GRAPHIC RECORDING OF THE VESSEL'S PATH. In order to judge the safety of navigation, navigate the environment and correctly choose courses for further movement, the navigator must know the position of his vessel at any time. To do this, he conducts a navigation chart. Before the vessel sets out on a voyage, under the guidance of the captain, the navigation conditions for the entire upcoming passage are studied using maps and navigation aids. Based on these data, preliminary installation is performed. However, it only gives a general idea of ​​the transition conditions. From the moment of departure on a voyage, the final choice of courses and all factors taken into account are determined by the specific navigation situation. Therefore, executive routing is carried out during the flight. It includes dead reckoning, calculations and plotting on a map, maneuvering calculations for divergence from other ships.

Dead reckoning is the continuous accounting of the elements of a vessel's motion (speed and direction) and the influence of external forces in order to determine the coordinates of the vessel (reckoning place) without observing coastal landmarks and celestial bodies (observations). This accounting is carried out based on the values ​​of the course, speed and drift vector of the vessel. The starting point for counting on the map is determined by the captain. Such a point can be taken as the exact location of the vessel, obtained immediately after leaving the port water area, a lightship, receiving buoy, etc. Its coordinates are recorded in the ship's log. By the time the execution starts, you should turn on the log, determine the compass correction along the alignments, or in another way.

MAKING COUNTING WHEN SWIMMING WITHOUT DRIFT AND CURRENT. When sailing without drift and current, the vessel's path line on the map coincides with the IR line, therefore, the movement of the vessel on the map is taken into account along the IR lines, along which the distances traveled by the vessel along the log are plotted, taking into account its coefficient Kl. A first course line is drawn from the starting point on the map. The IR taken from the card is transferred to the CC, on which it is placed according to the magnetic compass. On the map above the IR line the compass course and its correction are indicated. The distance Sl traveled along the course is determined by the lag: Sl = Cl (ol 2 - ol 1); (Where ol 2 is the lag count at the point where the vessel is located, ol 1 is the lag count at the starting point, K is the lag coefficient).

On the IR line, in the cases indicated below, the number of the ship is marked, i.e., the place calculated according to the course and navigation. If the voyage is carried out near the coast, countable points are marked every hour; in the open sea - at the end of the watch. In addition, the countable place is applied at the points of the beginning and end of turns, when changing speed, when receiving observations. Near the ship's place, the moment is recorded in the form of a fraction on the ship's clock with an accuracy of 1 minute (T) and the log reading with an accuracy of 0.1 mile (ol). (See Figure 31).

In real conditions of sea navigation, three main options are possible, which determine the corresponding practical methods of dead reckoning the yacht's path: sailing in conditions of stable full wind; sailing in steady headwind conditions; sailing in winds that are unstable in strength and direction.

In the first case, the yacht is usually driven along path lines laid during preliminary installation. The calculation conditions here are favorable. In the second case, a tack is performed relative to the general course, while the actual path laid on each tack does not coincide with the preliminary laying. If the tacking tack is not too steep, then the helmsman accurately maintains the given course, which simplifies dead reckoning and increases its accuracy. In such conditions, the duration of the tacks depends on the tacking angle (the angle between the general course and the yacht's path). If the angles of the right and left tacks are equal, their duration is the same, and the tacking can be symmetrical. If not, dead reckoning and track laying are performed on each particular tacking tack according to instrument data. If there is no lag, it is recommended to evaluate the speed on each tack.

When tacking, it may happen that the helmsman, on the instructions of the yacht captain, does not pay attention to the compass when heading into the wind. Here, after small but equal intervals of time (15 - 30 minutes), the average QC and the corresponding IC are determined and recorded, according to which the data obtained by lag or speed are stored. In unstable winds, the helmsman is not given a course, but is given the task of steering along the sail in search of the wind, keeping as close as possible to the general course. Sometimes in such a situation, depending on local signs and the weather forecast, it may be advantageous to deviate from the general course in order to get a full steady wind sooner (for example, an offshore breeze). In all these cases, in the interests of dead reckoning, all turns on the yacht are recorded and on each tack (at the beginning and end of the tack it is obligatory) with a certain frequency (1-2 times per hour, depending on conditions) data on the movement of the vessel (time, course) are recorded , speed, lag count). These records are processed by averaging the course and speed of each tack, and then plotted on a chart.

Practice shows that the accuracy of dead reckoning in such conditions increases with increasing discreteness of observations. Errors in approximating curved sections of swimming to rectilinear ones will be insignificant compared to other errors.

DRIFT OF THE SHIP. In navigation, drift (“a”) is the movement of a vessel from its course line under the combined action of the wind and the waves it causes. When drifting, a ship moves relative to the water under the combined action of ship engines and wind. The line of its actual movement (OM), called the ship's track during drift, does not coincide with the ship's course (OA). (See Figure 33). When the track line is shifted to the right of the vessel's port (the wind blows to the left side), a is assigned a plus sign (+), and when it is shifted to the left (the wind blows to the starboard side), a minus sign (-) is assigned. The relationship between the track angle taking into account drift (PUa), IR and a: PUa = IR + a ; IR = PUa - a ; a = PUa - IR

The drift angle can be determined by comparing the actual path of the vessel, obtained from observations, with the IR. When following the coastline, a number of reliable navigational observations are carried out. By connecting the observed points, a line of actual movement of the vessel is obtained, i.e., a line of path during the drift of the PUa (Fig. 34). The angle between the track line and the IR line drawn on the map corresponds to the drift angle. The found drift angle with its sign is taken into account in further calculations. If there is a current in the navigation area, then the resulting drift angle will be the result of the influence on the ship not only of the wind, but also of the current.

