Drag Force
Drag force is the resistive force exerted by a fluid on a body moving through it, acting opposite to the direction of relative motion and composed of pressure drag (form drag) and skin-friction drag. For objects moving at moderate to high speeds, drag is proportional to the square of velocity, the fluid density, the frontal area, and a dimensionless drag coefficient that depends on shape and flow regime. Understanding and minimising drag is critical in vehicle and aircraft design, sports engineering, and offshore structure analysis.
Key Formula
F_D = (1/2) × C_D × ρ × A × v²
LaTeX: F_D = \tfrac{1}{2} C_D \rho A v^2
| Symbol | Meaning | Unit |
|---|---|---|
| F_D | Drag force | N |
| C_D | Drag coefficient (dimensionless, shape-dependent) | dimensionless |
| ρ | Fluid density | kg/m³ |
| A | Reference (frontal) area | m² |
| v | Relative speed of object through fluid | m/s |
Worked Example
Problem
A car with frontal area 2.2 m² and drag coefficient C_D = 0.30 travels at 30 m/s (108 km/h) through air (ρ = 1.2 kg/m³). Calculate the aerodynamic drag force.
Solution
Step 1 — Identify values: C_D = 0.30, ρ = 1.2 kg/m³, A = 2.2 m², v = 30 m/s. Step 2 — F_D = 0.5 × 0.30 × 1.2 × 2.2 × 30². Step 3 — v² = 900 m²/s². Step 4 — F_D = 0.5 × 0.30 × 1.2 × 2.2 × 900 = 0.5 × 0.396 × 2.2 × 900. Step 5 — F_D = 0.5 × 0.8712 × 900 = 0.5 × 784.08 = 356.04 ≈ 356 N.
Answer
F_D ≈ 356 N
Drag Coefficients for Common Object Shapes in Air
| Object / Shape | C_D (approx.) | Flow Regime | Design Relevance |
|---|---|---|---|
| Flat plate (perpendicular) | 1.28 | High Re | Maximum resistance, parachutes |
| Sphere | 0.47 | Re ~ 10⁵ | Balls, droplets, particles |
| Long cylinder (cross-flow) | 1.0–1.2 | High Re | Bridge cables, pipes |
| Streamlined aerofoil | 0.04–0.06 | High Re | Aircraft wings, turbine blades |
| Family saloon car | 0.28–0.35 | Road speeds | Fuel economy |
| Human cyclist (crouched) | 0.70 | Road speeds | Sports aerodynamics |
Interactive Tools
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Related Terms
Terminal Velocity
Terminal velocity is the constant maximum speed attained by an object falling through a fluid when the downward gravitational force equals the sum of the upward drag force and buoyancy force, resulting in zero net acceleration. At terminal velocity the object no longer accelerates; its speed depends on its mass, size, shape, and the fluid's density and viscosity. Terminal velocity is encountered in skydiving, raindrop formation, sedimentation in liquids, and the design of parachutes and falling bodies in engineering.
Turbulent Flow
Turbulent flow is a chaotic, irregular fluid motion characterised by rapid fluctuations in velocity and pressure, eddies, vortices, and vigorous lateral mixing between fluid layers. It occurs when inertial forces overcome viscous forces, typically at Reynolds numbers above 4000 in pipe flow, and is the dominant regime in most industrial, atmospheric, and oceanic flows. Despite its complexity, turbulent flow enhances heat and mass transfer, making it beneficial in heat exchangers and combustion systems.
Reynolds Number
The Reynolds number (Re) is a dimensionless quantity that predicts the flow regime of a fluid by comparing inertial forces to viscous forces within the flow. A low Reynolds number indicates that viscous forces dominate, resulting in smooth laminar flow, while a high value signals that inertial forces dominate, leading to turbulent flow. It is indispensable in scaling model experiments to full-size systems, designing pipelines, and predicting aerodynamic behaviour around aircraft and vehicles.
From Old English "dragan" (to pull or drag), related to Old Norse "draga". In fluid mechanics, "drag" has been used since the 18th century to describe resistance forces on bodies moving through air or water. The formal drag coefficient was introduced alongside dimensional analysis in the late 19th and early 20th centuries.