Chartwork & Pilotage Book 1 Student Handbook Preview by MI Student Resources

Fishing Master Program Chartwork & Pilotage Book 1 Student Handbook | Version 2.0

Except as provided by legislation governing the use of materials for educational purposes, no part of this publication may be reproduced, stored in a database or a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without prior written permission from the Marine Institute of Memorial University. Care has been taken to ensure that ownership of any copyright material contained in this publication is being traced and permission for its use obtained. The Marine institute would welcome any information that would correct any errors or omissions in assigning appropriate credit or reference in future editions.

Table of Contents

Table of Contents Chapter 1 Introduction to Navigation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 1-3 1.1

Types and Phases of Navigationø1-4

1.2 Modern Navigation Technique· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 1-7 1.3 Dangers Associated With Over-reliance on Electronic Navigation Tools· · · · · · · · · · · · · 1-13

Unit1: Self Test· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 1-14

Chapter 2 Latitude & Longitude· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-3 2.1 Introduction to the Terrestrial Sphere · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-5 2.2 Cardinal Direction· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-6 2.3 Properties of Circles · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-7 2.4 Properties of Spheres · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-12 2.5 Introduction to the Geographic Grid · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-14 2.6 Latitude · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-15 2.7 Longitude· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-29 2.8

Observed Position· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-39

Unit2: Self Test· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2-44

Chapter 3 The Nautical Chart· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-3 3.1

Introduction to the Nautical Chart· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-5

3.2 Carriage Requirements· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-6 3.3

Chart Projections· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-8

3.4 Chart Scale· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-13 3.5 Chart Datum · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-17 3.6 Chart Information · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-22

Unit3: Self Test· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-39

Chapter 4 Navigational Aids & Chart Symbols· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 4-3 4.1 Introduction to Navigation Aids and Chart Symbols · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 4-4 4.2 Floating Aids to Navigation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 4-6 4.3 Fixed Aids to Navigation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 4-15 4.4 Chart 1: Symbols, Abbreviations and Terms· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 4-19

Unit4: Self Test· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3-28

Fishing Master Program Chartwork & Pilotage Book 1

Chapter 5 Plotting Coordinates · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5-3 5.1

Care of Charts· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5-4

5.2

Tools for Chartwork· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5-5

5.3 Plotting Coordinates on a Nautical Chart · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5-7 5.4 Determining Coordinates on a Nautical Chart· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5-18 5.5 Measuring Distance on a Nautical Chart · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5-32

Chapter 6 Ship’s Heading· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 6-3 6.1 True Direction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 6-5 6.2 Magnetic Direction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 6-13 6.3 Compass Error – An Overview · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 6-16 6.4 Variation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 6-18 6.5 Deviation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 6-36 6.6

Calculating Compass Error· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 6-85

Chapter 7 Elementary Plotting: Courses and Bearings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 7-3 7.1 Ship’s Course · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 7-5 7.2 True Course between Positions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 7-8 7.3 Course Conversion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 7-16 7.4 Simultaneous Bearings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 7-21 7.5 Range and Bearing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 7-48 7.6

Transit Bearings· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 7-68

Chapter 8 The Dead Reckoning Plot· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8-3 8.1 Introduction to Dead Reckoning (DR)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8-5 8.2 The Rules of DR· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8-6 8.3 Time· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8-7 8.4 Distance/Speed/Time Calculations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8-12 8.5 Constructing the DR Plot · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8-19 8.6 Maintaining a Log · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8-26 8.7 Passage Planning· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8-28

Chapter 9 The Effects of Wind and Current on a Ship· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 9-3 9.1 Positioning Review· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 9-4 9.2 Wind and the Effects of Leeway· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 9-9 9.3 Current and the Effects of Set, Drift and Rate· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 9-20

Sample Exams· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · E-3 References · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · R-3 Deviation Card A· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · DC-3

Chapter 1 Introduction to Navigation

Chapter 1 | Introduction to Navigation

Introduction This unit is designed to develop your awareness that navigation is both an art and science. The evolution of navigation is briefly examined from the magnetic compass to Radar, GPS and Electronic Charting Systems. While the modern fishing skipper is surrounded by very powerful electronic navigational aids that are normally very reliable - it is without doubt they can fail! There are many instances of groundings and other mishaps that cite human failure or over reliance on electronic navigation aids as a root cause.

Overview 1.1 Types of Navigation 1.2 Modern Navigation Technique 1.3 Dangers Associated with Electronic Navigation

Learning Outcomes 1. Define navigation. 2. Differentiate between the various categories of navigation including dead reckoning, piloting, celestial navigation, radar and satellite. 3. Identify the various phases of navigation including inland waterway, harbour/harbour approach, coastal and ocean 4. Describe how the Global Positioning System (GPS) works. 5. Explain the importance of the Global Positioning System (GPS) to the modern navigator 6. Describe the operational functions of marine radar. 7. Explain the importance of Radar to the modern navigator 8. Explain the operational function of a magnetic compass 9. Explain why over-reliance on electronic navigation can be dangerous.

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Chapter 1 | Introduction to Navigation

1.1 Types and Phases of Navigation Lesson Introduction In this lesson we will define and explore the basic types and phases of navigation that have prevailed and evolved for hundreds of years.

Learning Outcomes At the end of this section the learner should be able to: 1. Define navigation. 2. Differentiate between the various types of navigation including dead reckoning, piloting, celestial navigation, radar and satellite. 3. Identify the various phases of navigation including inland waterway, harbour/harbour approach, coastal and ocean

Assigned Reading The following excerpt is used with permission from: Bowditch, N. The American Practical Navigator: An Epitome of Navigation. 1995 Edition (Online). Bethesda. National Imagery and Mapping Agency http://en.wikisource.org/wiki/The_American_Practical_Navigator/Chapter_1#100._The_Art_ And_Science_Of_Navigation

Lesson Notes Art and Science of Marine Navigation Marine navigation blends both science and art. A good navigator constantly thinks strategically, operationally, and tactically. He plans each voyage carefully. As it proceeds, he gathers navigational information from a variety of sources, evaluates this information, and determines his ship’s position. He then compares that position with his voyage plan, his operational commitments, and his predetermined “dead reckoning” position. A good navigator anticipates dangerous situations well before they arise, and always stays “ahead of the vessel.” He is ready for navigational emergencies at any time. He is increasingly a manager of a variety of resources-electronic, mechanical, and human. Navigation methods and techniques vary with the type of vessel, the conditions, and the navigator’s experience. The navigator uses the methods and techniques best suited to the vessel, its equipment, and conditions at hand.

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Chapter 1 | Introduction to Navigation

Some important elements of successful navigation cannot be acquired from any book or instructor. The science of navigation can be taught, but the art of navigation must be developed from experience.

Types of Navigation Methods of navigation have changed throughout history. New methods often enhance the mariner’s ability to complete his voyage safely and expeditiously, and make his job easier. One of the most important judgments the navigator must make involves choosing the best methods to use. Each method or type has advantages and disadvantages, while none is effective in all situations. Commonly recognized types of navigation are listed below. • Dead reckoning (DR) determines position by advancing a known position for courses and distances. A position so determined is called a dead reckoning (DR) position. It is generally accepted that only course and speed determine the DR position. Correcting the DR position for leeway, current effects, and steering error result in an estimated position (EP). • Piloting involves navigating in restricted waters with frequent or constant determination of position relative to nearby geographic and hydrographic features. • Celestial navigation involves reducing celestial measurements taken with a sextant to lines of position using calculators or computer programs, or by hand with almanacs and tables or using spherical trigonometry. • Radio navigation uses radio waves to determine position through a variety of electronic devices. • Radar navigation uses radar to determine the distance from or bearing of objects whose position is known. This process is separate from radar’s use in collision avoidance. • Satellite navigation uses radio signals from satellites for determining position. Electronic systems and integrated bridge concepts are driving navigation system planning. Integrated systems take inputs from various ship sensors, electronically and automatically chart the position, and provide control signals required to maintain a vessel on a preset course. The navigator becomes a system manager, choosing system presets, interpreting system output, and monitoring vessel response. In practice, a navigator synthesizes different methodologies into a single integrated system. He should never feel comfortable utilizing only one method when others are also available. Each method has advantages and disadvantages. The navigator must choose methods appropriate to each situation, and never rely completely on only one system. With the advent of automated position fixing and electronic charts, modern navigation is almost completely an electronic process. The mariner is constantly tempted to rely solely on electronic systems. But electronic navigation systems are always subject to failure, and the professional mariner must never forget that the safety of his ship and crew may depend on skills that differ little from those practiced generations ago. Proficiency in conventional piloting and celestial navigation remains essential.

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Chapter 1 | Introduction to Navigation

Phases of Navigation Four distinct phases define the navigation process. The mariner should choose the system mix that meets the accuracy requirements of each phase. • Inland Waterway Phase: Piloting in narrow canals, channels, rivers, and estuaries. • Harbor/Harbor Approach Phase: Navigating to a harbor entrance through bays and sounds, and negotiating harbor approach channels. • Coastal Phase: Navigating within 50 miles of the coast or inshore of the 200 meter depth contour. • Ocean Phase: Navigating outside the coastal area in the open sea. The navigator’s position accuracy requirements, his fix interval, and his systems requirements differ in each phase. The following table can be used as a general guide for selecting the proper system(s).

Inland

Harbor/Approach

Coastal

Ocean

Piloting

X X

Celestial Radio Radar

Satellite

Table 1.1 Navigator’s Position Accuracy System Requirements

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Chapter 1 | Introduction to Navigation

1.2 Modern Navigation Technique Introduction As a navigator, knowing your exact position at all times is paramount. Your location on the surface of the earth can be described in a variety of ways depending on the type of equipment found on the vessel, visibility, and the proximity of land. In this course, the position of the vessel will be obtained using one or more of the following navigation instruments: • GPS • Radar • Magnetic Compass These navigation tools are considered by most seasoned navigators as the most important of all the equipment found on the bridge of a vessel. In this course we will learn to use all three to determine the position of the vessel.

Learning Outcomes At the end of this section the learner should be able to: 1. Describe how the Global Positioning System (GPS) works. 2. Explain the importance of the Global Positioning System (GPS) to the modern navigator. 3. Describe the operational functions of marine radar. 4. Explain the importance of Radar to the modern navigator 5. Explain the operational function of a magnetic compass

Lesson Notes The following excerpt is used with permission from Garmin International: http://www8.garmin.com/aboutGPS/

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Chapter 1 | Introduction to Navigation

GPS What is GPS? The Global Positioning System (GPS) is a satellite-based navigation system made up of a network of 24 satellites placed into orbit by the U.S. Department of Defense. GPS was originally intended for military applications, but in the 1980s, the government made the system available for civilian use.

Figure 1.1 GPS

GPS works in any weather conditions, anywhere in the world, 24 hours a day. There are no subscription fees or setup charges to use GPS.

How GPS Works GPS satellites circle the earth twice a day in a very precise orbit and transmit signal information to earth. GPS receivers take this information and use triangulation to calculate the user’s exact location. Essentially, the GPS receiver compares the time a signal was transmitted by a satellite with the time it was received. The time difference tells the GPS receiver how far away the satellite is. Now, with distance measurements from a few more satellites, the receiver can determine the user’s position and display it on the unit’s electronic map.

Figure 1.2 GPS Receiver

A GPS receiver must be locked on to the signal of at least three satellites to calculate a 2D position (latitude and longitude) and track movement. With four or more satellites in view, the receiver can determine the user’s 3D position (latitude, longitude and altitude). Once the user’s position has been determined, the GPS unit can calculate other information, such as speed, bearing, track, trip distance, distance to destination, sunrise and sunset time and more. Today’s GPS receivers are extremely accurate, thanks to their parallel multi-channel design. Garmin’s 12 parallel channel receivers are quick to lock onto satellites when first turned on and they maintain strong locks, even in dense foliage or urban settings with tall buildings. Certain atmospheric factors and other sources of error can affect the accuracy of GPS receivers. Garmin® GPS receivers are accurate to within 15 meters on average.

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Chapter 1 | Introduction to Navigation

Figure 1.3 Wide Area Augmentation System

Newer Garmin GPS receivers with WAAS (Wide Area Augmentation System) capability can improve accuracy to less than three meters on average. No additional equipment or fees are required to take advantage of WAAS. Users can also get better accuracy with Differential GPS (DGPS), which corrects GPS signals to within an average of three to five meters. The U.S. Coast Guard operates the most common DGPS correction service. This system consists of a network of towers that receive GPS signals and transmit a corrected signal by beacon transmitters. In order to get the corrected signal, users must have a differential beacon receiver and beacon antenna in addition to their GPS.

The GPS satellite system The 24 satellites that make up the GPS space segment are orbiting the earth about 12,000 miles above us. They are constantly moving, making two complete orbits in less than 24 hours. These satellites are travelling at speeds of roughly 7,000 miles an hour. GPS satellites are powered by solar energy. They have backup batteries onboard to keep them running in the event of a solar eclipse, when there’s no solar power. Small rocket boosters on each satellite keep them flying in the correct path. Some interesting facts about the GPS satellites (also called NAVSTAR, the official U.S. Department of Defence name for GPS):

Figure 1.4 NAVSTAR

• The first GPS satellite was launched in 1978. • A full constellation of 24 satellites was achieved in 1994.

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Chapter 1 | Introduction to Navigation

• Each satellite is built to last about 10 years. Replacements are constantly being built and launched into orbit. • A GPS satellite weighs approximately 2,000 pounds and is about 17 feet across with the solar panels extended. • Transmitter power is only 50 watts or less.

Radar Radar is an acronym for: RADIO DETECTION AND RANGING Radar is an electronic navigation tool capable of detecting and measuring the distance (or range) and angle (or bearing) of objects 360° around the horizon of a vessel. Professional navigators know that radar is the most important of all electronic navigation aids – even more so than GPS! Radar operates by emitting a series of very short radio wave transmissions from the antenna called pulses. These pulses reflect off most objects and return to the antenna as an echo of the original pulse.

Figure 1.5 Radio Wave Transmissions

The radar measures the distance to the object by measuring the time taken for the pulses to go out and return back to the antenna. Similarily, the angle (or bearing) of the object from the vessel is determined by the position of the rotating antenna when the pulse is sent out and when it is received back.

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Chapter 1 | Introduction to Navigation

Figure 1.6 Radar Display

Magnetic Compass A magnetic compass is a navigational instrument for determining direction relative to the Earthâ&#x20AC;&#x2122;s magnetic poles. It consists of a magnetized pointer (usually marked on the North end) free to align itself with Earthâ&#x20AC;&#x2122;s magnetic field. A compass can be used to calculate heading and determine bearings of objects. A big advantage of the magnetic compass over the GPS and Radar is that it does not require electricity to operate; therefore, if all else fails the navigator can rely on the compass. Figure 1.7 Magnetic Compass

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Chapter 1 | Introduction to Navigation

As a navigator, knowing your exact position at all times is paramount. Your location on the surface of the earth can be described in a variety of ways depending on the type of equipment found on the vessel, visibility, and the proximity of land. For example, before GPS a navigator with only a magnetic compass and radar might describe its position as being 5 miles east of St. John’s harbour. However, since the GPS revolution the navigator can instantly supply you with the ‘co-ordinates’ or degrees, minutes and seconds of latitude and longitude anytime of the day – 24/7. In reality, GPS is generally very reliable; however, it is an electronic device which means it can fail. In order to be a competent, professional navigator you should be capable of determining your position with a magnetic compass only; if you have radar to assist the job will be that much easier.

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Chapter 1 | Introduction to Navigation

1.3 Dangers Associated With Over-reliance on Electronic Navigation Tools Learning Outcomes At the end of this section the learner should be able to: 1. Explain why over-reliance on electronic navigation can be dangerous.

Lesson Notes With the advent of automated position fixing and electronic charts, modern navigation is almost completely an electronic process. The mariner is constantly tempted to rely solely on electronic systems. This would be a mistake! Electronic navigation systems are always subject to failure and the professional mariner must never forget that the safety of his ship and crew may depend on skills that differ little from those practiced generations ago. While proficiency in conventional piloting and celestial navigation remains essential, this course focuses on GPS navigation and pilotage techniques as they would be applied on a nautical chart.

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Chapter 1 | Introduction to Navigation

Unit 1: Self-Test 1. What type of navigation technique are you using when you depart a port and determine your future position based on course, speed and time only?

A. celestial navigation

B. dead reckoning

C. piloting

D. radar navigation

2. According to Bowditch, how many distinct phases of navigation exist?

A. 2

B. 3 C. 4 D. 5 3. Radar is an acronym meaning RAdio Detection And Ranging.

A. True

B. False

4. Radar is the most important electronic navigation tool in the wheelhouse (or bridge) of a vessel because it can be used to detect other vessels and land masses in restricted visibility.

A. True

B. False

5. Distance to an object as measured by radar is also known as the range to that object. A. True

B. False

6. A radar does not have the ability to determine the relative position (bearing) of a detected target i.e. how many degrees the target is off your port or starboard bow.

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A. True

B. False

ÂŠ Marine Institute of Memorial University

Chapter 1 | Introduction to Navigation

7. During the early era of navigation, mariners could determine how far they were north of the equator (latitude) in the northern and part of southern hemisphere by using Polaris (North Star) A. True

B. False

8. In order to use ‘celestial navigation’ to determine the vessel’s position, mariners need a ? sextant and a

A. binoculars

B. good calculator

C. marine chronometer

D. speed log

9. GPS is an acronym for Global Positioning Satellites. A. True B. False 10. There are at least 24 operational GPS satellites orbiting the earth at all times. A. True

B. False

11. DGPS receivers are better than earlier GPS receivers because they improve accuracy from about 15 meters down to about 3-5 meters. A. True B. False 12. A WAAS enabled GPS is the most accurate GPS currently available and improved accuracy to less than 3 meters. A. True B. False 13. GPS has the ability to calculate a mariner’s position and provide latitude and longitude coordinates. These coordinates are never in error. A. True B. False

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Chapter 1 | Introduction to Navigation

14. Radar can be used to verify the GPS position in restricted visibility and you are within the range of land. A. True B. False 15. It is possible to find the latitude and longitude coordinates of the vessel by Radar only.

A. True

B. False

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Chapter 2 Latitude & Longitude

Chapter 2 | Latitude & Longitude

Unit Goals The goal of this chapter is to enable the student to demonstrate proficiency in using the geographic coordinate system of latitude and longitude to describe and determine position.