ACCOUNTING FOR DRIFT IN COUNTING. If the ship is drifting, then when plotting, the line of the ship's path during drift is plotted on the map. It is inscribed with KK, compass correction and the accepted drift angle a with its own sign. The distances Sl traveled along the log are plotted along the path line. It is believed that when a

If the navigator is not sure of the accuracy of the drift angle, then to control the safety of navigation, in addition to the drift line, it is recommended to put an IR line on the map. Both of these lines must be clear in relation to underwater obstacles. Reckoning is carried out only along the track along which the vessel moves.

SEA CURRENTS. Sea currents are the horizontal movements of large masses of water. A flow is characterized by its elements: direction and speed. The direction of the current Kt is indicated in degrees according to a circular count or in bearings and is set according to the point on the horizon to which the current is directed. Current speed Vt is measured in knots, and small current speeds are measured in miles per day. According to the nature of the flow, they are classified into constant, the elements of which hardly change from year to year, periodic, the elements of which change according to a certain law, and temporary (random), the elements of which can change sharply. In practice, the navigator most often has to deal with constant and periodic (tidal) currents. Information about the elements of constant and tidal currents is placed in sailing directions, current atlases and on maps. In this case, the average values ​​of flow elements are indicated, which may differ significantly from the actual ones. The movement of the vessel relative to the ground when sailing in the current is determined by the following factors (Fig. 36).

Under the influence of ship engines, the ship moves relative to the water in the direction of its DP, i.e., the line of the true course OA. The speed of the ship relative to the water is the speed Vl shown by the log. At the same time, together with the entire mass of water, the vessel is carried away relative to the ground in the direction of flow OD with flow speed Vt. As a result, relative to the ground, the ship moves along the resultant OB at a speed called the true speed of the ship V. In this case, the ship’s DP remains parallel line IR. The line OB along which the ship moves under the combined action of ship engines and the current is called the line of the ship's path on the current. The position of the track line relative to the true meridian is determined by the NOB angle, which is called the track angle along the PU flow. The angle " ", enclosed between the true course line of the vessel OA and the track line OB, is called the current drift angle. When a vessel drifts to the right of its DP (the current is directed to the left side), a “+” sign is assigned, and when it drifts to the left, a “-” sign is assigned. Dependence between (PU), IR and:

PU = IR + ; IR = PU - ; = PU - IR

CALCULATION WHEN SWIMMING WITH THE CURRENT. When sailing in a constant current, the ship's path along which it actually moves relative to the ground is drawn on the map. Above the track line, write KK, compass correction and drift angle with its own sign. For auxiliary calculations, the IR line is also drawn with a thin line, along which the distances Sl traversed by the vessel relative to the water are plotted according to the log readings. The points obtained on the IR line are transferred in the direction of the flow to the track line (Fig. 37). At the countable points on the track line, a time and lag counting mark is made, and at the corresponding points on the course line - only the lag counting. The points of traverse, opening and hiding landmarks are marked on the track line (Fig. 38).

CALCULATION WITH JOINT ACCOUNTING OF DRIFT AND CURRENT. Let's consider the case when a ship moves relative to the ground under the combined action of ship engines, wind and current. To carry out dead reckoning, a line of the vessel's path during drift and current is drawn on the map and the CC, compass correction and total drift angle c = a+ are written.

In addition, for auxiliary calculations, a drift track line is also laid on the map, along which the vessel’s navigation along the log Sl is plotted. Each point on the track during drift corresponds to a point on the line of the actual movement of the vessel. These points are connected to each other by the flow vector. Graphically, tasks related to finding on the map the track line during drift and current, the true speed V and the total drift angle c for given CC, Vl, a, and flow elements, plotting the countable place, precalculating the time and ol at the time of arrival at a given point, Finding abeam of a landmark is solved in the same way as when sailing on a current, but all auxiliary formations are made on the track line during drift, replacing the IR line.

ESTIMATES OF CUMULATION ACCURACY. As a result of the impact of unaccounted errors, the actual path of the vessel and the distance traveled (sailing) will not correspond to those taken into account when calculating on the map, and the actual position of the vessel will not correspond to the calculated one. To make an approximate judgment about errors in calculations, you can use the following data, which reflect the accumulated generalized experience of navigation and the research conducted. The duration of the voyage (hours) corresponds to the radial root mean square error of calculation, % of S: Up to 3 hours - 10%; 3 -6 hours - 9%; 6 -10 hours - 8%; 10 -14 hours - 7%; 14 -18 hours - 6%; 18 -23 hours - 5%; 23 -25 hours - 4%; more than 35 hours - 3%. When plotting the ship's path on the map at a certain distance from navigational hazards, it is necessary to take into account the possibility of the ship deviating from the route line, and the value of the deviation will increase with increasing distance traveled, especially when sailing with drift and current. Insufficient dead reckoning accuracy necessitates additional control over the vessel’s location, i.e., determining its location not only by dead reckoning, but also by observations: navigational, astronomical, or using GPS.

§ 26. Graphic and written dead reckoning of the ship's path

General information. Laying, carried out without checking the position of the vessel by determining its place by coastal objects or by celestial bodies, is called dead reckoning of the ship's path. Calculus performed on a map using the graphical construction method is called graphic dead reckoning of the ship's path, and performed using calculations using special formulas - written(analytical).

Graphical notation. The essence of this method is as follows. At the moment of determining the starting point a" (see Fig. 29), note the time on the ship's clock (up to 1 minute) and the readings of the log counter (up to 0.1 miles). The starting point a" is circled and an inscription is made near it in a free space in the form of a fraction: numerator - time, denominator - lag readings 18.00/2.5 If the observed point a" is sufficiently close to the starting point a, then from point a" a first course line is laid in the form of a straight line parallel to the line ac. After this, the AC line is erased from the map, and on the newly drawn line the number of degrees of the compass course is written and next to it, in parentheses, the general compass correction AK calculated for this course, so that you can always determine which course you were following.

