The principle of determining the corrections of any compass ΔK is to compare the compass direction (measured with a compass) with the true direction:

ΔK = IR - KK; ΔK = IP - KP.

There are three main methods for determining the compass correction:

-compared bearings;

- on alignment;

- by comparison of compasses.

Determination of ΔK by comparison of bearings

The method is based on the exact knowledge of the ship's position and the coordinates of the direction-finding landmark.

The true bearing is calculated, the bearing is found (KP).

The resulting CP is compared with the IP:

ΔK = IP - KP.

tgIP = Δλ cosφm/Δφ,

where: Δλ is the difference in longitude between the ship and the landmark;

Δφ is the difference in latitude between the vessel and the landmark;

φm = 0.5(φ1 + φ2) is the average latitude.

IP can also be measured on the map, however, this will add measurement errors using a gasket tool.

Determination of ΔК by alignment

A system of two or three beacons, signs, lights, located on the ground in a certain order, and forming a line of position (axis of alignment), is called a sea navigation alignment.

The alignments are mainly designed to ensure navigation along straight sections (elbows) of fairways in narrow areas, where there are many navigational hazards.

By appointment, the alignments are leading, rotary, secant and deviation

The method for determining the compass corrections along the alignment consists in comparing the CP measured on the alignment marks at the moment of crossing the alignment line with the alignment index indicated on the map:

ΔK = IPstv - Kstv.

To determine ΔK, you can also use the alignment of two natural landmarks shown on the map (mountain peaks, capes) or structures (pipes, masts), the IP of which is measured on the map using a plotting tool.

Determination of ΔK by comparison of compasses

The method is based on comparing a compass heading whose correction is determined with a compass heading whose correction is known. Based on the simultaneous comparison of rates, ΔK is calculated.

ΔK = Ko + ΔKo - K *,

where Ko is the compass heading, the correction of which is known;

ΔKo is a known correction;

K - compass heading, the correction of which is determined.

The difference Ko - K \u003d R is called comparison. From here

ΔK = R + Ko.

Example:

Determine ΔMK if KKmk + 6º, GKK = 354º, ΔGK = -2º.

Solution:

R \u003d Ko - K \u003d GKK - KKmk \u003d 354º - 366º \u003d -12º;

ΔK = R + Ko;

ΔMK = R + ΔGK = (-12) + (-2) = -14º.

Answer: ΔMK = -14º.

Formula output *:

IR = K + ΔK; IR = Ko + ΔKo; because IR = IR, then

K + ΔK = Ko + ΔKo; ΔK = Ko + ΔKo - K.

Determination of the gyrocompass correction

In order to reduce random errors, after the gyrocompass arrives at the meridian (at the parking lot), multiple bearing measurements are made every 10 - 15 minutes for 2.5 - 3.0 hours. Based on the measurement results, the average value of the GKP gyrocompass bearing is calculated:

GKPav = 1/p(GKP1+GKP2+GKP3+…+GKPp);

where n is the number of measurements.

Then the constant correction is determined:

ΔGK \u003d IP - GKPav.

At sea, the constant correction of the gyrocompass is determined at uniform motion ship. At the time of each measurement of the compass bearing, a high-precision observation is performed, relative to which the true bearing is calculated. For each gyrocompass bearing, the corresponding IP and the gyrocompass correction ΔGK are calculated. The average value of the correction is calculated by the formula

ΔGKav = 1/p(ΔGK1+ΔGK2+ΔGK3+…+ΔGKp);

where n is the number of measurements.

Determination of the magnetic correction

compass

The magnetic compass correction depends on the magnetic declination d and the deviation δ:

ΔMK = d + δ.

The declination changes with the ship's coordinates and over time, the deviation depends on the ship's heading.

Therefore, ΔMK, determined by comparing bearings, by alignment and by comparison, can only be used on the course on which it was determined.

In the general case, the correction of the magnetic compass is defined as the algebraic sum of the magnetic declination d, which is taken from the navigational sea chart and reduced to the year of navigation and the deviation δ, selected from the deviation table.

I bring to your attention a very interesting and useful post. Note the author's name. I think we'll hear from him again!

Every navigator encounters the Compass Observation Book daily. Let's figure out WHAT it is and WHY it is needed?

Compass Observation Book- This is a log of corrections for magnetic and gyro compasses. A completely logical question arises: “How often should this journal be filled out? And in general, what to write there?

For a better perception of information, you can download: Compass Observation Book Azimuth calculation

Let's figure it out in order. How often?- There are clear indications of this question in the well-known manual - "Bridge Procedures Guide", abbreviated as BPG (the Soviet equivalent - RShS - Recommendations for the organization of a navigation service on sea ​​vessels). Also, such instructions are probably present in MASTER’S STANDING ORDERS, and if you search carefully, you will also find in COMPANY SAFETY MANAGEMENT PROCEDURES in the Watch keeping section or similar in meaning. As you can see, the matter is serious and you still have to calculate the amendment :). In order not to be unfounded, here are a couple of quotes:

BPG Section3. Duties of the officer of the watch. Paragraph3.2.5.2. Routine tests and checks. Gyro and magnetic compass errors should be checked and recorded at least once a watch, where possible, and after any major course alternation.

BPG Section4. Operation and maintenance of bridge equipment. Paragraph4.6.3. Compass errors. Magnetic and Gyro compass errors should be checked and recorded each watch, where possible, using either azimuth or transit bearings. [Quoted from BPG 4th edition 2007].

