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| [[File:Sketch of Magnus effect with streamlines and turbulent wake.svg|thumb|The Magnus effect, depicted with a back-spinning cylinder or ball in an air stream. The arrow represents the resulting lifting force. The curly flow lines represent a turbulent wake. The airflow has been deflected in the direction of spin.]]
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| The '''Magnus effect''' is the commonly observed effect in which a spinning ball (or cylinder) curves away from its principal flight path. It is important in many [[List of ball games|ball sports]]. It affects spinning missiles, and has some engineering uses, for instance in the design of [[rotor ship]]s and [[Flettner airplane|Flettner aeroplanes]].
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| In terms of ball games, top spin is defined as spin about a horizontal axis perpendicular to the direction of travel, where the top surface of the ball is moving forward with the spin. Under the Magnus effect, top spin produces a downward swerve of a moving ball, greater than would be produced by gravity alone, and back spin has the opposite effect.<ref>http://math.ucr.edu/home/baez/physics/General/golf.html</ref> Likewise side-spin causes swerve to either side as seen during some baseball pitches.<ref>[http://library.thinkquest.org/11902/physics/curve2.html The Curveball], The Physics of Baseball.</ref>
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| The overall behaviour is similar to that around an [[airfoil]] (see [[lift force]]) with a [[Circulation (fluid dynamics)|circulation]] which is generated by the mechanical rotation, rather than by airfoil action.<ref>Clancy, L.J., ''Aerodynamics'', Section 4.6</ref>
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| It is named for [[Gustav Magnus]], the German physicist who investigated it. The force on a rotating cylinder is known as [[Kutta-Joukowski theorem|Kutta-Joukowski]] lift,<ref name= "Glenn" /> after [[Martin Wilhelm Kutta]] and [[Nikolay Yegorovich Zhukovsky|Nikolai Zhukovsky]] (or Joukowski) who first analyzed the effect.
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| == Physics ==
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| A valid intuitive understanding of the phenomenon is possible, beginning with the fact that, by conservation of momentum, the deflective force on the body is no more or less than a reaction to the deflection that the body imposes on the air-flow. The body "pushes" the air down, and vice versa. As a particular case, a lifting force is accompanied by a downward deflection of the air-flow. It is an angular deflection in the fluid flow, aft of the body.
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| In fact there are several ways in which the rotation might cause such a deflection. By far the best way to know what actually happens in typical cases is by wind-tunnel experiments. Lyman Briggs<ref name="Lyman">{{cite journal |last=Briggs |first=Lyman |title=Effect of Spin and Speed on the Lateral Deflection (Curve) of a Baseball and the Magnus Effect for Smooth Spheres |year=1959 |url=http://webusers.npl.illinois.edu/~a-nathan/pob/Briggs.pdf |bibcode=1959AmJPh..27..589B |volume=27 |pages=589 |journal=American Journal of Physics |doi=10.1119/1.1934921 |issue=8}}</ref> made a definitive wind tunnel study of the Magnus effect on baseballs, and others have produced interesting images of the effect.<ref name="Lyman" /><ref>{{cite book |last=Brown |first=F |title=See the Wind Blow |year=1971 |location=University of Notre Dame}}</ref><ref>{{cite book |last=Van Dyke |first=Milton |title=An album of Fluid motion |year=1982 |location=Stanford University}}</ref><ref name="Cross"/> The studies show a turbulent wake behind the spinning ball. The wake is to be expected and is the cause of aerodynamic drag. However there is a noticeable angular deflection in the wake and the deflection is in the direction of the spin.
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| The process by which a turbulent wake develops aft of a body in an air-flow is complex but well-studied in aerodynamics. It is found that the thin [[boundary layer]] detaches itself ("[[flow separation]]") from the body at some point and this is where the wake begins to develop. The boundary layer itself may be turbulent or not; this has a significant effect on the wake formation. Quite small variations in the surface conditions of the body can influence the onset of wake formation and thereby have a marked effect on the downstream flow pattern. The influence of the body's rotation is of this kind.
