As we know from the last chapter Mercator projection is a projection of the Earth on a flat plane. Mercator sailing is done on the Mercator chart where the distance between latitudes is not the same and the meridians are parallel lines at equal distance to each other. The Mercator sailing triangle consists of DMP, D’long and distance. This helps us to find the Rhumb line course and distance by the following formulas –

D’long/DMP = tan course

Distance = d’lat*sec course


Middle latitude can also be referred to as the true departure. Hence after substituting is the parallel sailing formula –

Dep = d’long*cosine middle latitude

Tan course = true departure/d’lat

Distance = d’lat*sec course or,

Distance = true departure*cosec course


The Transverse tables are used to solve plain sailing problems for a distance up to 600 miles and for each degree of course angle from 0 degree to 90 degrees just by observing the data in the table.


Days work is the calculations made by a mariner to find the distance, speed and course made good by a vessel when it is involved in steering a number of courses and distances i.e. when it follows an irregular track. It is done from noon till the noon of the other day ( noon to noon).

Some of the other component of days work are –

  • Dead Reckoning (DR) – It is the position obtained by applying course, speed and duration of time to the initial position.
  • Leeway – It is the effect of wind which causes bodily movement of the ship leewards. It is the angle between wake of the ship and fore and aft line of the ship.
  • Estimated Position (EP) – It is the position obtained after applying the true course, distance by log and effects of wind and current.
  • Fix – it is the actual position of the ship.
  • Set – It is the angle by which the fix is deviated from the DR position.
  • Drift – It is the distance by which fix is deviated from the DR position.
  • Current – Current is non-tidal horizontal movement of the sea due mainly to meteorological, oceanographical, or topographical causes.
  • Tidal Stream– A tidal stream is tidal horizontal movement of the sea due to tide raising forces of the Sun and the Moon.
Article by Ritika Singh(Tolani Maritime(2020-2022),Sailing as Deck Cadet now as in 2022)


Charts carry a lot of information for navigational use. They represent a portion of the Earth’s surface with a suitable scale on a flat surface.

Image credits –


Projection is “Cylindrical Orthomorphic Projection”.

  1. Projection is cylindrical.
  2. Meridians are represented by equidistance, parallel straight lines.
  3. Equator and parallel of latitudes are horizontal parallel straight lines is selected distance from equator and from each. It increases towards the pole due to distortion.

Lat*Scale= Long*Scale*sec (lat)

Meridional parts – The meridional parts of latitude is the number of longitude units from the equator to the latitude along the meridian.

Distance in meridional parts – DMP between two latitudes is the length of the meridian between those latitudes on a Mercator chart expressed in units of longitude scale.

Geographical Mile ( longitude unit )– It is the length of an arc along the equator that subtends an angle of 1’ at the center of circle.

Some important formulas:

D’lat = dis*cos (course)

D’long/DMP = Tan(course)

D’long = DMP.tan(course)


  1. The directions can be measured accurately.
  2. Easy to plot course on Mercator charts.
  3. Course lines are straight lines.
  4. Shapes stay true.
  5. The plotting lines can be moves anywhere on the chart as parallel lines.


  1. Distortion increases as we go towards the poles.
  2. Land masses cannot be compared.
  3. Polar regions cannot be represented.
  4. Great circle courses cannot be laid off easily.
GNOMONIC PROJECTION – image credits Wikipedia


  1. There charts are used for great circle sailing, as in these charts the great circles appear to be straight lines.
  2. The projection is tangential.
  3. These are small scale charts and therefore are not used for navigation.
  4. Meridians are straight line converging towards the pole.
  5. Meridians are not parallel to each other.
  6. Small circles and Rhumb lines are curved.
  7. After marking the shortest distance on Gnomonic chart, points are marked on the track at regular intervals of longitude and then transferred to the Mercator chart.


  1. Great circle track appear as straight line.
  2. Polar regions can also be represented on Gnomonic charts.


  1. As we go away from the centre the distortion for shape, size and distance increases.
  2. Rhumb line courses cannot be plotted as they appear to be curved lines.
  3. Plotting lines cannot be transferred from one portion of the chart to another.

Difference between Mercator and Gnomonic charts

Orthomorphism  (Shape retention). The shape is not retained.
Rhumb lines are straight.Rhumb lines are not straight.
Great circles are curved.Great circles are straight.
The projection is cylindrical.The projection is Zenithal.
There is no tangent point.There is a tangent point.
Meridians are parallel.  Meridians are not parallel.
Difference between Mercator and Gnomonic charts


Natural scale is the ratio of the length of 1’ of latitude on the chart to the length of 1 nautical mile on the surface of the Earth.

