COASTAL NAVIGATION Equipment needed fr each student: a set f dividers a set f parallel rules prtractr Fr general class use: 2 NOAA Mercatr charts # 13286, Cape Elizabeth t Prtsmuth 4 glbes 4 three arm prtractrs DISCUSSION: LATITUDE AND LONGITUDE If the earth were nat, it wuld be a simple matter t layff a series f grid lines, perpendicular t each ther t help us lcate ur psitin. Fr example, we culd set ur zer psitin in the left hand crner f ur nat earth and draw a series f parallel lines nrth and suth; then, perpendicular t these, draw anther series f lines east and west. By numbering these lines cnsecutively we culd determine any psitin n the nat earth as shwn belw in Figure 2-1. NORTH 8 6 AGURE 2-1 4 2 't \. '\ 0 2 4 6 8 10 12 14 EAST - 3N,6E T make the example mre like the actual crdinates used n maps, we culd expand it slightly, s that that were 4 quadrants instead f ne- a nrth/east quadrant as shwn abve, as well as nrth/west, suth/east and suth/west quadrants. This schematic is shwn belw in Figure 2-2. Again, n ur flat earth we culd define any psitin by this numbering and directin system. 15
AGURE2-2 WEST NORTHWEST QUADRANT EAST NORTHEAST QUADRANT -I-"'" 8.. ~ I - - I 6,.-... I... ~. ~ 2 I 0--2 ~4-~6--8.--- = 3N,4W ~ NORTH ~, ~ SOUTH i'.. i'.. SOUTHWEST QUADRANT SOUTHEAST QUADRANT ~ = 4S,6E If this grid system were n transparent clth and we tried t wrap it arund the spherical earth, it wuldn't fit, and there wuld be places where the clth wuld verlap. S fr the earth we need a different system, yet still adhering t the principles utlined abve. On the spherical earth, cnsider the east/west lines as a series f circles. Set ne circle at the earth's widest pint, the equatr, and designate that the zer line. Since the earth is apprximately a sphere, this largest circle can be divided int 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 t the largest circle separated by equal distances, culd we calculate hw far apart these circles (r parallels) wuld be? As a first apprximatin, we can assume the earth is a sphere with a circumference f 24,902 miles. Any plane cutting thrugh the center f the earth and intersecting the surface f the earth wuld frm a great circle with a circumference f 24,902 miles! A quarter f that circle, r 360 /4 =90, wuld have a arc length f 24,902/4 =6225 statute miles; S, 90 = 6225 statute miles (Fig. 2-3). 16
FIGURE 2-3 NOR~H ~ PO~ = 6225 statute miles EQUATOO If 90 0 =6225 statute miles, then 1 0 =apprximately 69 statute miles. Nw 69 statute miles is a difficult number t wrk with, especially since degrees can be divided up int 60 minutes, and each minute can be divided up int 60 secnds. S map makers and navigatrs came up with a new measurement length called the nautical mile.. In this case a degree is equal t 60 nautical miles, s each minute f arc is equal t 1 nautical mile. The nautical mile is slightly larger than a statute mile by abut 800 feet. The net result is that it's easy t cnvert degree measurements int nautical mile measurements by the fllwing: 1 degree =60 nautical miles =60 minutes f arc. Lngitude is a little mre cmplex. If we drew a series f circles extending frm the nrth t the suth ple, they wuld all have the same circumference - i.e., there wuld be n ne "largest" circle crrespnding t the equatr. S arbitrarily, we define ne f these great circles r meridians as the zer line, the ne that cuts thugh Greenwich, England. Again, cnsidering the earth as a sphere it can be divided int 180 degrees segments east and west f the zer r prime meridian (Fig. 2-4). / 17
