The Mathematics of Golf

1
The Mathematics of Golf

• By
• Jennifer Morgan

2
Getting Clubs

• Almost everything about golf is mathematical,
  from your clubs to practice to the course
• Before you can start a golfer must obtain a
  standard set of clubs which contains three woods
  (the 1-driver, 3, and 5), eight irons (3, 4, 5,
  6, 7, 8, 9, and Pitching Wedge), and a putter for
  a total of twelve clubs
• You need different clubs to hit the ball a
  certain distance with a certain trajectory based
  on the layout of each hole

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Getting to know your clubs

• Loft angle
• The angle of the face of the club is called loft
• Drivers and 2 -3 irons have little loft whereas
  short irons and the PW have more loft
• The more loft you have the higher the trajectory
  of the ball
• Loft angles are expressed in degrees

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Club Loft Angles
5
Club Distance
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Club Loft Angle Distance

• What pattern do you see here?
• Each clubs loft angle increases about 3
• What about distance?
• Distance increases about 20 to 30 yards with each
  club
• What connections can we make about distance and
  loft angle?
• As a clubs loft angle increases its distance
  decreasesa Drivers loft angle is about 13 and
  hits about 230 yards (for men) and a 3 woods
  loft angle is about 16 and hits about 210 yards
  (men)
• So one can make the conclusion that the steeper
  the loft angle of the club, the less distance the
  ball will travel when hit, but will have a higher
  trajectory

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Swinging

• A golf swing is not an easy thing to perfect,
  everyones is different depending on their
  ability and body type

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Are you ready to hit the ball?

• Before you go take a whack at it there are a few
  more essential steps
• First you need to pick a target, whether its on
  the driving range or the course always know where
  you are aiming
• Picking a target, say you are at the bottom of a
  hill in the rough and want to hit the ball about
  120 yards over the hill and onto the fairway,
  what club do you use?

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Choosing your club

• Based on your strength and club chart you would
  want to use a 5 7 iron for women or a 7 9
  iron for men
• Based on your strength plus the loft angle you
  will need to get it over the hill and into the
  fairway you choose a 7 iron
• Why? You have a fairly strong swing and would
  rather get out of the rough and over the hill
  using a club with a steeper loft angle

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Setting up

• Once you have the right club chosen you need to
  choose your target, aim, and properly set up
  before you hit the ball
• When choosing your target you must ensure that
  your feet, shoulders and clubface are all facing
  that direction, otherwise who knows where it will
  go!
• Your stance should form a right angle with your
  feet hips width apart, back bent at 25 degree
  angle, and arms hanging about 30 degrees

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Setting Up
12
Swinging

• You swing a golf club by rotating your shoulders
• You create an arc in your swing plane
• There are degrees of rotation, angles, and planes
  everywhere, so your sense of spatial reasoning
  and geometric knowledge is very important here
• Some of us are naturals, others of us have to
  practice, practice, practice!

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Tigers Swing

• Look at all the angles here!
• Legs
• Arms
• Backswing
• Downswing

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Backswing
Lets take a look at the planar swing of Mr.
Vijay Singh. Note that right angle again! Watch
how his swing stays in one plane here.
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Downswing
Hes still in the same swing plane!
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Swinging

• As you can see in Vijays swing, he stays within
  the plane, winds up and then releases the
  rotation letting arms fall down in the same
  plane, never slowing down, but accelerating
  toward the ball
• At this moment you build such momentum and are
  perfectly set up so your ball should fly
  beautifully towards your target
• Your swing should be the same for all of your
  clubs, however you can control the loft and
  distance of your shot other ways..

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Other ways to control your ball

• You do not always need to make a full swing
• To control the loft angle of your ball you can
  position it in certain spots in your stance so
  that you hit more behind the ball creating
  greater loft and further manipulating the
  trajectory of the ball

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Half Swing
If you want to use a particular club but hit the
ball a shorter distance you can use a half
swing. Start your backswing staying in the same
plan up but bringing the clubface only as high as
shoulders and begin downswing, this will build
less momentum because the torque of your body is
less.
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On the Course

• Now that we know our clubs, how to set up and how
  to hit them, lets play some golf!!!

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Hole 17 Stonebridge Golf Course
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Lets Play Hole 17!

