Fast Battleship League Table

[fsimon]

Clear day, calm seas.

Ranging accuracy:
Richelieu:
Type 284P FCR: 36m, ranging to 27km, blind fire / spotting to 19km
Renown:
Type 284P FCR: 36m, ranging to 27km, blind fire / spotting to 19km

Shooting will commence outside of 20km, but main battle range will be 20km.

Battle range: 20km.

Gun accuracy @ 20km:
Richelieu: True Mean Dispersion (TMD) @ 20km: 250m
Renown: True Mean Dispersion (TMD) @ 20km: 88m

Danger Zones @ 20km:
Richelieu’s guns Angle of Fall @ 20km = 15.6° Danger zone vs. Renown 10m high 25m beam = 59m
Renown guns Angle of Fall @ 20km = 20.3° Danger zone vs. Richelieu 10m high 30m beam = 57m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Richelieu: 59m / (250m +36m) = 20.6%
Renown: 57m / (88m + 36m) = 46.0%

Projectile times of flight @ 20km:
Richelieu: 31s
Renown: 36s

Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Richelieu: Hp = 2.66%
Renown: HP = 5.11%

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:
Richelieu: 8.47 shots per min
Renown: 5.79 shots per min

Rapid Fire rate (RF):
Richelieu: 9.58 shots per min (1.33 rpm x 8 guns -10% for missed shots)
Renown: 9 shots per min (36 sec. nominal firing cycle = 1.666 rpm x 6 guns -10% for missed shots)

Average rate (AR) of fire:
Richelieu: 9.03 shots per min
Renown: 7.39 shots per min

Expected hits per 10 min:
i.e. Hp x AR x 10
Richelieu: 2.40 hits per 10 min
Renown: 3.78 hits per 10 min

Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Richelieu: 21.8kg x 2.40 / 2 = 26.2kg
Renown: 22kg x 3.78 / 2 = 41.6kg

Side protection system penetration @ 30° inclination:
Richelieu could penetrate Renown @ >20km
Renown could penetrate Richelieu @ 3
However, Renown could also penetrate Richelieu through the upper belt (45mm) and the lower armor deck at >21km.

Summary:
1. Hits: Richelieu (90 shots) 2.4 : 3.78 (74 shots) Renown (0:1)
2.Explosives: Richelieu 26.2kg / 41.6kg Renown (0:1)
3. Belt pen: Richelieu >20km : 10km Renown (2:0) grave danger for Renown
4. Dec pen inside 25km: Richelieu (22-25km) 3km : 0km Renown (1:0)

Richelieu 3:2 Renown

[fsimon]

Night, star shell visibility 20km, intermittent low clouds and 5km visibility in rainsqualls

Ranging accuracy:
Richelieu:
Type 284P FCR: 36m, ranging to 27km, blind fire / spotting to 19km
Renown:
Type 284P FCR: 36m, ranging to 27km, blind fire / spotting to 19km

Battle range: 20km.
…
All the same as per day, but since no shooting commences outside 20km, there would be no catastrophic deck penetration expected.

Summary:
1. Hits: Richelieu (90 shots) 2.4 : 3.78 (74 shots) Renown (0:1)
2.Explosives: Richelieu 26.2kg / 41.6kg Renown (0:1)
3. Belt pen: Richelieu >20km : 10km Renown (2:0) grave danger for Renown
4. Blind Fire: Richelieu 19km : 19km Renown (1:1)

Richelieu 3:3 Renown

[fsimon]

November 1943, Clear day, calm seas..

Ranging accuracy:
Richelieu:
Type 284P FCR: 36m, ranging to 27km, blind fire / spotting to 19km
Vittorio Veneto:
EC3ter Gufo radar: 150m; max 30km range, poor range and angular resolution no blind fire
12m x 25:116m

Shooting will commence outside of 20km, but main battle range will be 20km.

Battle range: 20km.

