Navigation

Positions

Longitude and latitude The earth can be regarded as a spherical object, and since since we're we're dealin dealing g with with a 3-dime 3-dimensi nsiona onall shape shape we need coordinates of a different form than the usual xand and y-axes y-axes.. Thoug Though h addin adding g an extra extra z-axes z-axes would would make sense for submarines, we will most likely be foun found d on the the surf surfac ace e of this this sph sphere ere whil while e usin using g another system of coordinates, that covers our planet with imaginary lines called meridians and parallels, see figure 1. All these lines together provide the grid which ich enables us to describe any position in longitudes and latitudes. The obvious place to divide the Northern and Southern Hemisp Hemispher heres es was was the equa equator tor.. But the the divis division ion of the the Easte Eastern rn and and Wester Western n hemisp hemispher heres es was was the sourc source e of much much politi political cal turmo turmoil. il. Greenw Greenwich ich (Great (Great Britain) won, placing for example The Netherlands in the Eastern and Ireland in the Western Hemisphere. It takes the earth 24 hours for a full rotation of  360°. Thus, every hour we rotate 15° longitude, see figure 2. When it is 12:00 UTC (international standard time) - anywhere in the world - it is 12:00 Local Time in Greenwich and 24:00 Local Time at the other side of the planet: 180° E or 180° W: the datte lin da ine e. Cros rossin sing this this specia eciall merid eridia ian n changes not only the hour but also the date. The North Pole has a latitude of 90° N and the South Pole 90° S. The meridians cover twice

this angle up to 180° W or E. Meridians converge at the poles, whereas parallels run parallel to each other and never meet. All meridians and the equator - the biggest parallel - form great circles, and the remaining parallels form so-called small circles. A great circle divides the earth in two exact halves. In figure 3 the position of Boston in the United States is shown using latitude and longitude in degrees, minutes and seconds: 42° 21' 30" N , 71° 03' 37" W Most sailors will actually notate seconds in metric fractions of minutes: 42° 21,5' N , 71° 03,6' W or 42° 42° 21. 21.5' 5' N , 71° 71° 03. 03.6' 6' W

, see see the the notation style guide

On small scaled charts we want to be accurate within one minute or one nautical mile. On larger scaled charts the accuracy is more likely to be within a tenth of a mile (a cable). If the earth were a perfect sphere ere with ith a circu circumf mferen erence ce of roughl roughly y 40000 40000 kilome kilometr tres es all great circles - meridians plus the equator - would have the same length and could be used as a distance distance unit when divided divided into 360 degrees, degrees, or 360° 360° x 60' 60' = 2160 21600' 0' minu minute tes. s. In 1929 1929,, the the international community agreed on the definition of 1 international nautical mile as 1852 metres, whic which h is roug roughl hly y the the average leng length th of one one minute of latitude i.e. one minute of arc along a line of longitude (a meridian). Or to put it shortly: 1 nm = 1' We are are now now able able to desc describ ribe e any any posi positi tion on in lati latitu tude dess and and long longit itud udes es.. Moreover, we can state the distance between two of those positions using nautical miles or minutes. All we need now is a proper way to define speed. For that, sailors use knots, the number of nautical miles an hour.

RYA

&  ASA

sailing schools

To put this navigation course into practice a Royal Yachting Association or American Sailing Association approved sailing course is recommended. Sailing schools in Greece and Turkey for: RYA competent crew RYA day skipper (non-tidal) RYA coastal skipper (non-tidal) ASA basic coastal cruising (103) ASA bareboat chartering (104) ASA coastal navigation (105)

And the most enjoyable way to learn how to sail is by combining such courses with a yachting vacation in Greece or Turkey. Ideal areas for sailing courses are the Saronic Gulf near Athens and the Ionian Islands to the west of Greece, which provide reliable and gentle winds, dolphins and ancient

Greek monuments and temples.

A little History Mariners during the 15th century relied on charts called "portolans" to assist them on their voyages. Portolan comes from the Italian word  portolani  , which were medieval pilot books. The The port portol ola ans cont contai aine ned d maps aps of coas coastl tlin ines es,, loca locati tion onss of  harbours, river mouths, and man-made features visible from the sea. They were a compilation of centuries of seafarer obse observ rvat atio ions ns.. As sail sailor ors' s' skil skills ls impr improv oved ed and and the the use use of the the compass was more widespread, portolans improved in accuracy. Also Also Colum Columbu buss used used these these porto portola lans ns on his journ journey eys. s. Portu Portugu gues ese e char chartt makers added the meridian line, a point useful for latitude sailing as well as for navigating solely by compass. A geographic feature could now be located through the use of its distance in degrees of latitude from a ship's point of  departure. Note that the use of latitude and longitude was understood since the the time time of Ptolem Ptolemy y

, the the second second centu century ry CE.

Duri During ng the the fift fiftee eent nth h cent centur ury y Port Portug ugal al led led the the Euro Europe pean an worl world d in sea sea exploration. The golden age of discovery for Portugal lasted almost a century until the Dutch eventually seized their trade routes from them. As we move to the next chapter of this course we enter the sixteenth century when the Mercator chart was invented.

Glossary 1.

Parallels: Circles parallel to the equator, ranging from 0° to 90° N or

S. Only the equator is a great circle. 2.

Meridians: half-circles converging at the poles, ranging from 0° to

180° E or W. Each pair of opposing meridians forms a great circle. 3.

Prime meridian: 0° or the Greenwich meridian which - together with

the date line meridian - divides the Western and Eastern hemispheres. 4.

Great circle: The intersection of a sphere and a plane that passes

through the sphere's centre. 5.

Small circle: The intersection of a sphere and a plane that doesn't

pass though the sphere's centre. 6.

Time Tim e zon zones es: By conv conven enti tion on 24 zone zones, s, each each 15° 15° long longit itud ude e wide wide..

Hence, noon at Greenwich gives midnight at 180° E. 7.

outdated ed accron accronym ym GMT (Green (Greenwi wich ch Mean Mean GMT, GM T, UT UTC, C, Zu Zulu lu: The outdat

Time) is roughly the same as UTC or Zulu, and is also the local time at Greenwich when daylight saving isn't used. Note that UTC is an atomic time

scale which only approximates GMT, so best to use the modern term “UTC”. Antonym: Local time elsewhere. For example, local time in Athens = UTC + 2. 8.

Date line: The 180° meridian which extends from or is opposite to the

prime meridian. Here, not only the hour changes when crossing the meridian, but also the date. 9.

Latitude: Position property defined by the number of degrees north or

south of the equator, varies from 0° to 90°. 10.

Longitude: Position property defined by the number of degrees east

or west of the prime meridian, varies from 0° to 180°. 11.

Position: Latitude first and longitude second. For example: Athens in

Greece 37° 58' N , 23° 43' E. 12.

Nautical mile: One nm is one minute (') on the vertical scale on the

chart. 1' equals 1852 metres. Nautical miles are divided into 10 cables. 13.

Knots: Nautical miles per hour.

Chapter-2 Nautical charts char ts-sel -selff assignmen assig nmentt

Compass navigation Skip over navigation

Skip over navigation

Marine compass In China compasses have been in use since the Han dynasty (2nd century BCE to 2nd century CE) when they were referred to as “south-pointers”. However at first these magnets were only used for geomancy much like in the art of Feng Shui. Eventually, during the Sung dynasty (1000 CE) many trading ships were then able to sail as far as Saudi Arabia using compasses for marine navigation. Between 1405 and 1433, Emperor Chu Ti's Treasure Fleet of the Dragon Throne ruled the entire South Pacific and the Indian Ocean, a territory that ranges from Korea and Japan to the Eastern coast of Africa. At this time Western mariners were still rather ignorant of the navigational use use of the the magn magnet et.. Petr Petrus us Perig Perigri rinu nuss van van Marico Maricour urtt wrot wrote e a first first trea treati tise se on the magnet itself: “De Magnete” (1269). And though its nautical use was already mentioned in 1187 by the English monk Alexander Neckham, the use onbo onboar ard d only only came came abou aboutt arou around nd the the 13th 13th and and 14th 14th cent centur ury y in the the Mediterranean Sea. Much later, in 1545, Pedro de Medina (Sevilla 1493-1567) wrote the Spanish stan standa dard rd work work “Art “Arte e de Nave Navega gar” r” on mari marine ne comp compas asss navi naviga gati tion on.. This This masterpiece was first translated in Dutch (1580) and was -O Irony- used by Jaco Jacob b van Heems Heemske kerk rk when when the the Dutch Dutch dest destro roye yed d the Spani Spanish sh flee fleett near Gibraltar in 1607. The drawback was of course Van Heemskerk's own death during this victory.

Magnetic Variation In the the fin-d fin-de-s e-sièc iècle le of the the sixtee sixteent nth h centur century y marine mariners rs believ believed ed that that the the magnet gnetic ic nort north h pole ole coinc oincid ided ed wit with the geog eograp raphic nort orth pole. ole. Any

suggestion

otherwise

had

been

denied

by

Pedro

de

Medina.

Magnetic Magnetic observations observations made made by explorers explorers in subsequen subsequentt decades decades showed showed howe howeve verr that that thes these e sugg sugges esti tion onss were were true true.. But But it took took unti untill the the earl early y nineteenth century, to pinpoint the magnetic north pole somewhere in Arctic Canada (78° N , 104° W). From then on the angle between the true North and the Magnetic North could be precisely corrected for. This correction angle is called magnetic variation or declination. It is believed that the Earth's magnetic field is produced by electrical currents that originate in the hot, liquid, outer core of the rotating Earth. The flow of  electric currents in this core is continually changing, so the magnetic field produced by those currents also changes. This means that at the surface of  the Earth, both the strength and direction of the magnetic field will vary over secular ar variat variation ion of the the the year years. s. This This grad gradua uall chan change ge is call called ed the the secul the magnetic field. Therefore, variation changes not only with the location of a vessel on the earth but also varies in time. The The correc correctio tion n for magn magneti eticc variat variation ion for your your locat location ion is shown shown on the nearest! nautical chart's compass rose . In this example we find a variation of 4° 15' W in 2009, with an indicated annual correction of 0° 08' E. Hence, in 2011 this variation variation is estimate estimated d to be 3° 59', almost almost 4° West. West. This means means that if we sail 90° on the chart (the true course), the compass would read 94°. Another example: let's say the compass rose gives a variation of 2° 50' E in 2007, with a correction of 0° 04' E per year. In 2009 this variation is estimated to be 2° 58', almost 3° East. Now, if we sail 90° on the chart, the compass would read 87°.

Correcting for variation

These overlayed compass roses show the difference between true north and magnetic north when the magnetic variation is 10° West. From the image we find: tc = cc + var in whic which h “cc” and “ tc” stan stand d for for “com “compa pass ss cour course se”” and and “tru “true e cour course se”, ”, respectively. To convert a true course into a compass course we need first assign a “-”  to a Western Western and a “+” to a Eastern Eastern variation. variation. Note that this makes sense! because of the clockwise direction of the compass rose. Here, the inner circle is turned 10° anticlockwise, anticlockwise, hence -10° . Now, use the same but re-written equation: cc = tc - var 235° = 225° - (-10°)

So, to sail a true course of 225°, the helmsman has to steer a compass course of 235°. To convert a compass course into a true course we can use the original equation. If we have steered a compass course of 200°, we have to plot a true true course course of of 203° 203° in the the chart chart if the the varia variatio tion n is 3° 3° East East of 190° 190° if the the var varia iati tion on is 10° 10° Wes Westt

or a true true cour course se

.

