Editing Magnus effect (section)

== Physics ==
The Magnus effect or Magnus force acts on a rotating body moving relative to a fluid. Examples include a "[[curve ball]]" in baseball or a tennis ball hit obliquely. The rotation alters the boundary layer between the object and the fluid. The force is perpendicular to the relative direction of motion and oriented towards the direction of rotation, i.e. the direction the "nose" of the ball is turning towards.<ref name="Seifert"/> The magnitude of the force depends primarily on the rotation rate, the relative velocity, and the geometry of the body; the magnitude also depends upon the body's surface roughness and viscosity of the fluid. Accurate quantitative predictions of the force are difficult,<ref name="Seifert">{{cite journal |last1=Seifert |first1=Jost |title=A review of the Magnus effect in aeronautics |journal=Progress in Aerospace Sciences |date=November 2012 |volume=55 |pages=17–45 |doi=10.1016/j.paerosci.2012.07.001 |bibcode=2012PrAeS..55...17S }}</ref>{{rp|20}} but as with other examples of aerodynamic lift there are [[Lift (force)#Simplified physical explanations of lift on an airfoil|simpler, qualitative explanations]]:

===Flow deflection===
[[File:Sketch of Magnus effect with streamlines and turbulent wake.svg|thumb|The Magnus effect, depicted with a backspinning cylinder or ball in an airstream. The arrow represents the resulting lifting force. The curly flow lines represent a [[turbulence|turbulent]] wake. The airflow has been deflected in the direction of spin. <br>Air is carried around the object; this adds to the velocity of the airstream above the object and subtracts below resulting in increased airspeed above and lowered airspeed below.]]

The diagram shows lift being produced on a back-spinning ball. The wake and trailing air-flow have been deflected downwards; according to [[Newton's laws of motion#Third law|Newton's third law of motion]] there must be a [[reaction force]] in the opposite direction.<ref name=Halliday>{{cite book

| last = Halliday
| first = David
| title = Fundamentals of Physics
| publisher = John Wiley and Sons
| edition = 3rd Extended
| date = 1988
| location = 
| pages = E6 - E8
| language = English
| quote=The result is that the wake is not symmetrical; the airflow is deflected to one side, and the sphere experiences a reaction force in the opposite direction... The direction and strength of this force will depend on the rate and direction of spin. This phenomenon is known as the Magnus effect... }}</ref><ref name=NASA>{{Cite web
| url = https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/what-is-lift/
| title = What is Lift?
| access-date = 20 Sep 2024
| author = Glenn Research Center
| language = English
| quote = Lift occurs when a moving flow of gas is turned by a solid object. The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton’s Third Law of action and reaction. 
}}</ref>

===Pressure differences===
The air's [[viscosity]] and the surface roughness of the object cause the air to be carried around the object. This adds to the air velocity on one side of the object and decreases the velocity on the other side. [[Bernoulli's principle]] states that under certain conditions increased flow speed is associated with reduced pressure, implying that there is lower air pressure on one side than the other. This pressure difference results in a force perpendicular to the direction of travel.<ref name=Halliday2>{{cite book

| last = Halliday
| first = David
| title = Fundamentals of Physics
| publisher = John Wiley and Sons
| edition = 3rd Extended
| date = 1988
| location = 
| pages = 278–279
| language = English
| quote=Without viscosity and the boundary layer, the spinning ball could not carry air around in this way... the velocity of air below the ball is less than that above the ball. From Bernoulli's equation, the pressure of air below the ball must be greater than that above, so the ball experiences a dynamic lift force. }}</ref>
{{multiple image
|image_style=border:none;
|align=center
|image1=08. Магнусов ефект.ogv
|caption1=While the pipe rotates, as a consequence of fluid friction, it pulls air around it. This makes the air flow with higher speed on one side of the pipe and with lower speed on the other side.
| image_gap = 20
|image2=Magnus effect.gif
|caption2=Magnus effect in a particle simulation of a 2D liquid
}}
{{clear}}

===Kutta–Joukowski lift===
[[File:Magnus-anim-canette.gif|thumb|The topspinning cylinder "pulls" the airflow up and the air in turn pulls the cylinder down, as per Newton's third law]]
On a cylinder, the force due to rotation is an example of [[Kutta–Joukowski theorem|Kutta–Joukowski lift]]. It can be analysed in terms of the vortex produced by rotation. The lift per unit length of the cylinder <math> L^{\prime}</math>, is the product of the freestream velocity <math> v_{\infty}</math>, the fluid density <math> \rho_{\infty}</math> and circulation <math> \Gamma</math> due to viscous effects:<ref name="Glenn" />

:<math> L^{\prime}= \rho_{\infty} v_{\infty} \Gamma,</math>

where the vortex strength (assuming that the surrounding fluid obeys the [[no-slip condition]]) is given by

:<math>\Gamma = 2 \pi \omega r^2</math><ref name="Glenn" />

where ''ω'' is the angular velocity of the cylinder (in rad/s) and ''r'' is the radius of the cylinder.

=== Inverse Magnus effect ===
In [[wind tunnel]] studies, (rough surfaced) baseballs show the Magnus effect, but smooth spheres do not.<ref name="Lyman" /> Further study has shown that certain combinations of conditions result in turbulence in the fluid on one side of the rotating body but laminar flow on the other side.<ref>{{cite journal |last1=Kim |first1=Jooha |last2=Choi |first2=Haecheon |last3=Park |first3=Hyungmin |last4=Yoo |first4=Jung Yul |title=Inverse Magnus effect on a rotating sphere: when and why |journal=Journal of Fluid Mechanics |date=10 September 2014 |volume=754 |doi=10.1017/jfm.2014.428 |bibcode=2014JFM...754R...2K }}</ref> In these cases are called the ''inverse Magnus effect:'' the deflection is opposite to that of the typical 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 |access-date=10 February 2013}}</ref>