1 Marine chart methods

Contents

1.1 Review of bearing and distance

1.2 Distance and direction on marine charts 1.3 Dead reckoning

Chapter review

1

Marine chart

methods

Syllabus subject matter

_Syllabus

guide chapter 1

Maps and compasses—navigation

■ Nautical miles and knots

■ Use of maps and charts, compasses, dividers and parallel rulers or their equivalent

1.1

Review of bearing and distance

In Year 11, you learnt that directions on the Earth are given in terms of the angle between a north line and the desired direction. However, three different north directions may be used, depending on the purpose and the map used.

Maps and diagrams are usually drawn so that north is to the top of the page.

True bearings, grid bearings and magnetic bearings

The bearing of a directional line is the clockwise angle between north and the direction. The bearing is stated as a three-digit number between 000° and 360°. The bearing is stated as a true bearing (T), grid bearing (G) or magnetic bearing (M), depending whether true north (TN), grid north (GN) or magnetic north (MN) is used. The angles between true, grid and magnetic north vary from place to place. The angle between true north and magnetic north is called the declination (variation or magnetic variation). An easterly variation means that magnetic north is east of true north. Magnetic variation changes over time as the magnetic field of the Earth changes, so maps and charts specify the variation for a particular year, and usually give an estimate of the annual change.

The angle between true north and grid north is called the grid convergence and does not change.

The angle between grid north and magnetic north is called the grid/magnetic angle and changes with time.

On a map or chart, the angles between true north, grid north and magnetic north are shown by a grid declination diagram or compass rose.

Magnetic north is usually shown by a half-arrow , and true north may be shown by a star or full arrow .

GN TN

MN

GRID/MAGNETIC ANGLE 8°26′ GRID

CONVERGENCE 0°45′

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1975. ANNUAL CHANGE IS 05′ EASTERLY.

!

How do you use a map to find where you are? How do you use it to find the correct direction to travel in order to reach your destination? How long will it take to get there? These are questions about navigation—whether on land, in the air or at sea. The main methods of navigation were developed for marine

When using a grid declination diagram, you must take account of the change in variation between the date shown on the map and the date for which the bearing is calculated. When dealing with accurate bearings, you may need to convert between degrees and minutes. Find the bearing of K from P.

Solution

You can use a 180° or 360° protractor. Place the protractor so that the centre is at the vertex of the angle. Make sure that the 0° or 180° line is on the north line.

Measure the angle, being sure to use the correct scale.

For a 180° protractor, calculate the bearing, if necessary.

Bearing= 180°+ 32° = 212°

Write the answer. The bearing of K from P is 212°.

N P K 90 100 110 120 130 140 150160 170 180 80 70 60 50 40 30

20 _{10 0}

90 80 70 60 50 40 30 20 10 0 100 110 120 130 140 150 160 _{170 180}

N P K 90 80 70 60 50 40 30

20 10 0

100 110 120 130 140 150

160 ₁₇₀ 180

270 280 290 300 310 320 330 340 350 260 250 240 230 220 210 200 ₁₉₀ 350 340 330 320 310 300 290 280 270 260 240 250 230 210 200 220 190 10 ₂₀ 30 40 50 60 70 80 90 100 120 110 130 150 160 140 170 N P K

Example

1

Angle units

Each degree is divided into 60 minutes of arc. Each minute of arc is divided into 60 seconds of arc. The symbols used for degrees, minutes and seconds are °, ′ and ″ respectively.

1° = 60′ (1 degree = 60 minutes) 1′= 60″ (1 minute = 60 seconds)

From Example 2, we can work out a general rule for the change in a bearing as the direction of north is changed.

In 1975, the bearing of a water tower from the town hall was 215°18′ M. The annual change in magnetic variation is 3′ easterly. What is the bearing in 2006?

Solution

Draw a diagram showing information. The diagram shows that the new bearing is

less than the old bearing.

You should be able to calculate the difference by entering 215°18′ − 1°33′ directly on

your calculator using the or key.

Calculate the time difference. Time= 2006 − 1975

= 31 years Calculate magnetic change. Change of variation= 3′× 31 = 93′

=1°33′ easterly

Calculate new bearing. New bearing= 215°18′− 1°33′

Subtract degrees and possible minutes. = 214°− 15′

Subtract remaining minutes. = 213°45′

Write the answer. The bearing in 2006 is 213°45′ M.

2006 1975

Water tower

Town hall

215°18′ 1°33′ easterly change

DMS ° ′ ″

Example

2

Alternative

method

Bearing changes

An easterly change of the north direction (a change towards the east) reduces

the bearing.

