Calculated "base" dispersion of guns based on energy delivered

[Kurfürst]

Originally posted by 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

Indeed... except of course that we, HoHun as well are speaking about aimed bursts here, not just pushing your luck.

Therefore the weapon with larger dispersion has better probability to hit.

It has more chance to hit the target at least one time, and at the same time much more rounds will MISS the target in case of a similiarly well aimed burst.

You appear to propagate that larger dispersion is actually good. I am left to wonder why then EVERYONE in the end tried to minimise dispersion, instead of increasing it. Using cannons instead of batteries of MGs was on this track, too. A single cannon shell concentrated the power of all those MG bullets in one single place; goal being zero dispersion if you like.

Large dispersion makes one or two flashes on the target every time, which is fairly irrelevant in itself as an effect. Most of your ammo is wasted, even if you do everything right, and the final destructive effect under a given time is always LESS than with tightly grouped hits. The latter is the goal, to kill the enemy not just to score a few hits on him and be happy about it.

[gripen]

Originally posted by Kurfürst
Indeed... except of course that we, HoHun as well are speaking about aimed bursts here, not just pushing your luck.

If we assume that aiming is allways perfect, then the less dispersion is better. But as noted above, for one reason or another only 2% of projectiles shoot by an average LW pilot actually hit something (I found a page which claims that number comes from gun camera film analyses). So it appears that 1 mil accuracy of aiming as claimed by HoHun above seems to be more or less science fiction.

Originally posted by Kurfürst
You appear to propagate that larger dispersion is actually good.

Actually I believe that some amount of dispersion is good and I know that in some cases dispersion is purposedly "built in" to the mounting.

Another thing to note is that higher velocity of the projectile increases accuracy of the aiming because less lead is needed in the deflection shooting. This means that long barrel might improve accuracy despite it might cause larger dispersion.

gripen

[HoHun]

Hi Kurfürst,

>It has more chance to hit the target at least one time, and at the same time much more rounds will MISS the target in case of a similiarly well aimed burst.

That's exactly the point :-)

The shotgun example is misleading only if you consider "something hit the target" as 100% hits.

However, once you ask "How many pellets actually hit?", you'll see that if, for example, the shotgun cone is three times as large as the target, you're hitting only with an average of 11% of your pellets if your random aiming error is smaller than the dispersion.

Exchange your shotgun for one with two times the dispersion of the target size, and you'll hit with 25% of your pellets on the average. However, the permissible random aiming error drops to just 44% of the area it had before because of the smaller shotgun cone.

This leads to the following situation:

Dispersion      Pellets Hit  Permissable Error  Total Hits
3 * Target Area         11%               100%         11%
2 * Target Area         25%                44%         11%

Both shotguns give an identical total hit percentage.

The more accurate your aim is, the greater the benefit from a small dispersion because you don't get into the far-off-target area where the larger dispersion weapon has an advantage.

If you consider the aiming errors random, there's no total advantage for the larger dispersion weapon at all because random errors are centered at the correct aiming point, and large dispersion gives you a big disadvantage there.

That's what's shown in my graph.

You can see that the only way to gain a benefit from a large-dispersion weapon would be to avoid aiming at the correct aiming point and stay in the areas around it. Of course, that's a bad idea as even a large-dispersion weapon will be more lethal if you aim at the correct aiming point, and to avoid hitting it, you'd have to know where it is, which is the practical difficulty in air-to-air gunnery.

(The only situation where one might expect a small benefit from a large-dispersion weapon could be with wing-mounted weapon, which systematically miss the aiming point at distances short of and beyond convergence. Systematical really is the keyword here.)

Regards,

Henning (HoHun)

[Tony Williams]

Originally posted by HoHun
You can see that the only way to gain a benefit from a large-dispersion weapon would be to avoid aiming at the correct aiming point and stay in the areas around it. Of course, that's a bad idea as even a large-dispersion weapon will be more lethal if you aim at the correct aiming point, and to avoid hitting it, you'd have to know where it is, which is the practical difficulty in air-to-air gunnery.

Exactly. The aiming skills of the great majority of WW2 fighter pilots were known to be atrocious, and the greater the angle of deflection, the worse they were. They consistently uinderestimated the lead required so a tight dispersion setup would miss almost every time unless they were at short range and 6 o'clock. That's why the extra dispersion was useful - at least they should get SOME hits which might do some damage.

