COASTAL NAVIGATION

Equipment needed for each student:

a set of dividers a set of parallel rules protractor

For general class use:

2 NOAA Mercator charts # 13286, Cape Elizabeth to Portsmouth 4 globes 4 three arm protractors

DISCUSSION: LATITUDE AND LONGITUDE

If the earth were nat, it would be a simple matter to layoff a series of grid lines, perpendicular to each other to help us locate our position. For example, we could set our zero position in the left hand corner of our nat earth and draw a series of parallel lines north and south; then, perpendicular to these, draw another series of lines east and west. By numbering these lines consecutively we could determine any position on the nat earth as shown below in Figure 2-1.

AGURE 2-1

NORTH

8

6

4

2

o

't \.

'\

0 2 4 6 8 10 12 14 EAST

-- 3N,6E

To make the example more like the actual coordinates used on maps, we could expand it slightly, so that that were 4 quadrants instead of one- a north/east quadrant as shown above, as well as north/west, south/east and south/west quadrants. This schematic is shown below in Figure 2-2. Again, on our flat earth we could define any position by this numbering and direction system.

15

SOUTHEAST QUADRANT SOUTHWEST QUADRANT

8 I -6 ,.-...­-I ...­~ . ­ ~-I-"'" . ­ .

~ I

2 I

0--2­ ~4-~6--8­

~,~

i'.. i'..

AGURE2-2

WEST EAST NORTHWEST QUADRANT NORTHEAST QUADRANT

= 3N,4W.---­NORTH

~

SOUTH

~ = 4S,6E

If this grid system were on transparent cloth and we tried to wrap it around the spherical earth, it wouldn't fit, and there would be places where the cloth would overlap. So for the earth we need a different system, yet still adhering to the principles outlined above.

On the spherical earth, consider the east/west lines as a series of circles. Set one circle at the earth's widest point, the equator, and designate that the zero line. Since the earth is approximately a sphere, this largest circle can be divided into 360 degrees, as all circles can. A half circle is 180 degrees and a quarter circle is 90 degrees. If we drew 90 circles parallel to the largest circle separated by equal distances, could we calculate how far apart these circles (or parallels) would be?

As a first approximation, we can assume the earth is a sphere with a circumference of 24,902 miles. Any plane cutting through the center of the earth and intersecting the surface of the earth would form a great circle with a circumference of 24,902 miles! A quarter of that circle, or 360°/4 =90°, would have a arc length of 24,902/4 =6225 statute miles; So, 90° = 6225 statute miles (Fig. 2-3).

16

FIGURE 2-3

= 6225 statute milesNOR~H ~ PO~

EQUATOO

If 900 =6225 statute miles, then 1

0 =approximately 69 statute miles. Now 69 statute miles is a difficult number to work with, especially since degrees can be divided up into 60 minutes, and each minute can be divided up into 60 seconds. So map makers and navigators came up with a new measurement length called the nautical mile.. In this case a degree is equal to 60 nautical miles, so each minute of arc is equal to 1 nautical mile. The nautical mile is slightly larger than a statute mile by about 800 feet. The net result is that it's easy to convert degree measurements into nautical mile measurements by the following:

1 degree =60 nautical miles =60 minutes of arc.

Longitude is a little more complex. If we drew a series of circles extending from the north to the south pole, they would all have the same circumference - i.e., there would be no one "largest" circle corresponding to the equator. So arbitrarily, we define one of these great circles or meridians as the zero line, the one that cuts though Greenwich, England. Again, considering the earth as a sphere it can be divided into 180 degrees segments east and west of the zero or prime meridian (Fig. 2-4).

/

17

18

0° (Equator)

90 EAST

135 EAST

- - - - - -North Pole

....--60 nm ----1~

one degree of longitude

0--------------0-------· 16 west 15 west

AGURE2-4

FIGURE 2-5

TOP VIEW LOOKING DOWN ON NORTH POLE

180

90 WEST

135 WEST

What this means in practical terms is that a degree of longitude at the equator is 60 nautical miles. However, at 45 degrees north latitude, that same degree of longitude is a little over 40 nautical miles, because the meridians or longitude lines are converging (Fig.2- 5).

o Prime Meridian

One of the main differences between meridians and parallels is that the meridians converge north to south, while the parallels always remain equidistant.

Because the change in distances between meridians over the globe are dependent on latitude, we make most of our distance measurements on charts using the latitude scale. Normally, Mercator charts are used in navigation. On any Mercator chart the degrees of latitude are given on the y axis of the chart and degrees of longitude are on the x axis. The most common approach for distance determination is to measure the length of the line on the chart and then "lay" that distance off with either a ruler or dividers on the latitude scale. The distances will follow the rule that 1 degree =60 minutes, and 1 minute =1 nautical mile (Fig.2-6).