A westerly change of the north direction (a change towards the west) increases

the bearing.

!

A map has the grid declination diagram shown. In 1985, a pond had a true bearing of 128°46′ from the top of a hill.

a What is the grid bearing in 2005? b What is the magnetic bearing in 2005?

GN TN

MN

GRID/MAGNETIC ANGLE 10°12′ GRID

CONVERGENCE 1°24′

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC ANGLE IS CORRECT FOR 1985. ANNUAL CHANGE IS 04′ WESTERLY.

Solution

Redraw the grid declination diagram for 2005, moving magnetic north 1°20′ to the west.

Grid/magnetic angle= 10°12′ − 1°20′

= 8°52′

Draw a diagram to show the true bearing, true north and grid north in 2005.

b Draw a diagram to show the true bearing, true north and magnetic north in 2005.

True/magnetic angle= 8°52′ − 1°24′

= 7°28′

Calculate the time difference. Time= 2005 − 1985

= 20 years Calculate magnetic change. Change of variation= 4′× 20 = 80′

=1°20′ westerly

a True bearings do not change. True bearing in 2005= 128°46′ T

Grid north is west of true north, so the bearing is increased.

Grid bearing in 2005= 128°46′+ 1°24′

= 130°10′ G

Magnetic north is east of true north, so the bearing is reduced.

Magnetic bearing in 2005= 128°46′− 7°28′

= 121°18′ M

GN

TN MN

GRID/MAGNETIC ANGLE 8°52′ GRID

CONVERGENCE 1°24′

2005

GN TN GRID CONVERGENCE 1°24′

2005

Pond 128°46′ Hill

TN

TRUE/MAGNETIC ANGLE 7°28′

2005

Pond 128°46′ Hill

MN

A map has the grid declination diagram shown. From a fire tower, a hill has a magnetic bearing of 258°22′ in 2000. Calculate:

a the grid bearing in 2000 b the true bearing in 2020 c the magnetic bearing in 2020.

GN TN MN

GRID/MAGNETIC ANGLE 3°58′

GRID

CONVERGENCE 1°32′

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1971. ANNUAL CHANGE IS 04′ EASTERLY.

Solution

a Draw a diagram to show the magnetic bearing, magnetic north and grid north in 2000.

b Draw a diagram to show the grid bearing, grid north and true north in 2020. The grid bearing doesn’t change (from 2000).

c Draw a diagram to show the grid bearing, grid north and magnetic north in 2020. The grid bearing doesn’t change (from 2000).

You could also work from the true bearing and true north or the original magnetic bearing. Calculate the time differences for 2000 and 2020 from 1971.

Time 1= 2000 − 1971 Time 2= 2020 − 1971

= 29 years = 49 years

Calculate magnetic change. Change 1= 4′× 29 Change 2= 4′× 49

= 116′ = 196′

=1°56′ easterly =3°16′ easterly

Redraw the grid declination diagrams for 2000 and 2020, moving magnetic north 1°56′ and 3°16′ east respectively.

Grid/magnetic angle in 2000= 3°58′− 1°56′

= 2°02′

Grid/magnetic angle in 2020= 3°58′− 3°16′

= 42′

Grid north is east of magnetic north, so the bearing is reduced.

Grid bearing in 2000 = 258°22′− 2°02′

= 256°20′ G

True north is westof magnetic north, so the bearing is increased.

True bearing in 2020 = 256°20′+ 1°32′

= 257°52′ T

Magnetic north is west of grid north, so the bearing is increased.

Magnetic bearing in 2020= 256°20′+ 42′

The Universal Transverse Mercator Projection (UTM), used as the base for most modern land maps, has three north directions.

Work in groups to compare the magnetic variations and grid declinations of adjacent maps based on the UTM. You should use maps at a scale of between 1 : 50 000 and 1 : 250 000. Use at least three maps that are side by side to see if there is any pattern in the differences between the north directions. If you have the maps available, you could also compare the variations and declinations on maps that are above each other.

The grid declination diagrams below are taken from some adjacent maps of Queensland areas, covering an area from Brisbane westwards towards the border. These maps are all at a scale of 1 : 100 000 and are from zone 56 of the UTM. This zone has the 153° line of longitude as its central meridian, and covers 3° either side. The Brisbane map is just east of the central meridian.

If you have maps of a more northerly or southerly area available, you should compare these to this strip.

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1976. ANNUAL CHANGE IS 0.1° EASTERLY EVERY 4 YEARS.

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1975. ANNUAL CHANGE IS 0.1° EASTERLY EVERY 4 YEARS.