I think that the parameters may well have changed with the introduction of the gyro gunsight in 1944. This greatly improved the hit probability of the average pilot and probably made concentration of fire more effective.

Tony Williams: Military gun and ammunition website and Discussion forum

[HoHun]

Hi Tony,

>The aiming skills of the great majority of WW2 fighter pilots were known to be atrocious, and the greater the angle of deflection, the worse they were.

That might be true of some air forces, but other air forces, like the US Navy (oops :-) or the Luftwaffe put considerable emphasize on training their pilots in deflection shooting. The rest is von Clausewitz' "friction" - in war, the simplest thing becomes very difficult.

As I already mentioned, USAF tests documented a tracking accuracy of 1 mil for an experienced pilot. That's the potential of the man-machine interface in a controlled environment.

>They consistently uinderestimated the lead required so a tight dispersion setup would miss almost every time unless they were at short range and 6 o'clock. That's why the extra dispersion was useful - at least they should get SOME hits which might do some damage.

Well, if you picture the effect of insufficient lead, you'll see that you'll quickly lag far behind the target with the entire pattern at even minor estimation errors. A 20% error in range estimation against a target at 250 m, travelling at 100 m/s, will result in the aiming point being 6 m off. An 10 mil diameter dispersion will result in the 100% border being just 1.25 m closer to the target than a zero-dispersion shot, and only 0.625 m closer than a 5 mil dispersion weapon. (Successful deflection shots were most likely at short range anyway, where dispersion wasn't a great factor yet.)

A larger dispersion might be useful, though, to fill in the gap between the two patterns of wing guns at ranges out of convergence, which was an additional ballistic problem the RAF was facing.

>I think that the parameters may well have changed with the introduction of the gyro gunsight in 1944.

In my opinion, the value of the gyro gunsight often is a bit overestimated. It requries a steady tracking shot with a full second spent by both the target and the shooter in a stabilized flight situation, and commits the attacker to a pursuit curve. Experienced pilots actually disliked the gyro gunsights, preferring a fixed sight and collision course attacks, because you can press these to a closer range (making the range problem easier) and at the same time avoid committing yourself to a turnfight. Besides, it allows greater angles-off, which increases the damage if you hit.

The Luftwaffe in particular avoided pursuit curve attacks on bombers because that while that made the firing solution for the attacker easier, the firing solution for the bombers' gunners became much easier, too :-)

Regards,

Henning (HoHun)

[Tony Williams]

Hi Henning,

If you turn to page 94 of your copy of 'Flying Guns: World War 2' you will see an official British diagram of the benefits of a larger dispersion in deflection shooting. In the case of an attack at 7 degree angle against a 250 mph target at 250 yards, it shows that if the pilot aims straight at the target (i.e. no lead) a 0.3 degree dispersion would result in a miss while a 1 degree dispersion would result in hits.

I agree with you that the most skilled pilots probably gained no benefit from gyro sights. But these represented only a small percentage of the pilots. When USAAF officers observed tests of the GGS they reckoned it would double the chance of an average pilot scoring hits.

Tony Williams: Military gun and ammunition website and Discussion forum

[HoHun]

Hi Tony,

>If you turn to page 94 of your copy of 'Flying Guns: World War 2' you will see an official British diagram of the benefits of a larger dispersion in deflection shooting.

Sounds like a book I ought to have, but the price tag deterred me :-/

>In the case of an attack at 7 degree angle against a 250 mph target at 250 yards, it shows that if the pilot aims straight at the target (i.e. no lead) a 0.3 degree dispersion would result in a miss while a 1 degree dispersion would result in hits.

Beggars' hits, I'd call them ... I've just calculated that in the outer ring between the 75% and the 100% dispersion, you have only 25% of the hits, but 75% of the pattern area. That's just 9% of the firepower you have in the central area. (And in fact, near the outer rim it's even less than 9%.)

You're better off walking the fire of a low-dispersion gun over the target by NOT trying to track, but pulling through. That way you get the same spread vertically, but much better accuracy horizontally.

And 7° deflection, wow :-) That's almost a straight six shot.

But I've to admit that while at first, I thought not pulling any lead at all sounded a bit contrived, I now consider the setup as simulating a higher-deflection shot with some, but not enough deflection - so it might be a valid example anyway.