If the observed point a" is so far from point a that the ship's path passes close to the dangers (dotted line in Fig. 29), then a new course is plotted as was shown above in § 25.

The ship's countable positions are marked hourly along the route. To do this, the distance traveled by the ship in 1 hour is plotted on the map scale with a meter along the ship’s path from the starting point. In the place marked by the meter, a notch is made in the form of a short straight line perpendicular to the track line, as well as an inscription of the time and log readings.

If the ship needs to change the direction of movement, then at the moment of changing course the time and the lag count are again noted. Having calculated the voyage completed from the last counting point, they lay it down along the route, mark the turning point with a notation in the form of a fraction (04.37/70.2) and plot a new course from this point. If for some reason the ship ends up at point c, which is significantly removed from the point c planned by preliminary plotting, then a new course is laid so as to reach point d of the second turn. After this, line cd is also erased from the map, and on line c “d” inscribe the number of degrees KK and next to it, in brackets, the general correction of the compass AK for THIS course.

Maintaining a graphic plot allows the navigator to have a clear idea of ​​the vessel’s position in relation to navigational hazards.

The accuracy of the plot depends on how correctly the course is laid and the distance traveled is taken into account. The accuracy of the gasket is expressed by the following formula:

where Sо is the amount of voyage completed by the vessel;

Ek - error in the general compass correction;

Es is the error in the lag correction, %.

Example 26. Determine the radius of the circle within which there should be a place for a ship traveling 60 miles on one course, if the possible error in heading is ±1°, and the possible error in the log correction is -2.0%.

Solution. According to formula (31)

Turning the ship from one course to another introduces some additional error into the laying, since after shifting the rudder the ship does not instantly change the direction of movement, but describes a certain curve (circulation) with its center of gravity.

Circulation accounting has great importance when sailing in tight waters, narrow waters, skerries, etc. Circulation is taken into account as follows.

The vessel (Fig. 30), following in the direction of K1, at point A must turn in the direction of K2 (the angle of rotation is equal to a). To take into account the circulation, draw a bisector of the internal angle of rotation (3 = 180°-a and on it look for the center O of a circle with a radius equal to half the tactical circulation diameter Dc, which is determined experimentally and is usually expressed in the lengths of the ship’s hull.

Having drawn a circle, mark points B and C where it touches lines K1 and K2. Point B is considered the beginning of the turn.

Written reckoning. The ship's reckonable position can be obtained by the analytical method of written dead reckoning in cases where it is irrational to use graphic dead reckoning of the ship's path: when sailing in high latitudes, during ice navigation, whaling, etc.

Rice. thirty.

The essence of written reckoning is to determine the coordinates of the arrival point given the known coordinates of the departure point, the course and navigation of the vessel. Using written reckoning, you can solve the inverse problem: determine the navigation and course of the ship using the known coordinates of the points of arrival and departure.

Based on formulas (4) and (5), the coordinates of the arrival point can be expressed as follows:

If navigation occurs at low latitudes, then expressions for the RS and RD can be easily obtained by considering the so-called navigation triangle ABC (Fig. 31), in which:

A - departure point with coordinates cp1 and L2;

B - arrival point with coordinates cp2 and L2;

K = LCAB - ship's course when moving from point A to point B;

AB=S - distance between points of departure and arrival;

AC=RSh and BC=OTSH.

If we assume that triangle ABC is flat and right-angled, then directly from Fig. 31 we get:

Next, substituting the value OT Ш from formula (6), we obtain
In fact, ААВС is not flat and not rectangular (the figure АВС" is a spherical trapezoid). Therefore, РД1 = РД2(срB=cpA), but the real value
Where

- average latitude.

To facilitate the work of the navigator, the MT-63 has auxiliary tables: table. 24 gives the values ​​of RS and OTSh based on the arguments S (swimming) and K (course); table

25-a - RD values ​​based on the arguments φm and OTS.

Rice. 31.

If reckoning is carried out on a passage made by a ship on the same course, then it is called simple, and if there are several courses - compound. Composite reckoning is used when swimming in currents, especially tidal ones; in this case, the course is taken into account as a separate additional course (courses). In composite calculation, RS and RD are calculated or selected from tables for each individual course and swim. By compiling the algebraic sum of all RS and OTS, we obtain the general RS and general OTS. Next, calculate the latitude of the arrival point using the formula

φ2 = φ1 + general РШ

And the general formula

Purpose and types of notation. Main goals,

Solvable on the map

Reckoning is the process of obtaining the position of a ship at any moment based on its movement from a point taken as the starting point.

Dead reckoning is the basis of navigational (instrumental) navigation. The captain's assistants perform the counting on a watch basis under his control during the entire voyage. They begin counting immediately upon leaving the port or lifting the anchor, and end with arrival at the roadstead of the port of destination. The place and time of the beginning and end of counting is determined by the captain. The most accurate position of the ship that can be obtained under the given conditions is taken as the starting point. If a large dead reckoning error is discovered during a voyage, then transferring it to a new starting point and changing the elements of movement taken into account are also done with the knowledge of the captain.

The position of the ship on the map obtained by dead reckoning and its coordinates j c, l c are called reckonable. Near such a point, a horizontal line is drawn, above which the ship's time is written (hours, minutes), and below - the log count (miles without indicating hundreds, tenths). If the log does not work, then a dash is placed below.

Keeping the essence of notation, it is divided into three types: graphic, analytical and automatic. Regardless of this, if necessary, they stipulate what conditions are taken into account - drift, flow, circulation.