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1973. ANNUAL CHANGE IS 02′ EASTERLY.

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1973. ANNUAL CHANGE IS 02′ EASTERLY.

TNGN MN

Kogan (9043) 1st Ed.

151°30′ 151°00′ 150°30′ GRID/MAGNETIC ANGLE 8°45′ GRID CONVERGENCE 1°02′

TNGN MN

GRID/MAGNETIC ANGLE 9°00′ GRID

CONVERGENCE 0°48′

Dalby (9143) 1st Ed.

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1978. ANNUAL CHANGE IS 0.1° EASTERLY EVERY 3 YEARS.

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1983. ANNUAL CHANGE IS 0.1° EASTERLY EVERY 2 YEARS.

TNGN MN

Caboolture (9443) 1st Ed.

153°34′ 153°00′ 152°30′ GRID/MAGNETIC ANGLE 10.5° GRID CONVERGENCE 0.1° TN GN MN GRID/MAGNETIC ANGLE 11.3° GRID CONVERGENCE 0.1°

Brisbane (9543) 2nd Ed.

TNGN

MN

Oakey (9243) 1st Ed.

152°30′ 152°00′ 151°30′ GRID/MAGNETIC ANGLE 9.6° GRID CONVERGENCE 0.6° TNGN MN GRID/MAGNETIC ANGLE 9.9° GRID CONVERGENCE 0.3°

Esk (9343) 1st Ed.

1 Use the diagram below to find the bearings of P, Q, R, S, T, U and V from C.

2 Use the diagram below to find the direction (bearing) that must be taken at each point to travel the route ABCDEFG.

N

P

Q

R

S

T U

V

C

N

A

N

N N

N N

B

E

D C

F G

Exercise 1.1

Review of bearing and distance

Additional exercise

3 In 1971, the bearing of a hill from a trig point was 297°12′ M. The annual change in magnetic variation is 08′ westerly. What is the magnetic bearing in:

a 1980? b 1990?

c 2003? d 2010?

Modelling and problem solving

4 The diagram at right shows the grid declination for a particular area. What are the grid and magnetic bearings in 2005 for the following true bearings?

a 235°46′ b 080°24′

c 303°13′ d 188°45′

e 348°56′

5 The diagram at right shows the grid declination for a particular map. The following magnetic bearings were obtained in 2000 for the directions of some points shown on the map. What are the grid bearing and true bearings in 2010?

a 003°05′ b 109°18′

c 067°53′ d 294°41′

e 277°36′

6 The grid declination diagram for a map is shown at right. The following grid bearings were found using the map. Work out the true bearings and magnetic bearings in 2013.

a 342°28′ b 027°59′

c 123°41′ d 236°20′

e 197°16′

GN TN

MN

GRID/MAGNETIC ANGLE 7°32′ GRID

CONVERGENCE 0°24′

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1979. ANNUAL CHANGE IS 06′ WESTERLY.

GN TN MN

GRID/MAGNETIC ANGLE 8°16′

GRID

CONVERGENCE 1°55′

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1973. ANNUAL CHANGE IS 09′ EASTERLY.

GN TN

MN

GRID/MAGNETIC ANGLE 5°08′ GRID

CONVERGENCE 2°13′

1.2

Distance and direction on marine charts

The maps used in sea navigation are called marine charts. They are usually based on the Mercator projection because it shows directions correctly. Lines of latitude and longitude are marked on the charts so that positions can be determined. The scale of a Mercator projection changes with latitude. The scale changes so that, as you move further away from the equator, areas and distances are magnified. This means that any given scale can be used on only part of the chart.

Even though the scale changes on a marine chart, traditional measurements make it relatively easy to find distances.

Nautical miles and knots are used in both marine navigation and air navigation. Extra

material

Map projections

A nautical mile is the distance of 1 minute of latitude, along a meridian. It is equal to 1852 m. One degree of latitude is 60 nautical miles.

Speed is measured in knots.

1 knot (kn) = 1 nautical mile/h = 1.852 km/h

!

A boat travels along a meridian from 32°47′S 163°E to 38°26′S 163°E. How far does it travel? Give your answer in both nautical miles and kilometres.

Solution

Calculate angle along meridian. Travel angle= 38°26′− 32°47′

Change 1° to 60′. = 37°86′− 32°47′ = 5°39′

Change to minutes. = 5 × 60′+ 39′ = 339′ of latitude 1′ of latitude = 1 nautical mile Distance= 339 nautical miles ≈ 628 km 1 nautical mile = 1.852 km = 339 × 1.852 km

Write the answer. The boat travels 339 nautical miles or about 628 km.

