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.
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Terminal Velocity Guide
What's the key thing to understand about 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, with its large area, so dramatically reduces terminal velocity compared to free-falling without one.
What do I need to know about 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 the stratosphere in 2012 reached speeds briefly exceeding the speed of sound, since the extremely thin air at that altitude offered far less drag than at normal skydiving altitudes.
What do I need to know about 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 have evolved shapes specifically to minimise their terminal velocity, letting the wind carry them much further from the parent plant before they land.