Magnetic compass correction (MC). Astronomical definition of compass correction See what “Magnetic compass correction” is in other dictionaries

It is generally accepted that magnetic field lines emerge from the south magnetic pole and converge at the north, forming closed curves. The vertical plane passing through such a magnetic needle is called plane of the magnetic meridian.

The angle by which the magnetic meridian is deviated from the true meridian is called magnetic declination, or compass declination.

Magnetic declination, calculation for a year of sailing. MP, MK, WMD.

Magnetic declination- W,E change is multiplied by the difference between years, taking into account the sign.

Magnetic course - an angle in the plane of the true horizon, measured from the northern part of the magnetic meridian clockwise to the bow of the ship's center plane;

Magnetic bearing– angle in the plane of the true horizon, measured from the northern part of the magnetic meridian clockwise to the direction to the landmark.

Reverse magnetic bearing– an angle that differs from the MP by 180.

Ship magnetism and its influence on magnetic compass readings. Compass meridian Deviation of the magnetic compass. Compass meridian. Magnetic compass deviation. Deviation table. KK, KP, OKP. Relationship between compass and magnetic heading.

The steel structure of the vessel and its hull acquire magnetic properties from the moment of construction and are preserved for years. The compass is influenced by the magnetic forces of hard and magnetically soft iron, and their effects are different. In addition, the compass is affected by forces arising from the magnetic field of operating ship units.

The angle in the plane of the true horizon of the observer between the magnetic and compass meridians is called the deviation of the magnetic compass; this angle is measured from the northern part and the magnetic meridian to Ost or to W from 0 to 180. Based on the nature of their occurrence, semicircular, quarter and roll deviations are distinguished.
Semicircular - created by magnetically hard iron, quarter - soft, roll occurs during rolling. Compass meridian is an imaginary line of intersection of the observer’s true horizon plane with the compass meridian plane passing through a given point on the ship.

Compass heading is the angle at the center of the compass, measured from the north part of the compass meridian to the direction of the bow of the ship's centreline, clockwise from 0 to 360. Compass bearing is the angle at the center of the compass, measured from the north part of the compass meridian to the direction towards the object from 0 to 360 360.
Reverse compass bearing is an angle different from the CP by 180. To ensure reliable operation of the compass, the deviation is eliminated. The principle of destruction is to compensate for the magnetic field of the ship near the compass (magnets - destroyers and soft iron bars - are installed near the compass). It is impossible to completely destroy it, therefore, after carrying out the work, the residual deviation is determined and a table of its values is compiled.

The needle of a magnetic compass always points north. This feature of the magnetic needle was noticed back in the 13th century and they began to use a compass for orientation, primarily at sea. The device is extremely simple and its use seems no more difficult. However, if you draw a straight line on the map from the point of departure to the destination, and without deviating a single degree follow the plotted course, using a magnetic compass as a course indicator, then you are unlikely to be lucky enough to end up exactly at the planned location, especially if the distance between the points is sufficient big.
To deviate your course ( compass course) from the course that you drew on the map (it is called true course), two phenomena influence:

Distortion of compass readings - magnetic deviation
Discrepancy between the magnetic pole and the true pole - magnetic declination

To calculate the compass course according to the true one or vice versa, you need to substitute the magnetic declination values for a given area, as well as the deviation values for your compass, into the appropriate fields of the calculator. The default values calculate the compass heading from Cadiz (Spain) to Cape St. Vincent (Portugal). To make the calculation, I first determined the true course using the calculator. Track angle and the distance between two points along the loxodrome (rumba line). , where I substituted the coordinates of points from Google Maps. The magnetic declination value was obtained from a marine chart of the Western Mediterranean Sea.
You can find detailed explanations below.

Compass Magnetic True

Magnetic declination changes over time, here you should indicate the year for which the magnetic declination was determined

The amount by which magnetic declination changes each year

Update...

Date for which the calculation is carried out

Compass direction

Magnetic direction

True direction

Magnetic deviation

Those who read Jules Verne remember where the 15-year-old captain took the ship after Negoro placed an ax under the compass binnacle. On the ship, even without an ax in the binnacle, there are plenty of other objects that can influence the magnetic compass. To eliminate this effect, deviation tables are calculated for each ship's compass, showing the deviation of the compass readings for various compass courses. Over time, deviation may change due to the installation of new equipment or magnetization of old iron parts, so the tables are regularly updated. Using the value of the deviation table, you can bring the compass course to the course measured from the magnetic meridian, i.e. magnetic course. To do this, the deviation value for a given compass course is added to the compass course if the deviation is to the east (E) or subtracted if it is to the west (W).

Magnetic declination

Magnetic declination does not depend on the ship's equipment, but depends on its location and, like deviation, changes over time, but more predictably. The magnetic declination value is indicated on the map, with the obligatory indication of the year of measurement and the average annual change. To go to the true course, we first get the magnetic course, then add the value of the magnetic declination to the east (E) or subtract the one to the west (W), then the average annual change in the magnetic declination is taken into account in the same way (adding or subtracting multiplied by the number of years that have passed since moment of declination fixation).

How to remember how to correct or translate rumbas

The process of transition from compass courses to true ones is called correction of rhumbs, the reverse process from true to compass - translation of rhumbs.
In the English-language literature on navigation, there is a simple rule that makes it easy to remember how to move from one type of direction to another; for this you need to remember one simple word: CadET.
It deciphers like this: C(ompass) - to the compass direction ad(d) - add E(asterly error) - correction to the east T(rue) - we get the true direction. The reverse transformation is performed in a similar way, only instead of adding the eastern corrections, we subtract them.

