Types of analytical (written) notation. Graphic dead reckoning of a vessel graphic dead reckoning

Taking into account the movement of a vessel in order to determine its current coordinates or plot a place on a map is called dead reckoningways vessel.

Through simple calculations or graphical constructions, dead reckoning should at any time display the ship’s position relative to the surrounding environment with an accuracy that ensures navigational safety, i.e. it must be continuous, visible and accurate.

There are two types of dead reckoning: graphic, in which it is performed in the form of graphical constructions on sea navigation charts, and analytical, or written, in which the coordinates of the ship are calculated using formulas.

Both types of calculation can be performed automatically and manually. In navigation, graphical reckoning has become most widespread, as it meets all the requirements, especially in terms of clarity.

Automatic graphical calculation is carried out using special devices - autocalculators.

Graphic dead reckoning is performed manually by the ship's navigator using a spacer tool. In this case, it is necessary to solve direct and inverse problems.

Straighttask comes down to taking into account the already completed movement of the vessel, when the helmsman is given a course and the log readings at the initial and given points at the time of calculation are known.

In this case, formulas (26), (34) are solved for calculating IR.

If there is no drift from the wind and no drift by the current, then by drawing a line of the true course from the starting point, we will have on the map the direction of the actual movement of the vessel. This is true if the correction of the heading indicator is known without error, and the yaw of the helmsman is insignificant and symmetrical relative to the specified CV.

The course line on the map is drawn with a simple pencil of softness “TM”, with a thickness equal to the thickness of the meridians and parallels. Above it the value of the compass heading and compass correction is indicated (Fig. 32).

The found distance is laid off from the starting point in the direction of the true course. The point thus obtained using dead reckoning is called reckonable and is indicated on the map in the form of a 5 mm long stroke perpendicular and symmetrical to the line of movement of the vessel. The point is signed as a fraction: in the numerator the ship's time is hours and minutes, in the denominator is the corresponding log reading value with an accuracy of 0.1. The fraction line is drawn horizontally along the ruler.

If there is current and wind in the navigation area, then appropriate calculations and constructions are performed to take them into account.

Often the skipper has to decide reversetask. It occurs every time the direction of the vessel’s upcoming movement is indicated on the map or calculations are made of arrival at a given point.

In this case, from the starting point on the map, the line of the vessel’s upcoming voyage is drawn and its direction is recorded. In the absence of drift from wind and current, the resulting direction is the true heading of the vessel. Based on this, the compass course for the helmsman is calculated using formulas (27) and (35).

where T 1, ol 2 - time and lag count at the starting point;

T 2, ol 2 - time and countdown of the lag of arrival at a given point.

Let's consider what is the accuracy of the place to be reckoned in the absence of external factors (wind and current).

Suppose that the ship needs to move on the same course from a point A to a point distant from it at a distance S IN(Fig. 33).

Due to the fact that the compass correction is known to the navigator with some error ± m 0 Δk , then the ship, having passed the distance S, depending on the sign of the error, it may end up either at the point IN", either at the point IN" .

Thus, the error in the ship's position due to an error in the compass correction will be depicted as an arc BB"= BB", the value of which is easily determined from the expression

or for approximate calculations

Error in accounting for the distance traveled by the vessel ΔS due to an error in the lag correction ±t Δl, expressed as a percentage, or the lag coefficient ±m kl, expressed in fractions TOl, can be determined by the formulas

Rice. 33. Area of ​​probable location - Fig. 34. Elliptic error

location of the ship at the ship's place

With a positive value ΔS the ship, taking into account the error in its course, will end up on an arc D"D", if negative - on the arc S "S".

From this we can conclude that with the simultaneous effect of errors in the readings of the compass and log, the ship’s position will be within the so-called figures errorsC"D"D"C".

Replacing the resulting error figure with a circle with a radius MWith, we get

(61)

Radius circle MWith usually called all arounderrors, and the radius MWith - circular (radial)mistakeReckoning.