Overview 2.1 Introduction to the Terrestrial Sphere 2.2 Cardinal Direction 2.3 Properties of Circles 2.4 Properties of Spheres 2.5 Introduction to the Geographic Grid 2.6 Latitude 2.7 Longitude 2.8 The Observed Position

Learning Outcomes 1. Describe the geographic properties of the earth including the shape and direction of rotation. 2. Identify and define the axis of rotation, geographic poles. 3. Describe the four cardinal directions. 4. Identify various parts of a circle including the diameter, radius, circumference and arc of a circle. 5. Describe how â&#x20AC;&#x2DC;arc of a circleâ&#x20AC;&#x2122; is measured in degrees. 6. Explain that a circle is comprised of 360 degrees and that a degree is 1/360th of a circle. 7. Explain the concept of circumscribing an infinite number of circles at the surface of a sphere. 8. Define great circle and small circle. 9. Describe the attributes of great and small circles. 10. Describe the basis for the geographic grid and how it is composed of intersecting great and small circles. 11. Define latitude and longitude. 12. Explain the relationship the poles, equator and latitude

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Chapter 2 | Latitude & Longitude

13. Define nautical mile. 14. Explain the relationship between degrees of latitude and the nautical mile. 15. Describe how a degree can be subdivided into minutes and seconds. 16. Explain how practical chartwork describes latitude in degree, minutes and tenths of minutes. 17. Demonstrate proficiency converting seconds of latitude to tenths of minutes. 18. Identify and describe a latitude coordinate on a GPS display screen. 19. Define longitude, meridian and prime meridian. 20. Explain why longitude measures to 180Â° East or West. 21. Identify and define the International Date Line (IDL) on a globe. 22. Describe how a degree of longitude can be subdivided into minutes and seconds. 23. Identify longitude coordinates on a GPS display screen. 24. Explain the relationship between the earthâ&#x20AC;&#x2122;s rotation and time zones. 25. Define observed position and fix. 26. State the correct procedure for notating an observed position on a nautical chart.

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Chapter 2 | Latitude & Longitude

2.1 Introduction to the Terrestrial Sphere Lesson Introduction In this lesson we will identify general characteristics of the earth as it rotates on its axis and revolves around the sun.

Learning Outcomes 1. Describe the geographic properties of the earth including the shape and direction of rotation. 2. Identify and define the axis of rotation, geographic.

Assigned Reading Small Craft Piloting & Coastal Navigation by Saunders: Pg. 36 and Figure 26.

Lesson Notes For the purposes of this course the terrestrial sphere, our Earth, is a sphere. As viewed from the Pole Star (Polaris), at the North Pole, the Earth rotates in the counter-clockwise direction. For our purposes, the earth makes one complete rotation in 24 hours on its Axis of Rotation. The axis of rotation marks the exact location of the Geographic North and South Poles which are also known as the True North and South Poles.

Figure 2.1 Axis of Rotation

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Chapter 2 | Latitude & Longitude

2.2. Cardinal Direction Lesson Introduction In this lesson we will identify cardinal direction.

Learning Outcomes 1. Describe the four cardinal directions.

Lesson Notes Rotation of the earth gives rise to the 4 Cardinal directions: East – corresponds to the direction of earth’s rotation. All other directions are relative to East. West – It is the reciprocal (or opposite) of East. North – It is the direction 90° to the left of an observer facing east. It is in the direction of the North geographic pole South – It is the direction 90° to the right of the same observer. It is in the direction of the South geographic pole

Figure 2.2 Four Cardinal Directions

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Chapter 2 | Latitude & Longitude

2.3 Properties of Circles Lesson Introduction In this lesson we examine the various properties and characteristics of a circle (especially angles). Circles are important to navigation because distance along the circumference of a circle can be measured in by angles in degree units – which are the fundamental units of measurement in navigation.

Learning Outcomes 1. Identify various parts of a circle including the diameter, radius, circumference and arc of a circle. 2. Describe how ‘arc of a circle’ is measured in degrees. 3. Explain that a circle is comprised of 360 degrees and that a degree is 1/360th of a circle.

Lesson Notes Circle Components Since the Earth is a sphere and the circumference of a sphere circumscribes a circle we must examine some properties of circles. A circle is the set of all points equidistant from a fixed point center point (or center) of the circle. Circumference (c): The length around the outside of a circle. Diameter (d): A straight line segment passing through the center of a circle, and whose endpoints are on the circumference of the circle. Radius(r): A straight line joining the center of the circle to any point on its circumference. Figure 2.3 Circle components

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Chapter 2 | Latitude & Longitude

Measuring Circle Circumference Arc of a circle is a section of the circumference of the circle, lying between two points on the same circle (L). A useful way to determine the length of an arc in a circle is to plot two lines from the arc’s endpoints to the center of the circle, then measure the angle where the two lines meet the center. Angles are measured in degrees, denoted by (°) – the degree symbol. A complete circle has 360° 1° represents 1⁄360 of a circle. Figure 2.4 Arc of a Circle

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Chapter 2 | Latitude & Longitude

Exercise 2.1: Degrees of Arc and Direction 1. How many degrees of arc are represented by the green shaded portion of the circle? A. 90° B. 45° 2. How many degrees of arc are represented by the green shaded portion of the circle? A. 30° B. 60° 3. How many degrees of arc are represented by the green shaded portion of the circle? A. 10° B. 45° 4. How many degrees of arc are represented by the green shaded portion of the circle? A. 45° B. 90° 5. How many degrees of arc are represented by the green shaded portion of the circle? A. 150° B. 180° 6. Which direction is to the right of an observer who is facing the North Pole? A. North B. West C. South D. East

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Chapter 2 | Latitude & Longitude

7. Which direction is to the right of an observer who is facing the South Pole? A. North B. West C. South D. East 8. Which direction is to the right of an observer who is facing West? A. North B. West C. South D. East 9. Which direction is to the right of an observer who is facing East? A. North B. West C. South D. East 10. Which direction is to the left of an observer who is facing the South Pole? A. North B. West C. South D. East

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Chapter 2 | Latitude & Longitude

Exercise 2.2: Calculate Degrees of Arc Example: How many degrees of arc in 1/10 of a circle?

Answer:

No.

Fraction of a Circle

1/2

1/4

1/6

1/8

1/12

Degrees of Arc

6. Plot the degrees of arc from above using a protractor.

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Chapter 2 | Latitude & Longitude

2.4 Properties of Spheres Lesson Introduction In this lesson we will examine the relationship between circles and how they can circumscribe the surface of a sphere.

Learning Outcomes 1. Explain the concept of circumscribing an infinite number of circles at the surface of a sphere. 2. Define great circle and small circle. 3. Describe the attributes of great and small circles.

Lesson Notes Degrees So far, we have established that a degree (°) measures distance between two points on the circumference of a circle. We also know that the circumference of the earth is a circle; therefore a degree must be a measurement of distance on the earth – and it is! It just depends on which circles on the surface we are measuring. Let’s investigate this idea. If you took a ball and a marker you could start at any random point on the ball and begin to drawing a line in any direction. If this line went all the way around the entire surface of the ball to re-connect with its own starting point, we could say that you have circumscribed a circle on the surface of the ball.

Figure 2.5 Circumference

Building on the example above, we can deduct that there are an infinite number of circles that can be circumscribed on the surface of a sphere. The next step is to categorize these circles at the surface of the earth so that they can be used in a practical manner.

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Chapter 2 | Latitude & Longitude

Great and Small Circles All circles found at the surface of a sphere fall in one of two categories; Great or Small Circles.

A great circle (G in the diagram) has the following attributes: It divides the surface of a sphere in two equal parts. It is the largest circle that fits on the sphere. It has the same center C as the sphere that it lies on. The shortest route between two points, measured across the sphere, is part of a great circle.

Figure 2.6 Great and Small Circles

A small circle (B), on the other hand, is not the largest circle that can fit on a sphere and its center does not coincide with the center of the sphere. Specific order imposed on strategic great and small circles give rise to the geographic grid.

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Chapter 2 | Latitude & Longitude

2.5 Introduction to the Geographic Grid Lesson Introduction This lesson contains an essential building block of navigation. Here we examine how small and great circles are aligned to form the geographic grid.

Learning Outcomes 1. Describe the basis for the geographic grid and how it is composed of intersecting great and small circles. 2. Define latitude and longitude.

Assigned Readings Small Craft Piloting & Coastal Navigation by Saunders: Pg. 72, 73, & 74. Closely review Figures 62, 63, and 64.

Lesson Notes After centuries of ambiguity, cartographers eventually developed a standardized grid to accurately measure exact positions on the surface of the earth. Interestingly, this grid is constructed of great and small circles which intersect at right (90°) angles at the surface. Measurement on the grid is denoted by: i) Latitude – how many degrees of arc North or South of the Equator and ii) Longitude – how many degrees of arc East or West of the Prime Meridian

Figure 2.7 Latitude & Longitude

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Chapter 2 | Latitude & Longitude

2.6 Latitude Lesson Introduction This lesson explains the relationship between parallels of latitude, the equator and poles. It also describes the relationship between the minutes of latitude and the nautical mile.

Learning Outcomes

Explain the relationship the poles, equator and latitude

Define nautical mile.

Explain the relationship between degrees of latitude and the nautical mile.

Describe how a degree can be subdivided into minutes and seconds.

Explain how practical chartwork describes latitude in degree, minutes and tenths of minutes.

Demonstrate proficiency converting seconds of latitude to tenths of minutes.

Identify and describe a latitude coordinate on a GPS display screen.

Lesson Notes Latitude To define latitude cartographers had to agree on reference points – for this they chose the Equator and the North and South Geographic Poles. Geographic North Pole is the northern point at which the Earth’s axis of rotation meets the surface. It is also defined as True North From the Equator which is referenced at 0°, the distance to the North Pole is ¼ of a circle or (360°)/4=90° North Pole is located at Latitude 90° North South Pole is the southern point at which the Earth’s axis of rotation meets the surface

Fishing Master Program Chartwork & Pilotage Book 1

Figure 2.8 Geographic Poles

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Chapter 2 | Latitude & Longitude

South Pole is located at Latitude 90° South and is known as True South The North and South poles are separated by 180° Therefore, latitude measures how many degrees of arc north or south of the equator a position is located. Lines of latitude are represented on a map or globe by a series of east-west running lines that are parallel the equator. Hence, they are referred to as parallels. Note: The Equator is referenced at 0°, which is halfway between the poles. Except for the equator, which is a great circle, parallels of latitude are small circles The suffix “N” or “S” must appear after the number given for the latitude since the numbering is from 0° to 90° in each hemisphere.

Latitude and Distance

Figure 2.9 Parallels of Latitude

Suppose you are aboard your vessel, at the Equator. You travel from 0° to 1°North in a straight line, heading toward the North Pole. How far did you go? You know you travelled 1°North…but what does that mean in the real world?? It means that you travelled a linear distance of 69 statute miles, or 60 nautical miles A degree of latitude is equal to 60 nautical miles of linear distance. The nautical mile is the primary unit of distance measurement at sea. It measures 1852 meters.

Figure 2.10 Latitude & Distance

ONE DEGREE (°) OF LATITUDE 1° Latitude

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= =

60 NAUTICAL MILES (‘) 60’

Chapter 2 | Latitude & Longitude

Exercise 2.3: Calculate Degrees and Nautical Miles Example 1: How many degrees from 10°N to 23°N? How many nautical miles? Answer:

Example 1: How many degrees from 5°N to 5°N? How many nautical miles? Answer: Note: When the names of latitude are different, they are added!!

Example 1: How many degrees from 45°S to 45.5°S? How many nautical miles? Answer:

1. How many degrees from the Equator to the North Pole? A. 60° B. 70° C. 80° D. 90°

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Chapter 2 | Latitude & Longitude

2. How many nautical miles from the Equator to the North Pole? A. 5400’ B. 4800’ C. 4200’ D. 3600’ 3. How many degrees from the North Pole to the South Pole? A. 90° B. 135° C. 180° D. 200° 4. How many nautical miles from the North Pole to the South Pole? A. 9800’ B. 10 800’ C. 11 000’ D. 12 000’ 5. How many degrees halfway between the equator and the North Pole? A. 45° B. 47.5° C. 50° D. 51.5° 6. How many nautical miles halfway between the equator and the North Pole? A. 3090’ B. 4500’ C. 2850’ D. 2700’

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Chapter 2 | Latitude & Longitude

7. How many degrees of latitude are there between 1°N and 3°N? A. 1° B. 2° C. 3° D. 4° 8. How many nautical miles are there between 1°N and 3°N? A. 60’ B. 80’ C. 100’ D. 120’ 9. How many degrees of latitude are there between 44°N and 50.5°N? A. 6° B. 6.5° C. 94.5° D. 100° 10. How many nautical miles are there between 44°N and 50.5°N? A. 1000’ B. 755’ C. 410 D. 390’ 11. How many degrees are there between 1°N and 1°S? A. 0° B. 1° C. 2° D. None of the above

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Chapter 2 | Latitude & Longitude

12. How many nautical are there between 1°N and 1°S? A. 0’ B. 60’ C. 120’ D. None of the above 13. How many degrees are there between 3.5°N and 3.5°S? A. 7° B. 5° C. 1° D. 0° 14. How many nautical miles are there between 3.5°N and 3.5°S? A. 0’ B. 60’ C. 300’ D. 420’ 15. How many degrees are there between 5°S and 13°S? A. 18° B. 8° C. 0° D. None of the above 16. How many nautical miles are there between 5°S and 13°S? A. 0’ B. 1080’ C. 480’ D. None of the above.

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Chapter 2 | Latitude & Longitude

17. How many nautical miles are there between 0.5°S and 0.5°N? A. 60’ B. 100’ C. 120’ D. None of the above 18. How many nautical miles are there between 89°S and 90°S? A. 60’ B. 100’ C. 120’ D. None of the above 19. How many nautical miles are there between 50°N and 50°S? A. 100’ B. 1000’ C. 5000’ D. 6000’ 20. How many nautical miles are there between 3 °S and 2°N? A. 240’ B. 300’ C. 360’ D. 420’

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Chapter 2 | Latitude & Longitude

Subdividing Latitude We know that 1° of latitude equals 60 nautical miles of linear distance. What happens when we want to describe the positions that are less than 60nm apart? For example, what if two ships are only 30 miles apart? Well, we can use decimals of a degree...that is 30nm/ 60nm = 0.5° However, for practicality, decimals of degrees are not used, rather degrees are further divided into minutes of arc (similar to an hour divided into 60 minutes of time). 1 degree of arc = 60 minutes of arc A minute of arc is represented by an apostrophe: ’ 1° = 60’ Now let’s think about linear distance again; 1° = 60 nautical miles 1° = 60 minutes of arc

Therefore; 1 minute of arc = 1 nautical mile One minute of latitude is equal to one nautical mile 1’ latitude= 1 nautical mile A latitude reading to the minute level, then, would be written like this: N 47°37’ (St. John’s Airport) If you really need even more precision (you need to find a single string of crab gear), you can break a minute of arc down, just as with time, into seconds of arc. One minute of arc contains 60 seconds (as with time). Put another way, one second of arc is 1/3600th of a degree, and that means there are 3600 seconds in a degree (kind of like there are 3600 seconds in an hour). Seconds of arc, like seconds of time, are represented by a quotation mark: “ One second of arc is about 30 meters or 100 ft. A latitude reading including seconds would be: N 47° 37’ 07” (St. John’s Airport). A latitude reading to the minute level, then, would be written like this: N 47°37’ (St. John’s Airport)

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Chapter 2 | Latitude & Longitude

If you really need even more precision (you need to find a single string of crab gear), you can break a minute of arc down, just as with time, into seconds of arc. One minute of arc contains 60 seconds (as with time). Put another way, one second of arc is 1/3600th of a degree, and that means there are 3600 seconds in a degree (kind of like there are 3600 seconds in an hour). Seconds of arc, like seconds of time, are represented by a quotation mark: “ One second of arc is about 30 meters or 100 ft. A latitude reading including seconds would be: N 47° 37’ 07” (St. John’s Airport).

Degrees, Minutes and Tenths of Minutes The structure of the nautical charts that we use in this course (and most chartwork courses) is such that latitude and longitude are represented at the sides of the charts, along the border. We will examine this much closer in Chapter 3, but suffice it to say the scale is represented so that seconds are not used. The chart scale shows latitude (and longitude) as degrees, minutes, and tenths of minutes – no seconds! This is written as: N 47° 37.1’ (St. John’s Airport). This also corresponds to the typical GPS display screen found on most fishing vessels. To convert seconds to minutes simply divide the seconds by 60.

Example: Convert latitude N 47° 37’ 07” (St. John’s Airport) to degrees, minutes and tenths of minutes. Step 1: Take seconds (“) from the Coordinate 47° 37’ 07”

In this case - 7

Step 2: Divide seconds by 60

7÷60=0.11 or 0.1 (round to one decimal place

Step 3: Add tenths of minutes to minutes of the coordinate

37’ + 0.1’=37.1’

Step 4: Present answer

N47˚37.1’

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Chapter 2 | Latitude & Longitude

Exercise 2.4: Convert seconds to minutes in the following coordinates. Degrees, Minutes Seconds

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N 44° 24' 12"

S 10° 59' 48"

N 60° 30' 30"

S 10° 10' 18"

N 01° 01' 47"

N 48° 29' 17"

S 09° 19' 19"

N 59° 59' 50"

S 00° 01' 10"

10.

N 01° 10' 19"

Degrees, Minutes

Chapter 2 | Latitude & Longitude

Difference of Latitude (D.Lat.) The distance, in nautical miles, separating two distinct parallels of latitude can easily be found by adding or subtracting one coordinate from the other. They are added if they are of different names i.e. one South and one North or subtracted if both are of the same name. The result is known as d.lat. D.Lat. is to be reduced to minutes by multiplying the number of degrees by 60 and adding odd minutes, if any. When finding d.lat, the most important thing to remember is that both coordinates must be written in the same format. In practical chartwork this will most often be degrees and minutes only (no seconds) i.e. 44° 24.70'. Also remember to borrow 1° = 60' when necessary to enable the calculation.

Example: Calculate d.lat between the following parallels of latitude. Lat A: N 46° 59.2' Lat B: N 47° 38.4' Step 1: Set up the equation for subtraction by placing the greatest latitude above the smaller

N 47° 38.4' -N 46° 59.2'

Step 2: Subtract the minutes, then the degrees (if necessary). First, borrow 60’ from the 47°. Next, add the borrowed 60’ to the 38.4’, which gives 46° 98.4’. Finally, make the subtraction.

46° 98.4’ N 47° 38.4' -N 46° 59.2' 0° 39.2’

Step 3: Add tenths of minutes to minutes of the coordinate

39.2’ (miles or minutes... they mean the same thing!)

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Chapter 2 | Latitude & Longitude

Exercise 2.5: Calculate D.Lat Calculate d.lat from the following sets of parallels. Degrees, Minutes Seconds

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Lat A: N 44° 24.2' Lat B: N 44° 21.2'

Lat A: S 10° 59.8' Lat B: S 10° 47.5'

Lat A: N 60° 30.5' Lat B: N 59° 41.6’

Lat A: S 10° 10.3' Lat B: S 09° 23.5'

Lat A: N 01° 01.8' Lat B: N 01° 01.2'

Lat A: N 48° 29.3' Lat B: N 48° 27.9'

Lat A: N 59° 59.8' Lat B: N 58° 59.9'

Lat A: S 00° 01.1' Lat B: N 00° 01.1'

10.

