Drag Coefficient — 2D Drop Test

Terminal velocity & the Cd–Re curve

Object

Shape Size (diameter) Fluid

Air 1.2 kg/m³

Water 1000 kg/m³

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ShapeSphere

Velocity v0 m/s

Reynolds Re–

Drag coeff. C_d–

Terminal v_t–

Falling body: gravity F_g = m·g pulls down, drag F_d = ½·ρ·v²·C_d·A opposes motion. As v grows, drag grows with v², so the body stops accelerating once F_d = F_g — the terminal velocity. Near Re≈2×10⁵ a sphere's boundary layer turns turbulent, C_d drops sharply (the drag crisis), and terminal velocity jumps.

C_d(Re) curve — current shape current operating point