Current Program

Topic: Bearing Triangulation


Teacher Resources:

Printable PDF Version of this Lesson Plan

Downloadable PPT of Lesson (33mb)


Click here to launch PowerPoint for Lesson 5

image from lesson 5 Primary Goal : Introduce students to the history of charts and maps and how they are used today

Topic: Bearing Triangulation

Primary Goal : Students will learn how to determine their location by triangulation.  They will accomplish this by taking bearings of surrounding objects.  This lesson will build on their work with the hand-bearing compass and demonstrate one of the primary uses of a compass.

Lesson Objectives :

· Understand the reasons why you would need to determine your location

· Understand how you would use a compass to take bearings of objects around you

· Learn how to transfer those bearings onto a chart using navigation tools

Lesson Outline :

I. Piloting

a. This is a great opportunity to give an overview of the 3 different types of navigation

i. Electronic Navigation – used inland but critical offshore

ii. Celestial Navigation – used primarily offshore

iii. Piloting – the use of landmarks, aids to navigation, soundings to navigate a boat while operating along the coast or near land

b. Chapman gives a great explanation of piloting as both a science and an art (Chapter 16)

i. Science – uses math principles based on centuries of observation, analysis, and study

ii. Art – interpretation of observations and other information require individual judgment and skill

c. In this lesson we first go over the math and science of triangulation, and then build skills through the practice of taking bearings to determine our location (introduce fix)

II. Triangulation

a. This is the process of pinpointing your location by taking bearings from 3 remote points

b. Each of these bearings are considered a Line of Position or “LOP”

c. What happens if you have only 1 LOP?

i. This means that your location could be anywhere along this line

d. What about 2 LOPs?

i. This is more precise because it tells you where your location might be along your first LOP

e. In order to get an accurate fix you should get 3 LOPs which should create a triangle

i. This triangulation tells you that your location is somewhere within the triangle

III. Triangulation Quality & Reliability

a. After plotting your 3 bearings (or LOPs), what if your triangle is very big?

i. This is unreliable, as it means you could be anywhere within the triangle

ii. You must take another bearing

b. What if 2 of your bearings are from the same location?

i. This results in shallow angles and makes it difficult to achieve an accurate fix

ii. If possible you should use 3 objects at 60 degree angles

IV. Obtaining a fix

1. Using your magnetic compass, take a bearing from yourself to a landmark in your vicinity (ensure that this landmark is on your chart)

2. Find the landmark on your chart, and draw a line (LOP) from the landmark using the inverse of your bearing

a. This is done using the compass rose on your chart, and a slide ruler (make sure you use the inner circle for magnetic)

3. Find a second landmark and take a bearing using your magnetic compass

a. Plot on your chart and ensure that the 2 lines intersect

4. Find a third landmark and repeat the previous steps to determine your location

V. What type of landmarks or objects should you use?

a. Objects or landmarks that are affixed (lighthouse, water tower, bridge span, day markers)

b. Objects that are far away

i. The closer you are to an object, the harder it is to get an accurate bearing

c. Are buoys good for obtaining an LOP?

i. Not ideal because many buoys move with the current

ii. But, buoys can be used if they are your only option

Supplemental Resources :

YouTube Video by Nautica : https://www.youtube.com/watch?v=V8j00E89Bq4

Exercises/Activities :

Provide the students with charts and navigation tools to complete the 3 exercises at the end of the PPT.

Next Lesson


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Topic: Dead Reckoning


Teacher Resources:

Printable PDF Version of this Lesson Plan

Downloadable PPT of Lesson (3mb)


Click here to launch PowerPoint for Lesson 6

image from lesson 6 Primary Goal : Students will learn how to navigate by determining their expected future position based on current course and speed.  After learning how to properly take a fix using both GPS and visual bearings, this introduces the concept of time, speed, distance, and direction.

