Navigation in large expanses of sea put forward two special requirements for the Mercatorial projection of a nautical chart. Enormous sea distances in the ocean the ship passes mostly with a constant course of navigation. Keeping the ship on a constant course for many hours of shift is quite convenient for the skipper. To display the line of the ship’s path on the sea charts at a constant course and the simplest line shape is chosen – a straight line.

## Marine nautical charts, determining directions and locations in marine navigation.

This simplifies the laying of a route consisting of a set of straight lines on sea charts. This is the first of the above requirements. If the vessel moves at a constant course, then it crosses all the meridians at the same angle. Such a line crossing all meridians at a constant angle is called loxodrome. The second requirement is related to ensuring orientation of the vessel at sea by bearings and angles between coastal landmarks. It is performed when the angles and directions measured on the terrain and on the sea map are identical, and the shapes of the objects are similar. Such projections are called equiangular..

The construction of the Mercator projection of the sea map is illustrated in the figure below. At the first step of construction, the meridians are straightened so as to touch the inner surface of the cylinder. The distances between the projected meridian lines are equal to the distance between the meridians at the equator. The parallels are stretched and become equal along the length of the equator.

At the second step, the surface of the cylinder with a cartographic grid is turned into a plane. All meridians on it are parallel and perpendicular to the parallels. Loxodrome at this step will be depicted as a straight line. However, the similarity of the figures on the terrain and the map is not provided due to the stretching of the parallels, that is, in the projection there is no equilibrium property. To obtain equilateral angle, now the meridians at each point must be stretched in proportion to the stretching of the parallels. After that, the construction of the Mercator projection will be completed. Please note that on the resulting projection, the distances between the parallels grow with increasing latitude..

The scale of such a sea map is different at different latitudes. When used on a small area of the card, it can still be considered permanent. For the convenience of moving from map to map, all scales on the maps of one region of the ocean or one sea are equated to one parallel, called the main one. For example, for the Baltic Sea, the main parallel has a latitude of 60 degrees, for the White – 66, for the Black – 44. Disadvantages of the Mercator projection: the inability to use at high latitudes and the image of the shortest distance line between two points in the form of a curve.

Distances in nautical navigation are measured in nautical miles. The nautical mile equals the length of the arc of the meridian in one minute. On the vertical frame of the map there is a peculiar “ruler” graduated in miles. After measuring the length of the segment on the map, for example, with a compass gauge, lay it on the frame at the latitude of the location of this segment. Then from the frame and determine the length of this segment in miles. Long distances are broken into pieces. On the side of the map frame at the desired latitude, take a segment equal to 10, 20 miles and so on, and consider how many times it will fit in the measured line. One mile equals 1852 meters; 0.1 miles – 1 cable (kbt) = 185.2 meters.

## Marine nautical charts are divided by scale.

Plans with a scale of 1: 500 to 1:25 000, used when entering raids, ports, bays.

Private nautical charts with a scale of 1:25 000 to 1:50 000, used when sailing when passing narrownesses, in skerries and directly off the coast.

Traveling sea charts with a scale of 1: 100,000 to 1: 500,000, which are used when sailing a vessel at a considerable distance from the coast.

General sea charts from 1: 1 000 000 to 1: 5 000 000.

Sea charts do not have a regular system for covering sea open spaces, the so-called markup. Therefore, the selection of maps is made according to catalogs issued, for example, for Russian maps by the Navy’s Main Directorate for Navigation and Oceanography.

## Determining directions and locations in maritime navigation.

Let’s get acquainted with the definition of directions used in marine navigation. Counting directions (angles) in the circular system is carried out from the northern part of the meridian, the observer from 0 to 360 degrees clockwise. As characteristics of directions, the concepts of course and bearing (azimuth) are used. To the corners defined by these concepts, the word “true” is often added. This allows you to distinguish between similar parameters whose values are read from navigation devices: gyrocompass or magnetic compass.