Sources:
V. S. Mikhailov, V. G. Kudryavtsev, V. S. Davydov Navigation and pilotage.
Tim Bartlett An Introduction to Navigation. R.Y.A.

Calculation of true directions using known compass directions is called correctiondirectionny(rumbas). Correcting the bearings is necessary to plot a course or bearing line on the map. By selecting b from the table according to the known CC, you can first find the magnetic directions using dependence (15), and then the true ones using relation (13). Substituting (15) into (13), we obtain formulas for correcting the directions

(23)

Calculation of compass directions using known true ones is called translationdirectionny(rumbas). Translation of bearings is necessary, for example, to determine the course of a ship using a compass in order to move from one point to another. First, using (14), the magnetic course is calculated

MK=IR - d,

and then using (16) they find the compass heading

The deviation is selected from the table according to the magnetic course, taking into account that the MK and KK differ by a small amount. In cases where the deviation exceeds 4° and the table interval is 1°, it is advisable to make a second approximation. To do this, after calculating the CC, they again enter the deviation table with the obtained compass-course value, find b and calculate the compass course a second time.

Substituting (14) into (16), we obtain the dependences of the direct translation of the rhumbs

(24)

The algebraic sum of declination and deviation geometrically represents (Fig. 15) the angle in the horizon plane between the northern part of the true and compass meridians, called the compass correction (ΔMC),

ΔMK = d +δ. (25)

If the northern part of the compass meridian is deviated to E from the true one, the compass correction is positive, if to W it is negative.

Taking into account dependence (25) from (23) and (24), we obtain formulas for correcting and converting the bearings with a known compass correction:

(26)

(27)

All problems of correction and translation of rhumbs can be checked graphically (Fig. 16).

To do this, for example, first build the true meridian, then using known values (ΔMK, d or IR) draw other lines (compass, magnetic meridian or heading) and determine unknown quantities. The location of the meridians relative to each other is determined by logical reasoning, taking into account the sign and magnitude of δ, d or ΔMK. Graphic control is carried out in order to eliminate errors in signs.

Correction and translation of bearings are most often carried out by calculating the compass correction using formulas (26) and (27), for which the declination value is taken from the map, and the deviation is selected from the table.

The reliability of the compass correction determines the accuracy of determining the true directions, and therefore the accuracy of the vessel's navigation. This implies the need for systematic control of the amendment. The compass correction is determined by comparing true and compass directions. For this purpose, it is necessary to know the value of the true course or bearing and at the same time measure the corresponding compass direction. From (26) we have that

(28)

To determine ΔMK, methods similar to methods for determining deviation can be used: using alignment bearings, the true direction of which is given on the map or can be taken from the map; by the bearing of a distant object, when the location of the ship is known with high accuracy, and the object is plotted on the map, by the bearings of celestial bodies. On some river vessels, where it is not possible to measure bearing from a magnetic compass, the correction can be determined by comparing the IR and CC when sailing along targets whose direction is known. To do this, being on the alignment line, bring the vessel with its bow exactly to the alignment marks and note the compass course.

The magnetic compass correction can also be obtained by comparison with the gyrocompass, if its correction is known:

ΔMK = GKK - KK + ΔGK. (29)

Whenever determining the magnetic compass correction, the deviation should be calculated using the formula

δ = ΔMK - d (30)

to control the reliability of the table.

Compass correction. Calculation and accounting of compass corrections. Determination and correction of rhumbs.

The rhumb system for counting directions has come to our century from the era of the sailing fleet. In it, the horizon is divided into 32 points, which have corresponding numbers and names. One rhumb is equal to 11.25 degrees. The directions N, S, E, and W are called the main directions, NE, SE, SW, NW are the quarter directions, and the remaining 24 are the intermediate directions. Even intermediate bearings are named from the nearest major and quartering bearings, for example, NNW, WSW, ESE, etc. The names of odd intermediate bearings include the Dutch prefix “ten”, which means “to”, for example, NtE is read as “north-shadow-east” and means that the direction N is “shifted” by one point to E, etc.

The rhumb counting system is used to indicate the directions of wind, current and waves - this is the traditional counting system.

Magnetic declination d– this is the angle in the plane of the true horizon between the geographic (true) and magnetic meridians.

For 1985, d = 1 o W, annual change Dd = 0.2 o, declination in 2000 - ?

Dt = 2000-1985 = 15 years

d 2000 = d + DdDt = +2 o E
Two different compasses are usually installed on a ship: the main compass for determining the ship's position and the way compass for steering the ship. The main compass is installed in the ship's DP, in a place that provides all-round visibility and maximum protection from the ship's magnetic fields. Usually this is the ship's navigation bridge.

Deviation calculation:

d i = MP - CP i

And they create a table or graph of deviation as a function of the compass heading.

If a comparison is made between the traveling and main magnetic compasses or the traveling and gyrocompass, then the following relations are valid:

KKp + dp = KKgl + dgl

KKp + dp = GKK + DGK - d

Naval units of length and speed. Correction and lag coefficient. Determination of the distance traveled by ROL.

The metric system is inconvenient for measuring distances at sea, since during navigation one has to solve problems related to measuring angles and angular distances.