AGURE2-4 TOP VIEW LOOKING DOWN ON NORTH POLE 180 135 WEST 135 EAST 90 WEST 90 EAST Prime Meridian One f the main differences between meridians and parallels is that the meridians cnverge nrth t suth, while the parallels always remain equidistant. What this means in practical terms is that a degree f lngitude at the equatr is 60 nautical miles. Hwever, at 45 degrees nrth latitude, that same degree f lngitude is a little ver 40 nautical miles, because the meridians r lngitude lines are cnverging (Fig.2-5). ne degree f lngitude FIGURE 2-5 - - - - - -Nrth Ple...--60 nm ----1~ 0 (Equatr) 0--------------0------- 16 west 15 west 18
Because the change in distances between meridians ver the glbe are dependent n latitude, we make mst f ur distance measurements n charts using the latitude scale. Nrmally, Mercatr charts are used in navigatin. On any Mercatr chart the degrees f latitude are given n the y axis f the chart and degrees f lngitude are n the x axis. The mst cmmn apprach fr distance determinatin is t measure the length f the line n the chart and then "lay" that distance ff with either a ruler r dividers n the latitude scale. The distances will fllw 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 B N i 46 00' 45 00' Answer the fllwing questins: A. Examine the NOAA chart #13286, Cape Elizabeth t Prtsmuth that is psted in the rm. Hw many minutes f latitude are shwn n the vertical scale? Hw many minutes f lngitude are n the hrizntal scale? minutes f latitude, minutes f lngitude B. Determine the psitin f the lighthuse n Bn Island in latitude and lngitude in degrees, minutes and secnds. latitude psitin f lighthuse degrees mm sec lngitude psitin f lighthuse degrees mm sec C. Hw many nautical miles is it frm the lighthuse n Bn Island t the lighthuse at Cape Neddick (Nubble light)? Use the dividers and the vertical latitude scale (hint: remember 1 minute = 1 nautical mile) nautical miles between Bn Island Light and Cape Neddick Light'-- nm 19
D. Hw many feet lng is Richmnd Island (near Cape Elizabeth) frm its suthwestern mst pint t its nrtheastern mst pint? (hint: hw many feet in a nautical mile?) length f Richmnd Island ft DISCUSSION: VECTORS AS USED IN NAVIGATION In ceangraphy, mst measurements are lengths f bjects, temperatures, salinities, time intervals, and numerus ther quantities that can be described by a single number representing the magnitude f the quantity. These are called.sc.alar quantities. Hwever, when cnsidering bth magnitude and directin, the quantities are knwn as vectrs. Fr example, if we cnsider the speed f a ship as 10 knts (10 nautical miles per hur) this is scalar quantity. But if we were t cnsider the speed and directin (10 knts due east), this wuld be the velcity f the ship and is a Y..ectill: quantity. Vectr quantities can be represented by lines whse lengths are scaled t the magnitude f the quantity, and whse rientatins are the cmpass directin. Fig. 2-7 belw shws examples f vectrs. FIGURE 2-7 1.5 units 1.5 units 1 unit nrtheast due suth nrth 2 units due east Vectrs can be added graphically t give simple slutins t trignmetric prblems. Example: A small bat crsses a river frm A t B at 10 knts, but the river has a current flwing at 5 knts right acrss the prpsed curse (Fig. 2-8). Assuming n curse change was made after starting, where n the river bank wuld the bat land? 20