Countable points are supposed to be plotted on the map during any changes in the course and speed of the vessel, during other changes in sailing conditions, as well as during all events that are recorded in the ship’s log. If the course and speed are constant, then when sailing along the coast, countable points are plotted on the map every hour, and when sailing in the open sea (in the ocean) - after four hours when changing watches.

Usually the countable place is found at the current moment of the ship's time. Sometimes it is necessary to find the estimated countable place at a given moment in the future or, on the contrary, it is necessary to restore the countable place at the time of some event in the past. Similar and any other number problems can be solved graphically or analytically.

To graphically solve various navigation problems, they use a measuring compass, a parallel ruler and a navigation protractor.

A measuring compass is used to measure and plot distances on a map. Distances are measured in nautical miles. The scale is the side (vertical) frame of the map opposite the place where the measurement is made. One minute of this scale is equal to one nautical mile.

A parallel ruler is used to draw straight lines on a map parallel to a given direction. It consists of two rulers connected by metal rods on hinges. This connection allows you to move the ruler while maintaining a given direction, which is necessary when laying course and bearing lines. An ordinary drawing compass is also used, with the help of which arcs are drawn on the map - when determining a location by distances to coastal objects.

A navigation protractor is needed to plot and measure angles on a map. It is a graduated semicircle with a ruler centered at point "0". On its outer arc there are degree divisions. The division bars, multiples of five degrees, are elongated. Opposite the strokes marking tens of degrees are two numbers differing by 180°. The upper numbers correspond to the directions of the northern half of the compass card, and the lower ones – to the southern half. In order to draw a line on the map at a certain angle to the meridian, it is necessary to place a protractor on the map so that the central stroke “0” and the line on the arc, indicating a given number of degrees, coincide with the meridian line. Then a line drawn along the upper edge of the ruler in the appropriate direction will give the desired direction.

When laying, it is necessary to solve the following main tasks:

1) remove the latitude and longitude of a given point from the map;

2) use a given latitude and longitude to plot a point on the map;

3) plot a course or bearing from a given point on the map;

4) set aside a certain number from a given point in a given direction

5) determine the direction of the course or bearing marked on the map;

6) measure the distance between two points on sea ​​map;

7) plot a course on the map from the starting point at a given distance from

this item;

8) move a point from one map to another.

1. Take the latitude and longitude of a given point from the map. This problem is solved using a compass. Having placed one needle of the compass at a given point, move it apart so that the second needle falls on the nearest parallel. By drawing a part of the circle with a compass, make sure that its needle touches the nearest parallel at only one point. Then, without changing the solution of the compass, transfer it to the side of the map frame and, attaching one of its needles to the same nearest parallel that touched part of the circle, and directing the other along the frame towards this point, i.e. to N or S from this parallel, take the latitude corresponding to this point.

To measure longitude, place one needle of a compass at a given point and, expanding it to the nearest meridian, use the second needle to describe a circle tangent to the meridian. Without changing the solution of the compass, transfer it to the lower or upper part of the map frame and, placing one of its needles on the meridian to which part of the tangent circle was drawn, place the second needle on this frame towards the given point and take the longitude.

Latitude and longitude are recorded with an accuracy of 0¢.1, if the scale allows.

2. Using the given latitude and longitude, plot a point on the map. To plot a point on the map, look for a division on the side frame that corresponds to the number of degrees and minutes of a given latitude, and, applying a parallel ruler to the parallel closest to this division, move the ruler so that one of its cuts falls on the division of the given latitude; then, in the rectangle where the point should approximately be located, a line is drawn between the two meridians along the cut of the ruler. Having found a division on the lower or upper part of the map frame that corresponds to the number of degrees and minutes of a given longitude of a place, and using a compass to take a segment from this division to the nearest meridian, lay this segment on a line drawn with a pencil from the same meridian and get the point you are looking for.

The same task can be accomplished using just one ruler. To do this, having found the given latitude on the side frame and applying the ruler to the nearest parallel, bring its cut to the given latitude, along which a short line is drawn with a pencil in the rectangle where the desired point is located. Then, having found a division corresponding to a given longitude on the lower or upper part of the map frame, apply a cut of the ruler to the nearest meridian and, moving the ruler, bring one of its cuts to the division of the given longitude, along which a short line is also drawn. The intersection of two drawn lines gives the desired point.

3. From this point on the map, plot a course or bearing. To solve this problem, use a protractor and a ruler. Before you begin solving the problem, you need to imagine the direction of a given course or bearing, i.e. in which quarter of the horizon this direction will be located. Having placed a protractor with an attached parallel ruler on the map so that the lower section of the ruler is approximately the given direction with the meridian, turn the protractor without moving the central stroke away from the meridian either to the right or to the left until the division of the protractor corresponding to the given course coincides with meridian.

Having achieved a match, remove the protractor and, bringing the cut of a parallel ruler to this point, draw a course line, drawing it with a pencil along the cut of the ruler. If the protractor ruler is located almost in the direction of the meridian at courses close to zero or 180°, then it is better to apply the protractor to the parallel and set it to reference the given course ±90°.

The inscriptions on the protractor divisions are made in such a way as to indicate the direction of course or bearing; so for courses directed to N, or upward, the corresponding inscriptions on the protractors are at the top, while for courses or bearings directed to S, or downward, the inscriptions are at the bottom.

4. Set aside a certain number of miles from a given point in a given direction. When solving this problem, it is necessary to remember that a nautical mile is Mercator map depicted by segments of varying lengths, depending on latitude.

The specified distance is taken using a compass on the side of the map frame from a latitude approximately corresponding to the latitude of a given point. This distance is taken to N from this point if the course is directed to N, or to S if the course is directed to S, and is laid off from this point on the line of the plotted course or bearing. If the value of a given distance cannot be measured with one solution of a compass, then this distance is laid off in parts, and each part is taken at the latitude corresponding to this part.

