Presets
Playback
Parameters
Model checks
The science
Flight: gravity and quadratic drag
A small iron sphere of radius r and mass m = 4/3 π r³ ρ obeys m dv/dt = m g + ½ ρair Cd π r² |v| v (drag opposite to the velocity). It reaches a terminal speed vt = √(8 ρ r g / (3 ρair Cd)), and falling from rest its speed is exactly vt tanh(g t / vt). In vacuum the range at launch angle α is v² sin 2α / g; drag shortens it and tilts the optimum angle below 45 degrees.
Cooling by radiation
A glowing grain loses heat by thermal radiation, m c dT/dt = -ε σ 4πr² (T&sup4; - Ta&sup4;). With Ta neglected this gives dT/dt = -k T&sup4; with k = 3εσ/(ρ c r), so 1/T³ = 1/T0³ + 3 k t: small sparks go dull red much sooner than large ones. The colour on screen follows the temperature.
Honest simplifications: real iron sparks also burn (oxidation releases heat and they may burst), cool by convection, and have size-dependent Cd; here every spark is a solid sphere cooled by radiation only, with a fixed Cd, and launch speeds and sizes are drawn from simple lognormal distributions.
What to try
- No air drag preset vs Forge: compare the range curve peak angle.
- Fine fast sparks stop glowing in under a second; Heavy slow bits glow much longer.
- Moon forge: low gravity throws the same sparks several times farther.
- Click the anvil to add your own strike.