Length of 1’ of latitude (l) on the chart = length of 1’ of long (L). sec (L)

Length of 1 nautical mile on the Earth = 1852.3 – 9.4 cos2L (in min)

Article by Ritika Singh(Tolani Maritime(2020-2022),Sailing as Deck Cadet now as in 2022). Verified by Swapnil Singh.


As the great circle track crosses the various meridians at different angles the ship has to alter the course throughout the passage. Therefore rhumb line track is used even though the shortest distance between two points on Earth is the shorter arc of the great circle through those points.

Rhumb Line – A Rhumb Line or Loxodrome is a line on Earth’s surface, crossing all meridians at the same angle. For example the Equator, all parallel latitudes and meridians

Departure – The departure between two places is the east-west distance between them in nautical miles.

When the distance between the two latitudes is small the departure is taken as the distance between the two meridians measured along the mean latitude.

When the distance between the two latitudes is large the departure is taken as the east-west distance between the meridians measured along the middle latitude ( latitude in which true departure lies, when sailing between them ) between them.


It is the same as the Departure between two places as the starting and destination position DOES NOT lie on the same latitude. The ship sails along the rhumb line, due east or west.

Dist = d’long (in min) cos lat


Here the starting and the destination position are on the same latitude. Sailing is done along the Rhumb line.


Dep = d’long cos (mean lat)

D’lat= dist cos (course)

Dep = dist sin (course)

Dep/d’lat(in min) = tan (course)

Article by Ritika Singh(Tolani Maritime(2020-2022),Sailing as Deck Cadet now as in 2022)



Japan Reporting System (JASREP) is a system whereby ships are encouraged to participate in the reporting system to establish contact, monitor ship’s position and to rescue vessels that are in distress through positive utilization of the system. Position reports and relevant information from ships are processed by the computer and maintained under strict control. The system is to ensure the safety of the vessels in that the Japan Coast Guard contacts the participating vessel if she fails to report in a 24-hr sequence, and in the possible event of an unfortunate distress case, it enables prompt and effective search and rescue operation. The Japan Coast Guard dispatches its assets and if necessary requests the JASREP participating vessel in the vicinity to proceed to the scene for their support.


JASREP service area is latitude 17 degrees and northward and longitude 165 degrees and westward.

Send an e-mail report to: with the subject line which reads: JASREP


SP: Sailing Plan – Sailing Plan is the basic information to estimate a ship’s position, and it should be sent at the time when the ship participates in this system. Reports should therefore be made when the ship departs from a port within the service area or when the ship enters the area.

PR: Position Report – Position Report is the information to verify if the ship’s position input according to the Sailing Plan is correct. The 1st report should therefore be sent at an optional time within 24 hours of departure from a port or entering the service area, and then the reports should be sent subsequently no less frequently than every 24 hours until Final Report.

DR: Deviation Report – Deviation Report is the information to be used for necessary correction of pre-reported Sailing Plan when a ship deviates from the intended course due to a change in the Sailing Plan. Reports should be sent whenever the Ship’s position deviates 25 miles or more from the original track, the port of destination is changed, or other changes occur with a resultant change in Sailing Plan.

FR: Final Report – Final Report is the information to terminate participation in the system. Accordingly, the report should be sent prior to or on arrival at the port, or when a ship departed from the service area of the system


Australian Reporting System (AUSREP) is an integral part of the Maritime Search and Rescue (SAR) system in Australia. AUSREP is operated by the Australian Maritime Safety Authority through the Rescue Coordination Centre (RCC Australia). The objective of the AUSREP system is to contribute to the safety of life at sea by – limiting the time between the loss of a ship and the initiation of search and rescue action, in cases where no distress signal is sent out; limiting the search area for a rescue action; and providing up-to-date information on shipping resources available in the area, in the event of a search and rescue incident.

Concept of the AUSREP system: On departure from an Australian port or on entering the AUSREP area from overseas:

The Captains are to send a Sailing Plan (SP) to RCC Australia. A computerized plot will be maintained of the ship’s position; Captains are to make their ships available for polling and notify AMSA by inserting the word ” POLL” in the appropriate section of the SAIL PLAN; or Where Polling is unavailable,

Captains should send a Position Report (PR) each day at a convenient time nominated by the ship 2200 UTC and 0800 UTC. The Maximum time between any two reports is not to exceed 24 hours.

