Please read the intro paragraph to the Disclaimer on the Physics FAQ
updated 18-Jul-1997 by PEG
updated 17-NOV-1993 by CDF
original by Craig DeForest
The dimples, paradoxically, do increase drag slightly. But they
also increase `Magnus lift', that peculiar lifting force experienced by
rotating bodies travelling through a medium. Magnus lift is present
because a driven golf ball has backspin. The same Magnus effect can
cause a ball to hook or slice if there is sideways spin.
Contrary to Freshman physics, golf balls do not travel in inverted
parabolas. They follow an 'impetus trajectory':
(golfer) * *
* * -- trajectory
\O/ * *
| * *
This is because of the combination of drag (which reduces
horizontal speed late in the trajectory) and Magnus lift, which supports
the ball during the initial part of the trajectory, making it relatively
straight. The trajectory can even curve upwards at first, depending on
conditions! Here is a cheesy diagram of a golf ball in flight, with some
F(drag) <--- O -------> V
\----> (sense of rotation)
A golf ball leaves the tee with a speed of about 70 m/s and a backspin
of at least 50 rev/s. The Magnus force can be thought of as due to the relative drag on
the air on the top and bottom portions of the golf ball: the top portion is
moving slower relative to the air around it, so there is less drag on the
air that goes over the ball. The boundary layer is relatively thin, and
air in the not-too-near region moves rapidly relative to the ball. The
bottom portion moves fast relative to the air around it; there is more drag
on the air passing by the bottom, and the boundary (turbulent) layer is
relatively thick; air in the not-too-near region moves more slowly relative
to the ball. The Bernoulli force produces lift. (Alternatively, one could
say that `the flow lines past the ball are displaced down, so the ball is
The difficulty comes near the transition region between laminar
flow and turbulent flow. At low speeds, the flow around the ball is
laminar. As speed is increased, the bottom part tends to go turbulent
first. But turbulent flow can follow a surface much more easily
than laminar flow.
As a result, the (laminar) flow lines around the top break away
from the surface sooner than otherwise, and there is a net displacement
up of the flow lines. The magnus lift goes negative.
The dimples aid the rapid formation of a turbulent boundary layer
around the golf ball in flight, giving more lift. Without 'em, the ball
would travel in more of a parabolic trajectory, hitting the ground sooner
(and not coming straight down). This was discovered by accident in the
early days of golf when golfers noticed that old roughened golf balls
Despite the drag, a dimpled golf ball can even go further
in air than it would in vacuum given the same initial velocity
and low angle. However, a golf ball shot at 45 degrees and 70 m/s
in vacuum would go 500 metres to the first bounce, which exceeds
Lord Rayleigh, "On the Irregular Flight of a Tennis Ball", _
Scientific Papers I_, p. 344
Briggs Lyman J., "Effect of Spin and Speed on the Lateral Deflection of
a Baseball; and the Magnus Effect for Smooth Spheres", Am. J. Phys. _27_,
589 (1959). Briggs was trying to explain the mechanism behind the `curve
ball' in baseball, using specialized apparatus in a wind tunnel at the NBS.
He stumbled on the reverse effect by accident, because his model `baseball'
had no stitches on it. The stitches on a baseball create turbulence in
flight in much the same way that the dimples on a golf ball do.
R. Watts and R. Ferver, "The Lateral Force on a Spinning Sphere
Aerodynamics of a Curveball", Am. J. Phys. _55_, 40 (1986)
Steve Haake, "Physics and Golf? You must be joking!"
Physics World _10_, 76 (1997)
Journal of Applied Physics 20, 821 (1949) by Davies.
American Journal of Physics 56, 933 (1988) by McPhee and Andrews.
"The Physics of Golf" by Theodore P. Jorgensen
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