Military topography. Directional angle and azimuths

Zones of rectangular coordinates and direction to a landmark. Directional direction angles with an accuracy of 1-60 arc seconds can be determined by geodetic, astronomical and gyroscopic methods, as well as by space geodesy methods.

Approximate values of directional direction angles with an accuracy of the order of 10-25 arc minutes can be calculated from the value of the magnetic direction azimuth, which is determined using a reference compass, which is included in the set of additional equipment for theodolites and tacheometers. The reference compass is designed to determine magnetic azimuths of directions. To move from the magnetic azimuth to the directional angle, it is necessary to know the compass correction (PB), which is determined, as a rule, at the initial geodetic point in the area where the work is being performed...

The directional angle of direction to a landmark can be calculated by solving the inverse geodetic problem if the plane rectangular coordinates of the starting point and the landmark are known.

Directional angles of directions can be measured with an accuracy of about 30-60 arc minutes from a topographic map using a protractor. When measuring directional angles on a topographic map, you can use the following definition of directional angle: directional angle ɑ is the horizontal angle, measured clockwise from 0° to 360°, between the north direction of the vertical line of the kilometer grid of flat rectangular coordinates and the direction to the landmark.

The directional direction angle can be approximately determined with an accuracy of about 0.5-3 angular degrees on the ground based on the value of the magnetic azimuth of the direction measured using a compass by entering a direction correction (DC) into the measured value of the magnetic azimuth, taken from topographic map on the date of observation.

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See what “directional angle” is in other dictionaries: directional angle - The angle between the direction passing through a given point and a line parallel to the abscissa axis, measured from the north direction of the abscissa axis clockwise. Note Depending on the choice of surface coordinate system or projection... ...

Technical Translator's Guide - (by this, see previous page). Direction angle. Dictionary, included in the Russian language. Chudinov A.N., 1910. DIRECTIONAL ANGLE Direction angle. Explanation of 25,000 foreign words that came into use in the Russian language, with the meaning ... Dictionary of foreign words of the Russian language

- (from Latin directio, gen. case directionis direction * a. directional angle; n. Richtungswinkel, Richtwinkel; f. angle directeur; i. azimut del cuadriculado, angulo director) the angle between a line parallel to the x-axis of a rectangular... ... Geological encyclopedia

See what “directional angle” is in other dictionaries:- The angle between the north direction of the vertical grid line and the direction towards the object, measured clockwise... Dictionary of Geography

Between the north direction of a straight line parallel to the x-axis in a system of rectangular coordinates on a plane (projection, topographic map), and the direction to a given point; counted clockwise from 0 to 360.. Used in... ... Big Encyclopedic Dictionary

Directional angle- PARAMETERS OF GROUND NAVIGATION INFORMATION 4. Directional angle According to GOST 22268 76 Source: GOST 19156 79: Ground-based odometric navigation equipment. Terms and Definitions … Dictionary-reference book of terms of normative and technical documentation

- (from the French direction direction) an angle characterizing the direction of an arbitrary straight line relative to the original direction and, in particular, relative to the coordinate axis. In geodesy, a distinction is made between geodesy. on an ellipsoid and D. at. on the plane (projection... Great Soviet Encyclopedia

See what “directional angle” is in other dictionaries:- direkcinis kampas statusas T sritis Gynyba apibrėžtis Kampas pagal laikrodžio rodyklę tarp linijos, lygiagrečios su žemėlapio koordinačių tinklo vertikaliąja linija (ašiniu kartografinės projekcijos dienovidiniu), šiaurinio galo ir stebėjimo… … Artilerijos terminų žodynas

Directional angle (α) - this is the angle between the direction to the landmark passing through a given point and a line parallel to the abscissa axis, measured from the northern direction of the abscissa axis clockwise from axis 0 to 360°.

Figure 1. — Directional angle.

Directional angles of directions are measured mainly from a map or determined from magnetic azimuths.

