Cookbook: blasts, craters and digging

The guides behind these: explosions, terrain. Each recipe says what to build and what to expect; the runnable versions, with the numbers they must produce, are in tests/unit/examples/physics-cookbook-blasts-and-ground.test.ts.

1. Danger rings for a charge#

How far must the player stand? Overpressure falls with distance by the scaled law, so a ring for each level of harm is one call:

const lethal  = radiusFor(200e3, 5);     // radius in metres where a 5 kg charge gives 200 kPa
const eardrum = radiusFor(35e3, 5);
const glass   = radiusFor(2e3, 5);
const there   = blastAt(eardrum, 5).overpressure;

Higher pressure, smaller ring. Eight times the charge gives twice the radius. Draw the rings on the ground as the player's warning, or apply explosion:exposure damage by pressure band.

2. A crater in sand, and in rock#

The crater radius is k W^(1/3.4); the constant k is a property of the soil. Rock gives a small crater, sand a wide one, and a bigger charge opens a bigger one slowly: ten times the charge gives 10^(1/3.4) times the radius.

const sand = craterRadius(EXAMPLE_CRATERS.sand, 50);
const rock = craterRadius(EXAMPLE_CRATERS.rock, 50);

Plug in your own CraterLaw (k, depthRatio, camouflet, throw) per soil with explosions({ craters }).

3. A charge buried too deep#

Bury it and the ground swallows the blast; deep enough and no crater opens at all: a camouflet. A mine works by being shallow; a mining charge by being deep.

craterRadius(law, 10, 0);                                       // on the surface
craterRadius(law, 10, 0.5);                                     // slightly buried: bigger, the ground couples the blast
craterRadius(law, 10, law.camouflet * Math.cbrt(10) * 1.01);    // past the limit: 0

In a world, detonate({ burst: 'buried', burial }) returns camouflet: true for the deep case and emits explosion:camouflet; the terrain stays flat.

4. A crater in a real terrain#

Hook a terrain to the capability and a surface burst excavates it; the heap that is thrown out equals the hole times the soil's bulking, so no matter is lost.

const ground = new Terrain({ nx: 121, nz: 121, cell: 0.25, soils: new SoilLibrary(EXAMPLE_SOILS),
                             strata: [{ soil: 'sand', thickness: 5 }] });
const blast = explosions({ terrain: ground });
host.register(blast);
host.enable('explosion');
const result = blast.detonate({ at: [15, 5, 15], tnt: 50, burst: 'surface' });

result.crater has the radius, the depth and the volume removed. The explosion:crater event carries the speed at the rim and the range of the fastest ejecta. See terrain for what the ground does next: the sides slump to their angle of repose.

5. A wall that shields#

A body between the charge and a target blocks the rays; the target receives only the transmission share (0.1 by default). Two bodies at equal distance, one with a static shield in front of it:

make('open', -10); make('hidden', 10); make('shield', 5, 'static', 2);
blast.detonate({ at: [0, 0, 0], tnt: 10 });

The open one receives the impulse the blast law gives times its cross-section; the hidden one a tenth of it. A thin screen has a transmission of 0.5, a bunker door 0.01. Set it per entity.

6. Water carries a blast further#

Water is almost incompressible, so an underwater burst gives a much higher pressure at the same distance, and the front travels at 1480 m/s:

const air = blastAt(20, 10), water = underwaterAt(20, 10);

detonate({ burst: 'water' }) uses the liquid curve for everything in range: a hull is pushed far harder than the same charge in air would push it, which is why depth charges work.

7. A trench that holds, and one that slumps#

A vertical cut in cohesive soil stands to the critical height (4c/γ) tan(45° + φ/2); deeper and the walls slump. Dry sand stands no vertical cut at all.

const limit = criticalHeight(clay);
const result = terrain.dig({ footprint: { box: [4, 4, 6, 6] }, depth: 0.9 * limit, tool, dt: 1 });
result.slump.moved;        // 0 at 90 % of the limit, more than 0 at 110 %

DigResult.slump reports what the walls did after the dig. Use criticalHeight and culmannHeight (for a sloped face) in your own tool tips: "this trench will fail at 1.6 m". Shore it up (a lined tunnel, a wall) and it stands.