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| It is said{{citation needed|date=February 2013}} that Magnus himself wrongly postulated a theoretical effect with laminar flow due to skin friction and viscosity as the cause of the Magnus effect. Such effects are physically possible but slight in comparison to what is produced in the Magnus effect proper.<ref name="Lyman" /> In some circumstances the causes of the Magnus effect can produce a deflection opposite to that of the Magnus effect.<ref name="Cross">{{cite web |last=Cross |first=Rod |url=http://www.physics.usyd.edu.au/~cross/TRAJECTORIES/Fluidflow%20Photos.pdf |title=Wind Tunnel Photographs |publisher=Physics Department, University of Sydney |page=4 |accessdate=10 February 2013}}</ref>
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| The [[#diagram at head|diagram]] at the head of this article shows lift being produced on a back-spinning ball. The wake and trailing air-flow have been deflected downwards. The boundary layer motion is more violent at the underside of the ball where the spinning movement of the ball's surface is forward and reinforces the effect of the ball's translational movement. The boundary layer generates wake turbulence after a short interval.
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| On a cylinder, the force due to rotation is known as Kutta-Joukowski lift. It can be analyzed in terms of the vortex produced by rotation. The lift on the cylinder per unit length, F/L, is the product of the velocity, V, the density of the fluid, <math>\rho</math>, and the strength of the [[vorticity|vortex]] that is established by the rotation, G:<ref name= "Glenn" />
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| :<math>F/L= \rho V G</math>
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| == History ==
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| German physicist [[Heinrich Magnus|Heinrich Gustav Magnus]] described the effect in 1852.<ref>G. Magnus (1852) "Über die Abweichung der Geschosse," ''Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin'', pages 1-23.</ref><ref>G. Magnus (1853) [http://gallica.bnf.fr/ark:/12148/bpt6k15173v.pleinepage.r=Annalen+der+Physic.f13.langFR "Über die Abweichung der Geschosse, und: Über eine abfallende Erscheinung bei rotierenden Körpern" (On the deviation of projectiles, and: On a sinking phenomenon among rotating bodies)], ''Annalen der Physik'', vol. 164, no. 1, pages 1-29.</ref>
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| However, in 1672, [[Isaac Newton]] had described it and correctly inferred the cause after observing [[Real tennis|tennis]] players in his [[Cambridge]] college.<ref>Isaac Newton, "A letter of Mr. Isaac Newton, of the University of Cambridge, containing his new theory about light and color," ''Philosophical Transactions of the Royal Society'', vol. 7, pages 3075-3087 (1671-1672). (Note: In this letter, Newton tried to explain the refraction of light by arguing that rotating particles of light curve as they moved through a medium just as a rotating tennis ball curves as it moves through the air.)</ref><ref>Gleick, James. 2004. Isaac Newton. London: Harper Fourth Estate.</ref>
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| In 1742, [[Benjamin Robins]], a British mathematician, ballistics researcher, and military engineer, explained deviations in the trajectories of musket balls in terms of the Magnus effect.<ref>Benjamin Robins, ''New Principles of Gunnery: Containing the Determinations of the Force of Gun-powder and Investigations of the Difference in the Resisting Power of the Air to Swift and Slow Motions'' (London: J. Nourse, 1742). (On page 208 of the 1805 edition of Robins' ''New Principles of Gunnery'', Robins describes the experiment in which he observed the Magnus effect: A ball was suspended by a tether consisting of two strings twisted together, and the ball was made to swing. As the strings unwound, the swinging ball rotated, and the plane of its swing also rotated. The direction in which the plane rotated depended on the direction in which the ball rotated.)</ref><ref>Tom Holmberg, "[http://www.napoleon-series.org/military/organization/c_velocity.html Artillery Swings Like a Pendulum...]" in "The Napoleon Series"</ref><ref>Steele, Brett D. (April 1994) "Muskets and pendulums: Benjamin Robins, Leonhard Euler, and the ballistics revolution," ''Technology and Culture'', vol. 35, no. 2, pages 348-382.</ref><ref>Newton's and Robins' observations of the Magnus effect are reproduced in: Peter Guthrie Tait (1893) "[http://books.google.com/books?id=vyVWAAAAMAAJ&pg=PA356 On the path of a rotating spherical projectile]," ''Transactions of the Royal Society of Edinburgh'', vol. 37, pages 427-440.</ref>
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| == In sport ==
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| The Magnus effect explains commonly observed deviations from the typical trajectories or paths of spinning balls in [[sport]], notably [[association football]] (soccer), [[table tennis]], [[tennis]],<ref>[[John Strutt, 3rd Baron Rayleigh|Lord Rayleigh]] (1877) "On the irregular flight of a tennis ball," ''[[Messenger of Mathematics]]'', vol. 7, pages 14–16.</ref> [[volleyball]], [[golf]], [[baseball]], [[cricket]] and in [[paintball marker]] balls.