The directional angle of the reference direction can be determined geodetic or gyroscopically, from astronomical observations, using a magnetic compass needle and from contour points on a map (aerial photograph).

With the geodetic method of orientation, the directional angle of the reference direction can be obtained directly from the catalog (list) of coordinates, by solving the inverse geodetic problem using the coordinates of geodetic points, when making intersections or laying a polygonometric traverse simultaneously with determining the coordinates of the anchored points, as well as by transferring the angular traverse from the direction with a known directional angle.

With the gyroscopic method of orientation, the true (astronomical) azimuth of the reference direction is determined using a gyrocompass, and then proceed to the directional angle of this direction. The azimuth of the reference direction using a gyrocompass is determined by two, three (four) reversal points. Increasing the number of reversal points to three (four) provides control and increases the accuracy of determining the directional angle.

With the astronomical method of orientation, the directional angle of the reference direction is determined by moving from the azimuth of the luminary to the azimuth of the reference direction, and from the latter to the directional angle. The azimuth of the luminary is calculated from the results of observations made on the ground from a given point. The azimuth of the reference direction from astronomical observations can also be obtained using the ANB-1 azimuthal attachment to the PAB-2A compass directly on the ground without performing calculations.

The method for determining the directional angle of the reference direction from astronomical observations is the most accurate.

Work in the field with this method consists of measuring the horizontal angle Q between the direction towards the luminary and the given direction at the moment of pointing the device at the luminary. Based on the time of observation of the luminary, the azimuth is calculated A luminaries, from it they move to the astronomical azimuth A directions to landmark: A' = a + Q. Knowing the meaning of the convergence of meridians at at the observation point, determine the directional angle from the reference direction: a = A - y.

When determining the directional angle of the reference direction using a magnetic needle, compasses on the ground are first obtained magnetic azimuth reference direction, and then, taking into account the correction of the compass, move on to the directional angle. The directional angle of the reference direction is determined by the formula: a = At + (±dAt).

Using a map (aerial photograph), the directional angle of the reference direction is obtained by solving an inverse geodetic problem using the coordinates of two contour points. The coordinates of the contour points are determined from a map (aerial photograph) using a measuring compass and a transverse scale. The greater the distance between the starting and reference points and the more accurately the coordinates of these points are determined, the higher the accuracy of the resulting directional angle.

The directional angle on the map can also be determined using a chord angle meter. To do this, identify the starting and reference points on the map, draw a straight line through them and get the reference direction on the map. By measuring the angle between the northern direction of the vertical line of the map's kilometer grid and the reference direction using a chord angle meter, the directional angle of this direction is obtained.

Properties of directional angles: directional angles α 1 =α 2 =α 3 since parallel lines intersect with one line. Therefore, the angles are equal.

Figure 2. — Directional angles.

Directional angles can be direct or reverse (they differ by 180°):

Figure 3. - Direct and reverse directional angles.

Depending on the choice of the surface coordinate system or the projection of the earth's ellipsoid onto the plane, the directional angle may have its own name. For example, geodesic directional angle, Gaussians directional angle, etc.

Directional

DIRECTORIAL oh, oh. direction f. 1 . ABOUT tn. to the directorate. Sl. 18. The provincial government is just as guilty, and they... for it is a directorate. Letters from the Masons 35. Ivan Arnoldiy, who is at the Theater Directorate in the position of treasurer... is to be dismissed from the directorate service. ATD 398. If only one objects, in this case it is possible for any member of the directive or private Commission, which composed the project, to defend it before the meeting, and verbally refute the opinion of the contradictory, and then proceed to the balls in discussing that article. Ek. II. // Bibikov Zap. 111. Directional. 1799. AIT 1 3 3. Gedeonov, although he agreed that “children’s theater performances can have a significant impact on city directorate performances,” nevertheless referred to the highest approved position of the directorate of the imp. theaters Driesen Mat. 1913 232. Yesterday's unprecedented gathering for ours continued to serve as a topic of conversation for the entire troupe, and according to the old director's records, it turned out to be a record gathering. 1916. D. Alperov In the arena. // Bogoroditskaya 328.

