The height of an eruption column scales with the heat and mass delivered at the vent. Mastin et al. (2009) fitted observed plumes with H = 2.00 V0.241, H in km above the vent and V the dense-rock-equivalent volume flux in m3/s. A tenfold increase in flux therefore raises the plume only by about 74%. Mass flux is V times a magma density near 2500 kg/m3.

Volcanic bombs (blocks thrown from the vent) follow projectile motion with quadratic drag in an exponential atmosphere: m dv/dt = m g − ½ ρ(z) Cd A |v| v, ρ(z) = 1.225 e−z/8500, Cd = 0.47 for a sphere, dense rock 2500 kg/m3. Small bombs lose range quickly; very large ones approach the vacuum parabola R = v² sin 2θ / g, which is checked numerically.

Simplifications: the column lean in the cross-section is schematic; no gas-thrust phase, no supersonic Cd rise, no spinning or fragmentation; bombs launched from the vent altitude over level ground. Educational physics, not a hazard map.