Gun accuracy @ 20km:
Richelieu: True Mean Dispersion (TMD) @ 20km: 250m
Vittorio Veneto: True Mean Dispersion (TMD) @ 20km: 194m

Danger Zones @ 20km:
Richelieu’s guns Angle of Fall @ 20km = 15.6° Danger zone vs. Vittorio Veneto 10m high 30m beam = 64m
Vittorio Veneto guns Angle of Fall @ 20km = 14.1° Danger zone vs. Richelieu 10m high 30m beam = 68m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Richelieu: 64m / (250m +36m) = 22.4%
Vittorio Veneto: 68m / (194m + (116m/2m)) = 27.0%

Projectile times of flight @ 20km:
Richelieu: 31s
Vittorio Veneto: 30s

Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Richelieu: Hp = 2.89%
Vittorio Veneto: HP = 3.6%

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:
Richelieu: 8.47 shots per min
Vittorio Veneto: 9.72 shots per min

Rapid Fire rate (RF):
Richelieu: 9.58 shots per min (1.33 rpm x 8 guns -10% for missed shots)
Vittorio Veneto: 9 shots per min (36 sec. nominal firing cycle = 1.666 rpm x 6 guns -10% for missed shots)

Average rate (AR) of fire:
Richelieu: 9.03 shots per min
Vittorio Veneto: 10.13 shots per min

Expected hits per 10 min:
i.e. Hp x AR x 10
Richelieu: 2.61 hits per 10 min
Vittorio Veneto: 3.65 hits per 10 min

Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Richelieu: 21.8kg x 2.61 / 2 = 28.5kg
Vittorio Veneto: 10.16kg x 3.65 / 2 = 18.5kg

Side protection system penetration @ 30° inclination:
Richelieu could penetrate Vittorio Veneto @ 13km
Vittorio Veneto could penetrate Richelieu @ 15km

Summary:
1. Hits: Richelieu (90shots) 2.61 : 3.65 (101shots) Vittorio Veneto (0:1)
2.Explosives: Richelieu 28.5kg / 18.5kg Vittorio Veneto (1:0)
3. Belt pen: Richelieu 13km : 15km Vittorio Veneto (1:1)

Richelieu 2:2 Vittorio Veneto

[fsimon]

November 1943, night, prevailing 20km visibility with star shell illumination, intermittent low clouds and 5km visibility in rainsqualls

Ranging accuracy:
Richelieu:
Type 284P FCR: 36m, ranging to 27km, blind fire / spotting to 19km
Vittorio Veneto:
EC3ter Gufo radar: 150m; max 30km range, poor range and angular resolution no blind fire
12m x 25:116m

All remains as per day, except for blind fire capability.

Summary:
1. Hits: Richelieu (90shots) 2.61 : 3.65 (101shots) Vittorio Veneto (0:1)
2.Explosives: Richelieu 28.5kg / 18.5kg Vittorio Veneto (1:0)
3. Belt pen: Richelieu 13km : 15km Vittorio Veneto (1:1)
4. Blind fire: Richelieu 19km : 5km Vittorio Veneto

Richelieu 3:2 Vittorio Veneto

[fsimon]

27. November 1940 (Battle of Cape Spartivento / Teulada) Clear day, calm seas.

Ranging accuracy:
Vittorio Veneto:
12m x 25:116m 20km
Renown:
30ft (9.1m) x 25: 153m @20km

Shooting will commence at 27km, but main battle range will be 20km.

Battle range: 20km.

Gun accuracy @ 20km:
Vittorio Veneto: True Mean Dispersion (TMD) @ 20km: 194m
Renown: True Mean Dispersion (TMD) @ 20km: 88m

Danger Zones @ 20km:
Vittorio Veneto’s guns Angle of Fall @ 20km = 15.6° Danger zone vs. Renown 10m high 25m beam = 63m
Renown guns Angle of Fall @ 20km = 20.3° Danger zone vs. Vittorio Veneto 10m high 30m beam = 57m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Vittorio Veneto: 63m / (194m +116m/2) = 25.0%
Renown: 57m / (88m + 153m/2) = 34.7%

Projectile times of flight @ 20km:
Vittorio Veneto: 30s
Renown: 36s

Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Vittorio Veneto: Hp = 3.33%
Renown: HP = 3.85%

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:
Vittorio Veneto: 9.72 shots per min
Renown: 5.79 shots per min

Rapid Fire rate (RF):
Vittorio Veneto: 10.53 shots per min (1.3 rpm x 9 guns -10% for missed shots)
Renown: 9 shots per min (36 sec. nominal firing cycle = 1.666 rpm x 6 guns -10% for missed shots)