Magnetic deviation Magnetic deviation is the second correctable error. The deviation error is caused by magnetic forces within your particular boat. Pieces of metal, such as an engine or an anchor, can cause magnetic forces. And also stereo and other other electr electric ic equipm equipment ent or wiring wiring,, if too close close to the compas compass, s, introd introduce uce errors in compass heading. Furthermore, the deviation changes with the ship's heading, resulting in a deviation table as shown below. The vertical axis states the correction in degrees West or East, where East is again positive.

The horizontal axis states the ship's heading in degrees divided by ten. Thus, when you sail a compass course of 220°, the deviation is 4° W. (Note, that on most modern sailing yachts the deviation is usually not larger than 3°). When a compass is newly installed it often shows larger deviations than this and needs needs compen compensat sation ion by carefu carefully lly placin placing g small small magn magnets ets around around the the compass. It is the remaining error that is shown in your deviation table. You can check your table every now and then by placing your boat in the line of a pair of leading lights and turning her 360 degrees.

Correcting for both deviation and variation Converting a compass course into a true course, we can still use our equation but we need to add the correction for deviation: cc + var + dev = tc Example 1: The compass course is 330°, the deviation is +3° (table) and

the variation is +3° (chart); 330° cc + 3° var + 3° dev = ?° tc

giving a true course of 336° which we can plot in our chart Example 2: The compass course is 220°, the deviation is -4° (table) and the

variation is still +3° (chart). 220° cc + 3° var + -4° dev = ?° tc

giving a true course of 219°. Example 3: The compass course is still 220°, therefore the deviation is still

-4° (table) but let's use a variation of -10° this time. 220° cc + -10° var + -4° dev = ?° tc

giving a true course of 206°. Converting a true course into a compass course is a little less straight forward, but it is still done with the same equation. Example 4: The true course from the chart is 305° and the variation is +3°

(chart), yet we don't know the deviation; ?° cc + 3° var + ?° dev = 305° tc

Luckily, we can rewrite this so this reads: cc + dev = 305° tc - + 3° var = 302°

In plain English: the difference between the true course and the variation (305 - + 3) = 302 should also be the summation of the compass course and the deviation. So, we can tell our helms person to steer 300°, since with a cc of 300° we have a deviation of +2° (As can be deduced from the deviation table above).

Example 5: The true course from the chart is 150° and we have a Western

variation of 7 degrees (-7°). We will use the rewritten equation to get: 150° tc - - 7° var = cc + dev = 157°

From the deviation table we find a compass course of 160° with a deviation of -3°. Voilà!

Magnetic course The magnetic course (mc) is the heading after magnetic variation has been considered, but without compensation for magnetic deviation. This means that we are dealing with the rewritten equation from above: tc - var = cc + dev = mc.

Magnetic courses are used for three reasons: 1. To convert convert a true course course into into a compass compass course course like we saw saw in the last last paragraph. 2. On vessels vessels with more than than one steering steering compass, compass, also more more deviation deviation tables are in use; hence only a magnetic or true course is plotted in the chart. 3. Bear Bearin ings gs take taken n with with a han handhel dheld d com compass pass ofte often n don't on't requ requir ire e a correction for deviation, and are therefore useful to plot in the chart as magnetic courses. Note, that the actual course lines the navigator draws in the chart are always true courses! These can subsequently be labeled with the true course or the corresponding magnetic or compass course if appropriate. In the next chapter we will be plotting courses in the chart. To summarise, we have three types of “north” (true, magnetic and compass north north)) like like we have have three three types types of course courses: s: tc, mc and cc. All these these are related by deviation and variation.

Glossary 1.

Maps Ma ps wi with th is isog ogon oniic lin ine es

World - overview 2000 World - detailed 2000 World - detailed 2005

:

World Wor ld - anim animate ated d in tim timeeVariation:

The angle between the magnetic north pole

and the geograph geographic ic north north pole. Also called called the the magne magnetic tic declin declinatio ation n 2.

.

Secular variation: The change of magnetic declination in time with

respect to both strength and direction of its magnetic field. 3.

West (-) , East (+): Western variations or deviations are designated

with a negative sign by convention due to the compass card's clockwise direction. 4.

Deviation: The error in compass heading caused by electric magnetic

currents and or metal objects. 5.

Deviation table: A table containing deviations in degrees versus the

ship's heading (compass course) in degrees. Usually plotted in a graph. 6.

True course: Course plotted in the chart i.e. course over the ground

or “course made good”. The course corrected for compass errors. 7.

Compass course: The course (ship's heading) without the correction

for compass errors. 8.

cc + var + dev = tc: This equation shows the connection between the

compass course, its errors and the true course. It can also be read as: tc var = cc + dev.

Plotting and piloting Skip over navigation

Lines of position The The mode modern rn char chartt show showss us posi positi tion onss of many many recog recogni niza zabl ble e ai aids ds to navigation like churches and lighthouses, which facilitate the approach to a coas coasta tall area area.. This This conce concept pt origi origina nate ted d from from a char chartt by Waghe Waghena naer er and and proved a milestone in the development of European cartography. This work was call called ed “Spieg “Spieghe hell der Zeevae Zeevaerd rdt” t” and inc includ luded ed coast coastal al profil profiles es and tida tidall information much like the modern chart. It enables us to find the angle between the North and for example an offshore platform, as seen from our position.

Compass courses

True courses

Taking a bearing on this oil rig with a compass provides us with a compass course. This course first needs correction for both variation and - via ship's heading - deviation before plotting a Line of Position (LOP) in the chart as a true course. Our position is somewhere along this line.

Ranges

A precise way to obtain a LOP, and without a compass, is to locate two aids to navigation in line. The map of  Laura Island on the right shows four examples of  ranges, each consisting of  two aids to navigation. Please, note that: More distance between the two landmarks enhances accuracy. And less distance between the vessel and the closest aid to navigation also enhances accuracy. One of these four ranges consists of two lights that are intentionally placed to provide a LOP. These pairs of lights are called range lights or leading

lights. In this case they indicate the approach towards the marina and mark

the the chan channe nell betw betwee een n the the dang danger erou ouss rock rockss along long a true true cours course e of 50°

.

When When looki looking ng towar towards ds any leadi leading ng light lights, s, the neare nearest st one will will be lower lower

.

Therefore, in the middle of the channel both lights will appear vertically above each other. Even when there are no man-made structures available, a range can be found by using natural features such as coastlines and islets. The example on the left shows a yacht that will avoid the dangerous wreck as long as the islets don't overlap.

Position fix If two LOPs intersect we can construct a position fix: the ship's position on the earth. Oft Often howev owever er,, a tria riangle occ occurs urs when a third ird LOP is add dde ed in the construction. This indicates that there are errors involved in at least one of  the bearings taken. In practice, we should consider each LOP as the average bear bearin ing g in a wid wider er sec secto torr of for for inst instan ance ce 10° 10°

.

optimu imum m ang angula ular r spr spread ead is 90° (two The opt (two objec objects ts)) or 120° (three objects). Moreover, bearings on distant objects bring about more uncertainty in our position fix as the sector widens. Finally, if moving fast you should not put any time between the bearings.

The next example features a nocturnal landfall on Willemsen Island - you are welcome to visit, but mind the rocks. The position fix is plotted by taking

bearings at two light-vessels as their lights appear over the horizon . The variation is -1° and the ship's compass heading is 190°. Since we use our stee steeri ring ng com compass pass for for our our beari bearin ngs, gs, we can can use use the same same deviation table. That means a deviation of -4° with which we can calculate ( cc + var + dev = tc ) the true courses. ction ompass earing on Will. is 72° rue rue cour course se is 7° lot lot LOP LOP with with me & true ourse ompass earing on Will. is 173° rue rue cour course se is 68° lot lot LOP LOP with with me & true ourse raw an ellipse here the OPs intersect otate time nd “Fix ” longside osit ositio ion n is 32° 32° 4,2' N , 24° 6,7' E

With Withou outt a thir third d LOP LOP - form formin ing g the the drea dreade ded d tria triang ngle le - ther there e is the the fals false e suggestion of accuracy. Yet, instrument errors, erroneous identification of an aid to navigation, sloppy plotting, etc. can and will cause navigation errors. Therefore, if close to e.g. rocks, you should assume to be at the worst possible position (i.e. closest to the navigational hazard). The lines plotted in the chart are always true courses and these are labeled with true courses by default; the “ T ” is optional. If labeled with the magnetic etic cour course se or com corresponding magn compas pass cours ourse e add an “M ” o r “C ”, ”, respectively.

Estimated position It is some someti time mess impo imposs ssib ible le to obta obtain in more more than than one one LOP LOP at a time time.. To dete determ rmin ine e the the ship ship's 's posi positi tion on with with one one aid aid to navi naviga gati tion on we can can use use a

running fix. However if a running fix is not possible, we can determine an estimated position.

An est estimat imated ed posi positi tion on is based ased upon upon whatever incomplete navigational information is available, such as a single LOP, a series of depth measurements correlated to charted depths, or a visual observation of the surroundings. In the example on the right we see an estimated position constructed constructed using a reckoning ning posit position ion (DR) . Th single single LOP and the the ship' ship'ss dead recko T his is i s do done by by drawing a line from the DR position at the time of the LOP perpendicular to the LOP. An EP is denoted by a square instead of an ellipse.

Do not rely on an EP as much as a fix. The scale of reliability, from best to worst: Fix Running fix Estimated position DR position

Dead reckoning Dead Dead reckoni reckoning ng is a tech techniq nique ue to dete determi rmine ne a ship' ship'ss approx approxima imate te posit position ion by applying to the last established charted position a vector or series of  vectors representing true courses and speed. This means that if we have an earlier fix, we plot from that position our course and “distance travelled since then” and deduce our current position. e start off with a Fix and plot a DR position or 15 minutes later. ur estimation about our speed and course as correct, so we don't have to charge the R position. nd so on… ed through water (not over ground) rse through water (not over ground) True course (default)

= Magnet Magnetic ic course course for handhel handheld d compas compasss (no correction) Compass course for steering compass (deviation n) h an arrow, a semi-circle (circular arc) and “ DR”.

Dead reckoning is crucial since it provides an approximate position in the future. Each time a fix or running fix is plotted, a vector representing the ordered course and speed originate from it. The direction of this course line represents the ship's course, and the length represents the distance one would expect the ship to travel in a given time. This extrapolation is used as a safety precaution: a predicted DR position that will place the ship in water 1 metre deep should raise an eyebrow… In the example above the true courses are plotted in the chart, and to assist the the helm helmsm sman an thes these e cour course se line liness are are labe labell lled ed with with the the corre corresp spon ondi ding ng compass courses. Guidelines for dead reckoning: Plot a new course line from each new fix or running fix (single LOP). Never draw a new course line from an EP. Plot a DR position every time course or speed changes. Plot a corrected DR position if the predicted course line proofed wrong, and continue from there.