Simply put, the navigator must calculate and enter the correction in the log at least once per watch, if possible. I pay special attention to the clause " ". This is where the first mistakes begin. Very often I met a similar entry instead of an amendment: “Sky overcast”. And the navigator's argument is ironclad at first glance. there were clouds." So, such an approach is doomed to failure, because. in such a case, a log entry must be made every watch by each assistant (ie at least 6 times a day), which, to tell the truth, I have never seen. Most often, you will see by dates that the amendment is either written down, or it is written that “... there were clouds ...” or even a couple of days, and sometimes even weeks, there are no records. And if the Port State Control Officer or any other inspector wants to find fault with you, he will do it with ease. Because it is clearly seen that the correction is not calculated once per shift, but, God forbid, at least once a day. It will be more competent to make only calculated corrections to the journal. And if at some time there is no information, then you can easily hide behind the very clause “ …if possible» = « …where possible…". And the proof that it was not possible is your records in the Bridge Log Book about the state of the weather, which are made every watch. With this approach, no one will ever tell you that you do not follow the rules for filling out the Compass Observation Book. As a corporate auditor once told me during an internal ISM audit - "...this is not weather log book.". So don't create evidence against yourself and only write what you need to.

We figured out the question of how often to record, now let's figure out what exactly needs to be written.

Inside the "Compass Observation Book" you will find the following table:

Columns 1, 2, 3. We write down the Greenwich time and the date of the observation, as well as the position of the vessel.

Column 4. Ship's Head. We record the course followed by the ship at the time of the observation. 4.1 Gyro- gyrocompass course, 4.2 standard– magnetic course. 4.3 Steering- the course according to the compass that you are currently following. For example, if you go on an autopilot using a gyrocompass, then you record the gyrocompass heading, i.e. value 4.3 = 4.1. I confess that once I came across a colleague who desperately proved to me that there is a third type of compass on the ship, which is called the steering compass. True, he could not find this unprecedented device and show it to me. Probably because it simply does not exist :). By entering data in column 4, you indicate which of the compasses you are currently following: magnetic or gyro.

Column 5. Bearing. 5.1 True is the true bearing to the object. To calculate it, you will need the notorious Brown's Nautical Almanac and Norie's Nautical Tables. Alternatively, you can still calculate the correction for "Rapid Sight Reduction Tables for Navigation", however, the accuracy then comes down to whole degrees. You can also see how colleagues consider the amendment by program (there are many of them, the most popular, perhaps, is sky mate). If you are too lazy to count according to the tables, then do not be too lazy to at least make sure that the program you are using is licensed for your ship or ship owner. Then, in case of verification, you will be able to refer to the calculations for this program, but if your "Sky mate" Licensed to: -=skyhacker1986=- or something like that, then it's better not to even stutter what you think about the program, and maybe you lucky. In general, be prepared for the fact that you will have to re-calculate your last correction in front of the inspector, this happens, albeit very rarely. In his lessons, Eugene (the author of the project, if someone did not understand) explained in more than detail and very clearly how to calculate the amendment. I confess that this knowledge was very difficult for me in my academic years - I ate more than one cobblestone of the granite of science, while I figured out what was what. So do not be lazy and watch the corresponding video tutorial.

Columns 5.2 and 5.3. Gyro bearing and magnetic bearing to the selected object. At first glance, everything is very simple, and it is not clear where you can go wrong. But before entering data into the column 5.3 Standard bearing make sure it is practical to find a bearing with a magnetic compass. I often met systems that allow displaying magnetic compass readings on the course indicator, then everything is clear, they switched to a magnetic compass and took a magnetic bearing. And if this is not possible, and in fact you are not able to take a magnetic bearing to an object, then it is better not to write anything in this column - put a dash.

To Column 6. Object. Write down the name of the celestial body by which you calculate the correction. To personalize your posts, you can also add an object symbol next to it. These symbols can be found in Brown’s Nautical Almanac on page 5. It is also worth noting that the correction can be calculated not only by the luminaries, but also by alignment, for example, or standing in the port - along the berth line.

Column 7. Error. So we come to the main part of the magazine, namely the amendments themselves. Gyro error= True bearing - Gyro bearing . Calculation standard error: if you took a magnetic bearing to a landmark, then the calculation is similar to the previous one: Standard error = True bearing - Standard bearing . If you put a dash in column 5.3, then the correction is calculated by comparing the true course and the magnetic one. The true heading is obtained by adding the gyro compass correction with its sign to the gyro heading: . We obtain magnetic compass corrections by subtracting the magnetic from the true course: . In column 7.3 we write down the correction of the compass that the ship is currently following (similar to column 4.3).

Column 8. Variation. Translated into Russian - magnetic declination, take from the map. There are also cases where variation taken from the indications of the GPS indicator. Here we are already talking about the level of trust in the sources of information. You can refer to the map data with a clear conscience - in most cases the maps are published by the UKHO (United Kingdom Hydrographic Office), but there is less confidence in the magnetic declination data taken by GPS, because. their source is not so well known, if known at all.