Lesson Objectives :

· Understand the concept of time, speed, and distance and how they interrelate

· Understand the reasons why you would need to predict your future position for safe navigation

· Review the different ways to obtain a fix: visually and using GPS

Lesson Outline :

I. Review the ways of obtaining a fix

1. Visual Fix

a. Take a bearing from yourself to a landmark and draw a line (LOP) from the landmark using the inverse of your bearing

b. Find a second landmark and take a bearing using your magnetic compass

i. Plot on your chart and ensure that the 2 lines intersect

c. Find a third landmark and repeat the previous steps to determine your location

2. GPS

a. Observe the latitude and longitude of your position on GPS

b. Using the borders of your chart, determine where the Latitude and Longitude intersect to obtain your GPS fix

II. History of Dead Reckoning

1. Dead reckoning has nothing to do with death, but could potentially lead to just that if you don’t use it properly

2. “Dead” is an abbreviation for “deduced”, and is thus the calculation used when determining your vessel’s whereabouts using your course and distance traveled

a. Columbus and most other sailors of his era used this method by estimating the course and distance they had sailed

III. Dead Reckoning

1. Process of navigation by advancing your position on a chart by using your last accurately determined fix

2. In order to accomplish this, you need 3 variables

a. Course – what direction you are sailing

b. Speed – how fast you are sailing

c. Time – how long you have been sailing

3. Using the time-distance forumla

a. This makes sense when you write out the units

Speed * Time = Distance

miles/hour * hour = miles

IV. Dead Reckoning in Practice

Supplemental Resources :

YouTube Video by Nautica : https://www.youtube.com/watch?v=V8j00E89Bq4

Exercises/Activities :

Provide the students with charts and navigation tools to complete the 3 exercises at the end of the PPT.

Next Lesson


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Topic: Global Positioning System (GPS)


Teacher Resources:

Printable PDF Version of this Lesson Plan

Downloadable PPT of Lesson 8 (7mb)

Downloadable PTT of Lesson 8 WITH FINAL EXAM REVIEW (14mb)


Click here to launch PowerPoint for Lesson 8

Click here to launch PowerPoint for Lesson 8 WITH FINAL EXAM REVIEW

image from lesson 8 Primary Goal : Students know how to use GPS, but will now learn how GPS actually works.  Understanding the history and development of GPS is critical to allowing the students to look at the concept as an innovator or entrepreneur.  Every day people are discovering ways to make our lives easier through GPS and this lesson aims to provide the students with a foundation behind the science.

Lesson Objectives :

· Learn the history of GPS and how it was developed

· Understand the science of how GPS receivers work and how they determine your location

Lesson Outline :

I. Overview

1. GPS is a satellite-based navigation system transmitting radio signals to users all over the world

i. Used in everything from ATMs, to dog collars, to farming equipment, to sailboats

2. Made up of a network of 24 operational satellites maintained by the US Air Force

i. They have been flying 31 satellites to ensure that there is always sufficient availability of signals

3. The satellites are arranged into six equally spaced orbital planes to ensure at least four satellites are available at any point on the earth

II. History of GPS

1. While there were many predecessors, GPS is a relatively new concept

2. Created and owned by the US Department of Defense, GPS was initially created in 1973 to be used by the military

3. The first GPS satellite system was launched from Vandenberg Air Force Base in 1978 and became fully operational in 1995

4. Reliable use by civilians began in 2000 when President Clinton directed that the “Selective Availability” feature be turned off

i. Prior to that, GPS use for civilians was inaccurate and could be off by as much as 100 yards

III. How GPS Works

1. GPS satellites orbit the earth twice a day in a very precise orbit and transmit signal information to the earth

i. Travel at speeds of up to 7,000 mph

ii. Powered by solar energy.  Interesting fact – they contain backup batteries in the event of a solar eclipse

2. GPS receivers (e.g. your cell phone) take this information and use trilateration to determine your exact location

i. Does this by taking the time a signal was transmitted by a satellite to the time it was received by your device

ii. The precise difference in time tells the GPS receiver how far away you are and sends an exact line of position

3. While 3 satellites can be used to determine your 2D location, 4 satellites are needed to determine your exact location (latitude, longitude, and altitude)

