Drag Force Calculator
Enter drag coefficient Cd, fluid density ρ, frontal area A and relative velocity v to compute the fluid drag force Fd = ½·Cd·ρ·A·v².
輸入資料
計算結果
重點速覽：When a body moves through a fluid (air, water) or a fluid flows past a stationary body, the body experiences a force opposing the relative motion — fluid drag. The drag equation: Fd = ½ × Cd × ρ × A × v², where Fd is drag (N), Cd the drag coefficient (dimensionless), ρ fluid density (kg/m³), A the frontal projected area (m²) and v the relative velocity (m/s). The term ½·ρ·v² is the fluid's dynamic pressure; multiplying by A gives a force scale, and Cd corrects for shape and flow. Drag scales with v²: doubling speed quadruples drag. Cd is set by shape and Reynolds number (sphere ≈ 0.47, cylinder ≈ 1.0–1.2, flat plate ≈ 1.28, streamlined ≈ 0.04–0.1, car ≈ 0.25–0.35).
計算公式
Drag: Fd = ½ × Cd × ρ × A × v² (N).
Cd drag coefficient (dimensionless), ρ density (kg/m³), A frontal area (m²), v relative velocity (m/s).
Drag scales with v²: double v → 4× Fd.
$$F_d = \tfrac{1}{2}\,C_d\,\rho\,A\,v^{2}$$使用說明
- Enter drag coefficient Cd (sphere ≈ 0.47, plate ≈ 1.28).
- Enter fluid density ρ (air ≈ 1.225, water ≈ 1000), frontal area A and relative velocity v.
- The tool computes drag via Fd = ½Cd·ρ·A·v².
Drag vs relative velocity at Cd=0.47, ρ=1.225, A=0.5 m²
| Relative velocity v (m/s) | ≈ km/h | Drag Fd (N) | Note |
|---|---|---|---|
| 5 | 18 | 3.60 | Breeze |
| 10 | 36 | 14.39 | Baseline |
| 20 | 72 | 57.58 | v×2, Fd×4 |
| 30 | 108 | 129.54 | Strong wind |
| 40 | 144 | 230.30 | Typhoon scale |
Drag ∝ v²: speed 10→20 m/s (×2) lifts drag 14.4→57.6 N (×4). Wind-resistant design is especially sensitive at high speed.
理財情境案例
Wind load on a greenhouse panel
Approximate Cd ≈ 1.2, frontal area A = 0.5 m², air ρ = 1.225, wind v = 20 m/s (72 km/h).
Fd = ½ × 1.2 × 1.225 × 0.5 × 20² ≈ 147 N.
At 30 m/s (strong typhoon), drag rises to ≈ 331 N (×2.25), showing why anchoring against high winds matters.
Double the speed, quadruple the drag
Sphere Cd = 0.47, A = 0.5 m², in air, v from 10 to 20 m/s.
Fd goes from 14.39 N to 57.58 N — exactly 2² = 4×.
Confirms drag ∝ v² — why drag dominates energy use at high speed; saving fuel means lower speed and streamlining.
常見問題
Why does drag scale with the square of velocity?
Drag is dominated by the fluid's dynamic pressure ½ρv² — the kinetic energy per volume that the fluid carries into the body, reflecting the impact pressure. Multiplying by frontal area A gives a force, then Cd corrects for shape. Dynamic pressure ∝ v², so pressure-dominated drag ∝ v². Intuition: doubling speed doubles the mass of fluid hitting the body per second (flow ∝ v) and doubles the momentum of each parcel (∝ v), so the force (rate of momentum change) becomes 4×. That is why drag dominates at high speed. At very low Reynolds numbers (viscosity-dominated) use Stokes drag ∝ v instead.
How do I choose the drag coefficient Cd?
Cd is set by shape and Reynolds number, usually from wind-tunnel or towing-tank tests. Common values: streamlined (airfoil, teardrop) ≈ 0.04–0.1; car ≈ 0.25–0.35; smooth sphere ≈ 0.47 (subcritical); long cylinder (cross-flow) ≈ 1.0–1.2; flat plate normal ≈ 1.28; hemisphere concave-to-flow ≈ 1.4; parachute higher. Cd drops sharply near the critical Reynolds number (sphere 0.47 → ≈ 0.1) as the boundary layer turns turbulent and the wake narrows, so pick Cd for the actual flow regime.
What is the frontal area A?
A is usually the frontal (projected) area — the body's silhouette area on a plane perpendicular to flow, i.e. what the fluid 'sees head-on'. For a sphere/cylinder use the circular/rectangular front area; for a vehicle the front-profile area; for a plate the plate area (if normal to flow). But some fields use a different reference area — e.g. wing lift/drag coefficients use planform area, ships may use wetted area. Key: Cd and A must match — use whichever area the Cd was defined against. This tool uses the common frontal projected area.
Air and water densities differ a lot — how much does drag change?
Drag ∝ fluid density ρ. Water ≈ 1000 kg/m³ vs air (15°C sea level) ≈ 1.225 kg/m³ — about 816×. So at the same Cd, A, v, drag in water is ~800× that in air — why swimming and rowing are far harder than moving in air, and why hydrodynamic drag matters for ships, submerged structures and aquatic life. Water density varies slightly with temperature and salinity (seawater ≈ 1025); air density varies with temperature, pressure and altitude (hotter or higher → lower, less drag). Use the actual fluid and conditions.
How do I reduce fluid drag?
From Fd = ½Cd·ρ·A·v²: lower v (most effective via v² — slight speed cuts slash drag), streamline to lower Cd (teardrop shapes cut wake separation, Cd can fall below 0.1), shrink frontal area A, or surface treatment (golf-ball dimples trigger earlier turbulent boundary layer at certain Re, delaying separation and lowering Cd). Practically combine: vehicles via streamlining + lower A, athletes via posture + fabric, structures via reducing exposed area and shaping.
相關工具
參考資料
Content reviewed by the Hong Kong Calculator science team. Fd = ½Cd·ρ·A·v²; Cd varies with Reynolds number, use Stokes drag at very low Re.