Column 9.1 Standard Deviation. The translation is obvious - the deviation of the magnetic compass. The deviation table immediately comes to mind, but do not rush to rejoice. As practice shows, the data between the real deviation and that indicated in the table are very different. There are many reasons for this, ranging from the influence magnetic field weight on the compass and ending with the banal human factor when compiling the deviation table. I personally saw several times on the courts tables, where all values ​​= zero, i.e. there was no deviation at all, which is a priori impossible. But there were plenty of bulky seals and beautiful sweeping paintings on the table, only there were not enough monograms and the official seal of the Queen of England :). How to be, you ask? So the answer is obvious, we will calculate the deviation ourselves. We recall the navigation course, where they said that the magnetic compass correction consists of magnetic declination and deviation. Thus, we get that Deviation = Standard Error - Variation . If the calculations were carried out correctly on the ship, then after some time, you can create your own deviation table, the confidence in which is directly proportional to the confidence in the calculations of your colleagues. I sincerely wish that life does not put you in conditions under which the value of the deviation of the magnetic compass will be essential for the safety of navigation. But anyway, all calculations and records should be made as competently as possible, otherwise why are you reading this article :)?

Column 9.2. If the vessel follows a magnetic compass, then the value is equal to the previous value. If you follow a gyrocompass, then we are talking about speed and latitude deviations, which are usually taken into account and corrected automatically by the gyrocompass. Personally, I put a dash in this column, because. whatever the value is, it is part of the already calculated Gyro Error.

Column 10. Heel. We are talking about the roll of the vessel, if you are shaking - write "+ -" a couple of degrees.

Column 11. Indicate from which pelorus you took the bearing (Port Repeater / Starboard Repeater). Surprisingly, but here you can make a mistake, for example, the ship follows due north, bearing the star on the right on the beam, then it would be correct to indicate that you took the bearing from the pelorus on the right wing, and not on the left :). This will seem obvious to many, but believe me, there have been cases of such recordings. You can see for yourself by looking through the magazine and studying the entries of the predecessors and you will understand how neglected everything is :). To tell the truth, this is what inspired me to write this article. Also, don't make stupid mistakes like taking the bearing of the sun at noon on a boat with covered wings, as this is clearly impossible and calls into question all entries in the journal as well as the competence of those who made them. And what could be worse for a navigator than a justified accusation of incompetence. So before you put your signature on any journal entry, make sure it's correct.

Well, since we are talking about signatures, it's time to put your beautiful autograph in the column 12.Observer and close the magazine until the next watch, provided " …if possible» = « …where possible…».

P.S. I am attaching a file to the article - Azimuth Calculation. In it you will find table forms for calculating the correction of the gyrocompass. The tables are created on the basis of the calculation algorithm given in Brown's Nautical Almanac on pages 12 and 13. Also, for convenience, lines have been added to continue calculating the correction for Norie's Nautical Tables (ABC tables). Print the forms, keep a separate folder and file the completed forms. You can also practice your eloquence skills and convince fellow navigators to use your innovation.

With respect, to all those who have read the article to the end :) Gusev Valery

Post updated by Evgeny Bogachenko after comments.

The fact is that Valery cannot promptly answer the question now, so for now I will write, and he will add it when he is in touch again. As I understand the question, I want to decide how much it is necessary to calculate the compass correction and keep a compass correction log.

First, ability to correct STCW required. These requirements include officers responsible for keeping a navigational watch on ships of 500 tons gross tonnage and over. Those. theoretically, with any check, they may be required to calculate the compass correction.

But that's not the point. That's why second. Amendments should be correctly applied (accounted for) to courses and bearings. And then the question is, how to take them into account, if not count? And if you do not keep a journal, then how to prove that the amendments were taken into account?

But captains and senior officers should not relax either. Since the requirements for them are no less stringent. Not a reproach, as I understand that everyone has a lot of work. However, I do not think that every captain and first mate will be able to immediately calculate the compass correction.

Well finally. When taking a watch, among all the points that must be taken into account, there is a mention of the corrections of gyro- and magnetic compasses. Again, you can be able to calculate the correction, you can verbally transmit its value. But then some inspector will rest and prove to him later without the Compass Correction Journal that everything was done.

I understand that you can take a folder and collect leaves with calculations there. At the same time, without filling the log. There is nothing to add here. Since I have not met a specific international requirement for the presence of a compass correction journal on the bridge. But there are Company Regulations, often you can find this requirement there. Yes, and try to prove to someone that this is how it is, and there is no need for anything else - a waste of time and nerves. There are so many extra entries on a ship, so many unnecessary procedures and reports to cover up one place, that the Compass Correction Log pales in their background.

Clippings of texts brought from STCW 2011. Additionally, I post for download the page from where I took these texts.

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

The angle at which the magnetic meridian deviates from the true meridian is called magnetic declination, or compass declination.

Magnetic declination, calculation for the year of navigation. MP, MK, WMD.

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

Magnetic heading - an angle in the plane of the true horizon, counted from the northern part of the magnetic meridian clockwise to the bow of the centerline of the ship;

Magnetic bearing– angle in the plane of the true horizon, counted 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's magnetism and its influence on the readings of the magnetic compass. Compass meridian Deviation of the magnetic compass. compass meridian. Deviation of the magnetic compass. Deviation table. KK, KP, OKP. Relationship between compass and magnetic heading.

The steel frame of the vessel, its plating acquire magnetic properties from the moment of construction and are preserved for years. The compass is influenced by the magnetic forces of magnetically hard and soft iron, and their action is different. In addition, the compass is affected by the 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 nordic part and the magnetic meridian to Ost or to W from 0 to 180. According to the nature of occurrence, semicircular, quarter and roll deviations are distinguished.
Semicircular - is created by magnetically hard iron, quarter - by soft, roll occurs during pitching. The compass meridian is an imaginary line of intersection of the observer's true horizon plane with the compass meridian plane passing through given point on the ship.