Lat A: N 00° 10.3' Lat B: S 00° 07.6’

Degrees, Minutes

Chapter 2 | Latitude & Longitude

Latitude Coordinate and GPS When considering the coordinates for a specific position as displayed on a GPS receiver, the latitude is always on top. North or South of the Equator is indicated with a capital N or S. Note: There are no seconds displayed; just degrees, minutes and decimals of minutes (three places after the decimal or thousandths) Practical chartwork uses degrees, minutes and decimals of minutes which is also how most Figure 2.11 Typical GPS receiver display fishermen also operate their GPS receivers. Note: Distance on nautical charts is measured using the latitude (vertical) scale.

Example: How many nautical miles is N 48° 34.497’ north of the equator? Step 1: Identify the conversion factors:

1° = 60' 1' = 1 nautical mile

Step 2: Convert degrees to minutes and miles:

48° x 60'= 2880' = 2880 nautical miles

Step 3: Convert remaining minutes to miles:

34.497' x 1=34.497 or 34.5' (round to one decimal place)

Step 4: Add all miles for total:

2880' + 34.5' = 2914.5'

Step 5: Present Answer:

48° 34.5' = a parallel of latitude that is 2914.5 nautical miles north of the equator.

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Chapter 2 | Latitude & Longitude

Exercise 2.6: Calculate Distance from the Equator Calculate the distance from the equator in both minutes and nautical miles. Latitude

Minutes

Nautical Miles

1. N 01° 30.0' 2. N 05° 05.0' 3. N 33° 33.3' 4. N 47° 37.1' 5. N 50° 50.5' 6. S 03° 19.4' 7. S 15° 15.9' 8. S 38° 59.9' 9. S 87° 18.2' 10. S 90° 00.0'

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Chapter 2 | Latitude & Longitude

2.7 Longitude Lesson Introduction This lesson introduces longitude – defining the reference points, explaining the importance of the 180° meridian and how linear distance between meridians is not constant and that degrees of longitude DO NOT equate to 60 nautical miles.

Learning Outcomes 1. Define longitude, meridian and prime meridian. 2. Explain why longitude measures to 180° East or West. 3. Identify and define the International Date Line (IDL) on a globe. 4. Describe how a degree of longitude can be subdivided into minutes and seconds. 5. Identify longitude coordinates on a GPS display screen. 6. Explain the relationship between the earth’s rotation and time zones.

Assigned Reading Small Craft Piloting & Coastal Navigation by Saunders: Pgs. 36, 37, 38, 70 & 72. Figures 27, 28, 59, 60, 61, 62, 63 & 64

Lesson Notes Longitude is east or west degree measurement as referenced from the Prime Meridian (0°).

Prime Meridian After centuries of debate, the Prime Meridian was eventually established as passing through the Royal Observatory in Greenwich, England. The prime meridian is the reference meridian for longitude and as such it has a value of 0°. The Prime Meridian is half a Great Circle – the other half, at 180°, is the International Date Line (IDL).

Fishing Master Program Chartwork & Pilotage Book 1

Figure 2.12 Prime Meridian

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Chapter 2 | Latitude & Longitude

Longitude is measured in degrees from 0° to 180° east or west of the Prime Meridian. This is easiest to understand when looking down from the North Pole. From this perspective it is easy to see the angle that is formed between the Prime Meridian and the line of longitude. Because lines of longitude are measured east or west of the Prime Meridian it is important to place ‘E’ or ‘W’ after the coordinate. Halfway around the globe from the Prime Meridian is 180°. This line of longitude (along with the prime Meridian) does not have an ‘E’ or ‘W’ designation as 180° defines a single line. This is not the case for 150°or any other line of longitude. Longitude measurements can only go from 0° to 180°

Figure 2.13 Longitude

Longitude and Linear Distance Lines of longitude, or meridians, run north and south, cut the Equator at right angles (90°) and converge at the poles. Because of this convergence the distance from one line of longitude to the next is not constant. As one moves towards the poles from the equator the east-west distance between lines decreases. While a degree of longitude does contain 60 minutes of arc, these minutes DO NOT equal a nautical mile (except at the equator).

Figure 2.14 Meridians

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Chapter 7 | Elementary Plotting: Courses and Bearings

Alternatively, if (on an exam) you are given values for variation and deviation you can calculate compass error and apply very quickly: True Course

°T

Compass Error

°E or W (error east/west, compass least/best)

Compass Course

°C

Compass to True

When applying separate corrections to convert a compass course to a true, deviation is always applied first and variation applied second as follows: Compass Course

°C

Deviation (for the Compass Course)

°E or W (deviation east/west, compass least/best)

Magnetic Course

°M

Variation

°E or W (variation east/west, magnetic least/best)

True Course

°T

The mnemonic you can use to help remember the overall order of operation: Can Dead Men Vote Twice

Alternatively, if (on an exam) you are given values for variation and deviation you can calculate compass error and apply very quickly: Compass Course

°C

Compass Error

°E or W (error east/west, compass least/best)

True Course

°T

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Exercise 7.3: Plotting the True Course to Determine Compass Course Chart 3624 1. At 1300hrs a vessel observed her position to be N50º 52.3' W128º18.2'. At 1500hrs her position was observed to be N50º 43.6' W128º 40.5'. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 20°E. True Course: C/E:

Compass Course:

Distance:

2. At 1700hrs a vessel observed her position to be N50º 11.2' W128º 03.8'. At 1930hrs her position was observed to be N50º 21.4' W128º 31.7'. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 20°E. True Course: C/E:

Compass Course:

Distance:

3. At 0200hrs a vessel observed her position to be N50º 38.8' W128º 21.5'. At 0415hrs her position was observed to be N50º 22.9' W128º 15.6'. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 20°E. True Course: C/E:

Compass Course:

Distance:

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Chapter 7 | Elementary Plotting: Courses and Bearings

Chart 4025 4. At 0345hrs a vessel observed her position to be N50º 06.3' W 063º 21.5'. At 0552hrs her position was observed to be N49º 49.4' W062º 42.5’. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 20°W. True Course: C/E:

Compass Course:

Distance:

5. At 0637hrs a vessel observed her position to be N49º 43.4' W 060º 05.8'. At 1046 hrs her position was observed to be N48º 54.6' W 060º 36.4’. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 20°W. True Course: C/E:

Compass Course:

Distance:

6. At 0130 hrs a vessel observed her position to be N49º 01.3' W 061º 42.0'.At 1939 hrs her position was observed to be N49º 01.3' W 063º 21.4’. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 20°W. True Course: C/E:

Compass Course:

Distance:

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Chapter 7 | Elementary Plotting: Courses and Bearings

7. At 1529 hrs a vessel observed her position to be N49º 23.1' W 061º 55.0'.At 1913 hrs her position was observed to be N50º 08.7' W 061º 55.0’. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 18°W. True Course: C/E:

Compass Course:

Distance:

8. At 1608 hrs a vessel observed her position to be N50º 02.5' W 059º 52.7'.At 2031 hrs her position was observed to be N49º 56.7' W 061º 38.0’. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 19°W. True Course: C/E:

Compass Course:

Distance:

9. At 1919 hrs a vessel observed her position to be N49º 24' W 061º 45.5'. At 1913 hrs her position was observed to be N49º 53.1' W 060º 45.0’. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 17°W. True Course: C/E:

Compass Course:

Distance:

10. At 2101hrs a vessel observed her position to be N49º 20.2' W 061º 37'. At 2359 hrs her position was observed to be N49º 07.6' W 060º 48.4’. Find the true course, compass error, compass course and distance. Use Deviation Card A, Variation 13°W. True Course: C/E:

Compass Course:

Distance:

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Chapter 7 | Elementary Plotting: Courses and Bearings

7.4 Simultaneous Bearings Lesson Introduction This lesson examines how to find an accurate position (or fix) of the vessel without the use of a GPS. These fixes are determined by way of bearing lines plotted on the chart.

Learning Outcomes 1. Define position ‘fix’. 2. Define Lines of Position (LOP). 3. Explain how intersecting LOP’s yield position. 4. Define the various types of ‘bearings’ including true, compass, magnetic, and relative. 5. Define ‘angle of cut’ and the importance of bearing lines being separated on the horizon. 6. Describe methods for measuring bearings including the magnetic compass, azimuth ring, pelorus and radar. 7. Demonstrate proficiency plotting simultaneous bearing lines to determine the vessels position. 8. Define ‘cocked hat’. 9. Explain the relationship between a ’cocked hat’ and accuracy of obtained bearings.

Assigned Reading Small Craft Piloting & Coastal Navigation: Ch. 9; Pgs. 106 – 123; Figures 83 – 97

Lesson Notes According to Saunders (2009) a ‘fix’ is simply an accurate determination of the vessel’s location. A ‘fix’ can be found by the intersection of two or more Lines of Position (LOP). A LOP is basically a line on which the vessel is located and can be plotted on a chart. In most instances LOPs are bearing lines – and a bearing is simply the angular measurement between the point of reference used and the line of sight of the object. Note: In chartwork problems the word bearing can be stated in its present or past terms, for example, a problem can state ‘an object is bearing’ or ‘an object bears’ or ‘an object bore’.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Note that bearing lines can be obtained in a variety of ways: Visual bearing: this method involves the use of a set of sight vanes (pelorus) or situated atop of the compass for accuracy. Azimuth ring: sighting device similar to a pelorus used for sighting bearings. However, most often bearing lines will be obtained from the radar using the electronic bearing line (EBL) – this is generally faster and more accurate.

Types of Bearings

Figure 7.4 Azimuth Ring

For the most part, the points of reference used to measure bearings are similar to those used for ship’s heading as follows: 1. True Bearing: Angular measurement from the True North Pole and the line of sight to the object or target as viewed from the vessel.

Figure 7.5 True Bearing

If we were aboard the vessel in the above diagram, we would notice that the ship’s heading and course was 085°T. In unrestricted visibility, we would have a line of sight on Chance Island which is off the starboard bow. If a satellite compass, gyro compass or ‘stabilized’ radar was used to measure from the True North to our line of sight on Chance Island we would find the bearing to be 115°T.

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Chapter 7 | Elementary Plotting: Courses and Bearings

2. Compass Bearing: Angular measurement between the compass North and the line of sight to the object or target as viewed from the vessel.

Figure 7.6 Compass Bearing

This example is an exact replica of the one above. The physical position and heading of the vessel has not changed – neither has the line of sight on Chance Island. The only thing that has changed is the reference (or starting point) of the degree measurement. Instead of starting at True North, a magnetic compass measures from magnetic north yielding a different result when compared to True – of course this is a result of compass error. In this example the magnetic compass was used to determine ship’s heading as 106°C and the bearing to Chance Island to be 136°C. A mathematical comparison of the true and magnetic measurements would return the following results: Ship’s head compass: Ship’s head true: Compass error:

106°C

- 085°T 021°W

Chance Island compass bearing: Chance Island true bearing: Compass error:

136°C - 115°T 021°W

The mathematical example above proves that the only difference between true and compass bearings is compass error. Again, compass error depends on the ship’s head – because deviation changes with every change in ship’s head.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

3. Relative Bearing: While all bearings are in a sense relative (to the North Pole or magnetic north), what we generally refer to as relative bearings are those relative to the stem or heading marker of an ‘heads-up’ or ‘unstabilized’ radar display. For this type of bearing the angular measurement is made from the stem of the vessel or heading marker (which is considered to be 0°) to the line of sight to the object or target viewed from the vessel.

Figure 7.7 Relative Bearing

Again, in this example, nothing has changed from the previous two. However, the bearing is now stated as being 30° on the starboard bow or 30° green (bearings on the port side being red!) Naming bearings in this manner is a very common practice for mariners. The main concern here is the ability to first calculate ship’s head in true, and then apply the relative bearing (red or green) to obtain a true bearing that can be plotted on the chart. Ship’s head compass: 106°C Compass error:

021°W (error west, compass best)

Ship’s head true:

085°T

Chance Is. Relative bearing:

030° relative

Chance Is. True bearing:

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115°T

Chapter 7 | Elementary Plotting: Courses and Bearings

True Bearing – Stabilized Radar View In the diagram below we are looking at the same situation as in the previous three examples – but on a stabilized radar screen. A stabilized radar is one that uses a heading sensor input to maintain the locations of targets on the screen in specific orientations. In this example the radar is set in the North-Up mode. In this configuration the radar can distinguish true direction because of the gyro compass input. Notice how the land around the vessel has the same orientation as that of the chart in the examples above. In the upper right corner we can see that the COG (course over ground) is 085°T which corresponds to the direction of the heading marker (yellow line) on the screen.

Figure 7.8 Stabilized Radar View

The radar operator can set the electronic bearing line (EBL), which is the red-dashed line extending from us at the center to intersect with Chance Island on our starboard side. The highlighted box labeled ‘SET EBL1 115.0°’tells us that, in fact, the true bearing to Chance Island is 115°T. Note: Students will learn radar features and operation in the SEN-L course which is part of the FMIV curriculum. Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Simultaneous True Bearings As previously discussed, two or more intersecting LOPs will yield an accurate ‘fix’ of the vessel. This process is known as Position by Simultaneous Observation. In this section we learn to find the position of the vessel by using simultaneous bearing lines as LOPs. In the real world this process entails sighting two bearings at the same time, or nearly the same time. For improved accuracy, it is important when deciding which two objects to sight that the ‘angle of cut’ is as close to 90° as possible. The ‘angle of cut’ (see below) can be defined as the angle of measurement between the two bearing lines.

Figure 7.9 Position by Simultaneous Observation

In this example the ‘angle of cut’ can be calculated by subtraction as follows: 2nd Bearing:

200°T

1st Bearing:

115°T

Angle of cut:

085°

Note: The angle of cut should never drop below 30°.

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Chapter 7 | Elementary Plotting: Courses and Bearings

Example: Chart: 4855 At 0530hrs a fishing vessel on a course of 085°T observes Chance Island bearing 115°T. At the same time the North-West Point of Deer Island bears 200°T. What are the latitude and longitude co-ordinates of the vessel’s position?

Figure 7.10 Example - Plotting Bearing Lines

Solution: Note: The most important part of plotting bearing lines is to remember that they originate at the object being sighted (point of land, lighthouse, or buoy, etc.) and are drawn to extend out into the open ocean to where the vessel is located. All bearing lines must be plotted in True degrees.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Step 1: Since the bearings are already given in true degrees in this problem, no mathematical conversions are necessary. It’s just a matter of selecting a bearing to plot first; in this example we will plot the Chance Island bearing first. Chance Island bearing: 115°T

North-West corner of Deer Island bearing:

200°T

Step 2: Decide which compass rose to use – always choose the closest one!

Step 3: Line up the parallel ruler so that the fine black line on the top edge of the parallel ruler cuts through 115°T (the bearing of Chance Is.), the center of the compass rose, and 295°T (which is 180° opposite of 115°T).

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Chapter 7 | Elementary Plotting: Courses and Bearings

Step 4: While maintaining orientation of the ruler, transfer the upper edge to Chance Is.\

Step 5: Plot the bearing line from the Chance Island to your observation point (out in the ocean). Getting this step right is critical!

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Step 6:

Label the bearing line with degrees true and an arrow head on the end.

Step 7: Repeat steps 3 â&#x20AC;&#x201C; 6 for the second bearing line. The intersection of the two bearing lines is the position of the vessel.

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ÂŠ Marine Institute of Memorial University

Chapter 7 | Elementary Plotting: Courses and Bearings

Step 8: Circle the point of intersection of the bearing lines to indicate a ‘fix’. Label the position with time

Step 9: Using parallel ruler and/or divider, determine the coordinates of the vessel.

In this example the position is:

N 48° 33.5’

W 053° 40.0’

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Exercise 7.4: Determining Position by Simultaneous Observation – True Bearings Chart: 3624 1. At 0611hrs a fishing vessel on a course of 341°T observes Cape Scott light bearing 029°T. At the same time the Flashing light in Sea Otter Cove bears 084°T. What are the latitude and longitude co-ordinates of the vessel’s position?

Lat:

Long:

2. At 0717hrs a fishing vessel on a course of 131°T observes the western side of Winifred Island bearing 017°T. At the same time the northern tip of Commerell Point bears 101°T. What are the latitude and longitude co-ordinates of the vessel’s position?

Lat:

Long:

3. At 0837hrs a fishing vessel on a course of 001°T observes the light on Kains Island bearing 091°T. At the same time the western edge of Topknot Point bears 005°T. What are the latitude and longitude co-ordinates of the vessel’s position?

Lat:

Long:

4. At 1022hrs a fishing vessel on a course of 145°T observes the light on Donald Island bearing 104°T. At the same time the western edge of Kwakiutl Point bears 018°T. What are the latitude and longitude co-ordinates of the vessel’s position?

Lat:

Long:

5. At 1303hrs a fishing vessel on a course of 145°T observes the light on Donald Island bearing 104°T. At the same time the western edge of Kwakiutl Point bears 018°T. What are the latitude and longitude co-ordinates of the vessel’s position?

Lat:

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Long:

Chapter 7 | Elementary Plotting: Courses and Bearings

Simultaneous Compass Bearings – Converting to True Position by simultaneous observation involves the use of two bearing lines. A navigator can obtain accurate compass bearings on separate objects using a pelorus or azimuth ring on the magnetic compass. These compass bearings would have to be converted to true bearings before being plotted on a chart. The conversion process requires calculation of the compass error and the same steps for converting ship’s heading and course from compass to true.

Example: At 0532hrs a fishing vessel on a course of 107°C observes Chance Island bearing 137°C. At the same time the North-West Point of Deer Island bears 222°C. What are the vessel’s true course and latitude and longitude coordinates? Variation = 20°W, Deviation = 2°W.

Figure 7.11 Example True Bearings

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Step 1:

Calculate compass error. C/E = Variation + Deviation = 20°W + 2°W= 22°W

Step 2: Convert both compass bearings to True by applying C/E, then plot both.

A. Chance Island compass bearing:

C/E:

Chance Island true bearing:

B. Deer Island compass bearing:

C/E:

Deer Island true bearing:

137°C 022°W (Error west; Compass best) 115°T

222°C 022°W 200°T

Step 3: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection.

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Chapter 7 | Elementary Plotting: Courses and Bearings

Step 4: Calculate ship’s course true:

Ship’s course compass:

C/E:

Ship’s course true

Fishing Master Program Chartwork & Pilotage Book 1

107°C 022°W (Error west; Compass best) 085°T

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Chapter 7 | Elementary Plotting: Courses and Bearings

Exercise 7.5: Simultaneous Bearings – Compass to True Chart 4855 1. At 0430hrs a fishing vessel steering 260°C observes Little Denier Is Lt. bearing 322°C. At the same time, the FL G Lt on the Public Wharf in Tickle Cove bears 198°C. Find the ship's latitude and longitude and true course. Variation: 21°W. Deviation Card A.

Step 1: Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to both Compass bearings to convert to True

Step 4: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection.

Lat:

Long:

2. At 0530hrs a fishing vessel steering 210°C observes Chance Is bearing 263°C. At the same time the northern tip of Plate Cove Head bears 163°C. Find the ship's latitude and longitude and true course. Variation: 21°W. Deviation Card A.