Average rate (AR) of fire:
Vittorio Veneto: 10.53 shots per min
Renown: 7.39 shots per min

Expected hits per 10 min:
i.e. Hp x AR x 10
Vittorio Veneto: 3.51 hits per 10 min
Renown: 2.85 hits per 10 min

Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Vittorio Veneto: 10.16kg x 3.51 / 2 = 17.8kg
Renown: 22kg x 2.85 / 2 = 31.4kg

Side protection system penetration @ 30° inclination:
Vittorio Veneto could penetrate Renown @ >20km
Renown could penetrate Vittorio Veneto @ <10km


Summary:
1. Hits: Vittorio Veneto (101 shots) 3.51 : 2.85 (74 shots) Renown (1:0)
2.Explosives: Vittorio Veneto 17.8kg / 31.4kg Renown (0:1)
3. Belt pen: Vittorio Veneto >20km : <10km Renown (2:0) grave danger for Renown
4. Dec pen inside 25km: Vittorio Veneto (23-25km) 3km : 0km Renown (1:0)

Vittorio Veneto 4:1 Renown

[fsimon]

Night, star shell visibility 20km, intermittent low clouds and 5km visibility in rainsqualls

Ranging accuracy:
Vittorio Veneto:
12m x 25:116m 20km
EC3ter Gufo radar: 150m; max 30km range, poor range and angular resolution no blind fire

Renown:
30ft (9.1m) x 25: 153m @20km
Type 284M3/P FCR: 36m, blind fire / spotting to 19km

Both will find each other with radar. Both are now interested in closing to inside 20km, Renown to get into radar spotting range and Vittorio Veneto into star shell illumination range.

Battle range: 20km.

…

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Vittorio Veneto: 63m / (194m +116m/2) = 25.0%
Renown: 57m / (88m + 36m) = 46.0%

...

Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Vittorio Veneto: Hp = 3.33%
Renown: HP = 5.11%

…

Average rate (AR) of fire:
Vittorio Veneto: 10.53 shots per min
Renown: 7.39 shots per min

Expected hits per 10 min:
i.e. Hp x AR x 10
Vittorio Veneto: 3.51 hits per 10 min
Renown: 3.77 hits per 10 min

Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Vittorio Veneto: 10.16kg x 3.51 / 2 = 17.8kg
Renown: 22kg x 3.77 / 2 = 41.5kg

...

Summary:
1. Hits: Vittorio Veneto (101 shots) 3.51 : 3.77 (74 shots) <20% difference, drawRenown (1:1)
2. Explosives: Vittorio Veneto 17.8kg / 41.5kg Renown (0:1)
3. Belt pen: Vittorio Veneto >20km : <10km Renown (2:0) grave danger for Renown
4. Blind fire: Vittorio Veneto 5km : 19km Renown (0:1)

Vittorio Veneto 3:3 Renown

[fsimon]

I am checking, if the better dispersion of Littorio would change much against Richelieu over Vittorio Veneto against Richelieu.

November 1943, Clear day, calm seas..

Ranging accuracy:
Richelieu:
Type 284P FCR: 36m, ranging to 27km, blind fire / spotting to 19km
Littorio:
EC3ter Gufo radar: 150m; max 30km range, poor range and angular resolution no blind fire
12m x 25:116m

Shooting will commence at 27km, but main battle range will be 20km.

Battle range: 20km.

Gun accuracy @ 20km:
Richelieu: True Mean Dispersion (TMD) @ 20km: 250m
Littorio: True Mean Dispersion (TMD) @ 20km: 148m This is the difference to Vittorio Veneto's 194m.

