Induced Drag Coefficient
Drag due to lift, decreasing with higher aspect ratio and span efficiency.
Formula
Variables
Example
Long, slender glider wings have high aspect ratio and therefore very low induced drag.
How it works
This formula estimates the drag penalty created whenever a wing generates lift: the wing must create lower pressure below and higher pressure above, which forces the airflow to turn downward and leaves a trailing vortical wake. That downwash tilts the lift vector slightly rearward, producing induced drag; the effect grows with lift demand, so it scales with the square of the lift coefficient. A wing with larger aspect ratio and better span efficiency spreads lift more evenly along the span, weakens the tip vortices, and therefore reduces induced drag.
When to use it
Use this when analyzing lift-related drag on wings, especially in low-speed flight, takeoff, landing, climb, or for comparing wing planforms in aerodynamic design. It is also useful in performance calculations where lift coefficient, aspect ratio, and span efficiency are known or estimated.
Worked example, step by step
Given: C_L = 0.8 AR = 9.5 e = 0.82 Step 1: Square the lift coefficient C_L^2 = (0.8)^2 = 0.64 Step 2: Compute the denominator πeAR = π × 0.82 × 9.5 πeAR ≈ 3.1416 × 0.82 × 9.5 ≈ 24.49 Step 3: Divide to find induced drag coefficient C_{D,i} = C_L^2 / (πeAR) = 0.64 / 24.49 ≈ 0.0261 Final answer: C_{D,i} ≈ 0.026
Common mistakes to avoid
- Using the formula with drag coefficient data from cruise conditions without checking whether lift is actually the dominant drag contribution
- Forgetting that induced drag depends on C_L squared, so doubling lift coefficient quadruples induced drag
- Confusing aspect ratio with wing area instead of using AR = b^2 / S
Did You Know?
Induced drag is the price of making lift — it's why long, slender wings are so efficient.
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