in aerodynamics, the part of the aerodynamic resistance of a wing that is caused by the vortices whose axes originate on the wing and are directed downward against the flow. These so-called free vortices of the wing originate from the flow of air near the wingtips (Figure 1) from the region beneath the wing to the region above it. Above the wing, the airflow near the tip results in a flow directed from the tips toward the plane of symmetry; below the wing, from the plane of symmetry toward the tip. As a result, each particle in the wake, behind the wing, rotates about an axis that passes through the particle and is parallel to the velocity vector v of the oncoming flow; here the direction of rotation is opposite for the left and right halves of the wing (Figure 2). Thus, a continuous system of vortices that emanate from every point of the wing surface arises.

Figure 1. Diagram of the appearance of a tip vortex as a result of the flow of air from the area under the wing to the area above it

Figure 2. Cross section of the flow behind the wing in the plane perpendicular to v. The airflow at the wingtips causes a system of free vortices.

In the region between the end planes of the wing, free vortices induce velocities directed downward, and when the flow induced by the free vortices is superimposed on the oncoming flow, it directs it downward through the angle Δα (the flow rake angle). Since the lift of the wing should be perpendicular to the oncoming flow, it is deflected downward through the same angle a (Figure 3). Resolving this force into components along and perpendicular to v, we obtain the induced drag dQ_indand the lift dY. If the wing has infinitely large span, there is no induced drag.

Figure 3. Formation of induced drag as a result of the downwash of the flow by free vortices of the wing: v_u is the velocity induced by the free vortices, and Δαis the flow rake angle