Magnetic declination, deviation, magnetic compass correction. Correction and translation of courses and bearings. Compass correction What course is taken from the magnetic compass

Question No. 9

ASTRONOMICAL DETERMINATION OF COMPASS CORRECTION

Determining the compass correction (∆K) at sea is one of the most important tasks in navigation. Without knowing the correct value of ∆K, the navigator is not able to provide the necessary accuracy of dead reckoning of the ship's path, as well as navigation observations. As is known, corrections to ship compasses are determined by coastal alignments. However, over time, for various reasons, the correction values of gyroscopic and especially magnetic compasses undergo changes. As a result, when the ship is on a voyage, it is necessary to systematically determine the correct values of compass corrections. On the open sea, this can only be done using celestial bodies, i.e. astronomical methods.

To determine the compass correction at sea, it is necessary to obtain the true direction to the luminary C, i.e. its IP (Fig. 99), and the compass direction to the luminary, i.e. its CP, then the magnitude and sign of ΔK are determined by the formula ΔK = IP - KP.

The true bearing of the luminary, equal to its azimuth in a circular calculation, at sea is calculated using formulas, tables, nomograms, instruments or computers. Azimuth is a function of three arguments, i.e.

A = A 1 (φ, δ, t) = A 2 (φ, δ, h) = A 3 (φ, h, t)

In practice, two observation methods can be used: the method of moments and the method of heights. In the first case, simultaneously with taking the CP, the exact Grivichsky time is noticed, and in the second, the height of the direction-finding luminary is measured.

Method of moments. If, when taking the direction of the luminary, the moment is noticed by the chronometer and φ c, λ c are taken from the map, then the following elements can be obtained in the parallactic triangle PnZC:

Side 90 - φ c, where φ c is taken from the map according to the noticed Tc and ol;

Side 90-, where it is selected from the MAE according to Tgr observations, is removed from the map;

Angle = where it is selected from the MAE according to T gr observations and removed from the map.

Therefore, given the three known elements, the azimuth of the luminary can be calculated from the triangle PnZC using the cotangent formula:

ctg A = tg δ cos φ c cosec t M - sin φ c ctg t M . (1.1)

Using this formula, the azimuth in a semicircular account is calculated, converted to a circular account and taken as an PI. However, to obtain the azimuth from three known quantities φ c, special tables are more often used.

Height method.

If, when taking the direction of a luminary, its height h is measured, then the azimuth can be calculated from the other three known sides of the parallax triangle. Using the cosine formula for the side PnC

cos A = sin δ sec φ c sec h - tg φ c tan h

Used when the height can be calculated in advance

Method of heights and moments. If, after observing the heights of a star, take its compass bearing and notice Txp, then simultaneously with obtaining the ship’s position or position line, you can also obtain a compass correction.

To calculate h and A, a system of formulas is used:

is used if the height of the luminary is obtained in advance, and the azimuth is calculated along the way.

The method of heights and moments is also used when determining ΔK from the North Star, but its height is not measured, but is taken equal to φ.

DETERMINING COMPASS CORRECTION. GENERAL CASE

When the stars are visible, the compass correction can be determined at any time of the day using the method of moments, which represents the general case of determining the compass correction. To determine the compass correction in this way, any luminary can be used, regardless of the magnitude of its declination. Observations can be made both during the day and at night, at any latitude. All this allows us to consider the method universal.

The formula for calculating azimuth (1.1) is non-logarithmic and requires symbolic analysis during calculations.

Preliminary operations. Selection of observation conditions. For the scheduled time, select a star with a height of up to 10° (and no more than 20°) using a star globe or by eye. Checking instruments, Observations. Observe a series of three bearings and a control point. Receive navigation information: Ts, ol, φ, λ, KK, ΔK.

Processing observations. Analyze ΔK; compare with the accepted constant - the discrepancies should not exceed the accuracy of heading guidance (from ±0.3° in good conditions, to 1.5° in bad conditions);

VAS-58. TVA-57. COMPUTER.

BY SUNRISE (SUNSET)

At the moment the upper edge of the Sun touches the line of the visible horizon, the center of the luminary is located below the true horizon, i.e. has a negative height. With the height of the observer's eye e=12m, the most typical for most ships, the decrease in the center of the Sun at the time of its apparent sunrise or sunset is 57.8 minutes. It consists of horizon inclination, average semi-diameter, parallax and refraction. With a known decrease, the azimuths of the Sun at the moment of its apparent sunrise or sunset can be calculated in advance using the altitude method. These azimuth values, calculated using the converted formula, are given in tables 20a and 20b MT-75.