Step 1:

Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to both Compass bearings to convert to True

Step 4: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection. Lat:

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Long:

Chapter 7 | Elementary Plotting: Courses and Bearings

3. At 0630hrs a fishing vessel steering 045°C observes the Southern tip of Gulch Is bearing 300°C. At the same time, Puffin Island Light bears 265°C. Find the ship's latitude and longitude and true course. Variation: 21°W. Deviation Card A.

Step 1: Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to both Compass bearings to convert to True

Step 4: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection. Long:

Lat:

4. At 0730hrs a fishing vessel steering 080°C observes the Eastern tip of Little Harbour Head bearing 008°C. At the same time, Halfway Islet (North side) bears 294°C. Find the ship's latitude and longitude and true course. Variation: 21°W. Deviation Card A.

Step 1:

Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to both Compass bearings to convert to True

Step 4: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection. Lat:

Fishing Master Program Chartwork & Pilotage Book 1

Long:

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Chapter 7 | Elementary Plotting: Courses and Bearings

5. At 0841hrs a fishing vessel steering 200°C observes Little Denier light bearing 282°C. At the same time, Western Head bears 204°C. Find the ship's latitude and longitude and true course. Variation: 21°W. Deviation Card A.

Step 1:

Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to both Compass bearings to convert to True

Step 4: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection. Lat:

Long:

The Cocked Hat While two intersecting LOPs can yield an accurate ‘fix’ of the vessel, a third LOP can sometimes improve accuracy by verifying the result. However, in practice, it is uncommon for the third bearing line to intersect at the same point as the other two thereby forming a triangle known as a ‘cocked hat’. The formation of the triangle is due to errors in the bearing information which can be caused by several factors including the time it takes to sight three separate bearings, especially if the vessel’s speed is relatively high, the sighted objects are relatively close to the ship, or some combination of those and other factors. The size of the ‘cocked hat’ is an indication of accuracy where larger triangles suggest less precise bearings.

Figure 7.12 Cocked Hat

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Chapter 7 | Elementary Plotting: Courses and Bearings

While it is likely that the vessel is inside the ‘cocked hat’ it is always possible that it could be outside. Most navigators assume they are in the center of the triangle provided it is not too large and there are no hazards nearby! If there are hazards in the vicinity it is common practice to assume the vessel is at the most dangerous point of the triangle – the closest point to the danger. Having assumed the vessel is at the most dangerous position, the navigator will take immediate action to remedy the situation, for example, an alteration of course away from the danger. This action would be followed by another ‘fix’ to ascertain the vessel’s new position and to verify that that the vessel has cleared the danger.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Exercise 7.6: Three Simultaneous Compass Bearings – Cocked Hat Chart 4025 1. At 1017hrs when a fishing vessel was steering 260°C an observer noted the following:

Illes Saint Marie light bore 030°C

The eastern tip of Lie Matchiatic bore 351°C

Rochers au Cormoran light bore 315°C.

Find the ship's latitude and longitude and true course. Variation = 19°W. Dev card A.

Step 1: Calculate Compass Error.

Step 2: Calculate Ship’s head true.

Step 3: Apply C/E to all three Compass bearings to convert to True

Step 4: Plot and label all three bearing lines. When the result is a ‘cocked hat’ the position is assumed to be the closest to any immediate danger, if any. If there is there is no immediate danger, the position would be the point on the triangle closest to land.

2. At 1259hrs when a fishing vessel was steering 290°C an observer noted the following:

Illes Triples light bore 071°C

Pte Chicoutai bore 023°C

Pointe de Kegaska light bore 315°C.

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Find the ship's latitude and longitude and true course. Variation = 18°W. Dev card A.

Chapter 7 | Elementary Plotting: Courses and Bearings

Step 1: Calculate Compass Error

Step 2: Calculate ship’s head true:

Step 3: Apply C/E to all three Compass bearings to convert to True

Step 4: Plot and label all three bearing lines. Using the dividers, find the latitude and longitude at the center of the triangle – if there is no danger.

3. At 0254hrs when a fishing vessel was steering 090°C an observer noted the following:

Pte de Natashquan bore 107°C

Ile Joncas light bore 076°C

Red Lights on Tower in Aguanish bore 020°C.

Find the ship's latitude and longitude and true course. Variation = 21°W. Dev card A.

Step 1: Calculate Compass Error

Step 2: Calculate ship’s head true:

Step 3: Apply C/E to all three Compass bearings to convert to True

Step 4: Plot and label all three bearing lines. Using the dividers, find the latitude and longitude at the center of the triangle – if there is no danger.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Relative Bearings As previously mentioned, a bearing can be measured with a magnetic compass or a radar. A bearing measured by a magnetic compass will yield in a compass bearing. However, modern navigational technique dictates that the navigator will generally use the radar to take a bearing – it is easier, faster and probably more accurate. Most small vessel radar operates in the unstabilized or head’s-up mode where the heading marker always points to the stem of the vessel. In this mode, any bearing measured with the radar will be relative to the heading marker. In the example below, the red-dashed Electronic Bearing Line (EBL) is placed on a target off the vessel’s starboard bow. The resultant bearing to the target is measured as 029° on the starboard side. This bearing can also be stated as 29°Green; both names indicate the target is 29° to the right, or clockwise of the heading marker. These bearings are independent of the ship’s head or course because no matter which direction the vessel is travelling, the heading marker on the radar always points to the stem of the vessel

Figure 7.13 Relative Bearings

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Chapter 7 | Elementary Plotting: Courses and Bearings

Naming of Relative Bearings • Red 0° to 180° (Port side) or Green 0° to 180° (Starboard side) • Clockwise 000° to 359° in 3-figure • Point system at 11¼° per point Special relative bearings: ahead (000°), astern (180°) and probably the most common is ABEAM which means 90°Red or Green to ships head.

Figure 7.14 Special Relative Bearings - ABEAM

All Bearings must be plotted in TRUE degrees on a paper chart. Relative bearings are applied to the ship’s head. If ship’s head is given in true degrees, then the calculation is a simple addition or subtraction. However, if ship’s head is given in compass degrees, conversion is required.

Rule: A relative bearing on the port (red) side of the vessel’s fore and aft line is SUBTRACTED from ship’s head. A relative bearing on the starboard (green) side of the vessel’s fore and aft line is ADDED to the ship’s head.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Example: Ship is steering 130° C; the skipper uses the electronic bearing line on the radar to obtain a relative bearing 60°G to a target. Variation is 19°E; deviation (from card A) is 8° E. What is the True bearing?

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Step 1: Calculate C/E

C/E = 19°E + 8°E = 27°E (remember deviation is based on ship’s head)

Step 2: Apply C/E to ship’s head

S. H. compass C/E compass least) Ship’s head true

Step 3: Determine if relative bearing is added or subtracted to ship’s head

Relative bearing: 060°Green - on stbd side of fore and aft line, so added.

Step 4: Apply Bearing to ship’s head true

Ship’s head true: C/E: Bearing:

Step 5: Present Answer

True Bearing is 217°T

130°C +027°E (error east, 157°T

157°T + 60°G 217°T

Chapter 7 | Elementary Plotting: Courses and Bearings

Exercise 7.7: Simultaneous Relative Bearings – Convert to True 1. At 1945 a fishing vessel heading 259°T has Egg Island Light bearing relative 124° and Jeddore Rk Light bearing relative 60°. What is the position of the vessel?

Step 1:

Apply relative bearings to ship’s head true.

Step 2: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection. Lat:

Long:

2. At 2022 a fishing vessel on course 223°T has Half Island Point bearing relative 166° and Devil's Island Light bearing relative 65°. What is the position of the vessel?

Step 1:

Apply relative bearings to ship’s head true.

Step 2: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection. Lat:

Fishing Master Program Chartwork & Pilotage Book 1

Long:

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Chapter 7 | Elementary Plotting: Courses and Bearings

3. At 2110 a fishing vessel on course 331°T has Chebucto Head bearing Red 21° and Devil's Island Light bearing Green 35°. What is the position of the vessel?

Step 1:

Apply relative bearings to ship’s head true.

Step 2: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection. Lat:

Long:

4. At 2205 a fishing vessel on course 084°T has Sambro Island light bearing Red 50° and Betty Island Light bearing 231° relative. What is the position of the vessel?

Step 1:

Apply relative bearings to ship’s head true.

Step 2: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection. Lat:

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Long:

Chapter 7 | Elementary Plotting: Courses and Bearings

5. At 2312 a fishing vessel on course 352°C and bound for St. Margaret's Bay, observes Halibut Rk. Light bearing Green 22° and White Point bearing Red 20°. Var 20°W Dev. 6°E. What is the position of the vessel?

Step 1:

Step 2: Apply compass error to ship’s head compass to convert to true.

Step 3: Apply relative bearings to ship’s head true to calculate true bearings

Calculate compass error

Step 4: Plot and label both bearing lines. Using the dividers, find the latitude and longitude of the point of intersection. Lat:

Fishing Master Program Chartwork & Pilotage Book 1

Long:

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Chapter 7 | Elementary Plotting: Courses and Bearings

7.5 Range and Bearing Lesson Introduction In this lesson we examine how range is a line of position (LOP) and how it can be used in various ways to find the position of the vessel.

Learning Outcomes 1. Define range. 2. Describe how to measure range using a radar 3. Describe radar range error and demonstrate proficiency in applying range error to range measurements. 4. Demonstrate proficiency plotting a simultaneous ranges to determine the vessels position. 5. Demonstrate proficiency plotting simultaneous range and bearings to determine the vessels position.

Assigned Reading Small Craft Piloting & Coastal Navigation: Ch. 9; Pgs. 106 – 123; Figures 83 – 97

Lesson Notes Range is defined as the distance from the vessel (or observation point) to an object. Range is usually measured in nautical miles (or cables = 1/10th of a nautical mile). Range information is y determined with the radar.

Range Accuracy Since the accuracy of radar range depends on the exact measurement of the time interval between when the pulse of energy is transmitted and returning echo received, errors can occur. These errors can be caused by several factors including improper synchronization - starting the sweep on the indicator before the pulse of energy leaves the antenna, line voltage, frequency drift and calibration. While range inaccuracies are minimal in modern radars, they can still occur – especially with older units. It is important that you know how to correct a range when the radar has a known fixed error.

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Chapter 7 | Elementary Plotting: Courses and Bearings

Example: 1. Calculate the correct radar range when it is measured to be 5.0’ and the range error is 5% long.

Step 1: Calculate adjustment percentage: 100% - 5% = 95%

Step 2: Convert percentage to a decimal: 95% = 95/100 = 0.95

Step 3: Calculate correct range: 5.0 x 0.95 = 4.75’

2. Calculate the correct radar range when it is measured to be 5.0’ and the range error is 5% short.

Step 1: Calculate adjustment percentage: 100% + 5% = 105%

Step 2: Convert percentage to a decimal: 105% = 105/100 = 1.05

Step 3: Calculate correct range: 5.0 x 1.05 = 5.25’

As previously mentioned, a minimum of two intersecting LOPs yield are necessary to yield an accurate ‘fix’. In the case of range and bearing the intersecting LOPs are the bearing line and a range arc.

Example: At 0330hrs a fishing vessel steering 000°T observes by radar the northern tip of Cutler Head bearing 281°T at a range of 1.8'. What are the coordinates of the vessel?

Figure 7.15 Example - Vessel Coordinates

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Note: In this example the stabilized radar is set in the North-Up mode. In this configuration the radar can distinguish true direction in the same manner as a gyro compass. The heading marker is pointing straight up the screen toward 000°T, the EBL and VRM are set to intersect with the northern edge of Cutler Head reading 281°T and 1.8’ respectively. Steps 1. Plot and label the bearing line

2. Plot the arc (of radius 1.8') to intersect the bearing line on the chart.

Note: Use the dividers to measure 1.8' from the latitude scale. 7-50

Chapter 7 | Elementary Plotting: Courses and Bearings

3. Circle the point of intersection to indicate a â&#x20AC;&#x2DC;fixâ&#x20AC;&#x2122;. Label with the time.

4. Using the parallel ruler and divider, determine the coordinates of the vessel.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Exercise 7.8: Range and True Bearing Chart: 4855 1. At 1715hrs, on a fishing vessel steering 021°T, an observer noted that Western Rk bore108°T at a radar range of 1.39'. What are the coordinates of the vessel? Range error is known to be 4% short.

Step 1:

Use known range error to calculate actual range.

Step 2: Plot true bearing line and actual range to determine position

Lat:

Long:

2. At 1820hrs, on a fishing vessel steering 120°T, an observer noted that Cottel Island light bore dead astern at a radar range of 1.13'. What are the coordinates of the vessel if range error is 3% long?

Step 1:

Use known range error to calculate actual range.

Step 2: Apply relative bearing to ship’s head true to calculate the true bearing.

Step 3: Plot true bearing line and actual range to determine position

Lat:

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Long:

Chapter 7 | Elementary Plotting: Courses and Bearings

3. At 1925hrs, on a fishing vessel steering 213°T, an observer noted that a small rock (2) located close to Spracklins Pt bore 293°True at a radar range of 0.42'. What are the coordinates of the vessel if range error is 9.5% short?

Step 1:

Use known range error to calculate actual range.

Step 2: Plot true bearing line and actual range to determine position

Lat:

Long:

4. At 2029hrs, on a fishing vessel steering 225°T, an observer noted that the FL R light on the public wharf in Cannings Cove bore dead ahead at a radar range of 2.5'. What are the coordinates of the vessel if range error is 4% long?

Step 1:

Use known range error to calculate actual range.

Step 2: Apply relative bearing to ship’s head true to calculate the true bearing.

Step 3: Plot true bearing line and actual range to determine position

Lat:

Fishing Master Program Chartwork & Pilotage Book 1

Long:

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Chapter 7 | Elementary Plotting: Courses and Bearings

5. At 1900hrs, on a fishing vessel steering 177°T, an observer noted that Western Head bore 129°T at a radar range is 4.41’. What are the coordinates of the vessel if range error is short?

Step 1:

Use known range error to calculate actual range.

Step 2: Plot true bearing line and actual range to determine position

Lat:

Long:

Range and Compass Bearing – Convert to True Just as ship’s head compass is measured from Compass North, a compass bearing is also the angular measurement between Compass North and the line of sight to the object or target as viewed from the vessel. A navigator can obtain an accurate compass bearing on an object by using a pelorus or azimuth ring on a magnetic compass. This compass bearing would have to be converted to a true bearing before being plotted on a chart. The conversion process requires calculation of the compass error and the methodology is the same as it is for converting ship’s heading and course from compass to true.

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Chapter 7 | Elementary Plotting: Courses and Bearings

Example: A vessel is on a compass course of 107°C. At 0809hrs the navigator observes Chance Island (using the magnetic compass and pelorus) bearing 137°C at a range of 1.7’. Variation = 20°W, Deviation = 2°W. What are the vessel’s true course and latitude and longitude coordinates?

Figure 7.16 Example - Convert to True

Once the compass bearing is obtained it would have to be converted to a true bearing before being plotted on the chart.

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Chapter 7 | Elementary Plotting: Courses and Bearings

Solution: Step 1:

Calculate compass error.

C/E = Variation + Deviation = 20°W + 2°W = 22°W

Step 2: Convert Chance Island compass bearing to True by applying C/E.

Chance Island compass bearing:

C/E:

Chance Island true bearing:

137°C 022°W (Error west; Compass best) 115°T

Step 3: Plot the True Bearing and range arc on the chart. As always, the point of intersection is the position. Indicate the ‘fix’ with a circle and label with time.

Convert the compass course to a True course by applying C/E.

Ship’s course compass:

C/E:

107°C 022°W (Error west; Compass best)

Ship’s course true 085°T

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Chapter 7 | Elementary Plotting: Courses and Bearings

Exercise 7.9: Range and Compass Bearing – Convert to True Chart: 4025

Deviation Card A

1. A vessel is on a compass course of 300°C. At 2351hrs the navigator observes the light on Point du Sud-Ouest bearing 014°C at a range of 12.1’. What are the vessel’s latitude and longitude coordinates and true course? Variation = 20°W; Use Deviation Card A.

Step 1:

Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to the compass bearing to convert to True

Step 4: Plot and label the bearing line. Using the dividers to measure range and find the point of intersection. Lat:

Long:

2. A vessel is on a compass course of 190°C. At 2244hrs the navigator observes the light on Cap de la Table bearing 240°C at a range of 8.4’. What are the vessel’s latitude and longitude coordinates and true course? Variation = 20°W; Use Deviation Card A.

Step 1:

Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to the compass bearing to convert to True

Step 4: Plot and label the bearing line. Using the dividers to measure range and find the point of intersection. Lat:

Fishing Master Program Chartwork & Pilotage Book 1

Long:

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Chapter 7 | Elementary Plotting: Courses and Bearings

3. A vessel is on a compass course of 080°C. At 2116hrs the navigator observes the light on Illes Sainte-Marie bearing 023°C at a range of 8.4’. What are the vessel’s latitude and longitude coordinates and true course? Variation = 20°W; Use Deviation Card A.

Step 1:

Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to the compass bearing to convert to True

Step 4:

lot and label the bearing line. Using the dividers to measure range and find P the point of intersection. Long:

Lat:

4. A vessel is on a compass course of 290°C. At 2001hrs the navigator observes the light on Rocher au Cormoran bearing 063°C at a range of 8.1’. What are the vessel’s latitude and longitude coordinates and true course? Variation = 20°W; Use Deviation Card A.

Step 1:

Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to the compass bearing to convert to True

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Step 4: Plot and label the bearing line. Using the dividers to measure range and find the point of intersection. Lat:

Long:

Chapter 7 | Elementary Plotting: Courses and Bearings

5. A vessel is on a compass course of 143°C. At 1947hrs the navigator observes the light on Pointe Carleton bearing 164°C at a range of 11.3’. What are the vessel’s latitude and longitude coordinates and true course? Variation = 20°W; Use Deviation Card A.

Step 1:

Calculate Compass Error

Step 2: Calculate ship’s course true:

Step 3: Apply C/E to the compass bearing to convert to True

Step 4: Plot and label the bearing line. Using the dividers to measure range and find the point of intersection. Lat:

Long:

Simultaneous Radar Ranges As mentioned, for the most part radar information is used to fix position either alone or combined with other information as follows: 1. Radar Range and Visual Bearing 2. Radar Range and Radar Bearing 3. Radar Ranges as Position Arcs Older textbooks state that inaccuracy caused by the beam-width of the radar lobe, a visual bearing should be used in preference to radar bearings. However, with the technological advances of modern radar (and relatively low prices for really good radar) this statement is not necessarily true anymore. For example, a 6 foot radar scanner (antenna) horizontal beam width is reduced to just 1.9°, which results in a very high degree of bearing precision. Obviously, the shorter the radar scanner the less accurate it is for bearings. Radar bearings are more prone to error than radar ranges therefore ranges are preferable to bearings and should be used whenever possible. The use of position arcs is normally the most accurate method of fixing position when using radar information alone.