Due to the unequal influence on the calculation accuracy of errors in the ship's heading and in the distance traveled, the probable location of the ship is better characterized by an ellipse with semi-axes (Fig. 34):

The significance of errors in instrument corrections is unknown to the navigator, since they are random. For calculations, their values ​​are taken on the basis of practical sailing experience.
Analysis of formula (61) shows that the error in knowing the vessel’s position increases in proportion to the distance traveled. For this reason, the need periodically arises to eliminate the accumulated counting error with the help of observations (observed places), i.e. determining the vessel's position by visual, radio and astronomical methods. The discrepancy between the countable and observed places at the same moment is called discrepancy. The discrepancy is expressed by the direction from the countable point to the observed one and the distance between them in miles. It is written as follows: C = 305° - 2.8 miles. The residual sign on the map is a wavy line connecting both points (see Fig. 32). Graphic image on sea ​​map the route traveled by the ship, performed automatically or manually based on measurements and calculations, is called a navigation plot.
Navigation plotting of a vessel's route, performed in advance on the basis of the intended route of the vessel that meets the requirements of safe navigation, assigned tasks and economic feasibility, is called preliminary plotting.
Navigation plotting is carried out with the vessel leaving continuously until it arrives at the port or anchors. The starting point for laying is taken to be the passage of the port's entrance piers, boom gates, entrance buoy or the observation area of ​​the vessel.
During the passage, the navigator’s task is to ensure that the actual movement of the vessel coincides as closely as possible with the previously planned route. This will make it possible to use calculations made during the preliminary laying process and, therefore, will facilitate the work of the navigator at sea.

Dead reckoning of a ship (reckoning) is the calculation of the current coordinates of a ship from known coordinates in time, course and speed, taking into account the influence of wind and current on the ship. Graphic dead reckoning is performed directly on a marine navigation chart using navigator's tools (parallel ruler, protractor and measuring compass) and is called graphical dead reckoning or navigation plot. A navigation plot is a graphic representation on a sea chart of the route traveled by a ship (or part of it), made automatically or manually based on measurements and calculations. If calculation is performed using formulas and tables, it is called analytical (written). The laying can be preliminary and executive. Preliminary routing is the navigational routing of a vessel's route, carried out in advance, based on the intended route that meets the requirements of navigation, assigned tasks and economic feasibility. When choosing a vessel's route, two conditions are followed:

1. navigation safety,

2. cost-effectiveness of the transition (as a rule, this is the least time required).

The selected route is shown on the navigation charts. general cards indicating courses, duration of travel on the course and turning points or landmarks at turning points. The further task of the navigator comes down to ensuring the movement of the vessel along the intended path and monitoring this movement (executive routing). The navigation route begins from the moment the vessel leaves the port waters and ends when the vessel arrives at the port (from berth to berth). The main method of continuously recording the position of the vessel is graphical dead reckoning. It consists of systematically plotting the position of a vessel on a map based on data on its movement and distance traveled, as well as information on currents and drift. The starting point must be known. The position of the ship, the coordinates of which are obtained by dead reckoning, are called dead reckoning.

Control of the laying is carried out by measuring various navigation parameters (bearings, distances, differences in distances and heights of luminaries) and obtaining the position of the vessel by observation along two, three or more position lines.

Geometric quantities measured directly or obtained indirectly to determine the ship’s position at sea using coastal and celestial bodies are called navigation parameters.

The geometric location of the points corresponding to a constant value of the value measured for the observation (navigation parameter) is called an isoline. In general, an isoline is a curved line. For observation, it is necessary to have only small segments of isolines at the point of their intersection at an angle to each other. Segments of isolines can be replaced without much error by segments of straight lines tangent to the isoline or their secants. A tangent or secant to an isoline is called position line. Isolines can be bearing, isostage (circle), isogon (circle), hyperbola.