For Krasovsky’s reference ellipsoid, the length of one minute of such an arc is expressed by the following formula:

D = 1852.23 – 9.34cos2f

A standard nautical mile corresponds to the length of a minute of the meridian of the Krasovsky reference ellipsoid at latitude 44 0 18’. It differs from the values at the poles and the equator by only 0.5%.

One tenth of a nautical mile is called cables (kb) 1kb = 0.1 miles = 185.2 m

The unit of speed in maritime navigation is a knot (kt) - 1kt = 1 mile/hour.

The transition from speed in knots to speed in cables per minute is made according to the formula:

V kb/min = V knot /6

For calculations related to wind speed and in other cases, the unit meter per second (m/s) is used - 1m/s = 2kt.

The distance S o from a certain zero is recorded by a special counter, and its instantaneous value at the moment is called the lag count (LC). The distance traveled by the vessel is determined using the relative log as the difference between its successive readings (ROL) at points in time taken from the log counter:

ROL = OL i+1 - OL i

The log, like any device, determines speed with an error. The systematic error in the lag readings can be compensated by the lag correction D L, which has the opposite sign. This correction, expressed as a percentage, is called a lag correction. It is calculated using the following formulas and can have both positive and negative signs:

D L = (S o – ROL)/ROL * 100%

D L = (V o – V l)/ V l * 100%

S o – the actual distance traveled by the ship.

V o and V l – the speed of the vessel relative to the water and shown by the lag.

Instead of a correction, a lag coefficient is often used:

K l = 1 + D L/100 = S l /ROL

S l = ROL * K l

The speed of the vessel and the correct operation of the lag, that is, the correction of the lag, is determined during sea trials.

Classification of charts used in navigation. Contents of maps. Guides and aids for swimming. SOLAS requirements for charts and navigation aids.

Nautical charts and other navigation aids for all areas of the oceans and seas are published by the Main Directorate of Navigation and Oceanography (GUNiO), and in foreign countries - by hydrographic services (departments).

Nautical charts are published mainly in the Mercator projection and, according to their purpose, are divided into three types:

Navigation cards are intended for dead reckoning and determining the ship's position at sea. Marine navigation charts include general navigation, radio navigation, etc.
Special ones are designed to solve a number of navigation problems using special technical means. Special ones include roll and route maps, etc.
Auxiliary and reference marine charts, under the name of which various cartographic publications of the State University of Universities and Oceans are united. This group includes: grid maps, maps in gnomonic projection for laying out the arc of a great circle, radio beacons and time zone radio stations, etc.

General navigation charts are the main subgroup of sea charts that ensure the safety of navigation. They most fully reflect the bottom topography, the nature of the shores and the entire navigation situation (lights, signs, buoys, fairways, etc.).

Depending on the scale, general navigation Mar maps are divided into: general, with a scale from 1:1000000 to 1:5000000; travel – from 1:100000; private – from 1:25000 to 1:100000; plans - from 1:100 (for various hydrographic works) to 1:25000.

Private craters contain all navigational details. In addition to the maps, various manuals and reference books are published, from which you can glean a lot of useful, necessary information. Such manuals include navigation manuals (pilot directions), which contain all the information necessary for a navigator, including recommended routes and navigation tips when sailing near the coast.

To select maps and manuals, a special “Catalogue of Maps and Books” is published. All cards and benefits have their own number, which is called Admiralty.

The card numbers consist of five digits, which mean: the first - the ocean or part of it (1 - Arctic Ocean, 2 and 3 - North and South Atlantic, 4 - Indian Ocean, 5 and 6 - South and North Pacific Ocean), the second is the scale of the map (for each group the scale corresponds to a number from 0 to 4), the third is the area of the sea within which the map is located, the fourth and fifth are the serial number in this area.

Nautical charts and grid charts are numbered with the first digit being 9. The second digit designates the ocean or part of it; the third number is the scale; the last two are the serial numbers of the map in the ocean.

6. The ability to determine the drift of the vessel. Accounting for drift and current during dead reckoning, dead reckoning accuracy.

Drift vessel is the deviation of a moving vessel from the intended course line under the influence of wind and wind waves. The direction of the wind is determined by the point on the horizon from which the wind blows (the wind blows into the compass) and is expressed in points or degrees.

Drift occurs under the influence of the pressure force of the oncoming air flow on the surface of the vessel. The speed and direction of this flow corresponds to the speed vector of the apparent (observed) wind.

Where n is the true wind speed vector; V – vessel speed vector; W is the apparent wind speed vector.

Asymmetrical deviations from the course under the influence of gusts of wind, wave impacts, and rudder deflection cause the vessel to yaw, which can be either downwind or to the wind.

Speaking about the definition and accounting of drift, the term “drift” will mean the resulting deviation of the vessel from the true course line.

Full strength A apparent wind pressure is applied to the center of the sail of the surface part of the vessel and is directed downwind.

In general, strength A is determined by the equality:

Where C q is the resistance coefficient of the surface part of the vessel.

Corner a between the true course line and the ship's track is called drift angle.

The angle between the northern part of the true meridian and the track line during drift is called track anglea .

,

Corner a has a “+” sign - if the wind blows to the left side, and a “-” - if to the right.

To take into account drift during laying, it is necessary to know the drift angle. The drift angle can be determined from observations or calculated using formulas, specially compiled tables or nomograms.