FIGURE 2-6

DISTANCE FROM A TO B =40 NAUTICAL MILES

A N

i 46° 00'

B

45° 00'

Answer the following questions:

A. Examine the NOAA chart #13286, Cape Elizabeth to Portsmouth that is posted in the room. How many minutes of latitude are shown on the vertical scale? How many minutes of longitude are on the horizontal scale?

minutes of latitude, _

minutes of longitude _

B. Determine the position of the lighthouse on Boon Island in latitude and longitude in degrees, minutes and seconds.

latitude position of lighthouse degrees mm sec longitude position of lighthouse degrees mm sec

C. How many nautical miles is it from the lighthouse on Boon Island to the lighthouse at Cape Neddick (Nubble light)? Use the dividers and the vertical latitude scale (hint: remember 1 minute = 1 nautical mile)

nautical miles between Boon Island Light and Cape Neddick Light'-- nm

19

D. How many feet long is Richmond Island (near Cape Elizabeth) from its southwestern most point to its northeastern most point? (hint: how many feet in a nautical mile?)

length of Richmond Island ft

DISCUSSION: VECTORS AS USED IN NAVIGATION

In oceanography, most measurements are lengths of objects, temperatures, salinities, time intervals, and numerous other quantities that can be described by a single number representing the magnitude of the quantity. These are called .sc.alar quantities.

However, when considering both magnitude and direction, the quantities are known as vectors. For example, if we consider the speed of a ship as 10 knots (10 nautical miles per hour) this is scalar quantity. But if we were to consider the speed and direction (10 knots due east), this would be the velocity of the ship and is a Y..ectill: quantity. Vector quantities can be represented by lines whose lengths are scaled to the magnitude of the quantity, and whose orientations are the compass direction. Fig. 2-7 below shows examples of vectors.

FIGURE 2-7

1.5 units 1.5 units 1 unit northeast due south north

2 units due east

•

Vectors can be added graphically to give simple solutions to trigonometric problems.

Example: A small boat crosses a river from A to B at 10 knots, but the river has a current flowing at 5 knots right across the proposed course (Fig. 2-8). Assuming no course change was made after starting,

where on the river bank would the boat land?

20

B

R (position on river bank)

? LANDING

POINT

RGURE2-9

10 knots

(construct this line:

LENGTH = SHIP'S SPEED

This is the method we will use in this exercise. Using the same example, the tail of the 5 unit current vector is shifted to the head of the 10 unit ship speed vector. Draw the same resultant (Fig. 2-10).

RGURE2-8

21

A

Layoff (draw) a vector to scale representing the proposed boat speed 10 units long in the direction the boat was intended to go. Construct another vector representing the current, 5 units in length directed south. Construct two lines parallel to these, and draw the resultant from the boat's initial position to the intersection of the two constructed lines. The length of the resultant will be equal to the ship's speed, and the angle will be the final course that was traversed. Its landing position will be as shown (Fig. 2-9).

There are two graphical ways to solve this problem.

5 knots

2. Head to Tail Method

1. Parallelogram Method

22

5 knots (current to the south)

USING THE HEAD TO TAIL METHOD WE SHIFTED THE 5 KNOT VECTOR HERE

(new position on river bank)

c

southeast bearing

(135 0 )

knots ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

/\,, = ship's speed " ,,,,,,,,,,,

" R

FIGURE 2-10

A

~ 10 ship's speed) A~----r-r---r-----,---r--::~-r-.......----,-....,8

FIGURE 2-11

LENGTH OF THE VECTOR = ACTUAL SHIP'S SPEED

5 knots

length

R (position on river bank)

3. Note that vector construction methods work even if the directions are not north/south or east/west. For example, in Fig. 2-11 we consider a similar problem as above, but now the boat is heading from A to C at 10 knots at a 135° compass heading (southeast). Given the same 5 knot current to the south, what is the new landing point?

Answer the following questions:

A. In the diagram below (Fig. 2-12) a ship is moving east at 2 knots (2 nautical miles per hour). Draw its position after 4 hours. Use the bow of the boat as the starting position.

FIGURE 2-12

B. Consider a slightly different problem. The ship still sets a due east heading on its compass, but now is acted on by a 2 knot current from the south. Where will its final position be after 4 hours? Show your plot on the same diagram (Fig. 2-12). Again use the bow of the boat at the same starting position.