RGURE2-8 A? LANDING POINT There are tw graphical ways t slve this prblem. 1. Parallelgram Methd Layff (draw) a vectr t scale representing the prpsed bat speed 10 units lng in the directin the bat was intended t g. Cnstruct anther vectr representing the current, 5 units in length directed suth. Cnstruct tw lines parallel t these, and draw the resultant frm the bat's initial psitin t the intersectin f the tw cnstructed lines. The length f the resultant will be equal t the ship's speed, and the angle will be the final curse that was traversed. Its landing psitin will be as shwn (Fig. 2-9). RGURE2-9 10 knts B 5 knts LENGTH = SHIP'S SPEED (cnstruct this line: R (psitin n river bank) 2. Head t Tail Methd This is the methd we will use in this exercise. Using the same example, the tail f the 5 unit current vectr is shifted t the head f the 10 unit ship speed vectr. Draw the same resultant (Fig. 2-10). 21
FIGURE 2-10 ~ 10 ship's speed) A~----r-r---r-----,---r--::~-r-...----,-...,8 LENGTH OF THE VECTOR = ACTUAL SHIP'S SPEED 5 knts (current t the suth) FIGURE 2-11 R (psitin n river bank) 3. Nte that vectr cnstructin methds wrk even if the directins are nt nrth/suth r east/west. Fr example, in Fig. 2-11 we cnsider a similar prblem as abve, but nw the bat is heading frm A t C at 10 knts at a 135 cmpass heading (sutheast). Given the same 5 knt current t the suth, what is the new landing pint? A,,,,,, knts 5 knts length,,,,,,,,,,,,,,,,,,,,,,,, /\,, sutheast bearing (135 0 ) c USING THE HEAD TO TAIL METHOD WE SHIFTED THE 5 KNOT VECTOR HERE = ship's speed ",,,,,,,,,,, " R (new psitin n river bank) 22
Answer the fllwing questins: A. In the diagram belw (Fig. 2-12) a ship is mving east at 2 knts (2 nautical miles per hur). Draw its psitin after 4 hurs. Use the bw f the bat as the starting psitin. FIGURE 2-12 N t I~ I~ I~ 0 15 10 N I~ 1... 15000 N B. Cnsider a slightly different prblem. The ship still sets a due east heading n its cmpass, but nw is acted n by a 2 knt current frm the suth. Where will its final psitin be after 4 hurs? Shw yur plt n the same diagram (Fig. 2-12). Again use the bw f the bat at the same starting psitin. C. Finally, the ship decides t travel nrth at 5 knts fr 1 hur. A wind sets up a 3 knt current mving frm the nrthwest which sets the bat ff curse. Where will it be after 1 hur? Shw yur wrk n the same diagram (Fig. 2-12). DISCUSSION: MAGNETIC DECLINATION Up t this pint we have assumed that ur ship's cmpass was always pinting t the gegraphic nrth ple as we navigated. Unfrtunately, the cmpass pints t the MAGNETIC Nrth Ple which is displaced frm the gegraphic nrth ple. The Magnetic Nrth Ple is lcated abut 70 nrth latitude and 1000 west lngitude in the vicinity f Prince f Wales Island in the Nrthwest Territries f Canada. This displacement between the tw ples is called the magnetic declinatin. Figure 2-13 belw indicates the relative psitin f the the tw ples. 23
FIGURE 2-13 VIEW LOOKING DOWN ON THE NORTH POLE MAGNETIC POLE NOTE: DECLINATION WEST OFNORTH POLE A Mercatr chart used fr navigatin shws bth true nrth as well as magnetic nrth. True nrth lines up parallel with the vertical axis n the Mercatr chart. On these charts, cmpass rses are shwn which shw magnetic nrth and its relatinship t true nrth (Fig.2-14). Fr navigatin, we must use the inside cmpass rse which crrespnds t the magnetic cmpass n the ship. 24
AGURE 2-14 DECLINATION 315 w (TRUE NORTH) * HERE WE HAVE INDICATED THE "M" FOR MAGNETIC / DIRECTIONS 45 M NOTE: THIS BEARING ", WOULD BE ABOUT 80,.. ;; DEGREES MAGNETIC /"/;;~ 0 M E 135 M Answer the fllwing questins: s M A. Inspect the rse diagram n NOAA chart #13286, Cape Elizabeth t Prtsmuth. Indicate belw the magnetic declinatin fr the chart. Chait #13286 (E r W) B. On each f the glbes in the labratry we have pltted a psitin representing the magnetic nrth ple(700 nrth latitude and 100 west lngitude). Frm the fllwing cities n the earth plt the angle (declinatin) that the magnetic ple deviates away frm the gegraphic nrth ple. Indicate if the deviatin is west r east f the gegraphic nrth ple. Use tw f the arms f the three armed prtractr t measure the angles. Azres San Francisc Hawaii (E r W) (Er W) (Er W) C. Indicate a majr city in the United States that wuld have llq magnetic declinatin. 25
