Dispersion Angle for rapid fire WW2 aircraft guns

[Crumpp]

There is no quesses, simply a large probability that an average pilot aimed pretty much allways with some error.

Gripen you’re guessing that designers purposely built in dispersion to increase the hit probability when facts are they do not.

That is not true.

Couple degrees is just a wild quess, in fact it might have been less. In the case of the ZU-23 (AA gun, not GSh-23, I forget the designation), the mounting is built to have something like couple mm loosenes in the support point. Notable thing is that support point is actually rectangular so I quess the pattern is also rectangular. While shooting the jumping of the gun in the support point is quite well visible as well as dispersion of the projectiles.

Design flaw not a feature when it comes to accuracy.  Simply examine the number of high performance aircraft that have been brought down by ZU-23 fire.  While considered a threat, it is hardly an effective one.  The advantage lies in the "bang for the buck" factor.  ZU-23's are realtively inexpensive compared to other AAA platforms.

I didn't know that. I thought it was mostly a negative side effect of high MV and high ROF usually accompanied by a too flexible mounting of the gun (eg. wing).

Correct.  The dispersion found in a design automatic weapon is a function of the engineering tradeoffs to achieve sustainable automatic fire.  Not a feature to improve hit probability.  

Looks to me like people are confusing the convergence of fighter’s weapons with the dispersion of the weapon itself.

When a suitable picture hanger becomes available again, I will post various convergence adjustments, individual weapon dispersion charts, and vulnerability reports.

Facts are the aerial gunnery problem was inherently difficult.  No individual weapon is purposely designed with "built in dispersion".  All weapons are engineered to eliminate as much dispersion as is possible within the design limits.

Convergence patterns can be changed to increase a pilot with poor aim chances of placing a vital portion of an enemy aircraft into the beaten zone of the individual weapons in the array.  This would increase his chances of achieving concentration of firepower on a vulnerable portion of the target.

All the best,

Crumpp

[gripen]

Originally posted by Crumpp
Gripen you’re guessing that designers purposely built in dispersion to increase the hit probability when facts are they do not.

I'm not quessing, I have seen that in the ZU-23. And the reason for the loosenes is actually described in the documentation. And the reason for dispersion can be proved with aiming error.

Originally posted by Crumpp

Simply examine the number of high performance aircraft that have been brought down by ZU-23 fire.  While considered a threat, it is hardly an effective one.  The advantage lies in the "bang for the buck" factor.  ZU-23's are realtively inexpensive compared to other AAA platforms.

 
The ZU-23 is probably one of the most succesful gun in it's class and it brought down plenty of high performance aircraft in Vietnam, Afganistan, Midle East etc. Current versions used by Finnish army feature motorized aiming as well as laser range seeker. Shortly a very succesfull and reliable weapon.

gripen

[Crumpp]

I'm not quessing, I have seen that in the ZU-23. And the reason for the loosenes is actually described in the documentation. And the reason for dispersion can be proved with aiming error.

I have seen them too, Gripen.  

You should probably check your statistics on the effectivenss.  There is a pretty good reason most first world armies do not rush out and buy them.

If you have original documentation please post it.  Getting it translated is no problem.

I would think the "looseness" of the mount has more to do with recoil forces not destroying the light mount of the weapon.

All the best,

Crumpp

[Bruno]

If the pilots aiming error is systematical as it probably is

Where does this assumption come from?

[HoHun]

Hi Beet1e,

>Given the environmental factors I've just described, this would seem incredible for any pilot to achieve. And even if he could, dispersion would account for 75% of the rounds missing the target no matter how could the aim was.

Do you think you could come up with a number for the random aiming error you would consider credible?

>And this scenario doesn't even take into account loss of kinetic energy and bullet drop due to gravity and air resistance.

Hm, I'm not sure what you are talking about, but my example does.

Regards,

Henning (HoHun)

[HoHun]

Hi Bruno,

>>If the pilots aiming error is systematical as it probably is

>Where does this assumption come from?

As far as my example is concerned, certainly from a misunderstanding.

Out to the distances described above, the pilot can simply put his crosshairs on the centre of the target and push the button. The hit results described above are what they are because the trajectory does not deviate far from the sight line.

So all the pilot has to do - since it's so difficult to grasp, I'll have to repeat it once again - is to put his crosshairs on the centre of the target and push the button.

