Calculated "base" dispersion of guns based on energy delivered

[GODO]

The purpose of this thread is to reach a calculated dispersion for these guns which real dispersion is unknown, and without considering where and how the guns were mounted.

I will start with the following page to calculate kinetic energy (1/2 * m * V^2) per minute for some representative guns (mass of the round (M) in Kg, muzzle vel (MV) in m/s, energy (E) per minute in Mj/min and rounds per minute (RPM) ):

Gun Tables

MG131 (unsync?): M 0.036Kg, MV 730 m/s, RPM 900 -> E 8.63
MG-FF: M 0.134Kg, MV 600 m/s, RPM 530 -> E 12.78
50"M2 (unsync): M 0.043Kg, MV 880 m/s, RPM 850 -> E 14.15
Type99(2): M 0.128Kg, MV 750 m/s, RPM 490 -> E 17.64
HO-5-2 (sync): M 0.096Kg, MV 715 m/s, RPM 750 -> 18.4
MG151/20 (sync): M 0.105Kg, MV 725 m/s, RPM 700 -> E 19.31
ShVAK (unsync): M 0.095Kg, MV 770 m/s, RPM 800 -> E 22.5
Mk108: M 0.330Kg, MV 505 m/s, RPM 600 -> E 25.24
Hispano MkII: M 0.130Kg, MV 880 m/s, RPM 600 -> E 30.2
NS37: M 0.748Kg, MV 890 m/s, RPM 250 -> E 74.06

From these values, and knowing the real dispersion of one of them (nose mounted), we can extrapolate the rest of dispersions for nose mounted guns. And the figure out how dispersion would be increased for other mountings.

[HoHun]

Hi Godo,

>From these values, and knowing the real dispersion of one of them (nose mounted), we can extrapolate the rest of dispersions for nose mounted guns.

Well, how that? :-)

Regards,

Henning (HoHun)

[Karnak]

Originally posted by HoHun
Hi Godo,

>From these values, and knowing the real dispersion of one of them (nose mounted), we can extrapolate the rest of dispersions for nose mounted guns.

Well, how that? :-)

I think he is talking about guestimating the dispersion as an educated guess is better than a generic setup.

With minor reservations, I agree with MANDOBLE in this case.

[GODO]

HoHun,
While real dispersion numbers arrive for every gun and mounting, it is better to have a generic dispersion, but not so generic like current one.

Now imagine you have a "generic" gun able to shot pretty different rounds, with different muzzle vels and weights, and that "imaginary" gun has a particular ROF for every round type. We can try to calculate "good-enough-for-the-moment" dispersions based on the energy delivered of that gun per minute. For this imaginary gun, the more the energy, the more the dispersion. Now, if we can match some of the energy values per round type with the corresponding real guns and their dispersion, we can extrapolate the rest of the "now-not-so-generic" calculated dispersions for that "generic" gun.

A very basic example, you have 3 real guns, A, B and C. The corresponding kinetic energies per minute at 10MJ/min, 20MJ/min, and 40MJ/min. You already know the real dispersion of a nose mounted gun type B, lets say 4 mils. Then you extrapolate for A and C resulting into 2 and 8 calculated mils respectively.

[HoHun]

Hi Godo,

>While real dispersion numbers arrive for every gun and mounting, it is better to have a generic dispersion, but not so generic like current one.

Well, it won't work.

Using d ~ ROF * m * v^2.5 gives good fit for the MG FF/M, MG151/20 and MK108. However, it would make the high-velocity MK103 look like a rapid-fire blunderbuss, and the RCMGs would become laser guns.

You just can't match historical values that way.

Regards,

Henning (HoHun)

[Tony Williams]

Agree with Henning. There is no necessary relationship between gun power and dispersion; it depends on the gun mechanism and ammunition.

The Browning was never a particularly accurate gun in any calibre - the short-recoil design meant that the barrel had to move around instead of being fixed. The Hispano was reckoned to be significantly more accurate.

Mixed ammo, such as the German 20mm where the M-Geschoss and AP/HE-T rounds had very different weights and muzzle velocities, would produce considerable dispersion.

The mounting of the guns - especially wing v fuselage - had considerably more effect than the weapons. This is not only because wings are less rigid, but also because the dispersion of the entire armament system is what matters in practice, and wing-guns obviously produced greater dispersion.