2. obsolete, military Guiding, pointing, orienting. The fourth should serve as a directional column, for it goes along the Brailovskaya road. 1809. Kutuzov 3 146.

Historical dictionary of Gallicisms of the Russian language. - M.: Dictionary publishing house ETS http://www.ets.ru/pg/r/dict/gall_dict.htm. Nikolai Ivanovich Epishkin [email protected] . 2010 .

See what “directional” is in other dictionaries:

directional- DIREK IYA, and, f. Governing body of what enterprises, institutions, educational institution, headed by a director or directorate. Discuss what n. at the directorate (at a meeting of the directorate). D. exhibitions. Dictionary Ozhegova. S.I. Ozhegov, N.Yu.... ... Ozhegov's Explanatory Dictionary

directional- directorial... Russian spelling dictionary

directional - … Spelling dictionary of the Russian language

Directorate District Leipzig- Direktionsbezirk Leipzig Coat of arms Federal state: Saxony ... Wikipedia

Directional angle- Directional angle is the horizontal angle, measured clockwise from 0° to 360°, between the northern direction of the parallel to the axial meridian of the rectangular coordinate zone and the direction to the landmark. Directional angles of directions with ... ... Wikipedia

INTRODUCTION

When considering the issue “Polar and bipolar coordinate systems”, it was noted that the location of any point is determined position angle , measured from the polar axis to the direction to the determined point, and distance from the pole to this point.
The following can be taken as the polar axis: the true or magnetic meridian, the vertical grid line and the direction to any landmark. Position angles measured from the true and magnetic meridians are called respectively true And magnetic azimuths . Angles measured from the vertical grid line - directorial corners . Angles measured from the direction to the landmark are called horizontal corners .
When surveying, designing and constructing forestry and gardening facilities, it is necessary to orient the axes of the objects under construction (forest roads, clearings, protective forest plantations, etc.).
Orient the line - this means determining its direction relative to the original, given or known direction. As initial directions in geodesy, the directions of the true (geographical) meridian, the direction of the magnetic meridian, and the direction of the axial meridian of the zone are used.
Orienting angle V general case called the horizontal angle, measured clockwise from the northern direction of the original meridian to the direction of the oriented line. Depending on the selected starting direction, the reference angle can be true azimuth, magnetic azimuth, directional angle or rumb.

8.1. ORIENTATION BY THE TRUE (GEOGRAPHICAL) MERIDIAN OF A POINT

True (geographical) azimuth (Ai) is the angle measured clockwise from the northern direction of the geographic meridian of the point to the direction of the oriented line (Fig. 8.1). The limits for changing the geographic azimuth are from 0º to 360º.

Rice. 8.1 True azimuth

The true azimuth of a straight line at its different points has different meanings. Differences in azimuths at points ABOUT And IN(Fig. 8.2) is explained by the non-parallelism of the directions of the meridians at different points of the line. True line azimuth OS at the point ABOUT(A I1 ) differs from the true azimuth at the point B(A AND 2 ) by the amount of convergence of the meridians (γ) passing through the points ABOUT And IN:

Rice. 8.2. Convergence of meridians at points ABOUT And IN

True azimuth at a point IN can be calculated using the formula: A AND 2 = A I1 + (±γ)
In geodesy, a distinction is made between forward and reverse direction of a line. The forward and reverse azimuth of the line at one point differ by 180º , however, for different points of the line this equality does not hold.