Distances along parallels of latitude cannot be so easily calculated. The parallels are smaller circles at higher latitudes, so the distance changes with the latitude. As you saw in Year 11, the cosine function is used to calculate these distances.

At latitude 40°S, 1′ of longitude = cos 40° ≈ 0.766 nautical miles

A speedboat travels south along a meridian through 2°45′ of latitude in 5 hours. Find its speed in knots and kilometres/hour.

Solution

Change angle to minutes. Travel angle= 2°45′

1°= 60′ = 2 × 60′+ 45′

= 165′ of latitude 1′ of latitude = 1 nautical mile Distance= 165 nautical miles

Use speed = Speed=

= 33 knots 1 knot = 1.852 km/h = 33 × 1.852 km/h

≈ 61 km/h

Write the answer. The speed of the boat is 33 knots or about 61 km/h.

distance time

--- . 165 nautical miles 5 hours

---Example

6

One minute of longitude, along a parallel, is a distance of cos θ nautical miles, where θ is the latitude.

!

Calculate the distance in nautical miles and kilometres when a plane flies from 28°S147°48′E to 28°S 144°14′E along a parallel of latitude.

Solution

Calculate angle along parallel. Travel angle= 147°48′− 144°14′

= 3°34′

Change to minutes. = 3 × 60′+ 34′

= 214′ of longitude at latitude 28°S Use 1′ = cos 28° nautical miles. Distance= 214 × cos 28° nautical miles

≈ 214 × 0.8829 nautical miles

≈ 189 nautical miles 1 nautical mile = 1.852 km = 189 × 1.852 km

≈ 350 km

Write the answer. The plane flies about 189 nautical miles or 350 km.

Marine charts based on a Mercator projection have latitude and longitude scales marked on the edges of the paper. Distance can be measured directly using the latitude scale on the side of the chart. The scale of the Mercator projection expands as latitude increases. Therefore, you must use the part of the latitude scale directly opposite the measurement.

The Transverse Mercator projection is sometimes used for large-scale charts that show only a small area, such as charts of the Moreton Bay islands used by local boaties. The grid on these charts normally has spacings in kilometres, usually 1 km or 2 km, although 10 km grids are used on smaller-scale UTM maps of larger areas of land. The grid is numbered in kilometres. Dividers are used to measure and transfer distances on charts. A Mercator chart is recognised by the latitude scale at the side. A UTM chart is recognised by the square grid marked on the chart, and numbered in kilometres along the edges.

Use of dividers on charts

1 Set the dividers to the distance on the chart.

2 • On a Mercator chart, move the dividers to the side scale opposite the

measurement and read the number of minutes of latitude. This is the distance in nautical miles.

• On a UTM chart, move the dividers to the grid to read the distance. The grid size is given on the edges in kilometres.

You can use a ruler instead of dividers but will need to take greater care.

!

Use dividers to find the distance from Cape Conway to Cape Hillsborough.

DEPTH IN FATHOMS Hillsborough Channel

Map © Australian Hydrographic Service

Solution

Place the dividers on the chart and open out to the required distance.

Transfer the dividers to the side, directly opposite the measurement, and read the number of minutes.

Write the answer. It is 23.5 nautical miles from Cape Conway to Cape Hillsborough.

DEPTH IN FATHOMS Hillsborough Channel

Map © Australian Hydrographic Service

DEPTH IN FATHOMS Hillsborough Channel

On marine charts, the relationship between magnetic bearings and true bearings is very important. A compass rose is normally printed on the chart, and shows the true bearings. It is like a 360° protractor printed onto the chart. On some large-scale marine charts showing small areas, the rose is printed with a (red) magnetic rose inside it. On other charts the magnetic variation is printed in the centre of the compass rose, with a line showing magnetic north. Small-scale marine charts showing very large areas may have magnetic variation curves printed on the chart. This is because in the oceans the magnetic variation changes in a systematic way unaffected by the mineral deposits in continents.

Use dividers to find the shortest distance between Heath Island and Flinders Reef off the northern end of Moreton Island on the chart shown below.

Solution

Note that this chart has a 2 km grid (edge numbering is in even numbers). Each centimetre is 1 km.

Place the dividers on the chart and open out to the required distance. Transfer the dividers to the grid, and read the distance in kilometres.

Write the answer. It is about 7.5 km between Heath Island and Flinders Reef.

