= Wingtip vortex
= Wingtip vortices
{synonym}
A <wingtip vortex> is a concentrated rotating part of the wake behind a finite lifting wing. Spanwise variation of the wing’s <circulation> produces trailing <vorticity>, which can roll up into a strong counter-rotating pair. The two rotating wakes induce downward motion between them and upward motion farther outside. NASA’s account connects the tip-region <pressure>-driven flow with the pair and its induced change of local flow direction.<Induced Drag Coefficient by NASA Glenn Research Center>[Air Pressure of a Wing]{ref}
A useful idealization treats each concentrated wake as a straight <line vortex>. Outside its core, circular symmetry and the definition of circulation give
$$
\Gamma=\oint\mathbf u\cdot d\boldsymbol\ell=2\pi r\,u_\theta,
\qquad \boxed{u_\theta=\frac{\Gamma}{2\pi r}.}
$$
For stipulated $|\Gamma|=20\,\mathrm{m^2/s}$ and $r=0.50\,\mathrm m$, the ideal tangential speed is about $6.37\,\mathrm{m/s}$. The singularity as $r\to0$ is a defect of the line model: a real vortex has a finite core and a nonuniform vorticity distribution.
Consider an original cross-flow model with cores separated horizontally by $d$, strengths $-\Gamma$ and $+\Gamma$, and orientations chosen to give <downwash> between them. Each ideal vortex induces downward speed $|\Gamma|/(2\pi d)$ at the other core. At $d=10\,\mathrm m$ and $|\Gamma|=20\,\mathrm{m^2/s}$, this pair-interaction speed is about $0.318\,\mathrm{m/s}$. At the midpoint, adding their two velocities gives $2|\Gamma|/(\pi d)\approx1.273\,\mathrm{m/s}$ downward. These are distinct locations and distinct speeds.
\Image[/wingtip-vortex-pair.png]
{title=An illustrative counter-rotating <wingtip vortex> pair produces <downwash> between its cores}
{description=Constructed instantaneous cross-flow perpendicular to a trailing-vortex pair. Core separation is 10 m and circulation magnitude is 20 square metres per second. Uniform-vorticity cores of radius 0.4 m regularize the line-vortex field; streamlines show the instantaneous superposed velocity, not particle paths in a time-independent aircraft wake. The clipped color scale displays vertical velocity. This is a model illustration, not measured aircraft data.}
The wake is not generally two permanently straight tubes with fixed strength. A distributed trailing sheet rolls up, the cores move under induced velocities, and viscosity, turbulence and ambient motion alter the field. A wing’s actual span loading and operating state determine the wake, so the illustrative circulation and core size cannot be assigned to an aircraft merely from its visible span.
The connection to <lift-induced drag> is the complete induced-flow and load system. A short line sketched at each wingtip is not an extra independent friction <force> to add to an already complete drag calculation. The flow carries momentum and kinetic energy while changing the <force> direction experienced by the finite wing.
A proposed laboratory wake survey places a finite wing at a controlled load in a wind tunnel and measures transverse velocity at a downstream plane using calibrated directional probes or timed tracer images. Reverse the sign of lift to check the expected reversal of rotation, and compare measured circulation on several enclosing paths outside the cores. Tracers must follow the flow adequately, while finite sampling, tunnel walls and the probe’s own disturbance limit the inference. A visible tracer pattern alone does not supply the full three-dimensional velocity or <pressure> field.
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