PLS HT look into Breda MG modelling!

[HoHun]

Hi Gripen,

>but please note that my second example is still a simplified single dimension model the like first one.

I'm using your model because I'm a nice guy trying to help you break the vicious circle :-) I'm well aware of its limitations, though.

>Well, normally teachers get paid for their work  

Glad you're trying to bring me up to speed for free :-)

However, you could have saved some work by using a more useful symbolic notation instead of some purely numerical scribbles which had me guessing about their significance.

Anyway:

Let's work with your second example since it actually includes the off-centre placement of the wing guns.

Further assumptions:

- Wing guns 2 m off centreline
- Convergence distance 200 m
- Aiming error is constant in angle

Results:

- 2x wing guns are inferior to 1x centreline gun below 110 m range,
- superior from 110 m range to 660 m range,
- inferior above 660 m range.

However, the example you picked is highly sensitive to aiming error.

Reducing the aiming error from 5 m to 2.5 m:

- 2x wing guns are inferior to 1x centreline gun below 130 m range,
- superior from 130 m to 330 m range,
- inferior above 330 m range.

Do we agree so far?

Regards,

Henning (HoHun)

[gripen]

HoHun,
Well, not much reason to disagree; seems that your calculation results are closing my thoughts. Generally it is easy to manipulate the model changing aiming error and/or target size. But lets look at that aiming error.

So whats your estimate for aiming error of a average pilot  in the case  where his plane and  target  plane are at same flight path ie head on or  directly behind case at range of 400m (meters or degrees)?

And what  about the aiming error in the case of the deflection shooting in the case of the when flight paths differ say 20deg and distance is again 400m?

About notation it should be noted that you started to talk about Gaussian so I was under impression that you knew what you were talking about. My samples are pretty much basic stuff, pretty clear for anyone who has played with statistics . Sorry if lack of notation caused too much work (IMHO that's good; you certainly learn when you have to figure system out) .

gripen

[HoHun]

Hi Gripen,

>About notation it should be noted that you started to talk about Gaussian so I was under impression that you knew what you were talking about.

I knew what I were talking about, the problem was finding out what the hell you were trying to say. The math was simple enough - the problem were poorly defined assumptions and uncommented numbers as well as a typo in two lines of example 2 which you seem to have missed during your edits. I've to admit I did not immediately gain the impression you were knowing what you were talking about.

>Well, not much reason to disagree; seems that your calculation results are closing my thoughts.

The interesting thing is that even by your own single-dimensional model, the advantages of wing guns are at medium ranges, not at long range. Now compare this to the two-dimensional dispersion graph I posted earlier:



(Yellow/orange denotes superior firepower for centreline guns, grey approximately equal firepower, blue superior firepower for wing guns.)

Regards,

Henning (HoHun)

[gripen]

HoHun,
Well, you "gaussian" model assumes constant  67% probability for the correct aim point without claiming target size (this means that accuracy of the aim increases when range increases), the only conclusion I can draw from this  is that  you had not much idea how gaussian  distribution works.

My first example shows actually my point ie aiming error at long range is much more signifigant than location of the guns in the plane. I purposedly used large 4m (ie same as distance between the wing guns) target to make example simple because most important thing is the variance caused by the aiming error.

My other exsample (after couple edits) is just for to show  how small must target and aiming error be to  make calculation to show advantage for the 1x armament in the fuselage at long range. If we set target and aiming error small enough, we can draw a conclusion that the fuselage armament is superior at all other ranges except convergence range and this is just what you did in your model. I see why you don't want to estimate real life aiming errors and how about the case of a larger (more realistic) target?

Anyway, adding third dimension will favor the  fuselage gun , adding dispersion will favor the wing guns and so on... It can be modeled but I'm far too  lazy to try. But good enough conclusions can be made with a bit of statistical knowledge; due to aiming error 2x armament in the  wings is better than 1x in the fuselage at long range.

gripen

[LUPO]

Hey guys!!!
When I started this thread I could never  imagined that would be so long and interesting...
...and, in a way,  so far from the initial question:
are the 12,7 MG Breda-SAFAT undermodelled in AH?
What do YOU think, HoHun and Gripen, about that???
I guess this thread will reach 200 post now...  

[-lynx-]

Galland was quite disappointed when the gondola cannon turned out to make the Me 109 inferior in fighter-to-fighter combat, but he actually saw them as a means of providing the necessary firepower for bomber interception.

Gents - you're arguing apples & oranges. Center-mounted gun is ideal for fighter/fighter combat delivering ammo accuartely on a small target. More guns required to bring down a bomber. Also, the need to be as accurate disappears when you're facing a Lancaster - it's not manoeuvering and it's big. No need for deflection shooting. Just unload as many rounds as quickly as possible to bring it down.

and yet RAF leaders like Stanford-Tuck considered the Messerschmitt's armament superior to the Spitfire's

It is the same RAF leaders who set convergeance to 500 yards, right? And which Spitfire were they talking about here? Spit I or II wth 8 0.303s? Sure. Spit V with 2 Hispanos and 4 0.303s? Versus 1 15/20mm cannon and 2 x 7.7s? Of please... It looks like Peter's principle (everyone gets promoted up to the level of their incompetence) was working in RAF.

For example, when jacked up on the firing range, the MG151/20-armed Ju 87D-5 produced a 70 cm x 70 cm pattern at a distance of about 100 - 200 m when firing bursts. I think that's about the accuracy you should expect from a smoothbore musket, not from a modern 20 mm rifle ;-)

Hmmm let's see that smoothbore firing 800 rpm and check it's distribution pattern then;). 70x70 looks pretty good to me although my experience with automatic weapons tops at 14.5mm turret mounted MG...