• Par 5 means you must take 5 shots from the tee to
  the hole to make Par
• Birdie is one stroke under par
• Bogey is one stroke over par
• 520, 509, 482, 412 The professional tees are
  the furthest from the hole (520 yards), you will
  be hitting from the Ladies tee which is usually
  red (412 yards)

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Lets Play Hole 17!

• Whats a Handicap?
• A number assigned to each player based on his
  ability and used to adjust each player's score to
  provide equality among the players. In simplified
  terms, a handicap number, based on the slope of a
  course, is subtracted from the player's gross
  score and gives him a net score of par or better
  half the time.

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Lets Play Hole 17

• Based on the great distance of the hole you will
  drive the ball of the ladies tees using the
  Driver!
• Setting up look at the hole and determine how
  far and in what direction you need to hit the
  ball so that you can get it in the hole in least
  amount of shots possible

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Lets Play Hole 17!

• If you hit the ball straight 200 yards youll
  potentially be in the sand trap or trees and
  thats hard to get out of sooooo
• Aim about 10 degrees to the left of center, for
  some even 20 degrees because some tend to slice
  (or hook) more often than not this is all about
  estimation!!!

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Hook, Straight Slice
Hook it and it will go about 20 degrees to the
left. Slice it and it will go about 20 degrees
to the right.
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Lets Play Hole 17!

• If you swing well you can drive the ball about
  220 yards so with that target and full swing you
  should drop the ball a little less than 1/3 up
  the fairway giving you more direct access to the
  hole
• What next? How many yards do you have to the
  hole?
• If the total yardage is 412 and you hit the ball
  200 yards how many yards do you have to go?

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Lets Play Hole 17!

• Thats right! 212 yards!
• Now you are on the fairway which is very narrow
  and travels on a diagonal a little to the right
  before getting to the green
• To the left of the fairway are hazards (trees
  etc..) and a sand trap abutting the green Where
  do you aim?

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Hitting from the Rough

• Slightly to right with a 3 wood
• Although you can hit a 3 wood 200 yards, you
  decelerate through impact and it went 140 yards
  and off the fairway into the rough, oh no!
• How many yards do you have left now?
• 412 200 212 yards
• 212 140 72 yards

With 72 yards left in the rough where and with
which club do you think you should use now? Do
you need a lot loft angle? Remember you are in
the rough where there's thick grass and cant tee
it up on the course!
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Lets Play Hole 17!

• The fairway snakes a little to the right before
  the green which is two tiered meaning it sits
  higher up than the fairway
• Aiming about 20 degrees to the left, using my 8
  iron I hope to plop it onto the green in about 65
  yards

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On the Green!

• Yes! You got it on the green but it did not stay
  there
• This green slopes from left to right therefore
  forcing the ball to roll away from the hole to
  the edge of the green about 8 yards from the hole
• How many yards are you away from the hole?
• 412 200 212
• 212 160 72
• 72 64 8

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On the Green!

• What club now?
• You need to hit it a very short distance and have
  it land with some spin and little speed on the
  ball
• To minimize the speed and give the ball some spin
  you use your Pitching Wedge to get it on top of
  the green so it does not continue to roll back
  down the green
• So in this case you want to hit it past the hole
  by 1 yard, about 9 yards
• Aiming about 45 degrees to the left you use a
  half swing and chip it up on the green

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Lets Play Hole 17!

• Success!
• How many yards left?
• 412 200 212
• 212 160 72
• 72 64 8
• 8 1 9 8 1
• Time for the . Putter!
• Reading the green is difficult because there are
  a lot of subtleties to its slopes and angles
• Since it slopes left to right and my ball is
  about 1 yard from the hole on the upper left of
  the green you need to hit it slightly downhill
  which means it is likely to fall right of the
  hole

• Aiming 10 degrees to the left of the pin you
  gently but firmly make the putt and its in the
  hole!

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Lets Play Hole 17!

• Shot by shot distance covered to the hole
• 412 200 212
• 212 160 72
• 72 64 8
• 8 1 9 8 1
• 1 1 0
• Made it in 5 shots, giving us a score of Par on
  Hole 17, way to go!

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Final Thoughts

• Time and precision is very important on the
  course
• You must arrive ahead of your scheduled tee time
  and keep you momentum, not only for the sake of
  your fellow players but those groups behind you
• Plan on 10-15 minutes a hole
• For 18 holes of golf plan on 4 4 ½ hours