Induced Drag Calculator Formula
Understand the math behind the induced drag calculator. Each variable explained with a worked example.
Formulas Used
Induced Drag Coefficient (CDi)
cdi = pow(cl, 2) / (pi * oswald * aspect_ratio)Induced Drag Force
induced_drag_force = pow(cl, 2) / (pi * oswald * aspect_ratio) * dynamic_press * wing_areaVariables
| Variable | Description | Default |
|---|---|---|
cl | Lift Coefficient (CL) | 0.5 |
aspect_ratio | Aspect Ratio (AR) | 10 |
oswald | Oswald Efficiency Factor (e) | 0.85 |
dynamic_press | Dynamic Pressure (q)(Pa) | 5000 |
wing_area | Wing Area (S)(m²) | 100 |
How It Works
Induced Drag
Induced drag is the aerodynamic penalty of generating lift. It arises because the wing creates trailing vortices that tilt the local flow downward, effectively rotating the lift vector backward.
Formula
CDi = CL² / (pi × e × AR)
where CL is the lift coefficient, e is the Oswald span efficiency (typically 0.7 to 0.9), and AR is the aspect ratio. Induced drag dominates at low speeds and high CL, which is why it is critical during takeoff and climb.
Worked Example
A wing with CL=0.5, AR=10, e=0.85, at q=5000 Pa with S=100 m².
- 01CDi = 0.5² / (pi × 0.85 × 10)
- 02CDi = 0.25 / (26.704) = 0.00936
- 03Di = 0.00936 × 5000 × 100 = 4681 N
Frequently Asked Questions
What is the Oswald efficiency factor?
The Oswald factor e accounts for the non-elliptical lift distribution. A perfect elliptical wing has e = 1. Real wings with taper, twist, and fuselage interference have e between 0.7 and 0.9.
How can induced drag be reduced?
Increasing aspect ratio is the primary method. Winglets, raked wingtips, and optimizing the lift distribution toward elliptical also help. Reducing weight (and therefore CL) also reduces induced drag.
At what speed is induced drag highest?
Induced drag is highest at low speed because the aircraft must fly at a higher CL to maintain lift. Since CDi scales with CL², slow flight dramatically increases induced drag.
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