All graphic work performed on the map consists of individual task elements. Such tasks include taking the ship’s coordinates from the map or plotting the ship’s location on the map, calculating and plotting courses and bearings, and measuring distances between certain points. When carrying out laying, two types of problems are solved: direct and reverse.

The first (direct) task involves only taking into account the movement of the vessel when the course is given to the helmsman.

IR = KK + Dk.

The true course is calculated and the course line is drawn on the map as a straight line from the starting point. In the absence of drift from current and wind (drift), the true course line will coincide with the heading angle, therefore, the ship will move along the course plotted on the map. On the map, at the point taken as the starting point for counting, the time is indicated with an accuracy of 1 minute and the log count with an accuracy of 0.1 miles (). Further plotting of the position of the vessel at any point in time is carried out according to the distance traveled by the vessel along the log from the starting point. The position of the vessel on the plotted course line is noted every hour when sailing near the coast and every watch when sailing in the open sea, as well as with any change in course or speed. Each counting point is indicated by a line about 5 mm long, perpendicular to the previous course. Each observed point is marked with a special sign assigned to this type of observation.

In navigation practice, the inverse problem occurs much more often and consists in the fact that the ship needs to follow given IC. In this case, the helmsman is given a pre-calculated CC based on the laid IC.

KK = IR - Dk.

AND OL 2 = OL 1 + ROL

The time of arrival at the design point is calculated:

T 2 = T 1 + DT = T 2 +

The ship's compass heading is written along the course line, with the compass correction in parentheses.

04°00E 04°20¢

Rice. 1.24

Direct problem Inverse problem

CC – set IR – removed from card

+(±)d - from the deviation table according to CC -(±)d – from the map

MK – magnetic course MK – magnetic course

+(±)d – declination from the map -(±)d – from the table. deviations according to MK

In the direct task, the selected declination and deviation with their own sign are added to the CC and MK, and in the inverse problem, they are subtracted from the IC and MK.

Taking into account drift and constant flow during laying.

Vessel drift is the displacement of a moving vessel from its true course line under the influence of wind. The ship's drift is caused by the apparent wind. The direction of the wind is the direction from which it blows (they say: the wind blows into the compass). If the wind blows to the left side of the ship, then the ship is said to be sailing on a port tack (l/g or l/b), relative to the wind.

If the wind is blowing to starboard, then the ship is sailing on a starboard tack (pr/g or pr/b). Direction of the resultant wind pressure forces ( R) in the general case does not coincide with the direction of the apparent wind speed vector (W).

The magnitude of the drift angle depends on many factors: draft, size and shape of the surface and underwater parts of the ship's hull, heading angle and apparent wind speed, and ship speed. To account for drift during laying, it is necessary to know the drift angle. There are a number of ways to determine it, but all of them are not accurate, which sometimes leads to a significant deviation from the path outlined on the map.

Let's break down this force ( R) into two components: longitudinal (P 1) and transverse (P 2).

(+), and in starboard tack wind the sign at drift angle a will be (-).

PU a =- IR + a. IR = PU a - a. (1.41)

When taking into account drift, only the line of the drift track angle is drawn on the map. Since the log takes into account the effect of wind on the speed of the vessel (P 1), the distance can also be taken into account by plotting along the track (Sl = ROL Cl).

R Rice. 1.25

Calculations for direct and inverse problems are longer compared to calculations without the influence of wind.

The transverse component P 2 causes the ship to drift. Therefore, when there is wind, the ship moves relative to the water not along the center plane, but at a certain angle to it (a), called the drift angle. The line AB along which the ship moves is called the drift track line, and the angle PU a, which it makes with the true meridian, is called the drift track angle. When there is wind on the left tack, the drift angle a is assigned a (+) plus sign, and when there is wind on the starboard tack – a (-) minus sign.

C

The forward movement of a water mass in the seas and oceans is called a current. The elements of flow are its speed and direction. The direction of the current is determined by the mnemonic rule: “the current comes from the compass.” The direction of the current is shown in degrees, and sometimes in points, speed is expressed in knots.