4. Once the GPS receiver knows your exact location, it can provide a great deal of information:

i. Speed, bearing/course, track, trip distance

Supplemental Resources :

Educational materials provided by www.GPS.gov: http://www.gps.gov/students/

Garmin GPS description: http://www8.garmin.com/aboutGPS/

NASA SciFiles Video: http://youtu.be/3zRlbboMvb0

DNews - How GPS Works: http://youtu.be/IoRQiNFzT0k

GPS Poster: http://www.gps.gov/multimedia/poster/poster-web.pdf

Exercises/Activities :

Allow the students to use hand-held GPS devices and give them some coordinates to determine their location.  Garmin makes a hand-held device which tells you which of the 24 satellites the device is using to determine location.

http://www.gps.gov/multimedia/tutorials/trilateration/

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Topic: Sailboat Design Project


Teacher Resources:

Printable PDF Version of this Lesson Plan

Printable PDF of the Rubric for the Sailboat Design Project

Downloadable PPT of Lesson (362kb)

Ratio Calculations Model (Excel workbook)


image from lesson 7 Click here to launch PowerPoint for Lesson 7

Primary Goal : As a final exercise for the class, student groups will create a basic sailboat design and prepare a report that identifies the specifications of the boat and the data used to calculate those specifications.

The report will also provide discussion as to the intended use of the vessel and why their design is optimally suited to that use, as well as a comparison to other boat types.


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Topic: How a Sailboat Works: Sails


Teacher Resources:

Printable PDF Version of this Lesson Plan

Downloadable PPT of Lesson (5.3mb)

Lesson 6 Handout - Sail Area Exercise (PDF)


image from lesson 6 Click here to launch PowerPoint for Lesson 6

Primary Goal: After this lesson, students should be able to determine the final piece of their sailboat design, the sails. After reviewing how sails generate speed for a sailboat, they will learn how to generate speed for their boat while also taking into account the many other factors affected by a boat’s sail area.

Lesson Objectives:

• Students will review how sails are able to generate lift, and thus speed

• Students will learn the importance of and how to calculate Sail Area

• Students will learn how to calculate Sail Area – Displacement ratio

Lesson Outline:

  1. Intro
    1. A sailboat uses her sails for propulsion by generating lift (upwind) or by blocking the wind and being pushed (downwind)
    2. Just like a sports car is interested in a high horsepower – weight ratio, sailboats use a similar type of measurement to determine the potential speed, or acceleration, of the sailboat
  2. Sail Area
    1. A sailboat’s propulsion comes from the wind on her sails and is proportional to the area of all the sailboat’s sails
    2. This is measured by calculating the area of a each of the sails and then simply adding those numbers together
      1. The measurement of sail area is calculated using square feet
    3. For more advanced courses you can discuss the measurements of E and P for the mainsail and I and J for the headsail
      1. It is also worth noting that actual sail measurements are more complicated because of the curvature shape of the sails
  3. Sail Area – Displacement Ratio
    1. In order to compare sailboats with one another, we use the Sail Area – Displacement ratio
    2. This shows how much power the sails generate compared to each pound of displacement
      1. Under this calculation, we are assuming that displacement is the sole limit of a boat’s speed due to the reasons discussed in previous lessons
      2. The calculation also involves dividing the displacement by 64. This is done because the weight of seawater is 64 lb/ cubic foot
    3. The higher the ratio indicates a high performance sailboat usually designed for racing
    4. Because of the large sail area, these boats are sometimes more difficult to handle and can become easily overpowered in high winds
      1. Low ratio – 8-13
      2. Medium ratio – 14-20
      3. High ratio – 21-40+

Supplemental Resources:

Sailboat-Cruising.com: Sail Area Calculations

Cruising World: How Sailboats Measure Up

Exercises/Activities:

The actual calculation for Sail Area–Displacement is quite complicated. This is a great opportunity to give students practice using a scientific calculator. Also, the excel model provided can make quick calculations easier and can be used to check student’s work.

Next Lesson


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