Mushroom Charm Valley. Valley of Charm - a mini canyon in the mountains of the Caucasian Mineralnye Vody
Azimuths and directional angles. When working with a map, it often becomes necessary to determine directions to some points of the terrain relative to the direction taken as the initial one.
As an initial 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 needle of the compass, 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 north direction of the vertical kilometer line and the direction to the point being determined. Using a vertical kilometer line as the initial direction allows you to easily and quickly build and measure directional angles at any point on the map.
Rice. 50. True azimuth (A), magnetic azimuth (Am) and directional angle (a)
The true or geographic azimuth A of the direction is the angle measured from the north direction of the geographic meridian clockwise to given direction. Like the directional angle, the true azimuth can be any value from 0 to 360°.
In order to measure the true azimuth of any direction on the 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 Am of the direction is the horizontal angle measured clockwise (from 0 to 360 °) from the northern direction of the magnetic meridian to the direction being determined. Magnetic azimuths are determined on the ground using goniometric instruments that have a magnetic needle (for compasses and compasses). Using this easy way direction orientation is impossible in areas of magnetic anomalies and magnetic poles.
Measurement and construction of directional angles on the map is carried out with a protractor. Protractor scales are built in degrees.
The directional angle of any direction, for example, from an observation post (OP) to a target (C), as shown in Fig. 51 are measured at the point O of the intersection of this direction with one of the vertical kilometer lines.
Obviously, when measuring a directional angle with a protractor, which has a value 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 reading obtained.
Rice. 51. Measuring the directional angle with a protractor
The construction on the map of directions according to their directional angles begins with the fact that a straight line parallel to the vertical kilometer line is drawn through a given vertex of the angle. From this straight line, the protractor builds the given angle. The accuracy of counting angles along the protractor is about 15 "- 30".
The transition from the directional angle to the magnetic azimuth and vice versa is carried out when it is necessary to find the direction on the ground using a compass (compass), the directional angle of which is measured on the map, or vice versa, when it is necessary to plot the direction on the map, the magnetic azimuth of which is measured on the ground using compass.
To solve this problem, it is necessary to know the magnitude of 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 the southern side of the frame in the form of a diagram that looks like that shown in fig. 52.
The convergence of meridians (y) - the angle between the true meridian of the 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 sheet of the map.
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 of surveying (updating) the map. 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 method is recommended. From the top of the corners in the diagram (Fig. 53), draw an arbitrary direction OM and designate the directional angle a and the magnetic azimuth Am of this direction with arcs. Then it will immediately be seen 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". determined taking into account the annual change in magnetic declination.
This is one of the orientation angles that is used in geodesy when orienting lines in a zonal coordinate system (Gauss-Kruger projection).
The directional angle is determined by topographic map or plan, or calculated analytically, first determining the azimuth of the line and the angle of approach of the meridians. On the ground, the directional angle cannot be measured.
It is counted from the northern direction of the axial meridian of the six-degree zone (or a direction parallel to it) in the direction of the clockwise movement from 0 ° to 360 ° and is denoted by the letter α.
The figure shows the directional angle of the BC line in one of the six-degree zones of the Gauss-Kruger projection.
It should be noted again that directional angle, unlike azimuths, is measured not from the geographic or magnetic meridians, but from the axial meridian of the zonal coordinate system.
The figure for the line BC shows its bearing angle α B-C and azimuth A B-C . It can be seen from the figure that knowing the true azimuth and approach angle of the meridians γ, the directional angle of the line can be calculated by the formula:
An example of calculating the directional angle of the line in azimuth:
calculate the directional angle of the line 1-2, if its true azimuth is A 1-2 = 15°25′, and the approach angle of the meridians γ = -0°02′.
according to the formula, we can write
α 1-2 = A 1-2 − γ = 15°25′ − (-0°02′) = 15°27′
Also, from the known directional angle of the line and the angle of approach of the meridians, you can calculate the true azimuth of the line:
where γ is the angle of approach of the meridians with their sign.
An example of calculating the azimuth of a line from its directional angle:
calculate the true azimuth of the line 3-4 if its directional angle is α 3-4 = 214°11′, and the approach angle of the meridians γ = -0°03′.
according to the formula we write
A 3-4 = α 3-4 + γ = 214°11′ + (-0°03′) = 214°08′.