Running fix Under some circumstances, such as low visibility, only one line of position can be obtained at a time. In this event, a line of position obtained at an earlier time may be advanced to the time of the later LOP. These two LOPs should not be parallel to each other; remember that the optimal angular spread is 90°. The position obtained is termed a running fix because the ship has “run” a certain distance during the time interval between the two LOPs.

e obtain a single OP on LANBY 1 nd plot a orresp orrespond onding ing (same (same ime) dead reckoning osition. The stima stimated ted positi position on is onstructed by rawing rawing the the short shortest est ine ine betw betwee een n the the DR nd the LOP: erpendicular. o LOPs at all. We ack and plot a DR osition. e obtain a LOP on ANBY 2. To use the irst LOP we advance over a construction ine between the two orresponding DR ositions. We use oth oth its its direc irecttion ion &  istance. To use the LOP obtained at an earlier time, we must advance it to the time of  the second LOP. This is done by using the dead reckoning plot. First, we measure the distance betw etween the two DR positi itions and draw a hich is para parall llel el to a line line conn connec ecti ting ng the the two two DR constructio const ruction n line, which positions. Note that if there are no intervening course changes between the two DR positions, it's easiest just to use the course line itself as the construction line. Now, ow, usin sing the parall rallel el rul rulers ers we adva advanc nce e the first irst LOP alon along g this construction line over the distance we measured. Et voilá, the intersection is our RFix. If there is an intervening course change, it appears to make our problem harder. Not so! The only DR positions that matter are the two corresponding with the LOPs. Guidelines for advancing a LOP: The The dista distance nce:: equal equal to the the distan distance ce betwee between n the the two two corres correspon pondin ding g DR positions.

The The direct direction ion:: equal equal to the direct direction ion betwee between n the two two corres correspon pondin ding g DR positions. Draw the advanced LOP with a dotted line and mark with both times. Label the Running Fix with an ellipse and " RFix " without underlining. underlining.

Danger bearing Like the dead reckoning positioning, the danger bearing is an important tool

to keep the ship out of harm's way. First, the navigator identifies the limits of safe, navigable water and determines a bearing to for instance a major light. This bearing is marked as “No More Than” (NMT ) or “No Less Than” (NLT ), ), depending on which side is safe. Hatching is included on the side that is hazardous, along with its compass bearing. In the the exam example ple on on the the right right a true true cour course se of 325° 325° is is plott plotted ed (5° (5° varia variatio tion n ), marked with the magnetic course of 320°, practical for a handheld compass that requires no deviation correction. Were we see that light at 350° magnetic - which is definitely “More Than” the rocks and wreck would be between us and the major light. A possible cause could be a (tidal) stream from east to west. When a distance is used instead of a direction, a danger range is plotted much the same way as the danger bearing.

Turn bearing The Turn bearing - like the danger bearing - is constructed in the chart in advance. It should be used as a means of anticipation for sailing out of safe waters (again like the danger bearing and dead reckoning). The turn bearing is taken on an appropriate aid to navigation and is marked “ TB”. As you pass the object its bearing will slowly change. When it reaches the turn bearing turn the vessel on her new course.

This type of bearing is also used for selecting an anchorage position or diving position.

Snellius construction

Will Willeb ebro rord rd Snel Snelli lius us - a 16th 16th centu century ry math mathem emat atic icia ian n from from Leid Leiden en,, the the Netherlands - became famous for inventing the loxodrome and his method of  triangulation. The Snellius construction was was firs firstt used used to obta obtain in the the len length gth of the the meri meridi dian an by measu measuri ring ng the dista distanc nce e betw betwee een n two two Dutc Dutch h citi cities es . He took took angl angles es from from and and to chur church ch towe towers rs of villa village gess in betw between een to reac reach h his his objective. Nowadays we use the Snellius method to derive our position from three bearings without the use of LOPs, and while leaving out deviation and variation, which simplifies things. Also, since only relative angles are needed a sextant can be used to measure navigation aids at greater distances. Closer in a compass can be used. The construction: See figure 1: Compass bearings are 320° on A; 360° on B; 050° on object C. The angle between A and B = 40°. The angle between B and C = 50°. Draw lines from A to B and from B to C. Add the two light-blue perpendicular bisectors of lines AB and BC. Draw at object A a construction line 40° inland of line AB. Draw at object C a second construction construction line 50° inland of line CB.

See figure 2: At object A: draw a line l ine perpendicular to the construction line. At object C: draw another line perpendicular perpendicular to the construction line. The two intersections with the light-blue lines indicate the centres of two circles. Finally, draw the first circle using A and B and the second circle using B and C. The off shore intersection of the two circle gives us our position fix.

The advantage: deviation and variation can be left out since the angles (here 40° and 50°) are relative ones. Moreover, a sextant can be used to obtain angles between objects at greater distances, that with a compass would be less precise.

International notation International notation conventions for plotting in the chart

Fix

LOP

Running Fix

LOP advanced

Estimated Position

Course & Speed

Dead Reckoning

Set & Drift

Electronic Fix (GPS) Electronic Fix (Radar) Note, that a few countries use an alternative symbol Plotting should be done with a soft pencil. Moreover, avoid drawing lines through the chart symbols. This is to prevent damage to the chart when you have to erase the construction. Learn sailing and navigation via yacht charters with instruction in Greece .

Glossary 1.

Line Lin e Of Pos Positi ition on (LO (LOP) P): The locus of points along which a ship's

position must lie. A minimum of two LOPs are necessary to establish a fix. It is standard practice to use at least three LOPs when obtaining a fix, to guard against the possibility of and, in some cases, remove ambiguity. 2.

Transit fix: The method of lining up charted objects to obtain an LOP.

3.

pair of ligh ights or day marks rks Leading Leadi ng light lights s or Ran Range ge lig lights hts: A pair

deliberately placed to mark a narrow channel. 4.

Position fix: The intersection of various LOPs.

5.

Cross bearing: The use of LOPs of several navigational aids to obtain

a position fix. Remember to use an optimal angular spread. 6.

Running fix: The use of an advanced LOP. Make sure to use only the

corresponding DR positions. Also don't use the EP for advancing the first LOP. 7.

Determini ining ng a posit position ion by plott plotting ing course coursess and and Dead reckon reckoning ing: Determ

speeds from a known position. It is also used to predict when lights become visible or to determine the set and rate of a current. 8.

Estimated Esti mated posit position ion: Combine a corresponding DR position with a

single LOP to get an EP position. 9.

Snellius construction: Anot Anothe herr way way to comb combin ine e thre three e comp compas asss

bearings to obtain a position fix. The advantage over a cross bearing is that both magnetic variation and deviation don't need to be taken into account. 10.

Course: (C) The direction in which a vessel is steered or is intended to

be steered (direction through the water). 11.

Speed: (S) The speed of the boat through the water.

12.

Set: (SET) The direction in which the current is flowing (see chapters

6,7 and 8).

13.

Drift: (DFT) The speed (in knots) of the current (see chapters 6,7 and

8). 14.

Default heading is True course (M = magnetic , C = compass).

15.

Default time is 24 hour clock ship time else UTC.

Piloting and navigation Skip over navigation

Doubled angle fix The Doubled angle on the bow fix resembles a running fix though only one navigation aid is used. In the example on the right the initial angle (30°) on the bow is doubled (60°) yielding an isosceles trian riang gle . The The dist istanc ance trave ravell lled ed betw etween een the bear bearin ings gs is the the same same as the the dist distan ance ce from from the the visible wreck.

α  = 30° , β = 60° δ = 120° ,  γ = 30° Isosceles

d1 = d2

Start with the visible wreck having a bearing of less than 45° off the bow ( α ), ), note the log distance. Proceed along the course until the angle on the bow is doubled ( β), read the log: d1 is 10 nm. Use the log distance to find the position on the second LOP. It is an isosceles triangle, so d2 is also 10 nm. Label it with an ellipse and " RFix " but realize it is less precise than a running fix that involves two navigation aids.

Four point fix If the first angle on the bow is 45°, a special situation occurs: The Four point fix, so called since 45 degrees equals equals 4 point pointss on the compas compasss (1 point point = 11,25° 11,25°

).

Start with a bearing with 45° on the bow ( α ), ), note the log. Proceed along the course till the angle on the bow is 90° (β), read the log: d1 is 4 nm

α  = 45° , β = 90° δ = 90° ,  γ = 45° Isosceles

d1 = d2

Use the log distance to find the position on the second LOP. Isosceles, so d2 is also 4 nm. Label it with an ellipse and " RFix ". ".

Special angle fix The Special angle fix requires the mariner to know some special pairs of  angles (a :  b) that give the distance travelled betw betwee een n bear bearin ings gs as equa equall to the the dist distan ance ce abeam

.

In the example on the right α  = 21° and β = 32° are used. Now, the log distance equals the shortest distance between wreck and course line (6 nm). A few practical pairs: 16 : 22 25 : 41 37 : 72

α  = 21° , β = 32° d1 = d2

21 : 32 32 : 59 40 : 79

Remember: the greater the angular spread the better. Hence, of these three fixes the four point fix is the most precise one. Top of Form

Enter α  (1-45°):

β: Bottom of Form

Mathematics: Mathematic s: isosceles triangle fixes

Distance horizon

of

the

On a flat world there would be no diff differ eren ence ce betw betwee een n the the visi visibl ble e and sensib sensible le horizo horizon. n. Howeve However, r, visibl ible e hor horizo izon n on Eart arth the vis app ppea ears rs sever evera al arc minu inutes below the sensible horizon due to two opposing effects: the curvature of the earth's surface; atmospheric refraction. Atmospheric refraction bends light rays passing along the earth's surface toward the earth. Therefore, the geometrical horizon appears elevated, forming the visible horizon. The distance of the visible horizon is a (semi-empirical) function of Eye Height:

Mathematics: horizon distances

Dipping range If an object is observed to be just rising above or just dipping below the visible horizon, its distance can be readily calculated using a simple simple formula. formula. The object's object's elevation (the height of a light above chart datum datum ) can be foun found d in the chart chart or othe otherr nautica nauticall public publicati ation on such such as the the 'List of Lights'. Note that in some charts elevation is referred to a different

datum than sounding ings magnificent lighthouse.

. Clic lick on the image on the right to view a

The formula contains the two distances from the visible horizon and can be sim simplif plifie ied d by the equa equati tion on:: 2.08 2.08 x (√El (√Elev evat atio ion n + √Eye √Eye heig height ht)) . Many Many nautical publications contain a table called "distances of the horizon" which can be used instead of the equation. Use the dipping range to plot a Distance LOP in the chart: a circle equal in radius to the measured distance, which is plotted about the navigation aid. Finally, take a bearing on the object to get a second LOP and a position fix. Top of Form

Enter Eye height (metres): Enter Elevation (metres):

Distance is (nm): Bottom of Form

Vertical sextant angle Similarly, a distance LOP can be obtained by using a sextant to measure the angle angle (arc) (arc) betw between een for for insta instance nce the the light light and and chart chart datu datum m of a light lighthou house se or any other structure of known elevation. Once the angle is corrected for index ind ex err error or the distance can be found in a table called: "Distances by Vertical Sextant Angle", which is based on the following equation.

The angle in minutes total, thus 1° 12' = 72' total, and corrected for index error. Elevation in in me metres

.

Water height in metres above or below chart datum of object. Distance or Range in nautical miles. Ascertain whether the base of the object is beyond the horizon Corrected angle should be greater than 20'. Though tables can be used for quick reference, this function is valid for object objectss higher higher than than usuall usually y tabula tabulated ted metres:

. An example example with with a lighth lighthous ouse e of 80

Measured angle is 1° 19', index error is +6': angle = 73'. Let's assume water height at 3 metres above Mean Level datum. Range = 1.854*(80-3/73) = 1.96 nm. The range can be used as a danger bearing. Together with a compass bearing one object with known elevation results in a positi position on fix. fix. If more more than than one vertical vertical sextant sextant angle angle is combin combined ed the optimum angular spread should be maintained. Top of Form

Ente Enterr Ang Angle le (min (minut utes es tota totall

):

Enter Elevation (metres):

Distance is (nm): Bottom of Form

Often, the correction for water height can be left out. Though, realizing that

the horizon horizon is closer closer than than one might might think think , another another correction correction is someti sometimes mes needed. In the Mediterranean Sea for example we can see mountain tops with bases lying well beyond the horizon. Mutatis mutandis, the structures, which they bear have bases beyond the horizon as well.

