Graphic notation and its accuracy. Graphical dead reckoning of the ship's path graphical Solution of the inverse problem

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 the maintenance of graphical dead reckoning becomes inaccurate due to large errors in graphical constructions on small-scale marine navigation charts.

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; determine 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. c¢ – departure(miles);

– navigation of a vessel along a rhoxodrome between a point A and dot c¢(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) 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”)

To ensure navigation safety, the navigator must know the position of his vessel at any time, which can be achieved by steering navigation pad. Plotting includes dead reckoning, calculations and charting to determine the ship's position, and maneuvering calculations to avoid other ships.

The navigation pad is divided into two types:

- pre-laying performed before departure to study the upcoming passage using maps, manuals and navigation manuals: it gives a general idea of ​​the transition conditions.

- executive gasket performed from the moment of departure and until its end. In this case, the choice of courses and all factors taken into account are determined by the specific sailing situation.

By dead reckoning is called recording the movement of a vessel on a sea chart. Depending on the sailing conditions, this accounting is carried out using two methods:

-written notation used during ocean voyages, when you have to rely on small-scale maps . Its essence consists in calculating the coordinates of the vessel, which is carried out by the navigator using formulas, followed by plotting the calculated location on the map.

- graphical notation used when sailing near the coast, when at relatively short distances from the course there may be dangerous depths, surface and underwater obstacles, the influence of wind on the ship, creating drift, and currents. In this case, the calculation must be carried out especially carefully and continuously.

The starting point for plotting the ship's path on the map is determined by the captain. The coordinates of the laying start point are recorded in the ship's log. By the time the installation begins, you should turn on the log and determine the compass correction.

A first course line is drawn from the starting point on the map. If navigation is carried out near the coast, countable points should be noted every hour, when sailing in the open sea at the end of the watch, at the beginning and end of turns, when changing speed, when receiving observations. Next to the countable place, in the form of a fraction, record the moment on the ship's clock with an accuracy of 1 minute and the log count with an accuracy of 0.1 mile. To control and clarify the dead reckoning, the ship's place on the voyage is determined by various navigation, radio navigation and astronomical methods. The resulting observation points put on the map. Upon receipt of an observed place, further navigation is carried out from the observed point, showing on the map the magnitude and direction of the vessel’s deviation from the dead reckoning. The curved line connecting the observed and countable points is called residual.

Graphical dead reckoning without taking into account 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 map is transferred to the CC (GKK), on which it is placed according to the magnetic (gyro) compass. On the map above the IR line the compass course and its correction are indicated. Distance traveled along the course S determined by lag:

S = Cl (OL 2 - OL 1);

(Where OL 2- counting the log at the point where the vessel is located, OL 1- lag count at the starting point, Cl- lag coefficient).

In the cases indicated below, the ship’s reckonable position is marked on the IR line, i.e., the position calculated based on the course and voyage. 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 position, 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 miles (OL).

When conducting laying, two types of tasks are possible:

Direct task. Known QC, v l (v rev), reference point (φ 1, λ 1, T 1, OL 1). Unknown IR, end point of reckoning (φ 2, λ 2, T 2, OL 2).
Solution:

or S = ROL k l

Take the countable coordinates φ 2, λ 2 and determine the time of arrival at this point T 2 = T 1 + S/v, note the readings of the lag OL 2.

Inverse problem. Known are IR, v l (v vol), φ 1, λ 1, T 1, ol 1.

Unknown KK, φ 2, λ 2, T 2, OL 2.
Solution:

• Draw an IR line from the starting point;
• Calculate KK = IR - ΔK and ask it to the helmsman;
• Calculate S l = v l t(if the counting point is calculated in advance), or S = ROL k l(if the countable point is calculated by the moment passed) and put it on the IR line;
• Take φ 2, λ 2 and determine the time of arrival at this point T 2 = T 1 + S/v, and at this moment take readings of the lag OL 2.

Graphic dead reckoning of the ship's path

The essence of graphical notation

Safety of navigation in terms of navigation is ensured by the correct choice of route between points and following the chosen path.