Selection of table azimuth from the table. 20a and 20b are produced according to the reckonable latitude and declination of the sun with interpolation according to both arguments. Table 20a includes those with the same latitude and declination, Table 20b includes those with different latitudes. Azimuths are obtained in a semicircular count. In northern latitude, the name of the azimuth will be NO at sunrise and NW at sunset. In the southern hemisphere, SO is at sunrise and SW is at sunset. The resulting compass corrections at the moment of apparent sunrise or sunset in practice boils down to the following. Using MAE, the ship's pre-sunset (sunrise) time is calculated and the compass plane of the upper edge of the luminary is taken at the moment it touches the visible horizon line.

The procedure for determining ΔK based on sunrise (sunset).

1. Observe the bearing of the Sun at the moment of its appearance (or descent) on the horizon of its upper edge.

3. Enter the table. 20-a for like φ and λ or 20-6 for unlike ones and choose the At value closest to φ and λ. Interpolate the azimuth along b and f and add corrections to A d. Give the resulting azimuth a name in the semicircular account and convert it into a circular account.

5. Analyze ΔK. comparison with the previously accepted one and evaluate possible errors in determining AK-

Determining the compass correction from observations of the North Star.

When sailing in low northern latitudes, a convenient object for determining the compass correction is the North Star. Since the polar distance ∆=90 of this star is approximately 0.9 degrees, in its daily motion it describes a parallel around the North Pole of the world, the spherical radius of which is very small. As a result, the height of the North Star at any moment remains close to the height of the pole, or, which is the same as the latitude of the observer. The azimuths of Polaris vary slightly and can range from 0 at the culmination of the star to 1.2 degrees NO or NW at elongations for latitudes less than 35 degrees. These circumstances make it possible to obtain a simplified formula for calculating the azimuth of the Polar Star.

Determining the compass correction according to the Polar Star is possible at latitudes from 0 to 15 N with direct direction finding of the star and up to 40-50 degrees N when using a reflective mirror.

Observations consist of obtaining three to five compass bearings of the star, taken in quick succession. The observation time, due to the slow change in azimuth, can be noted on the ship's clock with an accuracy of up to 5 minutes. It is enough to know the numerical coordinates of the vessel with an accuracy of 1 degree.

Having calculated the Greenwich time Tgr of observations, the Greenwich sidereal time Sgr is selected from MAE, which is converted by longitude to local Sm. The star azimuth selected from the table is converted into a circular count.

Example 73. May 5, 1977 in the South China Sea, following QC= 190° (+1°), V= 17 knots, determine AGK" along Polyarnaya.

Solution. 1. Observations. Near T in = 2 H 13 m (№ = -9) took bearings of Polar- GKP= 359.6°; f = 18° N; X = 116° 0 s ".

2. Processing observations:

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 rhumbic 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 the 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 radio stations of time zones, 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 incoming 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, we can state 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 mv2.

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 the 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.

Determining the 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 again 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 a 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 get:

When solving various navigation problems, most often it is 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 amount 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 correction 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 the corrections according to the Weekly Issues of Notices to Mariners published 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

§ 17. Magnetic and compass points, courses and bearings. General compass correction

The direction at sea is determined not only relative to the true meridian, but also relative to the magnetic and compass meridians, calling them in the general case magnetic compass points.

Rice. 21.

Let us depict three meridians on the plane of the true horizon (Fig. 21): true NiSi, magnetic MMSM and compass NKSK, the direction of the center plane OD and the direction from the ship to the coastal landmark OM. In the drawing, the angle N and OD is the true heading of the ship, and the angle N and O M is the true bearing. By analogy, it is believed that the NMOD angle is the magnetic heading (MC), the NKOD angle is the compass heading (CC), the NMOD angle is the magnetic bearing (MP), and the NKOM angle is the compass bearing (CP).

Thus, Magnetic course The vessel is called the angle at the center of the compass, measured from the northern part of the magnetic meridian to the direction of the bow of the ship's center plane clockwise from 0 to 360°. Compass heading- the angle at the center of the compass, measured from the northern part of the compass meridian to the direction of the bow of the centerline plane of the ship clockwise from 0 to 360°. Magnetic bearing an object is called the angle at the center of the compass, measured from the northern part of the magnetic meridian to the direction towards the object clockwise from 0 to 360°. Compass bearing an object is called the angle at the center of the compass, measured from the northern part of the compass meridian to the direction towards the object clockwise from 0 to 360°.

