Drag Polar
Total drag coefficient is the sum of parasite drag and lift-induced drag — the fundamental performance relationship for an airframe.
Formula
Variables
Example
CD0=0.02, CL=0.5, e=0.8, AR=8: CD = 0.02 + 0.25/(20.1) ≈ 0.032
How it works
The drag polar links an aircraft’s total drag to how much lift it is producing. The first term, C_D0, represents drag that exists even with no lift, while the second term grows with the square of lift because generating lift creates trailing vortices and downwash that cost energy. The factor \u03c0eAR shows that wings with higher aspect ratio and better span efficiency lose less energy to induced drag, so they have a “flatter” drag polar.
When to use it
Use this relation when estimating aircraft performance from aerodynamic coefficients, especially in cruise, climb, and turn analyses. It is also useful for comparing wing designs or finding the lift coefficient that minimizes total drag for a given airframe.
Worked example, step by step
Given: C_D0 = 0.028, C_L = 0.9, e = 0.85, AR = 10 Step 1: Compute the induced-drag denominator \u03c0eAR = 3.1416 \u00d7 0.85 \u00d7 10 = 26.70 Step 2: Square the lift coefficient C_L^2 = 0.9^2 = 0.81 Step 3: Compute induced drag term C_L^2/(\u03c0eAR) = 0.81/26.70 = 0.0303 Step 4: Add parasite drag C_D = C_D0 + C_L^2/(\u03c0eAR) = 0.028 + 0.0303 = 0.0583 Final answer: C_D \u2248 0.058
Common mistakes to avoid
- Using the formula with dimensional quantities instead of nondimensional coefficients
- Forgetting that induced drag scales with C_L squared, not linearly with C_L
- Confusing Oswald efficiency e with physical efficiency or using values greater than 1
Did You Know?
The drag polar plots drag against lift — every airframe has one, and it sets the best glide and cruise speeds.
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