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Free Fall Simulator

Free Fall & Terminal Velocity Simulator

Vary mass, drag coefficient, and cross-sectional area to integrate free fall numerically. Compare vacuum vs. air-drag fall and experience terminal velocity hands-on.

Parameters
Presets
Mass m 1.0 kg
Drag coefficient Cd 0.47
Sphere: 0.47 / Streamlined: 0.04 / Flat plate: 1.17
Cross-sectional area A 0.0100 m²
Air density ρ 1.225 kg/m³
Sea level: 1.225 / 10 km alt.: 0.41 / Vacuum: 0
Initial height h₀ 200 m
Initial velocity (downward) v₀ 0.0 m/s
Terminal velocity v_t [m/s]
Landing time [s]
Landing speed [m/s]
Time to terminal v [s]
With air drag
Vacuum (Cd=0)
Terminal velocity
Velocity v(t) [m/s]
Altitude h(t) [m]

Theory

$$m\frac{dv}{dt} = mg - \frac{1}{2}C_d \rho A v^2$$

Terminal velocity (when $dv/dt = 0$):

$$v_t = \sqrt{\frac{2mg}{C_d \rho A}}$$

Vacuum fall ($C_d=0$): $v = v_0 + gt$, $h = h_0 - v_0 t - \frac{1}{2}gt^2$

Numerical integration: Euler method (Δt = 0.01 s) over all time steps

CAE Connection: Initial velocity setting for drop impact analyses (LS-DYNA / Abaqus Drop Test) / Cd validation for automotive aerodynamic drag (CFD) / preliminary terminal velocity estimation for spacecraft re-entry / coupling with Reynolds number calculations.