# What aircraft gun round had the flattest trajectory?



## DAVIDICUS (Mar 8, 2005)

I understand that the .50 BMG was extremely flat shooting. Were there other cartridges that shot flatter?


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## delcyros (Mar 9, 2005)

How about MG 131, MK 103 and MG 213B/20mm? They should come close if not better...


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## DAVIDICUS (Mar 9, 2005)

I don't know. It depends on their muzzle velocity and ballistic coefficient (how easily they can slip through the air).


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## delcyros (Mar 10, 2005)

Muzzle velocity was excellent on these guns but I think, I don´t have enoug datas to post a solution. Maybe Lunatic can help with that. (My books are still packed)


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## The Jug Rules! (Mar 10, 2005)

I've never heard of an mg 213? Any info on it???


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## CharlesBronson (Mar 10, 2005)

The MG-213 o Mk-213 is a revolver cannon wich was developed in the very late stage of war








It was available in 2 calibers one was the 20x135mm derived from 20mm flak, and 30x85B 

The rate of fire was 1100-1300, the modern series of Aden, Defa, and Mauser BK-27 was derivated from it.


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## The Jug Rules! (Mar 11, 2005)

If that had made it into the war, things could have really gotten messy...


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## Anonymous (Mar 24, 2005)

The MK213 did not make WWII, it was still a good ways off when the war ended.

The MG131 13mm had poor ballistics, its sectional density of 0.256 (grams/sq. mm) is one of the poorest of all HMG's/cannon of WWII, and its velocity less than 750 m/s was not great either. The API round would have a little better SD, but lower veloctiy. This gun did not have good ballistics, but they were well matched to the MG151/20.

In my opinion, the BK5 firing AP ammo probably had the flattest trajectory. At 50mm and weighing 1540 grams, the sectional density of this round was a wopping 0.785 (grams/square mm), over twice that of .50 BMG AP round. Combine with its initial velocity of 920 m/s and it was probably the flattest shooting, longest ranged round of WWII aircraft.

The Soviet NS37 was a close contender, with a sectional density of 0.696 and an initial velocity of 890 m/s. The US M9 was similar (though very slightly less velocity and SD).

Generally speaking, it is hard for a small round to compare to a large one, as the sectional density tends to be relatively low. The .50 BMG had a high sectional density (0.383) because the round is quite long for its caliber. The .50 had the best ballistic shape of any round in WWII, but this is overcome by the huge SD advantage of some of the larger rounds (but none in the 20mm class).

=S=

Lunatic


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## DAVIDICUS (Mar 24, 2005)

Good info. Thanks.

I always suspected that the .50 BMG was a flatter shooter than the Hispano 20mm's.


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## Anonymous (Mar 24, 2005)

http://members.cox.net/rg_lunatic/gunpage/

The page is damaged (part of it is missing) but the table is still good.

=S=

Lunatic


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## DAVIDICUS (Mar 24, 2005)

Outstanding collection of data.


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## delcyros (Mar 22, 2006)

absolutely.
Excellent work, Lunatic. I only miss the soviet UKB and the german MG 151 with 15 mm AP cartridge. I expect both to have a somehow similar and/or better trajectory compared with the 0.50 cal BMG. And both are nearly around the same weight class.

Can You tell me more about the Baltraj software?
Keep up Your good work!


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## lesofprimus (Mar 22, 2006)

Dude, u do know that the post above yours was from last year right???


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## delcyros (Mar 22, 2006)

correct. But I had a refreshed interest in the matter. Esspecially for the interesting part of projectiles decelerating and the maths behind. The Ballitsic-link from Lun was a quantum leap for me...


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## book1182 (Mar 22, 2006)

Anonymous said:


> Generally speaking, it is hard for a small round to compare to a large one, as the sectional density tends to be relatively low. The .50 BMG had a high sectional density (0.383) because the round is quite long for its caliber. The .50 had the best ballistic shape of any round in WWII, but this is overcome by the huge SD advantage of some of the larger rounds (but none in the 20mm class).
> 
> =S=
> 
> Lunatic



Didn't they base the X-1 off of the shape of a .50cal bullet???


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## delcyros (Mar 23, 2006)

Yes for so far. The hull diameter is based somehow but not directly on the 0.50 bullet.
The sectional density of the 0.50 BMG is LOWER than both, soviet Berezin univerzal 0.50 (which also was the base for the US API bullet in some aspects) and MG 151 with 15 mm cartridge firing AP rounds. All three are exceptionally good for their calibre class. The 0.50´s both have excellent projectile shapes but the 151/15 isn´t that bad either (except for blund shaped HEI rounds), especcially the lighter APR round.


