Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp53 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (10846/30·(4−0.5)/1000 + 0.5)·30 = 53 m
Max Vert Disp31.8 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 53 × 0.6 = 31.8 m
Med Horiz Disp16.9 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 53 × 0.319 (σ=2) = 16.9 m
Med Vert Disp10.2 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 31.8 × 0.321 (σ=2) = 10.2 m
AP Pen Close441.7 mm
Canonical community AP formula (jcw780/wows_shell), evaluated at muzzle velocity: 1e-7 × Krupp × mass^0.69 × caliber_m^-1.07 × v0^1.38 = 1e-7 × 2950 × 51^0.69 × 0.15^-1.07 × 960^1.38 = 441.7 mm. Matches the in-game spec card.
AP Pen Far179.5 mm
Same formula at the ship's max firing range (13.6 km), where the shell has slowed to 499.9 m/s: 1e-7 × 2950 × 51^0.69 × 0.15^-1.07 × 499.9^1.38 = 179.5 mm.
HE penetration38 mm
38 mm ≈ 150 mm caliber / 4 (improved HE penetration: German BBs, Yamato-class, and a handful of others).
Improved HE PenYes
This ship's HE shells use a 1/4 (~0.25) caliber-to-pen ratio instead of the standard 1/6 (~0.167) - 0.253 in this case. Lets HE pen ~37mm armor instead of ~25mm. Hits every German cruiser (150mm CL, 203mm CA) and BB (350mm+), British heavy cruisers / Lion / Nelson, a handful of other premiums.
AP overmatch10 mm
floor(150 mm caliber / 14.3) = 10 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius15
AP shell over-penetration splash radius; scales with shell mass. Wickes 102mm = 3, standard 152mm CL ~ 20, Iowa 406mm ~ 270, Yamato 460mm = 400, Incomparable 650mm = 550 (max). Larger value = bigger splash damage area when AP over-pens.
Broadside guns used for alpha6
All 6 barrels bear on the broadside.
Turret turn time18 s
180 degrees / 10 deg/s traverse speed = 18 s.
HE full-salvo alpha10,200
1,700 HE damage x 6 broadside guns = 10,200.
AP full-salvo alpha24,600
4,100 AP damage x 6 broadside guns = 24,600.
Base HE DPM81,600
10,200 HE full-salvo alpha x 60 / 7.5 s base reload = 81,600.
Base AP DPM196,800
24,600 AP full-salvo alpha x 60 / 7.5 s base reload = 196,800.
Installed HE DPM90,000
10,200 HE full-salvo alpha x 60 / 6.8 s installed reload (Main Battery Mod. 3 = -10%) = 90,000.
Installed AP DPM217,059
24,600 AP full-salvo alpha x 60 / 6.8 s installed reload (Main Battery Mod. 3 = -10%) = 217,059.
Base shells/min48
6 broadside guns x 60 / 7.5 s base reload = 48.
Installed shells/min52.9
6 broadside guns x 60 / 6.8 s installed Artillery reload = 52.9.
Base fires/min3.84
6 HE shells x 60 / 7.5 s reload x 8% fire chance = 3.84.
Installed fires/min4.24
6 HE shells x 60 / 6.8 s installed reload x 8% fire chance = 4.24.
Torpedoes
Torpedo detectability1.2 km
Estimated torpedo reaction time9.2 s
detectability / (speed kt x 2.6 community game-speed factor).
Torpedo speed50 kt
Travel time to max range103.8 s
range / (speed kt x 2.6 community game-speed factor).
Tube count10
2 launchers x 5 tubes.
Per-side salvo10 torpedoes
10 (centerline launchers train across - full salvo to either side).
Full-salvo damage155,330
tube count x per-torpedo simulated damage (all torpedoes hitting).
Per-side salvo damage155,330
per-side salvo x per-torpedo simulated damage.
AA defense
Close-range AA DPS419
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (25×3.5×1) + (87×3.5×0.95) + (12×3.5×1) = 419. Covers AA-only mounts plus dual-purpose secondaries (Bismarck 105mm, USN 5"/38 cruiser secondaries) and dual-purpose main batteries (Sumner-class 5"/38, Akizuki-line 100mm). Formula validated against in-game captures on California, Sumner, Manfred von Richthofen, Dante Alighieri (exact) and within +/-17% on the remaining verified ships.
Maximum AA range6 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index1557
SUM over AA auras of (aura DPS x aura range km). A plane crossing the AA bubble is exposed to each aura for a time proportional to that aura's range, so long-reach DPS is worth more than the same DPS in a short bubble. Units: DPS*km; used to rank overall AA threat across the cohort.
Near aura range3 km
Damage Control Party
Smoke Generator
Defensive AA Fire