5. Determine the direction of the course or bearing shown on the map. By attaching a ruler to the course or bearing line marked on the map and attaching a protractor to it, bring the ruler together with the protractor to the nearest meridian, aligning the central stroke of the protractor with the meridian. The reading on the protractor will give the value (in degrees and fractions) of the course or bearing being determined. If the course or bearing direction lies in the NE or NW quarters, i.e. in the N direction, then the upper reading is taken on the protractor, but if the direction is in the SE or SW quarters, i.e. in the direction to S, then the lower reading is taken.

6. Measure the distance between two points on a sea map. When measuring the distance between two points, place one compass needle at one point, and the other at the second, and measure the distance between these points. Then the compass is moved to the side of the frame and the distance taken with the compass is determined in the latitude corresponding to the distance being measured.

If the distance between points cannot be measured with one compass solution, then it is measured in parts - each part in the corresponding latitude.

7. Plot a course on the map from the starting point at a given distance from the given object.

To solve this problem, remove a given number of miles from the side frame of the map, in that part of it that falls opposite the given object.

Place a compass needle on the map at a point corresponding to the location of a given object, and use a compass pencil to describe an arc.

From the starting point, draw a tangent to the circumscribed circle.

8. Move a point from one map to another.

This problem can be solved in two ways:

· take the latitude and longitude of a given point from one map and use them to plot the point on another map;

· take from one map the true bearing of some object marked on both maps, and, having measured the distance from this object to a given point, plot the taken true bearing on the other map and lay off the measured distance from the object on the bearing line, taking it on the scale of the second cards.

Wind accounting

Graphic dead reckoning (laying) consists of calculations and plotting on a map, which should reflect the movement of the vessel as accurately as possible.

A simple laying at a constant course, when there is no wind or current, is as follows (Fig. 1.15). On the map, from the initial (previous numeral or observed) point M o, draw a line of the intended path and measure the corresponding true course IR with a protractor. Above this line (in such conditions it coincides with the course line) the course according to the main compass is written, and its correction is written in brackets. This course and correction are rounded to the nearest half degree so that their algebraic sum gives IR (in Fig. 1.15 IR = 67.5°).

Based on the difference in lag roll readings for the desired countable point M c and taken as the initial Mo (in Fig. 1.15 roll = 62.5), the vessel's navigation along the lag S = V roll is calculated using the formulas. This voyage is plotted on a map scale along the course line and a countable place M s is obtained. Such a place is marked with a dash across the course line and, as always, the ship's time and log count are inscribed. Of course, they don’t put on the map those shown in Fig. 1.15 designations IR, M o, S l and M s.

The ship is located on the border between air and water. When a ship moves, the movement of air masses (wind) deviates it from the intended course and changes its speed; In addition, the wind spreads the wave (which leads to the yaw of the vessel) and creates a drift current.

The wind gets its name from the point on the horizon from which it blows

If, for example, the wind blows from NE, then it is called NE.

It is customary to say: the wind "blows into the compass" A the ship "goes from the compass".

The angle between the direction of the wind and the centreline of the ship is called the ship's heading relative to the wind. If the wind blows to starboard, then they say that “the ship is sailing on starboard tack.” If the wind blows to the port side, then they say that “the ship is sailing on port tack.”

When the angle between the center plane of the vessel and the wind line is less than 8 points, or, for that matter, less than 90°, then they say that “the ship is on a close-hauled course”, adding the name of the tack: “hauled course of the starboard tack” or “ close-hauled course on port tack.”

The left tack is abbreviated as l/g, and the right tack is abbreviated as p/g.

The close-hauled course can be steep and complete.

A close-hauled course will be when the angle between the center line of the vessel and the wind direction is less than 6 points. If this angle is more than 6 points, then in this case the course is called full close-hauled.

When the angle between the center plane of the ship and the wind line is 8 points, or 90°, then the ship's course is called galfind, or half the wind (Fig. 1.16.).

When the angle between the center plane of the vessel and the wind line is more than 8 points, but less than 16 points, then the course relative to the wind is called the backstay (Fig. 1.16).

When the wind blows directly astern, the ship's course is called jibe.

When the wind blows directly into the bow of the ship, they say: “the wind is blowing straight across the bow” or “the ship is going against the wind” (leventik).

While the ship is moving, a stream of water remains behind its stern, called the wake. When heading gybe or left, the center plane of the vessel coincides with the wake.

On other courses the ship is blown into the wind; such drift is called drift. During drift, the diametral plane makes an angle with the wake jet, which is called the drift angle (Fig. 1.17.).

Thus, the drift angle a is the angle made by the centerline plane of the vessel with the direction in which it actually moves in the presence of wind (path-drift or track angle with drift PU a)

Sailing ships have the greatest drift when heading close-hauled. Vessels with a mechanical engine, on the contrary, have the greatest drift during galfind courses, i.e. when the wind blows perpendicular to the board.

In general, the magnitude of the drift depends on various reasons. For example, the greater the freeboard, the less the vessel's draft and the stronger the wind blows, the greater the vessel's drift.

Under equal conditions, a deep-draft vessel will have less drift than a shallow-draft vessel.

The amount of drift on sailing ships can reach up to 1-2 points and even more. With a large stroke, the drift will be less than with a small stroke.

The amount of drift can be determined using the azimuthal circle of the compass, for which the direction finder is installed in the direction of the wake stream, thus obtaining on the azimuthal circle the angle between the center plane of the vessel and the line of its movement, in some cases formulas are used, but the most reliable measurement of the drift angle is obtained according to observations.

As can be seen from the definitions to Fig. 1.18, fair

.

However, the main task is to follow the intended path. To do this, with the appearance of drift, you need to change the course by an angle a in the direction of the wind, as they say, “take to the wind.” In this case, using the formula we find

.