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## Lunatic (Mar 23, 2006)

delcyros said:


> How about MG 131, MK 103 and MG 213B/20mm? They should come close if not better...



The MG131 had poor ballistics. In fact, they were almost identical to those of the MG151/20, which made it a good gun to pair with that 20mm. The 13mm's sectional density is poor and mv is releatively low.

The MK103 did indeed have very good ballistics, especially when firing AP rounds which were pointed. The BC of the round was not as good as that of the .50 BMG, but the sectional density (weight vs. horizontal section) was very high, more than overcomming the difference in ogive shape. Genrally speaking, larger caliber rounds tend to have better overall ballistics because the volume is increasing as a cube function, where the frontal area is increasing as a square function so doubling the size of a round increases its frontal cross section by 4x but its weight by 8x. The .50 has an unusually high BC because the projectile is quite long for its daimeter, leading to a high sectional density.

=S=


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## delcyros (Mar 23, 2006)

Well said. I understand now the shortcomings of MG 131 and MG 151/20.
But what about the UKB and 151/15 in direct comparison to the 0.50 cal. BMG? The UKB had the same calibre, a comparable shaped projectile, when firing AP or API rounds but more weight (and therefore a higher sectional density). The 151/15 firing AP rounds isn´t that bad either but has more muzzle velocity. When firing the lighter APR round it has substantially more muzzle velocity but I expect the shell to loose it´s velocity advantage quite soon due to a lower sectional density. Corretc?


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## Lunatic (Mar 24, 2006)

delcyros said:


> Well said. I understand now the shortcomings of MG 131 and MG 151/20.
> But what about the UKB and 151/15 in direct comparison to the 0.50 cal. BMG? The UKB had the same calibre, a comparable shaped projectile, when firing AP or API rounds but more weight (and therefore a higher sectional density). The 151/15 firing AP rounds isn´t that bad either but has more muzzle velocity. When firing the lighter APR round it has substantially more muzzle velocity but I expect the shell to loose it´s velocity advantage quite soon due to a lower sectional density. Corretc?



The Brezin UBK was an excellent gun. The .50 BMG had the advantage of firing M8 API rounds, in almost every other respect the UBK (or UBS or UBT) was the better gun.

The MG151/15's only drawback was a lower RoF, something around 600 650 real world RoF IIRC, about 100-150 rpms less than the 20mm version. Other than that it was a pretty powerful gun for its caliber. The MG151/15 also had good sectional density figures - better than those of the MG151/20. I believe the round and projectiles were the same length, so that means higher SD. Personally I feel the Germans abandon this caliber too early, but their objective was to destroy 4 engine bombers, and for that the HE of the 20mm gives a clear advantage.


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## delcyros (Mar 24, 2006)

By the time the Luftwaffe replaced the 151/15 in mid 1942, there wasn´t a serious problem with four engined heavies. Not intending to say there weren´t but it seems they preferred the higher HE ordenance generally. I read once that pilots with good marksmanship preferred the 151/15 while the average pilot found it more simple to get kills with 20mm HE rounds. 
I do personally agree that the 151/15 was rejected too early. 600-650 rpm with average gunwear is ok And I never understood why they replaced the 15mm variant in fighter bombers. The penetration figures of the 151/15 are way superior to those for the 151/20.


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## Jabberwocky (Mar 24, 2006)

Probably because the general purpose bomb and Anti armour submunitions were more effective and less risky when engaging enemy tanks and or supply elements. Also, I imagine that when pilots were already complaining of the 15mms lack of punch against fighters, its a very difficult thing to engage a tank with what is percieved to be an underpowered gun and come away with some hope of sucess.


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## Soren (Mar 24, 2006)

*15mm MG151/15:* 

MV (AP): 850 m/s
MV (HE): 960 m/s

AP projectile weight: 72 gram (1,111.12 grains)
HE Projectile weight: 57 gram (879.64 grains)

AP projectile SD: .456
HE projectile SD: .361

*20mm MG151/20:* 

MV (API): 720 m/s 
MV (HET): 720 m/s
MV (HE"M"): 800 m/s

API projectile weight: 117 gram (1,805 grains)
HET projectile weight: 115 gram (1,774 grains)
HE"M" projectile weight: 92 gram (1,419 grains)

API projectile SD: .416
HET projectile SD: .409
HE"M" projectile SD: .327

*30mm MK108:* 

MV (HE"M"): 505 m/s

HE"M" projectile weight: 330 gram (5,092 grains)

