杏吧原创

Ten-bob swerver

Question: I am well aware (having played many ball sports) of the Magnus
effect which causes a ball that is spinning clockwise (when viewed from above)
to swerve towards the right. Similarly, a ball struck with backspin will travel
with a long, floating flight. These effects can be seen with leather footballs,
tennis balls and table tennis balls. However, when applying spin to one of those
plastic footballs sold at petrol stations and on beaches, the opposite is
observed: clockwise spin produces right to left swerve, and back-spin produces a
viciously dipping shot. These balls are really only larger versions of table
tennis balls, and similarly devoid of dimples and surface markings, so why
should their responses to spin be opposite?

Answer: This phenomenon was dealt with in some detail in `The seamy side of
swing bowling鈥� (New 杏吧原创, 21 August 1993, p 21) and is best
explained in terms of 鈥渂oundary-layer separation鈥�.

When a ball travels through the air its surface is covered by a thin coating
of air that is dragged along with it. Beyond this lies undisturbed air. Between
the dragged air and undisturbed air lies a thin boundary layer. At the front of
the ball, this layer moves slowly. But as it travels round the ball, it speeds
up and exerts less pressure (as dictated by Bernoulli鈥檚 law, which states that
the faster a fluid flows, the less pressure it exerts).

At some point, the boundary layer separates from the ball鈥檚 surface. If the
ball is smooth and not spinning, this happens at the same point all round the
ball. But if the ball is spinning, the boundary layer separates asymmetrically,
so the boundary layer covers a larger area on one side than on the other. The
result is a larger region of low pressure on one side of the ball than the
other, which pushes the ball to one side.

In a conventional swing (produced by the Magnus-Robins effect), the spin of
the ball carries a very thin layer of air along with it. This pushes the point
of boundary-layer separation towards the back on the side of the ball where the
spin is moving in the same direction as the surrounding airstream, and towards
the front on the side that is moving against the air stream. The result is lower
pressure on the side where the boundary layer has become extended, which causes
the ball to swing in that direction. That鈥檚 why a clockwise spin causes the ball
to move from left to right. (Another way of describing what happens is to say
that the shift in the point of boundary-layer separation pushes the flow lines
of the air round the ball鈥攖he ball鈥檚 wake鈥攖o one side, so that the
ball swerves to the other.)

All this assumes that the flow in the boundary layer is laminar, with smooth
tiers of air on top of each other. In practice, part of the airflow may be
turbulent, with air moving chaotically throughout the layer, and this is where
reverse swing can occur. Experiments show that turbulent layers stick to the
surface of the ball longer than laminar layers. So if the boundary layer is
turbulent on one side and laminar on the other, the pressure will be lower on
the turbulent side and the ball will swing to that side.

Under certain circumstances, turbulence can develop first on the side of the
ball which is moving against the airstream, so that the boundary layer here
separates later. The result is a reverse swing. Whether turbulence will develop
depends on the type of ball, its speed, size and spin, so reverse swing is seen
more commonly in some sports than others (see the following answers).

Sports such as cricket, which use balls with seams, give bowlers additional
opportunities to produce both swing and reverse swing though turbulence. Skilful
players can bowl so that the ball spins with its stitched seam always facing at
a particular angle to the oncoming air. The seam affects the airflow, making the
boundary layer turbulent on only the seam side of the ball. The boundary layer
thus separates later on this side of the ball and the result is a vicious
swing.

Bowl fast enough and that swing can be made to reverse. At the very high
speeds produced by world-class bowlers (more than 130 kilometres per hour), the
air moves so fast that the boundary layer becomes turbulent even before it
reaches the seam of the ball. In this case the seam pushes the boundary layer
away, encouraging it to separate from the ball earlier on the seam side. The
ball then unexpectedly swerves in the opposite direction from usual. This is the
notorious ten-bob swerver.

The effect can be produced by ordinary cricketers too, if their ball is
scuffed, as a rough surface allows a turbulent boundary layer to develop more
easily. Deliberate scuffing is, of course, against the rules鈥擡d

Answer: The reverse swerve on a plastic football is due to boundary-layer
separation. On the side of the football where the relative velocity of the air
and football is larger, the flow in the boundary layer becomes turbulent. On the
other side it remains laminar. The laminar boundary layer separates from the
ball鈥檚 surface once the airstream is no longer pushing it onto the surface. By
contrast, the turbulent boundary layer remains in contact with the surface
farther round the ball. This results in the wake behind the ball being deflected
in the opposite direction to the rotation of the ball. And it produces a force
towards the side of the ball that is moving in the opposite direction to the
airstream (from right to left for a ball spinning clockwise).

Experiments show that the main factor governing the direction in which a ball
swerves is the ratio of the rotational speed of its surface to the ball鈥檚
translational speed. The reverse swerve occurs when this ratio is small (less
than 0.4), while the Magnus effect occurs at higher ratios, which probably
explains why the faster-spinning tennis ball swings in the opposite direction
to the football.

Oliver Harlen

University of Leeds

Answer: The swerve of a spinning ball is commonly ascribed to the Magnus
effect, but more than a century before Heinrich Magnus, Benjamin Robins studied
spinning cannon balls and in 1742 he published a description of why, even on
windless days, they swerved off course.

Brian Wilkins

Wellington, New Zealand

Many publications do now refer to the Magnus-Robins effect. It is perhaps
worth remembering that Isaac Newton commented in 1672 on how the flight of a
ball was affected by spin鈥擡d

This week鈥檚 questions

Talon teaser: Fingernails appear to grow from the base of the nail to the
tip. However, they are firmly bonded to the underlying flesh. Do they slide over
the flesh? If not, and the flesh migrates to the fingertip with the nail, what
happens to it there?

Howard Medhurst

Crawley, West Sussex