This is the equation for finding the distance of an object of known elevation loca locate ted d beyo beyond nd the the hori horizo zon. n. In the the den denomin ominat ator or of this this equa equati tion on a compensating factor is included by which the measured angle should be reduced. Top of Form

Enter Eye Height (metres):

Ente Enterr Ang Angle le (min (minut utes es tota totall

):

Enter Elevation (metres):

Distance is (nm): Bottom of Form

Mathematics: Mathemat ics: vertical sextant angles

Estimation of distance The most obvious way to estimate distances is of course by using the distance between our eyes. If we sight over our thumb first with one eye then with the other, the

thumb moves across the background, perhaps first crossing a tower second crossing a bridge. The chart might tell that these structures are 300 m apart. Use the the ratio ratio of: distan distance ce betwee between n eye and outst outstret retche ched d arm/d arm/dist istanc ance e between pupils: usually 10 . The objects are 3 kilometres away. Other physical relationships are useful for quick reference. For example, one finger width held at arm's length covers about 2° arc, measured horizontally or vertically. Two fingers cover 4°. Three fingers cover 6° and give rise to the three finger rule: "An object that is three fingers high is about 10 times as far away as it is high."

Estimation with horizon The image on the right shows us that it is possible to esti estima mate te the the heig height ht of any any objec objectt that that cros crosse sess the the horizon as seen from our own point of view. This picture of the 'Pigeon Rocks' near Beirut harbour was taken from a crow's nest at a height of 34 metres. The distance of the visible horizon (12 nm) is far larger than than 34 metr metres es . Ther Theref efor ore, e, we can can - witho ithout ut any other other info inform rmat atio ion n estimate that these rocks have a height of 34 metres as well. Factum: All tops crossing the horizon and with bases at sea level are on eye level

.

Furthermore, if we see these rocks over a vertical angle of for example 7° = 0.1225 rad., then the range is 34/0.1225 = 277 metres. Finally, plot both range and bearing in the chart to construct an EP, et Voilà!

Fix by depth soundings A series of depth soundings - in this example every 10 minutes - can greatly improve your position fix:

1.

corre correct ct your your sou sound ndin ings gs for for tid tide, e, etc etc..

;

2.

copy copy the the DR DR cou cours rse e lin line e on on a tra trans nspa pare rent nt shee sheet; t;

3.

writ write e the the dep depth thss adj adjac acen entt acco accord rdin ing g to the the time timess of the the soun soundi ding ngs; s;

4.

move the sheet over the chart to find its best location.

Due to leeway, currents or other factors the two course lines need not be parallel to or of same length as each other. Yacht charters and learning how to sail in Greece with instruction .

Overview 1.

Line Lin e Of Pos Positi ition on (LO (LOP) P): The locus of points along which a ship's

position must lie. A minimum of two LOP's are necessary to establish a fix. It is standard practice to use at least three LOP's when obtaining a fix, to guard against the possibility of and, in some cases, remove ambiguity. 2.

Range or Distance LOP: Obtained by using a stadimeter, sextant or

radar. A circle equal in radius to the measured distance is plotted about the navigation aid; the ship must be somewhere on this circle. 3.

Runnin Run ning g fix: A posi positi tion on dete determ rmin ined ed by cros crossi sing ng line liness of posi positi tion on

obtained at different times and advanced or retired to a common time. 4.

Determini ining ng a posit position ion by plott plotting ing course coursess and and Dead reckon reckoning ing: Determ

speeds from a known position. It is also used to predict when lights become visible or to determine the set and drift of a current. DR positions are drawn in advance to prevent sailing into danger. A DR position will be plotted: 1.

every hour on the hour;

2.

at the time of every course change or speed change;

3. for th the ti time at at wh which a (run running) fix fix is ob obtained, al also a new co course line will be plotted; 4.

for the time at at which a single LOP is obtained;

5. 5.

and never draw a new course line from an EP position! Estimated position: The most probable position of a craft determined

from incomplete data or data of questionable accuracy. Such a position might be determined by applying a correction to the dead reckoning position, as for estimated current; by plotting a line of soundings; or by plotting a LOP of  questionable questionable accuracy. 6.

Double angle on the bow: A method of obtaining a running fix by

measuring the distance a vessel travels on a steady course while the relative bearing (right or left) of a fixed object doubles. The distance from the object at the time of the second bearing is equal to the run between bearings, neglecting drift. 7.

Four point fix: A special case of doubling the angle on the bow, in

which the first bearing is 45° right or left of the bow. Due to angular spread this is the most precise isosceles fix. 8.

Special angle fix: A construction using special pairs of relative r elative angles

that give the distance travelled between bearings as equal to the navigation aids' range abeam. 9.

Distance Dist ance from horiz horizon on: The distance measured along the line of 

sight from a position above the surface of the earth to the visible horizon. 10.

Sensible horizon: The circle of the celestial sphere formed by the

inte inters rsec ecti tion on of the the cele celest stia iall sphe sphere re and and a plan plane e thro throug ugh h the the eye eye of the the observer, and perpendicular to the zenith-nadir line. 11.

Visible horizon: The line where Earth and sky appear to meet. If 

there were no terrestrial refraction, visible and geometrical horizons would coincide. Also called : apparent horizon. 12.

Originall ally, y, the celest celestial ial horizo horizon; n; now now more more Geometrica Geom etricall horizo horizon n: Origin

commonly the intersection of the celestial sphere and an infinite number of  straight lines tangent to the earth's surface and radiating from the eye of the observer. 13.

Dipping Dipp ing range or Geogr Geographic aphic range: The maximum distance at

which the curvature of the earth and terrestrial refraction permit an aid to navigation to be seen from a particular height of eye (without regard to the luminous intensity of the light). 14.

Elevation: The height of the light above its chart datum in contrast to

the height of the structure itself. 15.

Chart Ch art Da Datu tum m:

Offi Offici cial ally ly:: Char Chartt Soun Soundi din ng Datu Datum: m: An arbi arbitr trar ary y refe refere renc nce e plan plane e to whic which h both both heig height htss of tide tidess and and wate waterr dept depths hs are are expressed on a chart. In the same chart heights can be related to other datums than depths. 16.

Vertical sextant angle: The method of using the subtended angle of 

a vertical object to find its range. 17.

Index error: In a marine sextant the index error is primarily due to

lack of parallelism of the index mirror and the horizon glass at zero reading. A positive index error is subtracted and a negative index error is added.

18.

Estimation with horizon: Estimation of heights using the horizon: All

tops crossing the horizon and with bases at sea level are on eye level. 19.

Estimation with depth effect : .

20.

Estimated position with soundings: .

Mathematics: isosceles triangle fixes Mathematics: horizon distances Mathematics: sextant angles

Tides

Skip over navigation

Tidal movements The tide is the vertical rise and fall of the sea level surface caused primarily by the change in gravitational attraction of the moon, and to a lesser extent the sun. As the earth spins on its axis the centrifugal force results in slightly deeper water near the equator as opposed to shallower water at the poles. In fact it causes a flow low from the poles to the equator. The earth is also in orbit around the sun (one revolution in one year) creating not only another centrifugal force but also a gravitational interaction. These two yield a bulge on the night site (centrifugal) and a bulge on the day site (gravitational) both of them moving as the world turns. Therefore, a certain place on this world will expe experi rien ence ce two two high high and and two two low tide tidess each day. With With thes these e forc forces es alon alone, e, we woul would d not not have sprin and neap tides . spring g tide tides s Spring Spring tides tides have have higher higher high high tides tides and and lower low tides whereas neap tides have lowe lowerr high high tid tides and and high higher er low low tid tides. es. Hence, the range (difference in water level between high and low tide) is much larger in a spring tide than in a low tide.

This an This anim imat atio ion n sh show ows s ho how w the tid tide e cha change nges s dur during ing the luna lu nar r cy cycl cle. e. Wh When en th the e su sun, n, moon moo n and ea earth rth are ali aligne gned d : spring tide. Whe Wh en at ri righ ghtt an angl gle es the forces are not aligned: neap tide. The time between spring and neap is approximately 7 days.

These differences in range can be explained if we include the moon into our earth-sun system. The moon and the earth orbit each other around around a point point (called (called the barycent barycenter er or baricenter) baricenter) 2000 odd kilo kilomet metres res insid inside e the earth earth,, creatin creating g a centrif centrifuga ugall and and a gravita gravitatio tiona nall bulge. Moreover, despite the sun's immensely larger mass, the moon exerts a 2.25 times larger gravitational attraction, since the moon is much closer to our earth. It is the combined effect of the sun and moon that creates spring and neap tides. In the animation the gravitational forces of both the sun and the moon are taken into account. When aligned with the earth they combine their

attr attrac acti tion on and and othe otherw rwis ise e they counteract their attraction. The sun is located in the corner right below, far outside this pictu picture re (note (note the the eclips eclipse) e) while the moon is revolving roun round d the the eart earth. h. One One full full circle circle corres correspon ponds ds to one lunar cycle (about 28 days). The figure below shows the ideal sinusoids of both spring and neap tides. Vertically the water height is shown versus horizontally the time. Ideally, the time between a low and a successive high is somewhat more than 6 hours. The time difference between spring tide and neap tide is normally 7 days and is in accordance with the phases of the moon. Yet, water has mass and therefore momentum. Moreover, it is a viscous fluid that generates friction if  moved. Therefore, the actual spring tide lags a day or so behind a full moon or new moon occurrence. So, tidal movements are intrinsically periodical, resulting in a Tidal day of  24 hours and 50 minutes containing one tidal cycle, namely two highs and two lows. This basic pattern may be distorted by the effects of landmasses, constrain constrained ed waterway waterways, s, friction, friction, the Coriolis Coriolis effect, effect, or other factors. factors. Hence, Hence, predictions are possible and we expect the the next day's high tide to come about 50 minutes later. However, a closer look at the orbit of the moon reveals that the moon is not always in the equatorial plane, resulting in three types of tides: Semi-diurnal tide: Featu Featurin ring g two two highs highs and and two two

lows each day, with minimal variation in the height of successive high or low waters. This type is more likely to occur when the moon is over the equator. Only a single single high high and and a single single low Diurnal tide: Only duri during ng each each tida tidall day; day; succ succes essi sive ve high high and and low low waters do not vary by a great deal. This tends to occu occurr in cert certai ain n area areass when when the the moon oon is at its its furthest from the equator. Mixed tide: Characterized by wide variations in heights of successive high

and low waters, and by longer tidal cycles than those of the semi-diurnal cycle. These tides also tend to occur as the moon moves furthest north or south of the equator.

Chart Datums

The depths and heights in the chart need a plane of reference: the Chart Datum Datum (see (see intera interact ctive ive figure figure below) below).. Depth Depthss are usua usually lly descri described bed with with respect to low water reference planes (yielding lower charted depths, which are safer) and heights are shown with respect to high water reference planes (again, yielding lower vertical clearances on the chart, which are safer). As such, the chance that the observed depth or vertical clearance beneath a bridge is smaller than the charted depth or height is rather small.