40 42 44 46 48 50 52

16

14

12

10

8 18

DEPTH IN METRES Cape Moreton

Map © Marine Cartography Unit, Department of Transport, Queensland

This reproduction not to be used for navigation. Visit Maritime at www.transport.qld.gov.au

Parallel rulers or a rolling ruler may be used with a compass rose to find directions. Parallel rulers are placed over the map so that the edge of one ruler is along the desired direction. The other ruler is then swung across to the compass rose to read the bearing. A rolling ruler is rolled across from the desired direction line to the compass rose.

Find the bearing of Stephens Island from Cape Egmont, using the Cook Strait chart shown below.

Solution

The placement of parallel rulers is shown below. One ruler is lined up on the points. The other is then slid across to the compass rose. On full-size charts, the parallel rulers can be ‘walked’ across to the compass rose.

Write the answer from the rose. The bearing is 172°.

0°

180°

90°

0

80°

70° 60°

50° 40° 30° 20° 10°

280 290°

300° 310°

320°

330°

340° 350°

100°

110°

120°

130°

140°

150°

160°

170°

260 °

250°

240°

230°

220°

210° 200°

190°

DEPTH IN METRES Cook Strait

Map © Australian Hydrographic Service

Example

10

Alternative

1 Work out the distance travelled in nautical miles when a plane flies along a meridian through:

a 2° of latitude b 13°8′ of latitude c 5°28′ of latitude d 7°51′ of latitude.

2 Work out the distance travelled in kilometres when a ship sails through: a 4° of latitude b 1°38′ of latitude c 11°44′ of latitude d 8°3′ of latitude.

3 Work out the distance in nautical miles for travel along a parallel of latitude through: a 5°12′ of longitude at latitude 34°N b 21°30′ of longitude at latitude 75°S c 2°21′ of longitude at latitude 17°S d 6°57′ of longitude at latitude 42°N.

4 Work out the distance in kilometres for travel through:

a 1°59′ of longitude at latitude 23°S b 5°22′ of longitude at latitude 58°N c 12°35′ of longitude at latitude 37°N d 3°2′ of longitude at latitude 44°S.

Modelling and problem solving

5 A balloon is carried directly north from 32°12′S, 128°E to 29°45′S, 128°E. How far has it travelled:

a in nautical miles? b in kilometres?

6 A liner travelled from 2°27′S, 162°E to 3°48′N, 162°E in 2 days and 10 hours. a How far did it travel:

i in nautical miles? ii in kilometres? b What was its speed:

i in knots? ii in kilometres/hour?

7 An aircraft travelling at 600 km/h flies due south from the position 57°N, 23°E. After 6 hours’ flying:

a how far has it travelled in kilometres? b how far has it travelled in nautical miles? c what is its new position?

8 A submarine can travel at 14 knots. How long will it take to travel 400 km?

Exercise 1.2

Distance and direction on marine charts

Additional exercise

9 Use dividers on the Cook Strait chart below to find the distance between: a Cape Egmont and Stephens Island

b Wanganui and Cape Campbell c Cape Farewell and Picton d The Brothers and Westport e Cape Campbell and Cape Palliser.

10 Use dividers on the Mackay Waters chart on page 18 to find the distance between: a Dudgeon Point and Hay Point

b Round Top Island and Dudgeon Point c East Point and Round Top Island d Mount Bassett and Flat Top Island

e the 249 m point on Mt Hector and Oyster Rock.

0°

180°

90°

270°

80°

70° 60°

50° 40° 30° 20° 10°

280° 290°

300° 310°

320°

330°

340° 350°

100°

110°

120°

130°

140°

150°

160°

170°

260°

250°

240°

230°

220° 210°

200° 190°

DEPTH IN METRES Cook Strait

11 Use dividers on the Western Bass Strait chart on page 19 to find the distance between: a Cape Wickham and Wilsons Promontory

b Rocky Cape and Western Port c Cape Otway and Cape Liptrap d Stokes Point and Cape Grim e Cape Otway and Cape Wickham.

0°

180°

90°

270°

80°

70° 60°

50° 40° 30° 20° 10°

280° 290°

300° 310°

320°

330°

340° 350°

100°

110°

120°

130°

140°

150°

160°

170°

260°

250°

240°

230°

220°

210° 200°

190°

21°

149°

DEPTH IN FATHOMS Mackay Waters

12 Use dividers on the Redcliffe chart on page 20 to find the distance between: a the Water Tower (Deception Bay) and Osbourne Point

b Dohles Rocks and Otter Rock c Garnet Rock and Clontarf Point

d the Hospital Chimney (Redcliffe) and Woody Point e the western end of the Airfield and Redcliffe Point.

13 Use dividers on the orthophotographic map of Fisherman Islands on page 21 to find the distance between:

a the F.I. Ampol Crude Oil Wharf and the F.I. Coal Barge Wharf b Luggage Point and Bishop Island

c South Point and the Boat Passage Bridge d Bishop Island and South Point.

