Nothing in this simulation has a hit-point bar: a hull cell is priced in joules, and a ship part (an engine, a tank) banks the energy it absorbs against a strength in joules and breaks when the bank is full. A collision arrives carrying energy, and
every outcome it can buy — a fold, a tear, a thrown fragment, a degree of heat, a cubic metre
of excavated rock — has a price taken from the materials literature. When the energy is spent,
the damage stops.
21damage causes
18damage types
8physical regimes
63ground materials
Counted in the build of 28 October 2026 (its damage-cause, damage-type and ground-material tables).
What the model is for: deciding which parts of a
hull leave it, how large the pieces are, and where the energy went. Photograph —
the Sólheimasandur wreck, Iceland. A real airframe, not a render.
Nomenclature — every symbol used below
σp projectile strength, Pa · σc target strength, Pa
· ρp projectile density, kg/m³ · V impact velocity, m/s
· Ea absorbed energy, J · wp specific plastic work, J/m³
· Gc critical energy release rate, J/m² · ε̇ strain rate, s⁻¹
· KIc fracture toughness, Pa·m½ · c wave speed, m/s
· β Taylor–Quinney coefficient, dimensionless · ρcp volumetric
heat capacity, J/(m³·K) · Z scaled distance, m/kg⅓
· R standoff, m · W charge mass, kg TNT-equivalent
· ex specific excavation energy, J/m³.
This inequality sorts each hit into a soft one (the striker is spent, the target survives) or a hard
one (the target loses material), evaluated per component rather than per ship. Hit angle, free edges and
part size then choose the shape of the damage; how much damage there is, the energy ledger below decides.
How it works
Grazing hits: incidence angle is not in the
inequality, so a grazing hit and a square one at identical speed would classify identically. Grazing
is tested separately, on the hit angle — the difference between a hull
that skids and one that craters.
BudgetConservation, applied
The energy ledger
Ea absorbed energy · the five sinks: plastic work, separation, fragment kinetics, heat, excavation
The budget is the whole design. The absorbed energy is divided between the hull (cells removed,
metal bent, parts broken), thrown fragments, heat and the ground, so granite craters less than sand
because granite costs more, not because a table says granite is tough. Heat is not a separate purchase:
it is about nine tenths of the metal-bending work and four tenths of the tearing work at crack tips. The
game’s own books also show a leftover share
that no outcome has claimed yet, and it can be large.
How it works
Absorbed, not total:Ea is the
absorbed energy, not the kinetic energy. A ship that bounces keeps most of its ½mv².
Spending the total instead of the absorbed fraction would over-damage every glancing contact.
Outcomes are bought in order of price until the energy runs out. Part way through, the ground changes from sand to granite and nothing else is touched — watch the crater collapse.
The numbers
Available energy climbs across four decades and each sink is bought at its own price as it becomes affordable, saturating when there is no more of that outcome left to buy — the crumple volume runs out, then the surface a hull can create runs out, and everything past that goes into the ground. No branch in the film reads the material’s name: granite craters less because a cubic metre of it costs 112× what sand costs. The readout prints the closure: the four purchased terms sum to Ea, every frame, to 100.0 %. Note that heat is not a fifth additive sink: it is where the plastic work went, so it is drawn as a dashed line over the plastic band rather than as a competing band. Illustrative constants. Not the shipped chain.
Crumple is the cheapest outcome per joule and therefore the one most impacts buy. The volume is
measured from the geometry that moved — destroyed cells at full volume, dented cells at their
dent depth — never inferred from the energy.
How it works
Measured, not inferred: deriving the deformed volume from the
energy cancels the energy out of the temperature entirely, and the hull then heats by a fixed amount
regardless of how hard it was hit. The measurement keeps the thermal term honest.
What you will actually see: a dent is stored
by displacing the corners of the voxel lattice, and how far a corner may move is a tuning decision
rather than a law of the format. Ships imported at 0.125 m resolution allow up to
0.375 m of cumulative displacement per corner — about 0.85 % of a
44 m hull — which is why deep crumple reads as a wide fold rather than a deep pit. The wider cap produced fewer inverted faces than the coarser hull it
refines. Editing vertices by hand is capped separately and more tightly, at one cell. A destroyed cell, by contrast, removes its
whole volume. So removal is the only outcome whose visible amplitude clears the cap — and on the heaviest impacts the fold may receive no energy at all — which is why heavy damage reads as cut blocks rather
than as folded metal. The ledger accounts for the energy; it does not describe what the
surface ends up looking like.
