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The Magnus effect has been studied on spherical projectiles such as golf balls, tennis balls, and soccer balls. The backspin of a golf ball leads to Magnus lift that opposes gravity, thus allowing the ball to fly further. The dimples of a golf ball enhance the effect.

I am interested to know whether there is also a lift produced on a back-spinning prolate spheroid, such as the balls used in rugby, Australian rules football (also known as AFL, footy), and American football (also known as gridiron).

My understanding of the Magnus effect is that it usually applies to a spherical ball with backspin in an oncoming stream of air (either because the air is moving, or because the object is moving through the air). The backspin means that the top of the ball is moving with the air, whereas the bottom of the ball is moving in the opposite direction to the air. The slower relative speed at the top of the ball preserves laminar flow around the top of the ball that curves downwards over the top of the ball, whereas the bottom of the ball produces turbulent flow that quickly separates from the ball. The downward air steam over the top of the ball means that there is net downward momentum imparted to the air particles, and thus an equal and opposite force acting to lift the ball. What I am wondering, is whether the profile of a rugby ball would enhance this effect (if we think of a rugby ball as a sphere with 2 long shallow dimples shaved off), or whether it would destroy the effect completely, thus resulting in nothing but drag.

(I'm aware that handballs and certain kicking styles can result in torpedo rotation about the long-axis, and thus the Magnus effect applies to the circular cross-section in a cross-wind. But in this question I'm specifically interested in the effect when a vertically oriented rubgy ball is kicked directly into oncoming air and rotating about it's short-axis end-over-end)

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  • $\begingroup$ This dissertation looks like it has quite a good coverage of this phenomenon. $\endgroup$ – user3823992 Apr 23 '15 at 4:11
  • $\begingroup$ Sorry, the TL;DR on that is: Back spin gives lift, has little effect on drag. Also, it's thesis not a dissertation. $\endgroup$ – user3823992 Apr 23 '15 at 4:23
  • $\begingroup$ Almost any method of inducing circulation produces lift by deflecting the airstream. Simple example: take a strip of paper 1/2" wide by a few inches long. Hold it the long way between your hands and drop it, with backspin. It keeps backspinning and glides quite nicely. $\endgroup$ – Mike Dunlavey Apr 23 '15 at 17:02
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The Magnus effect was discovered when an explanation for the low precision of guns was needed. It affects the cylindrical, pointed grenades just as much as any ball.

It does not matter how long the rotating body is: Once it rotates, it will create a low pressure area on one side orthogonal to the crosswind direction and a corresponding high pressure area opposite to it.

If the body rotates around its short axis, friction will slow the rotation down much more quickly compared to a spherical body. This could be the main difference between a rotating rugby ball and a rotating soccer ball.

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I believe that when an oblong ball tumbles with backspin its range is increased due to the magnus effect. Most studies of oblong balls analyze spinning rotation about the long axis, but there is some evidence that tumbling about the short axis may enhance the Magnus effect:

"The Magnus effect is also exploited in a number of Nature’s designs. Many seed pods, including maple keys, are shaped such that they tumble as they fall (Figure 5a; Vogel 2003). The coupling of the resulting rotational and translational motions can give rise to a Magnus lift force that considerably extends the range of these seed pods…" - JWM Bush, Dept. of Mathematics, MIT, page 181 of http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/11/Beautiful-Game-2013.pdf

Figure 5 in the article cited above shows the trajectory of an oblong box mite which increases its range due to tumbling about the short axis.

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