Gun precision / dispersion

[TTTT]

Gentlemen, I found the following from user "fsimon" on the "Was the battleship Bismarck really the best of its time?" thread (page 7) interesting. It wasn't commented on in the followup replies, so I thought I could take it here. I have edited a bit to make things clearer.

"2.1.1 Gun precision / dispersion:

Bismarck/Tirpitz
“One of the charts and graphs from GkDos100 shows the 50% Längenstreuung of the various German naval guns as % of range. The 38cm SKC/34 shows a curve of about 0.42% of the range from 16km through about 27km. It is less than 0.5% from about 12km through 30km. Even at 36km it is no more than 0.6%. The Tirpitz practice shoot photos at 25,000 meters (27,400 yards) indicate that the scatter was actually a bit less than predicted.”
I don’t know how the 50% Längenstreuung is comparable to other figures of pattern size of other navies, but this seems to be rather tight.

Other information: 120meters at 20km is from Tirpitz 2-gun 38cm gunfire. Same guns had about 140m at 25km.

New US battleships.
Massachussets Casablanca 1942: 220m@ 20-24km =1%

Fast US BB Jurens/Fischer study Mark8 AP Projectile 1.6%

"The Bureau of Ordnance expected the nine-gun patterns given by the 16-inch batteries mounted aboard the Washingtons, South Dakotas and Iowas to be slightly larger than the eight-gun pattern sizes for the old 16-inch guns mounted aboard Colorado, Maryland and West Virginia. Specifically, eight old guns were expected to yield an average range pattern of 1.8% of range while nine new guns would give a 1.9% pattern. These were ideal figures; in practice the old 16-inch guns gave a seven-gun pattern size of about 2.2% of range during their last firings in 1941. The dispersion of the 16"/45 and 16"/50 guns, incidentally, was essentially identical; ranging sheets at Dahlgren often listed dispersions for the two types interchangeably. Today, the 16"/50 yields a 9-gun pattern size of about 1.5% of range at short ranges, slightly less if the range is long. Viz. Bulletin of Ordnance Information, No.3, 1945, FTP 2101, Reports on Gunnery Exercises 1940-41 and Naval Weapons Laboratory Tech. Report No. K-26167."
Dispersion of 8-gun salvos (full salvos) was 2.4% - 2.6% of range for the old 16" at ranges of 27000 yards.

Queen Elisabeth class: 250m @16-21km 1.56%

My comment: According to Wikipedia "According to an American report produced after World War II, the British 15 inch Mk I was the most reliable and accurate battleship main armament of the war, though other guns and mountings had superior individual features."

Littorio class:
381/50 (OTO manufacture) at 21.000m horizontal spread 290m range spread 267m
381/50 (Ansaldo manufacture) at 22.500m horizontal spread 416m range spread 364m

My comment: A bit surprising, as these guns are often said to have been very accurate.

Richelieu:
At 25km Spreads of 1.4-1.8km 6.84%; after correction in 1948 577m 2.31%
2 guns per turret (4guns per ship): 450m @16-25km = 2.8-1.8%
Single gun 270m 1.69%

My comment: Even when firing 2-gun salvos, this seems pretty poor!

My comment: I have not found any datas on the British 14-inch gun (KGV) or Japanese 18-inch gun.

Comments?

[TTTT]

I understand gun accuracy isn't just a matter of the gun itself, but the design of turret, as well as the seakeeping qualities of the ship.

In Bismarck you have very good high velocity guns with good quality shells in a big twin turret with good distance between the two guns (thus less inteference from the other gun when firing), as well as a ship that is very stable.

In the British 15-inch twin turrets the guns are closer together, but that was probably compensated by firing just one gun at a time.

It is interesting to see that US Navy actually expected their new triple turrets to be slightly less accurate than the old twins in the Colorado class, but that it was a trade-off they were willing to take.

Before her upgrades, it seems that Richelieu would be happy to even hit a target the size of a small island! If the numbers are correct. Quad turrets seem to have been generally troublesome. Richelieu struggled with accuracy and slow ROF, KGV with output.

The British 14-inch gun on KGV is generally regarded as a very accurate gun, but I haven't been able to find any number. I would guess the dispersion would be different between the twin vs. the quads?

There's a trade-off whatever design you go with: Twin,triple or quad turrets.

