The Mathematics of GolfBy

Jennifer Morgan

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

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

Club Loft AnglesClub Loft Angle

Driver 13°

3 wood 16°

5 wood 19°

2 iron 18°

3 iron 21°

4 iron 25°

5 iron 28°

6 iron 31°

7 iron 34°

8 iron 37°

9 iron 41°

Pitching Wedge 45°

Club DistanceClub Men Yards Women Yards

Driver 230 + 180 +

3-wood 210-230 170-185

5-wood 170-190 140-155

2 iron 170-190 140-155

3 iron 160-180 140-160

4 iron 150-170 130-150

5 iron 140-160 120-140

6 iron 130-150 110-130

7 iron 120-140 100-120

8 iron 110-130 90-110

9 iron 100-120 80-100

Pitching Wedge 90-110 70-90

Club Loft Angle& Distance• What pattern do you see here?

– Each club’s 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 club’s loft angle increases its distance decreases…a Driver’s

loft angle is about 13° and hits about 230 yards (for men) and a 3 wood’s 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

Swinging

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

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 it’s 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?

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

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

Setting Up

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!

Tiger’s Swing

Look at all the angles here!

•Legs•Arms•Backswing•Downswing

Backswing

Let’s 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.

Downswing

He’s still in the same swing plane!

Swinging• As you can see in Vijay’s 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…..

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

Half SwingIf 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.

On the Course

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

Hole 17 Stonebridge Golf Course

Let’s 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)

Let’s Play Hole 17!

• What’s 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.

Let’s 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

Let’s Play Hole 17!• If you hit the ball straight

200 yards you’ll potentially be in the sand trap or trees and that’s 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!!!

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.

Let’s 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?

Let’s Play Hole 17!

• That’s 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?

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 can’t tee it up on the course!

Let’s 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

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

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

Let’s 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 it’s in the hole!

Let’s 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!

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