SeparationGriffith · Grady–Kipp
Separation — tearing costs area
Gc critical energy release rate, J/m² · A new surface created, m²
Tearing is priced by the surface it creates, which is why a long clean split can cost less than a
small ragged one. Separation is expensive and therefore rare — most impacts cannot afford it,
which is the correct outcome and the reason hulls dent far more often than they tear.
How it works
Correction: using JIc here
overprices separation by orders of magnitude for a thin plate. Separation is expensive only when it
genuinely tears — not when it shears along a seam the builder already put there.
FragmentsGrady–Kipp · 1985
Fragmentation — how many pieces, and how big
s characteristic fragment size · KIc fracture toughness · ε̇ strain rate · ρc density × wave speed
Fragment size falls as strain rate rises — a fast impact makes many small pieces, a slow one
makes few large ones. The sizes are drawn from a power law rather than an average, because an average
fragment size produces a debris field that looks manufactured.
Known limitation
At the energies a landing accident
produces, this law returns fragments of 11–33 cm, too small to see on a 44 m hull. What a
player sees are the pieces that break away whole: each becomes its own body that tumbles and falls.
Strain rate climbs four decades; the block on the left is partitioned at the characteristic size the law returns. On the right is the law itself, log–log.
The numbers
Sizes are drawn from a power law rather than an average, because an average fragment size produces a debris field that looks manufactured. The printed d log s / d log ε̇ is measured from two live samples of the solver, not asserted: it reads −0.667 because the law is a two-thirds power. The shaded band is 11–33 cm, where a landing accident actually lands — physically right and effectively invisible on a 44 m hull. Illustrative steel constants. Not the shipped chain.
ThermalTaylor & Quinney · 1934
Heat — where the plastic work goes
β ≈ 0.9, the fraction of plastic work becoming heat · ρcp volumetric heat capacity · Vol the volume it lands in
About nine tenths of plastic work becomes heat. The denominator decides whether that is visible:
steel's ρcp is ~3.9 MJ/(m³·K), so spreading a 22 MJ crash over a
316 t hull raises it 0.09 K — correct, and completely invisible.
The physics
Why bulk crumple does not glow: confined to the cubic metres that
actually deformed it is a few degrees; confined to the millimetres-thin skin a grind heats, it
is hundreds of kelvin per second. Crash sites smoke and skidding hulls glow, from one equation.
ExcavationSpecific energy, measured ratios
Excavation — the ground has a price
ex specific excavation energy, J/m³ · per surface type,
calibrated against Mellor’s dimensionless performance index Es/σc
A crater is energy spent lifting material out of the world, so it is billed to the impact. Sixty-three
surface types carry physical properties, and the spread across rock, soil and sand is roughly
66 : 5 : 1.
Energy spent digging is energy not spent on the hull: hitting stone damages the ground less and
the ship more, and no rule says so.
The physics
Why the spread is not a bug. That 66 : 1 was twice challenged as
implausible — the intuition being that specific energy ought to track material strength in
proportion. It does not, because soil and rock obey different laws, not different
constants. Rock is fracture-controlled, so its specific energy falls as the removed
fragment gets larger; soil is shear-and-lift controlled, so by Reece’s earthmoving equation its
specific energy rises with cut depth. Opposite signs. Flattening the spread into
proportionality would have been a regression dressed as a correction.
BlastHopkinson–Cranz · Kinney–Graham
Blast — scaled distance
Z scaled distance · R standoff, m · W charge mass, kg TNT-equivalent
Two charges produce the same overpressure at the same scaled distance, so one curve covers every
charge size. Overpressure and impulse are read from it and handed to the same four-number reduction
every other cause uses.
In the game, not yet seen on a hull. The RPG warhead uses this law: on detonation,
every exposed hull cell whose reflected overpressure exceeds its crush strength is crushed, from the surface
inward, until the charge’s energy is spent, and the warhead’s fragments add their own hits. The
detonations played so far (build of 28 October 2026) had no hull within reach, so no blast crater has been
seen yet. A blast that bends or snaps a whole ship from a distance is not in the game.
Damage budget of a real crash
This section showed cell counts from staged ground impacts on an imported 44 m hull.
They are withdrawn: they came from an earlier, superseded energy reading that understated a real crash,
and no build was named for them. A crash measured in a named build will take their place.
About these readings
The staged impacts were not what a player creates: a real crash excavates thousands of cubic metres.