In thi his s ex exa ampl ple e the   Thi This s ex exam ampl ple e sh show ows s Char Ch arte ted d De Dept pths hs ar are e the various spring and related to LAT. neap tides around  The Observed Depth or mean water level. Note Drying Height is a that spring low water is comb co mbin inat atio ion n of Ti Tida dall the lowest. Both Height & Charted ranges are indicated. Depth.

In th this is ex exam ampl ple e th the e light elevation is reduced to high water. Also a clearance under a bridge is charted in thatt wa tha way. y. The 'he 'heigh ight' t' refe re fers rs to th the e bu buil ildi ding ng itself. On land yet another CD can be in use.

Some Chart Datums and their abbreviations: 1.

MHWS : Mean High Water Spring

2.

HW : High Water

3.

MHWN : Mean High Water Neap

4.

ML : Mean Level

5.

MLWN : Mean Low Water Neap

6.

MLWS : Mean Low Water Spring

7.

LAT : Low Astronomical Tide

Overview 1.

Tide: The vertical rise and fall of the surface of a body of water caused

primarily by the differences in gravitational attraction of the moon, and to a lesser extent the sun, upon different parts of the earth when the positions of  the moon and sun change with respect to the earth. 2.

Spring Tide: The tidal effect of the sun and the moon acting in

concert twice a month, when the sun, earth and moon are all in a straight line (full moon or new moon). The range of tide is larger than average. 3.

Neap Tide: This opposite effect occurs when the moon is at right

angles to the earth-sun line (first or last quarter). The range of tide is smaller than average. 4.

Range: The vertical difference between the high and low tide water

levels during one tidal cycle. 5.

Tidal Day: 24 hours and 50 minutes. The moon orbits the earth every

month, and the earth rotates (in the same direction as the moon's orbit) on its axis once every 24 hours. 6.

Tidal Cycle: One high tide plus a successive low tide.

7.

Semi-diurnal Tide: The most common tidal pattern, featuring two

high highss and and two two lows lows each each day, day, with with mini minima mall varia variati tion on in the the heig height ht of  successive high or low waters. 8.

Diurnal Tide: Only a single high and a single low during each tidal

day; successive high and low waters do not vary by a great deal. Such tides occur, for example, in the Gulf of Mexico, Java Sea and in the Tonkin Gulf. 9.

Mixed Tide: Characterized by wide variation in heights of successive

high and low waters, and by longer tide cycles than those of the semidiurnal cycle. Such tides occur, for example, in the U.S. Pacific coast and many Pacific islands. 10.

Chart Datum or Tidal reference planes: These fictitious planes are

used as the sounding datum for the tidal heights. 11.

Drying Height: Clearance in meters (or feet in old charts) above the

chart datum. 12.

Charted Depth: Clearance in meters (or feet in old charts) below the

chart datum. 13.

Observed Depth: Height of tide + charted depth: the actual depth in

meters. 14.

Height of light: The height of light above the bottom of its structure.

15.

Elevation: The height of the light above the chart datum.

16.

Rule of Twelve: Assuming a tidal curve to be a perfect sinusoid with

a period of 12 hours. The height changes over the full range in the six hours betwee between n HW and and LW with with the the follow following ing fracti fractions ons during during each each respec respectiv tive e hour: 1/12 2/12 2 /12 3/12 3/12 2/12 1/12.

17.

Rule of Seven: The change from spring range to neap range can be

assu assume med d line linear ar,, each each day day the the rang range e chan change gess with with 1/7t 1/7th h of diff differe erenc nce e between the spring and neap ranges. Hence, the daily change in range = (spring range - neap range)/7.

Tides

&  tidal

prediction

1 - Information from the chart Most often the chart presents succinct tide tide table tabless for certa certain in positi positions ons.. These These positions are marked with the “square”. The table below shows us an example for two different positions. The first refers to Cowe Cowess (UK) (UK),, the the seco second nd to a posi positi tion on south of Cowes.

Heights above LAT Position

Mean HW

Mean LW

Spring Neap Spring Neap Cowes

1,7 m 1,5 m 0,2 m 0,4 m 5,2 m 4,3 m 0,4 m 1,2 m

This This data data only only prov provid ides es us with with aver averag age e high high and and low low wate waters rs heig height hts. s. Moreover, it is merely valid at spring or neap tides. To use it we need to first find out how many hours we are from high water. Secondly, we need to know know if it is spri spring ng or neap neap or some someti time me in betw betwee een n at that that part partic icul ular ar moment. We shall use this table to solve two types of problems. Finding height of tide at a particular location at a particular time: To get over a shoal. To pass under a bridge. Almanacs and many other nautical publications contain predictions of the times times of high high and and low low tides tides at man many y major major stand standard ard port portss

. Also Also listed listed are are

differences in times of tides from these ports for additional secondary ports . To work with this succinct data we need two extra tools: To interpolate between high and low water heig height htss we use use the the Rul Rule e of Tw Twel elve ve. We assum ssume e the tida idal curv curve e to be a perf perfec ectt sin sinusoi usoid d with with a peri period od of 12 hour hours. s. The The height changes over the full range in the six hours between HW and LW. ○

During first hour after heigh water (HW) the water drops 1/12th of the full range.

○

During the second hour an additional 2/12th.

○

During the third hour an additional 3/12th.

○

During the fourth hour an additional 3/12th.

○

During the fifth hour an additional 2/12th.

○

During the sixth hour an additional 1/12th. Hence, two hours after the HW the water has fallen 3/12 of the full range. To interpolate between spring and neap tides we use the Rule of Seven. Since the change from spring range to neap range can be assumed linear (instead of sinusoid), each day the range changes with 1/7th of difference between the spring and neap ranges. Hence, the daily change in range is (spring range r ange - neap range)/7. Shoal problem:

Our shoal near Cowes has a charted depth of 1 meter and we would like to cross it at about 15:00 hours with our yacht (draft 1,5 m). From any nautical almanac we find that HW occurs at 03:18 15:53 and LW occurs at 09:45 22:03 at a standard port nearby. We also find that at our location HW occurs one hour later and that spring tide is due in two days. Hence, we have a HW around 17:00. Via the rule of seven we find out that today the range is: spring range - 2 x ( (spring range - neap range)/7 ) 4,8 - 2 x ( ( 4,8 - 3,1)/7 ) 4,8 - 2 x 0,25 = 4,3 m.

We also need today's HW height: which is Spring HW - 2 days x ( (5,2 -4,3)/7 ) = 5,0 m

.

Via the rule rule of of twelv twelve e we find find out out that that at two two hours hours before before high high water water height is: 5,0 - 3/12 x 4,3 = height at 15:00 hours = 3,9 m.

the the

So, after three interpolations we derive the water height at 1500 hours. Considering the charted depth leads to an observed depth of 4,9 meters, enough for our draft of 1,5 meters. Bridge problem:

An overhanging rock, power lines or bridges have their clearances charted with respect to another chart datum than LAT. Normally, 'high water' or 'MHW spring' are used as reference planes. An example: Above our shoal hangs the 'Cowes bridge'. At 15:00 hours we would like to pass this bridge, which has a charted height of 20 meters to HW. Our mast is 23 meters high. In the example above we found that the water height was 1,1 meters below HW level at that time. Obviously, we will have to wait! So, at what time will we be able to pass under this bridge? The water height must be 3 meters lower than HW level (5,0 m). That is almos lmostt 9/12 of the range (4,3 m) indica icating four hours after HW Conclusion, we will have to wait at least six hours in total.

.

2 - Information from tide tables Instead of mere averages, a tide tide table table provid provides es us each each day day with ith the the time timess of high high and low water for a particular plac place. e. Basi Basica call lly, y, it is same same table like the one we found in the chart, but is extended for every day in a year. By using this this meth method od we get get more more accu accura rate te wate waterr heig height htss sinc since e it invo involv lves es less less interpolation. The example shows us a part of a very detailed tide table, which even includes heights for every hour.

3 - Information from tidal curves In most tables the tides can also be characterized by a tidal curve. This method substitutes the rule of twelve providing more accurate heights. The left side contains the water height information with the lowest heights to the left where also the chart datum is indicated. The low water height will be marked at the bottom and the high water height will be marked at the top.

The area under the curve will be marked with the time information. To find the water height at a specific time we need to know first how many hours before or after the HW this is. Then

Often this is done when the curve is not sinusoid and the rule of twelve is rendered useless.

Overview 1.

Tide: The vertical rise and fall of the surface of a body of water caused

primarily by the differences in gravitational attraction of the moon, and to a lesser extent the sun, upon different parts of the earth when the positions of  the moon and sun change with respect to the earth. 2.

Spring Tide: The tidal effect of the sun and the moon acting in

concert twice a month, when the sun, earth and moon are all in a straight line (full moon or new moon). The range of tide is larger than average. 3.

Neap Tide: This opposite effect occurs when the moon is at right

angles to the earth-sun line (first or last quarter). The range of tide is smaller than average. 4.

Range: The vertical difference between the high and low tide water

levels during one tidal cycle.

5.

Tidal Day: 24 hours and 50 minutes. The moon orbits the earth once

earth month, and the earth rotates (in the same direction as the moon's orbit) on its axis once every 24 hours. 6.

Tidal Cycle: A successive high and low tide.

7.

Semi-diurnal Tide: The most common tidal pattern, featuring two

high highss and and two two lows lows each each day, day, with with mini minima mall varia variati tion on in the the heig height ht of  successive high or low waters. 8.

Diurnal Tide: Only a single high and a single low during each tidal

day; successive high and low waters do not vary by a great deal. Gulf of  Mexico, Java Sea and in the Tonkin Gulf. 9.

Mixed Tide: Characterized by wide variation in heights of successive

high and low waters, and by longer tide cycles than those of the semidiurnal cycle. U.S. Pacific coast and many Pacific islands. 10.

Chart Datum or Tidal reference planes: These fictitious planes are

used as the sounding datum for the tidal heights. 11.

Drying Height: Clearance in meters (or feet in old charts) above the

chart datum. 12.

Charted Depth: Clearance in meters (or feet in old charts) below the

chart datum. 13.

Observed Depth: Height of tide + charted depth: the actual depth in

meters. 14.

Height of light: The height of light above the bottom of its structure.

15.

Elevation: The height of the light above the chart datum.

16.

Rule of Twelve: Assuming a tidal curve to be a perfect sinusoid with

a period of 12 hours. The height changes over the full range in the six hours betwee between n HW and and LW with with the the follow following ing fracti fractions ons during during each each respec respectiv tive e hour: 1/12 2/12 2 /12 3/12 3/12 2/12 1/12. 17.

Rule of Seven: The change from spring range to neap range can be

assu assume med d line linear ar,, each each day day the the rang range e chan change gess with with 1/7t 1/7th h of diff differe erenc nce e between the spring and neap ranges. Hence, the daily change in range = (spring range - neap range)/7.