True courses and bearings are related to the magnetic following algebraic relations:

Example 19. I K = 355°, d = 11°5W.

Solution(formulas 19)

Example 20. MP = 132°, d = 5° O st .

Solution(formulas 20)

Magnetic courses and bearings are related to the compass by the following algebraic relationships:
Example 21. CC = 357°; 5 = 5°O st .

Solution(formulas 21)

Example 22. MP = 4°: CP = 358°

Solution(formulas 22)

The combined action of the forces of earthly magnetism and the magnetic field of the ship leads to the fact that the magnetic needle deviates from the true meridian by a certain total angle, called general compass correction. It is designated by the symbol AK.

The general correction is called the truss or leading and is given a “plus” or “minus” sign depending on whether the northern part of the compass meridian is deviated towards the truss or the leading from the northern part of the true meridian. For example:

AK = +3° or AK = -10°.

The general compass correction, declination and deviation are related by the following algebraic relationships.

Vessel's heading - the angle between the centerline of the ship and the direction to the north. Measured in degrees clockwise from 0° to 359°. Vessel's true heading (IR)- this is the angle between the northern part of the true meridian (NS line) and the center line of the ship (the direction of the ship's bow). The true course is counted clockwise from 0 to 360°.
Magnetic course (MC)— the angle between the magnetic northern meridian N and the course line.
The action of a magnetic compass is based on the property of a magnetic needle to occupy a certain position in the earth’s magnetic field, namely: the northern end of the magnetic compass needle points to the north magnetic pole of the earth N. Magnetic and geographic poles do not coincide. The direction passing through the axis of the magnetic needle is called the magnetic meridian. The magnetic meridian does not coincide with the direction of the true meridian. Compass heading (CC) called the angle in the plane of the true horizon, measured from the north part of the compass meridian clockwise to the bow of the center plane of the ship. Compass courses and bearings can range from 0° to 360°.
Magnetic declination (d)— the angle between the northern part of the true meridian and the northern part of the magnetic meridian is called magnetic declination. Declination is measured from the northern part of the true meridian to the east or west from 0 to 180°. The eastern, or core, declination is assigned a plus sign, the western, or western, declination is assigned a minus sign. The magnetic declination for a given place is not constant; it constantly increases or decreases by a small constant amount. The magnitude of the declination in a given navigation area, its annual increase or decrease in the year to which the declination is given are indicated on navigation charts. Magnetic compass deviation (δ) is the horizontal angle by which the plane of the compass meridian deviates from the plane of the magnetic meridian (the difference between Nm and Nk). On each course, the deviation of ship compasses is different. This is explained by the fact that when the course changes, the position of the ship's iron relative to the magnetic compass needles changes. In addition, after the ship turns, the ship's iron is partially remagnetized, which also leads to a change in the ship's magnetic field.
Magnetic compass correction- the algebraic sum of deviation and magnetic declination, by the amount by which the compass directions differ from the true ones: ΔMK=δ+d MK deviation and declination must be taken with their own signs.

In order to find the true course (IR) knowing the magnetic course (MC) and the declination d of the compass in a given navigation area, it is necessary to algebraically add the declination given to the year of navigation with its sign to the magnetic course: IR=MK+(±d) hence: MK=IR-(±d)

Example:True heading(IR) = 90°Deviation (δ) = 5°E (deviation to the east (E) sign “+”, if to the west (W) sign “-“)Declination given to the year of navigation (d) = 10°W (we have a declination to the west, then the sign will be “-“, i.e. -10°)1) Find ΔMKΔMK=δ+d=5+(-10°)=-5°2) Find MKMK=IR-(±d)=90°-(-10°)=100°3)Find QCCC=IR-(±d)-(± δ )= 90°-(-10°)-(+5°)=95°
To make the calculations clearer, I’ll make a sketch, since the example is interesting:

It is also necessary to remember that: a) the course does not have negative values, if one is obtained during calculations, the result should be subtracted from 360°; b) if the course obtained in calculations is more than 360°, then 360° should be subtracted from the result.

Sometimes, when interviewing 3rd mates, I jokingly ask: “How does the morning begin for the 3rd mate and for the captain?”

The young guys are confused and try to come up with something to answer my unexpected question.

I explain to them all that the captain’s morning begins with a cup of aromatic coffee, and for the 3rd mate, the morning begins with adjusting the compass. A joke of course, but with a grain of truth. This is what I want to talk about.

