Home/Aerospace Engineering/Aerodynamics/Induced Drag Coefficient

Formula & Calculator

Induced Drag Coefficient

Portion of total drag coefficient arising from the generation of lift (wingtip vortices).

Written by the Vorzep Team

AerodynamicsDragWing Design

Induced Drag Coefficient Calculator

CDi = CL2 / (π · e · AR)
Select the variable to solve for, then enter the other three values
CDiCLeAR
Solve for:
Enter the other three values
—
—
—
—
Typical e: 0.7–0.9 (aircraft), 1.0 (ideal) AR = b² / S

Variables

SymbolQuantityUnit
C_DiInduced drag coefficient
C_LLift coefficient
eOswald efficiency factor
ARAspect ratio

What it means

Induced drag is the drag that arises from the generation of lift, caused by downwash and tip vortices. The formula C_Di = C_L²/(π e AR) shows that induced drag decreases with higher aspect ratio and efficiency factor. It is a significant component of total drag at low speeds (takeoff, climb) and becomes less important at high speeds. The Oswald efficiency factor e accounts for non‑elliptical lift distributions and is typically 0.7‑0.9 for real wings. Minimising induced drag is crucial for range and endurance. The formula is used in performance analysis and in designing winglets (which increase effective AR). Understanding induced drag is fundamental to understanding the drag polar and aircraft efficiency.

Worked example

Induced Drag Coefficient – Two Examples

Real‑World
Scenario: C_L = 0.5, AR = 8, Oswald efficiency e = 0.8. Find induced drag coefficient.
ParameterValue
C_L0.5
e0.8
AR8
1C_Di = C_L²/(π·e·AR) = 0.25/(π×0.8×8) = 0.25/20.106 = 0.01243
Result C_Di = 0.0124 ✓ Moderate
Scenario: C_L = 0.8, AR = 10, e = 0.85. Find C_Di.
ParameterValue
C_L0.8
e0.85
AR10
1C_Di = 0.64/(π×0.85×10) = 0.64/26.704 = 0.02397
Result C_Di = 0.0240 ✓ Higher
Key insight: Induced drag increases with C_L² – it's the drag due to lift generation.

Common mistakes

  • Induced drag coefficient C_Di: C_Di = C_L² / (π·e·AR).
  • Oswald efficiency factor e: Between 0 and 1 – accounts for non‑elliptical lift distribution.
  • AR: Aspect ratio.
  • Elliptical lift distribution: e = 1 for elliptical; real wings have e ≈ 0.7‑0.9.
  • Units: All dimensionless.

Applications

Induced drag coefficient, C_Di = C_L²/(π·e·AR), accounts for the drag caused by the generation of lift (trailing vortices). It depends on lift coefficient, aspect ratio, and the Oswald efficiency factor e (which accounts for non‑elliptical lift distributions). Reducing induced drag is a key goal in aircraft design, especially at low speeds (takeoff, climb). Engineers use this formula to design wing shapes (elliptical lift distribution is optimal), winglets, and other devices that reduce vortices. This coefficient is essential for calculating total drag and performance, particularly for high‑aspect‑ratio aircraft. By understanding induced drag, aerospace engineers can improve aerodynamic efficiency, range, and fuel economy.

  • Drag breakdown and performance analysis
  • Design of winglets and wingtip devices
  • Optimisation of wing planform and twist
  • Calculation of takeoff and climb performance
  • Trade‑off studies between induced and parasitic drag