A Group Collaboration by:
Keeton Crowder
Brittain Fish
Patrick Kennery
[ Photo of a golf bag taken by Patrick Kennery, 2003 ]
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What is Golf?
Golf began as a pastime of the "Kingdom of Fife," off the eastern coast of Scotland, during the Fifth Century. Originally, participants hit small rocks or pebbles around sandy grounds using a basic stick. The sport developed from there as a leisure activity, and found itself amidst controversy during the mid-15th Century, as Scotland and England were in conflict. As a means of restricting the Scottish people, King James II banned the sport, which was later lifted by King James IV. The popularity of the sport rapidly spread to include much of Europe.
Apart from the history of the game itself, golf is a sport designed to loft a small ball a large distance into a small hole. So why is physics important to golf? Well, fundamental to golf is the golf swing, and a successful golf swing is based on many physics concepts.
What are some physics concepts of the golf swing?
The golf swing is a combination of the force applied by the golfer in swinging the club, the force applied by the club face on the ball, the lie angle (or angle of the club face), and the initial velocity of the ball. Furthermore the positioning of the body during a golf swing is extremely important; one’s stance and grip are important, as well as the movement of the shoulders, arms, and hips, which determine the alignment of the club as it accelerates toward the ball.
Velocity of the Club Head:
Assuming that all golfers stride for the ideal body positioning, the physics left in the golf swing begins with the velocity with which the club head moves toward the ball. For an ideal swing, the club head speed (tangential speed) should be approximately 100 miles-per-hour when it contacts the ball. The ball then accelerates from the tee and travels with an approximate velocity of 140 mph towards its destination. The ball accelerates because, as described by Newton’s Second Law, the net force of the club head is proportional to the acceleration of the club head multiplied by its mass ( F = m a ). Thus, a net force is applied to the ball, and the ball is set in motion, just as Newton’s First Law of Motion describes.
The “lie” angle of the club face:
The lie angle of the club face is most accurately described as the angle formed between the center of the shaft of the club and the base of the club. This lie angle determines the projection angle with which the ball is “pitched” into the air. Thus, if the ball begins its flight at a steeper angle (caused by a greater lie angle of the club face, i.e. a 7-wood), the displacement of the ball will be less than if it were pitched at a less steep angle (caused by a smaller lie angle of the club face, i.e. a 1-wood), under normal Earth atmospheric conditions.
The elasticity of the impact between the club face and the ball:
The elasticity of the collision between the club face and the ball is dependent on the material with which both the club face and the ball are constructed. A perfectly elastic collision is one in which both momentum and kinetic energy are conserved. Momentum is the product of mass and velocity ( p = m v ), and kinetic energy is defined as (1/2) m v^2. If the club face is mostly wood, and the ball is constructed of some polymer combination, then the elasticity is decreased somewhat because the wood tends to absorb some of the kinetic energy and momentum during the collision impact. However, if the club face is constructed of a metal, most commonly a titanium-alloy, then the collision is more perfectly elastic, and the momentum and kinetic energy of the collision are more conserved. To see how the momentum of the golf ball changes once it is hit, refer to:
So what happens after your swing?
Once the club face collides with the ball, the ball is set into motion and obtains a horizontal displacement. For most circumstances, this displacement can be calculated using the range equation, given that the elevation of the ground is equal at both the initial and final location of the ball. This allows one to calculate the displacement of the ball from take-off to touch-down, not including any movement after the ball lands lans on the ground. The range equation is defined as: R = ( vi^2 (sin 2 ( theta ) ) ) / g. To see the range equation in action, refer to:
http://www.unc.edu/~kennery/golf/Range_and_Angle.html
Some other physics factors of golf include. . .
There are seemingly infinite physics concepts involved in golf. For instance, once the ball begins its flight, both the back spin applied by the club face and the dimpled surface of the ball serve to decrease the drag on the ball, causing the ball to have a longer time of flight and, therefore, a greater displacement. "Drag" is defined as the resistance the ball encounters in the presence of air flow. "Lift," however, is the consequence of air filling the dimpled pockets of the ball, which causes it to stay in the air longer and to travel farther. Furthermore, the composition of the club shaft is responsible for creating a "whipping" effect that increases the acceleration of the club head towards the ball. The amount of friction between the golfer and the club is also important because, with increased friction, the "grip" on the club is more secure, which allows for a greater force applied by the golfer, thus a greater acceleration of the ball. (This could be why so many golfers choose to wear gloves while teeing off.) Nonetheless, in order to assure maximum acceleration of the ball, the ball must be hit cleanly by the club face and, ideally, in the center of the club face, or the "sweet spot".
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This site, a collaboratory work of three Physics 024 students at the University of North Carolina at Chapel Hill, is meant to serve as a starting point from which to begin your analysis of the game of golf. This is primarily interested in evaluating the physics of a golf swing and the contact between the club head and the golf ball.
For more information about other various concepts of golf and their relation to physics, visit these other sites:
http://puttingzone.com/Science/cjp-putting.pdf
http://www.kent.k12.wa.us/staff/trobinso/physicspages/PhysOf99/Golf-Henry/putting.html
http://entertainment.howstuffworks.com/question37.htm
http://www.golf.com/content/html/homepages/home_GDC.htm?ck=234783351
http://www.golfclubsetc.com/shaftstutorial.html
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Fun Golf Links to Other Sites:
http://golf.about.com/gi/dynamic/offsite.htm?site=http%3A%2F%2Fwww.golflafs.com%2F
http://golf.about.com/cs/apparel/index.htm
http://207.10.97.102/explrsci/dswmedia/range.htm
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Sources Cited:
http://www.golfeurope.com/almanac/history/history1.htm
http://www.hhs.homewood.k12.al.us/compsci/projects98/eteam/paper.html
http://www.geocities.com/Tokyo/Towers/9728/physicsfair.html
http://www.wired.com/wired/archive/8.05/golf.html
http://kingfish.coastal.edu/physics/projects/2000_Spring/golf/
http://brp.arc.nasa.gov/Science/Y_GBL/bsc_resrch.html#moon
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For a description of this Web Project, visit:
If you have any comments or concerns, please contact the webmasters:
Keeton Crowder ( pcrowder@email.unc.edu )
Brittain Fish ( bfish@email.unc.edu )
Patrick Kennery ( kennery@email.unc.edu )
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[ Created on April 10, 2003. ]