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The Magnus Effect
The Magnus Effect.
Or "Why do cricket balls swing and curve balls curve?"
This page on the Magnus or Robin's Effect was born out
of a seminar I presented circa 1987 as a potential topic for my Master's
Thesis in Mechanical Engineering.(Actually I was going to investigate the
Reverse Magnus Effect :-) My advisor at the time, Dr.
Robert G. Watts has numerous papers and a popular book
on the physics of baseball and he is considered an authority on the
subject.
Seeing the spate of recent posts on rec.sport.cricket
on this topic, gave me the motivation to dig up all my old references and
start writing something that will be more than just speculation. This page
will focus on cricket ball aerodynamics(at least in the beginning) and
will soon include discussions of the "other" sports.
Disclaimer: This contains no original work of mine. All information
is from the references listed at the end.(Some wordings and phrases are
borrowed literally with no fear of Copyright violations :-) Heck, I am
not making any money out of this and I am certainly not asking for glory!!
I am continuing to work on writing to provide more information and grow
this section to include more related topics (baseball and golf balls).
I am not very happy with the figures I have created. I will hopefully have
more meaningful and better looking diagrams/graphs up soon. I welcome all
comments/corrections/suggestions from you. Send them to mak@b-bop.com
or krishna.achutarao@laitram.com
A brief history of scientific studies of the "Magnus Effect":
Newton in 1672(Did this guy have something to say about everything?) noted
how a tennis ball's flight was affected by spin. In 1742, Robins showed
that a transverse aerodynamic force could be detected on a rotating sphere.
(Hence it is also referred to sometimes as the "Robin's Effect"). The first
explanation of the lateral deflection of a spinning ball is credited by
Lord Rayleigh to Magnus,
from which the phenomenon derives its name, the "Magnus Effect". Rayleigh
also gave a simple analysis for a "frictionless fluid," which showed that
the side force was proportional to the free stream velocity and the rotational
speed. This was all before the introduction of the boundary-layer concept
by Prandtl in 1904.
The commonly accepted explanation is that a spinning object creates
a sort of whirlpool of rotating air about itself. On the side where the
motion of the whirlpool is in the same direction as that of the windstream
to which the object is exposed, the velocity will be enhanced. On the opposite
side, where the motions are opposed, the velocity will be decreased. According
to Bernoulli's principle, the pressure is lower on the side where the velocity
is greater, and consequently there is an unbalanced force at right angles
to the wind. This is the magnus force.
The more recent studies agree that the magnus force results from the
asymmetric distortion of the boundary layer displacement thickness caused
by the combined spinning and flow past the spherer. In the case of a sphere(or
cylinder), the so-called whirlpool, or more accurately the circulation,
does not consist of air set into rotation by friction with a spinning object.
Actually an object such as a sphere or a cylinder can impart a spinning
motion to only a very thin layer next to the surface. The motion imparted
to this layer affects the manner in which the flow separates from the surface
in the rear. Boundary layer separation is delayed on the side of the spinning
object that is moving in the same direction as the free stream flow, while
the separation occurs prematurely on the side moving against the free stream
flow. The wake then shifts toward the side moving against the free stream
flow. As a result, flow past the object is deflected, and the resulting
change in momentum flux causes a force in the opposite direction(upwards
in the case shown in figure 1).
Figure 1. (Flow from right to left)
This phenomenon is influenced by the conditions in the thin layer next
to the body, known as the boundary layer, and there may arise certain anomalies
in the force if the spin of the body introduces anomalies in the layer,
such as making the flow turbulent on one side and not the other. One such
is the reverse Magnus effect which may occur for smooth spheres. Rough
balls such as cricket balls, baseballs, golf balls and tennis balls, do
not show this anomalous effect.
Aerodynamics of Cricket Balls:
A cricket ball has six rows of prominent stitching, with typically 60-80
stitches in each row(primary seam). The seam is along the "equator" of
the two hemisphere ball. Better quality balls are made of 4 pieces of leather
so that each hemisphere has a line of internal stitching forming the "secondary
seam". The secondary seams of the two hemispheres are at right angles to
each other.
Fast bowlers make judicious use of the primary seam to swing the ball.
The ball is released into the air flow with the seam at a slight angle.
