The Physics of Golf

1. The Physics of Golf By Drew Thomassin Drew Thomasson

2. Types of Clubs • Driver/Woods-Longest club, used for long distances, either: wood, titanium or stainless steel • Irons- Range from a 2 iron, less angled for farther distance to greater angled wedge for short distance • Putter- Used for puts on the green

3. Parts of the Club • Head- Woods-wood, titanium, stainless steel Irons- stainless steel, titanium, iron • Shaft- steel, carbon fiber, resin composite • Grip- rubber or leather

4. Contact with the Ball • The contact between the club head and the ball is less than a thousandth of a second. • The average force between the ball and the club head is around 3000 lbs, the ball becomes flattened against the clubface • The ball when hit it rolls up the clubface due to friction and flies off with a high speed above the horizontal (where the clubface made contact with the ball) • The momentum of the collision is conserved because of the high speed of the ball after the collision and the slowing down of the club head during the collision • The collision is not elastic meaning that mechanical energy was lost during the collision when the ball flattened and rolls up clubface due to friction • The clubface has grooves on it, to produce friction for the ball to roll up clubface and to produce a spin on the ball

5. The D Plane • This is a representation of perfect contact between the clubface and the ball • The path which the club is moving at impact • The normal to the clubface and the path after the collision • As well as the aerodynamic lift force

6. A Hook Shot • A hook shot is when a right handed golfer makes first contact with the side of the ball furthest away from him • A clean hit will cause the ball to spin at a horizontal axis • Contact like this results in a spinning axis to the left causing the ball to curve to the left • The whole D plane is shifted to the left

7. A Slice Shot • A slice shot happens when a right handed golfer makes first contact with the ball on the inner side • Like in a hook shot this contact results in the ball to spin towards the right making it curve to the right

8. History of the Golf Ball • The “feathery” was the first golf ball. It was a leather spherical pouch filled tightly with feathers and then stitched. When the ball hardened it became very hard, then was oiled and painted. • These golf balls would reach up to150 to 175 yards • Featheries were used until 1848 when the gutta-percha was invented. • The gutta-percha is a gum from trees in Malaysia. • Became roughened, people realized they’d go much further than smooth balls • Modern golf ball range in they’re made of these days, the typical golf ball has a core made of polybutadiene, a type of rubber • Harder core, farther they go • Golf balls today can reach up to 300 +

9. Flight of the Ball

10. Diagram A • Streamline flow – still, straight airflow • Turbulent flow- disturbed air flow • Slow streamline air flow past smooth ball • At a low velocity there is a thin layer of air near the surface of the ball called the boundary layer, where the speed of air is zero, as it extends out the air speed becomes greater in the streamline flow • Air in contact with the ball is at rest relative to the surface of the ball • Momentum is transferred across the boundary layer from the flowing air to the surface of the ball • From A to B the boundary layer is going from high pressure to low pressure, the pressure difference helps increase velocity Direction of Ball

11. Diagram B • Air flow at a higher speed past a smooth ball, showing turbulence • From A to B streamline is similar to diagram A • At B the turbulent wake forms • Energy is lost, from the energy of motion (Kinetic Energy), • A drag is created from the difference of pressures between the front and back of the ball Direction of Ball

12. Diagram C • Turbulent flow past a dimpled ball, no spin • The dimple surface makes the boundary layer turbulent • Instead of air slowing near B, the fast moving air carries the turbulent boundary along with the ball, to extend further along the surface of the ball from the lower air pressure level at B to the higher air pressure level at C • Drag of the dimpled ball is smaller than the smooth ball, less energy is dissipated in the smaller wake Direction of Ball

13. Diagram D • Air flow downstream from a rotating dimpled ball, golf ball flight • When hit, the ball slides up the face of the club due to the friction of the ridges • The ridges cause the ball to spin on a horizontal axis spinning towards the golfer • The turbulent layer is moving with the surface of the ball as it spins • Air at top is moving more rapidly than air at the bottom, the pressure is less above the ball than below the ball • A lift force is exerted perpendicularly on the ball • The wake behind the ball starts lower than the wake of the non-spinning ball • Ball receives a downward momentum, the ball recoils in upward motion Direction off Ball

14. Drag and Lift • Depend on three variables: speed of ball through the air, the rate of spin on the ball, surface texture of the ball • Drag on the ball increases with speed through the air and spinning rate • Lift increases with rate of spin at a given air speed and vise versa • Different clubs vary in loft resulting in a more intensive spin or less intensive spin • Clubs also vary in the power to be given to the ball • Depends a lot on the club for the amount of drag and lift

15. References • entertainment.howstuffworks.com/golf-club.html • Jorgensen, Theodore P., The Physics of Golf, American Institute of Physics Press, Woodbury, NY. 1994 • sportsillustrated.cnn.com/augusta/cool_stuff/physics/tiger.html