Drag Force
Aerodynamic drag on a moving body.
Formula
Variables
How it works
This formula estimates the resistive force a fluid exerts on an object moving through it, and it grows with the square of speed because faster motion creates a much larger pressure difference and more momentum transfer to the fluid. The factor 1/2 and the drag coefficient C_D bundle together the messy fluid-flow effects, such as shape, orientation, surface roughness, and whether the flow is laminar or turbulent. The area A is the projected frontal area, since that is the effective size the flow "sees."
When to use it
Use this when you need an estimate of aerodynamic or hydrodynamic drag on a body moving through air, water, or another fluid, especially at moderate to high Reynolds number. It is common in vehicle dynamics, sports physics, aerospace, and any problem where drag depends on speed, shape, and cross-sectional area.
Worked example, step by step
A cyclist and bike have an effective frontal area of A = 0.45 m^2 and a drag coefficient of C_D = 0.88. The rider is moving through air of density ρ = 1.20 kg/m^3 at speed v = 12 m/s. Use F_D = (1/2)ρv^2C_DA. F_D = 0.5 × 1.20 × (12)^2 × 0.88 × 0.45 F_D = 0.5 × 1.20 × 144 × 0.88 × 0.45 F_D = 34.56 × 0.45 F_D = 15.552 N So the drag force is about 15.6 N, acting opposite to the cyclist's direction of motion.
Common mistakes to avoid
- Using the side area or total surface area instead of the projected frontal area A
- Forgetting that drag acts opposite the direction of motion, so the force should be treated as a resisting force
- Using this formula at very low speeds or in regimes where the drag coefficient is not approximately constant
Did You Know?
Air drag rises with the square of speed, which is why fuel economy plummets at highway velocities.
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