(When bowled right)The seam trips the laminar boundary layer into turbulence
on one side of the ball. This turbulent boundary layer by virtue of its
increased energy, separates relatively late compared to the boundary layer
on the nonseam side, which separates in a laminar state. The asymmetric
boundary layer separation results in an asymmetric pressure distribution
that produces the side force responsible for the swing. When a ball is
bowled, with a round arm action as rules insist, there will always be some
backspin imparted to it. The ball being held alung the seam, the backspin
is also imparted along the seam. So the asymmetry of the boundary layer
separation is maintained. A prominent seam obviously helps the laminar
to turbulence transition process, whereas a smooth and polished surface
on the nonseam side helps maintain a laminar boundary layer. Mehta
has a really nice Wind tunnel Smoke photograph of flow over a cricket ball.
A schematic is in figure 2.
Figure 2.
Mehta goes on to report a lot of results from wind-tunnel tests and
also compares them with results obtained by Barton(1982)
and Bentley et al.(1982)
To come to the crux of their observations:
The two piece ball is in general found to have better swing properties
than the four piece ball. The secondary seam serves as an effective roughness
that helps to cause transition of the laminar boundary layer on the nonseam
side.
Barton concluded that the ball with a more pronounced seam than average
(> 1mm) swung more. Bentley et al. could not corroborate that as they found
that there was no correlation of swing with seam size or shape.
Bentley et al. found that the seam on all new balls is efficient at
tripping the boundary layer in the speed range 15 < U < 30 m/s (i.e
54 < U < 108 Km/hr). The swing properties obviously deteriorate with
age as the seam is worn and the surface scarred. For that matter the spin
or rotation of the ball is not theoretically necessary for swing! [Note
to non-cricket savvy people: the ball in cricket is only replaced after
a minimum fixed number of overs(deliveries if you will) have been bowled.
So the wear and tear is a natural consequence of the game. Only "natural"
sources like spit and saliva may be used in maintaining the shine on the
ball - usually achieved by polishing the ball on clothing . No means of
scuffing the ball may be used. Rolling the ball on the ground is legal.]
Figure 3. (The general shape of the curve for side force measurements
on a cricket ball at seam angle zero. 30 m/s would correspond to a Reynolds
number of approximately 150000.)
The two parameters that a bowler can control to some extent are the
ball seam angle and the spin rate.
The optimum seam angle for U = 30 m/s is about 20 degrees. At lower
speeds (especially for U < 15 m/s) a bowler should select a larger seam
angle than 30 degrees, so that by the time the flow accelerates around
the seam, the critical speed has been reached. It is better not to trip
the boundary layer too early(low angle), since the turbulent boundary layer
grows at a faster rate and will therefore separate relaively early(compared
with a later tripping). At the same time, the seam angle should not be
so large that the boundary layer separates before reaching the seam, since
this would result in symmetrical separation on the ball and hence zero
size force. In a case like this, if transition occurs in the boundary layer
upstream of the seam, then the effect of the seam will be to act as a boundary-layer
"fence" that thickens the boundary layer even further. This asymmetry would
lead to a negative side force for postcritical Reynolds numbers. This effect
can be produced even at low seam angles by inducing early transition of
the laminar boundary layer through an increase of the free-stream turbulence.
(Note: Could this be an explanaion for the reverse swing achieved by Wasim
Akhram and Waquar Younis? It seems unlikely that they get up in the Reynolds
number range required for that.........)
Spin on the ball helps stabilize the ball's seam orientation. Too much
spin is detrimental since the effective roughness on the ball's surface
is increased. This is more relevant at higher speeds (U> 25m/s). Barton's
results indicate that the optimal spin rate is 5 rev/s, whereas Bentley
et al.'s results indicate a much higher rate of 11 rev/s. These anomalies
are considered to be due to differences in experimental setups. In practice,
a bowler can impart upto 14 rev/s though it is not very easy to control.
Effect of weather conditions:
This has got to be one of the most discussed aspects of cricket. It is
believed that humid or damp days are more conducive to swing bowling, but
there is no scientific proof of this!
The flow pattern around the cricket ball depends on the properties of
the air and the ball itself. The only properties of air affected by weather
conditions are density and viscosity. These will influence the Reynolds
number. However, Bentley et al. found that the average changes in temperature
and humidity encountered in a day only affect the Reynolds number to the
tune of 2%. Several measurements have been made of the effect of humidity,
and even wetness of the ball (due to condensation etc.) and no significant
changes have been measured under laboratory conditions. Does the dampness
make the ball tackier and hence enable the bowler to impart a better spin
rate? This was the untested hypothesis of Bentley et al. This aspect of
cricket ball aerodynamics remains a mystery.
