INWIT™ — THE DIMPLED GOLF BALL
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The Dimpled Golf Ball
by Vincent Mallette
Copyright © 1999 Inwit Publishing, Inc.
In the early days of golf the balls were smooth. Players noticed that as balls became old and scarred, they traveled farther. After a while players would
take new balls and intentionally pit them.1 Eventually manufacturers caught on and supplied balls with dimples. "Some manufacturers even claim
that the shape of the dimples is significant; one states that polygonal dimples are superior to round ones!"2 In any case, the superiority
of dimpled golf balls is well established: modern experiments show that dimpled balls can travel more than four times farther than smooth ones.3
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 spinning sheath adds to the velocity of the translational
streaming; hence there is lower internal pressure at that point, and 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.4 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.5 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.6
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.7 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" airstream 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. This treatment follows Jearl Walker's excellent discussion in Scientific American, April 1979.
Nature used dimples millions of years before golf was invented; in particular many pollen grains are dimpled, to maximize their travel with a given gust of
wind. You can see a micrograph of a "dimpled" pollen grain that looks amazingly like a modern golf ball in Scientific American for June 1979, p. 13.
Dimple design can be tailored to the hitting style of the individual golfer: "If you have a tendency to hit your shots high, a dimple design that provides a
lower flight trajectory will bring [your ball’s path] closer to the ideal. The converse is also true." So says Sports Illustrated, no less!.8
So important are dimples today that designers have played around not only with different dimple shapes but also with different arrangements of the dimples on
the globe of the golfball. Two California scientists named Holmstrom and Nepela have patented a ball (U.S. Pat. 3,819,190) with only half as many dimples,
but the dimples are confined to an equatorial band; the "poles" are smooth. This ball doesn't fly as far as fully dimpled models, but reduces hooking and
slicing as much as 80%.9
To sum up, one might say that spin can make a moving object no longer obey the simple Newtonian laws for a projectile. This applies in the heavens as well
as the earth: comets that spin can't have their appearances predicted as well as non-spinning ones. In particular, a fast-rotating comet named Encke
misbehaves badly because of its spin. But who threw that curvy comet, and what is it spinning in?
1 Scientific American, April 1979, p. 180
2 University Physics, 7th edition — by F. W. Sears, M. W. Zemansky, and H. D. Young (Reading, Mass.: Addison-Wesley, 1987), p. 324
3 Scientific American, April 1979, p. 180
4 Franklin Miller's discussion of Magnus and the baseball is in his College Physics, 3rd ed., p. 276: "The whole phenomenon is called the Magnus effect, and depends on the viscous drag of the fluid as well as on Bernoulli's principle."
5 University Physics, Seventh Edition — by Francis W. Sears, Mark W. Zemansky, and Hugh D. Young (Reading, MA: Addison-Wesley Publishing Company, 1987), p. 324.
6 "Effect of Spin and Speed on the Lateral Deflection (Curve) of a Baseball; and the Magnus Effect for Smooth Spheres" — by Lyman J. Briggs, American Journal of Physics 27, 589 (1959)
7 Scientific American, April 1979, p. 180 and p. 183; illustration, p. 183
8 "The Golf Ball," Sports Illustrated, March 25, 1991, sidebar signed "D. E." on an unnumbered page.
9 Science, March 14, 1975, p. 941
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