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Chapter 7 | Elementary Plotting: Courses and Bearings

Example At 1410 hrs. a fishing vessel observes the following data from the radar: 1. Mosher Island Light

Radar Range: 1.6’

2. West Ironbound Island Light

Radar Range: 1.7’

Find the vessel’s position. Note: It is probably best to complete these exercises with a divider from a mathematics geometry set – one end is pointy, the other end has a piece of pencil lead. Step 1: Measure 1.6’ on the latitude scale with the divider (which corresponds to the radar range of Mosher Is. Lt.)

1.6’

Step 2: Maintain the measured spacing on the divider place the pointy end on Mosher Island light; now, plot a full circle with a radius of 1.6’.

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1.6’

Step 3: Measure 1.7’ on the latitude scale; plot a circle around West Ironbound Light (radius 1.7’).

1.7’

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1.6’

Step 4: Label the intersection of the radar ranges as the observed position and denote time. Use the parallel ruler and/or divider to find the latitude and longitude coordinates.

1.7’

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Note: You have to be careful; as you can see the circles can intersect in two places. The second intersection in this case occurs over land. Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 7 | Elementary Plotting: Courses and Bearings

Circular Lines of Position –Distance Off Navigating a vessel to maintain a specific ‘distance off’ is a very valuable, common application that can be used for routine navigation control or for maneuvering to avoid hazards. For example, there may be off-lying underwater rocks within 0.25 mile off a headland you must bypass, and for traffic or current reasons you wish to go around as closely as possible – looking for the shortest safe route. In cases like these, the shoreline will give a solid radar echo that you can depend on, and you can set your radar to the safe ‘distance off’ that you have constructed on the chart. This technique is especially valuable at night or in the fog!

Example: At 1703 a fishing vessel in position N50°41.5’ W128° 38.9’ wishes to pass Cape Scott at a distance of 1.7’. Variation 20°E. Deviation Card A. What is the True Course to Steer? What is the Compass Course to Steer? Steps: 1. Plot the initial position. Label it with time.

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Chapter 7 | Elementary Plotting: Courses and Bearings

2. Using the divider, measure the required distance off – 1.7’ 3. From the tip of Cape Scott, plot the arc (radius 1.7’) on the chart. 4. Insert a line with two arrow-heads to indicate distance off. 5. Plot the course line from the observed position tangential (touches in one place) to the arc.

6. Insert arrow-head on the course line to show direction. 7. Using the parallel ruler and the compass rose, determine the true course – 046°T 8. Label with degrees True (3-Figure notation). 9. Calculate the Compass Course:

i) Apply variation to convert the true course to magnetic: True Course:

046°T

Variation:

020°E (variation east – magnetic least)

Magnetic course: 026°M

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Chapter 7 | Elementary Plotting: Courses and Bearings

ii) Calculate deviation by entering the ‘magnetic side’ of Dev Card A to set up matrix.

iii) Set up equation. Cross multiply and solve for x

iv) Calculate overall

deviation.

Overall deviation = 9°W + 0.6° = 9.6°W

v) Apply deviation to the magnetic course to convert to compass.

Magnetic course:

026°M

009.6°W (deviation west – compass best)

Deviation:

Compass course:

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035.6°C

Chapter 7 | Elementary Plotting: Courses and Bearings

Exercise 7.10: Radar Ranges Chart: 4320 1. At 0225 a fishing vessel is situated to the south of Jeddore Rk and Egg Island. The navigator observes the following information from the radar:

Jeddore Rk light: Radar Range 5.2’

Egg Island light: Radar Range 5.8’

What is the position of the vessel? Lat:

Long:

2. At 0225 a fishing vessel is situated to the East of Indian Island and South of West Ironbound Island. The navigator observes the following information from the radar:

Southern tip of Indian Island: Radar Range 5.1’

West Ironbound Island light: Radar Range 4.4’

Variation 18°W. Deviation Card A.

i) What is the initial position of the vessel? Lat:

Long:

The skipper wishes to maintain a safe distance off Cross Island light of 2.0’.

ii) What is the True Course to steer?

iii) What is the Compass Course to steer? (Round to the nearest degree)

iv) What is the position of the vessel and distance travelled when Cross light is abeam? Lat:

Fishing Master Program Chartwork & Pilotage Book 1

Long:

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Chapter 7 | Elementary Plotting: Courses and Bearings

3. At 0123 a fishing vessel is situated to the South East of both Cross Island and Pearl Island. The navigator observes the following information from the radar:

Cross Island light: Radar Range 4.1’

Pearl Island light: Radar Range 4.0’

Variation 18°W. Deviation Card A.

i) What is the initial position of the vessel?

Lat:

Long:

While steaming in a somewhat North-Easterly direction, the skipper wishes to maintain a distance off Betty Island light of 1.5’.

ii) What is the True Course to steer?

iii) What is the Compass Course to steer? (Round to the nearest degree)

4. At 1302 a fishing vessel is steering a course of 090°C at which time Devil’s Island light is observed to be 226°relative x 1.5’.

Variation 18°W. Deviation Card A.

i) What is the initial position of the vessel?

Lat:

7-66

Long:

The skipper now wishes to alter the course of the vessel so that he passes 1.25’ south of Shut-In Island.

ii) What is the True Course to steer?

iii) What is the Compass Course to steer? (Round to the nearest degree)

Chapter 7 | Elementary Plotting: Courses and Bearings

5. At 1533 a fishing vessel is steering a course of 350°C at which time Betty Island light is observed to be abeam on the starboard side at 1.5’. Variation 18°W. Deviation Card A.

i) What is the initial position of the vessel? Lat:

Long:

The skipper now wishes to alter the course of the vessel so that he passes 1.0’ south of Peggy’s Cove light enroute to St. Margarets Bay.

ii) What is the True Course to steer?

iii) What is the Compass Course to steer? (Round to the nearest degree)

iv) What is the position of the vessel and distance steamed when Peggy’s Cove light is abeam to starboard? Lat:

Fishing Master Program Chartwork & Pilotage Book 1

Long:

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Chapter 7 | Elementary Plotting: Courses and Bearings

7.6 Transit Bearings Lesson Introduction In this lesson we examine the importance of a transit bearing and how it is used to determine compass error.

Learning Outcomes 1. Define transit bearings, clearing lines, clearing bearings, clearing soundings and clearing ranges 2. Demonstrate proficiency measuring transit bearings to calculate compass error.

Assigned Reading Small Craft Piloting & Coastal Navigation: Pg. 128

Lesson Notes When two conspicuous (charted) objects are in line – where one object can be seen directly behind the other; they are said to be in transit. Therefore to be in transit, simply means to be in line. A transit bearing is simply a bearing of two objects when they are in line as seen from the ship. That is, the two objects and the ship are on the same line of sight. The symbol for Transit Bearing is Ø.

Figure 7.17 Transit Bearings

Transit bearings provide very reliable position lines that are easily measured in True degrees from the chart. When available, transit bearings are the expected way to calculate compass error –specifically deviation this method takes precedence over the deviation card!

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Chapter 7 | Elementary Plotting: Courses and Bearings

The officer of the watch should always be on the lookout for suitable transit bearings to use as a check for compass error. The navigator must make a calculation to compare deviation value from the ‘Deviation Card’ and ‘transit bearing’ are in agreement. If the values do not match, the navigator must always use the deviation calculated from the transit bearing; it is most recent and reliable – this is of particular importance for the TC final exam. A deviation card can be ‘out of date’, in the sense that modifications to a vessel may occur after the deviation card is drawn up. These modifications can change the local magnetic fields of the vessel, thereby causing inaccuracies in the deviation card. Note: For the TRANSPORT CANADA FINAL EXAM it may be challenging to determine when to use transit bearings – it may not be explicitly stated. While not explicitly stated you will be expected to use transit bearings to calculate compass error when you see the following key phrases in a chartwork problem: - ‘observed in transit’ - ‘in line with’

Example: At 0534 a fishing vessel is observed to be steering a course of 240°C. Mosher Island light and West Ironbound Island light are observed in transit at 310°C. Determine the true transit bearing, compass error and deviation. Compare transit bearing deviation to deviation calculated from Deviation Card A. Variation is 19°W. Step 1: Line up the two lights using your parallel ruler. Draw and label the true bearing on the chart (shown in graphic above). Step 2: Walk the ruler to the compass rose to find the True transit bearing – 286°TØ. Step 3: Compare the true transit bearing to the compass bearing to get the compass error.

Compass transit bearing:

310°C

True charted transit bearing:

286°TØ

Compass Error

C/E = Variation + Deviation

24°W (Compass best - Error is west)

Therefore:

C/E – Variation = Deviation

24°W - 19°W = 5°W Deviation – based on transit bearing.

From Deviation Card A, we can see;

Ship’s head compass 240°C → 8°W Deviation – based on Deviation Card A.

Deviation calculated from the transit bearing is deemed more reliable!!!

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Chapter 7 | Elementary Plotting: Courses and Bearings

Exercise 7.11: Transit Bearings Chart: 4320 Deviation Card A 1. At 0820 a fishing vessel on a heading of 085°C observes East Ironbound Island light in line with Pearl Island light bearing abeam on the port side when variation = 23°W.

A. Calculate the following from the transit bearing.

i) True transit bearing

ii) Compass error

iii) Deviation

B. Calculate the following based on Deviation Card A.

i) Compass error

ii) Deviation

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iii) True Course

C. Compare the compass error for both calculations. Which is more accurate?

Chapter 7 | Elementary Plotting: Courses and Bearings

D. At the same time Cross Is light is dead astern. What are the latitude and longitude coordinates of the vessel?

2. At 2243 a fishing vessel steering 260째C observes West Ironbound Island light in line the south west tip of Gaff Point abeam to the starboard when variation = 20째W

A. Calculate the following from the transit bearing

i) True transit bearing

ii) Compass error

iii) Deviation

iv) True Course

B. Calculate the following based on Deviation Card A

i) Compass error

ii) Deviation

iii) True Course

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Chapter 7 | Elementary Plotting: Courses and Bearings

C. Compare the compass error for both calculations. Which is more accurate?

D. At the same time Cape La Have is bearing dead ahead. What are the latitude and longitude coordinates of the vessel?

3. At 0422 a fishing vessel steering 305°C observes Betty Island light in line with Middle Point bearing 24°Green when variation = 19°W

A. Calculate the following from the transit bearing

i) True transit bearing

ii) Compass error

iii) Deviation

iv) True Course

B. Calculate the following based on Deviation Card A

i) Compass error

ii) Deviation

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Chapter 7 | Elementary Plotting: Courses and Bearings

iii) True Course

C. Compare the compass error for both calculations. Which is more accurate?

D. At the same time Betty Island light is bearing 158째relative. What are the latitude and longitude coordinates of the vessel?

4. At 0717 a fishing vessel steering 130째C observes Sambro Island light in line with the light on Chebucto Head abeam on the port side when variation = 22째W

A. Calculate the following from the transit bearing

i) True transit bearing

ii) Compass error

iii) Deviation

iv) True Course

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Chapter 7 | Elementary Plotting: Courses and Bearings

B. Calculate the following based on Deviation Card A

i) Compass error

ii) Deviation

iii) True Course

C. Compare the compass error for both calculations. Which is more accurate?

D. At the same time Pennant Point is bearing 163°Red. What is the latitude and longitude coordinates of the vessel?

5. At 2000 a fishing vessel steering 149°C observes Jeddore Rock light in transit with the the eastern tip of Barren Island bearing 063°C when variation = 21°W

A. Calculate the following from the transit bearing

i) True transit bearing

ii) Compass error

iii) Deviation

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iv) True Course

Chapter 7 | Elementary Plotting: Courses and Bearings

B. Calculate the following based on Deviation Card A

i) Compass error

ii) Deviation

iii) True Course

C. Compare the compass error for both calculations. Which is more accurate?

D. At the same time Jeddore Rock is at a range of 3.0â&#x20AC;&#x2122;. What is the latitude and longitude coordinates of the vessel?

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Chapter 7 | Elementary Plotting: Courses and Bearings

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Chapter 8 The Dead Reckoning Plot

Chapter 8 | The Dead Reckoning Plot

Unit Introduction This unit is the culmination of the previous seven units. The purpose is to train you to plot the vessel’s position by various means (including relative bearings) and construct a dead reckoning plot using the Distance= Speed x Time formula. The concepts of all units (2 – 7) are integrated into the practical chartwork exercises contained in this section.

Overview – Major Headings 8.1 Introduction to Dead Reckoning (DR) 8.2 The Rules of DR 8.3 Time 8.4 Distance/Speed/Time Calculations 8.5 Constructing the DR Plot 8.6 Maintaining a Log 8.7 Passage Planning

Learning Outcomes 1. Define Dead Reckoning (DR). 2. Explain the importance of maintaining a DR plot. 3. Describe the rules of maintain an accurate DR plot. 4. Define Estimated Time of Arrival (ETA) and Estimated Time of Departure (ETD). 5. Demonstrate proficiency calculating ETA. 6. Identify the variables of the D = S x T formula. 7. Explain the importance of time units when using the D=S x T formula. 8. Demonstrate proficiency converting hours to minutes and minutes to hours. 9. Demonstrate proficiency re-arranging the D = S x T formula. 10. Demonstrate proficiency solving distance/speed/time problems. 11. Demonstrate proficiency constructing and labelling an accurate DR plot. 12. Explain the difference between a fishing log and an official log. 13. Identify the types of entries made in an official log. 14. State the importance of a log as a document in the event of court proceedings.

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Chapter 8 | The Dead Reckoning Plot

15. Describe the importance of developing a passage plan before departing on an intended voyage. 16. List the and describe the four stages of a passage plan 17. Describe rules to be followed when preparing a passage plan

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Chapter 8 | The Dead Reckoning Plot

8.1 Introduction to Dead Reckoning (DR) Lesson Introduction In this lesson we introduce the concept of the DR plot.

Learning Outcomes 1. Define Dead Reckoning (DR). 2. Explain the importance of maintaining a DR plot.

Assigned Reading Small Craft piloting & Coastal Navigation: Pgs. 91 â&#x20AC;&#x201C; 101

Lesson Notes Dead Reckoning (DR) is the process of estimating your position by advancing a known position using course, speed, time and distance to be traveled. In other words figuring out where you will be at a certain time if you hold the speed and course. Dead Reckoning is a deduction of your position assuming dead air and dead water conditions. That is, no effects of wind or current on the vessel. The DR plot will require some basic math skills such as addition and subtraction of time as well as multiplication and division using the following formula: Distance = Speed x Time

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Chapter 8 | The Dead Reckoning Plot

8.2 The Rules of DR Lesson Introduction In this lesson we examine the rules that apply for maintaining a DR plot.

Learning Outcomes 1. Describe the rules of maintain an accurate DR plot.

Lesson Notes Even though the modern navigator usually has a vast array of electronic navigational aids to determine the position of the vessel, the carriage of paper charts is still a requirement of law in Canada. In the spirit of compliance, it is essential that the navigator not only have the charts on board the vessel, but also have a complete understanding of the most basic navigational evolution: the DR plot. To maintain a DR plot, the navigator should plot the vesselâ&#x20AC;&#x2122;s expected position; 1. At least every hour on the hour. 2. After every change of course or speed. 3. If the vessel is without GPS, after every observed fix (range and bearing, etc.) Properly maintaining a DR plot is important for ship safety. The DR allows the navigator to examine a future position in relation to a planned track. It allows Master to anticipate charted hazards and plan appropriate action to avoid them. Recall that the DR position is only approximate.

â&#x20AC;&#x192;

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Chapter 8 | The Dead Reckoning Plot

8.3 Time Lesson Introduction In this lesson we examine time and how it applies to the DR plot.

Learning Outcomes 1. Define Estimated Time of Arrival (ETA) and Estimated Time of Departure (ETD). 2. Demonstrate proficiency calculating ETA.

Assigned Reading Small Craft piloting & Coastal Navigation: Pgs. 85 – 90

Lesson Notes Official local time used aboard a ship (on paper charts, in log books, conversing with Coast Guard Radio, etc.) is denoted by the 24 hour clock system. Under this system hours are counted consecutively from: 0000hrs → Midnight 0600hrs → 6AM 1300hrs → 1PM 1800hrs → 6PM Minutes are stated from: 0 → 59 1058hrs = 10:58AM= 10 hours and 58 minutes past midnight. 1702 = 5:02PM = 17hrs 02min past midnight. A vessel departs, or sails at a certain time. If her sailing time is requested, it is her Estimated Time of Departure, or ETD. The time a vessel plans to arrive at her destination is known as her Estimated Time of Arrival, or ETA. Time Interval - difference between the beginning (ETD) and end time (ETA)

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Chapter 8 | The Dead Reckoning Plot

Calculating ETA and Time Interval When calculating time for practical chartwork exercises, you will either find the time interval of a segment of the DR plot, or you will be given a start time and the time interval and have to calculate the end time (ETA). Rule: Separate hours and minutes to avoid confusion.

Example: 1058hrs Write as: 10 58 When adding or subtracting time, work from right to left â&#x20AC;&#x201C; dealing with minutes first, then hours.

Example 1: Departure time: 0345. Steaming time: 5 hours and 14 minutes. Calculate ETA.

03 45

+ 05 14

08 59

Answer: ETA is 0859

Example 2: Departure time: 1333. Steaming time: 3 hours and 42 minutes. Calculate ETA.

13 33

+ 03 42

16 75

Simplify: Minutes exceed 60. Deduct 60 minutes and add 1 hour. -

16 75 60 17 15

Answer: ETA is 1715

When subtracting always make sure that the number of minutes in the time from which you are subtracting is greater than the number of minutes in the time being subtracted. This is accomplished by borrowing 1 from the hours and adding 60 to the minutes.

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Chapter 8 | The Dead Reckoning Plot

Example 3: Departure time 1659. ETA 2133. Calculate hours steamed?

21 33 - have to borrow 60 minutes from the 21 hrs →

16 59 - 16 59

20 93

04 34 Answer: 0434

Be careful with date of day. Although it is unlikely that you will have to deal with time problems that span two separate days on the Transport Canada Final - be aware and prepared!!

Example 4: Vessel departs the St. John’s Traffic Zone at (CIP - 1N) at 2238 on December 12 and steams for 5hours 25 minutes. What is her ETA? 22 38 → December 12 + 5 25 → Steaming time 27 63 → December 13 -

24 00 → Subtract 24 00hrs to get correct time on December 13

03 63 → Can’t exceed 60 minutes

- 60 → Subtract 60 minutes, add an hour

04 03 → December 13

Answer: 0403 December 13.

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Exercise 8.1: Addition and Subtraction of Time 1. A vessel departs at 0415hrs and steams for 1hour 39minutes. What is the ETA?