The true heading IR (True Heading) is defined as the angle between the plane of the northern part of the true meridian (direction to the north) and the diametrical plane of the vessel, measured clockwise. A true IP bearing (azimuth, Bearing, BRG) for some object is the horizontal angle between the northern part of the true meridian (direction to the North) and the direction from the observation point to the object, measured clockwise. As you know, the needle of a magnetic compass points to the north magnetic pole, which, like the south, does not coincide with the geographical one. The North Magnetic Pole is located in the Canadian Arctic Archipelago and is constantly moving, about 20 kilometers per year. The angle between the directions to the geographic and magnetic poles is called magnetic declination..

Its value is different in different areas and can reach 28 degrees. The declination to the east is considered positive, and to the west – negative. The vertical plane passing through the axis of the freely suspended magnetic arrow is called the plane of the magnetic meridian, and the trace of its intersection with the horizon plane is called the magnetic meridian. The angle measured from the magnetic meridian to the object is called a magnetic bearing or magnetic azimuth (MP). The sign and magnitude of declination, as well as its annual change, with which you can calculate the actual magnitude of declination at the current moment, are placed on the navigation charts. Note that in GPS satellite navigators, the magnetic declination is calculated automatically based on the declination model recorded in the navigator’s memory, or is entered manually.

In addition to declination, the error in the compass readings is made by local magnetic anomalies, most often caused by the occurrence of iron ore; in such areas, declination can reach tens of degrees. The areas of magnetic anomalies are indicated on the navigation charts. Also, the compass can be mistaken near power plants, large metal structures and the like. Finally, when using the compass in a car or on a ship, an error arises from the influence of the metal hull, ship iron, electrical equipment, called deviation. Deviation varies depending on the magnetic course, roll and other factors. To move from a magnetic bearing (MP) to a true bearing (IP), one must know the magnitude and sign of magnetic declination (Ck). The calculation is performed according to the formula: IP = MP + SK.

## Typical graphic tasks solved on the sea map include:

Determining the coordinates of a given point and plotting a point on a nautical chart at given coordinates.

Laying from a given point of the line of the true course or bearing.

Positioning by bearings of two or three landmarks or distances to them.

Graphic position reckoning (Dead reckoning).

To perform graphical constructions, a compass, a protractor and a parallel ruler are used. The most important and interesting is the reckoning of the place, which is understood as determining the location of the vessel from the known values of the coordinates of the starting point, course and distance traveled.

## An example of determining directions and locations in marine navigation, working with nautical charts.

Assume that the vessel does not experience drift or current, a lag marine measuring device is used to determine the distance traveled. The simplest type of lag is an outboard turntable, the countdown of its testimony gives the distance traveled relative to the water. The ship began moving from point A. Shturman determined the coordinates of the ship, recorded the countdown of the lag OL1, and also plotted the true course from this point on the map. At the moment of rotation at point B, he must postpone a distance in scale equal to the difference between the samples of the lag OL2 – OL1 along the course line from point A. Having received a new point on the map, he records the turn time and lag count and draws a new true course from point B.

And so on. Thanks to this, no matter how many turns a ship makes, having only a compass and a lag, you can always get its approximate calculated number on the map. Such is the fundamental basis of number reckoning. In reality, the real situation is much more complicated, since the wind, acting on the ship, causes the ship to drift off course. The current also acts. In the presence of drift and current, the vessel does not move along the line of a given course, but along another line of the track line, which is deviated from the IR line. If it is possible to determine the drift angles caused by wind and current, then to determine point B in the above example, the distance must be delayed along the path.

GPS navigators and navigational cartographic systems greatly facilitate navigation, because they automatically calculate all navigational parameters, including the so-called heading relative to the ground (COG – Course Over Ground, ground angle). It is the latter that determines the direction of the path line. Nevertheless, reckoning gives only an approximate location. Therefore, it is periodically combined with other methods of determining coordinates, including using GPS navigators.

*Based on materials from the book All About GPS Navigators.*

* Naiman V.S., Samoilov A.E., Ilyin N.R., Sheinis A.I..*