The resulting true heading is converted into compass KK = IR - DK and is given to the helmsman or set on the autopilot.

Reckoning, taking into account drift, is carried out along the track line, postponing the navigation S l on it, designating and labeling the points to be counted as in the simplest laying. To obtain the vessel's position abeam any landmark, its bearing IP ^ = IR ±90° is carried out by notching on the track line.

The inscription on the map above the track line is made as shown in Fig. 1.18 with the calculation that the algebraic sum of the compass course, its correction and drift angle gives PU a, plotted on the map.

Wind waves cause the ship to yaw on course, especially when the wave bearing makes an acute angle with the ship's DP; The “yaw angle ¡” can reach £ 4°, and due to the complex interaction of the wind with the superstructure and the wave with the hull, the sign ¡ can become opposite to the sign of the angle a and larger in magnitude, i.e. the ship will not go downwind, but to the wind: for example, a = +2°. ¡ = -3°; total effect (a + ¡) ​​= -1° (with port tack wind the ship moves to the left!).

In conclusion, let’s consider a question that is specific only to a sailboat:

If a sailing vessel needs to reach a target “in the wind”, i.e. to go against the wind, it is necessary to use tacking, i.e. tack towards the wind (Fig. 1.19.).

The turning point (change of tack) is located at the moment when the object is at a speed equal to twice the optimal tacking angle plus a (optimal tacking angle = angle of greatest climb when moving into the wind).

Accounting for current

For various reasons, water in the seas and oceans has a forward movement, which is called a current.

A current has two elements: speed and direction. The speed of the current is the number of miles that water particles travel in an hour. When the current is weak, its speed is determined by the number of miles per day.

The direction of the current is taken to be the direction in which a floating object moves away from the observer solely under the influence of the current alone.

Usually the direction of the current is indicated in true bearings and gets its name, like the course of the ship, from the point on the horizon to which it is moving. It is customary to say about the direction of the current that the current, like the ship, comes from the compass.

Currents can be constant, periodic (tidal) and random.

Constant currents are those whose direction and average speed remain almost unchanged from year to year. The speed of the current varies and ranges from 10 to 120 miles per day.

Tidal currents are those that arise from the action of tides.

Tidal currents reach significant speeds in some areas (£15 knots)

Random currents occur as a result of winds blowing for a long time in the same direction, as well as from rains that last for a long time, etc.

Everything said earlier in this section about dead reckoning allows us to take into account the movement of the ship only relative to the water. Obviously, to ensure navigational safety, it is also necessary to take into account the current.

The current velocity vector V t is characterized by its direction relative to the meridian K t and the speed V t. Let us denote the vector of the relative speed of the vessel V c, and the vector of its absolute (relative to the shores and bottom of the sea) speed, which is also called the track speed V p. According to the meaning of the named speeds, we have the following vector equality:

If the relative speed V c and the course of the vessel IR = KK + DK, the drift angle a and the current vector V T are given, then in order to find out where the ship is going and at what speed, it is necessary to solve the vector equality. To do this, first find, as described in the previous paragraph, PU a and lay a path line without taking into account the current. Vector V c is constructed along this line, and vector V T is constructed from its end (Fig. 1.20). The closing vector V p gives the track angle of the launcher, the ground speed, and also reveals the drift angle b of the current. This angle is considered positive when drifting to the right, and negative to the left. From definitions and Fig. 1.20 see

.

The track angle PU c determines the direction of the vessel's track line, above which are inscribed, as before, KK, DK and the total drift angle c = a + b. Countable points are plotted on the same line, but the navigation S l is postponed along the line PU a, from where the notches are transferred to the path line PU c parallel to the vector V T (see Fig. 1.20).

If the action of the vector and current is assessed from observations, for example, from precise observations, then the drift angle is obtained With between the lines of the true course and the ship's track

.

The drift angle c is the angle between the bow of the ship's center plane and the vector of its ground speed V p. The drift to the right is considered positive, and to the left - negative.

More often in practice, the main problem of laying, taking into account drift and flow, is usually solved in a different formulation. Namely, the given path is the path along which the ship must move despite the action of wind and current. The drift angle a and the current vector V T are known. A graphical solution to this problem is performed as follows.

On the map, from the initial radix point, draw a line of a given path, which makes the angle PU relative to the meridian (Fig. 1.21). From the same point, a flow vector V T is constructed using its elements K t and V T, and from the end of this vector a notch is made on the path line with a compass solution equal to V c. This reveals the ground speed V p, the track angle of the launcher a and the drift angle b by the current (see Fig. 1.21).

Of course, instead of a vector triangle of speeds, the sides of which express the number of miles per hour, you can build a similar triangle of distances S = Vt for the same time interval t.

Countable points, as always, are plotted on the track line, for which the navigation S l is plotted along the line PU a and carried parallel to the vector V T onto the track line.

The ship is affected by the total (or total) current, the direction and speed of which are often known with large errors. If necessary, the direction K T and the speed V T can be determined by the “navigation” method using observations: with a sufficiently accurate account of the wind, K T is equal to the average value of several directions of discrepancies, and V T is the average value of several discrepancy values ​​reduced to the hour of sailing.

During the voyage, the navigator must pre-calculate the time and (sometimes) the timing of the lag for the occurrence of various events: traverse, the shortest distance to a landmark, the opening of a lighthouse fire, a reporting point, etc. For each event, a point is marked on the map, and the time T and the countdown of the lag OL are found according to the formulas (Fig. 1.22.):

;

; .

In Fig. 1.22 S p and S l are shown for the lighthouse abeam, OIP ^ = IP ^ ±180°, IP ^ =IR ±90°.

Circulation accounting

Circulation is the trajectory of movement of the ship's center of mass with a constant rudder laying.