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| The curved path of a [[golf ball]] known as ''slice'' or ''hook'' is due largely to the ball's spinning motion (about its vertical axis) and the Magnus effect, causing a horizontal force that moves the ball from a straight-line in its trajectory.<ref>Clancy, L.J., ''Aerodynamics'', Section 4.5</ref> Back-spin (upper surface rotating backwards from the direction of movement) on a golf ball causes a vertical force that counteracts the force of gravity slightly, and enables the ball to remain airborne a little longer than it would were the ball not spinning: this allows the ball to travel farther than a non-spinning (about its horizontal axis) ball.
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| In table tennis, the Magnus effect is easily observed, because of the small mass and low [[density]] of the ball. An experienced player can place a wide variety of spins on the ball. [[Table tennis racket]]s usually have a surface made of rubber to give the racket maximum grip on the ball, to impart a spin.
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| The Magnus effect is not responsible for the movement of the cricket ball seen in [[swing bowling]],<ref>Clancy, L.J., ''Aerodynamics'', Figure 4.19</ref> although it does contribute to the motion known as ''drift'' in [[spin bowling]].
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| In [[airsoft]], a system known as [[Hop-Up (Airsoft)|Hop-Up]] is used to create a backspin on a fired [[BB gun|BB]], which will greatly increase its range, using the Magnus effect in a similar manner as in golf.
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| In [[paintball]], Tippmann's [[Tippmann#Flatline_Barrel_System|Flatline Barrel System]] also takes advantage of the Magnus effect by imparting a backspin on the paintballs, which increases their effective range by counteracting gravity.
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| In [[baseball]], pitchers often impart different spins on the ball, causing it to curve in the desired direction due to the Magnus effect. The [[PITCHf/x]] system measures the change in trajectory caused by Magnus in all pitches thrown in [[Major League Baseball]].<ref>{{cite web |title=Determining Pitch Movement from PITCHf/x Data |url=http://webusers.npl.illinois.edu/~a-nathan/pob/Movement.pdf |last=Nathan |first=Alan M. |date=October 18, 2012 |accessdate=18 October 2012}}</ref>
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| The [[2010 FIFA World Cup#Match ball|match ball]] for the [[2010 FIFA World Cup]] has been criticised for the different Magnus effect from previous match balls. The current ball is described as having less Magnus effect and as a result flies farther but with less controllable swerve.<ref>SBS 2010 FIFA World Cup Show interview 22 June 2010 10:30pm by [[Craig Johnston]]</ref>
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| == In external ballistics ==
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| The Magnus effect can also be found in advanced [[external ballistics]]. Firstly, a spinning bullet in flight is often subject to a [[crosswind]], which can be simplified as blowing either from the left or the right. In addition to this, even in completely calm air a bullet experiences a small sideways wind component due to its [[Flight dynamics (aircraft)|yawing]] motion. This yawing motion along the bullet's flight path means that the nose of the bullet is pointing in a slightly different direction from the direction in which the bullet is travelling. In other words, the bullet is "skidding" sideways at any given moment, and thus it experiences a small sideways wind component in addition to any crosswind component.<ref>{{cite web |author=Ruprecht Nennstiel |url=http://www.nennstiel-ruprecht.de/bullfly/longr.htm#header_longranges |title=Yaw of repose |publisher=Nennstiel-ruprecht.de |date= |accessdate=2013-02-22}}</ref>
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| The combined sideways wind component of these two effects causes a Magnus force to act on the bullet, which is perpendicular both to the direction the bullet is pointing and the combined sideways wind. In a very simple case where we ignore various complicating factors, the Magnus force from the crosswind would cause an upward or downward force to act on the spinning bullet (depending on the left or right wind and rotation), causing an observable deflection in the bullet's flight path up or down, thus changing the point of impact.
