Terminal Velocity Calculator
Calculate terminal velocity — the maximum speed a falling object reaches when drag force equals gravity. With real-world examples from skydiving to raindrops.
Terminal Velocity Guide
The Terminal Velocity Formula
Terminal velocity occurs when drag force = weight. Vt = √(2mg / ρACd). Where m = mass (kg), g = 9.81 m/s², ρ = fluid density (kg/m³), A = cross-sectional area (m²), Cd = drag coefficient. For a typical skydiver (80 kg, belly-to-earth, A = 0.7 m², Cd = 1.0, sea-level air): Vt = √(2×80×9.81 / 1.225×0.7×1.0) = √(1569.6 / 0.858) = √1829.4 = 42.8 m/s ≈ 154 km/h. Head-down speed skydiving position reduces area and Cd, producing terminal velocities of 250-300 km/h.
How Drag Force Works
As an object accelerates downward, air resistance (drag) increases with velocity squared: Fd = ½ρACdV². At low speeds, drag is small and the object accelerates. As speed increases, drag increases. Terminal velocity is reached when drag exactly equals gravitational force (weight = mg). The V² relationship explains why terminal velocity is so sensitive to area — doubling the cross-sectional area reduces terminal velocity by 1/√2 (about 29%). This is why a deployed parachute (large area) so dramati
Terminal Velocities in Nature and Engineering
Typical terminal velocities: raindrop (2mm diameter) approximately 7-9 m/s (25-32 km/h) — raindrops are not teardrop-shaped as commonly depicted; they are spherical or slightly flattened. Cat (compact body position): approximately 27 m/s (97 km/h) — cats have survived falls from high buildings due to their low terminal velocity and righting reflex. Skydiver belly-to-earth: 53-55 m/s (190-200 km/h). Head-down speed skydiver: 70-80 m/s (250-290 km/h). Felix Baumgartner's record-breaking jump from
Applications in Engineering
Car aerodynamics: reducing the drag coefficient from 0.35 to 0.30 reduces aerodynamic drag force at 70 mph by approximately 14%, directly improving fuel economy. Bicycle aerodynamics: at 40+ km/h, aerodynamic drag accounts for 80%+ of total resistance — hence the extreme aerodynamic positions in time trialling. Space reentry: spacecraft reenter at 7-8 km/s and use atmospheric drag plus heat shields to decelerate to safe parachute deployment speeds. Seed dispersal: sycamore and dandelion seeds ha
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