DISCUSSION: POSITION LOCATION BY COMPASS HEADING, SHIP'S SPEED, AND MERCATOR CHART Hw d yu find yur way arund at sea when there are n rads, sign psts, r any f the given methds we nrmally use fr land travel? If yu are in sight f land and have a gd chart,)t may be relatively easy. But what if it's fggy r dark - hw d yu navigate yur bat? Celestial navigatin is ne way: making use f the stars' and the sun's psitin. Unfrtunately, mst weekend sailrs tday dn't bther t learn this skill, relying instead n mdem electrnic navigatin systems that enable navigatin in almst any weather cnditins (Lran, Radar, etc.). Hwever, this equipment may fail, and in many cases may be t expensive fr the weekend sailr. Prbably the simplest methd f castal navigatin is called Dead Reckning Navigatin (DRN). It is primarily based n the use f an accurate magnetic cmpass, an up-t-date chart, knwledge f the lcal water currents, an estimate f ship's speed, and - mst f all - a little luck! The example shwn in Figure 2-15 illustrates hw the methd wrks. Yu are sailing in calm waters (n current) and yur knwn psitin is pint "X". Fg is setting in, but yu still want t sail yur bat t the island "A". Yu can measure the cmpass directin between psitin "X" and the island ff the cmpass rse n yur Mercatr chart by using the parallel rules as illustrated. The parallel rules shw yu the curse directin f 75 degrees magnetic between yur knwn pint and the island. Fr all marine navigatin yu will always measure the cmpass bearing frm the magnetic cmpass rse, which differs slightly frm true nrth. Frm the chart yu can als estimate the travel distance by measuring the length between yur starting pint and destinatin with a pair f dividers. Remember, 60 minutes (60') f arc between tw pints n the glbe is equal t 60 nautical miles. Always measure the distance n the vertical scale f the Mercatr chart at the same general latitude as yur ship's curse. Finally, if yu knw yur ship's speed yu shuld be able t calculate the time it wuld take t g frm pint "X" t the island. 26
RGURE2-15 N Island Bat x true nrth * ~,,, ; ; ~ ~,, ; ; ~, Cnsider the fllwing navigatinal prblems and answer the questins: A. The ship's speed in Fig. 2-15 is 10 knts (10 nautical miles per hur). Hw far can yu travel in 6 hurs in degrees and nautical miles? distance traveled degree(s) nautical miles B. Plt the final psitin f the bat after 6 hurs travel time at 10 knts alng the path shwn tward the island frm pint X. C. What is the ttal distance t the island frm pint X in degrees and nautical miles? (hint: use yur dividers t measure the length; then cmpare it t the vertical scale) distance t the island..degree(s) nautical miles 27
D. Given the ship's speed and the distance, hw lng will it take yu t get t the island? travel time t the island (hurs) E. Cnsider a slightly mre cmplex situatin. Assume there is a current mving frm nrth t suth at 3 knts (3 nautical miles/hur). Where wuld yu end up after 6 hurs travel n the same curse? Put psitin n Fig. 2-15. The prblem can be slved as fllws: Cnstruct a vectr mving in the directin (suth) equal in length t the travel time (6 hurs) times the current speed (3 knts). The current vectr will be 18 nautical miles lng. Yu can measure this distance with dividers n the vertical scale f the Mercatr chart ("Y" axis) and draw it n the chart extending suth frm the bat's psitin after 6 hurs. Plt the ship's track frm the riginal pint "X" t the head f the current vectr. EXERCISE 1: PLOTTING A SHIP'S COURSE Use Figure 2-16 fr pltting this exercise. Use a pencil and plt directly n the chart. mstart at the beautiful castal twn f Butlerprt and plt a straight curse thrugh the ~."