Rice. 8.3. Forward and reverse azimuths

ABOUT the brother azimuth of the line is equal to the direct azimuth plus or minus 180º, plus the convergence of the meridians of the starting and ending points of the line.
A I2obr = A I1 ±180º+ (±γ)

There are eastern (positive) and western (negative) convergence of meridians. If the end point of the line is located east of the starting point, then the convergence of the meridians will be eastern and positive; if the end point of the line lies to the west of the starting point, then the convergence of the meridians will be western and negative. The amount of convergence of the meridians depends on the difference in longitude between the initial ( λ n ) and final ( λ To ) points and average latitude (SinφWed ) locations of points.
γ = (λ To - λ n )SinφWed

Since topographic maps in the Gaussian projection are created by zones, the convergence of meridians for any points in the zone is determined relative to the axial meridian of this zone and is called Gaussian convergence of meridians . Therefore, when working with topographic maps, the convergence of meridians is the angle at a given point earth's surface between the northern direction of its meridian and a line parallel to the x-axis or the direction of the axial meridian.
The maximum difference in longitude of the axial meridian with the western or eastern meridian, limiting the six-degree zone, is 3°. Consequently, the convergence of the meridians within the six-degree zone can have values from 0 at the equator to 3° in the polar regions.

Example. On the educational topographic map at a scale of 1:50,000, in the lower left corner there is the inscription: “The average convergence of the western meridians is 2º21.” Have the map compilers made the calculation correctly?
Solution. The average convergence of meridians, in our example, will be the angle between the axial meridian of the fourth zone with longitude λ 0 = 21º00"E (see Lecture 4) and the average meridian of a map sheet with longitude λ Wed = 18º07"30""E (western frame 18º00"E, eastern frame 18º15"E).
Middle parallel of map sheet φ Wed = 54º45"N.
Let's substitute the formula for the initial data:
γ G = (λ Wed - λ 0 )SinφWed = (18º07"30"" - 21º00") Sin54º45" = 2º21"

The resulting result 2º21" corresponds to the inscription on the map.

In Fig. 8.4. we see the angle between the eastern frame of the topographic map (the true meridian on the map) and the vertical line of the kilometer grid (the line parallel to the axial meridian of the zone). The magnitude of this angle determines the convergence of the meridians for a given map.

Rice. 8.4. Convergence of the true meridian of the map (eastern frame) and the axial meridian of the zone (vertical line of the kilometer grid)

If the axial meridian (vertical line of the kilometer grid) is deviated to the east from the true meridian of the point, then the convergence of the meridians is positive, i.e. The map sheet is located in the eastern part of the zone. And vice versa, if it is deviated to the west (Fig. 8.4), then the leaf is in the western part of the zone and the convergence of the meridians for it will be negative.
When working with a set of educational topographic maps, the difference between the Gaussian convergence of meridians given point and the average convergence of the meridians for a map sheet will be only a few minutes. Therefore, to solve educational geodesy problems, such a difference can be neglected and the already calculated value of the average convergence of meridians, which is written in the lower left corner of the map sheet, can be used.

8.2. ORIENTATION BY THE AXIAL MERIDIAN OF THE ZONE

Directional angle (α) line is the angle measured clockwise from the north direction of the vertical line of the kilometer grid (the axial meridian of the zone) to the direction of a given line(Fig. 8.5). Limits for changing the directional angle from 0º to 360º.

Rice. 8.5. Relationship between directional angle and geographic azimuth

Since the vertical lines of the kilometer grid on the topographic map are parallel, the directional angle of the straight line is the same at different points. From the above it follows that the directional angle can be measured at any point where a given line intersects with the vertical line of the kilometer grid.
If the given line is between the lines of the kilometer grid and does not intersect it, then it is necessary to extend our line until it intersects with the vertical line of the kilometer grid and measure the directional angle. If a given line, after its extension, does not intersect the vertical grid line (directional angle close to 0º or 180º), then it is necessary to measure the angle from the horizontal kilometer grid line and make a correction to the measurements ±90º.
The reverse directional angle of a straight line is different from right angle exactly 180º:

α OM = α M ABOUT ±180º

The relationship between geographic azimuth and directional angle of the same straight line is expressed by the formula:
A AND = α + (±γ)

where γ is the convergence of meridians.