14 Use parallel rulers or a roller ruler on the Cook Strait chart on page 17 to find the bearing of:

a Cape Farewell from Cape Egmont b Wanganui from Stephens Island c Mt Taranaki from Cape Palliser d Westport from Tapuae-o-Uenuku e Cape Farewell from Wanganui.

0°

180°

90°

270°

80°

70° 60°

50° 40° 30° 20° 10°

280° 290°

300° 310°

320°

330°

340° 350°

100°

110°

120°

130°

140°

150°

160°

170°

260°

250°

240°

230°

220° 210°

200° 190°

DEPTH IN METRES Western Bass Strait

15 Use parallel rulers or a roller ruler on the orthophotographic map of Fisherman Islands on page 21 to find the bearing from Luggage Point of:

a Bishop Island b the Boat Passage Bridge

c South Point d the F.I. Ampol Crude Oil Wharf.

16 Use parallel rulers or a roller ruler on the Mackay Waters chart on page 18 to find the bearing of:

a Oyster Rock from Round Top Island b Oyster Rock from Flat Top Island c Mt Bassett from East Point d Mt Griffiths from Dudgeon Point e Hay Point from Oyster Rock.

17 Use parallel rulers or a roller ruler on the Western Bass Strait chart on page 19 to find the bearing of:

a Bluff Hill Point from Rocky Cape b Cape Wickham from Cape Otway c Cape Liptrap from Cape Otway d Stokes Point from Cape Grim e Wilsons Promontory from Rocky Cape.

02 04 06 08 10 12 14

94

92

90

88

86

84

82

0°

180°

90°

270°

80°

70° 60°

50° 40° 30° 20° 10°

280° 290°

300° 310°

320°

330°

340° 350°

100°

110°

120°

130°

140°

150°

160°

170°

260°

250°

240°

230°

220° 210°

200° 190°

DEPTH IN METRES Redcliffe

Map © Marine Cartography Unit, Department of Transport, Queensland

18 Use parallel rulers or a roller ruler on the Redcliffe chart on page 20 to find the bearing of: a Dohles Rocks from Osbourne Point

b Otter Rock from Clontarf Point

c the Water Tower (Deception Bay) from Garnet Rock d Woody Point from Dohles Rocks.

16 17 18

73

72

71

70

69

0°

180°

90°

270°

80°

70° 60°

50° 40° 30° 20° 10°

280° 290°

300° 310°

320°

330°

340° 350°

100°

110°

120°

130°

140°

150°

160°

170°

260°

250°

240°

230°

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210° 200°

190°

DEPTH IN METRES Fisherman Islands

Map © Marine Cartography Unit, Department of Transport, Queensland

1.3

Dead reckoning

Marine charts are used by sailors to find their way. To do this, they must keep track of where they are and where they are going. The basic method is called dead reckoning.

There are a number of different methods for taking a fix, and these will be examined later. However, if the boat is starting from a port or other known point, then dead reckoning is used prior to taking a fix, since bearings must be taken from known points to correct the estimated position.

Dead reckoning carried out by plotting on a chart uses the distance and bearing measurement methods shown in the previous section.

Did you know?

Old sailing ships could be steered to an accuracy of only about 3°. As a result, old marine bearings were not specified to an accuracy of even 1°. The old method of stating bearings using compass points, ‘north by north-west’ etc., was sufficiently accurate for the time.

Dead reckoning

Dead reckoning is carried out by plotting or calculating the course of a boat using speed, time and direction from the original position of the boat, taking currents and winds into account wherever possible. The establishment of position is called a fix. The position obtained by dead reckoning is also called the estimated position and is normally given in terms of latitude and longitude.

A ship anchored just north of Sail Rock sailed due north at 6 knots for 2 hours. It then sailed at 069° at 5 knots for a further hour. Use dead reckoning on the Percy Isles chart shown below to find the ship’s position, and hence find the distance and bearing of Pine Peak Island from the ship.

Solution

Place the roller ruler on the compass rose to find due north. Move the ruler across to draw (in 2B pencil) the direction of travel from the starting point. Use dividers to transfer the correct distance (12′) from the side scale. Mark the point on the course line.

Place the roller ruler on the compass rose to find the correct direction, 069°. Move the ruler across to draw the direction of travel from the end of the first line. Use dividers to transfer the correct distance (5′) from the side scale. Mark the estimated position.