Several repairs have since landed in the damage chain
(ship debris that had never appeared, detached chunks that vanished, a wing that could never break off,
damage that was computed and then withheld), so read these as what a test harness recorded, not as what
happens when you hit something.
The chain was being handed the ship’s velocity after the contact solver had already
removed it — a 480 km/h impact reached the energy model as roughly 12 m/s, so every
figure here was measured against about one percent of the real crash energy. That read has been corrected;
the cell counts will rise. The figures are withdrawn and this account is kept, because a measurement that is
quietly replaced teaches nobody why it was wrong.
The material catalogue
Every voxel in the game is made of something, and that something carries measured
physical properties rather than a damage multiplier.
Three hundred-odd build materials each hold density, compressive and tensile strength, ductility,
melting point and fracture toughness, sourced where a real analogue exists from the published
datasheet for that alloy or mineral. Nothing in the model asks what kind of object it is
hitting: a decorative panel and a structural plate behave differently because their numbers differ, not
because a rule was written for each.
The numbers
The naval plate behind the hull is a
100 ksi-yield steel with its real yield, tensile and elongation figures. The aerospace aluminium
is 7075-T6, at an ultimate tensile strength of 572 MPa. Gold is annealed gold: soft, heavy, and useless as structure. Glass fails
elastically at a fraction of a percent of strain and has no plastic range at all, because that is what
glass does. Materials that were never anticipated still behave sensibly, and a
material that behaves absurdly is a wrong number — findable, and fixable — rather than a
missing special case.
Material strength versus structural strength
A voxel is not a solid block of steel. It is a metre of structure — plate, rib and void —
averaged into one cell, and a structure fails long before its material does. Using solid-material strength
would build a ship that cannot be hurt, so the model uses published cellular-solid scaling instead. That
mapping is a stated modelling choice constrained by the literature, not a law we claim to have derived.
The physics
An earlier build fed solid strength into the impact model: no ground in the game could take more than a
few percent of a crash, so the hull kept almost none of it and every collision was survivable.
The fix is the distinction between material strength and structural strength, which is
well-established physics — Gibson & Ashby’s cellular-solids scaling, and the superfolding
analysis Wierzbicki and Abramowicz built for crushed box sections. The literature
also says the mapping is not determined by density alone: at one fixed relative density, six standard
topologies span roughly an order of magnitude in crush strength, because the exponent itself changes with
how the cell is built.
A constraint we did not expect. The textbook-correct exponent for this load case
is unusable here, for a reason that has nothing to do with physics: our fill fractions were
assigned by asset-import batch, not by structure. Applied to those inputs the correct exponent inverts the
material hierarchy and makes a wooden voxel stronger than a hull plate. That shipped briefly
and an audit caught it. The exponent in the build is the largest one our inputs can carry without that
inversion, the crossover is recorded as a number, and the real fix — correcting the inputs — is
open work.
What the ledger does with that energy
The energy budget decides which cells leave the hull, what they become, and where the
damage stops. Status, build of 28 October 2026: the first two changes below are in the game; the third was
later reversed on purpose, as its own section says.
Pulverising is not fracturing
The mode selector used to send any sufficiently energetic impact down the powder path, because it
asked whether there was enough energy to fracture the material and used the answer to select
atomisation. The two are now separate outcomes: fracture below the pulverising threshold detaches
Voronoi chunks that keep their own physics and fall.
How it works
The test was ½v² > K, where K is specific fracture
energy. A logged 400 km/h impact produced no removed cells and spent none of its 520.83 MJ:
half a gigajoule chose the powder path and produced nothing. Pulverising now requires the energy to
reduce material to micrometre scale; the chunks keep mass, velocity and rotation.
Damage travels inward through layers
Damage no longer crosses one surface in a single pass. The hull is crushed from the point of contact
inward as the obstacle moves through it; each cell is charged at its own material’s price, so a marble
skin can shatter while the steel girders behind it stand, and the crash stops where the energy runs out.
How it works
Two mechanisms already existed: a 7×7×7 neighbourhood sample takes a count-weighted mean
σ for the energy split with the dominant material for categorical properties, and survival
is judged per cell, by that cell’s own material, so steel girders already stand where marble
shatters. What both lacked was direction: a crater used to be priced and stamped in a single pass against
one dominant material, so a nose of marble over plastic over girders was treated as one homogeneous shell
whose survivors happened to differ. The crush described above replaced that single pass.