Example. The measured directional angle is α = 240º.
Meridian convergence γ = - 2º21′. Calculate true (geographic) azimuth.
A AND = α + (±γ) = 240º + (- 2º21′) = 237º39′

8.2.1. The procedure for measuring the directional angle on a map using a protractor having a scale of 0º - 359º or a scale of 0º - 180, 180º - 360º

connect the points on the map with a straight line between which it is necessary to determine the directional angle;

Rice. 8.6. Measuring directional angles on topographic
maps using a protractor having scales 0º - 180 and 180º - 360º.

set the center of the protractor at one of the points of intersection of the given line with the vertical line of the kilometer grid, and align the 0º and 180º divisions with the northern (0º) and southern (180º) direction of the kilometer grid;
count the value of the directional angle.

If the protractor is made in the form of a semicircle with a scale of 0º - 180º, and it is necessary to measure the western directional angle from 180º to 359º, then measure the reverse directional angle ( east direction), and then recalculate it directly:
α etc = α arr. ±180º

8.2.2. Transfer of directional angle to the subsequent side through the angle between the previous and subsequent sides

Let there be two lines B.C. And CD; the angle between them at a point C equals β ETC (right along the way BCD angle) - fig. 8.7. Let's draw through the points B And C directions parallel to the axial meridian of the zone and show in the figure the directional angles α Sun and α CD . In the problem α are known Sun And β etc ; we need to find α CD .

Rice. 8.7. Right corner β etc

Let's continue the line B.C.(dashed line) and show on its continuation the angle α Sun . From Fig. 8.7 it is clear that
α CD = α Sun + (180º - β etc )

If measured left along the way BCD corner β a lion (Fig. 8.7), then the formula will take the form

α CD = α Sun + (β a lion - 180º)

Rice. 8.8. The left angle is measured β a lion

If, when calculating using the last two formulas, the directional angle takes negative values, 360º is added to it; if it is more than 360º, then 360º is subtracted from it.

Example.
Directional angle of the previous side α Sun = 280º. The angle between the previous side and the next side measured from the right along the path BCD β etc = 60º. It is required to determine the directional angle of the subsequent side - α CD

α CD = α Sun + (180º -β etc ) = 280º +180º - 60º = 400º.

If directional angle greater than 360º those. 400º > 360º, then,

400º - 360º =40º

8.3. ORIENTATION BY THE MAGNETIC MERIDIAN OF A POINT

It is known that our planet is a huge magnet with two poles. The direction in which a freely suspended magnetic needle is set under the influence of the force of earthly magnetism is called magnetic meridian . All magnetic meridians converge at magnetic poles. The position of the poles changes over time.
Magnetic azimuth (Am) called the angle measured clockwise from the north direction of the magnetic meridian of a point to the direction of a given line(Fig. 8.9). The limits for changing the magnetic azimuth are from 0º to 360º.

Rice. 8.9. Relationship between magnetic and geographic azimuths

The directions of the geographic (indicated by an asterisk in Fig. 8.9) and magnetic (indicated by an arrow) meridians, as a rule, do not coincide. The horizontal angle formed by the directions of the true and magnetic meridians is called magnetic declination - δ (declination of the magnetic needle). If the northern end of the magnetic needle deviates east of the geographic meridian, then the declination is considered eastern and positive; if to the west, then western and negative. Each point on the earth's surface has its own magnetic declination value, which changes over time. Distinguish century-old, annual And daily allowance change in magnetic declination.
During centuries There is a change in the declination of the magnetic needle within tens of degrees, while the full period of declination fluctuation occurs over more than four centuries.
Due to annual changes, magnetic declination changes differently for various points earth's surface. Thus, for Europe, the magnetic declination varies on average from +6′ to +8′ per year. The average value of the magnetic declination for the year the map sheet was taken, as well as the annual correction, are signed under the southern frame of each map sheet, for example: “Declination for 2002 eastern 6°15"" “Annual change in declination eastern 0°02"".

