Drag Equation
Reference for the drag equation F = 0.5pv2CdA.
Covers drag coefficient, frontal area, and fluid density for aerodynamic resistance on vehicles and projectiles.
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