Coming Soon.
The discussion will soon go on to baseball and golf ball aerodynamics.
While I work on it you can check out this
article on the effect of dimples on golf ball dynamics that appeared
in the August
1996 issue of Discover
Magazine.
References:
Print Journal Resources.
"Aerodynamics of sports balls", Rabindra
D. Mehta, in Annual Reviews of Fluid Mechanics, 1985. 17: pp. 151-189.
"On the swing of a cricket ball in flight",
N. G. Barton, Proc. R. Soc. of London. Ser. A, 1982. 379 pp. 109-31.
"An experimental study of cricket ball swing",
Bentley, K., Varty, P., Proudlove, M., Mehta, R. D., Aero. Tech. Note 82-106,
Imperial College, London, England, 1982.
"The effect of humidity on the swing of cricket balls", Binnie,
A. M., International Journal of Mechanical Sciences. 18: pp.497-499, 1976.
"The swing of a cricket ball", Horlock, J. H., in "Mechanics
and sport", ed. J. L. Bleustein, pp. 293-303. New York, ASME 1973.
"The swing of a cricket ball", Imbrosciano, A., Project Report
810714, Newcastle College of Advanced Education., Newcastle, Australia.
1981.
"The swing of a cricket ball", Lyttleton, R. A., Discovery,
18: pp.186-191. 1957.
"Aerodynamics of the cricket ball", Mehta, R. D., Wood, D.
H., New Scientist, 87: pp.442-447, 1980
"Factors affecting cricket ball swing", Mehta, R. D., Bentley,
K., Proudlove, M., Varty, P., Nature, 303: pp. 787-788, 1983.
"Aerodynamics of a cricket ball", Sherwin, K., Sproston,
J. L., Int. J. Mech. Educ. 10: pp. 71-79. 1982.
"The Aerodynamics of a cricket ball", BSc dissertation. Dept
Mech Eng. Univ. of Newcastle, England. 1983.
"Effect of spin and speed on the lateral deflection(curve) of a Baseball;
and the Magnus effect for smooth Spheres", Lyman J. Briggs , American
Journal of Physics 27:pp. 589-596. 1959.
"Magnus effect on spinning bodies of revolution", H. L. Power,
J. D. Iverson, AIAA Journal Vol. 11, No. 4, pp.417-418, April 1973.
"A Magnus Theory", H. R. Vaughn and G. E. Reis, AIAA Journal,
Vol. 11(?) No. 10 (?), pp.1396-1403, October 1973.
"The aerodynamics of Golf balls", John M. Davies, Journal
of Applied Physics, Vol. 20, No. 9, September 1949.
"The Magnus or Robins effect on Rotating Spheres", H. M.
Barkla and L. J. Auchterlonie, Fluid Mech. vol. 47, part 3, pp. 437-447,
1971.
"A boundary layer theorem, with applications to rotating cylinders",
M. B. Glauert, (I can't find the journal name on the paper, but it looks
like Journal of Fluid Mechanics circa 1956 or 1957, pp. 89-99)
"Aerodynamics of a knuckleball", Watts, R. G., Sawyer, E.,
American Journal of Physics, 43: pp.960-963. 1975.
"Keep your eye on the ball: The science and folklore
of baseball", Robert G. Watts, A. Terry Bahill. W. H. Freeman(publisher)
New York 1990.
"On the irregular flight of a tennis ball",
Lord Rayleigh, Scientific Papers I, 344(1869-1881)
"On the derivation of projectiles; and on a
remarkable phenomenon of rotating bodies." G. Magnus, Memoirs of
the Royal Academy, Berlin(1852). English translation in Scientific Memoirs,
London (1853)., p. 210. Edited by John Tyndall and William Francis.
Information Available on the Web.
http://www.planetary.caltech.edu/~eww/physics/node1274.html
http://www.hw.ac.uk/scifest/sport.htm
http://www.geom.umn.edu/docs/snell/chance/course/topics/curveball.html
http://oscar.teclink.net/~crogers/knobler.html
http://hookem.com/htm/sports/april/04-15/pitch.htm
http://math.gmu.edu/~vle3/proj2/top.html
Lift Hey! Somebody
references my page!!
The Swing
of a Cricket Ball
Dr.
Duane Knudson's Magnus Effect Lab
The Curve with Top Spin
Magnus
Effect???
Curve
Ball
My Home Page
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