Quadratic Drag Force (Newtonian)
Gives the aerodynamic drag on a body moving at moderate to high speeds: F = ½ρC_d Av²
The equation
What it solves
Gives the aerodynamic drag on a body moving at moderate to high speeds: F = ½ρC_d Av². The drag grows with the square of speed, which is why doubling your speed requires four times the force to maintain constant velocity.
When to use it
High-Reynolds-number flows: cars, cyclists, skydivers, balls in air. C_d (drag coefficient) and A (cross-sectional area) are looked up or given; ρ is the fluid density.
When NOT to use it
Overestimates drag at very low speeds (Stokes regime, Re ≪ 1). C_d changes with angle of attack and Reynolds number, so the formula is not exact for objects with complex shapes. Compressible flow (near or above Mach 1) requires separate treatment.
Common mistakes
Forgetting the ½ factor. Using the wrong area A — it is the frontal (cross-sectional) area, not the surface area. Mixing up C_d (dimensionless drag coefficient) with b (dimensional Stokes drag coefficient).