Dates and times contained in AUSREP are to be in Universal Coordinated Time (UTC); If polling is used, the requirements to pass manual position is removed.

Final Report (FR) is to be sent on arrival at the destination or on departure from the AUSREP area. Should a ship at any time be in a position more than two hours steaming from the position that would have been predicted from the last SP or PR, then a Deviation Report must be sent. Failure to send an AUSREP DR, may result in a search being concentrated in the wrong area and the possibility that survivors from a stricken ship may not be found.


Automated Mutual Vessel Rescue System (AMVER) is a ship reporting system for search and rescue. It is a global system that enables the identification of other ships in the area of a ship in distress, which could then be sent to its assistance.

AMVER information is used only for search and rescue and is made available to any rescue coordination center in the world responding to a search and rescue case. The Coast Guard actively seeks to increase participation in this voluntary reporting system. Each year, more vessels participate in the system and more lives are saved. Currently, ships from more than 143 nations participate. AMVER represents “free” safety insurance during a voyage by improving the chances for aid in an emergency. By regular reporting, someone knows where a ship is at all times on its voyage in the vent of an emergency. AMVER can reduce the time lost for vessels responding to calls for assistance by “orchestrating” a rescue response, utilizing ships in the best capability to avoid unnecessary diversions in response to a MAYDAY or SOS call. AMVER, SPONSORED BY THE United States Coast Guard, is a unique, computer-based, and voluntary global ship reporting system used worldwide by search and rescue authorities to arrange for assistance to persons in distress at sea. With AMVER, rescue coordinators can identify participating ships in the area of distress and divert the best-suited ship or ships to respond. AMVER’s mission is to quickly provide search and rescue authorities, on-demand, accurate information on the positions and characteristics of vessels near a reported distress.


a) Sailing Plan (SP)

This report contains the complete routing information and should be sent within a few hours before departure, upon departure, or within a few hours after departure. It must contain enough information to predict the vessel’s actual position within 25 nautical miles at any time during the voyage, assuming the Sailing Plan is followed exactly. Sailing Plans require A, B, E, F, G, I, L, and Z lines. The M, V, X, and Y lines are optional. (The Y line is required for U.S. vessels).

Sailing Plan (Example)



B/240620Z MAR//




I/LOS ANGELES/3343N/11817W/031300Z APR//


L/GC/210/4200N/18000E/280400Z/ L/RL/200/4200N/16000W/300030Z/ L/GC/188/3422N/12047W/030500Z APR//






b) Position Report (PR)

This report should be sent within 24 hours of departing port and a least once every 48 hours thereafter. The destination should be included (at least in the first few reports) in case Amver has not received the Sailing Plan information Position Reports require A, B, C, E, F, and Z lines. The I is strongly recommended. The M, X, and Y lines are optional. (The Y line is required for U>S. vessels).

Position Report (Example)



B/281330Z NOV//


E/090// F/200//

I/LOS ANGELES/ 3343N/11817W/031300Z DEC//




c) Deviation Report (DR)

This report should be sent as soon as any voyage information changes which could affect Amver’s ability to accurately predict the vessel’s position. Changes in coarse or speed due to weather, ice, change in destination, diverting to evacuate a sick or injured crewmember, diverting to assist another vessel, or any other deviation from the original Sailing Plan should be reported

Deviation Reports require A, B, C, E, F, and Z lines. The I and L lines are required if destination or route changes. The I line is always strongly recommended, even when not required. The M, X, and Y lines are optional. (The Y line is required for US. vessels).

Deviation Report (Example)



B/291200Z NOV//




I/LOS ANGELES/3343N/12047W/040100Z DEC//


d)Final Arrival Report (FR)

This report should be sent upon arrival at the port of destination. This report properly terminates the voyage in AMVER’s computer ensures the vessel will not appear on an AMVER SURPIC until its next voyage, and allows the number of days on plot to be correctly updated. Final arrival Reports require A, K, and Z lines. The X and Y lines are optional. (Y line is required for U.S. vessels).

Final arrival Report (Example)



K/LOS ANGELES/3343N/12047W/032200Z//



Other than these repoting one of the most common report is the NOON REPORT

Noon Position Report – is a daily report to the owner and charterer indicating ship’s position at noon whether the vessel is at anchor, at sea or in port including the meteorological conditions of a particular place such as wind force and direction, swell, wave height, vessel average speed for 24 hours, present course and speed, fuel oil and diesel oil consumption and remaining on board (ROB) including ETA at next port of call.



