Teeing Off |
Golf Pro
Applications of Mathematics 10 |
Lesson Idea by: David Ward, Rutland Senior Secondary School,
Central Okanagan School District
Golf professionals are expert golfers. While not on the pro circuit, they may work at golf clubs and driving ranges, where they teach others how to play golf. They help beginners and young adults, seniors and even very experienced golfers who still want tips on their play.
They also manage the pro shop, arrange tournaments, and consult on equipment.
Terry Graham of the Osoyoos Golf Club in Osoyoos, British Columbia, says his job encompasses a wide variety of duties. "I essentially manage the facility -- staff, membership relations, press communications, playing and organizing tournaments, and developing tourism and marketing strategies."
Ken Chan, a golf pro at Mikasa Golf Centre in Richmond, loves the teaching role of his job. "As a pro, I take on the responsibility of helping people learn the game so they will have fun."
Many factors will determine one's level of success and ultimate enjoyment of the game. For many golfers, striking the ball well each time a shot is taken is a major accomplishment. In this sense, golf is an art. Yet, many of the factors that ensure success can be described mathematically.
For instance, experienced golfers have mastered the use of different clubs, which vary in weight, length, and angle of the club face. Good golfers can determine the right club to use for a certain distance, along with the flight pattern needed to generate a desired shot. Swing speed is also a critical factor in terms of the successful execution of the shot.
Therefore, the knowledge of mathematics -- at both the conscious and subconscious levels -- may truly help a player complete the variety of shots required during a round of golf.
For those people who work at companies that develop new golf clubs, the knowledge of applied mathematics is essential. Similarly, aerodynamics is a significant area of study for companies that focus their research on golf balls. For those wishing to work in the technical branches of the golf industry, educational qualifications can be quite high.
Invite a golf pro to visit your school to help you analyse the mathematics involved in this sport. (Or find an experienced golfer in your school.)
A. In a field or open space, ask the pro to point out some of the main features of a golf swing. These include: how to hold a club properly, how to stand, how to make a proper swing in order to make good contact with the ball, and how to follow through.
B. Watch the pro take a half-dozen swings. What features of this activity can be described mathematically? If the golf pro changes the swing, does that affect what happens to the ball? Analyse how the following factors affect the success of the swing:
- swing speed, measured in kilometres per hour (km/h), or miles per hour (m.p.h.). Can you do the conversion?
- how length of arm and length of club are related to swing speed
- angle of club face or "loft," measured in degrees from the vertical
C. Ask the pro to hit a few easy shots with different clubs. What do you notice? Analyse the following:
- At the point of club/ball contact, what role does club velocity (speed) have?
- How does "force at impact" affect the ball's flight?
- How does "launch angle" affect the ball's flight?
- Does "follow through" affect accuracy and overall achievement?
D. Take turns taking practice swings yourself in attempt to get the fastest possible club speed. What do you need to do to produce the fastest controlled swing? How can those factors be described mathematically?
Special experiment
Locate the device known as a "photo-gate timer" in your school, district or local college. Using the specifications as set out at the end of this lesson, build a small box to house the timer. Fashion a fin out of Bristol cardboard or very thin sheet metal measuring 10 cm long and about five cm deep. Attach it the bottom of the driver using adhesive tape.
When a swing is made over the box and therefore "through the gate," the device can accurately measure its speed over a 10 centimetre distance. For example, a reading of "10 centimetres in 'x' number of seconds" will be accurate to .0001 (one-one thousandth!) of a second.
Have the guest golf pro (or experienced student golfer) make a regular golf swing with the adapted driver. Take care not to hit the box or timer.
Repeat the experiment four more times, recording the data on the Student Activity Sheet below. Calculate the average swing speed.
Note: If the experiment with photo-gate equipment is not possible, you may ask the golf pro to bring along a "swing speed" measuring device used to analyse student players. Note that this device may produce results in units of miles per hour, which may be used to compare with answers achieved in metric units in the activity below.
Bob Thurman is the principal engineer (Aerodynamics) for a major golf research testing facility in Tennessee. "Everyone hits the ball differently, and, unfortunately, most clubs in the golf bag have different lengths and swing weights-which therefore produce a variety of swing speeds."
The driver is the longest/lightest club, with a basic length of 111.76 cm (44") and a loft of nine, 9.5 or 10 degrees. The other clubs have the following characteristics:
| Club |
Length |
Loft (in Degrees) |
| 3 wood |
107.95 cm (42.5") |
12 to 15 |
| 3 iron |
97.79 cm (38.5") |
12 |
| 4 iron |
96.52 cm (38") |
13 |
| 5 iron |
95.25 cm (37.5") |
15 |
| 6 iron |
93.98 cm (37") |
17 |
| 7 iron |
92.71 cm (36.5") |
19 |
| 8 iron |
91.44 cm (36") |
22 |
| 9 iron |
90.17 cm (35.5") |
25 |
| pitching wedge |
88.9 cm (35") |
50 |
|
In pairs, use the information given below to calculate the distance the head of a golf club would travel if it made one complete revolution.
Player A:
Average female player
Arm length: 55.8 cm
Club: driver
Length: 117.76 cm
Player B:
Average male player
Arm length: 68.6 cm
Club: driver
Length: 117.76 cm
For each player, allow 10.2 cm for a handgrip.
Think about the best way to do these calculations before you do them. Discuss the differences between radius and diameter. Provide your answer in metres, corrected to two decimal places.
Check your answers against the Solution for Principles section below.
Discuss the following question with the class:
Does the difference in length of revolution offer a slightly more challenging situation for the golfer with a longer reach?
