updated 17-NOV-1993 by CDF
original by Craig DeForest

Why are Golf Balls Dimpled?

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. Contrary to Freshman physics, golf balls do not travel in inverted parabolas. They follow an 'impetus trajectory':

                                    *    *       
                              *             *
(golfer)                *                    *
                  *                          * <-- trajectory
 \O/        *                                *
  |   *                                      *
-/ \-T---------------------------------------------------------------ground

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 relevant vectors:

                             F(magnus)
                             ^
                             |
                F(drag) <--- O -------> V 
                          \     
                           \----> (sense of rotation)

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 pushed up.')

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).

References:

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)