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

The main axis of a working gyrocompass is always set in the plane of the so-called gyroscopic or compass meridian. The angle between the true and gyroscopic (or simply compass) meridians is called the correction of the gyroscopic compass.

In cases where the north part of the gyroscopic meridian deviates from the true meridian to the east, the gyrocompass correction is assigned a plus sign, and vice versa, when the north part of the compass meridian deviates from the true meridian to the west, the gyrocompass correction has a minus sign.
Consideration of the figure allows, when using a gyrocompass, to establish a relationship between true and compass directions, expressed by the formulas:

IR \u003d QC gk + ΔGK
IP \u003d KP gk + ΔGK (28)

The correction of the gyroscopic compass and its sign are determined by the formulas:

ΔGK \u003d IR - QK gk
ΔGK = IP - KPgk

The correction of the gyrocompass, generally speaking, consists of two components - a constant and a variable. However, here we will not consider its components and the reasons that give rise to them. This is studied in the theory of gyrocompasses. We will consider only the result - the deviation of the gyrocompass axis from the plane of the true meridian and consider this angle as the gyrocompass correction ΔGK, which should correct all measured directions if you need to get the true ones.

When using a magnetic compass, the compass correction will be the angle enclosed between the north part of the true meridian and the north part of the compass meridian. The correction of the magnetic compass ΔMK can be positive when the compass meridian is deviated from the true one to the east, and negative when the compass meridian is located to the west of the true one.
The correction of the magnetic compass, as can be seen from the figure, is the sum of its two components: the magnetic declination and the deviation of the magnetic compass

Calculation of true directions by known compass directions and correction of the magnetic compass is carried out according to the formulas:

IR \u003d QC MK + ΔMK
IP \u003d KP MK + ΔMK

Example 1. Taken from the map d = -4.5°; KK MK = 217.0°; deviation selected from the table, δ = +1.8°. Calculate the value and sign of Δ MK.
Solution. Δ MK \u003d - 4.5 ° + 1.8 ° \u003d - 2.7 °.

Example 2. The compass bearing to the beacon KP MK = 44.5° was measured from a ship sailing KK MK = 70.0°. For laying on the map, you need to know the IP for the lighthouse.

Solution. On the KK, we select the deviation from the table above: δ = - 1.5 °, and remove the declination from the map on which it is given to the year of navigation: d = - 2.4 °.
We find Δ MK = d + - 3.9 °; IP \u003d KP MK + ` MK \u003d 44.5 ° + (- 3.9 °) \u003d 40.6 °.

The compass correction, regardless of its type, is determined from observations by comparing the true directions (courses and bearings) with the observed compass (or reverse compass) directions:

Δ MK \u003d IP - KP MK
Δ MK = OIP - OKP MK
Δ MK \u003d IR - QC MK
Δ GK \u003d IP - KP gk
Δ GK \u003d IR - KK gk (32)

When using a magnetic compass, when to determine its correction on a given course by direct. observations are not possible, the latter is calculated by formula (30) on the basis of the magnetic declination calculated for the year of navigation and the deviation selected from the table for a given compass heading.
In the practice of navigation, the following methods for determining the compass correction can be applied:
- according to the bearing of the alignment, the true direction of which is known;
- according to the bearing of the landmark, the place of which is marked on the map;
- by comparison with another compass, the correction of which is known;
- according to the bearing of the heavenly body.

Determination of the compass correction by the alignment bearing. This method of determining the compass correction is the simplest. The essence of the method lies in the fact that at the moment of crossing the target, the compass or reverse compass (when using a magnetic compass) bearing of the target is measured. The compass correction is then obtained by comparing the true direction of the alignment with its measured compass direction (see figure):

Δ GK \u003d IP - KP gk

Δ MK = OIP - OKP MK

The values ​​of the true and reverse true directions of the alignments (PI, RIP) are usually shown on nautical charts along the alignment line. The true directions of the alignments are also indicated in the sailing directions. In some cases, when the direction of the alignment is not shown on the map, it can be easily measured using a protractor and a ruler.
To improve the accuracy of measuring the compass bearing, it is recommended to keep the rear alignment mark in the plane of sight as you approach the alignment and carefully observe the arrival of the front mark on the line of sight. At the moment when the signs (beacons) are created, that is, they are on the same line, the countdown of the compass bearing is noticed. If the ship crosses successively several alignments, then repeated observations on other alignments and subsequent calculations of the compass correction on all crossed alignments will make it possible to increase the reliability and accuracy of determining the compass correction. The most probable compass correction value in this case is calculated as the arithmetic mean of the results of all observations. If it is necessary to determine, together with the general correction, the deviation of the magnetic compass, the latter can be calculated as follows. The value of the magnetic declination for the area where the compass correction is determined is taken from the map. Then, according to the total compass correction calculated from the observations and the magnetic declination, the deviation is found using the formula

δ \u003d Δ MK - d.

Determination of the compass correction by the bearing of the landmark, the place of which is plotted on the map. The essence of this method is to compare the true bearing to a distant object with the compass bearing measured on it. For this, it is necessary that the positions of the spacecraft and the observed object (i.e., their coordinates) at the moment of observation be known. The true bearing from the ship to the lighthouse can be calculated (with the known coordinates of both) analytically or taken directly from a large-scale map, the compass bearing is measured using a compass. Then the compass correction to be determined can be found by the formulas

Δ MK \u003d OIP - OKP MK - for a magnetic compass
and
Δ GK \u003d IP - KP GK - for a gyroscopic compass.

