Golf Balls: Newsletter Challenge (08/23/05)

effect how the ball travels by catching "air".

It is an old topic in rational mechanics (fluid dynamics). Same reason why tennis balls are "hairy" or the fishes are squamose,... et cetera. It must trace back to the theorem of Kutta-Zukovskij.

The reason why golf balls have dimples is a story of natural selection. Originally, golf balls were smooth; but golfers noticed that older balls that were beat up with nicks, bumps and slices in the cover seemed to fly farther. Golfers, being golfers, naturally gravitate toward anything that gives them an advantage on the golf course, so old, beat-up balls became standard issue. At some point, an aerodynamicist must have looked at this problem and realized that the nicks and cuts were acting as "turbulators" -- they induce turbulence in the layer of air next to the ball (the "boundary layer"). In some situations, a turbulent boundary layer reduces drag. If you want to get deeper into the aerodynamics, there are two types of flow around an object: laminar and turbulent. Laminar flow has less drag, but it is also prone to a phenomenon called "separation." Once separation of a laminar boundary layer occurs, drag rises dramatically because of eddies that form in the gap. Turbulent flow has more drag initially but also better adhesion, and therefore is less prone to separation. Therefore, if the shape of an object is such that separation occurs easily, it is better to turbulate the boundary layer (at the slight cost of increased drag) in order to increase adhesion and reduce eddies (which means a significant reduction in drag). Dimples on golf balls turbulate the boundary layer. The dimples on a golf ball are simply a formal, symmetrical way of creating the same turbulence in the boundary layer that nicks and cuts do......so there :-)

Two early aerodynamicists, Kutta in Germany and Joukowski in Russia, worked to quantify the lift achieved by an airflow over a spinning cylinder. The lift relationship is Lift per unit length = L = rGV where r is the air density, V is the velocity of flow, and G is called the "vortex strength". The vortex strength is given by G = 2piwr2 where w is the angular velocity of spin of the cylinder. This may seem a bit mysterious, but it can be looked at in terms of a redirection of the air motion. If the cylinder traps some air in a boundary layer at the cylinder surface and carries it around with it, shedding it downward, then it has given some of the air a downward momentum. That can act to give the cylinder an upward momentum in accordance with the principle of conservation of momentum. Another approach is to say that you have exerted a downward component of force on the air and by Newton's 3rd law there must be an upward force on the cylinder. Yet another approach is to say that the top of the cylinder is assisting the airstream, speeding up the flow on the top of the cylinder. Then by the Bernoulli equation (effectively, higher velocities lead to lower pressures), the pressure on the top of the cylinder is diminished, giving a degree of effective lift.

Indentations change the surface of the ball of spheric form. (makes the surface rough) The boundary layer is the space next to the ball in which there is a gradient of velocity. That boundary layer finally turns into a turbulent flow. Then the boundary layers separated from the ball and cause turbulences. The turbulences after the separations decrease the presure of the rear part of the ball and cause a resistence force. The turbulences are bigger as sooner is the separation. The separation depends on the surface. For laminar flux, (low values of Reynolds -proportional to speed- ) the separation occurs at 80º aprox. The indentations makes the flux less laminar and it makes that the flux is already turbulent at 80º, so the separations suffer a delay. Therfore, with the indentations the separation of the boundafy layer occurs at 120º aprox and the pressure decrease is smaller. As a consecuence of the fact that the pressure decrease is less important, the force against the golf ball is lower. It permits us to threw the ball further which is a desirable characteristic of golfers.

As written in the 8/30 issue of Specs & Techs from GlobalSpec:

You tell him it's a matter of aerodynamics. The basic shape of a golf ball makes it subject to a larger drag force. As a smooth golf ball travels through space, air hits the front, creating a high-pressure area, and splits around to the sides. But because the ball is traveling at such high speeds (well-hit golf balls can go about 120 mph), the air can't make it to the back of the ball. It separates from the surface, creating a low-pressure area at the back of the ball. (This is similar to a boat's wake.) The combination of high pressure at the front of the ball and low pressure at the back creates drag on the ball. However, adding dimples to the ball creates turbulence in the thin layer of air next to the surface (referred to as the boundary layer). So rather than flowing in smooth, continuous layers (a laminar boundary layer), the air has a microscopic pattern of fluctuations and randomized flow. In effect, the turbulence creates "traction" so the air can better follow the curvature of the ball. The result is less separation of the air (a smaller wake), thus less drag on the ball. A dimpled ball has only about half the drag of a smooth one, allowing it to travel much farther.