PLS HT look into Breda MG modelling!

[HoHun]

Hi Gripen,

>I wonder what are you trying to say? You presented a theory without data so actually it's your problem to bring in some kind of data.

I was referring to the model I developed earlier:

Let's assume Gaussian distribution of the pilot's aiming error and homogeneous distribution of the bullet density within the pattern radius.

Let's have our pilot open fire at a range where he has a 67% chance of having aimed correctly. Additionally, let's assume that if he aimed correctly, bullet density will suffice to give him a 40% chance of a hit on the target aircraft for each bullet fired.

Firing 25 shots from a single accurate 20 mm gun, he'd score (long term average :-) 6.7 hits. That's a number the Luftwaffe considered high enough to kill a fighter reliably.

Now let's increase the pattern: At the range where the pilot can be expected to have his sights on target with a 67% chance only, increasing the pattern size might seem like a good idea. Doubling the pattern size will indeed give our pilot a 96% chance of being on target. However, bullet density within the pattern is down to one quarter of what it was before, meaning that with the pattern right on target, there'll be only a 10% chance of a hit for each bullet.

Firing 50 shots from his new twin guns of reduced accuracy, our pilot will now score (long-term average again) 4.8 hits only. That means by adding another gun and increasing the pattern size to increase hit chances, he's actually decreased firepower to just 72% of what he had before.

What I expect from you is a similar model demonstrating the superiority of wing guns. Be constructive: You've criticized my assumption of a Gaussian distribution long enough, give me something to criticize, too.

Regards,

Henning (HoHun)

[Tony Williams]

Originally posted by funkedup
With wing guns you get two areas of hits at close range.  But as you get near convergence they become one large area of hits.  But as range increases beyond the convergence distance,  the dispersion of each gun becomes so large that the effect of the gun spacing is minimized.  The two patterns are centered maybe 15 feet apart but their diameter is so large that they overlap for the most part.

Remember that dispersion is helpful for long range gunnery.  It is unlikely that you will have the enemy perfectly centered in your dispersion pattern, so the aircraft with the widest pattern can get hits even if the aim is off.  And at long range with low-time pilots and rudimentary WWII aiming devices I'm sure this was the rule.

The M61 Vulcan rotary cannon used in post-war jet fighters and AA units actually had to be modified because it was found that more dispersion increased the probability of a hit unless the pilot/gunner had perfect aim.  They altered the gun so that each barrel was "off center" a little bit, giving a nice fat pattern.
 

A couple of comments:

The patterns achieved by wing guns depend on the harmonisation set.  It was not uncommon to set each pair of guns at a different convergence distance. This would lead to a fairly distributed pattern at all practical ranges, but still tending towards the dumb-bell shape, with most bullets at any range striking to either side of the aiming mark.

It is true that increasing the spread of fire does increase the long-range hit probability. However, it really depends what kind of guns you were using, as the odd hit from a machine gun (even a .5") is unlikely to do much damage. The RAF's .303's had to deliver concentrated fire to stand any chance of a kill. Only a cannon shell stands a reasonable chance of inflicting serious damage with one or two hits.

The M61 is available with three different barrel clamps, which provide difference dispersion settings. However, I have the strong impression that the usual clamp provides a very tight group, as USAF pilots who have corresponded with me about this all praise the gun's very high degree of accuracy and limited dispersion.

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://website.lineone.net/~a_g_williams/index.htm
Military gun and ammunition discussion forum:
http://forums.delphiforums.com/autogun/messages

[HoHun]

Hi Funked,

>It's pretty easy to see what Gripen is describing if you try it in Aces High.

Thanks for the additional information! However, I think Gripen and I don't necessarily disagree on pattern size etc., but rather on the conclusions to draw from it.

Regards,

Henning (HoHun)

[gripen]

HoHun,
OK, as you wish. Let's assume  first that aims set what we got from long range is with 99,9% probability within 20m (you can change this to degrees or what ever) from the correct aim (probably optimistic in the case of the average pilot) and let's use standard Gaussian distribution which is very probably untrue because  we don't know if the correct aim is in the set nor  how correct aim and average of the aims set are related.  Then lets assume that target area is within 2m from the center of the aims area then the probability of the correct aim is about:

2/(20*0,33)=0,30 =>  2*0,118= 23,6%

Then lets assume that dispersion is same for wing and fuselage guns (probably untrue but the difference does not affect results very much) so we don't have care about it and the hits set for the wing guns is 2m larger (due to convergence) than aims set so probability of the single hit drops to  21%. But when we ad twice fire rate  ie 25 vs 50  then we got  5,9 hits with the 1x fuselage gun and 10,6 with the  2x wing guns. You can ad  dispersion if you want...

gripen

[Vermillion]

Ok... let me guess. Gripen and HoHun are actually siblings in RL

Is Not !
Is Too !
Is Not !
Is Too !
Is Not !
Is Too !
Is Not !
Is Too !
Is Not !
Is Too !