Danger Zones @ 20km:
Richelieu’s guns Angle of Fall @ 20km = 15.6° Danger zone vs. Littorio 10m high 30m beam = 64m
Littorio guns Angle of Fall @ 20km = 14.1° Danger zone vs. Richelieu 10m high 30m beam = 68m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Richelieu: 64m / (250m +36m) = 22.4%
Littorio: 68m / (148m + (116m/2m)) = 33.0%

Projectile times of flight @ 20km:
Richelieu: 31s
Littorio: 30s

Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Richelieu: Hp = 2.89%
Littorio: HP = 4.4%

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:
Richelieu: 8.47 shots per min
Littorio: 9.72 shots per min

Rapid Fire rate (RF):
Richelieu: 9.58 shots per min (1.33 rpm x 8 guns -10% for missed shots)
Littorio: 10.53 shots per min (1.3 rpm x 9 guns -10% for missed shots)

Average rate (AR) of fire:
Richelieu: 9.03 shots per min
Littorio: 10.13 shots per min

Expected hits per 10 min:
i.e. Hp x AR x 10
Richelieu: 2.61 hits per 10 min
Littorio: 4.46 hits per 10 min

Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Richelieu: 21.8kg x 2.61 / 2 = 28.5kg
Littorio: 10.16kg x 4.46 / 2 = 22.6kg

Side protection system penetration @ 30° inclination:
Richelieu could penetrate Littorio @ 13km
Littorio could penetrate Richelieu @ 15

Summary:
1. Hits: Richelieu (90shots) 2.61 : 4.46 (101shots) Littorio (0:1)
2. Explosives: Richelieu 28.5kg / 22.6kg Littorio (1:0)
3. Belt pen: Richelieu 13km : 15km Littorio (1:1)

Richelieu 2:2 Littorio

[fsimon]

November 1943, night, prevailing 20km visibility with star shell illumination, intermittent low clouds and 5km visibility in rainsqualls

All remains as per day, except for blind fire capability.

Summary:
1. Hits: Richelieu (90shots) 2.61 : 4.46 (101shots) Littorio (0:1)
2.Explosives: Richelieu 28.5kg / 22.6kg Littorio (1:0)
3. Belt pen: Richelieu 13km : 15km Littorio (1:1)
4. Blind fire: Richelieu 19km : 5km Littorio (1:0)

Richelieu 3:2 Littorio

Overall Littorio would fare better than Vittorio Veneto. Both would hit Richelieu more often than the other way around due to Richelieu’s poor dispersion. But Richelieu’s projectiles could cause more devastation.

[fsimon]

November 1939, clear day, calm seas. Let’s assume Scharnhorst was cut off by Hood.

Ranging accuracy:
Scharnhorst:
Optical range finders: 10.5m x 50=> 76m @20km

Hood:
Optical range finder: 30ft (9.1m) x 25 => 153m @20km

Battle range: 20km.

Gun accuracy @ 20km:
Scharnhorst: True Mean Dispersion (TMD) @ 20km: 152m
Hood: True Mean Dispersion (TMD) @ 20km: 88m

Danger Zones @ 20km:
Scharnhorst’s guns Angle of Fall @ 20km = 16.3° Danger zone vs. Hood 10m high 30m beam = 61m
Hood still fired projectiles with 4crh ballistic cap. Since I cannot find any data on this, I will use the 6crh numbers.
Hood guns Angle of Fall @ 20km = 20.3° Danger zone vs. Scharnhorst 10m high 28m beam = 55m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 61m / (152m + (76m/2)) = 32.1%
Hood: 55m / (88m + (153m/2)) = 33.4%

Projectile times of flight @ 20km:
Scharnhorst: 31s
Hood: 36s

Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 4.15%
Hood: HP = 3.71%

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
Hood: 7.71 shots per min

Rapid Fire rate (RF):
Scharnhorst: 16.23 shots per min
Hood: 13.5 shots per min; Hood had a faster firing cycle (32sec.) than Renown and QE (36sec.)

Average rate (AR) of fire:
Scharnhorst: 12.30 shots per min
Hood: 10.61 shots per min

Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 5.10 hits per 10 min
Hood: 3.93 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 5.1/ 2 = 38.8kg
Hood: 22kg x 3.93 / 2 = 43.2kg

Side protection system penetration @ 30° inclination:
Scharnhorst could penetrate Hood @ 10km (305mm belt)
Hood could penetrate Scharnhorst @ 5km (320mmKCnA belt + 105mm Wh slope)
However, Hood could also penetrate Scharnhorst through the upper belt (35mm) and the lower armor deck at >21km.