Taking into account drift when using automatic coordinate calculation is reduced to introducing an additional heading correction equal to the angle of the ship's drift. To do this, a heading correction D K is set on the device, equal to the algebraic sum of the compass correction and the drift angle:

7. Navigation contour, position line, position strip. UPC for determining the ship's position using two lines of position.

The geometric location of points corresponding to a constant value of the navigation parameter is called navigation contour. In navigation, the following navigation parameters and their corresponding isolines are used to determine the vessel’s position:

Bearing. The true bearing (IP) of object A was measured on the ship, equal to a. By plotting the AD bearing line on the map, it can be stated that the ship was on this line at the time the bearing was taken. The straight line of blood pressure that meets the conditions of the problem on which the ship was at the moment of observation will be called the bearing isoline or isopelengy.

Distance. The distance D between the ship and landmark A is measured. In this case, the ship will be located on a circle of radius D with the center at point A. This circle will be called the distance isoline or isostage.

Horizontal angle. If the horizontal angle between objects A and B is measured, equal to a, or this angle is calculated as the difference of two bearings
. This circle is called the horizontal angle isoline or isogony.

Distance difference. Some radio navigation systems measure the difference in distance to two landmarks. Then the isoline of the distance difference will be hyperbola.

The generalized theory of position lines made it possible to expand the method of obtaining observed coordinates, which can be divided into three groups: graphic (use of maps with isoline grids and direct laying of isolines), graphic-analytical (generalized method of position lines and the use of special tables of defining points for constructing position lines) , analytical (direct algebraic methods for solving equations and calculations using the method of chords or tangents).

When exposed to random measurement errors, the displacement of each position line is characterized by a linear value Dn, which is characterized by the linear error of the position line m D n, and the error in determining the location, which is the result of random errors in both lines of position, is characterized by the area of the parallelogram formed by two parameters m D n 1 And m D n 2.

The general procedure for calculating the parallelogram of the vessel observation error under the influence of random errors is as follows:

Set by mean square errors of measurements for specific sailing conditions m v1 And m v2.

Calculate the possible displacement of each position line
;
;
;
.

The resulting displacements are plotted from the obtained observation normal to the position line (in the direction of the gradients) and a parallelogram abcd is constructed. The probability of finding a ship in the parallelogram area is about 50%; if we take 2m for calculation, then the probability increases to 95%, and if we take the maximum error of 3m, then the probability increases to 99%.

For the convenience of analysis, it is more appropriate to evaluate the accuracy of the observation of the ship’s location not by area, but by one number. The mean square error of the observed location M is taken to be the radius of the circle enclosing the error ellipse. This radius is:

The probability that the ship's position is inside the radius of the circle M varies from 63.2 to 68.3% and depends on the ratio of the semi-axes a and b.

8. The idea of determining the position of a ship by measuring navigation parameters. Methods for determining the position of a ship.

Determining the location using two bearings:

The method of determining the ship's position using two bearings is one of the most common when sailing in narrow places or along the coast, near navigational hazards.

This is also explained by the fact that often there are not a large number of landmarks in the visibility of the ship at the same time. The essence of the method is as follows. In quick succession, take bearings of two objects (lighthouses, signs, capes, etc.). Calculate true bearings, if there is a compass correction, and plot them on the map.

At the point where the bearings intersect there will be the observation location of vessel F.

A Δ B Δ

This method has a number of advantages (simplicity and speed of determination), but also a number of disadvantages, the main one of which is the complete lack of control during a single determination.

The magnitude of the linear error of the observed location can be obtained using the formula for systematic error e k hail, substituting the gradient values into it:

; ; And
hail we get:

where AB is the distance between landmarks.

From this formula it is clear that the value of FF 1 will increase with decreasing Q (at constant AB and e k). Therefore, at 30 o >Q>150 o, when sinQ decreases especially quickly, determining the location using two bearings cannot be considered accurate.

The influence of random direction finding errors.

Direction finding, like any measurement, is accompanied by random errors, which include errors due to inaccuracy of pointing, oscillations at the moment of rolling, lack of stabilization in the vertical plane, etc. This leads to the fact that any measured bearing corresponds to an error
, deg. If we substitute such an error into the formula for assessing the accuracy of the observed location, we obtain a formula for the mean square observation error for two bearings:

.

The formula shows that at small and close to 180° angles Q, the errors increase. Consequently, the location will be obtained more accurately at Q = 90 o. The accuracy of the determination also depends on the distance to landmarks.

When determining a ship's position using two bearings, the error in the accepted compass correction can be significantly greater than random errors.

To determine the correct value of the compass correction from the bearings of two objects, it is enough to find the magnitude of its error, and then algebraically subtract this error from the accepted value

compass correction values:
, where DК is the compass correction, DКр is the accepted value of the compass correction, e к is the error of the accepted value with its sign.

Determination of location using three bearings.

When determining a location using three bearings, the bearings of three objects A, B, C are taken in quick succession. They are converted to true ones and plotted on the map. If the observations were free of error and the bearings were taken simultaneously, then all three bearings would intersect at one point F, representing the ship's position.

However, due to the inevitable action of a number of factors, bearings usually do not intersect at one point, but form a so-called error triangle. Its appearance can be caused by various types of errors:

Mistakes when reading the account and when correcting compass bearings;
Errors in landmark recognition;
Errors in the accepted compass correction;
Random direction finding errors in the gasket.