>I agree with you that the most skilled pilots probably gained no benefit from gyro sights. But these represented only a small percentage of the pilots. When USAAF officers observed tests of the GGS they reckoned it would double the chance of an average pilot scoring hits.

Oh well, from all I know, they might just have pulled a nice round number out of their hat.

(And note that getting hits is not the same as getting kills ... for a kill, you need to hit decisively.)

Regards,

Henning (HoHun)

[Tony Williams]

Some quotes from 'Flying Guns - World War 2: Development of Aircraft Guns, Ammunition and Installations 1933-45':

"German research in the early 1940s indicated that most successful attacks took place at zero deflection and the maximum angle of attack for effective shooting without a gyro sight was 15º. Many successful fighter pilots preferred to open fire at point-blank range in order to avoid the deflection problem altogether."

and:

"Gyro sights were first developed in the UK in the late 1930s, after combat tests using camera guns revealed the difficulties in estimating the amount of lead. The first model was tested in combat in 1941 in both fighters and bombers, but had many problems which were not resolved until 1943, when the sights were perfected as the GGS (gyro gunsight) Mk IIC (for turrets) and Mk IID (for fighters). These went into quantity production early in 1944 and, after demonstrations revealed the dramatic improvement in average shooting accuracy which resulted from their use, the USA adopted the sight as the Mk 18 (USN) and K-14 (USAAF). There can be little doubt that these sights contributed significantly to the excellent kill ratios achieved by Allied fighter pilots in the last year of the War."

Tony Williams: Military gun and ammunition website and Discussion forum

[Charge]

"There can be little doubt that these sights contributed significantly to the excellent kill ratios achieved by Allied fighter pilots in the last year of the War."

IMO there surely were other factors, too, which could have affected such results: Huge advantage in numbers, tactical advantage in height over combat area, bad quality of opposing force, to name few.

I'd imagine a lead computing sight to be most effective when accurate range can be calculated -and that would need a radar.
Otherwise it depends very much of the visual intepretation of the sight circle size relation to target.

-C+

[gripen]

Originally posted by HoHun
However, once you ask "How many pellets actually hit?", you'll see that if, for example, the shotgun cone is three times as large as the target, you're hitting only with an average of 11% of your pellets if your random aiming error is smaller than the dispersion.

Well, here HoHun understands whole idea of the dispersion wrong.

Let's assume that we need say 10 hits to destroy the target. With the large dispersion shotgun we get say in average 10 hits in every case but with the small dispersion shotgun we need to shoot in average ten times to actually hit target  but in that case we get in average 1000 hits. Which of these shotguns is more effective?

Besides aiming error is most likely systematic; too little lead.

gripen

[Charge]

So how many rounds do you have to actually shoot to get those hits with a high dispersion gun?

-C+

[HoHun]

Hi Tony,

>"German research in the early 1940s indicated that most successful attacks took place at zero deflection and the maximum angle of attack for effective shooting without a gyro sight was 15º. Many successful fighter pilots preferred to open fire at point-blank range in order to avoid the deflection problem altogether."

That's a good description :-) However, the last two sentences implicitely describe two extremes of a fluid relationship - long range, low deflection capability, and extremely short range with high deflection capability. At intermediate ranges, the possible deflection was something in between.

I'd say the point-blank range comment indicates that you agree on the value of short-range high-deflection attacks (I call them collision-course attacks)?

>"Gyro sights were first developed in the UK in the late 1930s, after combat tests using camera guns revealed the difficulties in estimating the amount of lead. The first model was tested in combat in 1941 in both fighters and bombers ...

The UK was certainly leading the field in defensive armament. I think the gyro sights were more valuable for bombers than for fighters, however - but of course I don't deny they were great for fighters, too. It's just think that the enthusiasm shown by some authors is a bit exaggerated. They were a useful tool, but not without limitations - for example, they required an accurate range estimation, and the ranging mechanism was quite similar to that of the British fixed gunsights. As you've pointed out, the RAF pilots had considerable ranging difficulties with those.

>There can be little doubt that these sights contributed significantly to the excellent kill ratios achieved by Allied fighter pilots in the last year of the War."

Hm, the Luftwaffe achieved excellent kill ratios against the Soviets, too, but without gyro gunsights. I'd be hesitant to attribute a general phenomenon to a single factor.

Regards,

Henning (HoHun)

[gripen]

Originally posted by Charge
So how many rounds do you have to actually shoot to get those hits with a high dispersion gun?

