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.
cl = 0.5aspect_ratio = 10oswald = 0.85dynamic_press = 5000wing_area = 100
- 01CDi = 0.5² / (pi × 0.85 × 10)
- 02CDi = 0.25 / (26.704) = 0.00936
- 03Di = 0.00936 × 5000 × 100 = 4681 N
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