Summary:
1. Hits: Scharnhorst 5.1 : 3.93 Hood (1:0)
2. Explosives: Scharnhorst 38.8kg : 43.2kg Hood (<20% difference ie. Draw 1:1)
3. Belt pen: Scharnhorst 10km : 5km Hood (1:0)
4. Dec pen inside 25km: Scharnhorst 0 : 4 (21km-25km) Hood (0:1)

Scharnhorst 3:2 Hood

[fsimon]

Night May 1941, prevailing 20km visibility with star shells, intermittent 5km in rainsqualls.

Ranging accuracy:
Scharnhorst:
Optical range finders: 10.5m x 50=> 76m @20km
FuMG 39 Seetakt (TS6, Radattlepeilung): 25m accuracy, 28-30km range, 21km blind fire / salvo spotting

Hood:
Optical range finder: 30ft (9.1m) x 25 => 153m @20km
Type 284 (no lobe switching, no ranging panel): 110m range accuracy, 21-25km range, no blind fire, salvo spot to 15km

Battle range: 20km.

Gun accuracy @ 20km:
Scharnhorst: True Mean Dispersion (TMD) @ 20km: 152m
Hood: True Mean Dispersion (TMD) @ 20km: 88m

Danger Zones @ 20km:
Scharnhorst’s guns Angle of Fall @ 20km = 16.3° Danger zone vs. Hood 10m high 30m beam = 61m
Hood still fired projectiles with 4crh ballistic cap. Since I cannot find any data on this, I will use the 6crh numbers.
Hood guns Angle of Fall @ 20km = 20.3° Danger zone vs. Scharnhorst 10m high 28m beam = 55m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 61m / (152m + 25m) = 34.5%
Hood: 55m / (88m + (110m/2)) = 38.5%

Projectile times of flight @ 20km:
Scharnhorst: 31s
Hood: 36s

Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 4.45%
Hood: HP = 4.27%

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
Hood: 7.71 shots per min

Rapid Fire rate (RF):
Scharnhorst: 16.23 shots per min
Hood: 13.5 shots per min; Hood had a faster firing cycle (32sec.) than Renown and QE (36sec.)

Average rate (AR) of fire:
Scharnhorst: 12.30 shots per min
Hood: 10.61 shots per min

Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 5.48 hits per 10 min
Hood: 4.53 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 5.48/ 2 = 38.8kg
Hood: 22kg x 4.53 / 2 = 49.8kg

Side protection system penetration @ 30° inclination:
Scharnhorst could penetrate Hood @ 10km (305mm belt)
Hood could penetrate Scharnhorst @ 5km (320mmKCnA belt + 105mm Wh slope)
However, Hood could also penetrate Scharnhorst through the upper belt (35mm) and the lower armor deck at >21km.

Summary:
1. Hits: Scharnhorst 5.48 : 4.53 Hood (1:0)
2. Explosives: Scharnhorst 41.7kg : 49.8kg Hood (<20% difference ie. Draw 1:1)
3. Belt pen: Scharnhorst 10km : 5km Hood (1:0)
4. Dec pen inside 25km: Scharnhorst 0:4 (21km-25km) Hood (0:1)
5. Blind Fire: Scharnhorst 21km : 5km Hood (1:0)

Scharnhorst 4:2 Hood

[Thorsten Wahl]

MWa considers a dependence between (Seelenlänge)and relative muzzleenenergy and accuracy of a gun.

Screenshot_20231105-115617_Drive.jpg

(113.14 KiB) Not downloaded yet

[fsimon]

Iowa vs. Yamato daytime
August 1943, daytime, clear weather
Yamato opened fire at 32km at Samar. US doctrine was to open fire at long ranges and close to within radar spotting range, which was ~27km with Mark 8 Mod 1 radar for 16” AP rounds, but decisive range would to be around 25km.