Calculate distance of first leg. Distance = 6 kn × 2 h

= 12 nautical miles

Calculate distance of second leg. Distance = 5 kn × 1 h

= 5 nautical miles

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DEPTH IN METRES Percy Isles

Map © Australian Hydrographic Service

Use the roller ruler and dividers to find the distance and bearing of Pine Peak Island. Read the latitude from the side scale. Latitude = 21°34.3′S

Read the longitude from the other scale. Longitude = 150°14.3′E

Write the answers. The boat is at 21°34.3′S, 150°14.3′E and Pine Peak Island is 2.5 nautical miles away (nearest point) at a bearing of 011°.

Handheld GPS

Dead reckoning can also be done by

calculation, using trigonometry, a calculator, nautical Traverse Tables or electronic equipment. The basic principle is to work out one leg at a time. Nautical tables, calculators and electronic methods all use trigonometry in a simplified form.

A right-angled triangle is used to work out the distance north and east that has been travelled according to the bearing and distance. Provided the distance is in nautical miles, the answer obtained for travel north and travel east is in minutes.

Travel north= d × cos θ Travel east= d × sin θ

Bearing

Distance

θ

d

The travel north is added to or taken from the original latitude to find the latitude of the estimated position. The change in longitude is calculated by dividing the travel east by the cosine of the average latitude of the original and estimated positions. This change in longitude is then added to or taken from the original longitude to find the longitude of the estimated position.

If you have nautical tables available, try this method for Example 11. There is also a graphics calculator program on the CD-ROM that shows how this is done electronically.

Investigation

Dead reckoning by calculation

Calculator

program

You should use photocopies of the charts or printouts from the CD-ROM for this work.

Modelling and problem solving

1 Use the Percy Isles chart shown on page 26 to find the final positions (give positions and place names) when a ship follows the following courses.

a From Allandale Island, sailing due north at 4 knots for 2 hours, then at 242° at 4.5 knots for 2 hours

b From Allandale Island, sailing at a bearing of 320° for 3 hours at 5 knots, then due north for 2 hours at 3 knots

c From Allandale Island, sailing at 010° for 2 hours at 4 knots, then at 250° for 3 hours at 3 knots, then at 315° for 4 hours at 2 knots

d From Sphinx Islet, sailing for 1 hour at 4 knots at 090°, then 2 hours at 3 knots at 166°

e From Hixson Islet, sailing for 2 hours at 5 knots at 219°, then 4 hours at 3 knots at 118°, then 2 hours at 7 knots at 341°

2 Use the Port Jackson–Port Stephens chart shown on page 27 to find the final positions (and give named locations) when a ship follows the following courses.

a From a point 5 nautical miles east of Broken Head, sailing for 5 hours at 5 knots at 045°, then 5 hours at 3 knots at 339°

b From a point 5 sea miles east of Broken Head, sailing for 2 hours at 11 knots at 021°, then 2 hours at 10 knots at 048°, then 1 hour at 5 knots at 335°

c From Broughton Island, sailing for 3 hours at 5 knots at 164°, then 5 hours at 6 knots at 223°, then 3 hours at 7 knots at 261°

d From Moon Island, sailing for 2 hours at 6 knots at 173°, then 2 hours at 7 knots at 209°, then 3 hours at 4 knots at 247°

e From Redhead Point, sailing for 2 hours at 8 knots at 110°, then 7 hours at 6 knots at 206°, then 4 hours at 4.5 knots at 268°

3 Use the Auckland chart shown on page 28 to find the final position when a ship sails: a from New Plymouth, for 10 hours at 12 knots at 350°, then 5 hours at 10 knots

at 035°

b from Hokianga Harbour, for 4 hours at 10 knots at 206°, then 10 hours at 9 knots at 165°, then 5 hours at 12 knots at 103°

c from Mokohinau Island, for 13 hours at 5 knots at 338°, then 17 hours at 5 knots at 300°, then 10 hours at 5 knots at 277°

d from Three Kings Islands, for 15 hours at 17 knots at 155°, then 3 hours at 20 knots at 210°, then 1 hour at 14 knots at 140°

e from Kawhia Harbour, for 10 hours at 5 knots at 270°, then 10 hours at 5 knots at 010°, then 6 hours at 5 knots at 065°.