Rice. 8.10. Values of corrections to reference directions on a topographic map

Taking with some assumptions the magnitude of the annual change is the same for each year, it is possible to determine the magnetic declination for any year with an accuracy of tenths of a degree. In calculations when solving orientation problems, the value of the annual change in magnetic declination is used ( Δδ ), which is used to recalculate magnetic declination from the date recorded on the topographic map (usually the year of publication) tK , to magnetic declination ( δ tK ) current year ( tT ):
δ tT = δ tK + Δδ(tT -tK ).

Daily change in magnetic declination in middle latitudes it does not exceed 15", so when working with topographic maps this value can be ignored.
There are areas on the earth's surface in which the magnetic declination differs sharply from the declination at neighboring points in the area, and the difference sometimes reaches tens of degrees and even 180°. Such areas are called districts magnetic anomalies , for example, Kursk, Magnitogorsk, Nikopol, Kola anomalies. You cannot use a compass or magnetic compass in areas of magnetic anomalies.

From the known true azimuth (see 8.10) and the magnetic declination (entries in the lower left corner of the map), the magnetic azimuth can be calculated:
Am = Au - (±δ)

Rice. 8.11. Dependencies between reference directions

If the topographic map is oriented to the terrain, i.e. If the compass scale value is 0º aligned with the north direction of the grid line, and 180º with the south direction, then the deviation of the magnetic needle (OMS) from the vertical grid line will be expressed by the formula:
Compulsory medical insurance = (±δ) - (±γ)
Taking into account the magnitude of the annual change in magnetic declination, the magnetic needle will deviate from the northern direction of the coordinate grid by the amount:
Compulsory medical insurance = (±δ tT ) - (±γ)
Where: δ tT = δ tK + Δδ(tT -tK ) - magnetic declination at this year;
tT - this year; tK - the year in which the magnetic declination was measured and recorded in the lower left corner of the map; Δδ - annual change in magnetic declination.

Example. Magnetic declination δK for the map sheet for 2002, eastern 6º15". The average convergence of meridians γ western (minus) 2º21". Annual change in magnetic declination ( Δδ ) east 0º02". It is required to calculate the deviation of the magnetic needle of the compass from the vertical grid line in 2012, provided that the zero division of the compass scale is aligned with the vertical grid line.

Magnetic declination for 2012 is
δ tT = δ tK + Δδ(tT -tK ) = 6º15" + 0º02"(2012 - 2002)= 6º35".

The deviation of the magnetic needle from the north direction of the coordinate line will be
Compulsory medical insurance = (±δT) - (±γ)= 6º35" -(-2º21") = 8º56".

To simplify the conversion of the directional angle to magnetic azimuth, a correction to the directional angle is written on the topographic map. For example, for a map at a scale of 1:50,000, “Adjustment to the directional angle when transitioning to magnetic azimuth minus 8º36" is written. This correction will be equal in magnitude to the OMC, but with the opposite sign.
P = - compulsory medical insurance
Where P- correction to the directional angle.

By measuring the directional angle on a topographic map, you can quickly calculate the magnetic azimuth on the date of measurement of magnetic declination (Am tK ):
Am tK = α +(±P)

To calculate the magnetic azimuth at this year it is necessary to introduce a correction for the annual change in magnetic declination:
Am tT = Am tK + Δδ(tT -tK )

Example.
The measured directional angle is α = 240º. Correction to the directional angle when transitioning to magnetic azimuth minus 8º36′. Calculate the magnetic azimuth for 2012.

Solution.
1. Calculate the magnetic azimuth for the year of measurement of the magnetic declination - 2002:
A M2002 = α +(±P) = 240º +(-8º36′) = 237º24′

2. Calculate the magnetic azimuth for the current year (in our example, 2014):

A M2014 = Am M2002 + Δδ(t T -t K ) = 237º24′ + 0º02"(2014 - 2002) = 237º48′

In addition to the verbal explanations, the topographic map contains a diagram of reference directions (Fig. 8.12, a). This diagram clearly demonstrates the relationship between directional angle, geographic azimuth and magnetic azimuth for a given map sheet. Using this scheme, you can check the correctness of the calculations of reference angles for the year of measurement of the magnetic declination. It is enough to supplement the diagram with a reference line, and we will be able to solve any problem of determining reference directions (Fig. 8.11, b).