No cap on what one impact can remove
The energy of the impact alone sets the damage: there is no limit on how much of a hull one impact can
remove. The largest connected piece always stays as the ship; pieces cut off from it fall away as debris.
How it works
This failed twice, by two unrelated routes. A connectivity pass once found 71 connected components
and deleted all 70 detached pieces (11,816 cells); detached pieces now fall as debris instead.
Separately, a cap on how much one impact may remove was tried here and removed again in October 2026:
a cap lets a number, not the energy, decide how much breaks.
A fix that removed nothing
A repair for unbaked damage types was credited with resolving eleven reports but removed zero
cells, for two independent reasons. It has been caught and the lesson kept.
How it works
It was priced at zero — every unbaked type was handed a purchase of zero, and the
applier divides by it, so the requested volume was zero. And it was unreachable — an earlier
branch skipped unbaked types before the applier was ever called. Its own diagnostic sat inside the
branch the zero switched off. An instrument that goes quiet when it fails is worse than no
instrument, because silence gets read as success.
How the numbers were checked
Roughly forty primary sources, read adversarially, with the explicit goal of refuting our
own constants. A number earns its place only with a source and a statement of what would refute it; design
decisions are labelled as such.
What the checks found
Two constants were challenged and upheld
Independent reviewers argued that our
rock and ice excavation energies were 3–30× too low. Both challenges were traced to
continuous-cutting and confined-indentation regimes — laboratory conditions a
metre-scale dig does not operate in. Read against Mellor’s dimensionless performance index, the
shipped values sit inside the published attainable band. Nothing changed.
One of our own citations did not survive
A comment in our code credited a
published aircraft-impact paper with a strength-versus-density exponent. Two independent readings of the
source found no such relation, and the paper states that target geometry has no bearing on
its criterion. The numbers we used were genuinely theirs; the law we fitted to them was ours. The
attribution has been corrected.
An arithmetic error worth 9.56×
Relative density and wall-thickness ratio
are not the same quantity — they differ by roughly a factor of four, and the crush law is a 5/3
power, so substituting one for the other is wrong by an order of magnitude. Inverted correctly, our hull
lands exactly on the specimen geometry Abramowicz & Jones actually tested in 1984. Inverted naively it
lands outside the theory’s stated validity range entirely.
A regression we shipped and withdrew
The strength-ordering inversion described above was caught
in about an hour by printing the resulting strength ordering and reading it
— a check that takes seconds and was not run before shipping.
What this model does not do
Ship-on-ship crashes are not shown yet
Two ships can collide, and in the build of 28 October 2026 the struck ship takes damage worked out from the same impact, using both masses. It has not yet been seen in play, and this page has no measured ship-on-ship crash to show.
Two types have no cause
A pressure vessel bursting and a hull column buckling are priced and reachable by nothing: the catalogue can select them and the game cannot ask. A hard enough impact can cut a hull in two; bending load alone cannot.
Blast stays near the warhead
An RPG warhead’s blast is aimed at the hull cells around it; no played detonation has yet had a hull within reach. A blast that bends or snaps a whole ship from a distance is not modelled.
Small fragments are too small to see
The 11–33 cm fragments the law returns for a landing accident are too small to see on a 44 m hull; what a player sees are the larger pieces that break away whole and fall as debris.
Provenance
Sources (31)
Kǒechlin, P. & Potapov, S. (2009). Classification of soft and hard impacts. Nuclear Engineering and Design. — the mode inequality.
Taylor, G. I. & Quinney, H. (1934). The latent energy remaining in a metal after cold working. Proc. R. Soc. A. — the β ≈ 0.9 heat fraction.
Grady, D. E. & Kipp, M. E. (1985). Geometric statistics and dynamic fragmentation. J. Appl. Phys. — fragment size vs strain rate.
Griffith, A. A. (1921). The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. A. — separation priced by surface area.
Johnson, G. R. & Cook, W. H. (1983). A constitutive model for metals subjected to large strains, high strain rates and high temperatures. — flow stress behind the plastic work term.
Hopkinson, B. (1915); Cranz, C. (1926). — blast scaling. Kinney, G. F. & Graham, K. J. (1985). Explosive Shocks in Air, 2nd ed. — the overpressure curve (it replaced Sadovsky’s 1952 curve).
Riera, J. D. (1968). On the stress analysis of structures subjected to aircraft impact forces. Nuclear Engineering and Design. — force history of a deforming projectile.
