Why do dimples on a golf ball allow it to travel farther?
Asked by: Aric Simmons
Clearly, dimples on golf balls are going to create additional turbulence. And generally turbulence
is a bad thing for a body moving in a resisting medium. A swimmer, for example, wants as little
turbulence as possible, to give as little resistance as possible. But never say never. That is,
there can be situations in which localized and controlled turbulence can reduce drag. But before we
can discuss such a situation, let's talk about the curving of spinning balls in general. For a
hundred years, physics books have explained curve balls in terms of the Bernoulli effect -- the
spinning ball drags a sheath of air around with it; due to superposition, there is higher gas
velocity where the spin adds to the velocity of the streaming air of the translational motion, and
hence lower internal pressure at that point; the ball moves in the direction of the leading edge.
This is not so much incorrect as incomplete; Bernoulli is a necessary but not sufficient ingredient
for the amount of curve seen in spinning balls. The rest of the story is the Magnus effect; the
Magnus effect embraces turbulence and viscosity. To be specific, a region of turbulence develops
downstream of a ball; if the ball is spinning, the turbulent region becomes asymmetric -- the
turbulence is located more in the quadrant that the trailing edge points at; this quadrant
experiences greater pressure and exerts a force on the ball in addition to and in the same direction
as that produced by the Bernoulli effect. In a baseball, the two effects can exert a force as great
as one-third the weight of the ball, resulting in measured curves of more than 17 inches.
To return to the dimpled golf ball: the sheath of air traveling viscously with the moving ball is
called the boundary layer. It is an advantage, for fast travel, for the boundary layer to cling as
long as possible to the surface of the ball. In an undimpled ball the boundary layer separates from
the surface typically when the air has gone about halfway from the front to the back of the ball.
True streamlining would enable the boundary layer to cling much longer, but a golfball shaped like
the wing of a 747, even in miniature, would putt badly. In lieu of that, dimples serve much the same
purpose, enabling the boundary layer to cling all the way around nearly to the rear of the ball. The
Navier-Stokes equations for this situation have never been solved, so it's not completely clear just
how the local pockets of turbulence around the dimples help the boundary layer to cling longer, but
one explanation is as follows: when the boundary layer 'fits like a glove' around the ball, the
layer slows down rapidly and separates quickly. But turbulence provides coupling to the 'outside'
airsteam and enables the boundary layer to continue receiving momentum from the outside air. This
lets it 'stay on the ball' longer, makes the overall wake of the dimpled ball narrower, and the
pressure differential between the front and the rear of the dimpled ball is not as great as that of
a smooth ball.
Answered by: Anthony Laudani, Software Engineer
'The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.'