To avoid graphic errors during construction, you can calculate the parallel displacement of each position line when the correction changes by 3...5 o and construct a new error triangle, moving all position lines towards increase or decrease. To calculate the displacement, it is necessary to remove the distances to each of the three objects from the map. Then:

,
,
.

The influence of error caused by non-simultaneous taking of bearings can be eliminated in several ways. One of them is the correct choice of the order of taking bearings. The first to take bearings are objects located closer to the centerline plane of the vessel. The bearings of these landmarks change more slowly. If bearings of lighthouse lights are taken, then observation must be organized in such a way that one does not have to wait long for a glimpse of the light if it is not the first to be found. At speeds up to 15 knots, when plotting is carried out on route maps, this is enough to eliminate errors from non-simultaneous direction finding. At high speeds or when plotting on large-scale maps or plans, for clarification, the bearing should be brought to the average moment. To do this, take five bearings in the following order, take bearings of landmarks A, B and C, and then repeat bearings B and A in the reverse order. Assuming that the bearings change linearly, calculate the average value of the bearings of objects A and B.

,
.

Compass correction is the value of a parameter (course or bearing) that compensates for the systematic error in its measurement. In general terms, an amendment is a systematic error taken with the opposite sign.

The constant correction of the gyrocompass DGK for each landmark is determined as the difference between the true and average measured bearings:

Determination of distances at sea.

Distance at sea can be determined by several methods: using rangefinders, by vertical angle, measured by sextant, by radar data and by eye.

Rangefinders are optical instruments that measure distances to a visible object based on various principles.

Determination of the ship's position based on measured distances.

If there are two landmarks in the visibility of the vessel, to which the distances are measured (by the vertical angle or according to radar data), then the observed places of the vessel can be obtained from two distances. Let A and B be two objects to which the distances DA and DV are measured. It is known that the measured distance corresponds to an isoline - a circle with a radius equal to this distance and with a center at the point where the landmarks are located. If both observations are made simultaneously, then, by drawing two circles, we obtain the position of the ship at one of the points. The question of which of the two points is considered an observed place is easily resolved by comparing it with a countable place.

The mean square error of site observation at two distances is obtained by substituting the error values of the flood lines into the general formula, remembering that the distance gradient is equal to unity.

Determination of the ship's position by bearing and distance.

This method is most often used when using radar. Usually bearing and distance are measured to one landmark, but it may be more expedient to measure the bearing to a luminous beacon using a compass, and measure the distance to the shore. In the first case, the angle of intersection of the position lines will be equal to 90°, and in the second case, the difference in bearings taken from the map. The distance can be measured using a sextant along a vertical angle, or obtained approximately by opening a beacon or by eye, when sailing along a fairway or in narrows.

To reduce errors in non-simultaneity of observations, distances are first measured, and then a bearing is taken when the object is positioned closer to the beam and in the reverse order - at sharp angles. The observed place is obtained on the line IP at a distance from the object equal to D.

When measuring bearing and distance to one landmark, the mean square error of the vessel's position is equal to (angle
)

When measuring bearing and distance to different objects, you need to know the angle of intersection, then:

9. Gradients of navigation parameters. Methods for assessing the accuracy of a vessel's position during navigational determinations. UPC and 95% error at the ship's location. Practical consideration of errors in determining the vessel’s position for safe navigation. IMO requirements.

Any measurements contain errors, therefore, having measured the bearing, distance or angle and placing the corresponding isoline on the map, one cannot assume that the ship will be on this isoline. You can calculate the possible displacement of the isoline due to errors using the concept of function gradient.

Vector called gradient is a vector directed normal to the navigation contour in the direction of its displacement with a positive increment of the parameter, and the module of this vector characterizes the highest rate of change of the parameter in a given location. This module is equal to:

If, when measuring the navigation parameter v, an error Dv is made and the gradient is known, then the displacement of the position line is parallel to itself and is determined by the formula:

The greater the gradient g, the smaller the displacement of the position line for the same error Dv, the more accurate the determination of the vessel's position will be.

If, when measuring a navigation parameter, there was a random error m P, deg, then the error of the position line will be found using the formula:

.The position strip, the width of which is three times larger than the average, captures the ship's positions with a probability of 99.7%. This strip is called position limit band. Analytically calculated by the formula:
, where d is the auxiliary angle.

The value of angle d is obtained by calculating:

The position line offset in miles is:

,

where m’a is the angle error in arc minutes.

To prevent navigational accidents associated with grounding, along with other measures, attempts were made to standardize the requirements for the accuracy and frequency of observation depending on navigation conditions. Repeated discussions of these issues in the Maritime Safety Committee of the International Maritime Organization (IMO) led to the creation of a navigational accuracy standard, adopted in 1983 at the 13th IMO Assembly in resolution A.529.

The purpose of the adopted standard is to provide guidance to various administrations with navigation accuracy standards that should be used when assessing the effectiveness of systems designed to determine the position of a vessel, including radio navigation systems, including satellite ones. The navigator is required to know his place at any given time. The standard specifies factors influencing the requirements for navigational accuracy. These include:

the speed of the vessel, the distance to the nearest navigational hazard, which is considered to be any recognized or charted element, the boundary of the navigation area.

When sailing in other waters at speeds up to 30 knots, the current position of the vessel must be known with an error of no more than 4% of the distance to the nearest danger. In this case, the accuracy of the location should be assessed by the error figure, taking into account random and systematic errors with a probability of 95%. The IMO standard includes a table that contains requirements for position accuracy, as well as the permissible sailing time based on dead reckoning, provided that the gyrocompass and log (sailing time) comply with IMO requirements, the dead reckoning has not been adjusted, the errors have a normal distribution, and current and drift are taken into account with possible accuracy.

