Calculadora de Queda Livre com Resistência do Ar

This calculator simulates the fall of a body under gravity with air resistance, a real phenomenon that differs from ideal free fall. Instead of accelerating indefinitely, the body reaches a terminal velocity when drag force equals weight. The tool computes terminal velocity using v_t = √(2mg/(ρ·Cd·A)), where m is mass, g gravity, ρ air density, Cd drag coefficient, and A frontal area. It also determines the fraction of terminal velocity reached after a given time t, using a model with drag proportional to velocity squared.

To use the calculator, enter the body parameters (mass, area, drag coefficient) and environmental conditions (air density, gravity). Optionally provide a time t to get instantaneous velocity and fraction of terminal. Results show terminal velocity and, if time is given, velocity at time t and percentage of terminal reached. This tool is useful for designing parachutes, analyzing object falls in fluids, or understanding speed limits in sports like skydiving.

Important caveats: the formula assumes turbulent flow (high Reynolds number), common for large objects at moderate to high speeds. For very small particles or very low speeds, viscous drag (Stokes) would be more appropriate. Drag coefficient depends on shape: a sphere has Cd ~0.47, a parachute ~1.4. Air density varies with altitude; use 1.225 kg/m³ at sea level. Note that terminal velocity is an asymptotic limit; in practice, the body reaches 99% of it after a few time constants.