Due to the fact that the place of the observed landmark, as a rule, is known with high accuracy, the error in the determined compass correction depends mainly on how accurately the ship's revenge, i.e., its coordinates, is known. Therefore, the method under consideration for determining the compass correction is most often used when the ship is anchored in a harbor or in a roadstead, when the ship's position can be determined with high accuracy. On the move, this method can be applied only when there is a real opportunity to determine your place with an error not exceeding 25 - 50 meters.

The choice of a sufficiently remote landmark, when the compass correction is determined from the anchorage, should be made in such a way that the change in bearing due to the deployment of the ship on the anchor chain does not exceed the permissible error in the determined compass correction. Taking the permissible error in determining the bearing m p \u003d ± 0.2 ° and the radius of the turning circle of the ship on the anchor chain r \u003d 50 m, we find the minimum distance D min from the ship to the observed landmark, at which it is possible to apply this method of determining Δ K:

D min = r * ctg m p = r / tg m p = r / m p *arc 1° = 50 * 57.3° / 0.2° = 8 miles.

Therefore, in order to determine with an error not exceeding m p \u003d ± 0.2 ° the compass correction from the anchor position to a distant landmark, you need to choose the latter at a distance of at least 8 miles from the place of the ship.
If for some reason it is not possible to measure the compass bearing, but the KP can be measured on it, then the desired KP can be calculated by the formula

KP = KK + KU

In this case, simultaneously with the measurement of the heading angle to the landmark, it is necessary to notice the compass heading.

Determination of the compass correction by comparing the readings of two heading indicators. The correction of a compass can be determined by comparing its readings with those of another compass whose correction is known. The essence of the method lies in the fact that at the same moment, the courses on both compasses are noticed on the signal. After observations, the readings of the second compass are corrected by its correction, and from a comparison of the calculated true heading with the observed compass heading of the studied compass, the desired correction is found

CC gk + ΔGK = IR;
IR - QC MK = ΔMK
Δ MK \u003d (KK gk - KK MK) + Δ GK

The difference between the simultaneously observed readings of the courses of two compasses (KK gk - KK mk) is called a comparison.
Thus, the determined compass correction is equal to the comparison plus the correction of the compass with which the comparison is made. The example shows the procedure for determining Δ MK by comparison with the GC, although in principle it is possible to compare the readings of any heading indicators. It is only important that the correction of one of them be known. Most often, this method determines the magnetic compass correction.

Determination of the compass correction by the bearing of the celestial body. The essence of the method is that the compass correction is found as the difference between the calculated true bearing by heavenly body(Sun, Moon, planet, star) and the compass bearing observed on it. The calculation of the true bearing of the luminary at the time of observing the compass bearing is carried out according to the formulas of spherical trigonometry using special tables. are given. The results of calculating the true bearing (PI) to the luminary and observing it with the help of a compass (KP) are implemented to obtain the desired compass correction using formulas (32).

§ 16. Calculation of compass, magnetic and true directions

In the practice of ship navigation, when determining (calculating) directions, two types of problems have to be solved:
- according to the known compass directions, determine the true directions for further use in the laying;
- according to the given (taken from the map) true directions, calculate the corresponding compass directions.
The navigator encounters the first task most often when plotting courses and bearings on the map based on the results of observations. The second task corresponds to the cases when it is required to calculate the compass course for the helmsman, holding which the ship will follow the given true course. The same problem has to be solved when it is required to calculate, for example, a compass bearing to a landmark corresponding to the place where the ship begins to turn to a new course. The solution of problems of the first type is sometimes called the correction of directions or the correction of points, the solution of problems of the second type is called the translation of directions or the translation of points. The calculation of the true directions is made according to the formulas, and if necessary, a drawing is built. All formulas necessary for this are derived in the previous sections. When solving problems, magnetic declination, deviation, and compass correction should be considered as appropriate corrections, which must correct incorrect, i.e., containing errors, directions in order to obtain correct, true directions.

It is useful to remember that in order to obtain the correct value, the correction must be applied with its sign to the incorrect (containing an error) value. In relation to the categories we are considering, true directions relative to magnetic and compass should be considered true, and magnetic directions relative to compass. To correct the compass heading and compass bearing observed by the gyroscopic compass (repeater), it is enough to apply the gyrocompass correction to them and the corrected true heading and true bearing will be obtained:

IR \u003d QC gk + Δ GK
IP \u003d KP gk + Δ GK

To correct the compass heading and compass bearing observed with a magnetic compass, it is necessary, firstly, to select the deviation from the table (by the KK argument), and remove the magnetic declination from the map. Having given the deviation and declination to the observed compass heading and bearing, the corrected (true) heading and bearing are obtained:

IR \u003d QC MK + d + δ \u003d QC MK + Δ MK;
IP \u003d KP MK + d + δ \u003d KP MK + Δ MK.

