Horseshoe vortex

Horseshoe vortex

The horseshoe vortex model is a simplified representation of the vortex system of a wing. In this model the wing vorticity is modelled by a bound vortex of constant circulation, travelling with the wing, and two trailing vortices, therefore having a shape vaguely reminiscent of a horseshoe. [Millikan, Clark B., "Aerodynamics of the Airplane", Figure 1.35] [ McCormick, Barnes W., "Aerodynamics, Aeronautics, and Flight Mechanics", Chapter 3] (The starting vortex created as the wing begins to move through the fluid is considered to have been dissipated by the action of viscosity, as are the trailing vortices well behind the aircraft.)

The trailing vortices are responsible for the component of the downwash which creates induced drag. [ McCormick, Barnes W., "Aerodynamics, Aeronautics, and Flight Mechanics", Chapter 4]

The horseshoe vortex model is unrealistic in implying a constant vorticity (and hence by the Kutta–Joukowski theorem constant lift) at all points on the wingspan. In a more realistic model (due to Ludwig Prandtl) the vortex strength reduces along the wingspan, and the loss in vortex strength is shed as a vortex-sheet from the trailing edge, rather than just at the wing-tips. [ McCormick, Barnes W., "Aerodynamics, Aeronautics, and Flight Mechanics", Figure 4.21] 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.


* Clancy, L.J. (1975), "Aerodynamics", Section 8.10, Pitman Publishing Limited, London ISBN 0 273 01120 0
* McCormick, Barnes W., (1979), "Aerodynamics, Aeronautics, and Flight Mechanics", John Wiley & Sons, Inc. New York ISBN 0-471-03032-5
* Millikan, Clark B., (1941), "Aerodynamics of the Airplane", Section 1-6 John Wiley and Sons, Inc., New York
* Piercy, N.A.V. (1944), "Elementary Aerodynamics", Article 213, The English Universities Press Ltd., London.
* Von Mises, Richard, (1959), "Theory of Flight", Chapter IX - section 4, Dover Publications, Inc., New York ISBN 0-486-60541-8


See also

* Helmholtz's theorems
* Kutta condition
* Kutta–Joukowski theorem
* Prandtl's lifting-line model

Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Vortex lattice method — The Vortex lattice method, (VLM), is a numerical, Computational fluid dynamics, method used mainly in the early stages of aircraft design and in aerodynamic education at university level. The VLM models the lifting surfaces, such as a wing, of an …   Wikipedia

  • Vortex — A vortex (pl. vortices ) 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. The speed and rate of rotation of the… …   Wikipedia

  • Helmholtz's theorems — In fluid mechanics, Helmholtz s theorems describe the three dimensional motion of fluid in the vicinity of vortex filaments. These theorems apply to inviscid flows and flows where the influence of viscous forces is small and can be… …   Wikipedia

  • Vorticity — is a mathematical concept used in fluid dynamics. It can be related to the amount of circulation or rotation (or more strictly, the local angular rate of rotation) in a fluid.Clancy, L.J., Aerodynamics , Section 7.11] The average vorticity zeta… …   Wikipedia

  • 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. It is named for German mathematician and aerodynamicist …   Wikipedia

  • Wingtip vortices — are tubes of circulating air which are left behind by the 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 they are regions of very low pressure. The cores of… …   Wikipedia

  • 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. In this model, the vortex strength… …   Wikipedia

  • 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 (or Joukowski) who first developed its key ideas in the early 20th century. The theorem… …   Wikipedia

  • History of electromagnetism — The history of electromagnetism, that is the human understanding and recorded use of electromagnetic forces, dates back over two thousand years ago, see Timeline of electromagnetism. The ancients must have been acquainted with the effects of… …   Wikipedia

  • Space Mountain — Pour les articles homonymes, voir Space Mountain (homonymie). Space Mountain est l une des attractions phares des parcs à thèmes de Disney. Elle a été reproduite dans chacun des Royaumes Enchantés dans le land, Tomorrowland ou Discoveryland.… …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”