Module 3: Sail Area and Perimeter
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Module 3
Module 3: sail area and perimeter
What shape are sails and why?
Learn Sailing Right! Beginner Chapter 2 & Intermediate Chapter 3
Subject Areas
Math (Pythagorean Theorem, Algebra, Geometry, Measurement, Conversion, Area and Perimeter)
Physical Science
Summary
Students examine why most sails today are triangular in shape. They will investigate the properties
of a right triangle, compute and compare sail area, and perimeter.
Duration
Lesson Time:
Part I: 20 minutes
Part II: 40 minutes
Part III: 120 minutes
Part IV: 40 minutes
Skills
Measuring, Computing, Collecting and Organizing Data, Estimating Measurements, Calculating Area
Sailing Skills
Rigging, Know your Boat, Parts of a Sail, Sail Shape and Control of the Boat, Basic Science of
How a Sail Works
Vocabulary
Right Triangle, Hypotenuse, Leg, Pythagorean Theorem, Surface Area, Luff, Leech, Trade
Winds, Foot.
Standards
See Standards Correlation Charts related to the National Standards. Common Core Standards relate
to mathematics and the K-12 Framework for Science Education relate to Science.
Objectives
Students will:
u Measure the area of a triangle.
u Compute Pythagorean Theorem.
u Review the parts of a triangle base, height, and hypotenuse.
u Identify the parts of a sail, head, foot, luff, and leech.
u Compare the sail area of a main sail and a jib sail.
Sail Area and Perimeter
Materials
•One de-rigged instructional boat.
• Dinghy Main Sail (1 per group of 3)
• Dinghy Jib Sail ( 1 per group of 3)
• One Design Sail (1 per group of 3)
• Clipboards (1 per group)
• Measuring tape (1 per group of 3)
• Students sheets (1 per student)
• Calculators (1 per group)
Sailing Centers
Complete Parts I and II on day 1, with a lesson on rigging and de-rigging. Complete Part III on
day 2. Students measure and calculate sail area and perimeter and then apply that knowledge
to their sailing. The primary goal of this lesson is for students to connect math and sailing with
engineering and design.
Formal Classroom Settings
Complete Parts I on day 1, review the classification of triangles with students. Have them practice
solving problems using a square to find the area of a triangle. Complete Part II on day 2. You will
need to contact your local sailing center to borrow a few sails. The size of the sail and the condition
of the sail does not matter. Omit Part III. Implementent Part IV on day 4 and the Extension Activity
on day 5.
Career Connection
Sail Designers, Marine Surveyors, Architects, Engineers, and even construction workers need to
know geometry. Have students interview any of the previously listed professionals. Inviting a marine
surveyor to bring in blue prints or CAD drawings they may be working on is a great connection for
students. Please see the video links in reference to North Sails in the Resource section of the Module.
Module 3
Procedure
Part I: Features of Sails
Classroom - 20 minutes
1.Place the word “sail” on the board. Access Prior Knowledge: Ask students, “Have you ever
seen a sail before, what are they used for?” and have a student draw one on the board. Ask
students, “What are some of the features of sails? When do you see sails?” Originally, sails
were rectangular in shape in order to use the wind to “push” boats forward. Sailors used the
trade winds to leave from port and to eventually sail home again. Show students an image
of an early sailing vessel with rectangular sails.
2.Ask students, “What are some limitations of only using the wind to push your boat,
downwind sailing?”
3.Ask students, “What shape are most of the sails we use at the Sailing Center? (triangular)
Today we are going to calculate the area and perimeter of a few of our sails? What are some
of the reasons we may want to calculate area of our sails? Generate student response: order
new sails, to calculate the area of our sails to compare sail area to boat speed, or to identify
situations in which sailors would benefit from reducing sail area. Why do certain sized sails
go on certain boats?”
Part II: Measuring Surface Area of Sails
Outdoor Classroom - 40 minutes
Note: The main sails are not perfect right triangles, and kids may notice this. If they do, explain that you
can still use right triangles to measure the existing sail area on the leech.
1.Tell students, “Today we are going to learn more
about our sails. We will calculate the area of the
main sail and jib sail and the main sail of a laser
or other sails.” (Use sails that are easy to move
and measure.) This is one way that we can use
math in other parts of our life.
2.Roll out a sail and review the parts of a sail with
the class. Relate the parts of a sail to your body,
head at the top, foot at the bottom, then luff,
leech, tack, and clew.
3.Ask students, “How do we measure the perimeter
and area of a sail?” After students respond, put
the formula for Sail area on the board. Area of
a triangle = ½ Base (foot) * Height (luff.) Show
students a rectangle is made of 2 triangles.
Sail Area and Perimeter
½ (10 * 5) =
½ ( 50 ) =
25 square feet = Area of the triangle
1.Measurement Review: Tell students, “Today we are going to measure to the nearest inch.” ≥
½ round up to the nearest inch < ½ round down. Show students how a tape measure works.
Remind them to slowly walk the end in and not to let it snap. The ends are sharp and you
could get cut or smash your fingers.
