The horseshoe vortex model is a simplified representation of the vortex

Vortex

A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...

 system of a wing

Wing

A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...

. In this model the wing vorticity is modelled by a bound vortex of constant circulation, travelling with the wing, and two trailing vortices

Wingtip vortices

Wingtip vortices are tubes of circulating air that are left behind a wing as it generates lift. One wingtip vortex trails from the tip of each wing. The cores of vortices spin at very high speed and are regions of very low pressure...

, therefore having a shape vaguely reminiscent of a horseshoe. (The starting vortex

Starting vortex

The starting vortex is a vortex which forms in the air adjacent to the trailing edge of an airfoil as it is accelerated from rest in a fluid. It leaves the airfoil , and remains stationary in the flow...

 created as the wing begins to move through the fluid is considered to have been dissipated by the action of viscosity

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

, as are the trailing vortices

Wingtip vortices

Wingtip vortices are tubes of circulating air that are left behind a wing as it generates lift. One wingtip vortex trails from the tip of each wing. The cores of vortices spin at very high speed and are regions of very low pressure...

 well behind the aircraft.)

The trailing vortices

Wingtip vortices

Wingtip vortices are tubes of circulating air that are left behind a wing as it generates lift. One wingtip vortex trails from the tip of each wing. The cores of vortices spin at very high speed and are regions of very low pressure...

 are responsible for the component of the downwash

Downwash

In aeronautics downwash is the air forced down by the aerodynamic action of a wing or helicopter rotor blade in motion, as part of the process of producing lift....

 which creates induced drag.

The horseshoe vortex model is unrealistic in implying a constant circulation (and hence by the Kutta–Joukowski theorem

Kutta–Joukowski theorem

The Kutta–Joukowski theorem is a fundamental theorem of aerodynamics. It is named after the German Martin Wilhelm Kutta and the Russian Nikolai Zhukovsky who first developed its key ideas in the early 20th century. The theorem relates the lift generated by a right cylinder to the speed of the...

 constant lift) at all sections on the wingspan

Wingspan

The wingspan of an airplane or a bird, is the distance from one wingtip to the other wingtip. For example, the Boeing 777 has a wingspan of about ; and a Wandering Albatross caught in 1965 had a wingspan of , the official record for a living bird.The term wingspan, more technically extent, is...

. In a more realistic model (due to Ludwig Prandtl) the vortex strength reduces along the wingspan

Wingspan

The wingspan of an airplane or a bird, is the distance from one wingtip to the other wingtip. For example, the Boeing 777 has a wingspan of about ; and a Wandering Albatross caught in 1965 had a wingspan of , the official record for a living bird.The term wingspan, more technically extent, is...

, and the loss in vortex strength is shed as a vortex-sheet from the trailing edge, rather than just at the wing-tips. However, by using the horseshoe vortex model with a reduced effective wingspan but same midplane circulation, the flows induced far from the aircraft can be adequately modelled.

See also

• Helmholtz's theorems
  Helmholtz's theorems
  In fluid mechanics, Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex filaments...
  
  
• Kutta condition
  Kutta condition
  The Kutta condition is a principle in steady flow fluid dynamics, especially aerodynamics, that is applicable to solid bodies which have sharp corners such as the trailing edges of airfoils...
  
  
• Kutta–Joukowski theorem
  Kutta–Joukowski theorem
  The Kutta–Joukowski theorem is a fundamental theorem of aerodynamics. It is named after the German Martin Wilhelm Kutta and the Russian Nikolai Zhukovsky who first developed its key ideas in the early 20th century. The theorem relates the lift generated by a right cylinder to the speed of the...
  
  
• Prandtl's lifting-line model
  Lifting-line theory
  Lifting-line theory or Lanchester-Prandtl wing theory was published by Ludwig Prandtl in 1918–1919 after working with Albert Betz and Max Munk on the problem of a useful mathematical tool for examining lift from "real world" wings....