Under the action of the propulsion stop, the vessel receives movement relative to the water in the direction of the center plane (Vl).

If water moves relative to the Earth, then the speed of the ship relative to the Earth is determined by the geometric sum of the velocities:

And the ship will move in the direction of the vector, if the speed of the ship and the current are constant in magnitude and direction, the total speed will also be constant and the ship will move in straight line AC.

Rice. 1.27

The angle PU between the northern part of the true meridian and the direction of movement of the vessel is called track angle(by), and the path line AC will be the path line along the current. The angle b between the true heading (IR) and heading angle (PU) lines is called drift angle from the current.

The speed V will be the true speed of the vessel (relative to the bottom).

PU = IR + (±)b IR = PU – (±)b. (1.42)

The sign of b depends on the drift direction. If the current is directed to the left side, then the sign of b is (+), and if it is directed to the right side, then the sign of b is (-).

Taking into account the flow comes down to solving triangles (velocity and track). First, the vectors of ship speeds and currents are graphically added, and then the path triangle ABC is solved.

There are direct and inverse problems of graphically solving the velocity triangle. Direct task .

In the direct problem, given IR, Vl, Kt and Vt, it is necessary to calculate the angle b, PU and V (Fig. 1.27). To obtain the route line PU from point A, draw a line IR and on it from point A we plot a segment equal to the vector of the vessel’s speed along the log (V L) in conventional scale. Usually the number of miles on a map scale covered by a ship in an hour or half an hour is taken. From the end of the ship's speed vector (V L) we draw the current speed vector (V T) on the same scale. By connecting point A with the end of the current velocity vector (Vt), we obtain

vessel's track (PU). We take the direction of this path from the map to compare with the true one.

course (IR) and obtaining the drift angle from the current (b).

b = PU – IR. (1.43)

To obtain a countable point for any time period of navigation along a heading angle, it is necessary to plot the distance traveled along the log along the true course (IC) line (Sl = ROL Kl). We move the point obtained on the IR along the line of the direction of the current to the line of the track angle (PU) (points B and C). Inscriptions on the map are made above or below the track line (PU) and parallel to it. The order of recording is as follows: write the GKK next to it in parentheses, its correction, and then the value of drift from the flow with its sign (GKK 69° (-2°) b = +6°).

+(±)d = from the deviation table

+(±)d = from card

+(±)b = from construction

Inverse problem

In this problem, it is necessary to calculate the drift angle by the current (b) and IR (Fig. 1.28) for a given PU b, Vl, Kt and Vt.

The problem is solved as follows:

Let the PU (AK) line be drawn on the map. From point A we plot the current velocity vector V T , expressed in the number of miles. From the end of the current velocity vector V T with a compass solution equal to the vessel speed V L, we make a notch on the vessel’s line PU (point C). By connecting point C to the end of the current velocity vector, we transfer it in parallel to the starting point A, drawing a line of the true course AD.

Finding a countable point with an already constructed velocity triangle is done in the same way as in the direct problem. Using the distance Sl, we find point B on the IR line, and then through point B we draw a line parallel to the current velocity vector Vt. The intersection of this line with the PU line will be the ship’s countable position (point C).

In addition to graphical accounting of the current, there is also an analytical one, which is used in the automation of navigation.

T Fig.1.28

PU b = direction taken from the map

-(±)b = obtained by calculation (PU - IR)

-(±)d = from card

-(±)d = from the MK deviation table

Joint accounting of current drift

With the simultaneous action of wind and current, the vessel will be subject to both drift and drift. The angle by which the track line deviates from the true course line (IC) is called total drift angle (C).

C = PU – IR (1.44)

The sign of the total drift angle (C) is obtained from the given formula: if PU >IR, then the sign will be plus (+), if PU< ИК, то знак будет минус (-). Если же известны величины угла дрейфа (a) и угла сноса течением (b), то знак суммарного сноса определится из алгебраического их сложения. С= a + b (1.45)

In the presence of wind and current, the direct and inverse problems are also solved, as in the presence of only current. When solving a direct problem, the drift is first taken into account and the path line PUa is plotted on the map. Then the current is taken into account by constructing a triangle of speeds, and the speed of the vessel is plotted along the line of the drift angle (PUa), and not along the IR line.