[TTTT]

Yamato
At maximum range of around 45,000 yards the shell dispersion patterns were quite small—440 to 500 yards. USN reports of the battle off Samar commented on the tight patterns from Yamato.

[hans zurbriggen]

Hello Mr. TTTT,
I don't have any info re. US and Japanese guns, and very few for British ones.

Bismarck class 38 cm guns, according to German documents, were best guns among German large calibers (28 cm, 20,3 cm and even 15 cm) at least at usual battle distances. 28 cm from Scharnhorst class were the less good in terms of spread (due to higher muzzle velocity and interferences between guns). As you say, distance between guns, high quality ammunition and platform stability made German 38 cm in twin turret a very precise gun.

British 15" was very accurate and spread was small (also due to relatively slow muzzle velocity and, as you say, firing only odd or even guns at a time in salvoes).
British triple 14" turrets were very troublesome due to their complexity and reduced tolerances in mechanisms that transferred shells and powder from decks to rotating turrets, but I remember that accuracy and spread were good (British quadruple turrets fired only 2, distant, guns at a time in salvoes, e.g gun 1 and 3 in one salvo, gun 2 and 4 in another). Problems with turrets mechanisms were fixed only up to a certain extent after 1941.
I don't have data about British 16" but I suspect relatively larger spread due to their higher muzzle velocity.

Littorio's guns were indeed extremely powerful and accurate despite high muzzle velocity. However, usual practice of firing per turret (interference between three guns fired together) and very poor ammunition quality (in terms of tolerances between shells and charges) negatively affected dispersion. After a while, during war, Italian Navy complaints vs providers made things partially better.

Richelieu's guns were actually very good guns, design of quadruple turret was basically a double twin turret (not too complex design, however with small distances between a pair of guns, that were to be fired together). To make things worse, wartime and France invasion forced Richelieu (and Jean Bart) to leave French dockyards with poor powder and shell quality. Powder bags had even to be manufactured while in Dakar and in Casablanca, mixing Dunkerque's class powder bags, with huge differences between one charge and another. Problem was only partially solved when ammunition was provided by US manufacturers for Richelieu.

hans

[TTTT]

Thanks, interesting to hear about the 28cm guns - it makes sense. They seem to have done rather good in actual combat, though. One survivor from HMS Glorious said that already the very first salvo from the Twins "landed just 10 yards away". And they landed the first hit from around 25,000 meters with the third salvo - the longest hit, shared with Warspite. A bit ironically that the smallest battleship main guns, and one of the oldest, landed the longest hits in history.

No numbers, but all sources seem to agree on Nelson's 16-inch guns having rather large dispersion - which got better with time.

Also read somewhere that Iowa's guns fing the superheavies had initial accuracy problems.

[TTTT]

More on Yamato:

https://www.diepresse.com/4702366/die-s ... chtschiffs

"Als Nachteil erwies sich indes schon bald bei Testschießen, dass die Kanonen im Verhältnis zu ihrem Kaliber relativ kurz waren. Das reduzierte ihre Treffsicherheit und es ergab sich auf große Entfernung eine doch ziemlich große Streuung: Bei Maximalschussweite betrug der Streukreisradius 550 Meter und mehr und ließ einem Ziel darin also relativ viel Platz, um ungeschoren zu bleiben."

"However, test shooting soon revealed that the cannons were relatively short in relation to their caliber. This reduced their accuracy and there was a fairly large spread at long range: at maximum range, the grouping radius was 550 meters and more, leaving a relatively large amount of space for a target to remain unscathed."

[Bill Jurens]

The detailed and rather complex equations that deal with dispersion often present results apparently invalidating the oft-employed (but largely intuitive) solutions revolving around the idea that small dispersion, i.e. small pattern size, is always better than large. Especially as ranges increase, this is often not true; there is, in fact, an optimal dispersion for any target and fire control situation which balances 'scatter of shot' vs hitting probability. In other words, if the fire control solution is not robust, the target is relatively small, poorly located and/or maneuvering unpredictably, and time of flight is long, one might actually increase the percentage of hits on a target by somewhat by actually increasing pattern size. Sometimes a bigger pattern is better...