Ranging accuracy:
Iowa:
Mark 8 Mod 1 fire control radar: 39m @ 25km; max 39km range, blind fire ~27km
Yamato:
Optical range finder: 15m wide, 25 times magnification = accuracy @25km = ~146m
Mk2Model2Search radar: 35km range

Spotting accuracy: (Spotting accuracy for radar = ranging accuracy, if radar range and resolution allows spotting; otherwise one third the optical ranging accuracy for optical spotting.)
Iowa:
Mark 8 Mod 1: B-scope resolution 90m (i.e. individual splashes): accuracy: 39m
Yamato:
One third the optics accuracy: 146m / 3 = 49m

Average range error (RE) (Ranging accuracy in m plus 2 x spotting accuracy in m, divided by 3, as spotting accuracy is the dominant factor for keeping MPI on target after finding the range.)
Iowa: (39m + 2 x 39m) / 3 = 39m
Yamato: (146m + 2 x 49m) / 3 = 81m

Range rate error (RRE): (RE divided by 100 as generic range rate error per second x Time of Flight):
Iowa: 0.39m/s x 45s ToF = 18m
Yamato: 0.81m/s x 42s ToF = 34m

Resulting calculated Mean Point of Impact (MPI) error (RE + RRE):
Iowa: 39m + 18m = 57m
Yamato: 81m + 34m = 115m

Gun accuracy @ 25km:
Iowa: True Mean Dispersion (TMD): 100m (0.40%)
Yamato: True Mean Dispersion (TMD): 103m (0.41%, based on assumption of equal dispersion over elevation to US 16”L50 guns, based on estimations of pictures of battle of Samar)

Danger Zones @ 25km:
Iowa’s guns Angle of Fall @ 25km = 25.3° Danger zone vs. Yamato 10m high, 37m beam = 57m
Yamato guns Angle of Fall @ 25km = 22.4° Danger zone vs. Iowa 10m high, 33m beam = 57m +5m for underwater trajectory of Yamato’s shells =62m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+MPI) = X
Iowa: 57m / (100m+57m)= 36.3%
Yamato: 62m / (103m+115m) = 28.4%

Battle Errors Factor (BEF): Tracking errors, improper setup and calculation of ballistic data including atmospheric effects, alignment problems, indeterminate or human error, etc. These errors would affect both TMD and MPI placement. Generated as 38% of range for FTP, semi-automated input and output; 37% of range for RPC, semi-automated input and output
Iowa: RPC 9.25
Yamato: FTP 9.5

Hit Probability: X / BEF
Iowa: 36.3% / 9.25 = 3.92%
Yamato: 28.4% / 9.5 = 2.99%

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:
Iowa: 7.48 shots per min
Yamato: 7.84 shots per min

Rapid Fire (RF):
Iowa: 1.84spmpg as best rate by Alabama 1945 rapid fire x 9 guns -10% output loss: 14.99
Yamato: 1.5spgpm (35sec loading cycle plus 5sec) x 9 guns -10% expected output loss: 12 .15

Average rate (AR) of fire:
Iowa: 11.24 shots per min
Yamato: 10.00 shots per min

Expected hits per 10 min:
Hp x AR x 10
Iowa: 4.41 hits out of 112.4 shots per 10 min
Yamato: 2.99 hits out of 100 shots per 10 min

Explosive filler of Armor Piercing Round times hits divided by 2 (I expect 50% duds):
Iowa: 18.55kg x 4.41/ 2 = 40.9kg
Yamato: 33.85kg x 2.99 / 2 = 50.6kg

Both would plan to angle their ship towards incoming fire, thus increasing hitting angles / obliquity and so increasing armor resistance. Such a 30° inclination would decrease maximum battle range at which belt penetration could be achieved by roughly 30%.
Belt penetration @ 30° inclination:
Iowa could penetrate Yamato @ ~12km
Yamato could penetrate Iowa @ ~22km

Summary:
1. Hits: Iowa 4.41 vs. 2.99 Yamato (1.47:1)
2. Explosives: Iowa 40.9kg vs. 50.6kg Yamato (1:1.24)
3. Belt pen: Iowa 12km vs. 22km Yamato (1:1.83)

Iowa 3.47 vs. 4.07 Yamato

[fsimon]

Iowa vs. Yamato nighttime
April 1945, night time, prevailing 22km visibility with star shell, intermittent 5km in rainsqualls and broken low cloud ceiling

Both will find each other with radar at 30+km, but only Iowa can generate firing solutions outside the visibility of 22km. Yamato would likely start to maneuver and chase salvos. Both are now interested in closing to inside of 22km, Yamato to get visual contact with star shells and Iowa to start hitting a maneuvering opponent.