/ channel t the small island shwn n the chart. Calculate the distance between Butlerprt and the island, and estimate the curse heading using the parallel rules and measuring frm the magnetic cmpass rse. distance between Butlerprt and the island nautical mile(s) curse heading latitude f the island degrees N lngitude f the island W 2. At the island, plt the shrtest curse t Rseberg. Yur ship is ding 3 knts at this pint. Indicate yur curse heading and the time it will take t g frm the island t Rseberg. curse heading degrees travel time t Rseberg hurs, minutes 28
3. Next yu have t g directly t Hadleyville, but aviding the dangerus Ann's Ledge shwn n the chart. Yu mve yur ship slwly at 1 knt and can make nly 2 (tw) additinal curse changes-three different cmpass headings frm Rseberg. What is the shrtest distance between Rseberg and Hadleyville and hw lng will it take t get there? shrtest curse distance frm Rseberg t Hadleyville travel time frm Rseberg t Hadleyville nautical miles hurs, minutes 4. Yu leave Hadleyville and set a curse at 130 degrees magnetic, travelling exactly seven nautical miles. At this pint yu set a curse fr Natburg, and start "steaming" at 5 knts. Immediately after yu start, a strm blws up and sets up a current frm the west (270 degrees magnetic) at 4 knts. Plt yur final psitin 1 hur after turning nrth tward Natburg taking int accunt this current, and list yur latitude and lngitude. latitude lngitude N W 29
FIGURE 2-16 63 40' W 30 90 I t-----~r~-4~-----~i---.55010'n------...;.""..'--~ 210 island 1\[ ".., / I,, \ "",.. """~,,. BUTLERPORT '-.: 210 r--------~--...:;.3lir_----55 00' N------...".",...,...,~.,...,...- 30
Name _ Lab Sectin _ Date HOMEWORK COASTAL NAVIGATION Nte: This hmewrk exercise can be dne with a ruler and a prtractr if parallel rules are unavailable. 1. Nte the latitude scale n the hmewrk navigatinal chart (Fig. 2-17). One cm n the scale is equal t hw many nautical miles? (hint: 1 minute =1 nautical mile) 1 cm = nm 2. The cmpass rse diagram n Fig. 2-17 is fr magnetic nrth nly. What is the declinatin fr this chart? Hw can yu tell? 3. Yur ship has a tp speed f 6 knts. At this speed, hw lng will it take yu t leave Prt Tren, a high technlgy center, and arrive at the beautiful castal twn f Brynberg making nly ne curse change after yu started. Be sure t avid the rcks and navigate as quickly as yu can arund Harmny Island. Indicate yur tw curses belw in degrees, and the ttal travel time fr the cruise. D all yur wrk n the chart in pencil! first curse _ degrees secnd curse _ degrees ttal travel time hurs, minutes 4. Yu begin a sampling cruise which starts at Prt Tren. Yu will g sequentially frm statin 1 thrugh 10 at a speed f 2 knts. Yu spend 1 hur at each statin taking water samples. Hw many hurs will it take yu t sample all ten statins and put int steel twn f Tristanville at the end f the cruise? D all pltting n Fig. 2-17 and shw yur wrk. 5. What were yur curse headings in degrees frm: statin tw t three? statin six t seven? degrees degrees 31
FIGURE 2-17 JULIA 9 6 1 0 CARLETON.\, ",, 3 0 0 30 ", 60 \ 270 90 "",, 4 0 PORT TOREN ""...,..."" 120 '''' 180..,,4ft -..." ",... JENNy......~~.. 2.,. " 0 1 0... 32