Drag Force (F = ½CdρAv²)

Above walking pace, resistance through a fluid follows the quadratic law $F = \tfrac{1}{2} C_d \rho A v^2$, 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.