HE"M" projectile SD: .522

*12.7mm M2 Browning:* 

MV (API): 890 m/s

API projectile weight: 43 gram (663.5 grains)

API projectile SD: .379

*13mm MG131:* 

MV (API): 710 m/s
MV (APT): 710 m/s
MV (HET): 750 m/s

API projectile weight: 38 gram (586.4 grains)
APT projectile weight: 38.5 gram (594.1 grains)
HET projectile weight: 34 gram (524.7 grains)

API projectile SD: .321
APT projectile SD: .325
HET projectile SD: .287
_______________________________________________

Now for comparison's sake the German standard issue 7.92mm rifle round at 792 m/s with a FMJ boat-tail projectile at a weight of 12.8 grams (198 grains) with a SD of .292, has a BC of around .560-.580. That means that at 600m distance the velocity has dropped to around 509-517 m/s, and the time of flight to that distance is 0.94 sec. The time of flight out to 300m, which could be considered a medium range for opening fire on your target, will take the round 0.42 sec to reach, much quicker than any enemy fighter can react on being fired upon. At a 200m distance, which could be considered the normal range for opening fire on your target, the round will reach its target in 0.27 sec, and again this leaves the enemy fighter no chance of evading.

Now I think we can all agree that the 7.92mm rifle projectile didn't have the same ballistic qualities of the much heavier machinegun and cannon projectiles on the late war fighters, so if the 7.92mm round can hit without a problem out to 300m without leaving the enemy fighter a chance to evade, the cannons should do an even better job.

The gun above with the slowest MV is the 30mm MK108, however its projectile has a high SD, and all else being equal a higher SD means a higher BC. An educated and calculated guess of its flight time out to 300m gives a time of 0.63 sec, still fast enough for the enemy being unable to react and evade in time. So this gun is perfectly capable as a Fighter vs Fighter armament, and requires only a single hit to destroy its target. (And with the exception of usually not destroying its target with the first hit, the exact same applies for the MG151/20)

Now on to the question of which of the guns above has the flattest trajectory, it is clearly the 15mm MG151.


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## delcyros (Mar 25, 2006)

I don´t think this explenation hits the point, Jabberwoky. According to may analysis the 15 mm MG151 has an initial armorpenetration at 0 degrees impact angle and zero distance (basic penetration) of 46mm for AP-rounds and even 60-62mm for APR rounds. The 20mm variant using API-rounds will not exceed 34 mm of basic penetration! The 15mm rounds will also keep their energy much better due to a higher SD and BC (nose shape). In this view the 20mm is underpowered, not the MG 151/15, at least against armoured targets. Against soft ones, the 20mm HE round carries nearly twice as much HE-ordenance and therefore is better. 

Soren, Your datas sounds convinving. However, the 30mm round will suffer a drawback due to it´s worser ballistic shape. The BC is influenced a lot by this. Can You tell me how to calculate the time to range figures and, more important, the striking velocity at range figures (or the deceleration rate at range)?


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## Jabberwocky (Mar 25, 2006)

delcyros said:


> I don´t think this explenation hits the point, Jabberwoky. According to may analysis the 15 mm MG151 has an initial armorpenetration at 0 degrees impact angle and zero distance (basic penetration) of 46mm for AP-rounds and even 60-62mm for APR rounds. The 20mm variant using API-rounds will not exceed 34 mm of basic penetration! The 15mm rounds will also keep their energy much better due to a higher SD and BC (nose shape). In this view the 20mm is underpowered, not the MG 151/15, at least against armoured targets. Against soft ones, the 20mm HE round carries nearly twice as much HE-ordenance and therefore is better.



However, when we look at German ground attack aircraft we see that it was the 20mm and not the 15mm that was fitted as the standard armament, even when the 15mm clearly has better AP perfomance. After the 109F1/F2, very few LuftWaffe planes carried the 15mm.

The HS-129 had a pair of MG151/20s
The HS-123, used primarily as a dive bomber, sometimes mounted a pair of 20mms.
The 190F, a specialised ground attack 190, mounted 2 MG 151/20s.

So the question is why? We know that the MG 151/15 had excellent AP performance. I'm sure that the LuftWaffe did as well. But they chose to stick with the 20mm or go for larger calibres like 30mm, 37mm, 50mm and even 75mm in specalised AT roles.

My guess is that the LuftWaffe judged the 20mm calibre to be more effective against soft targets and thought that was more important than effectiveness against armoured targets like tanks. When they were serious about using aircraft to knock out armour, they went to the 30mm or higher.