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| Overall, the effect of the Magnus force on a bullet's flight path itself is usually insignificant compared to other forces such as [[aerodynamic drag]]. However, it greatly affects the bullet's stability, which in turn affects the amount of drag, how the bullet behaves upon impact, and many other factors. The stability of the bullet is affected{{Citation needed|date=March 2011}} because the Magnus effect acts on the bullet's centre of pressure instead of its [[Center of mass|centre of gravity]]. This means that it affects the [[yaw angle]] of the bullet: it tends to twist the bullet along its flight path, either towards the axis of flight (decreasing the yaw thus stabilizing the bullet) or away from the axis of flight (increasing the yaw thus destabilizing the bullet). The critical factor is the location of the centre of pressure, which depends on the flowfield structure, which in turn depends mainly on the bullet's speed (supersonic or subsonic), but also the shape, air density and surface features. If the centre of pressure is ahead of the centre of gravity, the effect is destabilizing; if the centre of pressure is behind the centre of gravity, the effect is stabilizing.{{Citation needed|date=March 2011}}
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| == In flying machines ==
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| Some flying machines have been built which use the Magnus effect to create lift with a rotating cylinder at the front of a wing, allowing flight at lower horizontal speeds.<ref name="Glenn">{{cite web |url=http://www.grc.nasa.gov/WWW/K-12/airplane/cyl.html |title=Lift on rotating cylinders |publisher= NASA Glenn Research Center |date=2010-11-09 |accessdate=2013-11-07}}</ref> The earliest attempt to use the Magnus Effect for a heavier than air aircraft was in 1910 by a US member of Congress, [[Butler Ames]] of Massachusetts. The next attempt was in the early 1930s by three inventors in New York state.<ref>{{cite book |url=http://books.google.com/?id=xSgDAAAAMBAJ&pg=PA26&dq=Popular+Science+1931+plane#v=onepage&q&f=true |title=Whirling Spools Lift This Plane |publisher=Popular Science |date=Nov 1930 |accessdate=2013-02-22}}</ref>
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| == Ship stabilization ==
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| The effect is used in a special type of [[Stabilizer (ship)|ship stabilizer]] consisting of a rotating cylinder mounted beneath the waterline and emerging laterally. By controlling the direction and speed of rotation, strong [[lift (force)|lift]] or [[downforce]] can be generated.<ref>{{cite web|url=http://www.youtube.com/watch?v=9CwPHTN2pSs#t=1m26s|title=Quantum Rotary Stabilizers|date=Jun 2, 2009}}</ref> The largest deployment of the system to date is in the [[Eclipse (yacht)|Eclipse]] yacht.
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| == See also ==
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| *[[Air resistance]]
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| *[[Ball of the Century]]
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| *[[Bernoulli's principle]]
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| *[[Boundary layer]]
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| *[[Coandă effect]]
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| *[[Flettner airplane]]
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| *[[Fluid dynamics]]
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| *[[Kite types]]
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| *[[Navier–Stokes equations]]
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| *[[Reynolds number]]
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| *[[Rotor Ship]]
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| *[[Tesla turbine]]
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| == References ==
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| {{Reflist|colwidth=30em}}
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| == Further reading ==
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| *{{Cite journal |last=Watts |first=R. G. |lastauthoramp=yes |last2=Ferrer |first2=R. | title=The lateral force on a spinning sphere: Aerodynamics of a curveball| journal=American Journal of Physics | year=1987 | volume=55 |issue=1 | page=40 | doi=10.1119/1.14969 |bibcode = 1987AmJPh..55...40W |postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}.
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| *{{Cite book |last=Clancy |first=L. J. |year=1975 |title=Aerodynamics |publisher=Pitman Publishing Limited |location=London |isbn=0-273-01120-0 |postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}} }}.
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| == External links ==
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| * [http://richannel.org/tales-from-the-prep-room-magnus-cups, Magnus Cups], Ri Channel Video, January 2012
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| * [http://www.mathpages.com/home/kmath258/kmath258.htm Analytic Functions, The Magnus Effect, and Wings] at MathPages
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| * [http://www.nennstiel-ruprecht.de/bullfly How do bullets fly? Ruprecht Nennstiel, Wiesbaden, Germany]
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| * [http://www.fulton-armory.com/fly/ How do bullets fly? old version (1998), by Ruprecht Nennstiel]
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| * [http://www.cit.gu.edu.au/~anthony/kites/rotor/ Anthony Thyssen's Rotor Kites page]
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| * [http://www.rexresearch.com/flettner/flettner.htm Has plans on how to build a model]
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| * [http://www.magenn.com/about.php Harnessing wind power using the Magnus effect]
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| * [http://www.ats.org/news.php?id=199 Technion Researchers Observe Magnus Effect in Light for First Time]
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| * [http://www.quantumhydraulic.com/pages/stabilizers-maglift.php Quantum Maglift ]
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| {{Use dmy dates|date=March 2011}}
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| [[Category:Fluid dynamics]]
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