Terminal Velocity
Steady fall speed where drag balances weight: √(2mg / ρ·C_d·A).
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The engineering
Fall long enough and acceleration retires: drag grows with V² until it equals weight, and you coast at V_t. A belly-down skydiver runs about 55–60 m/s; pull the parachute and you've multiplied C_d·A a hundredfold, dropping V_t to a survivable ~5 m/s. Same equation, different area — that's the entire parachute industry.
The ballistic coefficient m/(C_d·A) is the real character in the formula: heavy-and-slick falls fast (hail, bombs, reentry capsules), light-and-fluffy falls slow (snow, dandelion seeds, dust that never seems to land). And since ρ thins with altitude, V_t is higher upstairs — skydive math always says *at what altitude*.
Where this math comes from
Galileo's Discorsi (1638) argued all bodies fall alike *in vacuo* and correctly blamed the air for the differences we see — the conceptual birth of terminal velocity. Newton quantified the V² resistance regime (1687), and Stokes handled the gentle end (1851), where mist droplets obey a linear law instead.
The parachute went from Louis-Sébastien Lenormand's 1783 tower jump to André-Jacques Garnerin's 1797 balloon descent on showmanship and courage, but the twentieth century engineered it: Leslie Irvin's 1919 free-fall jump proved humans could deploy at V_t, and drop-test programs from mail sacks to Mars landers have been sizing C_d·A against this card's square root ever since.
- 1638Galileo GalileiAir resistance identified as why falling bodies differ.
- 1687Isaac NewtonV² drag regime quantified.
- 1797André-Jacques GarnerinFirst parachute descent from a balloon.
- 1919Leslie IrvinFirst premeditated free-fall parachute jump — V_t survived by design.
See the full timeline of the math behind every calculator →
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