Currents

& 

navigation Skip over navigation

Currents Curren Currents ts reflec reflectt the horizo horizonta ntall movem movement ent of water water wherea whereass tides tides reflec reflectt vertical vertical movement movements. s. These These currents currents influence influence the ship's ship's position position and are therefore important to understand. The The horiz horizont ontal al moveme movement nt is prima primaril rily y caused caused by the the gravit gravitati ationa onall pull pull of  celestial bodies. But also other factors are in play: differences in water temperatures caused by heating and cooling due to the earth's atmosphere; differences in salinity caused by rain, evaporation and estuaries; wind induced friction; the Coriolis force which is a consequence of the earth's rotation. oceanic c surface currents Prominent features in the map of the major oceani include the subtropical gyres centered on 30 degrees latitude in each of the major ocean basins. The earth's rotation (origin of the Coriolis force) and the

change in wind direction with latitude (from the east in the tropics and from the west at mid-latitudes) cause the circulation of the gyres to be clockwise in the the Nort Northe hern rn Hem Hemisp isphere here and and coun counte terc rclo lock ckwi wise se in the the Sout Southe hern rn Hemisphere. The well-known Gulf Stream in the Atlantic and its counterpart in the the Paci Pacifi fic, c, the the Kuro Kurosh shio io Curre Current nt,, are stron strong g curren currents ts that that carry carry heat heat northward from the tropics. The deep oceanic currents (not shown) are caused primarily by water density differences and in general return the (now colder) water back towards the tropics.

Click chart to see the whole world!

To predic predictt the the behav behavior ior of major major ocean ocean curren currents ts severa severall refere reference ncess are Saili ling ng Di Dire recti ction ons s Pl Plann annin ing g Gu Guid ides es cont avai availa labl ble. e. The The Sai contai ain n some some inf inform ormation ion on norm ormal loca ocations ions and stre stren ngth gths of ocea ocean n curr curren entts. Nevertheless, the Pilot Charts are by far the best reference for predicting the direction and speed of these currents. On these charts, arrows indicate the direction of the prevailing current; a number printed above the arrow indicates the average speed. Since this information is based upon historical averages, it won't predict the actual ocean current encountered with 100% accuracy. Ocean surface currents need not be considered in coastal areas. Usually, when close to the continental shelf, the horizontal movement of water is defined by two terms: 1.

tidal stream or tidal current: gravitational gravitational

2.

current: grafitational, rivers, wind

In order to predict tidal stream one needs to use tide tables in conjunction with a tidal atlas, or a chart diamond. Tidal streams are described by drift /  /rate and set, in which drift/rate is the speed and set is the direction of the current.

Tidal Atlases

Tidal stream atlases show the tidal currents for each hour of the tidal cycle. They comprise a total of 13 tidal charts ranging from 6 hr befo before re HW HW till till 6 hr hr after after HW HW . So, So, these these charts charts are rela relativ tive e to the time of HW and to use them we must know the absolute time of HW. Though several layouts can be used, usually the direction of the tidal stream is shown by arrows, which are heavier where the tidal streams are stronger. Figures against the arrows give the mean neap and spring drift or rate in tenths of knots. For examp example, le, indica indicates tes a mean mean neap neap drift drift of 2.1 knots knots and and a mean mean spring drift of 4.6 knots. rotterdam

Chart Diamonds

Course to Steer Course rse to Ste Steer er process, where you know your present position and The Cou required Ground Track. You want to find the Course to Steer to allow for the tide, and stay on the Ground Track.

Lights and buoys

Aids to navigation special al struct structure uress like like light lighthou houses ses,, lights lightship hips, s, Aids Ai ds to na navi viga gati tion on are speci beacon beacons, s, buoys buoys,, etc that that are used used to enhan enhance ce safety safety by provid providing ing more more opportunities to obtain LOPs. These lights and marks are prescribed across the world by the International Association of Lighthouse Authorities (IALA). In 1977 this IALA endorsed two maritime buoyage systems putting an end to the 30 odd systems existing at that time. Region A - IALA A covers all of Europe and most of the rest of the world, whereas region B - IALA B covers only the Americas, Japan, the Philip Philippin pines es and Korea. Korea. Fortun Fortunate ately, ly, the the differ differenc ences es betwee between n these these two two systems are few. The most striking difference is the direction of buoyage . All marks within the IALA system are distinguished by: Shape Colour Topmark Light

Light identification During daytime, the identification of aids to navigation is accomplished by observing: location, shape, colour scheme, auxiliary features (sound signals, RACON

, RC

, etc) or markings (name, number, etc).

During the night, we use the features of the aid to navigation's light to both identify it and ascertain its purpose. There are three features to describe the light: Colour: Either white, red, green or yellow. If no colour is stated in the chart,

default is white. Period: The time in seconds needed for one complete cycle of changes.

The The arrow arrow indi indica cate tess the the 10 seco second nd peri period od of this this flashing light “Fl(3) 10s”. Phase charact characterist eristic ic: The The part partic icul ular ar patt patter ern n of chan change gess with within in one one

complete cycle (hence, within one period). Below are the most common types:

Fixed

F

This light shines with an unblinking and steady intensity and is always on. In this example a yellow fixed light is shown. Flashing

Fl:

The duration of the light is always less than the duration of the darkness. The frequency does not exceed 30 times per minute. Q:

Quick Flashing

Again, the duration of quick flash is less than the darkness. The frequency is at least 60 times per minute. Very Quick Flashing

VQ:

Also here, the duration of very quick flash is less than the darkness. The frequency is at least 100 times per minute. Interrupted Quick Flashing

Like darkness in one period. Isophase

IQ:

Quick Flashing with ith one

moment of 

Iso:

This Light has equal duration between light and darkness. A period consists of both a light and a dark interval. Also called Equal Interval (E Int). Gp Fl(x+x):

Group Flashing

This is actually a combination of two patterns in one period. In this example the first 2 flashes followed by the pattern of 3 flashes result in: Gp Fl(2+3). Occulting

Occ:

Occulting is the opposite of flashing, the light is more on then off. Alternating

AL:

An alternating light changes colour. This special purpose light is typically used for special applications requiring the exer exerci cisse of grea reat caution. ion. In this exam examp ple ALT. ALT.W WG is show hown, alternating between green and white. Morse U

Mo (U):

This This light light shows shows two two flash flashes es and and a longf longflas lash, h, which is equivalent to the letter “U” in Morse code. Long-Flashing

LFl:

This light has one long flash in a period. A long flash is at least 2 seconds long.

Let's look at some examples using colour, period and phase characteristics. The arrows mark the periods: Fl (4) 8s Oc (2+3) 10s Iso G 4s

All lighted aids to navigation are either major or minor lights, where major lights are used for key navigational points along sea-coasts, channels and harbour and river entrances. These lights are normally placed in lightships, lighthouses and other permanently installed structures, providing both high intensity and high reliability of the lights. Major lights are then subdivided in primary prima ry light lights s (very strong, long range lights used for the purpose of  making landfalls or coastal passages) and secondary lights (shorter range lights found for example at harbour and river entrances). Important details of (especially) primary lights can be found in a reference called the Light List where information (about pedestals etc.) can be found which is not included in the chart. Minor lights on the other hand are likely to be found within harbours, along channels and rivers. These have a low to moderate intensity and sometimes mark isolated dangers.

Six types of navigation buoys: Lateral Cardinal Isolated danger Safe water New wreck  Special

Lateral buoys and marks The location of lateral buoys defines the borders of channels and indicates the direction. Under IALA A red buoys mark the port side of the channel when returning from sea, whereas under IALA B green buoys mark the port side of the channel when sailing towards land. Red buoys have even numbers and red lights; green buoys have odd numbers and green lights. Lateral lights can have any calm phase characteristic except FL (2+1).

Generally, when two channels meet, one will be designated the preferred channel (i.e. most important channel). The buoy depicted on the right right indic indicat ates es the the preferre preferred d channe channell to starbo starboard ard

under under IALA IALA A. A. The ligh lightt

phase characteristic is R FL (2+1):

The buoy depicted depicted on the left indicat indicates es the preferred channel channel to port port under under IALA IALA A. A. These These buoy buoyss are are marke marked d with with the the names names and and num number berss of both channels. The light phase characteristic is G FL (2+1): For an example of lateral buoys used to mark a (preferred) channel, see direction of buoyage below.

Cardinal buoys The The fou four card cardiinal nal buoy buoyss indi indica catte the saf safe side ide of a danger with ith an approximate bearing. For example, the West cardinal buoy has safe water on its West and the danger on its East side. Notice the “clockwise” resemblance of the the ligh lightt phas phase e char charac acte teris risti tics cs.. The The top top mark markss cons consis istt of two two blac black k triangles placed in accordance with the black/yellow scheme of the buoy. When a new obstacle (not yet shown on charts) needs to be marked, two cardinal buoys - for instance a South buoy and an East buoy - will be used to indicate this “uncharted” danger. The cardinal system is identical in both the IALA A and IALA B buoyage systems.

Marks indicating isolated dangers

This This type type of buoy buoy indi indica cate tess the the posi positi tion on of an isola isolate ted d danger, contrary to cardinal buoys which indicate a direction away from the danger. Body: black with red horizontal band(s); Topmark: 2 black spheres. The light (when present) consists of a white flash: Fl(2).

Marks indicating safe water

Notice that whereas most horizontal stripi striping ng spell spellss “dange “danger”, r”, this this safe safe water water buoy buoy is vertic verticall ally y strip striped. ed. These These marks are for example seaward of all other buoys (lateral and cardinal) and can be used to make landfall. Body: red and white vertical stripes; Topmark (if any): single red sphere. Lights are typically calm and white: Morse A, Iso, Occ or LFl 10s.

Marks for new wrecks After the sinking of the “ Tricolor” in the Pas de Calais (Dover Straits) in 2002, several other vessels hit the wreck despite standard radio warnings, three guard ships and a lighted buoy. This incident spawned a new type of  buoy, the emergency wreck marking buoy, which is placed as close as possible to a new dangerous wreck.

The emergency wreck marking buoy will remain in position until: a) the wreck is well known and has been promulgated in nautical publications; b) the wreck has been fully surveyed and exact details such as position and least depth above the wreck are known; and c) a permanent form of marking of the wreck has been carried out. The buoy has the following characteristics: A pillar or spar buoy, with size dependant on location. Coloured in equal number and dimensions of blue and yellow vertical stripes (minimum of 4 stripes and maximum of 8 stripes). Fitted with an alternating blue and yellow flashing light with a nominal range of 4 nautical miles where the blue and yellow 1 second flashes are alternated

with an interval of 0.5 seconds. B1.0s + 0.5s + Y1.0s + 0.5s = 3.0s If multiple buoys are deployed then the lights will be synchronized. A racon Morse Code “D” and/or AIS transponder can be used. The The top mark mark,, if fitt fitted, ed, is is a standi standing/ ng/upr uprigh ightt yellow yellow cros crosss

.

It is important to realize - especially for the colour-blind - that this new buoy breaches breaches the useful useful and crucial conventio convention: n: vertical vertical stripes stripes equal equal safety, safety, horizontal stripes equal danger.

Special buoys and marks

I have saved these buoys for last since they lack an actual navigational goal. Most of the time these yellow buoys indicate pipelines or areas used for special purposes. I have drawn the five official IALA shapes, from left to right: conical, spar, cylindrical, pillar and spherical.

Chart symbols The The seaf seafar arin ing g nati nation onss of the the worl world d - membe embers rs of the the International Hydrographic Hydrographi c Organization - agreed in 1982 on an universal set of chart symbols, abbreviations, colours, etc to be used in the nautical chart, in order to obtain uniformity. On regular charts a white, red, yellow or green lights will be indicated by , and on GPS displays and modern multi-coloured charts in specific colours: , with the yellow coloured lobe indicating a white light. The precise position of a chart symbol is its center, or is indicated with a line and circle , the “position circle”. Two distinct types of sea mark are drawn differently in the chart: beacons - fixed to the seabed; drawn upright; buoys - consisting of a floating object that is usually anchored to a specific

loca locati tion on on the the sea sea floo floor; r; draw drawn n at an obli obliqu que e angl angle e and and with with obliq oblique ue numbering, descriptions of colours and light characteristics. characteristics.