This sort of concept has to be understood, and employed, carefully, as it implies that there is no need -- and it might actually be counter-productive -- for gunnery officers and operating personnel to spend much time in keeping the main battery in what otherwise might be called 'optimal' condition. Therefore, promoting this was seen, overall, to be perhaps not such a good idea.

We see somewhat idealized aspects of this concept when we note that although we may hunt deer with rifles, it's usually better to shoot at a duck using a shotgun.

Bill Jurens

[fsimon]

In the meantime after my earlier post on "Was the battleship Bismarck really the best of its time?" thread (page 7), I received some further infos. Here is what I gathered so far:

Bismarck / Tirpitz 38cm/52 SKC/34
Actual practice shoots battery spreads indicated 120meters at 20km from 2-gun 38cm gunfire. The same guns had about 140m at 25km. Battery spreads for 4-gun salvos at 25km showed less than 150 meters.
120m / 1.69 * n2 1.414 = 100.4m @ 20km = 0.5%
140m / 1.69 * n2 1.414 = 104.2m @ 25km = 0.417%
150m / 1.69 * n4 1.155 = 102.5m @ 25km = 0.41%
https://www.kbismarck.com/gkdos100a.html W.A.39,16 matches Tirpitz practice shooting very well.

Conversion to US Navy equivalent dispersion values according Delcyros:
https://www.tapatalk.com/groups/warship ... 9-s30.html
With this information it is possible to back-calculate 50% scatter to TMD:
20km: 12.1° elev = 0.5% = 100m x 1.45 = 145m battery dispersion / 1.69 = 85.8m apparent mean dispersion for n8 x 1.069 = 92m (0.458%) TMD @ 20km
23km: 15° elev = 108m x 1.5 = 162m / 1.69 = 95.86 x 1.069 = 102m (0.4455%)
25km: 16.7° elev = 0.44% = 110m x 1.5 = 165 / 1.69 = 97.6 x 1.069 = 104m (0.417%)
28.5km: 20° elev = 120m x 1.5 = 180m / 1.69 = 106x 1.069 = 114m (0.4%)
To put this in relation to 0.429% TMD of the US 16”/50 guns acc. Fischer, Jurens “US Fast battleship gunnery…” we can average this to 0.430% between 20 and 28.5km for Bismarck class, about the range where the US 16” gunnery was also averaged by Fischer, Jurens.

True mean dispersion 0.43% @ 20km = 86m
Average range pattern:
8 guns: 86 x 3.85 = 331m (1.66% of range)
4 guns: 86 x 2.89 = 249m (1.24% of range)

[fsimon]

North Carolina / South Dakota 16” (40.6cm)/45 Mark 6
Bill Jurens’ and Brad Fischer: “Gunnery exercise reports from the WW2...”
Average TMD of 0.383% with AP and service velocity:
True mean dispersion 0.383% @ 20km = 77m (with RPC ≥1943)
Average range pattern @ 20km:
9 guns: 77 x 4 = 306m (1.53% of range)
3 guns: 77 x 2.43 = 186m (0.93% of range)

USS Massachusetts reported 183 - 274m salvo pattern @ 20-24km firing AP rounds during the Casablanca action in 1942, when Massachusetts was still operating with “Follow the Pointer” gun control (i.e. no RPC available).
Average salvo pattern = 227.5m / 2.43 = 93.62m @ average range = 22km = 0.426%
True mean dispersion 0.426% @ 20km = 85m
Average range pattern @ 20km:
9 guns: 85 x 4 = 340m (% of range)
3 guns: 85 x 2.43 = 206m (% of range)

[fsimon]

Iowa 16” (40.6cm)/50 Mark 7
Iowa featured RPC from commission on. Bill Jurens’ and Brad Fischer: “Gunnery exercise reports from the WW2 era showed an average TMD of 0.429% with AP and service velocity.”
This translates to 1.716% of range for a 9-gun pattern.
True mean dispersion 0.429% @ 20km = 86m
Average range pattern @ 20km:
9 guns: 86 x 4 = 344m (1.72% of range)
3 guns: 86 x 2.43 = 209m (1.05% of range)

[fsimon]

Yamato 46cm/45 Type 94
400 to 500m spread at max range (assuming 42km)
450/ 42,000 = 1.07%
1.07% @ 20km = 214m
Assuming 3gun salvos 214/2.43 = 88m
True mean dispersion 0.44% @ 20 km = 88m
9 guns: 88 x 4 = 352m (1.76% of range)
3 guns: 88 x 2.43 = 214m (1.07% of range)

This is very vague!