It must be firmly remembered that when calculating the true directions, only the compass heading serves as an argument for choosing the deviation from the table, since the deviation of the magnetic compass depends on the compass heading. When correcting compass (or reverse compass) bearings, the deviation from the table must be selected for the compass course followed or on which the ship was when the bearing was measured,
The drawing is drawn in this sequence. A straight line N k - S k is drawn, denoting the compass meridian, on which an arbitrary point K is selected - the place of the compass on the ship. Through the selected point by eye at an angle equal to the compass course relative to the compass meridian, a line of the ship's course is drawn. At angles equal to the deviation selected from the table and the known declination, taking into account their signs, the magnetic and true meridians are drawn. Finding after such constructions the magnetic and true directions according to the completed drawing will not be difficult.
It is recommended to start building a drawing by drawing a compass meridian line. This is suitable for cases where compass directions are given as given values. In other cases, the construction of a drawing should be started from that meridian, the position of which is given by the course or bearing.
The transition from true directions to directions relative to the compass or magnetic meridian is carried out in this way. Based on the known true course and declination, the magnetic course is calculated. With the found magnetic course, they enter the deviation table and from it the deviation of the magnetic compass is selected according to the MK argument, since the KK is the desired one.
According to the calculated magnetic course and the deviation selected from the table, the desired compass course is found. For calculations that do not require high accuracy, one can restrict the choice of deviation, as mentioned above, to the magnetic heading. In this case, we obviously make some mistake, since the selected deviation will not exactly correspond to the found compass course. To improve the accuracy of solving the problem, we can recommend the use of the method of successive approximations. The essence of this method as applied to the problem under consideration is as follows. With the approximate deviation selected for the magnetic heading, an approximate compass heading is calculated. For this approximate compass heading, the corrected deviation is selected from the table. From the corrected deviation and the known magnetic heading, an improved compass heading is calculated, which can then be used again to select a more accurate deviation. Usually subsequent approximations are unnecessary, since they will improve the result by no more than 0.1-0.2 °.
Drawing up a drawing illustrating the task of calculating directions begins with drawing the N and - S lines on the drawing plane and denoting the true meridian, then the course and bearing lines are built relative to it; the construction ends with finding the compass and magnetic directions. The basis of the correct construction of the drawing is the correct drawing of the magnetic and compass meridians on the drawing according to the found magnetic declination and deviation of the magnetic compass.

Example 1. KK MK = 104.0°, d = + 6.6°, δ - from the table. Calculate IC.

Solution. IR \u003d QC MK + d + δ \u003d 104.0 ° + (+ 6.6 °) + (- 3?5 °) \u003d 107.1 °.

Example 2. IR = 216.0°, d = - 5.4°, δ - from the table. Calculate QC mk

Solution. MK = IR - d = 216.0° - (-5.4°) = MK = 221.4°.
From the deviation table, select MK = 221.4° δ = + 2.1°. KK" \u003d MK - δ " \u003d 221.4 ° - (+ 2.1 °) \u003d 219.3 °.
This is the first approximation. From the deviation table on KK" = 221.4 ° we select the deviation.
KK"" \u003d KK" + δ "" \u003d 219.3 ° + 2.0 ° \u003d 219.4 °.
Answer: KK MK \u003d 219.4 °.

Chapter 3

DETERMINATION OF THE SPEED OF THE SHIP, THE DISTANCE PASSED BY THE SHIP, AND THE LAG CORRECTIONS

§ 17. Determination of the distance traveled by the ship by speed and duration of navigation

Continuous recording of the movement of a ship navigating on the water surface of the Earth is necessary to determine its location at any time. To keep such records, it is necessary to know the direction of the ship's movement and the distance traveled by the ship in this direction. The direction of the ship's movement is determined using the ship's course indicators. The distance S traveled by the ship can be determined in several ways, one of which is to calculate the distance traveled by the formula
S = Vt (33)
The duration of the voyage t is determined using ship time meters (clocks, stopwatches). The speed of the ship can be obtained either from the Table of correspondence between the speed of the ship and the number of revolutions of the propellers, compiled on the basis of special tests, or from the readings of the lag.
The speeds of the ship at different revolutions of the propellers (propellers) are periodically determined on the measured line (special range). Measuring lines are located near the ship bases in areas that allow the necessary freedom of maneuvering and ensure the required accuracy of measurements. The landfill should, if possible, be sheltered from the effects of wind and sea waves from the directions prevailing in the area; the depth of the sea on the run line must be sufficient so that the determined speeds are not affected by the influence of shallow water; on the test site there should not be sharply variable currents with significant speeds; The polygon equipment must correspond to the chosen method for determining velocities. Speeds can be determined in various ways, which are reduced to measuring the time intervals and distances traveled by the ship during these intervals.


On the measuring line (see figure), the directions and lengths of the runs are determined in advance and fixed in place by a system of shore markers or floating equipment that facilitates observations.
To measure distances with the help of a radar station, special passive reflectors are installed at the range or local point reference points are used, which are clearly visible on the radar screen and plotted on a map.
To obtain high-precision observed places of the ship, between which the distances are then measured, it is necessary that the test site is in the coverage area of ​​high-precision radio navigation systems, and the ship has the appropriate receiving and indicating devices.
To determine velocities using a hydroacoustic station, it is necessary that the test site be equipped with underwater emitters or sound receivers. If neither one nor the other is available at the test site, ships installed in strictly defined places and armed with hydroacoustic stations can be used as a transmitter (or receiver).

