Horseshoe vortex

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File:Aircraft wing lift distribution showing trailing vortices (1).svg
A horseshoe vortex caused by a (purely theoretical) uniform lift distribution over an aircraft’s wing
File:Aircraft wing lift distribution showing trailing vortices (2).svg
Any change in lift distribution sheds a new trailing vortex, according to the lifting-line theory
File:Aircraft wing lift distribution showing trailing vortices (3).svg
A realistic lift distribution causes the shedding of a complex vorticity pattern behind the aircraft.

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.[1][2] (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.[3]

The horseshoe vortex model is unrealistic in implying a constant circulation (and hence by the Kutta–Joukowski theorem constant lift) at all sections 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.[4] 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.

References

  • Anderson, John D. (2007), Fundamentals of Aerodynamics, Section 5.3 (4th ed.), McGraw-Hill, New York NY. ISBN 978-0-07-295046-5
  • 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

Notes

  1. ↑ Millikan, Clark B., Aerodynamics of the Airplane, Figure 1.35
  2. ↑ McCormick, Barnes W., Aerodynamics, Aeronautics, and Flight Mechanics, Chapter 3
  3. ↑ McCormick, Barnes W., Aerodynamics, Aeronautics, and Flight Mechanics, Chapter 4
  4. ↑ McCormick, Barnes W., Aerodynamics, Aeronautics, and Flight Mechanics, Figure 4.21

See also

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