With your partner, discuss the steps required to calculate the velocity of the golf swing in the following scenario:
For an average female golfer, a swing with a driver often travels the bottom 10 centimetres in 0.003 seconds. If the same speed were maintained for one whole revolution, what is the speed in kilometres per hour (km/h)? Consider distances and time units carefully. Round off your answer to two decimal places.
| Hint: Speed = |
distance |
|
time |
Solutions
You may have come up with one or two methods to solve this problem. They are:
Solution 1
Using the circumference measurement for the average female golfer from the Solution to Principles section, the time for one revolution would be:
| Circumference (cm) |
x 0.003 sec. = |
1025.9 |
x 0.003 = .31 sec. |
| 10 cm |
|
10 cm |
|
| Therefore, |
1 sec |
= 3.23 revolutions per second. |
|
.31 |
|
Are you surprised?
Calculate the total distance travelled in one hour. State your answer in kilometres. (Hint: Use 60 sec. x 60 min. to calculate total distance in one hour.)
3.23 x 10.26 m x 60 x 60 = 119303.28 m
Convert to kilometres:
119303.28 / 1000 = 119.30 km/h
Solution 2
Use the swing speed for an average female golfer of 0.003 seconds for 10 cm. Therefore, the swing speed is 0.03 seconds for 1 metre. (10 cm x 10 = 1 metre; therefore, 0.003 x 10)
Using the formula speed = distance /time with the same numbers and dividing by 1,000 (to calculate kilometres) provides us with the following:
| Club Velocity = |
distance |
x |
60 x 60 |
| |
time |
|
1,000 |
|
| = |
1 metre |
x |
60 x 60 |
= 3,600 |
| |
0.03 sec. |
|
1,000 |
30 |
| = |
120 km/hr |
|
|
| |
|
|
|
Review the two methods. With your partner, discuss which is the most straightforward.
Are the results surprising? Discuss your thoughts with another pair of students.
The figures below show comparable average "swing speed" over a 10 cm distance for a male golfer, a female professional and a male professional. A measurement of speed for the "Grip and Rip It" pros John Daly and Tiger Woods is also listed.
Using the equation for Club Velocity in Solution 2 above, calculate the velocity in km/h for each player listed. (Use the data you derived from the photo-gate experiment to calculate the comparable speeds of your guest pro and student player who contributed to this lesson.)
| Average male golfer: |
10 cm in 0.0024 sec. |
| Female professional: |
10 cm in 0.0023 sec. |
| Male professional: |
10 cm in 0.0021 sec. |
| J. Daly / T. Woods: |
10 cm in 0.0018 sec. |
| Invited Pro: |
10 cm in _____ sec. |
| Student player: |
10 cm in _____ sec. |
Use a conversion figure of 1.6 km = 1 mi. to convert the km/h answers to m.p.h. Check your answers against those shown in Solution to Yes, You Can Do It below.
Discuss the following with the class:
Additional Activities
This lesson may be extended by studying other challenging mathematical questions. For example:
- the calculation of "change in ball velocity" from stationary to extreme speed in approximately 500 milli-seconds or 0.0005 seconds
- "Force at Impact," which uses the fact that a golf ball weighs close to 46 grams (0.10125 lb.)
- the impact on flight pattern due to the loft of a given club
- the basic trajectory, range and carry distance that may be possible with certain equipment designed to achieve special results for experienced players
For more information on golf, golf companies, golf products, player records and other golf news, visit the following Web sites or surf for others:
www.Wilsonsports.com
www.Topflite.com
www.Infogolf.com
www.Titleist.com
www.Spalding.com
| Course/Grade: Applications of Mathematics 10 |
Curriculum Organizer:
· Patterns and Relations
· Problem Solving |
Curriculum Sub-organizer(s):
· Demonstrate a commitment to solving new problems.
· Solve applied problems using algebra skills and appropriate technology - with attention to units.
· Use community resources.
|
Prerequisites:
· Some experience with metric and imperial units of measure.
· Some basic formula and simple algebra work.
|
Resources:
Pencil, golf balls, golf clubs, photo-gate timer and housing, golf professional and/or experienced student golfer.
|
Student Activity Sheet
Pro/Student
Golfer Swings |
Time (Sec.)
1/1000's |
| Swing 1 |
__________ |
| Swing 2 |
__________ |
| Swing 3 |
__________ |
| Swing 4 |
__________ |
| |
|
| Average of all swings = __________ |
Components of Golf Swing calculations:
Show your work for the analysis of circumference from the Principles section.
Analysis of Club Velocity calculations:
Show your work for the analysis of velocity from the Yes, You Can Do It section. |
Solution to Principles
Calculate the distance head of a golf club would travel if it made one complete revolution.
Use the formula:
Circumference = Pi x Diameter
To calculate the radius, you must add the arm length and club length, then subtract the handgrip allowance. Then, multiply the radius by two to get the diameter.
Player A
Circumference = Pi x Diameter
= 3.14 (55.8 + 117.76 - 10.2) x 2
= 3.14 x 163.36 x 2
Circumference = 1025.9 cm or 10.26 metres
Player B
Circumference = 3.14 x (68.6 + 117.76 - 10.2) x 2
= 3.14 x 176.16 x 2
= 1106.28 cm. = 11.06 metres
|
Solution to Yes, You Can Do It
| Average male golfer: |
150.00 km/h |
= |
93.75 m.p.h. |
| Female professional: |
156.52 km/h |
= |
97.83 m.p.h. |
| Male professional: |
171.43 km/h |
= |
107.14 m.p.h. |
| J. Daly / T. Woods: |
200.00 km/h |
= |
125.00 m.p.h. |
| Invited Pro: |
______________ |
= |
__________ |
| Student player: |
______________ |
= |
__________ |
|
