a dispersion of at least 12mils and probably more.

If you quote this data on other sites/bbs please precise the source being AAW. TIA

H means Height (or max dispersion diameter) as i previously used vertical and lateral dispersion values.

D means distance.

Units are metric.

German Weapons
-----------------------
MG-17 Cowling mounted (Bf 109F-2 / Bf 109F-1 actual tests)
H = 0.60 / 0.8 m
D = 100 m
R/D = 60/10000 80/10000
= 6 mils / 8 mils

MG-131 Cowling mounted (Fw 190A - theorical max)
H = 1m
D = 100m
H/D = 100/10000
= 10 mils

MG-151/15 Engine mounted (Bf 109F-2 actual test)
H = 0,35 m
D = 100 m
H/D = 35/10000
= 3.5 mils

MG-FF Engine mounted (Bf 109F-1 actual test)
H = 0,2 m
D = 100m
H/D = 20/10000
= 2 mils (very tight patern)

MG-FF Wing mounted (Bf 109E-3 actual test)
H = 0,35 m
D = 100m
H/D = 35/10000
= 3.5 mils

MG 151/20 Engine mounted (Bf 109G-6 - theorical max)
H = 0.3m
D = 100m
H/D = 30/10000
= 3 mils

MG 151/20 Wing mounted - inner (Fw 190A - theorical max)
H = 0.7m
D = 100m
H/D = 70/10000
= 7 mils

MG 151/20 Wing mounted - outer (Fw 190A - theorical max)
H = 0.8m
D = 100m
H/D = 80/10000
= 8 mils

MK 108 Engine mounted (Ta 152 - therorical max)
H = 0.35
D = 100m
H/D = 35/10000
= 3.5 mils

Allied Weapons
------------------
M2 Nose mounted P-38 (USAAF 1944 Gunnery manual)
H = 1.88 m
D = 229 m
H/D = 188/22900
= 8.2 mils (75% = 4.1 mils)

Hispano 20mm Nose mounted P-38 (USAAF 1944 Gunnery manual)
3 mils 75%
6 mils 100% assumed

[HoHun]

Hi again,

Here's an illustration for the change in hit probability due to different dispersions:

http://www.x-plane.org/users/hohun/Dispersion.png

(You'd lay the target silhoutte flat on the zero plane.)

For the example, the higher dispersion weapon has 120% of the dispersion of the lower dispersion weapon. The central peak rises right at the aiming point.

(Going out from the aiming point, you move vertically and horizontally away from the target.)

Everything greater zero indicates an advantage for the lower dispersion weapon, everything below zero an advantage for the higher dispersion weapon.

As you can see, decreasing dispersion yields markedly increased hit chances around the aiming point at the cost of slightly decreased chances relatively far from the aiming point.

If you increase the difference in dispersions, the peak becomes flatter, so the advantage of the low-dispersion weapon at the aiming point becomes less pronounced. However, at the same time the peak grows in area, and the higher dispersion weapon has an advantage only further out from the aiming point, and that advantage is even less pronounced than that of the low-dispersion weapon at the peak.

By the way, the total difference in hit probabilities is zero. That's the reason the peak is always much more pronounced than the "moot", and that the moot becomes less significant as it moves outwards - the moot covers a larger area, but has the same volume as the peak.

Regards,

Henning (HoHun)

[gripen]

Well, HoHun has created a beautiful chart again, but this issue is very easy to understand with a simple example of two shotguns, no calculations or beautiful charts needed. The first one has dispersion which results 100% of projectiles within 0,5 m from aimed point at certain range and the second shotgun has dispersion which results 100% of projectiles within 1,5 m from the aimed point at same range. Let's assume that the target is a round plate with diameter 1 m and  ammunition  used is salt loaded ie there is almost infinite number of projectiles, in addition we assume that just one hit is needed to destroy target.

Let's assume that accuracy of aiming is such that in the 100% of the cases aimed point is within 1,5 m from the center of the target so  the first shotgun won't get hits in every case but the second will get hit in every case.

gripen