10. Orthodromy, orthodromic correction. Methods for constructing an orthodrome on Mercator projection maps.
Orthodromic correction

When determining the IRP, the angle between the true meridian and the arc of the great circle along which the radio wave propagates from the source of its radiation M to the receiving location K on the sphere is measured (Fig. 13.4). The measured angle is the orthodromic bearing.

If on the Mercator projection from the position of the radio beacon AD, as is usually done, the line of the reverse IRP (ORI) is postponed, then the position of the ship will turn out not in the direction of MK, but in the direction of MKi.

In order for the line of bearing drawn on the Mercator chart to pass through the position of ship K, the measured orgodromic bearing must be
converted to loxodromic bearing (Lok P) by adding the angle y to it, called the orgodromic correction:

Lok P = IRP + y

The orthodromic correction is a correction for the curvature of the great circle image on the Mercator map. Let us find the value of this correction from Fig. 13.5, depicting the Northern Hemisphere of the Earth with a great circle drawn on it through points K and M. This arc makes angles Ai and Ad with the meridians of points K and M, respectively. These angles are not equal to each other, since the arc of the great circle intersects the meridians at different angles.

The difference between two spherical angles at which the arc of a great circle intersects the meridians of two given points is called the convergence of the meridians. The amount of convergence of the meridians of points K and M can be found if we apply Napier’s analogy to the KRM triangle. Based on it you can write:

From formula (13.7) it is clear that y cannot be greater than RD. As latitude increases, the convergence of the meridians increases. The largest value equal to
difference in longitude, the convergence of the meridians reaches at рт = 90°.

The value of the orgodromic correction can be found from the convergence
meridians in Fig. 13.6, depicting in Mercator projection a part of the globe with points K and M, through which passes the arc of a great circle, making angles Ai and Ad with the meridians of these points. On the Mercator projection, the arc of a great circle will be depicted as a curve with its convexity facing the nearest pole. A loxodrome passing through points K and M intersects their meridians at the same angle K.

Let us assume that the distance between points K and M is relatively small, as a result of which we can assume that the arc of a great circle passing through these points is represented by an arc of a circle. This assumption will be correct with sufficient accuracy for practice for distances up to several hundred miles. Then the arc of the great circle will make equal angles y with the loxodrome at points K and M.

From Fig. 13.6 it is clear that at point K the correction ip = K-At at point M the correction gr = A; - K. Summing these equalities, we get

This formula is approximate because in deriving it we assumed the equality of the orthodromic corrections at points K and M. In reality, the orthodromic corrections at these points are not equal.

Substituting these data into formula (13.8) we obtain:

When solving various navigation problems, it is most often necessary to find the loxodromic bearing at a given point with a known orthodromic bearing. This problem is solved using the algebraic formula (13.5).

If the vessel is located east of the radio station (bearing value is from 180 to 360°), the orthodromic correction has a “-” sign. In the southern hemisphere, the rule of signs will be reversed (Fig. 13.7).

When deriving the approximate formula for the orthodromic correction, the assumption was made that the arc of a great circle is represented on the Mercator map by an arc of a circle, as a result of which the orthodromic correction at both ends will be the same. A more rigorous study of the issue of the orthodromic correction shows that the arc of the great circle on the Mercator map is depicted by a curve that is not a circle, and the orthodromic correction will be different at different ends of the arc of the great circle.

At long distances, when DA > 10°, the exact orthodromic correction value should be used. The exact value of the orthodromic correction can be found using table. 23-6 MT-75, compiled according to the formula:

A 1 is the orthodromic direction determined from expression (13.2).

You can increase the accuracy of finding the orthodromic correction (at (p > 35°) by using a regular table compiled according to the approximate formula (13.8). This table should be entered not with the average latitude, but with the latitude of the point for which the orthodromic correction is found. Orthodromic the correction should be taken into account in all cases when its value is greater than the random errors of the gasket (they are usually taken equal to ± 0.3°).

Notices to mariners. Contents of notices to seafarers. Rules for correcting navigation maps.

Keeping charts and sailing guides up to date is called proofreading. Documents containing information about changes in the situation are called proofreading. They are published by the authorities of the Main Directorate for Civil Aviation and Oceanography of the Moscow Region in the form of issues of “Notice to Mariners” (IM). The most important and urgent information is transmitted by radio. IM is published weekly in separate issues, each of which has its own serial number. Issue IM No. 1 comes out at the beginning of the year and should always be on board. On the title page of an IM issue, indicate the number and date of its publication, the numbers of IM included in this issue, and general reference information. The notice is numbered continuously throughout the calendar year. The list contains chart numbers, Admiralty numbers and names of sailing directions, descriptions of lights and signs, radio navigation equipment and other navigation manuals and manuals, which must be corrected upon receipt of this issue.

The systematic process of correcting nautical charts and navigational manuals in order to bring them up to date is called proofreading maps and manuals. Among the marine charts, marine navigation charts are subject to correction, since they contain the elements that are most subject to change, and these maps are used for direct calculations during navigation.

All sailing manuals are also subject to revision to a greater or lesser extent.