C. Finally, the ship decides to travel north at 5 knots for 1 hour. A wind sets up a 3 knot current moving from the northwest which sets the boat off course. Where will it be after 1 hour? Show your work on the same diagram (Fig. 2-12).

DISCUSSION: MAGNETIC DECLINATION

Up to this point we have assumed that our ship's compass was always pointing to the geographic north pole as we navigated. Unfortunately, the compass points to the MAGNETIC North Pole which is displaced from the geographic north pole. The Magnetic North Pole is located about 70° north latitude and 1000 west longitude in the vicinity of Prince of Wales Island in the Northwest Territories of Canada. This displacement between the two poles is called the magnetic declination. Figure 2-13 below indicates the relative position of the the two poles.

0 15 10 N

N

t I~

I~

I~

I~

1.... 15000 N

23

FIGURE 2-13

VIEW LOOKING DOWN ON THE NORTH POLE

MAGNETIC POLE

NOTE: DECLINATION WEST OFNORTH POLE

A Mercator chart used for navigation shows both true north as well as magnetic north. True north lines up parallel with the vertical axis on the Mercator chart. On these charts, compass roses are shown which show magnetic north and its relationship to true north (Fig.2-14). For navigation, we must use the inside compass rose which corresponds to the magnetic compass on the ship.

24

25

C. Indicate a major city in the United States that would have llQ magnetic declination.

E o

135 M

M

HERE WE HAVE INDICATED THE "M" FOR MAGNETIC

• / DIRECTIONS

45 M NOTE: THIS BEARING ", WOULD BE ABOUT 80

, .. ;; DEGREES MAGNETIC

/"/;;~ 0 M

(E or W)

____(Eor W)

____(Eor W)

_____(E or W)

AGURE 2-14

s

(TRUE NORTH)

*

Hawaii

Azores

San Francisco

Chait #13286

o 315

w

DECLINATION

A. Inspect the rose diagram on NOAA chart #13286, Cape Elizabeth to Portsmouth. Indicate below the magnetic declination for the chart.

Answer the following questions:

B. On each of the globes in the laboratory we have plotted a position representing the magnetic north pole(700 north latitude and 100° west longitude). From the following cities on the earth plot the angle (declination) that the magnetic pole deviates away from the geographic north pole. Indicate if the deviation is west or east of the geographic north pole. Use two of the arms of the three armed protractor to measure the angles.

DISCUSSION: POSITION LOCATION BY COMPASS HEADING, SHIP'S SPEED, AND MERCATOR CHART

How do you find your way around at sea when there are no roads, sign posts, or any of the given methods we normally use for land travel? If you are in sight of land and have a good chart,)t may be relatively easy. But what if it's foggy or dark - how do you navigate your boat? Celestial navigation is one way: making use of the stars' and the sun's position. Unfortunately, most weekend sailors today don't bother to learn this skill, relying instead on modem electronic navigation systems that enable navigation in almost any weather conditions (Loran, Radar, etc.). However, this equipment may fail, and in many cases may be too expensive for the weekend sailor.

Probably the simplest method of coastal navigation is called Dead Reckoning Navigation (DRN). It is primarily based on the use of an accurate magnetic compass, an up-to-date chart, knowledge of the local water currents, an estimate of ship's speed, and - most of all - a little luck!

The example shown in Figure 2-15 illustrates how the method works. You are sailing in calm waters (no current) and your known position is point "X". Fog is setting in, but you still want to sail your boat to the island "A". You can measure the compass direction between position "X" and the island off the compass rose on your Mercator chart by using the parallel rules as illustrated.

The parallel rules show you the course direction of 75 degrees magnetic between your known point and the island. For all marine navigation you will always measure the compass bearing from the magnetic compass rose, which differs slightly from true north. From the chart you can also estimate the travel distance by measuring the length between your starting point and destination with a pair of dividers. Remember, 60 minutes (60') of arc between two points on the globe is equal to 60 nautical miles. Always measure the distance on the vertical scale of the Mercator chart at the same general latitude as your ship's course. Finally, if you know your ship's speed you should be able to calculate the time it would take to go from point "X" to the island.

26

, ~

~ ,, ;

; ~

~ ,,, ;

;

Island

true north

*

RGURE2-15

27

distance to the island. .degree(s) _____ nautical miles

distance traveled degree(s) ______ nautical miles

x

N

Boat

B. Plot the final position of the boat after 6 hours travel time at 10 knots along the path shown toward the island from point X.

