Terminal Velocity — Linear (F = k v) vs Quadratic (F = k v²)

Narrow fall column, graphs on the right, zoom up to 240 m. On-ball force arrows show mg (red) and drag (blue) dynamically.

Controls

Air
Fluid
Linear (F = k v)
Quadratic (F = k v²)
0.050
0.020
1.23
40.0
Quadratic: \(k_2=\tfrac12\rho C_d A\) (sphere \(C_d\approx0.47\)). Linear uses Stokes \(k_1=6\pi\eta r\) with \(\eta\approx10^{-3}\,\mathrm{Pa\,s}\times(\rho/1000)\).

Live values

Velocity v (m·s⁻¹)
0.00
Acceleration a (m·s⁻²)
9.81
Net force ΣF (N)
0.00

Simulation

mg Drag
On-ball arrows grow/shrink with the forces; they become equal at terminal velocity.

Graphs

v(t) a(t) vₜ
Dashed line marks terminal velocity \(v_t\) for the current parameters & model.