Structural strength of a cellular solid
Gibson, L. J. & Ashby, M. F. (1997). Cellular Solids: Structure and Properties, 2nd ed., Cambridge University Press, chs. 4–5. — the scaling laws separating material strength from structural strength.
Gibson, L. J., Ashby, M. F., Schajer, G. S. & Robertson, C. I. (1982). The mechanics of two-dimensional cellular materials. Proc. R. Soc. Lond. A382:25–42.
Ashby, M. F. (2006). The properties of foams and lattices. Phil. Trans. R. Soc. A364:15–30. — bending- versus stretch-dominated architectures; why the exponent is a property of topology, not of density.
Wierzbicki, T. & Abramowicz, W. (1983). On the crushing mechanics of thin-walled structures. J. Appl. Mech.50(4a):727–734. — the superfolding element.
Wierzbicki, T. (1983). Crushing analysis of metal honeycombs. Int. J. Impact Eng.1(2):157–174.
Abramowicz, W. & Jones, N. (1984, 1986, 1997). Dynamic axial crushing of square tubes; dynamic progressive buckling; transition from global bending to progressive buckling. Int. J. Impact Eng.2(2), 4(4), 19(5–6). — the effective crushing distance, and the specimen geometries our hull is compared against.
Abramowicz, W. (2003). Thin-walled structures as impact energy absorbers. Thin-Walled Structures41:91–107. — the energy-equivalent flow stress, which is the quantity these formulas actually take.
Baroutaji, A., Sajjia, M. & Olabi, A. G. (2017). On the crashworthiness performance of thin-walled energy absorbers. Thin-Walled Structures118:137–163. — the crush-mode map that bounds where these formulas may be used.
Najafi, A. & Rais-Rohani, M. (2011). Mechanics of axial plastic collapse in multi-cell, multi-corner crush tubes. Thin-Walled Structures49:1–12. — the explicit statement that the analytical law fails when the collapse mode changes.
Excavation and the price of ground
Mellor, M. (1977). Mechanics of Cutting and Boring, Parts IV–VIII. CRREL Reports 77-7, 77-19, 80-21, 81-26, 78-11. — the dimensionless performance index Es/σc, and the attainable band that calibrates every surface in the game.
Mellor, M. & Sellmann, P. V. (1976). General considerations for drill system design. CRREL. — ice and frozen-ground cutting energies.
Teale, R. (1965). The concept of specific energy in rock drilling. Int. J. Rock Mech. Min. Sci.2(1):57–73. — the definition; also the regime we explicitly do not operate in.
Zhang, H., Le, J.-L. & Detournay, E. (2022). An experimental investigation of brittle failure mechanisms in scratch tests of rock. Eng. Fract. Mech.275:108827. — ductile, fragmentation and brittle cutting regimes; why specific energy depends on fragment size.
Bilgin, N., Copur, H., Balci, C. and co-workers (1999–2005). Field and full-scale cutting studies, Tuzla–Dragos, Hereke and Küçüksu tunnels. — measured machine-level specific energies against known rock strength.
Reece, A. R. (1964). The fundamental equation of earth-moving mechanics. — why soil obeys an opposite-signed law to rock.
Miedema, S. A.The Delft Sand, Clay and Rock Cutting Model, §6.12. — saturated sand, where pore-water dilatancy dominates.
Hawkes, I. & Mellor, M. (1972). Deformation and fracture of ice under uniaxial stress. J. Glaciol.11(61):103–131. — ice strength as a function of strain rate.
Herron, M. M. & Langway, C. C. (1980). Firn densification: an empirical model. J. Glaciol.25(93). — snow and firn densities, which are not ice densities.
Material properties
ASTM A240, A36; AMS 4911; MIL-S-21952 and manufacturer datasheets (AK Steel, Rolled Alloys, Kaiser Aluminum, Toray). — yield, tensile and elongation figures for the alloys the game's materials are modelled on.
EN 1992-1-1 (Eurocode 2), Table 3.1. — concrete strain limits.
Corti, C. (1999). Metallurgy of microalloyed 24 carat golds. Gold Bulletin32(2):39–47.
Ashby, M. F. (1998). Checks and estimates for material properties. Proc. R. Soc. Lond. A454:1301–1321. — why material properties are treated on logarithmic rather than linear scales.
Schulson, E. M. (1999). The structure and mechanical behavior of ice. JOM51(2):21–27; Schweizer, Michot & Kirchner (2004), On the fracture toughness of snow. Ann. Glaciol.38.