Rice. 8.12. Dependencies between reference directions.
a - original diagram; b - supplemented diagram.

Example.
The directional angle α = 120º is measured on the map.
Calculate true (geographic) and magnetic azimuths.

Solution.
From the supplemented diagram (Fig. 8.12, b) it is clear that the geographic azimuth is less than the directional angle by 2º21′.
Au = 120º - 2º21′ = 117º39′
From the same diagram it can be seen that the magnetic azimuth, per year of measuring the magnetic declination, is 6º15′ less than the true azimuth.
Am = 117º39′ - 6º15′ = 111º24′
If we add the value of the annual change in magnetic declination to the calculated magnetic azimuth, we obtain the value of the magnetic azimuth for the current year.

8.4. RUMBLES OF LINES

In addition to geographic azimuth, magnetic azimuth and directional angle, reference angles also include bearings. Rumba (r) - is the acute angle from the nearest meridian direction (north or south) to the direction of the reference line. The limits for changing the rumba are from 0º to 90º. The name of the rumba depends on the name of the meridian: geographical, magnetic and directional (or axial).

To unambiguously determine the direction by the value of the rumba, it is accompanied by the name of the quarter:
I quarter NE (northeast);
II quarter SE (southeast);
III quarter SW (southwest);
IV quarter NW (northwest).

For example, r= 30º SE.

The connection between the direction and the corresponding azimuth is visible from Fig. 8.12.

Rice. 8.13. Relationship between the direction and the corresponding azimuth

NE: rI = AI , AI = rI ;
SE: rII = 180° - AII ,AII = 180° - rII ;
SW: rIII = A III - 180°,A III =180° + r III ;
NW: r IV = 360° - A IV , A IV = 360° - r IV .

The connection between the rumba and the corresponding directional angle is the same as the connection between the rumba and the corresponding azimuth. Having determined the value of the azimuth or directional angle, you can calculate the value of the corresponding direction.

Example. The measured directional angle is 246º. Calculate the rhumb.
Solution. The measured directional angle is within the range of 180º - 270º i.e. in the third quarter - SW (southwest). Replacing the azimuth with the directional angle in the corresponding formula, we obtain:
rIII = α III - 180°= 246º - 180º = 66º

When working with a map, the question often arises: how can you use a protractor that does not have a scale of 180º - 359º to measure the western directional angle? The solution to the problem comes down to the following. Any protractor can measure an acute angle, i.e. rhumb, and then convert it to azimuth.

Example. Determine the directional angle in the northwestern direction if the measured bearing (the angle measured to the left from the northern direction of the coordinate grid) is 30º.

Solution.
NW: α IV = 360° - r IV = 360 - 30º = 330º.

Questions and tasks for self-control

In what directions is it customary to orient the polar axis in the polar coordinate system?
What are the angles measured from the northern directions of the true meridian, magnetic meridian, and vertical line of the map grid called?
How is the vertical grid line oriented on a map?
What landmark directions can be determined using a topographic map?
What angle is called directional? Explain the procedure for determining the directional angle using a topographic map.
Define "true azimuth". Explain how to determine true azimuth using a topographic map.
Define “magnetic azimuth”. Explain the procedure for determining magnetic azimuth using a topographic map.
Define "rhumb". How to calculate the bearing of a reference line for each of the four quarters rectangular system Gaussian coordinates?
Define “magnetic declination.” How to calculate the annual change in magnetic declination?
Define “convergence of meridians.” How to calculate the convergence of meridians? Which maximum value can take the convergence of meridians on a topographic map?

Azimuths and directional angles. When working with a map, there is often a need to determine directions to some points on the ground relative to the direction taken as the initial one.

