Fast Battleship League Table

[Mostlyharmless]

There is a severe problem in estimating the chances of a shell hitting below the level of the main belt because we do not know how the various shells would behave after hitting the sea. Japanese Type 91 shells were designed to maintain a stable trajectory and estimated to loose half their velocity after 100 calibres. Unfortunately, the details of the testing have not survived so we do not know if they always or mostly performed as intended. The hits by cruisers are the best clues that it sometimes worked.

German shells also had a "sombrero" shape which should give a stable trajectory but might slow down quicker (and had much less fuse delay). Earlier Japanese and British shells could give underwater hits in tests such those involving Tosa in 1924 https://en.wikipedia.org/wiki/Japanese_battleship_Tosa or Emperor of India in 1931 https://en.wikipedia.org/wiki/HMS_Emperor_of_India. However, it is hard to know what fraction of shells maintained a stable trajectory. It has been suggested that violent changes of orientation could have disabled the fuse of the 38 cm shell from Bismarck that hit Prince of Wales deep under water.

What is obvious is that Yamato is well protected from such hits whilst Bismarck, Littorio and North Carolina are relatively vulnerable. King George V (and Vanguard) and South Dakota (and Iowa) are intermediate and have very similar protection against shells from the beam. However South Dakota may be more vulnerable at 30 degrees. Quantifying the advantages of deeper belts is just geometry if one can guess how the shells behave after hitting the water.

[Mostlyharmless]

A small issue with the encounters using radar is that some of the ships, such as Duke of York, were equipped with radar jamming equipment by 1943 as briefly mentioned in "German Capital Ships and Raiders in World War II: From Scharnhorst to Tirpitz, 1942-1944" which is a very respectable source as it is a compendium of four Battle Summaries or Naval Staff Histories produced soon after the war by the Naval Historical Branch of the Admiralty https://books.google.co.uk/books?redir_ ... ng&f=false.

[fsimon]

...
What is obvious is that Yamato is well protected from such hits whilst Bismarck, Littorio and North Carolina are relatively vulnerable. King George V (and Vanguard) and South Dakota (and Iowa) are intermediate and have very similar protection against shells from the beam. However South Dakota may be more vulnerable at 30 degrees. Quantifying the advantages of deeper belts is just geometry if one can guess how the shells behave after hitting the water.

Thank you very much for this. So, until we find a way to consider this better, I will give only Yamato one point advantage in penetration, like I described in the example earlier. Would you concur?

[fsimon]

A small issue with the encounters using radar is that some of the ships, such as Duke of York, were equipped with radar jamming equipment by 1943 as briefly mentioned in "German Capital Ships and Raiders in World War II: From Scharnhorst to Tirpitz, 1942-1944" which is a very respectable source as it is a compendium of four Battle Summaries or Naval Staff Histories produced soon after the war by the Naval Historical Branch of the Admiralty https://books.google.co.uk/books?redir_ ... ng&f=false.

This is an excellent point. Thank you. I am afraid, that this will also be very hard to quantify. If I remeber correctly, and the book, you pointed too, is desribing Scharnhorst and DoY at Northcape, did Scharnhorst hit the jammer on DoY and thereafter did the intensity and / or accuracy of Scharnhorst's fire increase. However Scharnhorst hit DoY despite the jammer. The accuracy could also have increased due to Scharnhorst's crew overcoming the surprise shock.
Scharnhorst carried the new FuMO 26 with the 1.9 x 6.2m antenna on the rear director and the even larger 3.2 x 6.5m antenna on the top director (knocked out by Norfolk). I have read that these radars were tunable in frequency specifically to avoid beeing jammed. So, it is very difficult to quantify the effectiveness of the jammer.

[fsimon]

Since the 9inch part of the belt of Renown protected the vitals at ranges inside 20km fairly well against Scharnhorst's projectiles, when at an 30 angle down to 11km, in combination with the 2inch slope, I am not seeing a grave danger for Repulse anymore. Only the 6inch belt portion could be penetrated to 20km, but projectiles fired inside 20km would most likely not reach the magazines or the mashinery.
So:
Summary day 1939:
1. Hits: Scharnhorst 4.54 : 2.62 Renown (1:0)
2. Explosives: Scharnhorst 17.8kg / 28.8kg Renown (0:1)
3. Belt pen: Scharnhorst 11km/20km : 3km Renown (1:0)

Scharnhorst 2:1 Renown

Summary night 1943:
1. Hits: Scharnhorst 4.54 : 2.62 Renown (1:0)
2. Explosives: Scharnhorst 19kg / 36.9kg Renown (0:1)
3. Belt pen: Scharnhorst 11km/20km : 3km Renown (1:0)
4. Blind fire: Scharnhorst 30km : 19km Renown (1:0)

Scharnhorst 3:1 Renown

[fsimon]

Ranging accuracy:
Scharnhorst:
2x FuMO 26 FCR: 25m, ranging to 40km, blind fire / spotting to 30km
Richelieu:
Type 284P FCR: 36m, ranging to 27km, blind fire / spotting to 19km

Battle range: 25km.

