# 3D Airflow & Induced Drag

> Wing tip vortices, downwash, and the creation of induced drag.

- **Subject:** 081 — Principles of Flight
- **Section:** 081-01 — Subsonic Aerodynamics
- **Topic code:** 081-01-04
- **Last reviewed:** 2026-04-01
- **Author:** Pablo Asensio Martínez
- **HTML version:** https://pilotsyllabus.com/en/principles-of-flight/subsonic-aerodynamics/three-dimensional-airflow-around-an-aeroplane/

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## Wing Tip Vortices
On a finite wing (3D), air flows from the high-pressure area (under the wing) to the low-pressure area (over the wing) around the wing tip.
*   This creates a rotating vortex at each wingtip.
*   **Direction**: Inwards over the top surface, Outwards under the bottom surface.
*   **Result**: Downwash behind the wing.

## Induced Drag ($D_i$)
The downwash tilts the local relative airflow downwards.
*   The lift vector (perpendicular to airflow) is tilted backwards.
*   The horizontal component of this tilted lift is **Induced Drag**.
*   **Formula**:
    $$ D_i \propto \frac{L^2}{\rho V^2 \times AR} $$
    Or in coefficient form:
    $$ C_{D_i} = \frac{C_L^2}{\pi \cdot AR \cdot e} $$

## Factors Affecting Induced Drag
1.  **Speed**: Induced drag is inversely proportional to $V^2$. High at low speed (Take-off/Landing). Low at high speed.
2.  **Lift**: Proportional to $L^2$. Heavier aircraft = More lift needed = More induced drag.
3.  **Aspect Ratio (AR)**: High AR (long narrow wings like gliders) reduces tip vortices and induced drag.
4.  **Winglets**: Physical barriers that reduce the flow around the tip, reducing vortex strength and induced drag.

## Wake Turbulence
The vortices persist behind the aircraft and constitute **Wake Turbulence**, which can be hazardous to following aircraft (especially light ones).

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