Thus, the methods for determining the speed of a ship on a measuring line differ from one another only by means and methods of measuring the length of the run line.
The most accurate travel speeds are determined on a measuring line equipped with several parallel secant sections, the sensitivity of which ensures accurate fixation of the moments of their intersection. The direction of the run line, on some polygons, is indicated by the leading alignment (figure) or a number of milestones. The distance along the run line between the secant alignments is determined on the basis of accurate geodetic works. .
To determine the speed on the measured line, the ship lays down on the course according to the compass with the expectation to go along the line of milestones or the alignment perpendicular to the secant alignments and develops the specified number of revolutions of the propellers. At the moment of crossing the first secant target, the stopwatches are started and with the arrival of the ship to the next target, the stopwatches stop. Based on the duration of the run t and its length S, the speed of the ship V is calculated in knots on a given tack according to the formula

V = S * 3600 / t (34)

where S is the length of the run in miles; t - travel time in seconds.
As a rule, the velocity calculated by formula (34) contains some error due to the influence of the unaccounted current acting in the region of the measuring line. To eliminate the influence of the current, not one run is made in each mode of movement, but two, three or four. With a constant flow (when its speed and direction remain unchanged during the tests), two runs are made on mutually opposite tacks. According to the results of measurements on two runs, the travel speed, free from the influence of a constant current, is calculated by the formula

V = (V 1 + V 2) / 2 (35)

where V 1 and V 2 - travel speeds at given number propeller revolutions, determined by the results of measurements on the first and second runs. The number of propeller revolutions N at a given engine operation mode is also determined as the average of those observed on both runs

N \u003d (N 1 + N 2) / 2 (36)

If the current in the region of the measured line does not remain constant, but changes uniformly, then three runs are made in succession (in one direction, back and again in the original direction); speed, free from the influence of the current, and the corresponding number of revolutions of the propellers are calculated by the formulas:

V = (V 1 + 2V 2 + V 3) / 4
N = (N 1 + 2N 2 + N 3) / 4 (38)

In cases where the speed of travel is required to be determined with increased accuracy or there is reason to believe that the speed of the current in the area of ​​the polygon changes unevenly, it is necessary to make four runs (alternately in the forward and reverse directions). Wherein average speed, free from the influence of the current, and the corresponding number of revolutions are calculated by the formulas:

V = (V 1 + 3V 2 + 3V 3 + V 4) / 8 (39)
N = (N 1 + 3N 2 + 3N 3 + N 4) / 8 (40)

All runs under a given mode of operation of the machines should be made along the same line. This is due to the need to maintain as much as possible the same conditions on all tacks.
In the above sequence, observations are made and the average speeds (free from the influence of the current) and the corresponding number of propeller revolutions are calculated for several main engine operating modes. Based on the results of processing the measurement materials, a graph of the dependence of the speed of the ship on the number of revolutions of the propellers is constructed. The chart is built in rectangular system coordinates: the abscissa shows the average speeds in knots, and the ordinate shows the average number of propeller revolutions for a given mode of operation of the machines. Through the points corresponding to the results of processing observations, the curve V = f (N) is drawn for the dependence of the speed V on the number of revolutions N of the propellers. To achieve the necessary reliability, this curve must be plotted at least five points. With a smaller number of points, the graph should be considered approximate.
From the drawn graph, data is taken to compile the Table of correspondence between the speed of the course and the number of revolutions of the propellers (propellers), placed in the navigation log. This table is usually compiled for various speeds with an interval of one knot at the normal displacement of the ship.
The table of correspondence between the speed of the propellers and the revolutions of the propellers allows you to set the speed developed by the ship by the number of revolutions of the propellers. Based on the known time of the ship's movement at a given speed, it is not difficult to calculate the distance traveled using formula (33). It is convenient to make this calculation on a slide rule or using tables 27-a, 27-6 MT (nautical tables).
The number of revolutions of the propellers on the trip may differ slightly from the specified one, so it needs to be controlled from time to time. To determine the actual number of revolutions of the propellers, tachometers or total counters are used. When using tachometers, control readings of the number of revolutions should be taken several times after 5 or 10 minutes, and then the average number of revolutions per minute should be taken.
When using total counters, readings on them are made at the beginning and at the end of an hour or half an hour.

Table of stroke speed correspondence to the number of revolutions of the screws

(Normal displacement G _n= 12,000 tons)

Full stroke	Average stroke	Slow move
nodes	propeller revolutions	nodes	propeller revolutions	nodes	propeller revolutions

Based on the difference in readings of the total counters, the number of revolutions of the screws per minute is calculated. If the number of propeller revolutions, determined using tachometers or total counters, does not correspond to the table, then the speed of the ship is selected from the table by linear interpolation.
When calculating the distance S traveled by the ship according to the speed V and the duration t of its navigation, it must be remembered that the speed selected from the table characterizes the movement of the ship relative to the water. The tabular data does not take into account the factors that affect the ship's speed: current, wind, waves, displacement and draft deviations from normal, roll and trim, hull fouling and shallow water. The effect on a moving ship of any of the listed factors or any combination of them leads to the fact that the actual speed of the ship at the transition differs from the speed selected from the Table (as a rule, in a smaller direction). Consequently, the distance S calculated from the speed V and the duration of navigation t contains an error, the value of which depends on how different the actual conditions of this navigation are from the conditions under which the speeds were determined on the measuring line. Greater than according to the tables, accuracy in determining the distance traveled by the ship can be achieved by using a lag for this purpose.