Only beyond 500 m for the MK108 and beyond 800 m for the Browning M2, trajectory drop becomes a factor, and range estimation and possible systematical errors in range estimation would have to be considered.

With the standard technique "Put the crosshairs on the target and push the button", systematical errors are not a factor.

(If you were bent on it, you could of course produce a systematic aiming error even for that technique. For example, you could suggest that the pilot never pushes the button when the crosshairs are on target, but only when they are off target. Instant systematic error :-) Not a very realistic suggestion, though.)

Regards,

Henning (HoHun)

[beet1e]

Hohun,

My interest in this topic has a lot to do with the viability of killer 800yd shots, and the way that in some versions of some aerial combat games, wings could be shot off with consummate ease at awkward trajectories at ranges of as much as 800yds or even more.

Gripen has estimated the total dispersion spread as a couple of degrees, maybe less. I did my own calculations based on a total spread angle of 1°, which is to say ½° in any direction from dead centre. Let us set aside the effects of gravity and air resistance until later...

In theory, the bullets would be discharged from the barrel of the gun(s) and would create a circular pattern on the target. The bullet stream would be conical in shape, with the point of the cone being at the gun barrel. But, at 800yds or 2400ft, the radius of that circle would be 2400xtan(½) = 20.94ft, and therefore the area of that circle would be just over 1377 square feet!! How much surface area is visible to an attacking pilot in the dead 6 position at 800yds? Well, the wingspan of a Spit V was in the order of 37ft. I don't know what the exact wing thickness was, what with fuel tanks - can we say an average wing thickness from tip to root of 4 inches? In this case, the surface area would be 37x0.33333 square feet = 12.33 square feet. Add to that the visible surface area of the tail and fuselage - asymmetrical, so difficult to calculate. Let's say the surface area was twice as much as the visible wing surface area - and that's being very generous. We end up with a value of 37 square feet, but as I have already shown above, the area covered by the guns at 800yds would be 1377 sq.ft.  Therefore, only one out of every ~37 bullets would find the target at a range of 800yds...

...and that's assuming perfect conditions - no bullet drop due to gravity, bullets that fly as straight as laser beams and which are unaffected by air resistance. It also assumes that the pilot can at all times keep the plane aimed to within a small fraction of a degree of the required attitude throughout the entire period needed for his guns to deliver the necessary destructive power to bring down the target. When these other factors are taken into account, it's clear to see that the chances of downing an enemy plane at such a huge range is infintesimal. Granted, a random ping could create an oil leak, to be followed soon afterwards by a forced landing, but that's about it.

The only way it could be done is if the bullets were as big as marrows - in some games, they were!

[2bighorn]

US Navy gunnery manual for pilots from 1944 says .50 cal dispersion was from 6 to 10 mil and max effective range was 1000 ft (333 yards).

Bullet drop due to gravity was about 15 ft at 900 yds (calc 11 ft at 800 yds)

[HoHun]

Hi Beet1e,

>But, at 800yds or 2400ft, the radius of that circle would be 2400xtan(½) = 20.94ft, and therefore the area of that circle would be just over 1377 square feet!!

Well, you're assuming that the bullets would spread out evenly over the entire area. However, with a random deviation caused by erratic movements of the aircraft nose, the crosshairs will be near the centre of the pattern much more often than on the edges.

Relying on the Gaussian distribution, I'll take your deviation of 0.5° as 3*sigma so that 99.7% of all hits are in the circle you describe.

With this, we arrive at the following hit distribution:

central 1/6° radius circle: 68% of the hits, 1/9 of the area => 153 sqft
ring 1/6° to 2/6°: 27.5% of the hits, 3/9 of the area => 459 sqft
ring 2/6° to 3/6°: 2.7% of the hits,  5/9 of the area => 765 sqft

So to hit the assumed area of 37 square feet, we get the following hit ratios:

central 1/6° radius circle: 68% of the hits => 24% strikes
ring 1/6° to 2/6°: 27.5% of the hits, 3/9 of the area => 8% strikes
ring 2/6° to 3/6°: 2.7% of the hits,  5/9 of the area => 0% strikes (rounded down :-)

The resulting total hit probability is:

Ph = 68% * 24% + 27.5% * 8% + 2.7% * 0% = 18.52%

That is closer to one out of every five bullets striking than to one out of every 37. With that kind of hit percentage, firing at 800 yards probably would be worthwhile.