Major Major float floating ing light light (light (light-ve -vesse ssel, l, major major lightlightfloat, LANBY) Light-vessel Major light; minor light Green or black buoys (symbols filled black): G = Green ; B = Black Green or black beacon (symbol filled black). Note the upright G, instead of an oblique G Sing Single le colo colour ured ed buoy buoyss othe otherr than than gree green n and and black: Y  = Yellow ; R = Red Coloured beacon other than green and black, the symbol is again filled black so only the shape of  the topmark is of navigational significance. Multiple colours in horizontal bands, the colour sequence is from top to bottom Multip Multiple le colour colourss in vertic vertical al or diagon diagonal al strip stripes, es, the darker colour is given first. W  = White Spar buoy (here a safe water mark) Light Lighted ed marks marks on multi multi-co -colou loured red charts charts,, GPS displays and chart plotters. Lighted red beacon on standard charts. Red Red beac eacon and gree green n buoy with ith topm opmark, rk, colo colour ur,, rada radarr refl reflec ecto torr and and desi design gnat atio ion. n. Red Red buoys and marks are given even numbers, green buoys and marks are given odd numbers. Wave-actuated bell buoy to the left, and to the right a Light buoy, with a horn giving a single blast blast every every 15 second seconds, s, in conjun conjunct ction ion with with a wave-a wave-actu ctuate ated d whistl whistle. e. Other Other sounds sounds inclu include de  “Gong”, “Siren”, “Diaphone” (Dia).

The fog signal signal symb symbol ol may be omitt omitted ed when when a description of the signal is given. Leading beacons - Leading line (firm line is the track to be followed) any two two objec objects ts in line line Leading Lead ing ligh lights ts (≠ : any under each other). Bearing given in degrees and minute minutes. s. The The lights lights are synch synchron ronize ized. d. The The red light has a shorter nominal range (the distance from which the light can be seen): 10 nautical miles.

All-round light with obscured sector

Sector light on multi-coloured charts. The elevation is 21 metres (height of the light structure above chart datum). datum). The The nom nomina inal ran range of the whit white e ligh lightt is 18 nautical miles. The range of the green and red light is 12 nautical miles. Main Main light light visibl visible e all-ro all-roun und d with with red subsi subsidia diary ry light seen over danger. The fixed red light has an elevation of 55 metres and a nominal range of  12 nautical miles. The flashing light is white, with thre three e flas flashe hess in a peri period od of 10 seco second nds. s. The The elevation is higher than the red light: 62 metres and the range range of the the white white light is 25 nauti nautical cal miles. Symbol showing direction of buoyage (where not obvious) Symbol showing direction of buoyage (where not obvi obviou ous) s),, on mult multii-co colo lour ured ed char charts ts (red (red and and green circles coloured as appropriate), here IALA A Full example of a light description in the chart : Fl(3)WRG.15s21m15-11M

Class of light: group flashing repeating a group of three flashes; Colours: whit white, e, red, red, gree green, n, exhi exhibi biti ting ng the the diff differ eren entt colo colour urss in defi define ned d

sectors; Period: the time taken to exhibit one full sequence of 3 flashes and eclipses: 15 seconds; Elevation of light : 21 metres; Nominal range(s): white 15 M, green 11 M, red between 15 and 11 M, where “M” stands for nautical miles.

Lateral Marks - direction of buoyage Lateral marks are generally for well-defined channels and there are two international Buoyage Regions - A and B - where these Lateral marks differ. Where in force, the IALA System applies to all fixed and floating marks except landfall lights, leading lights and marks, sectored lights and major floating lights. The standar standard d buoy shapes shapes are cylindrica cylindricall (can) pillar

and spar

, conical conical

, spherica sphericall

,

, but variations may occur, for example: minor light-floats

. In the illustrations below, only the standard buoy shapes are used. In the case of fixed beacons is of navigational navigational significance. significance.

n

d lia

si

- lit or unlit - only the shape of the topmark

n

as ine

Visibility of lights It is important to know at what distance we may (begin to) see a certain light, and when we can expect to lose sight of it, especially when making landfall. landfall. Several Several practica practicall ranges ranges are used to the describe describe the visibility visibility of  lights in navigation: The meteorological range is based on the current atmospheric conditions. The The tabl table e belo below w show showss that that the the atmo atmosp sphe here re imme immens nsel ely y infl influe uenc nces es the the visibility of light travelling through it. Meteorological Optical Range Table Code No. Weather

Distance (m)

Code No. Weather

Distance (nm)

0

Dense fog

Less than 50

5

Haze

1.0 - 2.0

1

Thick fog

50 - 200

6

Light haze

2.0 - 5.5

2

Moderate

200 - 500

7

Clear

5.5 - 11.0

3

Light fog

500 - 1000

8

Very clear

11.0 - 27.0

4

Thin fog

1000 - 2000

9

Exceptionally clear

Over 27.0

The geographic range is based on the elevation of the light. A higher light means that its horizon is farther away, see distance of horizon. Moreover, if the observer's height of eye is higher than sea level the light can been seen beyond its geographic range, the dipping range. However, on sailing yachts this potential is limited. The nominal range of a light is based on its candlepower, and is typically the the rang range e ment mentio ione ned d in the the char chart. t. The The nomi nomina nall rang range e is the the maxi maximu mum m distance at which a light can be seen in weather conditions where visibility is 10 nm. So, a minor light - perched on a 70m high cliff - with a geographic range of  20 nm nm

will not be detect detectable able by the the human human eye at at a distance distance of 6 nm

1. if the nominal range is just 5 nm. 2. if the meteorological range is just 5 nm due to a light haze.

Because of the limiting factor of the geographic range, most major lights will never be seen from a sailing yacht 20 nm away. Yet, it is sometimes possible to take a bearing on the loom of the light: its reflection against the clouds. Different coloured lights with equal candlepower have different ranges. White light is the most visible followed by yellow, green and then red. Therefore, at extreme ranges an “AL WG” can resemble r esemble a “Fl W”. The range of a lit buoy is never indicated - with the exception of a LANBY but on a clear night the maximum range is 3 nm, yet often considerably less. There are 2 visual clues to determine your distance from a buoy: at about 0.5 nm, the light will rise up from the horizon, and at about 200m, the light will reflect in the surface.

Buoy at Buoy at Buoy at less less less than 3 than than nm 0.5 nm 200m

Glossary

1.

Navigation aid: An onboard instrument, device, chart, method, etc.,

intended to assist in the navigation. 2.

Aid Ai d to na navi viga gati tion on: A devi device ce or stru struct ctur ure e ext externa ernall to the the ship ship,,

designed to assist in determination of position, to define a safe course, or to warn of dangers or obstructions. 3.

Mark, seamark, navigation mark: An artificial or natural object of 

easily recognizable shape or colour, or both, situated in such a position that it may be identified on a chart. A fixed artificial navigation mark is often called a Beacon. 4.

Light characte characterist ristics ics: The sequence and length of light and dark

periods and the colour or colours by which a navigational light is identified. 5.

Topmark: One of more objects of characteristic shape placed on top

of a buoy or beacon to aid in its identification. identification. 6.

Lateral Mark: An aid to navigation intended to mark the sides of a

channel or waterway. 7.

Cardinal Cardin al Marks: An IALA aid to navigation intended to show the

location of a danger to navigation based on its position relative to the danger using the “cardinal point”: north, east, south, west. 8.

Isolated danger Marks: An IALA aid to navigation marking a danger

with clear water all around it; it has a double ball topmark and is black with at least one red band. If lighted its characteristic is Fl(2). 9.

Sector light: A light having sectors of different colours or the same

colour in specific sectors separated by dark sectors. 10.

Light secto sector r: As defined by bearings from seaward, the sector in

which a navigational light is visible or in which it has a distinctive colour difference from that of adjoining sectors, or in which it is obscured. 11.

Lighthouse: A distinctive structure exhibiting a major navigation light.

12.

Light List: A publication giving detailed information regarding lighted

navigational aids and fog signals. 13.

Landfall: The first sighting (even by radar) of land when approached

from seaward. 14.

Range: Two or more objects in line. Such objects are said to be in

range. An observer having them in range is said to be on the range. Two beacons are frequently located for the specific purpose of forming a range to indicate a safe route or the centerline of a channel. 15.

Leading Leadi ng line: On a nautical chart, a straight line, drawn through

leading marks. A ship moving along such line will clear certain dangers or remain in the best channel. 16.

Range Rang e lig lights hts, lea leadin ding g lig lights hts: Two Two or more ore light ightss at diff ifferen erentt

elevat elevation ionss so situa situated ted to form form a range range (lead (leading ing line) line) when when brough broughtt into into transit. The one nearest to the observer is the from light and the one farthest from the observer is the rear light. The front light is at a lower elevation than the rear light.

17.

Lights in line: Two or more lights so situated that when observed in

transit they define a position: the limit of an area, an alignment used for anchoring, etc. Not to be confused with range lights, which mark a direction to be followed. 18.

buoy having having a boat-s boat-sha haped ped body. body. Light Light-fl -float oatss are Light-float : A buoy

nearly always unmanned and are used instead of smaller lighted buoys in waters where strong currents are experienced. 19.

Primary (sea-coast) light: A light established for purpose of making

landfall or coastwise past from headland to headland. 20.

Secondary Second ary light: A major light, other than a primary (sea-coast)

light, light, establ establish ished ed at harbo harbour ur entran entrances ces and and other other locati location onss where where high high intensity and reliability are required. 21.

Major light: A light of high intensity and reliability exhibited from a

fixed structure (lighthouse) or on marine site (except range lights). Major lights include primary sea-coast and secondary lights. 22.

Minor light: An automatic unmanned light on a fixed structure usually

showing low to moderate intensity. Minor lights are established in harbours, along channels, along rivers, and in isolated dangers. 23.

Visual range: The extreme distance at which an object of light can be

seen. 24.

Geographic range: The extreme distance limited by the curvature of 

the earth and both the heights of the object and the observer. 25.

Bobbing a light: Quickly lowering the height of eye and raising it

again when a navigational light is first sighted to determine if the observer is at the geographic range of the light. 26.

Luminous range: The extreme distance limited only by the intensity

of the the ligh light, t, clea clearn rnes esss of the the atmo atmosp sphe here re and and the the sens sensit itiv iven enes esss of the the observer's eye. 27.

Luminous range diagram: A diagram used to convert the nominal

range of a light to its luminous range under existing conditions. 28.

Charted or Nominal Range: The nominal range is indicated in the

chart next to the light or can be found in the Light List. This is the maximum distance at which a light may be seen at night based upon intensity and 10 nautical miles of visibility. 29.

Meteorological Range: The nominal range is indicated in the chart

next to the light or can be found in the Light List. This is the maximum distance at which a light may be seen at night based upon intensity and 10 nautical miles of visibility.