Any thread that these two start debating in, eventually grows to 100+ in just a couple of days.  

Just kidding guys.

[HoHun]

Hi Gripen,

I'm not quite sure I understand your example yet.

What is your assumption for the bullet dispersion radius for centreline guns and for wing guns respectively?

Do I understand it correctly that your target is a disk of 2 m radius in the centre of the Gauss curve?

Regards,

Henning (HoHun)

[gripen]

HoHun,
My example just counts deflection error ie it's a single dimensional model (real life situation is three dimensional and therefore error is much bigger then). Purpose of the model is just to show how the error caused by large variance (aiming error for deflection at long range) is much more signigant  than error caused by location of the guns.

As noted the model does not count dispersion at all , I have no idea about the size of the dispersion of the HS 404 or MG 151(I'm not gun expert like Tony). If it's as large as Funkedup told  and same for both guns then tthe wing guns combination has clear advantage at long range.

Otherwise model is just a bit of basic statistics ie standard one dimensional Gaussian distribution assuming that 99,9% range is about 2*20m and therefore average error is about 20/3  and the target set is 2*2m in the center of the aims set. I used traditional Z table from my old biometrics book for densityfunction; could not find that  feature from the spreadsheet  

gripen

[HoHun]

Hi Gripen,

>My example just counts deflection error ie it's a single dimensional model

Hm, I still don't understand. Does that mean you increase target area size increases linearly from 2 m for centreline guns to 4 m diameter for wing guns?

>As noted the model does not count dispersion at all

Here's a comparison of available firepower from centreline guns and from wing guns based on the assumption of Gaussian dispersion.

Bullets travel left to right, yellow/orange denotes superior firepower for centreline guns, grey approximately equal firepower, blue superior firepower for wing guns.



Poor quality rendering courtesy of Excel :-(

Regards,

Henning (HoHun)

[gripen]

HoHun,
No, the target size is same (4m for both combinations) as well as the aims set only thing which changes is convergence caused by the guns locations  which is about 2m from the center line in the wing guns plane and  at shooting range (ie 2x convergence range, 300-400m) and this is modeled simply by increasing the size of the hits set to 44m vs  40m in the case of the fuselage gun (no anykind of dispersion modeled).

Seems that you have no much idea what gaussian distribution means. You model assumes that error of the aim is very small. Here is samples assuming 1m target and 5m error which is a very little error at long range (again no dispersion modeled):

fuselage gun
0,5/(5/3)=0,3  => 2*0,1179=0,2358 => 5,9 hits/25 shots

Wing guns
(2-0,5)/1,167=0,9 => 0,3159  => 9,205 hits
(2-2,5)/1,167=1,5 => 0,4332 => 3,34 hits
9,205 -3,34 = 5,865 hits/50 shots

Well, I needed to edit it couple  times; long time since I've done these. Anyway, the samples should show effect of the accuracy at long range.

And if we  assume that dispersion is as large as Funkedup  claimed  (ie dispersion circles cover each other  above convergence range) and bullet density is even inside dispersion circles as your model assumed (which is not necessarily true) then the wing armament allways give better bullet density at the aim point at longer range than convergence range.

gripen

Ah, (edited again for formula error) I forget to ad effect of the smaller target to the wing guns (not really needed for 4m target).

gripen

[HoHun]

Hi Gripen,

Do I understand it correctly that you simulate wing guns by increasing standard deviation of the aiming error by 10% and then doubling the number of hits?

Regards,

Henning (HoHun)

[gripen]

HoHun,
In my first example I did so , but purpose of the example was just to show  effect of the increased variance (as noted and which is the one of the main problems of your model; you assume far too small aiming error) or in other words standard deviation ie square root of the variance.  My other example includes ( after couple  edits ) calculation for  error caused by location of the guns, still it does not include dispersion  which actually favors wing guns.

Anyway, we don't know if the distribution of the aims set behaves like Gaussian distribution; so overall these are just speculations.

gripen

[HoHun]

Hi Gripen,

(Nonsense deleted. Staring at a copy until it makes sense again ;-)

Regards,

Henning (HoHun)

[HoHun]

Hi again,

I posted nonsense, please disregard while I fix it :-)


Regards,

Henning (HoHun)

[HoHun]

Hi Gripen,

OK, I understand both of your examples now. Let's work with your second example since it actually includes the off-centre placement of the wing guns.

(Under construction)

Regards,

Henning (HoHun)

[gripen]

HoHun,
LOL... but please note that my second example is still a simplified single dimension model the like first one. Well, normally teachers get paid for their work  

gripen