Drag Force & Terminal Velocity

For turbulent flow the drag force is F = ½·ρ·v²·C_d·A, with ρ the fluid density, v the speed, C_d the drag coefficient and A the frontal area. The v² is what matters: doubling the speed quadruples the force and, since power is F·v, needs eight times the power. That is why a car's fuel use climbs so steeply above 90 km/h, and why the last few km/h of top speed are so expensive. The formula assumes quadratic drag — turbulent flow at a Reynolds number above a few thousand — not the linear Stokes drag of dust, mist or very slow motion.

A falling body accelerates until drag equals weight; setting ½ρv²C_dA = mg gives v_t = √(2mg ÷ ρC_dA). The approach is not instant: v(t) = v_t·tanh(gt ÷ v_t), so 95 % of it arrives after (v_t ÷ g)·artanh(0.95) seconds, and the page gives that time and the distance fallen. Buoyancy is ignored, which is right in air and wrong in water for anything near neutral; a tumbling or deforming body changes both A and C_d as it falls.

For air, ρ = p ÷ RT with the pressure from the ISA barometric formula p = 101 325(1 − 2.255 77 × 10⁻⁵ h)^5.255 88 and R = 287.05 J/(kg·K) for dry air — so temperature and altitude both change the answer, and humidity (not modelled) lowers it slightly. Any other fluid takes a density you enter. The drag coefficient is always yours: it depends on shape and Reynolds number, no table is stored, and quoting one without the conditions it was measured in is meaningless. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.