As a starting direction (Fig.

50) usually take:

Direction parallel to the vertical kilometer line of the map;

The direction of the geographic meridian, also called the true meridian;

The direction of the magnetic compass needle, that is, the direction of the magnetic meridian.

Depending on which direction is taken as the initial one, there are three types of angles that determine the directions to the points: directional angle a, true azimuth A and magnetic azimuth Am.

The directional angle of any direction is the angle measured on the map clockwise from 0 to 360° between the northern direction of the vertical kilometer line and the direction to the designated point. Using a vertical kilometer line as the initial direction allows you to simply and quickly construct and measure directional angles at any point on the map.

Rice. 50. True azimuth (A), magnetic azimuth (Am) and directional angle (a)

True or geographic azimuth A direction is the angle measured from the north direction of the geographic meridian clockwise to a given direction. Like the directional angle, true azimuth can have any value from 0 to 360°.

In order to measure the true azimuth of any direction using a map at a given point, a geographic meridian is first drawn through this point in the same way as when determining the geographic longitude of a point.

The magnetic azimuth of the Am direction is the horizontal angle measured clockwise (from 0 to 360°) from the northern direction of the magnetic meridian to the determined direction. Magnetic azimuths are determined on the ground using goniometric instruments that have a magnetic needle (compasses and compasses). Using this simple way direction orientation is impossible in areas of magnetic anomalies and magnetic poles.

Measuring and plotting directional angles on the map is done with a protractor. Protractor scales are built in degrees.

The directional angle of any direction, for example from an observation point (OP) to a target (C), as shown in Fig. 51, measured at point O of the intersection of this direction with one of the vertical kilometer lines.

Obviously, when measuring a directional angle with a protractor ranging from 0 to 180°, it is necessary to combine the zero radius of the protractor with the northern direction of the vertical kilometer line, and angles greater than 180° with the southern direction (Fig.

51). In the latter case, 180° is added to the resulting reading.

Rice. 51. Measuring the directional angle with a protractor

The construction of directions on the map based on their directional angles begins by drawing a straight line parallel to the vertical kilometer line through a given vertex of the angle. From this straight line the given angle is constructed using a protractor. The accuracy of reading angles using a protractor is about 15" - 30".

The transition from directional angle to magnetic azimuth and back is carried out when it is necessary to find a direction on the ground using a compass (compass), or vice versa, when it is necessary to plot on the map a direction whose magnetic azimuth is measured on the ground using compass.

To solve this problem, it is necessary to know the deviation of the magnetic meridian of a given point from the vertical kilometer line. This value is called the direction correction (P).

The direction correction and its constituent angles - the convergence of meridians and magnetic declination - are indicated on the map under south side frames in the form of a diagram, having the appearance shown in Fig. 52.

The convergence of meridians (y) - the angle between the true meridian of a point and the vertical kilometer line - depends on the distance of this point from the axial meridian of the zone and can have a value from 0 to ±3°. The diagram shows the average convergence of meridians for a given map sheet.

Rice. 52. Scheme of magnetic declination, convergence of meridians

and direction corrections

Magnetic declination - the angle between the true and magnetic meridians - is indicated on the diagram for the year the map was taken (updated). The text placed next to the diagram provides information about the direction and magnitude of the annual change in magnetic declination.

Rice. 53. Determination of the correction for the transition from the directional angle (a)

to magnetic azimuth (Am) and back

To avoid errors in determining the magnitude and sign of the direction correction, the following technique is recommended. From the tops of the corners in the diagram (Fig. 53), draw an arbitrary direction OM and designate with arcs the directional angle a and the magnetic azimuth Am of this direction. Then it will be immediately clear what the magnitude and sign of the direction correction are.

If, for example, a = 97º12" = 16-20, then Am = 97012" - (2°10" + 10°15") = 84°47". For more accurate calculations, for example, when preparing data for shooting, the direction correction is determined taking into account the annual change in magnetic declination.