Gun accuracy @ 25km:
Scharnhorst: True Mean Dispersion (TMD) @ 25km: 180m
Richelieu: True Mean Dispersion (TMD) @ 25km: 313m

Danger Zones @ 25km:
Scharnhorst’s guns AoF @ 25km = 24.6° Danger zone vs. Richelieu 10m high 31m beam = 52m
Richelieu guns AoF @ 25km = 22.4° Danger zone vs. Scharnhorst 10m high 28m beam = 51m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 52m / (180m + 25m) = 25.3%
Richelieu: 51m / (313m + 36m) = 14.6%

Projectile times of flight @ 25km:
Scharnhorst: 42s
Richelieu: 42s

Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 2.41%
Richelieu: HP = 1.39%

Initial rate of fire to find the range (IF):
i.e. 60s / (ToF + 20s observation + correction time) x no of guns -10% for expected output misses:
Scharnhorst: 7.84 shots per min
Richelieu: 6.97 shots per min

Rapid Fire rate (RF):
Scharnhorst: 16.2 shots per min
Richelieu: 9.58 shots per min

Average rate (AR) of fire:
Scharnhorst: 12.02 shots per min
Richelieu: 8.28 shots per min

Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 2.41 hits per 10 min
Richelieu: 1.15 hits per 10 min

Scharnhorst would fire a mixture of AP, HE base-fuse and HE nose-fuse rounds at long ranges, when not expecting penetrations and then change to AP round at shorter ranges, when expecting penetrations.

Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Scharnhorst: (7.84+16+21.8kg)/3 x 2.41/ 2 = 18.33kg
Richelieu: 21.9kg x 1.15 / 2 = 12.6kg

Side protection system penetration @ 30° inclination:
Scharnhorst belt:
Scharnhorst could pen Richelieu @ 5km
Richelieu could pen Scharnhorst @ 3km
However Richelieu could also penetrate Scharnhorst through the upper belt (45mm) and the lower armor deck at >22km. Hit probability of Richelieu is only 1.39% and the probability of hitting this section is only ~20% of the danger zone, i.e. ~0.28% probability of hitting through the upper belt. With 83 shots fired in 10 min that is 0.0023 probability.

Summary:
1. Hits: Scharnhorst (120 shots) 2.41 : 1.15 (83 shots) Richelieu (1:0)
2. Explosives: Scharnhorst 18.33kg : 12.6kg Richelieu 1:0)
3. Belt pen: Scharnhorst 5km : 3km Richelieu (1:0)
4. Deck pen inside 25km: Scharnhorst 0 : 3km (22-25km) Richelieu (0:1)

Scharnhorst 3:1 Richelieu

[fsimon]

Ranging accuracy:
Scharnhorst:
2 x FuMO 26 FCR: 25m, blind fire / spotting to 30km
Richelieu:
Type 284M3/P FCR: 36m, blind fire / spotting to 19km

Both will find each other with radar, but only Scharnhorst can spot for fall of shots outside of 20km. Richelieu will chase salvos outside of 20km. Both are now interested in closing to inside 20km, Richelieu to get into radar spotting range and Scharnhorst to start hitting a maneuvering opponent.

Battle range: 20km.

Gun accuracy @ 20km:
Scharnhorst: True Mean Dispersion (TMD) @ 20km: 158m
Richelieu: True Mean Dispersion (TMD) @ 20km: 250m

Danger Zones @ 20km:
Scharnhorst’s guns AoF @ 20km = 16.3° Danger zone vs. Richelieu 10m high 31m beam = 62m
Richelieu guns AoF @ 20km = 15.6° Danger zone vs. Scharnhorst 10m high 28m beam = 62m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 62m / (158m + 25m) = 33.9%
Richelieu: 62m / (250m + 36) = 21.7%

Projectile times of flight @ 20km:
Scharnhorst: 31s
Richelieu: 31s

Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 4.37%
Richelieu: HP = 2.8%

Initial rate of fire to find the range (IF):
i.e. 60s / (ToF + 20s observation + correction time) x no of guns -10% for expected output misses:
Scharnhorst: 9.53 shots per min
Richelieu: 8.47 shots per min

Rapid Fire rate (RF):
Scharnhorst: 16.2 shots per min
Richelieu: 9.58 shots per min

Average rate (AR) of fire:
Scharnhorst: 12.86 shots per min
Richelieu: 9.03 shots per min

Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 5.62 hits per 10 min
Richelieu: 2.53 hits per 10 min

Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Scharnhorst: (7.84+16+21.8kg)/3 x 5.62 / 2 = 42.7kg
Richelieu: 21.9kg x 2.53 / 2 = 27.7kg

Side protection system penetration @ 30° inclination:
Scharnhorst could penetrate Richelieu @ 5km
Richelieu could penetrate Scharnhorst @ 3km

Summary:
1. Hits: Scharnhorst 5.62 : 2.8 Richelieu (1:0)
2. Explosives: Scharnhorst 42.7kg / 27.7kg Richelieu (1:0)
3. Belt pen: Scharnhorst 5km : 3km Richelieu (1:0)
4. Blind fire: Scharnhorst 30km : 19km Richelieu (1:0)

Scharnhorst 4:0 Richelieu

[Bill Jurens]

To Mr. Simon:

You are certainly employing an interesting analysis procedure here, but without -- at least so far as I know -- revealing any data about exactly how some of your input values, e.g. true mean dispersions, were derived. Along similar lines, your computations for range error due to rangefinder size and magnification, though not unreasonable in principle, seems to neglect factors such as the ability of the rangefinder operator to actually keep the target in his field of view if magnification is large and the ship is rolling and pitching.

Might I respectfully ask how you are deriving some of these values?

Bill Jurens

[fsimon]

Dear Mr Jurens,
Yes, off course.
After reading through these forums, I realised, that many readers and posters had the desire to compare the battleships. It is obvious, that I have this silly desire myself (wife rolling eyes). I want to make this as reasonable as possible. I am fully aware, that all of this is totally irrelevant and also without much meaning, since most of the values are based on statistically not very significant few cases and often based on inaccurate reports. But I wanted to use the numbers that were available on these forums to make them a little more reasonable and a little more comparable.
Large magnifications with rolling ships is a point I had thought about. Do you suggest, not to use the largest magnifications? Were they often not usable?
I will not use them anymore on the night, poor weather examples.
As to the TMD values,..
We had a discussion on https://www.tapatalk.com/groups/warship ... 48445.html
And https://www.tapatalk.com/groups/warship ... 47862.html
This was very fruitful and shed some light on dispersions.
Best regards
Frank

[fsimon]

Richelieu 380mm/45
Richelieu had delay coils for the center guns of each turret fitted in 1947-1948 when a tighter dispersion pattern was desired in order to take the maximum advantage of radar fire control. During tests at Mers el-Kébir in May 1948, the measured average dispersion at 26,500 meters was 525m without the firing delay and 300m with a 0.06 second firing delay (at this time the guns had all fired more than 200 shells without refit).
525m for 26.5km battery dispersion divided by 1.692 = 310m apparent mean dispersion giving true mean dispersion for n8 = 310m x 1.069 = 331m equaling 1.25% of range.
True mean dispersion 1.25% @ 20km = 250m during WW2
Average range pattern @ 20km:
8 guns: 250m x 3.85 = 963m
4 guns: 250m x 2.89 = 723m

300m for 26.5km battery dispersion divided by 1.692 = 177m apparent mean dispersion giving true mean dispersion for n8 = 177m x 1.069 = 189m equaling 0.71% of range.
True mean dispersion 0.71% @ 20km = 143m after WW2
Average range pattern @ 20km:
8 guns: 155m x 3.85 = 549m
4 guns: 155m x 2.89 = 413m

[fsimon]

Littorio 381mm/50 using charge I parameters

Italian 381mm dispersion.jpg (55.74 KiB) Viewed 10734 times

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)

[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]

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
Denmark straight: PoW 55 shots (+4 shots Y-turret under local control) / 3 hits = 5.54% (5.08%) vs. Bismarck 93 shots / 6 hits = 6.45%

[fsimon]

German GKdoS 100a / W.A.39,16 taught me, that dispersion is not a gradual percentage of range, but is rather curved and having its best peak at around 20° elevation for modern guns. Giving a worse percentage dispersion at lower angels and also at steeper angels. In absolute numbers dispersion gets of course worse with long ranges.
I am using the TMD of the 1939 ADM gunnery report at ranges between 13 and 15km and apply the curvature of the German GKdoS 100a / W.A.39, 16 curves to get a TMD at 25km.
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)

Aproximately applying the curvature of the German curves would give an average spread of 1.38% at 25km equaling 345m. Assuming a typical 4 gun salvo: 345m / 2.89 = 119m TMD @ 25km

True Mean Dispersion (TMD) @ 25km: 119m

[fsimon]

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)

CVE-71_launching_FM-2s_Samar_25Oct1944 Yamato White Plainsat 34,547yds.jpg

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