Wind Resistance & Coefficients of Drag
Drag is the force that resists an object moving through a fluid (air, water, anything). It’s governed by one of the most important equations in fluid mechanics:
Fd = ½ρv²CdA
Breaking It Down
- ρ (rho) — fluid density (air at sea level ≈ 0.00238 slug/ft³ or 1.225 kg/m³)
- v² — velocity SQUARED. This is the big one. Double your speed, quadruple the drag.
- Cd — drag coefficient. A dimensionless number that captures the shape’s aerodynamic efficiency.
- A — reference area (usually frontal area — the “shadow” the object casts)
Why v² Changes Everything
The velocity-squared relationship has profound implications:
- Going from 60 to 80 mph increases drag by (80/60)² = 1.78×
- Since power = force × velocity, power needed grows with v³
- Going from 60 to 80 mph requires (80/60)³ = 2.37× more power
- This is why fuel economy drops sharply at highway speeds
- This is why a cyclist at 30 mph needs 8× the power of one at 15 mph
Drag Coefficients for Common Shapes
| Shape | Cd | Notes |
|---|---|---|
| Flat plate (perpendicular) | 1.28 | Worst case — blunt face into wind |
| Cube | 1.05 | Slightly better than flat plate |
| Cylinder (lengthwise) | 0.82 | Pipe, flag poles |
| Sphere | 0.47 | Smooth ball |
| Half-sphere (open back) | 0.42 | Parachute shape |
| SUV / truck | 0.35-0.45 | Box shape, high ride |
| Typical sedan | 0.25-0.35 | Modern design |
| Tesla Model 3 | 0.23 | Among the best production cars |
| Cyclist (racing tuck) | 0.88 | CdA ≈ 0.32 m² |
| Airfoil / teardrop | 0.04 | Theoretical best for a solid shape |
Practical Example: Wind Load on a Sign
A 4′ × 8′ sign faces a 90 mph wind gust. What’s the force?
- ρ = 0.00238 slug/ft³ (air at sea level)
- v = 90 mph = 132 ft/s
- Cd = 1.28 (flat plate)
- A = 4 × 8 = 32 ft²
- F = ½ × 0.00238 × 132² × 1.28 × 32 = 849 lbf
Almost half a ton of force on a sheet of plywood. This is why signs blow down in hurricanes.
Reynolds Number: When Cd Changes
Drag coefficient isn’t truly constant — it depends on the Reynolds number (Re), which captures whether flow is laminar (smooth) or turbulent:
Re = ρvL / μ
A golf ball’s dimples exploit this: they trip the boundary layer into turbulence at lower Re, which actually reduces drag by allowing the air to follow the ball’s surface longer before separating. Counter-intuitive, but that’s why a dimpled ball flies farther than a smooth one.
Key Takeaways
- Drag force scales with v² — double the speed, quadruple the drag
- Power to overcome drag scales with v³ — speed is expensive
- Shape matters enormously: a teardrop has 32× less drag than a flat plate
- Wind loads on buildings and structures use the same equation — it’s just bigger numbers
- Use our unit converter for force and power conversions when working drag problems