formula.expert

Drag Force (F = ½CdρAv²)

Also known as air resistance force · wind load on a body

FD=12CdρAv2F_D = \tfrac{1}{2} C_d \rho A v^{2}

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Above walking pace, resistance through a fluid follows the quadratic law F = ½C_dρAv², where C_d is a shape factor measured in a wind tunnel: about 1.1 for a flat plate, 0.47 for a sphere, 0.25–0.35 for a modern car, and roughly 0.04 for a sailplane fuselage. A car with C_d = 0.3 and 2.2 m² of frontal area meets 0.5 × 0.3 × 1.225 × 2.2 × 30² ≈ 364 N of drag at 30 m/s. Gustave Eiffel, having finished his tower, spent his later years dropping instrumented shapes down its side and then building France's first serious wind tunnel, producing the earliest reliable drag coefficients.

The v² is the entire story of highway fuel economy: drag force quadruples when you double speed, and since power is force times velocity, the power needed to overcome it grows with the cube — 8× the power from 50 to 100 km/h. That is why the last few km/h of top speed cost so much engine, why cyclists draft, and why the formula multiplies C_d by A rather than treating them separately; a slippery shape on a huge frontal area still pushes a lot of air.

Drag Force (F = ½CdρAv²)
FD=12CdρAv2F_D = \tfrac{1}{2} C_d \rho A v^{2}
Where
  • FDF_D= Drag force
  • CdC_d= Drag coefficient
  • ρ\rho= Fluid density
  • AA= Frontal area
  • vv= Speed
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