Drag Equation
Aerodynamic drag force on the aircraft, analogous to lift with a drag coefficient.
Formula
Variables
Example
Doubling airspeed quadruples aerodynamic drag — which is why cruise fuel burn climbs fast.
How it works
This equation estimates the aerodynamic force resisting motion through air. It says drag grows with air density, the square of speed, the chosen reference area, and a dimensionless drag coefficient that captures shape, surface roughness, and flow conditions. The v^2 term appears because faster flow carries more momentum and creates stronger pressure differences and shear around the body.
When to use it
Use it when estimating the drag on an aircraft, drone, missile, or any body moving through air, especially in steady or near-steady flight. It is also useful for comparing how changes in speed, altitude, shape, or configuration affect required thrust or power.
Worked example, step by step
Given: ρ = 1.225 kg/m^3 v = 70 m/s S = 16 m^2 C_D = 0.032 Step 1: Square the airspeed v^2 = 70^2 = 4900 m^2/s^2 Step 2: Multiply the constants (1/2)ρ = 0.5 × 1.225 = 0.6125 Step 3: Substitute into the drag equation D = (1/2)ρv^2SC_D D = 0.6125 × 4900 × 16 × 0.032 Step 4: Calculate the result 0.6125 × 4900 = 3001.25 3001.25 × 16 = 48020 48020 × 0.032 = 1536.64 N Final answer: D ≈ 1.54 × 10^3 N of drag
Common mistakes to avoid
- Forgetting that speed must be squared, which makes the drag change much less than it really does
- Using wing area without checking whether the chosen drag coefficient is based on the same reference area
- Mixing units, such as using speed in km/h or density in g/L without converting to SI units
Did You Know?
Drag also rises with the square of speed — which is why fuel burn soars at high cruise speeds.
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