I don't know if this is about my two shotgun example. Assume that the dispersion of the high dispersion shotgun  is larger than aiming error so some amount of salt projectiles (say at least ten) will hit in every case.

Basicly if the dispersion does not give any advantage, they would have been shooting birds with the rifles. Shooting large amount of projectiles (burst) without dispersion is basicly same thing as shooting a single round.

gripen

[HoHun]

Hi Charge,

>So how many rounds do you have to actually shoot to get those hits with a high dispersion gun?

I'll try to explain with a somewhat simplified example:

Assume a 12.7 mm MG that needs 60 hits on a target to bring it down. You have two versions of it, one with 2 mil dispersion and one with 4 mil dispersion radius.

Assume that pilot-induced aiming error increases total dispersion to 5 mil and 7 mil radius respectively.

Assume a target area of 1.54 m^2.

At 100 m, the target is completely within both dispersion radii. You get 100% hits with both weapons, so you need to fire 50 rounds.

At 200 m, the target fits perfectly into the the 75% dispersion radius of th large-dispersion weapon. You need to fire 80 rounds for a kill now.

The target also fits perfectly into the the 100% dispersion radius of the low-dispersion weapon. You still need to fire only 50 rounds for a kill here.

At 400 m, the target is caught firmly in the 75% dispersion circle of the large-dispersion weapon, filling only one quarter of it. That means only 18.75% of the rounds hit, or 320 have to be fired for a kill.

With the low-dispersion weapon, the target is caught just as firmly in the 75% dispersion circle, but fills 50% of it. That means you get the kill with just 160 rounds.

The idea that high dispersion improves kill chances is in error. It can only be justified by declaring that the pilot knows the correct aiming point and subconsciously avoids it.

The RAF initially used very long harmonization ranges, which gave them a large dispersion at normal (short) combat ranges. They were having all the aiming difficulties Tony described, and yet they quickly discovered that the way to get kills was to change harmonization to short ranges in order to keep dispersion to a minimum.

Whatever experiments were tried later, the RAF battle experience was "use the tightest possible pattern".

Regards,

Henning (HoHun)

[Charge]

"The idea that high dispersion improves kill chances is in error. It can only be justified by declaring that the pilot knows the correct aiming point and subconsciously avoids it. "

Gripen, the amount of rounds to achieve those hits is not irrelevant as the a/c cannot carry infinite amount of mg rounds.
So the choise of weapon dictates also how it has to be used in aircombat.

The 303s the Brits used in BoB had a high probability of pucturing a radiator or a fuel or oil line but they were hardly able to inflict critical damage without firing at an extremely close range. But that was enough in that strategic situation. Many a/c ditched into channel or fell in Britain.

Imagine same kind of weapons in German a/c. The losses for RAF would have been smaller as the lack of critical damage would have left the RAF a/c a high probability of surviving the encounter because they always would have been able to ditch near some of their own fields. So the LW had to have heavy armament to achieve even what they did.

***

"The idea that high dispersion improves kill chances is in error. It can only be justified by declaring that the pilot knows the correct aiming point and subconsciously avoids it. "

HoHun, the projectiles in high dispersion do not avoid the area in the middle of the hit pattern but spread randomly over it with the preference being in the center providing that the weapon is in a fixed mounting.

Firing a high dispersion gun at long ranges is obviously a waste of time but at certain ranges it has an advantage of the dispersion providing that the projectile has ability (at that range) to inflict damage where ever it may hit the enemy a/c. That is unfortunately not the case as the bad dispersion is usually related to a light projectile and high ROF. But if you hit the pilot, or a coolant, oil, or fuel line or radiator that is usually enough, depending on if the damaged a/c can handily RTB which was not the case for German a/c for example during BoB.

So what I am trying to say is that the effectiveness of a high or low dispersion gun depends on the strategic and tactical situation it is used in. Obviously during the last stages of WW2 the experience had shown that the increase in speeds and amount of defensive armament in bombers required lots of damage in shortest time possible -thus the cannon armament became a necessity.

I'd take a dangerous step here and claim that if the situation had gone to worse direction for the allies the US, too, would have had to introduce the cannons into aircraft participating in aerial battle. For ground strafing the 50Cal was surely better. But that probably belongs to another thread.

Sorry, I went quite far from the original subject.

-C+