§ 18. Determination of the distance traveled by the ship according to the readings of the lag

To determine the speed and distance traveled by the ship, they mainly use hydrodynamic logs, the operation of which is based on the principle of measuring the hydrodynamic pressure arising from the movement of the ship and changing according to the change in its speed.
The receiving device of the hydrodynamic log has two channels, through one of which the static pressure is transmitted to the sensitive element, depending only on the draft of the ship, and on the other, the total pressure, including, in addition to the static component, the component of the dynamic pressure, depending on the speed of the ship. Water pressure through both channels of the receiving device enters the sensing element, which is a chamber divided by a diaphragm into two cavities - lower and upper. The lower cavity of the chamber is connected by a pipeline to the channel receiving the total pressure, and the upper cavity - to the channel receiving the static pressure.
When the ship is at rest, the pressure in the lower cavity of the chamber is balanced by the pressure in its upper cavity, since both cavities receive static pressure due to the draft of the ship, and the diaphragm remains stationary. When the ship moves in the lower cavity of the chamber of the lag sensing element, an excess pressure is formed, proportional to the square of the speed, which is converted into a mechanical force that drives the lag compensation device, which generates the value of the speed in knots.
The value of the distance traveled as a function of speed and time is generated in the log by the integrating mechanism.
Another type of logs, fundamentally different from hydrodynamic ones, are spinner logs, the sensitive element of which is a spinner fired under the bottom of the ship. When the ship moves, the oncoming flow of water presses on the blades of the turntable and makes it rotate. The number of revolutions made by the spinner is proportional to the distance traveled by the ship. The rotation of the spinner is transmitted to a special counter, which records the number of revolutions of the spinner and converts it into the distance traveled by the ship. The distance meter scale is graduated in nautical miles. With the help of a special calculating mechanism, the distance traveled is converted into speed, which is shown on the counter in knots.
Hydrodynamic and spinner logs, as follows from their brief description, show the distance traveled by the ship relative to the water. These lags do not take into account the displacement of the mass of water itself.
The distance S l traveled by the ship is obtained from the log as the difference between two readings (ol 2 - ol 1) corresponding to the observation times T 2 and T 1 . Regardless of the design, any log shows the distance traveled and the speed of the ship with some error. The error in the indications of the distance traveled is relative and accumulates proportionally distance traveled. The magnitude of this error is different for different speeds of the ship.
To compensate for the error in the readings of the lag when calculating the distance traveled by the ship, it is necessary to introduce a lag correction into the difference in readings (the difference in readings of the lag rol = ol 2 - ol 1). The lag correction is the numerical value of the error in the indications of the counter of the distance traveled by the ship, taken with the opposite sign and expressed as a percentage of the difference in the readings of the lag.

After I started working under contracts, quite often they got some methods accepted all over the world, but completely different from the methods of the former Soviet Union. One such technique is to determine the compass correction. Knowing the compass correction is both an international requirement and often a company requirement, and just as no nation can claim to be a genius, so no nation is immune from stupidity. Was in a company in which it was required to determine compass correction every watch, and if this was not possible, then there should have been a mandatory entry in the log about the reason for the failure.

Nobody disputes that the most effective method determination of the compass correction by alignment. But what to do on the high seas? In fact, only astronomical methods remain.

The idea to somehow improve the process of determining the compass correction was prompted by my third, who regularly came to my watch and was engaged in taking the bearings of sunrise and sunset. After that, he toiled for about half an hour over some wild calculations. I had to look for a steamer in the nearest port, on which the forgotten MT-75 tables would be preserved. I made photocopies of the necessary pages and explained how to use them to the Filipino, who was our third navigator. His gratitude knew no bounds.

Maybe someone remembers, in MT-75, explanations are given for each table with the formulas by which this table was calculated. Therefore, the second stage of my activity in this direction was the translation of the table for determining the compass corrections into electronic form, namely in EXCEL. Still, it’s easier to carry one laptop for a contract, rather than a bunch of paper. After arriving on the ship, I printed out these tables and then used a paper copy.

But there were various routine actions that increased the calculation time. For example, when calculating, degrees and fractions are used to enter the table, and not degrees and minutes. It would seem that it is easier to divide minutes by 60 - you will get fractions of a degree. But all this is again an extra action, and therefore extra time spent. A more difficult stage is interpolation between adjacent table values, which already takes much more time, and at which the probability of making an error increases significantly. Why do all this if EXCEL spreadsheets will do it all for you? Therefore, the second stage of my automation was the programming of all these routine actions.

The third stage of automation is also possible - this is when the declination of the Sun will be automatically calculated. But this stage too complicated to implement it in practice, and it is completely unnecessary, because on any ship you can easily find the Nautical Astronomical Yearbook (MAE), because its presence on board is also an international requirement. It can be either a stand-alone publication or part of some other book. For example, MAE is included in Brown's Almanac.

So, if you are interested in this technique, then the calculation procedure is as follows:

Take the bearing of the upper edge of the sun at the time of sunset/sunrise

Record given bearing, latitude and time

Time to convert to Greenwich and use it from MAE to determine the declination of the Sun

Enter the required data in a spreadsheet and get the result

For example, this whole calculation takes me less than a minute. It is only necessary to remember that the MT-75 tables were calculated for predefined values, i.e. standard refraction, horizon visibility range, etc., but in most cases, the calculation error does not exceed 0.1 degrees, which is much less than the bearing error. And who needs special accuracy? The main thing is that if you use this method regularly and get about the same compass correction and suddenly get some incredible value, then there are quite a few options. Either you entered the wrong data, or something happened to nature, or your compass is about to be covered.