Fluid Mechanics Applications/A07 Dimples on Golf Ball

As a matter of fact, it was noted that break in surface area decreases the vortex formed behind the body. For example, to decrease the drag force on car spoilers are introduced. Dimples on golf ball also plays similar role but have many other uses. Dimples on it are responsible for the flight, trajectory and movement of golf ball. Basically it all depends on the aerodynamics of ball. As we study, there are two types of flows, namely, Laminar flow and Turbulent flow. Laminar flow, initially, experience less drag but also, it is prone to separation (boundary layer phenomenon). Due to this phenomenon drag force increases with time. But it is opposite in the case of turbulent flow. As the matter of fact, these dimples create turbulence in layer of air next to it. Thus reducing drag force.

HISTORY OF GOLF BALLS
In the beginning, golf balls were made of leathers and were scuffed with wet goose feathers. These balls were known to be called as "featheries". With the passage of time manufacturing of balls made from molded rubber sap started. These balls were called as “Gutta percha balls” as they were made from sap of gutta percha tree. These balls were designed in shape of perfect sphere on the basis that smooth ball will go farther and would experience less drag force. But this thought proved to be wrong when golfers experienced that balls that were beaten up by nicks, bumps and slices go farther. This was because of the reason that nicks and cuts were acting as the tabulators on the surface of ball. Thus, in 1930 dimpled golf balls were discovered accidentally and till then dimpled golf ball is used. There is not any limitation to the numbers on golf ball but a number from 300 to 500 is common. 392 dimples are conveniently used as this type of ball provides a golfer a satisfied result. After that people believed that more would be the number of dimples farther it would go but this theory was rejected. But the manufacturers tried various sets and combination of dimples. Now, there is variety of dimples available on golf balls. Some are deep, some are shallow and also, large and small. Shapes of dimples also vary. These may in shape of circle, ovals and even in the shape of hexagons.

ADVANTAGES OF DIMPLES
There are various advantages of dimples on the golf ball. These are:
 * Dimples convert the spin of golf ball into lift. It was discovered accidentally.
 * Dimples reduce the drag exerted on the ball. A dimpled ball experiences about half of drag experienced by a smooth ball.
 * Numbers and size of dimples on golf ball decides the trajectory or flight characteristics of golf ball. For instance, “Distance” balls are designed in such a manner to cause the ball to fly low and bounce far which is advantage during a long course or in high winds. But for short of greens “Control” balls are used. These balls are dimpled in the manner to induce lift at end of its arc so that ball falls almost vertical.
 * Dimples create turbulence in the layer of air around the ball. This results in smaller vortex.

MECHANICS OF LIFT AND DRAG
There are three forces which act on the golf ball when it is flying in the air. Two of them are clear to analyze which are gravity and drag. One force also appears on it which is due to Magnus effect and called as Magnus force. This is developed due to the spinning of ball. Initially it was believed that balls in the form of perfect sphere and are smooth experience less drag but it was not so. This perception would be correct if the ball doesn’t spin but actual condition shows that ball took spins just after the moment it leaves the tee. On an average, a golf ball leaves the tee with a speed of 80 m/s and about 60 rev/s of backspin. The Magnus force is experienced due to the relative drag on air at boundary at top and bottom of the ball. The top of the ball is moving with lower relative velocity compared to the air around it resulting in less drag on air that goes over the ball. Thus flow becomes laminar at that region. Similarly, bottom part moves faster relative to the air near it, thus experiencing less drag on air passing by. This develops turbulent layer at this region and resulting the air movement near the region slower relative to the ball. Thus Bernoulli force produces lift or we could also say that the flow lines past the ball are displaced down causing the ball to be pushed up. According to Bernoulli's equation, $$ \frac{p}{\rho} + \frac{V^2}{2} + gz = constant $$

where, Thus, dimples are what gives a golf ball lift. This is done by creating two layers of air going around the ball. Turbulence is created because the top layer is going faster than the bottom layer. This reduces the drag and allows the ball to travel farther than a smooth ball.
 * $$p$$-difference in pressures on body
 * $$\rho$$-density of body
 * $$V$$-velocity of fluid surrounding the body
 * $$g$$-acceleration due to gravity
 * $$z$$-height of body

TRAJECTORY OF GOLF BALL
The variety of dimples (different shapes and sizes) also determine the flight characteristic/ trajectory of ball. There are different kinds of golf ball available in the market and are produced by the manufacturers. Hexagonal balls with moderate intensity are used mostly, giving ball a structure similar to Buckminsterfullerene and also helping the golfer an accurate idea of path. most of the golfers need that the golf ball should fall vertically so as the ball drops in the hole with less efforts.