[Tony Williams]

Since I started the Stanford-Tuck hare running, I had better clarify.

This came from a survey reported in January 1942 (so, not 8x.303 Spitfires!) of senior RAF fighter officers, of whom Stanford-Tuck was one (the others I didn't note, but I recognised his name). This is a direct quote from the report:

"In spite of our superiority of fire power over that of the enemy, many pilots would prefer the armament of the Me 109 with its one cannon firing through the air screw hub and two MGs mounted in the fuselage. They feel that despite its inferiority to our armament the concentration of parallel fire more than counterbalances our criss-cross pattern."

This is not attributed to any individual fighter commander, but was obviously a commonly (but not universally) held view at the time. You may debate till the Spitfires come home about what basis they had for such a belief - I merely reproduce what was reported at the time.

Tony Williams
Author: "Rapid Fire: The development of automatic cannon, heavy machine guns and their ammunition for armies, navies and air forces"
Details on my military gun and ammunition website:
http://www.quarry.nildram.co.uk
Military gun and ammunition discussion forum:
http://forums.delphiforums.com/autogun/messages/

[funkedup]

HoHun nice graph there.  

One thing to remember is that the graph is not to scale (for good reasons), so one must consider that when getting a subjective impression.  

Considering that, it looks very similar to the results I observed in Aces High.  

Except near convergence range, centerline guns are better if the pilot has near-perfect aim.  But if the pilot's aim is not so good, which becomes more and more likely as range increases, or if there is a snapshot or tracking deflection shot, then a pair of wing guns is much more likely to score.  And I think that in WWII, poor aim and snapshots and deflection shots were quite common, making the number of guns more important than their distance from the thrust line.

[HoHun]

Hi Gripen,

>Well, you "gaussian" model assumes constant  67% probability for the correct aim point without claiming target size (this means that accuracy of the aim increases when range increases)

I approximated the complex shape of a real aircraft, the dispersion of fire and the effect of firing at a two-dimensional target by assigning a finite probability for hitting even with a correct aim.  You assume dispersion to be zero, limit the problem to one dimension, and consider the aircraft's shape that of a short line. It's the nature of simplified examples to be imperfect.

I could ridicule your skills on the basis of your example just like you're ridiculing mine. Since that's not the kind of discussion I'm looking for, I won't.

>But good enough conclusions can be made with a bit of statistical knowledge; due to aiming error 2x armament in the wings is better than 1x in the fuselage at long range.

Here are some numbers from your own example situation:

Range [m]; Phit 2 wing guns, Phit centreline gun
600; 8,97%;    7,53%
650; 7,46%;    7,14%
700; 6,24%;    6,74%
750; 5,47%; 6,35%
800; 4,78%; 5,96%
850; 4,14%; 5,56%
900; 3,64%; 5,17%

In short, beyond a certain range, the wing guns in your example lose their advantage and become inferior to the centreline gun.

I assume this is a terminology problem concerning the definition of "long range". However, in your example, the longer the range, the greater the superiority of the centreline gun.

Regards,

Henning (HoHun)

[HoHun]

Hi Lynx,

>Hmmm let's see that smoothbore firing 800 rpm and check it's distribution pattern then;)

Great example :-)

I don't doubt dispersion is large, I just wanted to illustrate it's mostly a function of the mount, not of the weapon itself.

Regards,

Henning (HoHun)

[HoHun]

Hi Funked,

>One thing to remember is that the graph is not to scale (for good reasons), so one must consider that when getting a subjective impression.

Exactly. It also shows a case where the dispersion conce is smaller than the inward firing angle necessary for convergence. If you'd want to get overlapping convergence zones, you could widen the dispersion angle so that the outward dispersion boundary is parallel to the sight line. However, that would require a very large dispersion angle or a very long convergence range, and still leave the centreline gun with a long-range advantage due to the large dispersion as only a small fraction of the bullets actually hit the overlapping area.

>And I think that in WWII, poor aim and snapshots and deflection shots were quite common, making the number of guns more important than their distance from the thrust line.

Well, and I believe that in WW2, short-range fire was a quite important way to achieve kills, for the exact opposite emphasis :-)

But your post actually reminds us that we shouldn't forget that the weapons' capabilities determined the tactics, i. e. whether the pilots would go for a tracking shot or for a snapshot, or whether they would fire at long range or at short range.

Regards,

Henning (HoHun)

[gripen]

HoHun,
I wonder what is the point of your correct aim based model in this discussion; I have agreed right from the beginning that in that case centerline armament is better?

You can certainly play with my simplified model and use it for purposes it was not made for; if the range is long enough, it will favor fuselage guns. But ranges beyond 500m are pretty unrealistic and if the dispersion is as high as Funkedup claimed and evenly distributed as in your model, then wing guns have advantage at very long range too.

BTW do you still disagree conclusion that the 2x wing guns combination is better for a average pilot than the 1x fuselage armament?

gripen

[gripen]

Let's have a little look on progress:

HoHun 31.01.2002: "centreline armement is better for inexperienced pilots at any range."

HoHun 01.02.2002: "Wing armament is superior at convergence range. It's inferior short of and beyond convergence range"

HoHun 05.02.2002: "Well, and I believe that in WW2, short-range fire was a quite important way to achieve kills"

Well, not much to ad.

gripen

[SageFIN]

Gripen, if you are trying to argue that those three quotes are somehow incoherent, I suggest that you look at them again.

[gripen]

Sage FIN,
Well, all quotes are from 1x fuselage vs 2x wing armament discussion. Please see above, you can easily find them above and see connections. And all I see is progress... (siis edistystä  ei ristiriitaisuutta)

gripen