To take into account when laying, the circulation of small and medium-tonnage vessels is taken as an arc of a circle with a radius R c (half the tactical diameter) and a time t 180 for turning by 180°. These agility characteristics are determined from field observations, usually with two rudder positions: half on board - 15° and on board - 35° for the ship loaded and unladen.

If the course lines before and after the turn are specified on the map, then the circulation is constructed as follows (Fig. 1.23). Draw a bisector MO of the angle of intersection of these lines and find a point O on it, from which an arc of radius R c is tangent to them. This determines the starting point H and end point K of the turn.

The time of rotation through angle a (in degrees) is estimated using the formula

.

In other cases, if the starting point H of the turn and the direction are specified

lines of the new course, taking into account circulation when laying is performed differently (see Fig. 1.23.).

From point H, a perpendicular HO is restored to the line of the previous course, a radius R c is plotted along it, and an arc with this radius is drawn from the resulting center O. Then, using a protractor and a parallel ruler, draw a new course line tangent to this arc, which determines the end point K.

The same points H and K for a given R c and rotation angle a can be obtained by calculations and construction of segments d 1 and d 2 or angle q and segment d.

Intermediate voyage heading angle , intermediate float value .

The arrival of the vessel at the initial point H should be pre-calculated based on time and log count. It is even more important to outline the secant bearing and distance of the landmarks for arriving at this point. The approach to the new course line must also be controlled using predetermined bearings and reference distances.

S T = V T. t a;

The direction of the segment S T is laid from point H in the direction opposite to the flow, the rest is obvious from the figure.

GRAPHIC RECORDING OF THE VESSEL'S PATH. In order to judge the safety of navigation, navigate the environment and correctly choose courses for further movement, the navigator must know the position of his vessel at any time. For this he leads.

navigation pad Before the vessel sets out on a voyage, under the guidance of the captain, the navigation conditions for the entire upcoming passage are studied using maps and navigation aids. Based on these data, perform pre-laying . However, it only gives a general idea of ​​the transition conditions. From the moment of departure on a voyage, the final choice of courses and all factors taken into account are determined by the specific navigation situation. Therefore, during the flight they carry out executive gasket

. is the continuous accounting of the elements of the vessel's motion (speed and direction) and the influence of external forces in order to determine the coordinates of the vessel (countable place) without observing coastal landmarks and celestial bodies (observations). This accounting is carried out based on the values ​​of the course, speed and drift vector of the vessel. The starting point for reckoning on the map is determined by the captain.

The exact position of the vessel obtained immediately after leaving the port waters, a lightship, receiving buoy, etc. can be taken as such a point. Its coordinates are recorded in the ship's log. By the time the execution starts, you should turn on the log, determine the compass correction along the alignments, or in another way. MAKING COUNTING WHEN SWIMMING WITHOUT DRIFT AND CURRENT. When sailing without drift and current, the vessel's path line on the map coincides with the IR line, therefore, the vessel's movement on the map is taken into account along the IR lines, along which the distances traveled by the vessel along the log are plotted, taking into account its coefficient Cl.

A first course line is drawn from the starting point on the map. The IR taken from the card is transferred to the CC, on which it is placed according to the magnetic compass. On the map above the IR line the compass course and its correction are indicated. Distance traveled along the course Sl MAKING COUNTING WHEN SWIMMING WITHOUT DRIFT AND CURRENT determined by lag:

Sl = Cl (ol2 - ol1)

; (Where

1. ol2
2. ol1
3. - lag coefficient).

In the first case, the yacht is usually led along the route laid during preliminary laying. The calculation conditions here are favorable. In the second case, a tack is performed relative to the general course, while the actual path laid on each tack does not coincide with the preliminary laying. If the tacking tack is not too steep, then the helmsman accurately maintains the given course, which simplifies dead reckoning and increases its accuracy. In such conditions, the duration of the tacks depends on the tacking angle (the angle between the general course and the yacht's path). If the angles of the right and left tacks are equal, their duration is the same, and the tacking can be symmetrical. If not, dead reckoning and track laying are performed on each particular tacking tack according to instrument data. If there is no lag, it is recommended to evaluate the speed on each tack.

When tacking, it may happen that the helmsman, on the instructions of the yacht captain, does not pay attention to the compass when heading into the wind.

Here, after small but equal intervals of time (15 - 30 minutes), the average QC and the corresponding IC are determined and recorded, according to which the data obtained by lag or speed are stored.

In unstable winds, the helmsman is not given a course, but is given the task of steering along the sail in search of the wind, keeping as close to the general course as possible. Sometimes in such a situation, depending on local signs and the weather forecast, it may be advantageous to deviate from the general course in order to get a full steady wind sooner (for example, an offshore breeze). In all these cases, in the interests of dead reckoning, all turns on the yacht are recorded and on each tack (at the beginning and end of the tack it is obligatory) with a certain frequency (1-2 times per hour, depending on conditions) data on the movement of the vessel (time, heading) are recorded , speed, lag count). These records are processed by averaging the course and speed of each tack, and then plotted on a chart. Practice shows that the accuracy of dead reckoning in such conditions increases with increasing discreteness of observations. Errors in approximating curved sections of swimming to rectilinear ones will be insignificant compared to other errors. DRIFT OF THE SHIP.) is called the drift of a ship from the course line under the combined action of the wind and the waves caused by it. When drifting, a ship moves relative to the water under the combined action of ship engines and wind. The line of its actual movement (OM), called the ship's track during drift, does not coincide with the ship's course (OA). (See Figure 33). When the track line shifts to the right from DP ship (wind blows to port) a a plus sign (+) is assigned, and when moving to the left (the wind blows to the starboard side) - a minus sign (-). Dependence between the track angle taking into account drift ( PUa), IR And a:

PUa = IR + a; IR = PUa - a ; a = PUa - IR

The drift angle can be determined by comparing the actual path of the vessel obtained from observations with IR. When following the coastline, a number of reliable navigational observations are carried out. By connecting the observed points, a line of actual movement of the vessel is obtained, i.e., a line of path during drift PUa(Fig. 34). Angle between the track line and the line drawn on the map IR corresponds to the drift angle. The found drift angle with its sign is taken into account in further calculations. If there is a current in the navigation area, then the resulting drift angle will be the result of the influence on the ship not only of the wind, but also of the current.