Ranging accuracy:
Iowa: Mark 8 Mod 2 fire control radar 34m @ 20km; max 39km range, blind fire ~27km
Yamato: 15m wide, 25 times magnification = accuracy @20km = 94m

Spotting accuracy: (for radar = ranging accuracy, if radar range and resolution allows spotting; otherwise one third the optical ranging accuracy for optical spotting.)
Iowa:
Mark 8 Mod 2: B-scope resolution 90m (i.e. individual splashes): accuracy: 34m
Yamato:
One third the optics accuracy: 94m / 3 = 31m

Average range error (RE) (Ranging accuracy in m plus 2 x spotting accuracy in m, divided by 3, as spotting accuracy is the dominant factor for keeping MPI on target after finding the range.)
Iowa: (34m + 2 x 34m) / 3 = 34m
Yamato: (94m + 2 x 31m) / 3 = 52m

Range rate error (RRE): (RE divided by 100 as generic range rate error per second x Time of Flight):
Iowa: 0.34m/s x 34s ToF = 12m
Yamato: 0.52m/s x 32s ToF = 17m

Resulting calculated Mean Point of Impact (MPI) error (RE + RRE):
Iowa: 34m + 12m = 46m
Yamato: 52m + 17m = 69m

Gun accuracy @ 20km:
Iowa: True Mean Dispersion (TMD): 88m
Yamato: True Mean Dispersion (TMD): 92m

Danger Zones @ 20km:
Iowa angle of fall @ 20km = 17.7° Danger zone vs. Yamato 10m high 37m beam = 68m
Yamato angle of fall @ 20km = 15.9° Danger zone vs. Iowa 10m high 33m beam = 68m +5m for underwater trajectory = 73m

Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+MPI) = X
Iowa: 68m / (88m+46m) = 50.7%
Yamato: 73m / (92m+69m) = 45.3%

Battle Errors Factor (BEF): Tracking errors, improper setup and calculation of ballistic data including atmospheric effects, alignment problems, indeterminate or human error, etc. These errors would affect both TMD and MPI placement. Generated as 38% of range for FTP, semi-automated input and output; 37% of range for RPC, semi-automated input and output
Iowa: RPC 7.4
Yamato: FTP 7.6

Hit Probability (HP): X / BEF
Iowa: 50.7% / 7.4 = 6.85%
Yamato: 45.3% / 7.6 = 5.96%

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:
Iowa: 9 shots per min
Yamato: 9.35 shots per min

Rapid Fire (RF):
Iowa: 1.84spmpg as best rate by Alabama 1945 rapid fire x 9 guns -10% output loss: 14.99
Yamato: 1.5spgpm (35sec loading cycle plus 5sec) x 9 guns -10% expected output loss: 12.15

Average rate (AR) of fire:
Iowa: 11.99 shots per min
Yamato: 10.75 shots per min

Expected hits per 10 min:
HP x AR x 10
Iowa: 8.21 hits per 10 min
Yamato: 6.41 hits per 10 min

Explosive filler of Armor Piercing Round times hits divided by 2 (I expect 50% duds):
Iowa: 18.55kg x 8.21/ 2 = 76.1kg
Yamato: 33.85kg x 6.41 / 2 = 108.5kg

Belt penetration @ 30° inclination:
Iowa could penetrate Yamato @ ~12km
Yamato could penetrate Iowa @ ~22km

Summary:
1. Hits: Iowa 8.21 vs. 6.41 Yamato (1.28:1)
2. Explosives: Iowa 77.4kg vs. 108.5kg Yamato (1:1.4)
3. Night fighting: Iowa 27km vs. 22km Yamato (1.23:1)
4. Blind fire: Iowa 27km vs. 5km Yamato (5.4:1)
4. Belt pen: Iowa 12km vs. 22km Yamato (1:1.83)

Iowa 9.91 vs. 6.23 Yamato

[spicmart]

@fsimon Very intriguing work!
Have you posted all this on Navweaps forum?
The reactions there would be interesting.

[fsimon]

Thank you, spicmart.
Most people on navweaps are probably aware of this forum as well, I think.
Best regards
Frank