Lights and shapes

Skip over navigation

Definitions

Masthead light

A white light placed over the fore and aft centreline of the vessel showing an unbroken light over an arc of the horizon of 225° and so fixed as to show the light from right ahead to 22.5° abaft the beam on either side of the vessel. Sidelight

means a green light on the starboard side and a red light on the port side each showing an unbroken light over an arc of the horizon of 112.5° and so

fixed as to show the light from right ahead to 22.5° abaft the beam on its respective side. In a vessel of less than 20 metres in length the sidelights may be combined in one lantern carried on the fore and aft centreline of the vessel. Sternlight

means a white light placed as nearly as practicable at the stern showing an unbroken light over an arc of the horizon of 135° and so fixed as to show the light 67.5° from right aft on each side of the vessel. Towing light

means a yellow light l ight having the same characteristics as the sternlight. All-round light

means a light showing an unbroken light over an arc of the horizon of 360°. Flashing light

means a light flashing at regular intervals at a frequency of 120 flashes or more per minute. Legend

White light Yellow light Green light Red light Yellow flashing light Optional white light

Power-driven vessel underway A power-driven vessel underway shall exhibit: a masthead light forward; a second masthead light abaft of and higher than the forward one; except that a vessel of less than 50 metres in length shall not be obliged to exhibit such light but may do so; sidelights; a sternlight. Power driven vessel underway, longer than 50 m

Abeam, port side

Ahead

Astern

Power driven vessel underway, shorter than 50 m

Abeam, port side

Ahead

Astern

Sailing vessels underway and vessels under oars A sailing vessel underway shall exhibit: sidelights; a sternlight. In a sailing vessel of less than 20 metres in length the lights may be combined in one lantern carried at or near the top of the mast where it can best be seen. A sailing vessel underway may, in addition to the lights, exhibit at or near the top of the mast, where they can best be seen, two all-round lights in a vertical line, the upper being red and the lower green, but these lights shall not be exhibited in conjunction with the combined lantern.

A sailing vessel of less than 7 metres in length shall, if practicable, exhibit the lights prescribed above, but if she does not, she shall have ready at hand an electric torch or lighted lantern showing a white light which shall be exhibited in sufficient time to prevent collision. A vessel under oars may exhibit the lights prescribed in this Rule for sailing vessels, but if she does not, she shall have ready at hand an electric torch or lighted lantern showing a white light which shall be exhibited in sufficient time to prevent collision.

Sailing vessel 1

Abeam, port side

Ahead

Astern

Sailing vessel 2

Abeam, port side

Ahead

Sailing vessel 3

Astern

Abeam, port side

Ahead

Astern

Sailing vessel 4

Abeam, port side

Ahead

Astern

Sailing and Motoring A vessel proceeding under sail which has her engine running shall exhibit forward where it can best be seen a conical shape, apex downwards. She shall exibit lights according to a power-driven vessel. Sailing and motoring

Day sign

Abeam, port side

Ahead

Astern

Anchoring Anchored vessel, longer than 50 m

Day sign (1 black sphere)

Abeam, port side

Ahead

Anchored vessel, shorter than 50 m

Astern

Day sign (1 black sphere)

Abeam, port side

Ahead

Astern

Anchored sailing boat

Day sign (1 black sphere)

Abeam, port side

Ahead

Astern

Towing A power-driven vessel when towing shall exhibit: two masthead lights in a vertical line. When the length of the tow, measuring from the stern of the towing vessel to the after end of the tow exceeds 200 metres, three such lights in a vertical line; sidelights; a sternlight; a towing light in a vertical line above the sternlight; when the length of the tow exceeds 200 metres, a diamond shape where it can best be seen. Tugboat longer than 50 m - tow longer than 200 m

Abeam, port side

Ahead, Day sign (diamond shapes)

Ahead

Astern

Tugboat shorter than 50 m - tow longer than 200 m

Abeam, port side

Ahead, Day sign (diamond shapes)

Ahead

Astern

Tugboat longer than 50 m - tow shorter than 200 m

Abeam, port side

Ahead, Day sign (no shapes)

Ahead

Astern

Tugboat shorter than 50 m - tow shorter than 200 m

Abeam, port side

Ahead, Day sign (no shapes)

Ahead

Astern

Towing an inconspicuous, partly submerged object An inconspicuous, partly submerged vessel or object, or combination of such vessels or objects being towed, shall exhibit:

if it is less than 25 metres in breadth, one all-round white light at or near the forward end and one at or near the after end except that dracones need not exhibit a light at or near the forward end; if it is 25 metres or more in breadth, two additional all-round white lights at or near the extremities of its breadth; if it exceeds 100 metres in length, additional all-round white lights between these lights so that the distance between the lights shall not exceed 100 metres; a diamond shape at or near the aftermost extremity of the last vessel or object being towed and if the length of the tow exceeds 200 metres an additional diamond shape where it can best be seen and located as far forward as is practicable. Tow shorter than 200 m, object shorter than 100 m

Abeam, port side Tow longer than 200 m, object shorter than 100 m

Abeam, port side Tow longer than 200 m, object longer than 100 m

Abeam, port side Tow longer than 200 m, object longer than 100 m & wider than 25 m

Abeam, port side

Ahead

Astern Tow longer than 200 m, any object size

Day sign, Abeam, port side

Pushing from ahead or towing alongside When When a push pushin ing g vess vessel el and and a vesse essell being eing push pushed ed ahea ahead d are are rigi rigidl dly y connected in a composite unit they shall be regarded as a power-driven vessel and exhibit the normal lights. A power-driven vessel when pushing ahead or towing alongside, except in the case of a composite unit, shall exhibit: two masthead lights in a vertical line; sidelights; a sternlight. A vessel or object being towed shall exhibit: sidelights;

a sternlight; when the length of the tow exceeds 200 metres, a diamond shape where it can best be seen. Provided that any number of vessels being towed alongside or pushed in a group shall be lighted as one vessel, a vessel being pushed ahead, not being part of a composite unit, shall exhibit at the forward end, sidelights; a vessel being towed alongside shall exhibit a sternlight and at the forward end, sidelights. Pushing from ahead

Abeam, port side

Ahead

Astern Towing alongside

Abeam, port side

Ahead

Fishing, Trawling

Astern

A vessel engaged in fishing, whether underway or at anchor, shall exhibit only the lights and shapes prescribed below. A vessel when engaged in trawling, by which is meant the dragging through the water of a dredge net or other apparatus used as a fishing appliance, shall exhibit: two all-round lights in a vertical line, the upper being green and the lower white, or a shape consisting of two cones with their apexes together in a vertical line one above the other; a masthead light abaft of and higher than the all-round green light; a vessel of less than 50 metres in length shall not be obliged to exhibit such a light but may do so; when making way through the water, in addition to the lights prescribed hereh, sidelights and a sternlight. when shooting nets, white light over white light (Flag Z by day); when hauling nets, white light over red light (Flag G by day); When nets are caught on the bottom, red light over red light (Flag P by day) Fishing vessel, trawling

Day sign

Abeam, port side

Ahead

Astern

Optional white light if shorter than 50 m

Optional white light if  shorter than 50 m

Fishing vessel, trawling, shooting nets (white over white, Z)

Day sign

Abeam, port side

Ahead

Astern

Fishing vessel, trawling, hauling nets (white over red, G)

Day sign

Abeam, port side

Ahead

Astern

Fishing vessel, trawling, nets caught on bottom (red over red, P)

Day sign

Abeam, port side

Ahead

Astern

Trawling in span When pair trawling, each vessel shows searchlights on water aiming forward (Flag T by day). Trawling in span, shooting nets

Ahead

Astern

Fishing, other than trawling A vessel engaged in fishing, other than trawling, shall exhibit: two all-round lights in a vertical line, the upper being red and the lower white, or a shape consisting of two cones with apexes together in a vertical line one above the other; when there is outlying gear extending more than 150 metres horizontally from the vessel, an all-round white light or a cone apex upwards in the direction of the gear; when making way through the water, in addition to the lights prescribed here, sidelights and a sternlight. Fishing vessel, other than trawling

Day sign

Abeam, port side

Ahead

Astern

Purse seining Purse Seiners will exhibit two all-round yellow lights in a vertical line, flashing alternately. Purse Seiner

Abeam, port side

Ahead

Astern

Constrained by draught A vessel constrained by her draught may, (and not “shall”!) in addition to the lights prescribed for power-driven vessels, exhibit where they can best be seen three all-round red lights in a vertical line, or as day sign a cylinder. Power driven vessel, underway, constrained by her draught

Day sign cylinder)

Abeam, port side

(black

Ahead

vertical

Astern

Not under command A vessel not under command shall exhibit: two all-round red lights in a vertical line where they can best be seen; two spherical shapes in a vertical line where they can best be seen; and when making way through the water also normal sidelights and a sternlight (not shown in the example below). Vessel not under command, not making way through the water

Day sign spheres)

(two

black

Abeam, port side

Ahead

Astern

Sailing boat, no wind, no mechanical propulsion

Abeam, port side

Ahead

Astern

Restricted in her ability to manoeuvre A vessel restricted in her ability to manoeuvre, except a vessel engaged in mine clearance operations, shall exhibit: three all-round lights in a vertical line where they can best be seen. The highest and lowest of these lights shall be red and the middle light shall be white; three shapes in a vertical line where they can best be seen. The highest and lowest of these shapes shall be balls and the middle one a diamond; when when maki making ng way way thro throug ugh h the the wate water, r, also also a mast masthe head ad ligh lightt or ligh lights ts,, sidelights and a sternlight Restricted in her ability to manoeuvre, not making way through the water

Day Day sign sign:: two two blac black k sphe sphere ress and in the middle a black diamond shape

Abeam, port side

Ahead

Astern

Restricted in her ability to manoeuvre, making way through the

water, longer than 50 m

Abeam, port side

Ahead

Astern

Dredging or underwater operations A vessel engaged in dredging or underwater operations, when restricted in her ability to manoeuvre Dredging or underwater operations, shorter than 50 m, not making way

Ahead, day signs

Ahead

Astern

Dredging or underwater operations, shorter than 50 m, making way

Ahead, day signs

Ahead

Astern

Dredging or underwater operations, longer than 50 m, making way

Ahead, day signs

Ahead

Astern

Small diving vessel Small diving vessel

Day signs

or

Abeam, port side

Ahead

Astern

Pilot boat A vessel engaged on pilotage duty shall exhibit: 1. at or near near the the masthea head, two allall-ro rou und lig lights in a vert vertic ica al line, ine, the the upper being white and the lower red; when underway, underway, in addition addition,, sidelight sidelightss and a sternligh sternlight; t; as shown in the example below. 2.

Pilot boat, shorter than 50 m

Abeam Abeam,, starbo starboard ard side side Ahead Ahead Astern Astern

Hovercraft An air-cushion vessel when operating in the non-displacement mode shall, besides a masthead light forward, (plus a masthead light abaft if longer than 50 m) sidelight sidelightss and a sternlight sternlight,, exhibit exhibit an all–round all–round flashing flashing yellow light (faster than 2 flashes per second). A hydrofoil ferry or high speed catamaran ferry when acting as ferry is often also allowed under local regulations to exhibit an all-round flashing yellow light. Hovercraft, longer than 50 m

Abeam, port side

Ahead

Astern

Minesweeper A vessel engaged in mine clearance operations shall in addition to the lights prescribed for a power-driven vessel, or to the lights or shape prescribed for a vessel at anchor, exhibit three all-round green lights or three balls. One of  these lights or shapes shall be exhibited near the mast head and one at each end of the fore yard. These lights or shapes indicate that it is dangerous for another vessel to approach within 1000 metres of the mine clearance vessel. Minesweeper, shorter than 50 m

Ahead, day signs (3 black spheres)

Ahead

Astern