For determining directional angle according to a topographic map or plan, they use a coordinate grid (kilometer grid), for which the protractor is applied to the coordinate line as shown in the figure.
Usage directional angles simplifies calculations - when calculating, it is not necessary to constantly take into account the angle of approach of the meridians, as when orienting lines using azimuths.
Determination of the directional angle of the orientation direction by the contour points of the map. Transfer of directional angles of reference directions.
METHODS OF DETERMINATION AND TRANSMISSION OF DIRECTIONAL ANGLES OF REFERENCE DIRECTIONS.
The direction, the directional angle of which is used when aiming guns, topographic and geodetic works, aligning instruments, orienteering is commonly called landmark .
1. The orientation direction on the ground is indicated by two points: the point from which the directional angle is determined (starting point), and the point to which the angle is determined (reference point).
The directional angle of the reference direction can be determined in the following ways:
1. Gyroscopic.
2. From astronomical observations
3. Geodetic.
4. With magnetic needle compass
5. By contour points of the map or aerial photograph.
6. Transmission from another reference direction with a known directional angle.
A) mutual sighting
B) Simultaneous marking of the heavenly body.
B) With the help of a gyro.
D) corner move.
Orientation transmission methods:
With the help of a gyrocourse indicator of an autonomous topographic location equipment;
Simultaneous marking on the heavenly body;
Angle move.
Artillery units use almost all methods of determining the directional angles of orientation directions. However, in each particular case, they choose the method that ensures, under given conditions of the situation, the timely determination of the directional angles of the reference directions with the required accuracy. (Table 7.1.)
Table 7.1. Characteristics of the accuracy of determining directional angles
| Method for determining directional angles | median error |
| 1. Geodetic | Not more than 0-00.3 |
| 2. Gyroscopic using gyrocompasses: 1G11. 1G17………………………………………………………… 1G25…………………………………………………………… | ………0-00,3 ………...20"" ………0-00,5 |
| 3. Astronomical: using theodolites………………………….………………… PAB-2A……………………………………………….. | …….……1" ….…….0-01 |
| 4. Using the magnetic needle of the compass: within a radius of 4 km from the place where the correction was determined……………………….. within a radius of up to 10 km from the place where the correction was determined…………………... | ….…….0-02 …….….0-04 |
| 5. Transmission of orientation: a) simultaneous marking of the celestial body: using a theodolite………………………………………………………………….. for no more than 20 min. from the moment of orientation with an accuracy of E ≤ 0-01 within no more than 1 hour from the moment of orientation with an accuracy of E ≤ 0-01 c) angular stroke: | ….……...2" …….….0-02 …….….0-03 …….….0-06 |
With the geodetic method of orientation, the directional angle for orientation directions can be obtained directly from the catalog (list) of geodetic points or calculated from the coordinates of points taken from the catalog (list).
1. GYROSCOPIC method - the main way to determine directional angles, as the most accurate and reliable. It is based on the property of a gyroscope to keep the position of its axis in the world space unchanged.
This method is the main one because almost all military equipment related to terrain orientation is equipped with built-in navigation devices that allow you to quickly determine the directional angle on any terrain.
The latest gyrocompasses are capable of giving out a ready-made directional angle of the orientation direction without any additional calculations and records. But since there are still many gyrocompasses of type 1 G 17 in service, which require additional calculations when measuring, we will consider the procedure for working on it.
The order of placement and launch of the gyrocompass, as well as the procedure for filling out the operator's form and calculating the dir. angle, you considered in the classes on AB and E.
I draw your attention to the fact that the gyrocompass as a device is designed to determine the true azimuth of the reference direction. Even those newest gyrocompasses that allegedly immediately independently determine the directional angle to the landmark initially determine only the true azimuth of this direction, and only then process it according to the formulas laid down in advance in the equipment and give the operator a ready directional angle.
In the last lesson, it was determined that
The median error in determining the true azimuth using a gyrocompass is
20" for 1G17
1.3* for Gi - E1
Working time - 7 - 12 min.