In the inverse problem, for a given PU, a triangle of velocities is solved, and from the construction they obtain not the direction of the IR, but the direction of the PUa. Then the direction of the drift path (PUa) is taken and the true course is found: IR = PUa - a, and also

b = PU - PUa and C = a + b.

On the map below (or above) the track angle line, a record is made of the compass course, its correction and the total drift angle (GKK (-2) С= -12)

In general, the solution to the problem looks like this:

Direct problem Inverse problem

+(±)d = from the deviation table - (±)b = from construction

+(±)d = from card-(±)a = accepted

+(±)a = accepted for counting - (±) d = from map

+(±)b =-(±) d = from table dv.

Example 1. At latitude j = 53°00¢ N With the bottom follows IR = 75.0° at a speed of 12 knots. A current of 335° is taken into account - 1.1 knots. Determine the angle of drift of the vessel by the current b.

Solution: From the starting point from which the IR is laid = 75.0°. We set aside the distance traveled by the ship in one hour (vessel speed) S L.

From the obtained point on the IR we plot in the direction of the current the drift of the vessel by the current in one hour (current speed) S T = 1.1 miles.

We connect the starting point with the one obtained on the flow vector and, using a parallel ruler and a protractor, take the reading PU = 69.0°.

- IR = 75.0°

Example 2. At latitude j = 53°00¢ N With the fishing rod follows at a speed along the log of 12 knots. On the map, PU = 52.8° is laid out from the starting point. The vessel takes into account a current of 143° - 1.0 knot. Determine IC and b.

Solution: From the starting point we draw a line of the direction of the current and on it we plot a segment equal to the current speed V T = 1.0 knot.

From the resulting point with a radius equal to the ship’s speed of 12 knots, we make a notch on the PU line and connect both points with a straight line.

Using the parallel ruler of the protractor, we take the value IR = 48.8°

We calculate the drift angle b.

- IR = 48.0°

Example 3. Given: PU = 356.6°, b = - 6.2°, a = + 4.0°, D GKK = -1.2°. Determine the GKK.

Solution: PU = 356.6

- b = - 6.2

- a = +4.0

- D GKK = -1.2

Solution: From NSSR -86 (table No. 3) we select m K = 0.7°, m DL% = 0.5%, then

b = 0.0174 * 0.7 * 100 = 1.218

a = 0.01 * 0.5 * 100 = 0.5

M = Öb 2 + a 2 = Ö1.48 + 0.25 = 1.3 miles.

Control questions

1. What sign (+) or (-) is assigned to the starboard drift angle?

4. What is the approximate dependence of the graphical dead reckoning SCP on the distance traveled?

5. Where do we begin to solve the inverse navigation problem when taking into account the current?

CHAPTER 17. ANALYTICAL (WRITTEN) CALCULUS

VESSEL COORDINATES

The essence and basic formulas of analytical

(written) reckoning

In addition to graphical dead reckoning of a ship's path, its voyage can be recorded using analytical (written) dead reckoning.

Analytical reckoning – calculating the geographic coordinates of a vessel based on its course and voyage(based on differences in latitudes and longitudes made by the ship) using formulas manually or using computers.

Analytical calculation is carried out according to the formulas and is used when sailing a vessel far from the coast on ocean crossings, when maintaining graphical dead reckoning becomes inaccurate due to large errors in graphical constructions on sea navigation maps small scale.

Most often, analytical notation is used:

1. with the continuous generation of current numerical coordinates of the ship’s position entered into the ship’s automation systems. The problem is solved using automatic computers (or computers);
2. when periodically calculating the reckonable coordinates of the vessel’s position in cases where it is necessary to eliminate dead reckoning errors due to the inaccuracy of graphical constructions associated with plotting the vessel’s path on a small-scale map. The problem is solved manually or using computers(to control the accuracy of graphical constructions on the map; determining the location of the ship based on observations of luminaries at different times).

