The horseshoe vortex model is a simplified representation of the

vortex In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in t ...

system present in the flow of air around a

wing A wing is a type of fin that produces lift while moving through air or some other fluid. Accordingly, wings have streamlined cross-sections that are subject to aerodynamic forces and act as airfoils. A wing's aerodynamic efficiency is exp ...

. This vortex system is modelled by the ''bound vortex'' (bound to the wing) and two '' trailing vortices'', therefore having a shape vaguely reminiscent of a

horseshoe A horseshoe is a fabricated product designed to protect a horse hoof from wear. Shoes are attached on the palmar surface (ground side) of the hooves, usually nailed through the insensitive hoof wall that is anatomically akin to the human ...

. A starting vortex is shed as the wing begins to move through the fluid, which dissipates under the action of

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

, as do the trailing vortices far behind the aircraft. The

downwash In aeronautics, downwash is the change in direction of air deflected by the aerodynamic action of an airfoil, wing, or helicopter rotor blade in motion, as part of the process of producing lift.Crane, Dale: ''Dictionary of Aeronautical Terms, thir ...

is associated with

induced drag In aerodynamics, lift-induced drag, induced drag, vortex drag, or sometimes drag due to lift, is an aerodynamic drag force that occurs whenever a moving object redirects the airflow coming at it. This drag force occurs in airplanes due to wings or ...

and is a component of the system of trailing vortices. The horseshoe vortex model is unrealistic in that it implies uniform

circulation Circulation may refer to: Science and technology * Atmospheric circulation, the large-scale movement of air * Circulation (physics), the path integral of the fluid velocity around a closed curve in a fluid flow field * Circulatory system, a bio ...

(and hence, according to the

Kutta–Joukowski theorem The Kutta–Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil (and any two-dimensional body including circular cylinders) translating in a uniform fluid at a constant speed large enough so t ...

, uniform lift) at all sections on the

wingspan The wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip. For example, the Boeing 777–200 has a wingspan of , and a wandering albatross (''Diomedea exulans'') caught in 1965 had a wingspan ...

. In a more realistic model, the

lifting-line theory The Prandtl lifting-line theory is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing based on its geometry. It is also known as the Lanchester–Prandtl wing theory. The theory was expressed inde ...

, the vortex strength varies along the wingspan, and the loss in vortex strength is shed as a vortex ''sheet'' all along the trailing edge, rather than as a single trail at the wing-tips. Nevertheless, the simpler horseshoe vortex model used with a reduced effective wingspan but same mid-plane circulation provides an adequate model for the flows induced far from the aircraft. The term horseshoe vortex is also used in

wind engineering Wind engineering is a subset of mechanical engineering, structural engineering, meteorology, and applied physics that analyzes the effects of wind in the natural and the built environment and studies the possible damage, inconvenience or benefits ...

to describe the flow pattern created by strong winds around the base of a tall building. This effect is amplified by the presence of a low-rise building just upwind. This effect was studied at the UK Building Research Establishment between 1963 and 1973 and the cause of the effect is described in contemporary wind engineering text books. In hydrodynamics, a form of horseshoe vortex forms around bluff bodies in the flowing water, for instance around bridge piers. They can cause scouring of bed materials from both upstream and downstream of the pier. In nature, a horseshoe vortex can cause a horseshoe cloud to form.

Notes

References

* Anderson, John D. (2007), ''Fundamentals of Aerodynamics'', Section 5.3 (4th ed.), McGraw-Hill, New York NY. *

L. J. Clancy Laurence Joseph Clancy (15 March 1929 - 16 October 2014) was an Education Officer in aerodynamics at Royal Air Force College Cranwell whose textbook ''Aerodynamics'' became standard. He was born in Egypt to Alfred Joseph Clancy and Agnes Hunter. I ...

(1975), ''Aerodynamics'', Section 8.10, Pitman Publishing Limited, London * Cook, N.J. (1985), ''The designer's guide to wind loading of building structures, Part 1'', Butterworths, London * McCormick, Barnes W., (1979), ''Aerodynamics, Aeronautics, and Flight Mechanics'', John Wiley & Sons, Inc. New York * Millikan, Clark B., (1941), ''Aerodynamics of the Airplane'', Section 1-6 John Wiley and Sons, Inc., New York * Penwarden, A.D., Wise, A.F.E., (1975) ''Wind environment around buildings'', HMSO, London . * 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

References

See also