Spall and Post-Penetration

Work in progress

This wiki is still being written. Pages are incomplete, numbers may change, and some mechanics are not covered yet.

A penetrating hit sprays a cone of fragments through the inside of the vehicle. Fragment count, cone width and fragment penetration all scale off how much penetration survived the plate.

Residual energy

Spall is generated on every successful penetration into a vehicle, and almost everything about it scales off how much penetration survived the plate. That surplus is expressed as a residual fraction $r$ , which is turned into a scale factor $s_r$ .

r = \operatorname{clamp}\!\left(\dfrac{P_{\text{left}}}{P_{\text{rated}}},\,0,\,1\right), \qquad s_r = 0.5 + r

A round that barely squeezed through scales at 0.5, a clean punch with full penetration left scales at 1.5.

Key idea

Overkill penetration is never wasted. It comes back as a denser, harder hitting fragment cone.

Fragment count

Chemical and kinetic rounds count fragments differently. A chemical jet counts off calibre alone, while a kinetic round counts off how much plate it actually punched through, so a thicker plate ejects more material.

N_{\text{chem}} = \left\lfloor \operatorname{clamp}\!\left(\left(\left(\tfrac{C}{30}\right)^{2} + 13\right) s_r,\ 10,\ 10^{4}\right)\right\rfloor

HEAT and chemical ATGM.

N_{\text{kin}} = \left\lfloor \operatorname{clamp}\!\left(\dfrac{t_{LOS}}{54.9\,m}\left(\tfrac{C}{20}\right)^{2} s_r + 5,\ 20,\ 10^{4}\right)\right\rfloor

t_LOS is the line of sight thickness in mm. The 54.9 mm constant is 70 over 357 studs expressed in millimetres.

Cone half-angle

All families share one curve and differ only by a coefficient $k$ . The cone is driven by calibre, not by speed.

\alpha = (kC)^{1.11}, \qquad k = \begin{cases} 0.24 & \text{AP, APHE} \\ 0.21 & \text{APDS} \\ 0.18 & \text{APFSDS, kinetic missiles} \\ 0.10 & \text{HEAT, chemical ATGM} \end{cases}

The ordering is AP, then APDS, then APFSDS, then HEAT, from widest to narrowest.

Two modifiers then apply, and the result is capped at 90 degrees:

\alpha \leftarrow \alpha\left(1 + 0.5\,\dfrac{\theta}{90}\right) \cdot \underbrace{\operatorname{clamp}\!\left(\left(\tfrac{700}{v}\right)^{0.4},\,0.65,\,1.5\right)}_{\text{kinetic only}}, \qquad \alpha \le 90^\circ

An oblique hit widens the cone. A fast rod carries debris forward into a narrower cone while a slow shot scatters. Chemical jets ignore the velocity term entirely.

Fragment directions are then spread uniformly within $\pm\alpha$ and rolled a random amount around the exit direction.

Interactive

Calibre: 120 mm Impact angle: 30° Speed: 900 m/s

Cone half-angle

32.0°

Calibre sets the base, an oblique hit widens it, and a faster kinetic round narrows it. Chemical jets ignore speed.

Fragment penetration

Each fragment gets its own penetration value, derived from residual penetration rather than from speed.

P_{\text{frag}} = \left(\dfrac{C}{20}\right)^{2} + P_{\text{left}} \cdot \begin{cases} 0.2 & \text{chemical} \\ 0.08 & \text{kinetic} \end{cases}

Chemical jets pass on a larger share of their leftover penetration to each fragment.

A fragment starts with a penetration debit equal to the square of its first air gap in studs, then works part by part. At each part it deals its damage, pays that part's effective thickness into the debit, and carries on while it still has budget. Fragments travel up to 30 studs.

\text{debit}_0 = g^{2}, \qquad \text{continues while } P_{\text{frag}} \cdot m > \text{debit} + t

The squared first gap is why internals packed close behind the plate take far more fragment damage than ones set back.

Damage per fragment

Fragment damage is driven by calibre, and for kinetic rounds by the residual speed after the plate.

\text{dmg}_{\text{frag}} = \begin{cases} \operatorname{clamp}\!\big((C/25)^{2},1,10^{4}\big)\cdot\operatorname{clamp}(v/700,1,10)^{2} & \text{AP, APHE} \\[4pt] \operatorname{clamp}\!\big((C/30)^{2},1,10^{4}\big)\cdot\operatorname{clamp}(v/700,1,10)^{2} & \text{APDS, APFSDS, kinetic} \\[4pt] \operatorname{clamp}\!\big((C/20)^{2},1,10^{4}\big) & \text{HEAT, chemical ATGM} \end{cases}

v here is the post-plate residual speed, which itself scaled with how much penetration survived.

What the cone can hit

Internal	Effect when hit
Ammunition	Can detonate, destroying the vehicle outright
Crew	Knocked out crew disable the gun, driving or reload
Fuel	Can start a fire that keeps dealing damage
Engine, transmission	Immobilises the vehicle
Gun breech	Stops the vehicle from firing

All of these sit at very high armour multipliers, so a fragment that reaches them is rarely stopped by them.

Spall and Post-Penetration

Residual energy #

Fragment count #

Cone half-angle #

Fragment penetration #

Damage per fragment #

What the cone can hit #

See also

Residual energy

Fragment count

Cone half-angle

Fragment penetration

Damage per fragment

What the cone can hit