C. What is the total distance to the island from point X in degrees and nautical miles? (hint: use your dividers to measure the length; then compare it to the vertical scale)

Consider the following navigational problems and answer the questions:

A. The ship's speed in Fig. 2-15 is 10 knots (10 nautical miles per hour). How far can you travel in 6 hours in degrees and nautical miles?

D. Given the ship's speed and the distance, how long will it take you to get to the island?

travel time to the island (hours)

E. Consider a slightly more complex situation. Assume there is a current moving from north to south at 3 knots (3 nautical miles/hour). Where would you end up after 6 hours travel on the same course? Put position on Fig. 2-15.

The problem can be solved as follows:

Construct a vector moving in the direction (south) equal in length to the travel time (6 hours) times the current speed (3 knots). The current vector will be 18 nautical miles long. You can measure this distance with dividers on the vertical scale of the Mercator chart ("Y" axis) and draw it on the chart extending south from the boat's position after 6 hours.

Plot the ship's track from the original point "X" to the head of the current vector.

EXERCISE 1: PLOTTING A SHIP'S COURSE

Use Figure 2-16 for plotting this exercise. Use a pencil and plot directly on the chart.

mStart at the beautiful coastal town of Butlerport and plot a straight course through the ~."/ channel to the small island shown on the chart. Calculate the distance between

Butlerport and the island, and estimate the course heading using the parallel rules and measuring from the magnetic compass rose.

distance between Butlerport and the island ______nautical mile(s)

course heading _______degrees

latitude of the island N

longitude of the island W

2. At the island, plot the shortest course to Roseberg. Your ship is doing 3 knots at this point. Indicate your course heading and the time it will take to go from the island to Roseberg.

course heading degrees

travel time to Roseberg hours, minutes

28

3. Next you have to go directly to Hoadleyville, but avoiding the dangerous Ann's Ledge shown on the chart. You move your ship slowly at 1 knot and can make only 2 (two) additional course changes-three different compass headings from Roseberg. What is the shortest distance between Roseberg and Hoadleyville and how long will it take to get there?

shortest course distance from Roseberg to Hoadleyville nautical miles

travel time from Roseberg to Hoadleyville hours, minutes

4. You leave Hoadleyville and set a course at 130 degrees magnetic, travelling exactly seven nautical miles. At this point you set a course for Natburg, and start "steaming" at 5 knots. Immediately after you start, a storm blows up and sets up a current from the west (270 degrees magnetic) at 4 knots. Plot your final position 1 hour after turning north toward Natburg taking into account this current, and list your latitude and longitude.

latitude N

longitude W

29

\

I­, ,

90

I

/

1\["..,

30o

210

210

island

o 63 40' W

FIGURE 2-16

30

"""~,, ."", . . '-.: BUTLERPORT

t-----~r~-4~-----~I---.55010'N------....;.""..'--~

o r--------~--.......:;.3lir_----55 00' N------...".",......,...,~.,...,...-

Name _ Lab Section _ Date

HOMEWORK

COASTAL NAVIGATION

Note: This homework exercise can be done with a ruler and a protractor if parallel rules are unavailable.

1. Note the latitude scale on the homework navigational chart (Fig. 2-17). One cm on the scale is equal to how many nautical miles? (hint: 1 minute =1 nautical mile)

1 cm = nm

2. The compass rose diagram on Fig. 2-17 is for magnetic north only. What is the declination for this chart? How can you tell?

3. Your ship has a top speed of 6 knots. At this speed, how long will it take you to leave Port Toren, a high technology center, and arrive at the beautiful coastal town of Brynberg making only one course change after you started. Be sure to avoid the rocks and navigate as quickly as you can around Harmony Island. Indicate your two courses below in degrees, and the total travel time for the cruise. Do all your work on the chart in pencil!

first course _ degrees

second course _ degrees

total travel time hours, minutes

4. You begin a sampling cruise which starts at Port Toren. You will go sequentially from station 1 through 10 at a speed of 2 knots. You spend 1 hour at each station taking water samples. How many hours will it take you to sample all ten stations and put into steel town of Tristanville at the end of the cruise? Do all plotting on Fig. 2-17 and show your work.

5. What were your course headings in degrees from:

station two to three? degrees

station six to seven? degrees

31

1 0

o

9 o

6

o

32

FIGURE 2-17

JULIA

CARLETON .\, "­

3 4

0 0 0

30 " ,,

60 \ , 270 90 "",,

120 '''' " 2

" 0.,.

180 -­....

..,,4ft

PORT

......................" .. TOREN

JENNy ........

",............ ...........................~~

"" ......... , ........."" 1

0