Tony Williams: Military gun and ammunition website and Discussion forum

[GODO]

Originally posted by HoHun
You just can't match historical values that way.

I know, I cant. Problem is that Pyro does not have historical values for every weapon and weapon mounting, so, AH is currently using a generic dispersion based only in caliber of the gun. Making dispersion a function of the energy and the placement of the weapon would give us a much better and much "rich" dispersion modeling.

And I do not pretend to calculate historical values, but "good-enough" relative values between the guns.

If kinetic energy * ROF is not good enough (I agree, but is still better than none), what other formula would you propose?


Tony, there are two threads already opened related to dispersion: one for real historical known dispersions and the other is this one. This one is to propose a mechanism to set the dispersion of guns when you dont have historical data about dispersion of these guns, but you still have accurate data about round weight, muzzle velocity and ROF.

[gripen]

I'm not convinced at all if there is sense to calculate dispersion. In the case of some Russian guns (at least in the case of the 23mm), the mountings were actually designed so that there were some amount of loosenes to have dispersion built in and to increase probability of the hit. Sort of shot gun effect infact.

Shortly, dispersion of a gun depends probably much more on mounting itself than location of the gun or kinetic energy or rate of fire.

gripen

[HoHun]

Hi Godo,

>If kinetic energy * ROF is not good enough (I agree, but is still better than none), what other formula would you propose?

We could have a look at something like v0 ^ (1/x1) * (bore ^(1/x2) * barrel length ^ (1/x3) or something, with a modifier for mechanism type. With suitably chosen 2 > x1, x2, x3 > 1 we might be able to match the historical data and get a plausible result for the rest.

(That's just an improvisation, I haven't really checked this formula yet.)

Regards,

Henning (HoHun)

[GODO]

Originally posted by gripen
I'm not convinced at all if there is sense to calculate dispersion.

Im convinced of the opposite.

[Wotan]

Is it possible that Pyro sent you on a wild goose chase so that you would discover on your own the futility of your argument...?

Ever consider that?

[GODO]

Originally posted by Wotan
Ever consider that?

Are you really considering that?

Hohun, what is X1, X2 and X3? Is that formula based on something?

[Wotan]

yup...

But only he knows...

[HoHun]

Hi Godo,

>Hohun, what is X1, X2 and X3?

Three arbitrary parameters adjustable to match a mathematical function to historic evidence.

>Is that formula based on something?

It's based on nothing but my idea that it might match historical evidence :-)

Regards,

Henning (HoHun)

[HoHun]

Hi everyone,

After toying around with the data for hours, I've come up with the following formula:

dispersion% = a1 * bore% ^ 4 + a2 * barrel_length% ^ 2 + a3 * rate_of_fire% ^ 2

(All input values as percentages relative to a random reference gun with known dispersion. I picked the MG FF/M, but you get the same results whatever reference you choose.)

The exponents are arbitrary, but it was my impression that large calibre was the most significant contributor to dispersion. (You can see this in the MK108 with low barrel length and medium rate of fire).

Surprisingly, muzzle velocity didn't seem to have much impact on dispersion. Probably the primary parameter really is barrel length since it actually determines muzzle velocity.

a1, a2, a3 were determined to fit historical values for the German guns. I got a1 = 0.266, a2 = 0.837, a3 = 1.101.

The formula matches the following historical dispersion values:

MG FF/M - 1.0 mil
MG 151/20 - 1.9 mil
MK 108 - 1.5 mil
MK 103 - 2.0 mil

It extrapolates the following dispersions:

Browning 12.7 mm - 2.1 mil
Browning 7.7 mm - 3.3 mil
Hispano II - 2.5 mil

The 12.7 mm Browning value seems fine, only slightly worse than the MG151/20, which is what the 6 mil resp. 5 mil figures for wing mounted weapons of this type suggested, too.

The 7.7 mm Browning had a reputation for wide dispersion, so I think this might be OK, too :-)

The Hispano II - well, I don't know. It has a longer barrel and a larger calibre than the Browning 12.7 mm, so it's not suprising it comes out slightly worse.

Regards,

Henning (HoHun)