2. A vessel departs at 1926hrs and steams for 43minutes. What is the ETA?

3. A vessel departs at 0000hrs and steams for 11 hours 59minutes. What is the ETA?

4. A vessel departs at 0300hrs and arrives at 1412hrs. What is the duration?

5. A vessel departs at 1314hrs and arrives at 2018hrs. What is the duration?

6. A vessel departs at 0111hrs and arrives at 0815hrs. What is the duration?

7. A vessel departs at 1213hrs and arrives at 1544hrs. What is the duration?

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Chapter 8 | The Dead Reckoning Plot

8. A vessel departs at 1603hrs and arrives at 2151hrs. What is the duration?

9. On December 16th a vessel departs at 2004hrs and steams for 3 hours 57 minutes. What is her ETA?

10. On November 26th a vessel departs at 1516hrs and steams for 4 hours 49 minutes. What is her ETA?

11. On November 26th a vessel departs at 1642hrs and steams for 7 hours 59 minutes. What is her ETA?

12. A vessel arrives at 1815hrs on November 26, after steaming for 12hrs 29minutes. What was her departure time? â&#x20AC;&#x192;

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Chapter 8 | The Dead Reckoning Plot

8.4 Distance/Speed/Time Calculations Lesson Introduction In this lesson we will examine how to convert time and the importance of consistent time units in the D = S x T formula.

Learning Outcomes 1. Identify the variables of the D = S x T formula. 2. Explain the importance of time units when using the D=S x T formula. 3. Demonstrate proficiency converting hours to minutes and minutes to hours. 4. Demonstrate proficiency re-arranging the D = S x T formula. 5. Demonstrate proficiency solving distance/speed/time problems.

Lesson Notes Time, speed, and distance are related by the formula: Distance = Speed x Time. Where;

D = Distance in nautical miles

S = Speed in knots (nautical miles per hour)

T= Time in hours

Therefore, if any two of the three quantities are known, the third can be found. The units must be consistent. The distance scales on nautical charts use nautical miles unless otherwise stated on the chart. If speed is measured in knots (nautical mile per hour) and time in hours, the answer is in nautical miles. Similarly, if distance is measured in nautical miles and time in hours, the answer is in knots.

Converting Time The tricky part of the D= S x T formula is the Time variable. The reason it is a little tricky is that most often a question will give time in hours and minutesâ&#x20AC;Śand sometimes minutes only. In both cases time will have to be converted to hours (and decimal hours) to be used in the formula. It is important that the navigator can convert minutes to hours (and vice versa) with ease.

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Chapter 8 | The Dead Reckoning Plot

Exercise 8.2: Convert Hours and Minutes to Hours Example: Convert 5 hours and 16 minutes to hours.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

No.

Isolate the minutes: 16 minutes Divide by 60 to convert minutes to hours 16 ÷ 60 = 0.2666 =0.27 (round to the nearest hundredths) Add for total hours: 5hrs + 0.267hrs = 5.27hrs 38’ ÷ 60 = 0.63333°E = 0.6°E Present Answer. 5hours 16minutes = 5.27hrs

Hours & Minutes

Hours

No.

Hours & Minutes

3hrs 33min

3hrs 12min

12hrs 20min

9hrs 18min

5hrs 05min

2hrs 31min

4hrs 48min

7hrs 44min

7hrs 55min

1hrs 36min

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Chapter 8 | The Dead Reckoning Plot

Exercise 8.3: Convert Hours to Hours and Minutes Example: Convert 3.33 hours to hours and minutes. Step 1:

Step 2:

Step 3:

No.

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Isolate the decimal portion: 3.33hrs = 3hrs + 0.33hrs Multiply by 60 to convert decimal hours to minutes. 0.33 x 60 = 19.8 = 20 minutes (round to the nearest minute) Present Answer. 3.33hrs = 3hrs 20minutes

Hours

Hours & Minutes

No.

Hours

3.40hrs

10.49hrs

4.11hrs

15.33hrs

5.24hrs

19.19hrs

3.90hrs

23.10hrs

7.17hrs

16.50hrs

Hours & Minutes

ÂŠ Marine Institute of Memorial University

Chapter 8 | The Dead Reckoning Plot

Applying the D = S x T Formula The standard D = S x T formula is easy to re-arrange, especially using the aid shown. Simply place a finger over the variable you are trying to find and the new, rearranged formula will appear. To find D, place a finger over D in the diagram, you have S X T

To find S, place your finger over S, you have

Figure 8.1 D = S x T

To find T, place your finger over T, you have

Example 1: A fishing vessel clears Cape Bonavista at 0400hrs on a course of 095°T and speed of 8 knots. How many nautical miles did it travel by 0800hrs? Identify the formula: D = S x T Step 1:

Step 2:

Remember: In order to solve this equation, two of the three variables must be given outright…or one given outright and one easily calculated. Identify the information given in the question. In this case speed is given as 8knots: Speed = S = 8kts.

Step 3:

Time is easily calculated as follows: T = 0800hrs – 0400hrs = 4hrs Enter values into the formula and solve:

Step 4:

Step 5:

D=SxT D = 8nm/hr x 4hr (hours cancel) D = 32’ Present Answer: The vessel travelled 32’

Fishing Master Program Chartwork & Pilotage Book 1

8-15

Chapter 8 | The Dead Reckoning Plot

Example 2: A fishing vessel clears Cape Bonavista at 0436hrs on a course of 095°T and at 0821hrs it had steamed 30.5’. What is the speed of the vessel?

Step 1:

Step 2:

Identify the formula: D = S x T Rearranging the formula we have: Identify the information given in the question. In this case distance is given as 30.5 nautical miles D = 30.5. Time is easily calculated as follows: T = 0821hrs – 0436hrs = 03hr 45min

Step 3:

Convert to hours and decimal of hours: 45/60 = 0.75 hr T= 03hr + 0.75hr = 3.75 hr Enter values into the formula and solve:

Step 4:

Step 5:

8-16

Present Answer: The speed of the vessel is 8.13 knots.

Chapter 8 | The Dead Reckoning Plot

Example 3: A fishing vessel steaming at 7.7 knots intends to travel a distance of 56 nautical miles. What is the vessel’s ETA if it departs at 0430? Step 1:

Step 2:

Identify the formula: D = S x T Rearranging the formula we have: Identify the information given in the question. In this case distance is given as 56.0’. D = 56.0’.

Step 3:

Speed is given as 7.7 knots. Enter values into the formula and solve:

Step 4:

Convert hours and decimal of hours to hours and minutes: Step 5:

0.27hr x 60 = 16.2 = 16 min Total time interval 07hr 16min Calculate ETA:

Step 6:

Step 7:

04 30 + 07 16 11 46 Present Answer: ETA of the vessel is 1146hrs.

Fishing Master Program Chartwork & Pilotage Book 1

8-17

Chapter 8 | The Dead Reckoning Plot

Exercise 8.4: Time/Speed/Distance Calculations 1. A vessel departs on a trip at 0400 with a speed of 7.8 knots. What is her ETA if distance travelled is 51.4'?

2. A vessel departs on a trip at 0625 with a speed of 8.2 knots. What is her ETA if distance travelled is 165'?

3. A vessel departs at on a trip at 1502. At 2333 she has travelled a distance of 70.2'. What is her speed?

4. A vessel departs at on a trip at 0247. At 0930 she has travelled a distance of 43.3'. What is her speed?

5. A vessel departs at on a trip at 0333 with a speed of 9.9kts. What distance did she travel by 0944?

6. A vessel departs at on a trip at 0105 with a speed of 10.5kts. What distance did she travel by 0720?

â&#x20AC;&#x192;

8-18

ÂŠ Marine Institute of Memorial University

Chapter 8 | The Dead Reckoning Plot

8.5 Constructing the DR Plot Lesson Introduction In this lesson we examine the procedure for constructing a DR plot.

Learning Outcomes 1. Demonstrate proficiency constructing a DR plot.

Assigned Reading Small Craft piloting & Coastal Navigation: Pgs. 85 – 90

Lesson Notes Dead reckoned plots are based on true courses, also known as the DR track, and should be clearly labeled for future reference. The following exercise will be used to illustrate all the elements of the DR plot. These plots will provide you with the opportunity to put to use all the things you have learned so far and to practice plotting and labeling a DR position. Note: A D.R. position (symbol: +) is not exact. It is a deduction of where you think you will be at some calculated time in the future. Whereas an observed position is your exact known position at a precise time.

Example: Chart: 4588

Variation 22°W Deviation 2°E

At 0400 a vessel departs position N 48° 49.80' W 053° 35.40' on a course of 152°C and speed of 7.5kts. What is the DR position and ETA after 1hour 10 minutes?

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 8 | The Dead Reckoning Plot

Step 1:

Plot the departure position.

Step 2: Calculate compass error.

C/E = 22°W + 2°E = 20°W

Step 3: Calculate the True course. Compass Course: 152°C

C/E:

20°W (error west, compass best)

True Course: 132°T

Step 4: Convert time interval to hours: 1hour 10 minutes = 1hr + 10/60= 1 + 0.17 = 1.17hrs

Step 5: Calculate Distance: D = S x T = 7.5kts x 1.17 hrs = 8.7'

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Chapter 8 | The Dead Reckoning Plot

Step 6: Plot the DR track on the chart.

i) Start at the departure position.

ii) Plot the 132°T course line, extending it nice and far.

iii) Measure 8.7' along the course line and mark with a small arc for clarity. This is the ‘DR’ position.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 8 | The Dead Reckoning Plot

Step 7: Label the DR position with a ‘+’ and ETA. Note: make sure you know the difference in labeling an ‘observed position’ and a ‘D.R. position’.

Step 8: Label the course line:

- True course

- Distance

Step 9:

8-22

Determine DR position: N 48° 44.0'

W 053° 25.6'

Chapter 8 | The Dead Reckoning Plot

Exercise 8.5: Dead Reckoning Chart: 4855 1. At 0120 a vessel on a course of 118°T in Morris Channel observes Bruce Cove Pt by radar and determines its range to be 0.75' while bearing 151° relative. If a speed of 6.0kts is maintained for 30 minutes what will be the coordinates and ETA of the DR position? Steps:

i). Plot initial position (range & bearing).

ii). Calculate distance.

iii). Plot course line.

iv). Measure distance on chart and plot the DR position.

v). Label the plot correctly

vi). Find the coordinates of the DR position

2. At 1956 a vessel in position N 48° 33.70' W 053° 32.70’ sets on a course of 256°C with a speed of 7.8kts. The skipper intends to steam for 28 minutes. What is the distance travelled? Plot and determine the coordinates and ETA of the DR position. Variation: 21°W Deviation: 2°E Steps:

i). Plot the initial position.

ii). Calculate True Course.

iii). Calculate distance.

iv). Plot the course line

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 8 | The Dead Reckoning Plot

v). Plot the DR position based on distance travelled along the course line.

vi). Label the plot correctly with course, distance and ETA.

vii). Find the coordinates of the DR position.

3. At 2219 a vessel on a course of 018°C on the SE side of Morris Island observes the Western tip of Athwart Island bearing 62° Red while the NE tip of Bakers Loaf Island bears 147°Red. If a speed of 6.2kts is maintained for 3.1nm, what will be the coordinates and ETA of the DR position? Variation 19° W. Deviation 1°E Steps:

i). Calculate compass error.

ii). Find the True course of the vessel.

iii). Convert the relative bearings to true bearings.

Athwart Island

iv). Plot the initial position.

8-24

Bakers Loaf Island

v). Plot the True course and distance of the DR position.

vi). Calculate the ETA. ______________________

vii). Label the plot

Chapter 8 | The Dead Reckoning Plot

vii). Find the coordinates of the DR position.

4. At 0713 a vessel on a course of 069°C in Bloody Reach observes the Northern tip of Mouse Island dead astern at a range of 0.47'. If a speed of 7.0 kts is maintained for 21 minutes, what will be the coordinates and ETA of the DR position? Variation 23° W. Deviation 3°W Steps:

i). Calculate compass error. ii). Find the True course of the vessel.

iii). Convert the relative bearing to a true bearing.

iv). Plot the initial position - range and bearing.

v). Calculate the distance travelled.

vi). Calculate the ETA.

vii). Construct and label the plot

viii). Find the coordinates of the DR position.

Fishing Master Program Chartwork & Pilotage Book 1

8-25

Chapter 8 | The Dead Reckoning Plot

8.6 Maintaining a Log Lesson Introduction In this lesson we look at the importance of a logbook aboard a fishing vessel.

Learning Outcomes 1. Explain the difference between a fishing log and an official log. 2. Identify the types of entries made in an official log. 3. State the importance of a log as a document in the event of court proceedings.

Assigned Reading Small Craft piloting & Coastal Navigation: Pgs. 102 â&#x20AC;&#x201C; 105.

Lesson Notes A log is a record of actions or incidents aboard a vessel. Most Canadian fishing vessels are required to complete a fishing log as a requirement of the Department of Fisheries and Oceans (DFO). This type of log is primarily concerned with data that is directly associated with the fishing operations such as lat/long of fishing gear, time gear was set, amount of gear, how much fish per set, etc. The official log is a record of incidents pertinent to the movement and navigation of the ship. The log provides an orderly way of noting all data that is required to maintain a DR plot. It is also an important document that can be used in the court of law in the event of an incident. Log books can be purchased commercially. It can also be something created in a Word or Excel document and printed very inexpensively.

8-26

ÂŠ Marine Institute of Memorial University

Chapter 8 | The Dead Reckoning Plot

Figure 8.2 Log Book

Note: If there is no official log aboard, the comment section in the fishing log can be used to record any significant event on a trip i.e. SAR incident, any training exercise carried out, or any type of navigational incident that you think is important to the safety of the vessel and crew.

Fishing Master Program Chartwork & Pilotage Book 1

8-27

Chapter 8 | The Dead Reckoning Plot

8.7 Passage Planning Lesson Introduction In this lesson we look at the importance of a logbook aboard a fishing vessel.

Learning Outcomes 1. Describe the importance of developing a passage plan before departing on an intended voyage. 2. List the and describe the four stages of a passage plan 3. Describe rules to be followed when preparing a passage plan

Assigned Reading Small Craft piloting & Coastal Navigation: Pgs. 231 â&#x20AC;&#x201C; 244.

Lesson Notes Now that a foundation in basic navigation has been laid it is important that you consider some basic rules when deciding on the route the vessel will actually follow at sea. The whole process of determining the route and having a well thought out plan is known as passage planning. When the skipper and mate take time to decide on the intended route, examine the chart and calculate various ETAâ&#x20AC;&#x2122;s, it makes for a much less stressful environment especially at night approaching land in bad weather. The passage plan should be comprehensive, detailed and easy to interpret. The full procedure is in four stages: 1. Appraisal 2. Planning 3. Execution 4, Monitoring The first two are the preparatory stages. Three and four are the essential elements of voyage execution and confirm that the voyage is being conducted according to the plan. The procedure must be supported by good information and data. For the bridge team to execute and monitor the safe progress of the ship, the plan should be prepared from berth-to-berth in accordance with STCW Code. It should contain:

8-28

ÂŠ Marine Institute of Memorial University

Chapter 8 | The Dead Reckoning Plot

• Identification of hazards such as shallow waters, rocks, tides, wrecks, tides and weather. • Course the vessel must follow. • Contingency plans to be followed if the vessels meet a hazard. • Establish priorities and delegation of responsibilities. • Reduce over-reliance on electronic aids to navigation • Allow the plan to be continuously monitored. Passage Plan – Summary When planning the voyage it is important to keep the following rules in mind: • Use the largest scale chart available for each area to be navigated. • Identify predicted areas of navigation and make note on the chart. • Plot the course clear of any danger (give yourself a wide margin). • Always be aware of Under Keel Clearance (UKC). Examine the intended course line thoroughly for depth; make sure of adequate water at all times.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 8 | The Dead Reckoning Plot

8-30

ÂŠ Marine Institute of Memorial University

Chapter 9 The Effects of Wind and Current on a Ship

Chapter 9 | The Effects of Wind and Current on a Ship

Unit Introduction In this unit we will build on the DR plot and examine the effects of external forces – wind and current – on the vessel.

Overview – Major Headings 9.1 Review of Positioning 9.2 Wind and the Effects of Leeway 9.3 Current and the Effects of Set, Drift and Rate

Learning Outcomes 1. Define leeway and drift 2. Explain how leeway and drift act on a vessel at sea. 3. Define observed position, DR position, estimated position, sea position, wind direction, leeway angle, set, rate, drift, ship’s heading, course, distance run, track, course made good and water track. 4. Identify symbols used in chartwork when leeway and drift are present. 5. Explain the relationship between leeway and current and if one can exist without the other. 6. Explain the relationship between the water track and the CMG if no current is present. 7. Describe factors that influence the magnitude of leeway force. 8. Explain the process for applying leeway to the vessel’s DR track. 9. Demonstrate proficiency applying leeway in various situations. 10. Describe the relationship between the 2nd observed position and the DR position in determining if current is present. 11. Demonstrate proficiency in determining the set, drift and rate of the current when the DR position does not coincide with the DR position. 12. Demonstrate proficiency in determining CMG, DMG and SMG when the DR position does not coincide with the 2nd observed position.

Fishing Master Program Chartwork & Pilotage Book 1

9-3

Chapter 9 | The Effects of Wind and Current on a Ship

9.1 Positioning Review Lesson Introduction In this lesson we review the terminology and symbols used in chartwork when leeway and drift are present.

Assigned Reading Small Craft Piloting & Coastal Navigation: Pgs. 187-194

Lesson Notes In unit 8 we learned about Dead Reckoning. A process of taking your initial position, applying a true direction and distance to obtain a future position. If you navigating DR only at sea you would notice that most of the time your fixed position would differ from your DR position. The difference in a ‘fix’ and DR can be a result human error such as; - Poor helmsmanship - Calculation errors - Plotting errors - Speed errors, etc.

9-4

Chapter 9 | The Effects of Wind and Current on a Ship

However, if human error is kept to a minimum and the observed position still does not coincide with the DR position it means the vessel was acted on by some external force. Leeway is the pushing force of wind on the above water portion of the vessel. Drift is the influence of a current acting on the underwater portion of the vessel. It is worthwhile to note that the effect of these forces change as the speed or direction of the vessel changes throughout an evolution. While the DR position excludes leeway and drift it is imperative that the OOW consider these forces when operating at sea – neglecting them would be imprudent and could easily result in an accident. In chartwork, the integration of wind and current requires usage and familiarity of symbols and terminology that must be fully understood by the entire bridge team. While in reality, a ship can only be in one position at any one time it is normal practice for a ship to be assigned several positions depending on the method used to fix, or estimate, such position. While interpretations of ‘position’ and ‘dead reckoning’ vary in textbooks and from country to country the following positions, based on the British Admiralty system, are used in this course as follows (see Figure 9.1):

Observed Position (Obs.Pos.) Obtained from visual bearings of terrestrial objects, simultaneous star sights or some combination of sun, moon, planet and star sights, or reliable positions obtained from electronic navigational aids (GPS).

Dead Reckoning Position (D.R.) A position obtained using ONLY the courses steered and the distances run. Distances are calculated with the D = S x T formula.