[fsimon]

UK 15” (38cm)/42 H.M.S. Hood Association-Battle Cruiser Hood: H.M.S. Hood Reference Materials - ADM 239/137: C.B. 3001 (39) Progress in Naval Gunnery 1939 ( (hmshood.org.uk)
Average spread:
246/15,000 = 1.64%
253/14,000 = 1.8%
(227/11,200 = 2%) excluded for short range
190/14,200 = 1.34%
258/13,400 = 1.93%
226/15,300 = 1.48%
182/14,400 = 1.26%
Average = 1.575% @ 20 km = 315m average spread
Assuming 4 gun salvos to be the normal firing procedure:
4 gun spread 315m / 2.89 = 109m
True mean dispersion 0.544% @ 20km = 109m
Average range pattern:
8 guns: 109 x 3.85 = 420m (2.1% of range)
4 guns: 109 x 2.89 = 315m (1.58% of range)

[fsimon]

King George V 14”(356mm)/45
UK 14" MK VII range accuracy WO195/7735 kindly provided by Neil Sterling
@ Mean range = 18.330yd => Mean 50% zone = 211.5yd / 1.692 = 125yd TMD = 114.3m
Or by delcyros: standard deviation 141.5 yd x 0.7971 = 112.7 yd TMD = 0.615%

Averaging TMD for salvo firings >20,000yd
4gun: 401/2.89=138.75/21,400=0.648%
5gun: 401/3.21=124.92/21,400=0.584%
4gun: 352/2.89=121.80/20,600=0.591%
5gun: 352/3.21=109.66/20,006=0.532%
4gun: 348/2.89=120.42/20,700=0.582%
5gun: 348/3.21=108.41/20,700=0.524%
4gun: 375/2.89=129.76/23,200=0.559%
5gun: 375/3.21=116.82/23,200=0.504%
5gun: 388/3.21=120.87/21,200=0.570%
True mean dispersion 0.566% @ 20km = 113m
Average range pattern @ 20km:
10 guns: 113m x 4.13 = 468m
5 guns: 113m x 3.21 = 363m

[fsimon]

Rodney 16”(40.6cm)/45 Mark I H.M.S. Hood Association-Battle Cruiser Hood: H.M.S. Hood Reference Materials - ADM 239/137: C.B. 3001 (39) Progress in Naval Gunnery 1939 ( (hmshood.org.uk)
Average spread:
269/17,300 = 1.55%
418/18,300 = 2.28%
276/17,700 = 1.56%
328/16,000 = 2.05%
178/19,400 = 0.91%
326/16,000 = 2.03%
Average = 1.73% @ 20 km = 346m average spread
Assuming 4/5 gun salvo as normal firing procedure.
4 gun spread 346m / 2.89 = 120m = 0.6%
5 gun spread 346m / 3.21= 108m = 0.54%
Average = 114m
True mean dispersion 0.57% @ 20km = 114m
Average range pattern @ 20km:
9 guns: 114m x 4 = 456m
4 guns: 114 x 2.89 = 329m

[fsimon]

Littorio 381mm/50

If Longitudinal Spread is the 50% zone as described in the Bagnasco book, then:
364m / 1.692 = 215m TMD @ 22.5 km = 0.96% => 191m TMD @ 20km Ansaldo
267m / 1.692 = 158m TMD @ 21km = 0.75% => 150m TMD @ 20km OTO
If longitudinal dispersion is the average of the deviation in range x 2 as described in the Bagnasco book and assuming nine shots (n9) being the basis, then:
416m/2=213m AMDx n9:1,061=226m TMD @ 22,500m = 1%=> 200m TMD @20km Ansaldo
290m/2=145m AMDx n9:1.061=154m TMD @ 21,000m = 0.73% =>146m TMD @ 20kmOTO
True mean dispersion 0.74% @ 20km = 148m OTO (0.98%; 196m Ansaldo)
Average range pattern @ 20km:
9 guns: 148m (196m) x 4 = 592m (784m)
3 guns: 148m (196m) x 2.43 = 360m (476m)