The Earth – Chapter 1


The shape of the earth is called an Oblate spheroid. The equatorial diameter is more than the polar diameter.

Equitorial radius = 6378.16 Km

Polar radius = 6356.77 Km

As the difference is negotiable the navigators consider it as a perfect sphere.


  • Axis – The axis of the Earth is the diameter about which it rotates.
  • Poles – The geographical poles of the earth are the two points where the axis meets the earth’s surface.
  • Equator – The Equator is a great circle on the surface of the Earth, the plane of which is perpendicular to the Earth’s axis. The Equator divides the Earth into the north and the south hemispheres.
Equator, North and South pole
  • Great Circle – It is the circle on the surface of the sphere, the plane of which passes through the center of the sphere.
  • Small Circle – It is the circle on the of a sphere, the plane of which does not pass through the center of the sphere.
Meridian, Great Circle, Equator image credits to

  • Parallels of latitude – Parallel of latitudes are small circles on the surface of the Earth’s surface, the planes of which are parallel to the plane of Equator. All parallels run East-West.
Parallels of latitude, Image credits to
  • Meridians – They are semi-great circles on the Earth, joining the two poles.
  • Prime Meridian – is the meridian which passes through Greenwich. The other meridians are named East or West from Prime meridian.
  • Difference in Latitude – The d’lat between two places is the arc of meridian or angle at the center of Earth contained between the parallel of latitude through the two places.
  • Longitude of a place – is the arc of the Equator or the angle at the poles contained between the Prime meridian and the meridian through that place.
  • Difference in Longitude – The d’long between two places is the shorter arc of the Equator or the smaller angle at the poles contained between the meridians through the two places.
  • Mean Latitude – The mean latitude between two latitudes is the arithmetic mean between them.
  • Nautical mile – The nautical mile at any place is the length of the arc of a meridian subtending an angle of 1’ at the center of curvature of that place. The arc subtended by the same angle of 1’ at the pole is larger as compared to the Equator. Therefore we use a standard value for the nautical mile.
    • 1 nautical mile = 1.852 Km
  • Knot – is a unit of speed equal to one nautical mile per hour.
  • Geographical mile – is the length of the arc of the equator subtending an angle of 1’ at the center of the earth.
  • Statute mile – or land mile is an arbitrary measure of length equal to 5280ft.
  • True north – The north direction of a meridian is true north.
  • True course – is the angle at the ship between True north and the ship’s head, that is, the angle between the true meridian and the ship’s fore and aft line. It is measured clockwise from true north and is expresses in three digits.
  • Ship’s head – Direction of head of ship at any point of time is ship’s head.
  • True bearing – The true bearing of an object is the angle at the observer between True North indicated by the meridian and the line joining the observer and the object.
  • Variation – is the angle between true meridian and magnetic meridian and is measured east or west from true north. It is purely due to Earth’s magnetism. It varies from place to place. The value of the variation at a place is not constant. It changes because the position of the magnetic poles of the Earth is constantly changing. This change is called the secular change in variation.
  • Deviation – is the angle between the magnetic north and the compass north and is measured east or west from the magnetic north. The deviation is because of the ship’s magnetism and it depends on the ship’s head.
  • Compass error – The compass error is the algebraic sum of the deviation and the variation.
Article by Ritika Singh(Tolani Maritime(2020-2022),Sailing as Deck Cadet now as in 2022)

Vessel’s Characteristics

Turning circle and terms


The distance traveled in the direction of the original heading measured from the point at which a helm was first applied. The maximum advance is usually between 3 to 5 ship lengths for a merchant ship of any size going at full ahead and using full helm.


The distance of the center of gravity of the ship from the original track line measured in the 90º to the original heading. The transfer for a turn of 90º is about two ship lengths

Tactical Diameter

It is the transfer for a turn of 180º which is almost equal to the maximum transfer. It is usually about the same distance as the maximum advance.

Drift Angle

It is the angle between the tangent to the turning circle at any point and the fore and aft line of the ship.

Pivot Point

It is the point about which the vessel pivots with the bow swinging inwards and the stern swinging outwards. It is about one third (1/3) of the vessels length from forward when going ahead. When going astern the vessel pivots about approximately one quarter of the length from astern.

Final Diameter

It is the diameter of a circle traversed by a vessel after turning through 360º and maintaining the same speed and rudder angle. This diameter is always less than the tactical diameter. It is measured perpendicular to the original course and between the tangents at the points where 180º and 360º of the turn have been completed.

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