Estimated Position (E.P.) A position based on course and distance since the last known position with an estimation made for leeway, set and drift of current or tidal stream.

Sea Position The point of termination of the water track (see later). Additional definitions which have relevance to position are as follows:

Wind Direction The direction FROM which the wind blows.

Leeway The effect of wind moving a vessel bodily to leeward (i.e. the side of the ship opposite to the wind).

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Chapter 9 | The Effects of Wind and Current on a Ship

Leeway Angle The angular difference between the WATER TRACK (see later) and the SHIP’S HEADING.

Set The direction TOWARDS which the current and/or tidal stream flows.

Rate The speed of the current or tidal stream expressed in knots

Drift The distance covered in a given time interval and due solely to the movement of a current and/ or tidal stream.

Ship’s Heading The horizontal direction of the ship’s head at any given time (underway or at anchor).

Course The intended heading of the ship.

Distance Run The distance derived from the D = S x T formula.

Track The path followed or to be followed between one position to another. This path may be ‘over the ground’ (ground track) or ‘through the water’ (water track).

Course Made Good (CMG) The track over the ground actually achieved over a given time interval.

Water Track The path THROUGH THE WATER between one position and another. This is sometimes referred to as Course Made Good Through the Water. Note: The student must appreciate that if an entire body of water is moving (because of a current and/or a tidal stream) the ship’s path in relation to fixed objects on land is different to its path in relation to the water through which it is moving.

9-6

Chapter 9 | The Effects of Wind and Current on a Ship

Figure 9.1 Illustration of definitions

Can leeway exist without current? Surface currents on the open ocean are generated by wind. Friction between the air and the surface of the water is such that a wind blowing for about 10 hours can produce a surface current in the water at about 2% of the wind velocity. So a steady wind blowing in a certain direction at 20 knots for about 10 hours will produce a surface water current at about 0.4 knots. However, it is still possible to encounter the effects of leeway without current, especially at the initial stages when winds first start to blow. Note: In the problems contained in this manual the forces of wind and current are isolated and treated separately and do not appear together in the same question. Since current is not present in leeway questions the water track becomes the Course Made Good (CMG) thereby eliminating the Sea position. Subsequently, the water track now terminates at the estimated position.

Figure 9.2 No Current: Water Track = CMG

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

Note: Modern electronic navigators do not really have to worry about leeway or drift as much as they did in the days when the paper chart, magnetic compass and speed log were the most important tools available to the navigator. Although these forces of nature are still present, they are not thought of in the same manner. What normally happens nowadays is that the skipper enters the coordinates of the destination (waypoint) into the GPS unit, then steams directly to that position. The Course Made Good (also known as Course Over Ground) information is provided in real-time allowing the operator to adjust the shipâ&#x20AC;&#x2122;s heading without having to estimate the effects of wind or current. In fact, it has been often stated that the COG information made available by the GPS is one of the most powerful features of the entire system.

9-8

ÂŠ Marine Institute of Memorial University

Chapter 9 | The Effects of Wind and Current on a Ship

9.2 Wind and the Effects of Leeway Lesson Introduction In this lesson we examine how the DR plot is manipulated and expanded to account for the force of leeway.

Learning Outcomes 1. Explain the relationship between the water track and the CMG if no current is present 2. Describe factors that influence the magnitude of leeway force. 3. Explain the process for applying leeway to the vessel’s DR track. 4. Demonstrate proficiency applying leeway in various situations.

Assigned Readings Small Craft Piloting & Coastal Navigation: Pgs. 170 -186

Lesson Notes Leeway is the effect of wind in moving a ship bodily to the leeward (downwind). Leeway angle is the angular difference between the water track and the ship’s heading. Therefore, it can be stated that the leeway angle is the amount (in degrees) which a vessel makes to the leeward of the intended heading (course). To find the water track (which is the CMG when no current is present), the estimated leeway angle is always ‘allowed’ away from the wind direction. In figure 9.3 the vessel is maintain a heading 240°T but leeway (8°) is forcing it off the DR track and causing a CMG of 232°T

Fishing Master Program Chartwork & Pilotage Book 1

Figure 9.3 Effect of leeway

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Chapter 9 | The Effects of Wind and Current on a Ship

Note: The word ‘allow’ or ‘allowing’ is used quite extensively in leeway problems (and especially on the TC final) and can cause some confusion. When reading a leeway question it may be stated…’a vessel is steering 240°T and allowing 8° leeway due to a northerly gale’, and if taken at face value you might assume that the OOW has already taken leeway into account by steering 240°T, however, it means that the ship’s head = 240°T and you must subtract the leeway angle to calculate the CMG of 232°T

Leeway Factors Factors which increase leeway include:

Wind angle A wind blowing on to the boat at an angle of 45° to the bow will cause more leeway than one on the beam. There will be none with the wind astern.

Boat design Vessels that are relatively beamy will slip sideways more when they heel than a yacht with a deeper draft.

Wind force The stronger the wind, the more leeway experienced.

Sea state Rough weather will increase leeway, because the boat will be carried sideways by breaking waves. In rough seas the boat can be felt to be swept a meter or two downwind when a wave breaks on the windward side of the vessel, this is especially the case if the boat is stopped by the force of a wave.

Boat speed Leeway increases as boat speed decreases. On a vessel that can make 20 knots, leeway will be minimal and for practical purposes can normally be ignored. However, if the sea state is such that the same vessel can only make 5 knots, the leeway may be considerable, especially on a high sided modern fishing vessel.

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Chapter 9 | The Effects of Wind and Current on a Ship

How to Apply Leeway Applying leeway is a similar process to applying compass error where the value for compass error is added or subtracted depending on if you need to convert from true to compass or compass to true as shown in the table below. Ship’s Head

Compass Error (C/E)

Add or Subtract C/E

Ship’s Head

1. True to Compass

165°T

10°W

Add

175°C

2. Compass to True

175°C

10°W

Subtract

165°T

Order of Conversion

The leeway angle separates course steered (or DR track) from the course made good (CMG), and like compass error, is added or subtracted depending on if you are given the ship’s head and need to find the course made good or vice versa. Example: Vessel is heading east, wind is from the north Order of Conversion

Given

Leeway Angle

Add/Subtract Leeway Angle

Final Answer

1. Ship’s head true (DR track) to CMG

Ship’s head: 90°T

7°

Add

CMG: 097°T

2. CMG to Ship’s head true (DR track)

CMG: 097°T

7°

Subtract

Ship’s head: 090°T

Rules for Leeway: When given the ship’s head, or course steered, and calculating the CMG Leeway angle is ADDED when the wind is on the port side of the vessel and always SUBTRACTED when it is on the starboard side. Starboard = subtract When given the Course to Make Good and calculating the Course to Steer (DR track) Opposite from above

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

Example 1: Find the water track (CMG) if a vessel is on a course of 230°T and the wind is SE with a leeway angle of 12°. Step 1: Determine the order of conversion. Here we are given the course steered, also known as the DR track or ship’s head true, and asked to find the CMG

Step 2: Draw a sketch of the DR plot to determine which side of the vessel the wind is striking. In this case the South East wind is striking the port side.

Step 3: Apply the leeway angle based on the above rules. In this case ADD because wind is striking the port side of the vessel. CMG

CMG = DR track + Leeway angle =

CMG = 230°T + 12° = 242°T

CMG = 242°T

Example 2: Find the true course made good, given a course of 304°C, Variation 16°W, Deviation 7°E, wind NNE, and Leeway Angle5°. Step 1: Determine the order of conversion. Here we are given the course steered, also known as the DR track or ship’s head true, and asked to find the CMG

Step 2: Apply compass error to convert ship’s head compass to ship’s head true Ship’s head compass: 304°C C/E

9-12

Ship’s head true (DR track):

9°W 295°T

Chapter 9 | The Effects of Wind and Current on a Ship

Step 3:

Draw a sketch of the DR plot to determine which side of the vessel the wind is striking. In this case the NNE wind is striking the starboard side.

Step 4: Apply the leeway angle based on above rules. In this case SUBTRACT because wind is striking the starboard side of the vessel.

Ship’s head true (DR track):

295°T

Leeway:

5°

CMG:

290°T

Example 3: A vessel requires a CMG of 180°T. Find the compass course to steer if variation 20°E, Deviation 2°E, wind Easterly, and Leeway Angle 5°. Step 1: Determine the order of conversion. Here we are given the CMG and asked to find the course to steer (which is also known as the ship’s head true or DR track).

Step 2: Draw a sketch of the CMG track to determine which side of the vessel the wind is striking. In this case the NNE wind is striking the port side.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 3: Apply the leeway angle based on above rules. Since we are converting from CMG to ship’s head true; Port = subtract Water Track (CMG): 180°T Leeway:

5°

Ship’s Head True: 175°T

Step 4: Calculate compass error.

C/E = variation + deviation

C/E = 20°E + 2°E = 22°E

Step 5: Apply compass error to convert from ship’s head true to ship’s head compass.

Ship’s head true:

C/E:

Ship’s head compass:

175°T 022°E 153°C

Abeam and Nearest Approach – No Leeway or Current Present In the absence of leeway or current, you are abeam and at nearest approach (NA) of an object when your relative bearing is 90° either Red or Green to your DR track (ship’s head true). Example: At 1500hrs, the OOW notes observes that the ship’s head is 090°T and speed is 12 knots. What is the time and vessel’s position when the tower is abeam if no leeway or current are present? Step 1:

Calculate the true bearing when the vessel is abeam:

DR track:

090°T

090° (Red)

Relative brg:

True brg:

000°T

Step 2: Plot the true bearing.

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 3: The point of intersection of the ‘abeam bearing line’ and DR track yields the vessels position when the object is abeam – it is also the point of nearest approach! From here you can calculate distance and time from the initial position to the 2nd observed (abeam) position.

Abeam and Nearest Approach – Leeway and/or Current Present When leeway or current are present, you are at nearest approach (NA) to an object where a relative bearing is 90° either Red or Green to your Course Made Good (CMG) track, or the CMG track is tangent to a specific ‘distance off’ circle. You are abeam when a relative bearing is 90° Red or Green to your DR track (ship’s head true); however, it is where this bearing intersects the CMG track that will give the vessel’s position.

Example: At 1500hrs, the OOW notes observes that the ship’s head is 090°T and speed is 12 knots. At what time and position does the closest approach to the tower occur? What is the vessel’s position when the tower is abeam? The vessel is experiencing 10° leeway due to a northerly wind. Step 1: Apply the leeway angle based on the above rules to calculate the CMG track. In this case ADD because wind is striking the port side of the vessel.

CMG = DR track + Leeway angle = CMG

CMG = 090°T + 10° = 100°T

CMG = 100°T

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 2: Calculate the true bearing when the vessel is at nearest approach: CMG track: 100°T Relative brg:

True brg:

090° (Red) 010°T

Step 3: Plot the true bearing.

Step 4: The point of intersection of the ‘nearest approach bearing line’ and CMG track yields the vessels position when the object is closest. From here you can calculate distance made good and speed made good to the closest approach.

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 5: To determine the vessel’s position when abeam, calculate and plot the true bearing when the vessel is abeam: DR track:

090°T

Relative brg:

090° (Red)

True brg:

000°T

The point of intersection between the ‘abeam bearing line’ and the CMG track yields the vessels position when the object is abeam and current and/or leeway are present. From here you can calculate distance made good and speed made good to when the object is abeam.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

Exercise 9.1: Leeway Chart 4320 1. Find the true course made good, given a course of 222°C, Variation 18°E, Deviation 9°E, wind NW, and Leeway Angle 12°.

2. Find the true course made good, given a course of 020°C, Variation 2°E, Deviation 16°W, wind East, and Leeway Angle 11°.

3. Find the true course made good, given a course of 164°C, Variation 10°E, Deviation 12°E, wind East, and Leeway Angle 6°.

4. A vessel departing Lunenburg alters course at the pilot station to pass one mile off Rose Point. If she allows 6° leeway for an easterly wind, what is the Gyro course to steer? Gyro error 3° low.

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Chapter 9 | The Effects of Wind and Current on a Ship

5. A vessel fixes her position by GPS as Lat. 44° 06.6N Long. 63° 49.5W. She sets a course of 340°T to enter St. Margaret’s Bay. If she is allowing 5° leeway for a westerly wind, what is the true course made good.

6. A vessel departing Halifax arrives at CIP (1B) at 1420. She then sets a course to pass five (5) miles off Egg Island allowing 10° leeway due to gale force easterly winds.

a. If the Gyro error is 2° high, what is the Gyro course to steer?

b. What is the ETA abeam Egg Island if the SMG is 8.2 knots.

7. At 0810 a vessel has East Ironbound Island light in transit with Pearl Island light, and Cross Island light abeam to starboard. She then sets a course to pass five (5) miles south of Sambro Island, allowing 10° leeway for a strong northerly wind.

a. If the compass error is 22° W, what is the compass course to steer?

b. What is the ETA to the nearest approach to Sambro Island if the SMG is 9.5 knots?

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

9.3 Current and the Effects of Set, Drift and Rate Lesson Introduction In this lesson we examine the effects of current on the DR plot.

Learning Outcomes 1. Describe the relationship between the 2nd observed position and the DR position in determining if current is present. 2. Demonstrate proficiency in determining the set, drift and rate of the current when the DR position does not coincide with the DR position. 3. Demonstrate proficiency in determining CMG, DMG and SMG when the DR position does not coincide with the 2nd observed position.

Assigned Readings Small Craft Piloting & Coastal Navigation: Pgs. 170 -186

Lesson Notes In the previous section we examined the effect of leeway on the vessel in the absence of current. In this section we are doing the opposite – here we have current but no leeway. The following example is used to illustrate how we know when current is acting on Figure 9.4 DR Plot the vessel – sometimes on an exam it is not obvious. Let’s assume we are aboard a fishing vessel in St. John’s harbour. The only tools available to us as navigators are a paper chart, magnetic compass, deviation card, speed log and a clock. Once we are up to cruising speed (10 knots) and clear the Narrows we determine our departure position at 1200hrs. Now we want to determine where we will be in one hour, based on a course of 070°T and speed of 10 knots. To do this we construct a typical DR plot. To see how accurate our plot is we have to execute our plan...that is, steam for an hour holding our course (070°T) and speed (10kts).

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Chapter 9 | The Effects of Wind and Current on a Ship

At the end of the time interval, we get a second fix. After plotting the second position we can clearly see that we did not end up at the DR position – where we thought we would! Some force pushed our vessel off course and slowed us down somewhat. In this course, the force that causes the difference between the DR position and the 2nd observed position is current. The current is represented by the blue vector with 3 arrow heads and is described by its set, drift and rate.

Figure 9.5 DR position and 2nd fix differ

Set (320°T) is the direction in which the current is moving or following from the DR to the 2nd observed position. Drift (3.0’) is the distance the ship would be moved by the current within the time interval. Rate is the speed of the current. It is calculated by: Rate = drift/time = 3/1 = 3kts.

Figure 9.6 Current Set, Drift and Rate

Course, Distance and Speed Made Good Up to this point we have been calculating the course, distance and speed of the vessel assuming there were no external forces on the vessel. However, when ‘current’ is present, it will introduce geographical error in dead reckoning. The DR position will not coincide with the 2nd observed position (as shown below). From this information the navigator can now determine the actual path, or Course Made Good (CMG) and Distance Made Good (DMG), the vessel followed over the ground. In this example, CMG and DMG are represented by the green vector. It is plotted from the initial position (1200) to the second observed position (1300). It is marked with a double arrow to indicate direction of travel.

Figure 9.7 Course and Distance Made Good

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

We can see in our example that if the current is setting 320°T with a rate of 3.0 knots it will yield a Course Over the Ground (COG), or CMG, of 063°T. The Distance Made Good (DMG) is also measured from the green vector and we can see that it is 9.0’ in length as compared to the DR plotted distance of 10.0’. Speed Made Good is found using the same formula as we used for calculating speed when constructing the DR plot (S=D/T), the only difference is we use DMG instead of the distance along the DR plot:

SMG = DMG/T SMG = 9.0’/1 = 9.0 kts. Some Examples to Clarify the Names Speed steamed = speed through the water – based on the DR track Speed made good = speed over the ground – based on the CMG track Course to steer = course through the water – based on the DR track Course made good = course over the ground – based on the CMG track

An example demonstrating these terms: A ship is in a river which has a current flowing at two knots downstream. The ship’s speed is 10 knots. When headed upstream the speed steamed is 10 knots through the water, but her speed over the ground or speed made good is 10knots – 2 knots = 8 knots. If the ship reverses her course, then the speed steamed (through the water) would still be 10 knots but the speed made good or over the ground would be10knots + 2 knots = 12 knots. If she stops her engine and drifts, the speed steamed is 0 but her speed made good is 2 knots downstream. If she steams up the river with a speed of 2 knots then the speed through the water will be 2 knots but her speed made good or speed over the ground will be zero (0). When two different forces act on the ship at the same time, the result will be a combination of the two forces. If a ship steams in one direction and current acts on the ship, the result will be, of course, the new position. If we can “subtract” the ship’s steamed course and distance from that new position we will have only the current and its direction left. We can do so by using vector calculation by construction.

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Chapter 9 | The Effects of Wind and Current on a Ship

Example: At 1520 hours a vessel steering 292°C observes Rochers au Cormoran bearing 026°Green at a distance of 14 nm. At 1720 hours Illes Triples light bears 081°green at a distance of 10’. The ship’s speed is 20 knots. Variation is 24°W. Deviation is 2°E. There is no leeway. i) Determine the set, drift and rate of the current, if any. ii) What is the vessel’s position and ETA when the starboard hand buoy C64 (near Rocher Cairnterr) is abeam? iii) What is the vessel’s position and ETA when the starboard hand buoy C64 (near Rocher Cairnterr) is at nearest approach?

Solution: Step 1:

Calculate compass error. C/E = 24°W + 2°E = 22°W

Step 2: Apply C/E to Ship’s head compass to calculate ship’s head true: Ship’s head compass: C/E:

Ship’s head true:

292°C 022°W (error west, compass best) 270°T

Step 3: Convert Rochers au Cormoran relative bearings to true:

Ship’s head true:

270°T

Rochers au Cormoran rel. brg: +

026° Green

Rochers au Cormoran true brg:

296°T

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 4: Plot the initial position.

Step 5: Complete the DR plot from the initial position.

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i) Calculate distance:

D = S x T = 20 kts x 2hr = 40.0â&#x20AC;&#x2122;

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 6:

Plot the DR track: 270°T for 40’.

Step 7: Convert Illes Triples light relative bearing to true:

Ship’s head true:

270°T

Illes Triples light rel. brg:

081°Green

Illes Triples light true brg:

Fishing Master Program Chartwork & Pilotage Book 1

351°T

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 8: Plot the 2nd observed position (Illes Triples light bears 351°T at 10’)

Step 9: Observe the chart to determine if the DR position and 2nd observed position coincide.

If there are in the same position no external force was acting on the vessel.

If there are in different positions an external force(s) were acting on the vessel. Note: in this course we handle leeway and current separately. In this problem the DR position does not coincide with the 2nd observed position therefore we can state that current has pushed the vessel off the DR track.