I'm not arguing that the 15mm would of been ineffective. I'm just trying to work out the logic of fitting the 20mm as standard over the 15mm in ground attack roles, where the planes are more likely to run into armour.


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## Soren (Mar 25, 2006)

delcyros said:


> Soren, Your datas sounds convinving. However, the 30mm round will suffer a drawback due to it´s worser ballistic shape. The BC is influenced a lot by this.



What your talking about is called the "Form Factor" or FF, and no the 30mm HE"M" projectile doesn't necessarily have a worse BC because of its FF, although it is true that some of the HE"M" projectiles aren't ballistically very efficient compared to their size and SD(Infact none of them really are, but some are definitely worse than others), which is because of their FF. However not all the HE"M" projectiles have such a inefficient FF.

Here you can see two different examples of the 30mm HE"M" projectiles used by the Mk108(The one to the left obviously the most efficient ballistically) : 








delcyros said:


> Can You tell me how to calculate the time to range figures and, more important, the striking velocity at range figures (or the deceleration rate at range)?



I used Norma's own ballistics program to calculate the trajectory and flight time of the 7.92mm projectile(You can choose yourself between Metric or Imperial units): http://www.norma.cc/sida/eng/index.html


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## delcyros (Mar 26, 2006)

I sadly couldn´t acces Norma.
From what I understand, the trajectory can be calculated via sectional density and form factor.
Here is what I got to this moment (am not sure if all is correct):
metric measurement:
W= projectile weight in grams x 1.422 (this seems to be a constantum but why?)
D(x2)= square of the calibre in mm
SD= W/D(x2)
The higher the SD the better the velocity retention (assuming an equal FF)
The FF (form factor) is more difficult to extrapolate. I lean on empiric datas:
FF=
flat nosed lead: 0.8
round nosed lead: 0.9
round nose-jacketed: 1.0
semi-pointed-soft point: 0.9-1.1 
pointed soft point (depending on sharpness): 1.2-1.6
pointed full jacket: 1.5-1.8
pointed full jacket and boat tailed: 2.0
The FF differs in supersonic and subsonic speeds, so a drop under Mach 1.3 will cause FF differences of the same projectile.
The result of SD x FF (correct relation?) gives the BC.
The BC will give the true deceleration rate but in how far? 
(for each 100m distance): BC=0.15--0.20--0.25--0.30--0.35--0.40--0.45--0.50--0.55--0.60
%=-25----18----14---11.5--9.5----8-----7-----6.5---?------?
I still have no clue how the deceleration rate develops at higher BC (and what formula is used for calculation of speed loss) and I also don´t know why the atmosspheric factor isn´t involved (high altitude=low air density=higher speed retention and vice versa in low altitudes).
Jabberwoky, I totally agree with you. No ww2 20mm gun present any harm for main battle tanks and soft targets were more often encountered anyway. Had they deal with tanks, they generally preferred bombs, heavy cannons and/or rockets.


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## Soren (Apr 6, 2006)

delcyros said:


> I sadly couldn´t acces Norma.



Try this one then: http://www.biggameinfo.com/BalCalc.aspx 




delcyros said:


> From what I understand, the trajectory can be calculated via sectional density and form factor.
> Here is what I got to this moment (am not sure if all is correct):
> metric measurement:
> W= projectile weight in grams x 1.422 (this seems to be a constantum but why?)
> ...



Accurately calculating the trajectory and deceleration rate by hand is impossible if you haven't got the exact specifications of the projectile as-well conducted real life firing tests.

Now I don't exactly remember the usual drag function of a bullet like the 7.92mm FMJ-BT projectile, but IIRC it is G7. (The standard used for all projectiles being G1, which however is not accurate for FMJ-BT projectiles)


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## Erich (Apr 6, 2006)

Soren your diagrahm shows the Incendiary and also Tracer round with Glimmspur on the left and the standard HE Minengeschoss on the right with blunt head

there are at least 8 rounds used for the Luftwaffe's arsenal including at leat 4-5 different practice rounds in the 3cm line-up

By the way your copyrighted image comes from the Bf 109 book by Robert Grinsell via Crown publishers, NY


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## Soren (Apr 6, 2006)

Thanks for the correction. Do you have any pictures of the different rounds Erich ? (Would be higly appriciated)


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## delcyros (Apr 7, 2006)

The link works fine, thanks.
I wonder why nowhere in the net is a basic calculating program for trajectory and deceleration (the link offers solutions for up to 20 mm rounds). 
Thanks again.


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