Depending on the volume and nature of the corrections, and also on whether these corrections are made by the organization that issued the chart, or by the navigator himself on the ship, the following types of correction of Admiralty charts are distinguished:

1) new map (“New Chart” - NC). The new card is called:

a map showing an area not previously shown on any Admiralty map;

map with modified layout;

a map for a specific area on a scale different from the scale of maps already existing for this area;

a map showing depths in other units of measurement.

For maps published after November 1999, under the lower outer frame on the left. The publication of a new chart is announced in advance in the Weekly Issues of Notices to Mariners;

2) new edition of the map (“New Edition" - NE). A new edition of a map is published when there is a large number of new information or a large number of corrections to an existing map have accumulated. The date of publication of the new edition of the map is indicated to the right of the date of publication of its first edition. For example:

On maps published after November 1999 - in a frame in the lower left corner of the map. The new edition of the map contains all the corrections that have appeared on the map since the publication of the previous edition. Since the release of the new edition, it is prohibited to use maps from previous editions;

3) urgent new edition (“Urgent New Edition“ - UNE).

Such a publication is published when there is a lot of new information on the chart area, which is of great importance for the safety of navigation, but due to its nature, such information cannot be transmitted to ships for correction in Notices to Mariners. Due to urgency, such a publication may not contain all the updates that have been made to a given chart since the last edition was printed, unless such information is critical to the safety of navigation in the area (see Chapter 2). Thus, an urgent new edition of the chart may require proofreading according to the Weekly Notices to Mariners published before its publication;

4) large proofreading (“Large Correction"). If significant changes must be made not to the entire map, but only to one or several of its sections, the organization that issued the map makes a major correction of this map. The date of the major revision is indicated to the right of the date of publication of the map. For example:

The major proof contains all the previous minor proofs (see below) and the proof published in the previous Weekly Notices to Mariners. Major map corrections were used until 1972;

5) small proofreading (“Small Correction"). Such adjustments are periodically made by the organization that issued the card. With this type of correction, all corrections according to the Weekly Issues of Notices to Mariners issued after the publication of the map (the last of the new editions) or its Big Correction, as well as technical corrections are applied to the map (“Bracketed Correction”). Minor correction information is provided in the lower left corner of the map. For example, the map is corrected according to notice No. 2926 for 1991:

882 - 985/01

T&P Notices in Force

IMO requirements for the form and content of ship information on the maneuvering properties of the vessel. Pilot card.

The main properties of a particular vessel related primarily to its propulsion, agility and inertial braking

1. Determining the correction of a magnetic compass and monitoring its operation at sea 1. 1. General provisions The magnetic compass is simple in design, it is autonomous and reliable. The main disadvantage is the low accuracy in determining directions. Errors reach 2–4°, especially when pitching. Sources of errors: magnetic declination, deviation, inertia and insufficient sensitivity of the magnetic needle system to the Earth's magnetic field. The magnetic compass card arrives at the meridian 3–4 minutes after maneuvering.

An accurate knowledge of the deviation of the magnetic compass is important in navigation. Deviation is destroyed at least once a year using the methods studied in the course “Technical means of navigation”. The residual deviation is determined by navigation methods and should not exceed several degrees. In accordance with good maritime practice, magnetic compass deviation is determined: – at least once a year; – after repair, docking, demagnetization of the vessel, as well as after loading and unloading cargo that changes the ship’s magnetic field; – with a significant change in magnetic latitude; – when the tabulated deviation diverges from the actual one by more than 1° for main compasses and 2° for way compasses; - before a long flight.

All methods for determining deviation are based on the use of formula (4.6) MP = CP + δ → δ = MP – CP Deviation depends on the ship’s course, so it is usually determined on 8 equally spaced compass courses, and intermediate values are found by linear interpolation. Usually these are courses corresponding to the main and quarter directions, i.e. courses 0, 45, 90, 135, 180, 225, 270, 315 degrees

It is assumed that the ship's magnetic field is symmetrical relative to the ship's DP, i.e., the deviation is symmetrical relative to the magnetic meridian, therefore the average value of the compass bearing to a distant object taken to a distant landmark on equally spaced courses can be taken as an estimate of the magnetic bearing. The formula will be as follows: MP = ∑KPi /8 + A (5. 1) Where A is some correction for the systematic error (constant deviation), which is determined for a specific compass during the destruction of deviation.

1. 2. Methods for determining deviation 1. 2. 1. Along the target The vessel crosses the target on 8 equally spaced compass courses, and the navigator takes KPi. Compass courses are 45 degrees apart. Magnetic bearing is calculated using the formula MP = IP – d (5.2)

The value of IP and magnetic declination is taken from the map. Magnetic declination leads to the year of voyage. When maneuvering in the vicinity of the target, you should take into account the inertial characteristics of the magnetic compass. If the magnetic declination is unknown, then use formula (5. 1) - then calculate the deviation on each heading: δi = MP - KPi (5. 3) and draw up a table or graph of deviation as a function of the compass heading. The table is compiled in 10 degrees according to the compass heading.

1. 2. 2. By a distant landmark The vessel circles at a distance D from the navigational landmark and takes bearings on 8 equally spaced compass courses. Determine δ using formula (5.3). Magnetic bearing can be calculated using formula (5.2) or using PI and d taken from the map.

It should be borne in mind that the distance to the landmark is selected taking into account the accuracy of determining the bearing and can be determined by the formula: D = r/sinά (5. 4) If the water area is limited for maneuvering, the vessel is anchored or barreled and turned around by tug.