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 10: Determine the magnitude and direction of the current. Using the parallel ruler plot a line from the DR position to the 2nd observed position. Label the track with three arrowheads pointing in the direction of travel. Measure the true heading of the track to determine the heading, or set, of the current (128°T).

Measure the length of the track to determine drift (5.5’).

Calculate the rate (or speed) of the current using Rate = Drift/Time: Rate = 5.5’/2hr = 2.75kts

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 11: Determine the course made good (CMG), distance made good (DMG) and speed made good by plotting a line (green) from the initial position to the 2nd observed position. This is the CMG line – label it with a double arrow.

Measure the direction (CMG - 264°T) and length (DMG- 35.5’) of the track.

SMG = DMG/T

SMG= 35.5’/2hrs= 17.75 = 17.8 knots

Step 12: To find the position when abeam of starboard hand buoy C64, which is 90° relative red or green to the ship’s head, use the DR track to convert the relative bearing to the true bearing: DR track:

270°T

090° (Green)

Relative brg:

True brg:

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000°T

Chapter 9 | The Effects of Wind and Current on a Ship

Step 13: Plot the true abeam bearing – make sure it intersects the CMG track. The point of intersection of the ‘abeam’ bearing line with the CMG track is the vessel’s position when abeam.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 14: Measure the distance made good (DMG) from the initial position to the abeam position and use this to calculate the ETA:

i) Calculate duration to abeam position:

Time = DMG/SMG = 22.5â&#x20AC;&#x2122;/17.8kts = 1.26hrs

ii) Convert hours to hours and minutes:

1hr + (0.26 hrs. x 60) = 1 hr. 15.6min = 1 hr. 17min

iii) Calculate ETA: 15 20 + 01 17 16 37

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ÂŠ Marine Institute of Memorial University

Chapter 9 | The Effects of Wind and Current on a Ship

Step 15: To find the position when at nearest approach to starboard hand buoy C64, use the CMG track to convert the relative bearing to the true bearing: CMG track: 264°T Relative brg:

+ 090° (Green)

True brg: 354°T

Step 16: Plot the true nearest approach bearing – make sure it intersects the CMG track. The point of intersection of the ‘nearest approach’ bearing line with the CMG track is the vessel’s position when at nearest approach.

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

Step 17: Measure the distance made good (DMG) from the initial position to the nearest approach position and use this to calculate the ETA:

i) Calculate duration to nearest approach position:

ii) Convert hours to hours and minutes:

Time = DMG/SMG = 21.8â&#x20AC;&#x2122;/17.8kts = 1.22hrs

1hr + (0.22 hrs. x 60) = 1 hr. 13.2min = 1 hr. 13min

iii) Calculate ETA:

15 20 + 01 13 16 33

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Chapter 9 | The Effects of Wind and Current on a Ship

Exercise 9.1: Current: Set, Drift and Rate Chart 4025 1. At 0247 the navigator on a vessel steering a course of 110°C observes Ile a Firmin light bearing 116° red; at the same time Petite Ile au Marteau light bears 057°C. If the course, and speed of 10kts, are maintained for 6hrs what is the true course, DR distance, DR coordinates and ETA to DR position?

At 0847 the navigator observes Ile Joncas light at 052°C and 7.2’. What are the coordinates of the second observed position?

What are the set, drift and rate of the current? What are the CMG, DMG and SMG?

Variation = 22°W

Deviation 2°E

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

2. At 0808 the navigator on a vessel observes the extreme westerly tip of Pointe de Natashquan in transit with the church spire on Pointe Parent abeam on the port side. At the same time the range to the westerly tip of Pointe de Natashquan is 3.5’.

i) If the course, and speed of 10 kts, is maintained for 3hrs 30minutes what will be the coordinates and ETA of the DR position?

At 1138 the navigator observes Iles Triplet light 90° Red at 7.0’.

ii) What is the 2nd observed position?

iii) What are the set, drift and rate of the current, if any?

iv) What are the CMG, DMG and SMG of the vessel during this time interval?

v) What is the vessel’s position and ETA when abeam of Pte de Kegashka light?

vi) What is the vessel’s position and ETA when at the nearest approach of Pte de Kegashka light?

Variation = 22°W

Deviation Card A

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Chapter 9 | The Effects of Wind and Current on a Ship

3. A vessel is on a course of 320°C. At 1815 the navigator observes Cap de la Table light bearing 264° relative at a range of 5.1’.

i) If the present course, and speed of 8.8 kts, is maintained for 5hrs 12minutes what will be the coordinates and ETA of the DR position?

After 5hrs 12 min have elapsed, the navigator observes Pointe Carleton bearing 276°C at a range of 8’.

ii) What is the 2nd observed position?

iii) What are the set, drift and rate of the current, if any?

iv) What are the CMG, DMG and SMG of the vessel during this time interval?

v) What is the vessel’s position and ETA when abeam of Pte de Kegashka light?

vi) What is the vessel’s position and ETA when at the nearest approach of Pte de Kegashka light?

Variation = 22°W

Deviation Card A

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Chapter 9 | The Effects of Wind and Current on a Ship

4. A vessel is on a course of 300°C. At 1942 the navigator observes Escarpement Bagot light abeam on the starboard side at a range of 6.0’. If the course, and speed of 8.0 kts, is maintained for 7hrs what will be the coordinates and ETA of the DR position?

After the 7hrs has elapsed, the navigator observes Point du Sud-Ouest bearing 065° relative at a range of 11.3’. What is the 2nd observed position?

What is the set, drift and rate of the current? What is the CMG, DMG and SMG?

Variation = 19°W

Deviation Card A

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Chapter 9 | The Effects of Wind and Current on a Ship

5. 0010 - A vessel steering 216°C observes Pointe de Kegaska Island light dead astern, range 6.9’, speed 8.6kts

0710 - Point Heath bears 68° green at 20.2’.

Find the following:

i) Initial position

ii) True course

iii) Distance steamed

iv) DR position

v) 2nd Observed position

vi) Set, drift and rate of the current.

vii) CMG, DMG and SMG

Variation = 20°W

Deviation 6°W

Fishing Master Program Chartwork & Pilotage Book 1

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Chapter 9 | The Effects of Wind and Current on a Ship

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ÂŠ Marine Institute of Memorial University

Sample Exams

SAMPLE EXAM: A CHART: 4320

DEV. CARD: A

VAR. 19Â°W

1. Answer the following questions from Chart 4320. (a) What type of projection is this Chart? (b) In what units are the soundings given on this Chart (c) What is the adjoining chart to the west of this chart? Chart number (d) What is the characteristic of Chebucto Head Light? (e) What is the height of Sambro I. Light (f) What is the fog signal of Betty I. Light? (g) What is the range of Egg Is. Light? (h) Is Chart 3624 a larger or smaller scale than Chart 4320? (i) What is the calculated variation for 2013 to the west of Halifax? (j) Up to what date and notice number has this chart been corrected through Weekly Notices to Mariners.

â&#x20AC;&#x192;

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

2. A vessel inbound St. Margaret's Bay obtains a radar range of White Pt. to be 4.4 miles and Peggy's Cove 3.2 miles. What is the vessels position.

Lat:

Long:

â&#x20AC;&#x192;

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Sample Exams

3. At 0825 Sambro Is. is bearing 317° Gyro, range 4 miles from a vessel steering 065° Gyro at 11 knots. At 1004 Jeddore Rock is bearing 049° Gyro, distance 7.8 miles. Gyro error is 2° High. What is the position in latitude and longitude at 0825 and at 1004?

0825 Position: Lat:

Long:

1004 Position: Lat:

Long:

What is the set and drift of the current? Rate:

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

4. At 2132 a vessel has Indian Island (South End) bearing 310°T, distance 6.2 miles. The course is 050°T and speed is 8 knots. At 2232 you have Mosher Is. and West Ironbound Is. lights in line bearing 286°T and Cross Island light bearing 359°T. Find the position in latitude and longitude at 2132 and 2232. What is the set and drift and rate of the current.

2132 Position: Lat:

Long:

2232 Position: Lat:

Long:

Set

Drift

Rate: 5. Find the compass course to steer to pass 3 miles off Pearl I. to 5 miles off Pennant Pt. using deviation card “A” and variation 19°W

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Sample Exams

SAMPLE EXAM: B CHART: 3624

DEV. CARD: A

VAR: 21°E

1. At 1706 a vessel on a course of 220°T observes Cape Scott abeam on the starboard side at a range of 2.2'. What is her position?

2. At 2001 a vessel finds her position to be N50° 27.3 W128° 24.4'. At 2116 she observed Donald Island Lt bearing 066°T while at the same time Solander Island Light was bearing 170°T. What is the true course, compass course and speed of the vessel?

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

3. At 0330 a vessel steaming at 10.2 kts on a course of 290°C observes Kains Is Light in line with Cliffe Pt. Light bearing 045°C at a range of 3.5 nm.

What is the initial position? Lat:

Long:

What is the Compass Error? What is the DR position at 0517?

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Sample Exams

4. At 1200 a vessel in position N50° 22.1' W128° 05.1' wishes to pass 0.6’ off Billard Rk buoy. What is the True course to steer if the wind is northwest and leeway is estimated to be 4°? What is the Gyro course if Gyro error is 2° Low?

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

SAMPLE EXAM: C CHART: 4320

DEV. CARD: A

VAR: 18°W

1. At 0249 a vessel on a course of 183°C has Pearl Island Lighthouse and East Ironbound Lighthouse in line dead astern. At the same time Cross Island Lighthouse is bearing 279°C. What is the vessel’s position?

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Sample Exams

2. At 2144 a vessel steering 135°C has Sambro Is. Lighthouse bearing Red 075° and Betty Is. Lighthouse bearing 210° relative. What is the vessel’s position and distance of each lighthouse?

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

3. At 1911 a vessel on a course of 330°C is southwest of Halifax and obtains two radar ranges; Pennant Pt., range 4.9 miles and the south point of Betty Island 3.7 miles. Radar range error is 6% long. Find the vessel’s position and the bearing and distance to whistle buoy E50.

4. At 14:00 a vessel obtains a Loran-C fix, Lat. 44 09.3'N, Long. 063 30.4'W.

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a) What is the range and bearing to Sambro Island light?

b) She then steers a course of 334°C, speed 8 knots to enter St. Margaret’s Bay. At 1630 Peggy’s Cove Lighthouse is bearing 356°C and Betty Island Lighthouse bears 100°C. What is the position at 1630, and the set and rate of the current experienced since 1400?

Sample Exams

5. A vessel is steering a course of 055 magnetic and allowing 5Â° leeway for an easterly wind.

a) What is the true course made good (TCMG.)

b) If the deviation is 6W, what is the compass course?

â&#x20AC;&#x192;

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

SAMPLE EXAM: D CHART NO. 4855

DEVIATION CARD “A”

VARIATION: 22°W

1. In chartwork, most of the time we work on the notion that we are without a GPS or Loran C for position fixing. Instead we rely on the intersection of two lines (which we usually have to plot on the chart) known as.

2. When completing the chartwork exam at Transport Canada and you read the words ‘in line with’ i.e. Pearl Is light in line with Sambro Is light refers to what type of problem?

3. When attempting the chartwork exam, what is the first thing you should notice about the deviation card?

4. When calculating ETA (estimated time of arrival) and you are using the formula Time = Distance/ Speed and obtain a result of 4.22, how would be convert it to something useful for our purposes?

5. Can a depth contour be used as a LOP (line of position)?

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Sample Exams

6. The deviation card at the exam is given to you in compass degrees. If you are steering 105째 T and variation is 15째W. Can you read the deviation right off the card or will you have to manipulate your card?

7. When you know a problem infers the use of transit bearings, what do you normally find first with this information?

8. If you are given a chart on the east coast of Canada, do you expect variation to be east or west?

9. We have been using bearing lines quite a lot in our chartwork class. These bearing lines are also known as LOP. What instrument would you use to obtain such a bearing line if you did not have a radar?

10. What function of your radar would yield the relative bearing of another vessel?

11. Adding 째E to 째W to is functionally the same as subtracting. How is the difference labeled?

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

12. If a Loran station is reported by Coast Guard Marine Radio to be shutting down for repairs on July 15 for 1430 ZULU to 1900 ZULU, what hours would it be off the air in NDST?

13. If you determine your position with three bearing lines (instead of two) to help improve accuracy, you may end up with the situation depicted in the image. This is known as a? â&#x20AC;&#x192;

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ÂŠ Marine Institute of Memorial University

Sample Exams

1. Convert the following to degrees and tenths of degrees. Show all workings.

a) 56° 12.4°

b) 24° 27.0°

c) 0° 45.3°

d) 47° 36.0°

e) 01° 33.0°

f) 89° 07.1°

g) 172° 54.3°

h) 21° 19.9°

i) 180° 20.0°

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

j) 10° 01.1°

2. Convert the following to minutes and tenths of minutes. Show all workings.

a) 19.1°

b) 17.9°

c) 179.9°

d) 0.9°

e) 10.4°

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Sample Exams

3. Solve the following short word problems (no chart is needed). Show all workings. a) A vessel is in position A at 2113 hrs. 95 minutes later, it is in position B, which is 12.3 miles away. What is the speed vessel and ETA to position B?

b) A vessel leaves Position A at 2330 hrs on November 17th at a speed of 15.7 kts. At 0119 on November 18 how far has it steamed?

c) At 0347 hrs a vessel departs position N 44° 29.8' W063 22.0' and steams 270°T for 21.7' to its destination. If the vessel averaged a SMG of 11.1 kts, what was its ETA? What is its latitude at its destination?

d) A vessel departs St. Anthony at 2121hrs on November 30th and maintains an average SMG of 12.3kts steering 110°M. It steams for 13 hours 14 minutes until it reached its first string of crab gear. How far did it go? What was the ETA to the gear?

e) A vessel finds itself in position N 49° 29.8' W051 06.0' at 1200 hrs steaming due south (180°T). What will be its DR position (lat/long) at 1520hrs if it is steaming 7.9kts?

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

f) A vessel departs the fishing ground at 2144 hrs on November 17. Distance to the wharf in Port Union is 126'. What is its ETA if it averages 7.3 kts?

g) A vessel observes Point A in line with Point B bearing 100° C. If the variation is 13.3°E and deviation is 3.3°W, what is the true bearing?

h) A vessel observes Point A in line with Point B bearing 225° C. If the true bearing is 237°T and variation is 13.7°E, what is the deviation?

i) A vessel is steaming true north for 4 hrs 44minutes from position N 60° 00.0' W 060° 00.0'. What will be its final position and ETA if it averages 9.9 kts.

j) A vessel steaming 090°T finds its latitude to be 0°. How many degrees of longitude will cover if is steaming 10kts for 360 minutes.

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Sample Exams

4. At 0101hrs a vessel steaming 7.7 knots on a course of 010°T is in position N48° 38.1 W053° 30.5. What is the DR position in 1 hour? At 0201 the vessel was observed Puffin island light to bear 278°T at a range of 4.7’. What is the set, rate and drift of the current? What is the course made good (CMG) and speed made good (SMG) of the vessel?

5. A vessel departing from Eastport is steaming 7.0 knots and on a course of 045°T. At 1313her position is observed to be 1.5’ due north of the northerly light in Bishop’s hr. At 1419 she observes Puffin Island Lt to be 237°T at a range of 4.9’. What is the DR position? What is the CMG? What is the SMG?

Fishing Master Program Chartwork & Pilotage Book 1

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Sample Exams

SAMPLE EXAM: E CHART NO. 4025

DEVIATION CARD “A”

VARIATION: 21°W

1. At 1800 a vessel, making a speed of 6 kts has Pointe Carleton Light bearing 192° T at a range of 2.5 nm. You wish to proceed to a position with Pointe Du Vieux Poste bearing 356° T and the Light on Pointe De Kegaska bearing 056° T.

True Co.

Var.

DMG

. Mag. Co.

. Dev.

. ETA

. Comp. Co.

. C/E

1800 Fix; Lat:

Long:

2. At 2300 a vessel is steering 072° T and Iles Triples Light and Mackenzie Pointe are in line bearing 020° C at a distance of 8 nm. From this position she continues for a distance of 15.7 nm.

What type of buoy will be found after the run?

True Co.

Var.

. Mag. Co.

. Dev.

. Comp. Co.

. C/E

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Sample Exams

3. At 0600 a vessel on a course of 200° T observes Escarpement Bagot Light to be bearing 160° Rel. and at a radar range of 15 nm.

True Brg.

0600 Fix; Lat:

Long:

4. What is the position when Pointe Heath Light bears 220° T at a radar range of 7 nm? Lat:

Long:

5. What does the purple shaded area in approximate position 49° 58’ N 059° 40’ W indicate?

6. If wish to use a chart for 48° 00’ N 062° 00’ W, which chart would you use?

A) What is the name of this buoy? B) If it has a topmark, what is it? C) If it has a topmark, what color is it? D) What are its light characteristics?

8. Q(6+LFl)15s What buoy would have these light characteristics?

VQ(6+LFl)10s What is its topmark?

Fishing Master Program Chartwork & Pilotage Book 1

E-23

Sample Exams

A) What is the name of this buoy? B) What color is it? C) What action would you take if it was encountered?

D) What are its light characteristics?

10. Name the following symbols.

E-24

ÂŠ Marine Institute of Memorial University

References

Coolen, E. J. (1987). Nichollsâ&#x20AC;&#x2122;s Concise Guide to Navigation, Volume 1, 10th Edition. Glasgow: Brown, Son & Ferguson, Ltd.

Monahan, K & Douglas, D. (1998). GPS Instant Navigation: A Practical Guide from Basics to Advanced Techniques. Washington: Fineedge.Com Llc.

Moore, D.A. (1981). Marine Chartwork, 2nd Edition. London: Stanford Maritime Limited.

Saunders, A. E. (1990). Small Craft Piloting & Coastal Navigation. Halifax: Binnacle Navigation Instruments.

Fishing Master Program Chartwork & Pilotage Book 1

R-3

Deviation Card A

DEVIATION CARD A

Ship’s Head Compass

Deviation

Ship’s Head Magnetic

Ship’s Head Compass

Deviation

000°C

2.0° W

358°M

180

2.0 E

010

4.0 W

190

1.0 E

020

7.0 W

200

3.0 W

030

9.0 W

210

6.0 W

040

10.0 W

220

9.0 W

050

8.0 W

230

11.0 W

060

6.0 W

240

8.0 W

070

6.0 W

250

5.0 W

080

3.0 W

260

2.0 W

090

1.0 W

270

1.0 E

100

0°

280

4.0 E

110

3.0 E

290

6.0 E

120

5.0 E

300

9.0 E

130

8.0 E

310

11.0 E

140

10.0 E

320

8.0 E

150

10.0 E

330

5.0 E

160

7.0 E

340

2.0 E

170

5.0 E

350

0°

113

Fishing Master Program Chartwork & Pilotage Book 1

Ship’s Head Magnetic

245

350

DC-3