Drag Equation
The drag equation F = ½ρv²CdA calculates aerodynamic drag force on an object moving through a fluid like air or water.
The Formula
The drag equation calculates the force that resists the motion of an object through a fluid. This force depends on the fluid density, the object's speed, its shape, and its cross-sectional area.
Drag increases with the square of velocity. Double your speed and the drag force quadruples.
Variables
| Symbol | Meaning |
|---|---|
| F_D | Drag force (in newtons, N) |
| ρ | Fluid density (in kg/m³; air at sea level ≈ 1.225 kg/m³) |
| v | Velocity of the object relative to the fluid (in m/s) |
| C_d | Drag coefficient (dimensionless; depends on shape) |
| A | Reference area — typically the frontal cross-sectional area (in m²) |
Common Drag Coefficients
| Shape | C_d |
|---|---|
| Sphere | 0.47 |
| Flat plate (perpendicular) | 1.28 |
| Streamlined body | 0.04 |
| Bicycle + rider | 0.9 |
| Typical car | 0.25 – 0.35 |
Example 1
A car with C_d = 0.30, frontal area 2.2 m², travels at 30 m/s (about 108 km/h or 67 mph) in air at sea level. What is the drag force?
F_D = ½ρv²C_dA
F_D = ½ × 1.225 × 30² × 0.30 × 2.2
F_D = 0.5 × 1.225 × 900 × 0.30 × 2.2
F_D = 0.5 × 1.225 × 900 × 0.66
F_D ≈ 363.8 N
Example 2
A skydiver (mass 80 kg) falls through air. Their drag coefficient is 1.0 and body area is 0.7 m². At what speed do they reach terminal velocity?
At terminal velocity, drag equals weight: F_D = mg
½ρv²C_dA = mg
v² = 2mg / (ρC_dA) = 2(80)(9.81) / (1.225 × 1.0 × 0.7)
v² = 1569.6 / 0.8575 = 1830.6
v ≈ 42.8 m/s (about 154 km/h or 96 mph)
When to Use It
Use the drag equation whenever an object moves through a fluid and you need to know the resistive force.
- Automotive and aerospace engineering (fuel efficiency, top speed)
- Terminal velocity calculations for falling objects
- Wind load on buildings and structures
- Sports science (cycling, swimming, running)
- Projectile motion with air resistance