Analytical calculation with the help of automatic calculating devices is carried out according to formulas taking into account the compression of the Earth. In the simplest systems, formulas are solved without taking into account the compression of the Earth.

Let us obtain the basic formulas for analytical notation (Fig. 17.1).

Ship from point A (j 1 l 1), following a constant course ( TO) according to rhoxodrome, came to the point IN (j 2 l 2).

If the latitude differences made by the ship are known ( RSH) and longitude difference ( RD) then the coordinates of the point IN (j 2 l 2) can be easily obtained from the relations:

Rice. 17.1. Analytical (written) dead reckoning of a ship's path

The value of the latitude difference ( RSH) and longitude differences ( RD) can be calculated using known elements of motion: TO® the ship's heading and S® navigation of the vessel on this course.

Considering the Earth to be a sphere (ball) from an elementary small triangle Аа¢в¢:

® latitude increment;

® increment of departure;

® distance increment,

where is the difference in latitude (miles);

– the distance between the meridians along the parallel from the point. a¢ until t. ¢ – departure(miles);

– navigation of a vessel along a rhoxodrome between a point A and dot ¢(miles).

If D Аа¢в¢ take it for flat, we can write differential equations:

As a result of integrating the values ​​and at K = const , we get:

that is . (17.4)

To calculate the longitude difference value - RD, we use the relationship between the length of the arc of the equator and the parallel:

Multiply the numerator () and denominator ( cos j ) on , then

since from D Аа¢в¢

Solving this equation leads to the well-known integral:

Then . (17.5)

To derive a direct connection between the departure ( OTS) and the difference in longitude ( RD), we use the theorem on the mean value of the integral, which gives:

Where jn – intermediate value of latitude in the interval between j 1 And j 2.

Then for the difference in longitude – RD you can write

Equating both values ​​of the difference in longitude ( RD), obtained using formulas (17.5) and (17.6), we obtain the value of the intermediate latitude jn:

where . (17.8)

Substituting the value сos j n(formula 17.8) into formula (17.6) for the difference in longitude ( RD) and taking into account that

we finally get:

where is the departure ( OTS) and latitude difference ( RSH) in miles.

Thus the departure ( OTS) represents the length of the parallel (in miles) between the meridians of the points A And IN, the latitude of which (parallels) is determined by the relation

In practice, when maintaining analytical records over short distances, it can be assumed that in the range from j 1 before j 2 meaning cos j changes linearly, then

and an approximate formula for calculating the difference in longitude - RD will take the form:

that is, the difference in longitude ( RD) is equal to departure ( OTS), divided by the cosine of the mean latitude ().

Using formulas (17.3) and (17.4) we compiled table 24 “MT-75” (p. 260¸272) and table 2.19 A“MT-2000” (p. 282¸294) “Latitude difference and departure.” In these swimming tables S(from 0 to 100 miles) and course (in 1°) you can get ready-made latitude difference values ​​( RSH) and departure ( OTS) , the values ​​of which are given in the table to hundredths of a mile and therefore can be used for navigation ( S) 10 and 100 times larger (or smaller) ® by moving a comma ® see table. 17.8.

Example: 1) S= 450 miles, TO= 37°, RSH= 359.4 miles to N And OTS= 270.8 miles to E;

2) TO= 230°, S= 1860 miles, RSH= 1195.6¢k S And OTS= 1424.8¢k W(see Table 17.1).

The MT-75 also contains special table 25 A“Difference of longitudes” (p. 273¸278) compiled according to formula (17.13).

Similar table 2.20 - see “MT-2000” (p. 296¸301).

Latitude difference and departure

(p. 271 “MT-75” or p. 293 “MT-2000”)

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 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 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 to the IR 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 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