MY SIMULATOR

Sandbox Impact Lab

Drop a ball. Measure the crater. Read the ejecta.

INTERACTIVE 3D

Ball -v 0 m/sE 0 mJD - cmFPS 0

Sandbox Impact Lab: Ball-Drop Craters, Scaling and Ejecta Rays

Drop a ball into a bed of sand and measure what it makes: a bowl, a raised rim and a blanket of thrown-out grains with rays. Change the ball, its speed, the angle, the sand and the planet, and see which of them really matter. Click the sand to drop where you like.

Preset

Ball and impact

Ball material

Impact speed fixes the energy; the equivalent drop height is shown below.

Sand and planet

Sand

Gravity

Gravity enters the crater size as g^-1/4: on the Moon the same impact digs a bigger crater, and the grains fly 6 times farther.

Prediction and measurement

Cross-section of the last crater (cm)

Rim crest and ejecta blanket are visible; measured from the 4 mm height-field grid vs the analytic profile.

Experiments (measured vs predicted)

Run an experiment. They use blank copies of the sand bed and do not touch the live one.

Independent numerical checks

Also run outside the browser: node src/check.js (free-fall integrator, ejecta ballistic range, volume conservation, measured-vs-model crater, scaling implementation, ejecta energy bound).

Educational model. The crater size law and its coefficient are empirical [assumption: coefficient 0.85, typical laboratory order of magnitude, not a fit to one dataset]; the ejecta blanket shape, ray pattern and the oblique-impact asymmetry are phenomenological. Grains are drawn larger than real sand and are a sample of the ejecta, not a granular-physics (DEM) simulation. Real craters in dry sand vary with packing, humidity and grain size.

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Hero, Top, Grazing buttons (keys H, T, G).
Click or tap the sand to drop the ball there; the Drop ball button drops at the last target. Slow motion slows everything, including the falling ball and the flight of the grains.
Impact angle below 90 degrees fires the ball obliquely from the chosen direction; below about 30 degrees the ejecta forms a butterfly pattern with an empty zone uprange.
Smooth the sand wipes all craters. Each new crater is added on top of the old ones.

The science

Energy. A ball of density ρ_b and diameter d has mass m = ρ_b π d³/6, hits at speed v (from a drop h = v²/2g) with kinetic energy E = ½ m v².

Crater size (gravity regime). Dimensional analysis: when strength is negligible the only combination of energy, sand density and gravity with the dimension of a length is (E / ρ_s g)^1/4, so D = C (E/ρ_s g)^1/4 (sin θ)^1/3 with an empirical coefficient C of order 1 (0.85 here, [assumption]). Laboratory studies of ball drops into granular beds find exactly this E^1/4 trend. Depth is a fixed fraction of the diameter that depends on packing (about 0.14 packed, 0.20 loose, 0.24 for fine flour, [typical values]). Doubling the speed multiplies D by 2^1/2; the same energy on the Moon (6 times weaker gravity) digs a crater 6^1/4 = 1.57 times wider.

Profile and mass balance. Inside the rim the bowl is a paraboloid z = -d(1 - s²) + T s⁴ (s = r/R). Outside, the ejecta blanket thins as T s^-3 out to 5 R (an exponent close to -3 is the classic result for crater ejecta). T is chosen so that the volume thrown out equals the volume of the bowl (no bulking); the check sums the height field on a grid and finds the net change within about 1 %.

Ejecta flight. Each sample grain is launched near 45 degrees and follows a parabola: range x = v² sin 2θ / g, flight time 2 v sinθ / g. The landing radii are drawn with probability ~1/r (mass in the blanket ~ thickness × area). Because x ~ 1/g, ejecta fly 6 times as far on the Moon, and the blanket appears when the grains land. Their total kinetic energy is a few per cent of the impact energy, as it must be below 100 %.

Rays and oblique impacts. Rays are modelled as random azimuthal modulation of the blanket. For an oblique impact the downrange side gets more ejecta; below about 30 degrees the pattern becomes a butterfly with empty zones uprange and downrange. Both are phenomenological [assumption] sketches of observed patterns, not derived from the physics of the impact.

Not modelled: grain-scale physics (jamming, force chains), air in the pore space, moisture, ball deformation or rebound, central peaks and jets, ball penetration depth. The ball just comes to rest in the crater.