Regards,

Henning (HoHun)

[gripen]

Originally posted by Crumpp

You should probably check your statistics on the effectivenss.  

I wonder what should I check, during last 40 years no other AA gun has seen as widespread use as the ZU-23 and probably no other AA gun has brought down as many aircraft (planes or helicopters) as the ZU-23 during that period.

Originally posted by Crumpp

There is a pretty good reason most first world armies do not rush out and buy them.

I can certainly say that Finnish army has been very happy with the weapon itself   and in it's current form will remain in service maybe next 10-20 years.

Originally posted by Bruno

Where does this assumption come from?

There is no reason to believe that the centre of the aim point set of a pilot is same as the correct aim point in long range deflection shooting.

Originally posted by Hohun

As far as my example is concerned, certainly from a misunderstanding.

The "example" has absolute nothing to do with the long range deflection shooting.

Originally posted by Hohun

With the standard technique "Put the crosshairs on the target and push the button", systematical errors are not a factor.

At long range deflection shooting the target is never in crosshairs except with gyroscopic gunsight.

gripen

[Crumpp]

I wonder what should I check, during last 40 years no other AA gun has seen as widespread use as the ZU-23 and probably no other AA gun has brought down as many aircraft (planes or helicopters) as the ZU-23 during that period.

Losses to AAA have been insignificant.

http://www.au.af.mil/au/afhra/wwwroot/short_studies/USAFMannedAircraftCombatLosses1990_2002.pdf

Considering the quantity employed and produced, the ZU-23 can hardly be considered a success.

can certainly say that Finnish army has been very happy with the weapon itself

Happy for them.  Hope they enjoy using them in combat.

At long range deflection shooting the target is never in crosshairs except with gyroscopic gunsight.

Where do you get deflection shooting from HoHun's post?

All the best,

Crumpp

[2bighorn]

Originally posted by HoHun
firing at 800 yards probably would be worthwhile.

Typical ww2 .50 cal M2 type 2 machine gun has only 13% hit rate (at 800yds) with a target area of 45 square feet. That would be with dispersion of a single gun.

If you would calculate in gunsight/guns harmonization error at typical distance of 350/400 yds of 6 guns package, aim of a typical airman, atmospheric conditions, speed of aircraft, bullet drop, different trajectory/balistics for mixed ammo loads, the fact that 90% of airman would completely miss banner target between 1000 and 1500 feet, then shooting at target at 800 yds for all practical purposes, was complete waste of ammo.

by US Navy 1944
Browning Aircraft Machine Gun, .50 Cal..,  MK 2, Mod 2. Range: Maximum effective - 1,000 feet.

Conservation of ammunition - don't waste ammunition firing out of range - only limited supply - main problem of combat fighters.

[gripen]

Originally posted by Crumpp
Losses to AAA have been insignificant.

Please check Vietnam.

Originally posted by Crumpp

Where do you get deflection shooting from HoHun's post?

I don't understand your (or HoHun's) logic here at all; Bruno asked from me from where comes my assumption that at longe range deflection shooting the error is probably systematical. HoHun answered and some how mixed in his "example" which has nothing to do with the deflection shooting.

gripen

[HoHun]

Hi 2bighorn,

>Typical ww2 .50 cal M2 type 2 machine gun has only 13% hit rate (at 800yds) with a target area of 45 square feet. That would be with dispersion of a single gun.

Interesting data point! :-) That would be a 100% dispersion circle of roughly 7.6 mil. For which type of mount is this data valid?

For my example, I'm using 4 mil for the P-38 and 6 mil for the P-47, which is a bit lower, but seems to match historical data from various sources.

(Of course, with half the dispersion, I get four times the hit percentage.)

>the fact that 90% of airman would completely miss banner target between 1000 and 1500 feet

Well, banner shooting was not from the dead six position against a stationary target, but involved dynamic pursuit-curve attacks and lead estimation, so the level of difficulty is considerably higher than in my example.

Regards,

Henning (HoHun)

[Crumpp]

The USAF maintained a .65% loss rate due to all enemy action causes.  

http://www.fas.org/man/crs/RS21141.pdf

Far more appear to have been brought down my SAMS and Air to Air Combat:

http://home.sprynet.com/~anneled/usloss.html

All in all, it seems pretty ineffective even back then.  

All the best,

Crumpp