Stones 0Landed 0Max D 0 mmMedian D 0 mmFPS 0

Drag to orbit, wheel or pinch to zoom. Coloured lines: sample stone paths inside the storm frame (colour = final diameter). Spheres on the ground: stones where they landed, at an exaggerated size. Grey disc: updraft core at the surface.

Hail Swath Lab: Embryo Ensemble, Ground Size Distribution and Impact Energy

Release hundreds of hailstone embryos into one storm updraft, let each grow by accretion, melt on the way down, and read the swath that lands on a moving storm's path.

Ready.

Storm

Embryos

Ensemble result

Ground swath (top view, storm moves up)

Size histogram at the ground

Impact kinetic energy vs diameter

Experiment: how strong must the updraft be?

Each row re-runs a 120-stone ensemble with the same settings except the peak updraft speed. Predicted = the largest stone an updraft of that speed can hold up at its strongest point (drag = weight).

Independent numerical checks

Controls

Pick a preset or move the sliders, then press Run ensemble. Changing a slider clears the old result.
Orbit with drag, zoom with the wheel or pinch. The three view buttons jump between the storm, the ground swath and a real-size ladder comparing the biggest stones with a coin, golf ball and tennis ball.
The same random seed is used every run, so presets are repeatable.

The science

Terminal velocity and drag. A stone of diameter D and density ρ_h falls through air of density ρ_a at v_t = √(4 ρ_h g D / (3 C_d ρ_a)) with C_d = 0.6 (a typical value for rough spheres at these Reynolds numbers; the real coefficient varies from about 0.5 to 0.8). An updraft of speed w holds a stone aloft when w = v_t, so the biggest stone it can support is D_sup = 3 C_d ρ_a w² / (4 ρ_h g).

Accretion. Supercooled droplets freeze on contact. Mass collected per second is dm/dt = E (πD²/4) |v_rel| · LWC with collection efficiency E = 1 (droplets are tiny and almost all stick; for small embryos the true E is lower), LWC the liquid-water content, and v_rel the stone speed relative to the air.

Dry and wet growth (Schumann–Ludlam). Latent heat must leave the surface: Q = h πD² (0 − T_a) with h from the Ranz–Marshall relation Nu = 2 + 0.6 Re^1/2 Pr^1/3. The most mass that can freeze per second is dm_crit/dt = Q / (L_f − c_w|T_a|). Below that the stone grows dry (white, porous, bulk density 600 kg/m³ here); above it the surface stays wet, clear ice (900 kg/m³) forms and the surplus water is shed. An evaporative-cooling term (vapour diffusion from the 0 °C surface into saturated cloud air, Sherwood number analogous to Nu) is added to Q. Spongy-hail retention of liquid water is neglected.

Melting. Below the 0 °C level the same convective heat flux, h πD² T_a, melts the outside at dm/dt = −h πD² T_a / L_f; meltwater is shed.

Storm. Updraft w = w_max sin(πz/Z_top) exp(−(r/R)²); temperature falls 6.5 K/km; air density ρ_a = 1.225 e^{−z/8.5 km}. Winds follow a turning shear profile, the storm moves with 75 % of the 5.5 km wind, and stones follow the air horizontally while drag acts on the relative velocity. Motion is integrated with fourth-order Runge–Kutta with an adaptive step.

Simplifications and honesty. The updraft is a fixed analytic shape, not a cloud model; LWC is a prescribed profile (the number you set is the peak in the core); stones do not deplete the cloud water; there is no electrification, no collisions, no hail fragmentation and no aggregation. Impact energy is ½ m v² at the first ground contact with no air-cushion or bounce. Size names (coin, golf ball, tennis ball) are typical sizes of everyday objects. The numbers are for teaching the mechanism, not for forecasting a particular storm.

Educational model. Family-friendly: targets are only ground and open field.