Choosing a route is one of the most important tasks in navigation, the decision of which is based on a thorough analysis of the entire situation during the transition.

The selected route of the vessel is plotted on maps - preliminary plotting is performed. Preliminary laying is carried out before the vessel leaves for the voyage by the captain. It is the result of work on choosing the safe and most profitable route for the vessel. To ensure navigational safety of navigation, places of course changes are marked on the map, for which turning points are chosen so that the moments of the vessel's arrival at these points can be quickly determined, for example, the moments of arrival on the beam, on the target, etc.

They outline the distance at which capes, lighthouses, and other landmarks will pass.

The declination is given to the year of voyage and its value is written in pencil along the entire voyage of the ship.

The true course values ​​are written above the track lines.

The distance in miles along each course is taken from the map and the number of miles of the entire passage is calculated.

On the route, the limits of the visibility range of beacons and lights for the height of the bridge are marked, and the most appropriate ways of determining the position of the vessel in individual areas are outlined. Time is kept from the operating time, counting the departure time of the vessel at 00 hours 00 minutes.

Before performing preliminary laying, the card is lifted (see § 45).

Calculations made during the preliminary laying process are approximate and must be adjusted during navigation.

Preliminary routing is carried out, as a rule, on route maps.

The second most important task– ensuring the movement of the vessel along the chosen path, for this purpose they continuously record the movement of the vessel – dead reckoning of the vessel’s path.

The main elements of dead reckoning are heading (by compass) and distance traveled (by log).

The graphical dead reckoning of the vessel is expressed in the conduct executive navigation pad. Its beginning coincides with the ship's departure from the pier (anchoring); when leaving the port, the navigator pays special attention to visual orientation in the surrounding environment, based on knowledge of the harbor or roadstead and the correct use of the navigation system, aids to navigation and natural landmarks.

Once in clear water, the vessel’s position is precisely determined and the laying is carried out from the obtained point.

Before arriving at this point, turn on the lag, near the starting point the time is written as a fraction in the numerator, and the lag count in the denominator.

An IR line is laid from the starting point, on which countable points are marked every hour or four hours, i.e. places obtained without measuring the navigation parameters of external landmarks.

Countable points are marked on the track line with a short transverse line, and the thickness of the track line itself should be approximately equal to the thickness of the meridians and parallels.

All laying and calculations are performed with a soft, finely sharpened pencil.

Locations of the vessel according to observations, i.e. Based on the results of measuring navigation parameters, external landmarks are plotted as often as possible and necessarily, if possible, when changing course.

Observed places are indicated by symbols in accordance with RShS-89.

The discrepancy between the observed point and the countable point is called a discrepancy, denoted by the letter “C”. Its direction and magnitude are recorded in the ship's log (С=225º -1.5’)

The direction of the discrepancy is calculated from the calculated point to the observed one.

The laying process ends when the vessel enters the port waters or at the point where maneuvers begin when the vessel is anchored.

Thus, a routing is a set of measurements, calculations and graphical constructions associated with choosing a ship’s path, taking into account its movement and determining the ship’s position.

Maintaining graphical notation and solution

problems in the absence of drift and flow

The absence of ship drift and drift simplifies both graphical construction on the map and calculations when solving various problems.

Firstly, the ship's path coincides with the direction of its DP, i.e. with IR line.

Secondly, the distance traveled by the ship relative to the water i.e. according to the log readings, corrected by its error, it is at the same time the actual distance traveled relative to the ground (S L = S I).

Solution of the direct problem

(Course correction tasks)

Solution of the inverse problem

(Tasks for course translation)

Solving specific problems

I.Plotting the ship's location on the map.

Given: T 1, OL 1, T 2, OL 2. Find: S L.

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

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 heading.

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)

Taking circulation into account is of great importance when sailing in cramped 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.

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

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:

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.

φ2 = φ1 + general РШ

And the general formula

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 plotted on navigation general charts 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.

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.

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) on a 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?