All navigators know that the compass correction must be determined every watch. How to do this?

In coastal navigation, when there are coastal landmarks, this is very simple and takes a few minutes. What to do if the ship is on the open ocean? There is nothing around, only the sky, the ocean, seagulls and the captain, who is watching with interest how the 3rd mate will solve the task. He probably considers you “GPS generation”. As they say, everything ingenious is simple.

There is a quick and easy way to determine the compass correction based on the lower or upper edge of the Sun. To do this, you need very little - install a direction finder on board where the Sun sets, and at the moment when the last segment disappears behind the horizon. After this, you should take a bearing, note the time, latitude, longitude and enter the data into the Navimate or Skymate computer program. If you don’t want to blush in front of the captain, or at some inspection, then show your class and calculate the correction manually.

For this we need a manual called Nautical Almanac.

So, we take a bearing on the Sun, record the current time and coordinates, record the course using the gyro and magnetic compass.

Example:

Date: 03/19/2013 LMT(UTC+2): 17:46:30 Lat: 35-12.3 N Long: 35-55.0 E

Gyro bearing: 270.6 Heading 005 Magnetic heading 000

We adjust the time to Greenwich Mean Time (2nd time zone) GMT 15:46:30

Finding GHA (Greenwich Hour Angle)

Finding DEC (declension)

To find them, go to the main table of the Almanac and find the current date. We write out GHA and DEC for the current hour, and also write out correction d for the Sun (bottom right of the table). In our case it is equal to 1.0.

Then you need to correct the Greenwich hour angle and declination by adjustments to minutes and seconds.

This information can be found at the end of the book. The pages are headed by minutes and a GHA correction is provided for each second. There is also a correction for declination on the right side, which is selected according to d.

M’S” = 11-37.5 corr = 0-00.8

Now we adjust the Greenwich hour angle to the local time zone. To do this, we add (if E) or subtract (if W) our longitude:

GHA = 54-42.5 + Long 35-55.0

LHA = 90-37.5

Go to the Sight reduction table and select the values A, B, Z1:

A = 55.0 B = 0 Z1 = 0

For the second entry in the table we need F and A.

To get F you just add B and DEC (+/-).

Our DEC is positive if the sign of declination and latitude coincides (N and N/S and S).

If our declination and latitude are different, then DEC is negative.

B=0

DEC=0-20.6S

F = 359 39.4 (rounded to 360)

Now having F and A, we enter the same table for the second and last time, and write out the second component of the azimuth Z2:

Z2 = 90

Then we add Z1 and Z2 and get the semicircular azimuth Z:

Z = 0 + 90 = 90

We convert semicircular azimuth to circular using the rule:

For northern latitude, if LHA is greater than 180: Zn = Z, if LHA is less than 180: Zn = 360 Z

For Southern latitude, if LHA is greater than 180: Zn = 180 – Z, if LHA is less than 180: Zn = 180 + Z

In our case Zn = 360 – 90 = 270

The desired bearing has been found. We take away our compass bearing 270 – 270.6 = - 0.6W

In order not to get confused in the order of calculations, I present the algorithm:

We make calculations, record bearing, position, time, and course.
We convert local time to Greenwich Mean Time.
We select the value of LHA and Dec from the tables.
We correct them by adjusting them for minutes and seconds.
Select the values A, B, Z1 from the table.
We calculate F and select Z2 from the table.
We find the azimuth and convert it to circular.
We find the compass correction (true bearing minus compass bearing).
WE HANG A LARGE ASTRONOMICAL MEDAL ON OUR CHEST.

At first glance, everything looks cumbersome and unclear. But after a couple of practical calculations, everything will fall into place.

By the way, by adjusting your compass as the sun sets, you will have a unique chance to see the green beam. The fact is that at sunset, at the moment when the Sun disappears behind the horizon, due to refraction and refraction of color, it is very rare, but you can observe a green ray for several seconds. This mysterious, enigmatic and very rare phenomenon is reflected in numerous legends of different peoples, and is overgrown with legends and predictions.

For example, according to one legend, the one who saw the green ray will receive a promotion, prosperity, and will be able to meet the one with whom he will meet his happiness.

And this is not a story, since the Captain, having seen and appreciated the efforts, as well as the competence of the young navigator, will, of course, recommend him for promotion.

So determining the compass correction based on sunset is a direct path to promotion and, as a result, to well-being and happiness.

I wish all young navigators calm seas, career advancement, and a return to their native shores. May the green ray bring you happiness in your life.