ACCOUNTING FOR DRIFT IN COUNTING. If the ship is drifting, then when plotting, the line of the ship's path during drift is plotted on the map. They write on it QC, compass correction and taken into account drift angle a with your sign. The distances traveled along the log are plotted along the path line. Cl. It is believed that when a

A first course line is drawn from the starting point on the map. The IR taken from the card is transferred to the CC, on which it is placed according to the magnetic compass. On the map above the IR line the compass course and its correction are indicated. Distance traveled along the course- counting the log at the point where the vessel is located, Sl- lag count at the starting point, MAKING COUNTING WHEN SWIMMING WITHOUT DRIFT AND CURRENT determined by lag:

If the navigator is not sure of the accuracy of the drift angle, then to control navigation safety, in addition to the drift line, it is recommended to draw a line on the map IR. Both of these lines must be clear in relation to underwater obstacles. Reckoning is carried out only along the track along which the vessel moves.

SEA CURRENTS. Sea currents are the horizontal movements of large masses of water. A flow is characterized by its elements: direction and speed. Current direction CT indicated in degrees according to a circular count or in reference points and set according to the point on the horizon towards which the current is directed. Current speed Vt is measured in knots, and its small speeds are measured in miles per day. According to the nature of the flow, they are classified into constant, the elements of which hardly change from year to year, periodic, the elements of which change according to a certain law, and temporary (random), the elements of which can change sharply. In practice, the navigator most often has to deal with constant and periodic (tidal) currents. Information about the elements of constant and tidal currents is placed in sailing directions, current atlases and on maps. In this case, the average values ​​of flow elements are indicated, which may differ significantly from the actual ones.

The movement of the vessel relative to the ground when sailing in the current is determined by the following factors (Fig. 36). DP Under the influence of ship engines, the ship moves relative to the water in the direction of its , i.e., the line of the true course OA. The speed of the ship relative to the water is the speed Vl Vt shown by the lag. At the same time, together with the entire mass of water, the vessel is carried away relative to the ground in the direction of the flow OD at the speed of the current . As a result, relative to the ground, the ship moves along the resultant OB at a speed called the true speed of the ship V DP. Wherein IR the vessel remains parallel to the line . The line OB along which the ship moves under the combined action of ship engines and the current is called the line of the ship's path on the current. The position of the track line relative to the true meridian is determined by the NOB angle, which is called the course angle on the current PU "" . DP Corner . The line OB along which the ship moves under the combined action of ship engines and the current is called the line of the ship's path on the current. The position of the track line relative to the true meridian is determined by the NOB angle, which is called the course angle on the current), IR, enclosed between the true course line of the vessel OA and the track line OB, is called the drift angle of the current. When the ship drifts to the right of its

(the current is directed to the left side) a "+" sign is assigned, and when drifting to the left - a "-" sign. Dependency between (

And : PU = IR + ; IR = PU - ; = PU - IR QC CALCULATION WHEN SWIMMING WITH THE CURRENT. IR When sailing in a constant current, the ship's path along which it actually moves relative to the ground is drawn on the map. There is an inscription above the path line Cl, compass correction and drift angle with your sign. For auxiliary calculations, a thin line is also drawn IR, transferred in the direction of the flow to the track line (Fig. 37). At the countable points on the track line, a time and lag counting mark is made, and at the corresponding points on the course line - only the lag counting. The points of traverse, opening and hiding of landmarks are marked on the track line (Fig. 38).

CALCULATION WITH JOINT ACCOUNTING OF DRIFT AND CURRENT. Let's consider the case when a ship moves relative to the ground under the combined action of ship engines, wind and current. To carry out dead reckoning, the line of the ship's path during drift and current is laid out on the map and inscribed QC, compass correction and total drift angle

c = a + .

In addition, for auxiliary calculations, a drift track line is also laid on the map, along which the vessel’s navigation along the log is delayed Cl. Each point on the track during drift corresponds to a point on the line of the actual movement of the vessel. These points are connected to each other by the flow vector. Graphically, tasks related to finding the track line on the map during drift and current, true speed . As a result, relative to the ground, the ship moves along the resultant OB at a speed called the true speed of the ship and total drift angle With according to given QC, , i.e., the line of the true course OA. The speed of the ship relative to the water is the speed, a, and flow elements, applying the number place, precalculating time and ol at the moment of arriving at a given point, by finding abeam of a landmark, they decide in the same way as when sailing on a current, but all auxiliary formations are made on the track line when drifting, replacing the line IR.

ESTIMATES OF CUMULATION ACCURACY. As a result of the impact of unaccounted errors, the actual path of the vessel and the distance traveled (sailing) will not correspond to those taken into account when calculating on the map, and the actual position of the vessel will not correspond to the calculated one. To make an approximate judgment about errors in calculations, you can use the following data, which reflect the accumulated generalized experience of navigation and the research conducted. % The duration of the voyage (hours) corresponds to the radial root mean square error, from:

S

Up to 3 hours - 10%; 3-6h - 9%; 6-10h - 8%; 10-14h - 7%; 14-18h - 6%; 18-23h - 5%; 23-25h - 4%; more than 35 hours - 3%.