Cursed Tank Simulator For Dummies

Units

Armour is measured in millimetres, but distances in the world are measured in studs. Both conversions matter, because penetration is spent per millimetre of armour crossed while decay and standoff are measured per stud flown.

Conversion	Value
1 metre	3.57 studs
1 stud	280.112 mm of armour

The armour multiplier

Every part carries a weakness multiplier $m$ . It works on both sides of the check at once: it thins the armour and it boosts the round.

t_{\text{eff}} = \dfrac{t}{m} \qquad\qquad P_{\text{eff}} = P \cdot m

A higher multiplier means a weaker part. Rolled steel sits at 1, so it is the baseline everything else is measured against.

Note

This is why a shot into crew or ammunition behaves so differently from a shot into a plate. Those parts sit at very high multipliers, so they barely resist anything. The full table is on the armour page.

Starting penetration

A shell begins with the penetration on its stat card. Kinetic missiles are the exception. They carry no flat value and are scored on kinetic energy every frame, launching at a fifth of their top speed and building up as they accelerate.

P_{\text{kin}}(v) = \min\!\left(\dfrac{v}{v_{\max}},\, 1\right)^{2} \cdot P

Kinetic missiles only. Penetration follows the square of the speed fraction, so a missile that has not spooled up yet hits far weaker.

Distance decay

Kinetic shells lose penetration the further they fly. The loss scales with the distance already travelled and shrinks with calibre, so a large gun holds its penetration over range far better than a small one.

P \leftarrow \max\!\left(P\left(1 - \dfrac{d\,\Delta t}{200\,C}\right),\ P_{\min}\right)

d is distance flown in studs and C is calibre in mm. Frame time cancels out, so the real rate is d over 200C per second, or roughly d over 56C per second when d is in metres.

P_{\min} = \begin{cases} C/3 & \text{AP, APHE} \\ 0 & \text{APDS, APFSDS} \end{cases}

AP and APHE never fall below a third of their calibre. Sabot rounds have no floor.

Note

HE, HESH, HEAT and ATGM do not decay with distance at all. Their warhead is created on contact, so range does not weaken them.

Standoff decay for chemical jets

A shaped charge jet loses penetration to air gaps between contacts. The first contact is free, and after that every gap costs a fixed fraction of the round's rated penetration per calibre of air crossed.

\Delta P_{\text{standoff}} = 0.03\,P \cdot \dfrac{280.112}{C}\ \text{mm per stud} \;=\; 0.03\,P \ \text{per calibre of gap}

Three percent of rated penetration is lost for every calibre of air the jet crosses.

P \leftarrow \operatorname{clamp}\big(P - \Delta P_{\text{standoff}} \cdot g,\ 0,\ P\big)

g is the gap in studs since the previous exit point. The jet dies outright at zero.

Note

This single rule is what makes spaced screens and reactive armour work against shaped charges. See armour.

Resolving a hit on a plate

At contact the plate is measured twice. Once along the surface normal for the normal thickness $t$ , and once along the travel direction for the line of sight thickness $t_{LOS}$ . The plate is defeated if either of two separate conditions is met.

\underbrace{P \cdot m > t_{LOS} \;\wedge\; \theta \le \rho}_{\text{power penetration}} \;\;\lor\;\; \underbrace{\dfrac{C}{M} > \dfrac{t}{m}}_{\text{overmatch}}

Here ρ is the shell's ricochet angle and θ is the impact angle from the normal. Overmatch is a separate branch, covered below.

On a successful penetration the budget pays the line of sight cost:

P \leftarrow P - \dfrac{t_{LOS}}{m} \qquad\qquad v \leftarrow v_0 \cdot \dfrac{P_{\text{left}}}{P_{\text{rated}}}

Remaining speed is scaled by how much penetration survived, and that speed is what drives spall damage.

Note

A chemical shell that got through on overmatch alone pays the normal thickness instead, and is floored at

\max(P - t,\ C/M)

.

Refraction inside the plate

Slope is not a plain divide by cosine. Inside the plate the path bends, the same way light bends entering glass, so the real line of sight cost sits between the flat thickness and the full sloped thickness. The bend is described by an index $n$ , built from a normalised thickness $\tau$ .

\tau = \dfrac{t/m}{P \cos\theta}

How thick the plate is relative to the penetration available at that angle.

The AP family bends away from the normal, which lengthens the path and punishes slope:

n = \Big[1 + \tau\left(\sin\rho - 1\right)\Big]^{-1} \qquad \text{AP, APHE, APDS}

With an index above 1 the path through the plate is lengthened.

APFSDS works on a reduced angle $\theta' = 0.3\,\theta$ and its second rated penetration value, and can end up with an index below 1, which shortens the path instead. That is slope normalisation.

n = \left[1 + \tau'\left(\left(1 + \dfrac{\theta'}{60}\left(\dfrac{2P_{60}}{P} - 1\right)\right) - 1\right)\right]^{-1}

A dart with a strong 60 degree rating gets an index below 1 and cuts through slope rather than being punished by it.

\sin\theta_r = n \sin\theta

The refracted direction. Overmatched plates are never refracted, the round goes straight through.

Interactive

Impact angle: 45° Plate thickness: 100 mm Penetration: 300 mm Armour mult: 1.00

Index n

1.029

Refracted angle

46.7°

Straight slope cost

141 mm

Refracted cost

146 mm

An index above 1 bends the path away from the normal and costs more than plain slope. A dart with a strong 60 degree rating can drop below 1 and pay less.

Overmatch

A plate is overmatched when the calibre is large compared to its effective normal thickness. The divisor depends on the shell family.

\dfrac{C}{M} > \dfrac{t}{m}, \qquad M = \begin{cases} 3 & \text{AP, APHE} \\ 6 & \text{APDS, APFSDS} \\ 7 & \text{HEAT, ATGM} \end{cases}

A 100 mm AP shell overmatches anything effectively thinner than 33.3 mm. A 120 mm dart overmatches below 20 mm, and a 120 mm HEAT below about 17 mm.

Overmatch changes three things at once:

Effect	What happens
Penetration	Guaranteed regardless of impact angle, bypassing the thickness comparison
Ricochet	Impossible, the ricochet branch requires the plate not be overmatched
Refraction	Skipped, the path does not bend inside the plate

Penetration lost to APS

A hard kill interception does not destroy a kinetic round. It cuts the round's penetration instead, by an amount that depends on calibre and on the system's degradation factor $F$ . Chemical shells simply detonate at the intercept point.

P \leftarrow \dfrac{1}{F}\cdot\begin{cases} \min\!\left(\frac{C}{80}P,\ P\right) & \text{AP, APDS} \\[4pt] \frac{C}{C+20}\,P & \text{APFSDS, kinetic missiles} \\[4pt] \min\!\left(\frac{C}{110}P,\ P\right) & \text{other} \end{cases}

A 120 mm dart keeps about 86 percent of its penetration through a basic system, while small calibre AP is nearly erased.

Note

The rest of the interception rules, including arcs and reaction time, are on the APS page.

Penetration

See also