1. 2. 3. According to the bearing of the star The method is similar to that described above. At eight compass courses, the compass bearings of the luminary are determined. Then its azimuth (AI) is calculated using astronomical formulas, and, knowing the declination (from the map), the MF is obtained. To calculate the deviation, formula (5.3) is used. To increase the accuracy of direction finding, choose a luminary located at a low altitude (no more than 30 degrees). A significant advantage of the method is that due to the great distance of the luminary, the accuracy does not depend on the coordinates of the vessel, i.e. there is more space for maneuvering.

1. 2. 4. By comparison with another magnetic compass or gyrocompass. Comparing compasses means simultaneously noticing their readings. Comparisons are made between the traveling compass and the main or gyrocompass. It is usually produced in 8 equally spaced courses. Deviation is determined by taking into account the equality of magnetic courses obtained from different course indicators. For example, when comparing a travel compass with the main one or when comparing it with a gyrocompass, the following expressions are correct: KPp + δp = KKgl + δgl (5. 5) Kpp + δp = GKK + ΔGK – d (5, 6) From these relations the unknown is calculated

1. 2. 5. By the method of mutual bearings (in extreme situations) A magnetic compass installed on the shore or on a non-metallic boat is taken from the ship, and a compass installed on the ship is synchronously taken from the shore or from the boat. It is clear that the MP is taken from the compass on the shore or on the boat. Deviation is determined: δi = (180 o + MP i) - CP i (5.7)

2. Determining the correction of the gyrocompass and monitoring its operation at sea 2. 1. General provisions Gyrocompasses generate a heading with an accuracy of 0.5° (with a probability of 95%) with a constant heading and pitching of no more than 2 degrees. With increased pitching and intense maneuvering, the gyrocompass error can reach 4°. Due to inertial errors, the highest measurement accuracy can be achieved 30 -40 minutes after the end of the maneuver. The gyrocompass has its own systematic errors, which must be compensated for by corrections. Well-known formulas are used as formulas for calculation: ΔK = IR – KK (5.8) ΔK = IP – KP (5.9) Where ΔK, KP are general designations for compass correction, compass course and compass bearing, measured using magnetic or gyrocompass.

The task comes down to determining the true directions, which are usually taken from the map or calculated by celestial navigation methods if direction finding of luminaries is carried out.

2. 2. Methods for determining the gyrocompass correction 2. 2. 1. By the bearing of a distant object The method is used if the ship is moored. Determine the exact compass coordinates on a map or plan and take an IP at a remote known navigation landmark.

For about an hour and a half, they take a bearing to this landmark after 1015 minutes, find the correction using the formula (5.9) for each direction finding, and then display its average value (line aa"). This will be the so-called constant correction of the main code. This operation is also should always be carried out after a new start of the GK, when it has entered the meridian ΔGK a a" ΔGKi ΔGKsr ΔGKi t

2. 2. 2. According to the bearing of the navigation alignment, the IP alignment is indicated on the map. Having found the target and compared the IP with our GKP, we obtain ΔGK (formula (5.9)). With this method, you can use not only artificial, but also natural alignments. 2. 2. 3. Using the true bearing of the luminary To do this, it is necessary to take the bearing of the luminary, calculate its azimuth (A), and this is the same as the IP. Comparing GKP and A, we obtain ΔGK. The most common way to determine ΔGK is by the bearing of sunrise and sunset, by the bearing of the North Star. The determination of ΔGK by celestial bodies is studied in more detail in the course “Nautical Astronomy”.

2. 2. 4. By comparison with the heading indicator, the correction of which is known. In this case, use the formulas obtained by equating IC: KKp + ΔMKp = KKgl + ΔMKl (5.10) KKp + ΔMKp = GKK + ΔGK (5.11) Equation (5.10), (5.11) are solved with respect to the unknown correction . The indicated formulas are used when switching from one compass to another if any of them fails.

If the instantaneous correction of the gyrocompass, determined by one of the methods at sea, differs by more than 1° from the constant correction determined in the port, then the alarm should be sounded. Determining the compass correction is one of the most important responsibilities of a boatmaster. Navigation service rules require that compass correction be determined whenever possible. Comparison of gyroscopic and magnetic compasses is carried out once during a watch (4 hours), if the course does not change and with each change of course. This is necessary in order to know the current compass correction in the event of a gyrocompass failure.

Conclusions: 1. 2. 3. Determining corrections for direction indicators is one of the most important responsibilities of a navigator. It is necessary to determine the compass correction whenever possible. The methods used to determine the correction of the magnetic compass and gyrocompass are the same, namely: along the alignment, using the bearing of the luminary, by the bearing of a distant landmark, by comparison with a heading indicator, the correction of which is known. But it should be remembered that the correction for the gyrocompass determined in this way is constant on all courses. For a magnetic compass, this correction is valid only on this course. Comparison of the gyroscopic and magnetic compasses is carried out once during the watch (4 hours), if the course does not change and with each change of course.

Contents of issues discussed at the seminar 1. Basic points, lines and planes for orientation on the earth's surface. 2. Horizon division systems: rhumb, circular, semicircular and quarter 3. Directions relative to the plane of the true meridian and the center plane of the vessel 4. Use of a magnetic compass, magnetic declination, magnetic compass deviation, magnetic compass correction. 5. The relationship between compass and true directions 6. Methods for determining direction indicator corrections 7. Calculation of directions using a gyrocompass and a magnetic compass