1 2

---Exercise 1.3

Dead reckoning

Additional

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DEPTH IN METRES Percy Isles

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DEPTH IN FATHOMS Port Jackson–Port Stephens

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DEPTH IN METRES Auckland

Map © Australian Hydrographic Service

Chapter

summary

Chapter

Review

Communication and justification

1 What is meant by a bearing?

2 Explain what is meant by an easterly variation.

3 What is meant by grid convergence?

4 Explain how to take account of changes in magnetic variation.

5 Explain how a westerly change of magnetic variation affects a magnetic bearing.

6 What do the terms ‘nautical mile’ and ‘knot’ mean?

7 Explain how dividers are used to measure distance on a marine chart.

8 How are parallel rulers used to measure bearings on a marine chart?

9 What is meant by dead reckoning?

10 What is meant by a fix?

Knowledge and procedures

11 What angle measures are used in navigation? How do latitude and longitude changes of angle relate to distance travelled?

12 Use the diagram below to find the bearings of A, B, C, D, E, F, G, H and I from P.

Ex 1.1

Ex 1.1

Ex 1.1

Ex 1.1

Ex 1.1

Ex 1.2

Ex 1.2

Ex 1.2

Ex 1.3

Ex 1.3

Ex 1.1

Ex 1.1

N

A

B

C

D

E G

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I

13 In 1982, the bearing of a water tower from an intersection was 346°28′ M. The annual change in magnetic variation is 06′ easterly. What is the magnetic bearing in:

a 1997? b 2010?

c 2025? d 1990?

14 Work out the distance travelled along a meridian of longitude in nautical miles and in kilometres when a ship sails through:

a 5° of latitude b 1°47′ of latitude c 7.2° of latitude d 4°36′ of latitude.

15 Work out the distance along the parallel of latitude in nautical miles and in kilometres when a plane flies through:

a 8° of longitude at latitude 46°S b 3°27′ of longitude at latitude 23°N c 4°56′ of longitude at latitude 78°N d 6.7° of longitude at latitude 63°S.

Modelling and problem solving

16 The diagram on the left below shows the grid declination diagram for a particular area. What are the grid and magnetic bearings in 1998 for the following true bearings?

a 123°28′ b 225°54′ c 006°17′

d 075°59′ e 357.6° f 287.3°

Use the same diagram to work out the true bearings and magnetic bearings in 1993 for the following grid bearings.

g 340° h 200°25′ i 042°29′

j 359°32′ k 137.2° l 001.5°

17 Use the diagram on the right above to work out the true bearings and magnetic bearings in 2001 for the following grid bearings.

a 176.6° b 014.9° c 039.4°

d 230.5° e 345°22′ f 103°35′

Now use the diagram to work out the grid bearings and true bearings for the following magnetic bearings taken in 1984.

g 158.2° h 312.8° i 045°

j 126.5° k 234°20′ l 069°55′

18 A balloon blows directly south from 15°27′S to 17°32′S in 15 hours. Work out its speed:

a in knots b in kilometres/hour. Ex 1.1

Ex 1.2

Ex 1.2

Ex 1.1

THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1973. ANNUAL CHANGE IS 0.1° EASTERLY. THE RELATIONSHIP BETWEEN TRUE NORTH, GRID NORTH

AND MAGNETIC NORTH IS SHOWN DIAGRAMMATICALLY FOR THE CENTRE OF THE MAP. MAGNETIC VALUE IS CORRECT FOR 1973. ANNUAL CHANGE IS 04′ EASTERLY.

GN

TN MN

GRID/MAGNETIC ANGLE 9°38′ GRID

CONVERGENCE 24′

GN

TN

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GRID/MAGNETIC ANGLE 11.5°

GRID

CONVERGENCE 0.2°

Ex 1.1

19 A ship sails due east along the 60th parallel at 15 knots for 15 hours. If it starts from 60°S, 130°E:

a how far does it travel? b what is its new position?

20 Use the Port Stephens chart below to find the distance and bearing of: a Point Stephens from Little Island

b Looking Glass Isle from Tomaree Head c Dark Point from the Tomaree Head light d Cabbage Tree Island from Dark Point.

Ex 1.2

Ex 1.2

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21 Use the Whitsunday Passage chart below to find the distance and bearing of: a Border Island from Pine Island (highest points)

b Pentecost Island from North Molle Island (highest points) c Double Cone Island from Hayman Island (highest points) d Molle Island from Hamilton Island (highest points).

22 Use (a photocopy of) the Port Stephens chart on page 31 to find the final positions when a ship follows the following courses.

a From Boondelbah Island, sailing at 3 knots for 2 hours at 085°, then 5 knots for 1 hour at 341°

b From Dark Point, sailing at 3.5 knots for 2 hours at 186°, then 4 knots for 15 minutes at 320°

c From Point Stephens, sailing at 12 knots for hour at 080°, then 15 knots for 20 minutes at 320°, then 14 knots for 15 minutes at 274°

Ex 1.2

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Map © Australian Hydrographic Service

Ex 1.3