2.Draw a triangle on the board and ask two students to help you find the perimeter and area of
the triangle. Ask one student to be the recorder: taking down the measurements and the other
to hold the end of the tape measurer. You as the instructor will read the measurements of the
base and height of the triangle. Have the rest of the class
practice rounding your measurements to the nearest inch.
3.Split class into groups of three; a recorder, measuring
tape reader, and measuring tape holder. Ask students to
measure the sail area of a main sail and jib sail, and one
design sail.
4.Once students have measured and calculated the sail area
of all three sails ask students to return to their individual
clipboards and transfer their measurements. Next, they
should calculate the sail perimeter.
5.From the data collected ask students to compare the sail
area and perimeter. How does sail area impact our sailing?
Module 3
Part III: Sail Area on the Water
On the Water - 120 minutes
Note: This Part has two options.
Option 1: Rig two dinghies, one with a reduced area sail (RAD) and one with a full size main.
Option 2: Rig two keel boats reef one of the main sails.
1.While rigging review the parts of the sail (leech, luff, head, and foot) with the students.
Ask students to predict how the different size sails will affect the boat’s speed?
2. Discuss proper sail trim for up and downwind sailing.
3.Once on the water have boats 1 and 2 sail a windward leeward course. Both boats will start
at the same time. This visual should show students that a boat with less sail area is slower
and a boat with more sail area is faster.
4.While sailing students should help trim sails and possibly help skipper the boats. Once
back on shore have students calculate the difference in sail area between the boats. As a
challenge calculate the boat speed versus sail area.
5.After students have measured and calculated the difference in sail area ask them if there
is ever a benefit to having less sail area.
6.Have students make a connection to racing or cruising. For racers, in heavy winds you can
not reef a 420 sail, but you can flatten the sail by tightening the vang and the outhaul which
reduces the sail area. For cruisers, you can reef the main sail and the jib to depower your
sails and still maintain control of the boat in heavy winds.
Images: Reefed Main by spinnaker–sailing.com
Part IV: Pythagorean’s Theorem
Classroom/Docks - 40 minutes
1.Now that we have calculated the sail area of the sails we have, I have another challenge
for you. Pass out Student Sheet 2.
2.US Sailing is designing a new boat. The new boat will need a sail. The sail will need to
be 15 feet high and 8 feet long. Find the length of the hypotenuse using Pythagorean’s
Theorem a² + b²= c² Design and calculate the sail dimensions for the new design.
(ANSWER: The hypotenuse is 17)
3.Take some time to review Pythagorean’s Theorem and show students how to solve a
sample problem. Leg a=2 Leg b=3
2²+3² =c²
4 + 6 = c²
10 = c²
√10 = c
3.16 =c
Sail Area and Perimeter
4.Using Student Sheet 3, explain to the students, their task is to design a main sail and a
jib sail for a new sail boat. Please note: There are not any specific requirement for the
dimensions of the boat. Using Pythagorean’s Theorem, calculate the length of the foot,
luff, and leech of the main and jib sails. Once you have the calculations for the production
team at North Sails, please provide a rough sketch of the sails for the new boat.
5.When your design is complete please add a short paragraph explaining the benefits of your
design and why US Sailing should use it.
Resources
How It’s Made: North Sail One Design- video of how sails are made.
(http://www.youtube.com/watch?v=7nE9q4L5hhM)
Math.com –area of a polygon (http://www.youtube.com/watch?v=7nE9q4L5hhM)
Sailing Secrets From Larry Leonard - Charleston Race Week –
Video about adjusting new sails to boats.
(http://www.youtube.com/watch?v=3G-PuxaBZVw)
Extension Activities
1.Have students research the evolution of sail shape throughout history. Ask students how
sailboats affected trade and commerce throughout history?
Module 3
Module 3: Student Sheet 1
Sail Area
Name: __________________________
Date: ________________________
Perimeter of a triangle = base + hypotenuse
Area of a right triangle = ½ (base * height)
Show all work.
Luff
Leech
Foot
Sail
Perimeter
Sail Area
Sail 1:
Sail 2:
Sail 3:
___________________
___________________
___________________
Sail Area and Perimeter
Sail Area
Name: _________________________________
Module 3: Student Sheet 2
Date: ____________________
Challenge: US Sailing is designing a new boat. The new boat will need a sail. The sail will
need to be 15 feet high and 8 feet long. Find the length of the hypotenuse using Pythagorean’s
Theorem a² + b²= c². Design and calculate the sail dimensions for the new design.
Module 3
Sail Area
Name: _________________________________
Module 3: Student Sheet 3
Date: ____________________
Challenge: US Sailing is working with North Sails to develop a new boat design with new sails.
Your task is to design a main sail and a jib sail for their new sail boat. Using Pythagorean’s
Theorem, calculate the length of the foot, luff, and leech of the main and jib sails. Once you have
the calculations for the production team at North Sails, please provide a rough sketch of the sails
for the new boat. When your design is complete please add a short paragraph explaining the
benefits of your design and why US Sailing should use it. Please note: There are not any specific
requirement for the dimensions of the boat.