:
1. High precision and reliability
2. Allows you to determine a at any time of the day and in any geomagnetic conditions.
Disadvantage and:
1. Long time to determine a
2. The need for operator training, the use of additional forms.
3. Dependence on power supply.
4. Impossibility of use at latitudes more than 70 *
2. FROM ASTRONOMIC OBSERVATIONS - a method subdivided into:
A) Using the azimuthal nozzle of the compass ANB - 1
The work of calculating the directional angle of the orientation direction is greatly simplified if it is possible to mechanically determine the direction of the true meridian at a given point. Those. , due to serious shortcomings of the gyroscopic method, the question arose of replacing the gyrocompass with another device, cheaper, not consuming additional food and easy to operate. To implement this, the azimuth nozzle ANB-1 is used.
The sighting axis of the nozzle according to the position of the stars a and b Ursa Minor is mechanically oriented to the celestial pole. Thus, the north direction of the true meridian is fixed and the task of determining the azimuth is reduced to measuring the horizontal angle between this direction and the direction to the landmark.
The place of the celestial pole on the celestial sphere is completely oriented relative to the stars and is determined by the angular distance to these stars
Ra - polar distance of the star a
Рb - polar distance of the star b
P - the pole of the world
With the daily rotation of the celestial sphere, the polar distances Ra and Pb remain unchanged. There are only minor annual changes in these distances. Let's put points a¢ and b¢ on the nozzle reticle so that they are located at the same angular distances relative to the crosshairs of the grid and one relative to the other, like stars a and b relative to the celestial pole.
If now, at any time, point the reticle of the nozzle at the North Star (a), and then unfold the reticle and correct the direction of the reticle so that the images of stars a and b on the reticle coincide with points a¢ and b¢, respectively, then the crosshair of the reticle will be directed to the pole peace.
You have already considered the order of placing the compass and preparing the NSA-1 for work in the classes on AB and E.
1. set zero readings on the compass ring and drum
2. bring bubbles to the middle
3. find the North Star in the sky and, with the help of a rear sight and a front sight, point a sight at it
4. observing through the eyepiece of the reticle, enter the image of the star b into the field of view of the large bisector, and the image of the star a into the small bisector, working with the adjusting worm handwheel, the micrometer screw of the vertical aiming mechanism of the reticle and the handwheel for turning the reticle head. Due to the annual changes in polar distances, it is necessary to introduce the star a into its bisector opposite the corresponding year.
5. take a countdown on the compass ring of the drum (Oo)
6. aim the crosshair of the sight grid at the landmark, acting with the reference worm of the compass and take the reading along the compass ring and drum (Op)
7. calculate the azimuth and directional angle of the reference direction using the formulas:
A \u003d Op - Ooa \u003d A- (±g)
To obtain an accuracy with an error of no more than 0 -01, it is necessary to make observations 3 times and take the average value. Differences on one landmark should not exceed 0-03.
Positive properties of the method:
1. High precision
Disadvantages:
1. Dependence on the time of day
2. Dependence on atmospheric transparency
Accuracy: 0-01
B) According to the hourly angle of the star
It is known that all celestial bodies (the sun, planets, stars) at a certain point in time occupy a certain position in world space. Knowing it, it is possible to determine (calculate) the azimuth of the star at any time with high accuracy.
Using the calculated azimuth of the direction to the luminary on this moment time, you can determine the azimuth of the reference direction.
The azimuth of the star is calculated using a computer, tables of logarithms, astronomical tables (CAT and TVA).
For convenience and to reduce the time of work, not the azimuths but the directional angles of the star are immediately calculated. The results of the calculations are summarized in a table that indicates:
The area for which the angles of the star were calculated;
Date and time interval for which the angles are calculated;
The luminary by which the angles were calculated;
Directional angles corresponding to each time interval.
District: Tambov (northern outskirts (apartment 5265))
directional angles of the sun
The calculated angle is set on a compass (or other angle measuring device), pointed at the luminary and accompanied by it until the exact moment of time for which this angle is calculated, while working only with an adjusting worm.
Positive properties of the method:
1. High precision
2. Independence from geomagnetic conditions
Disadvantages:
1. Dependence on the time of day and the transparency of the atmosphere.
2. The need for advance calculations.
Accuracy: 0 -01 d.c.
3. GEODETIC METHOD - way subdivided into:
A) Directly from the catalog (list) of coordinates of the geodetic network
State (SGS) and special (SGS) geodetic networks are a set of points identified and marked on the ground with a certain accuracy of coordinates and directional angles to each other.
When creating these networks, rectangular coordinates and absolute heights of points, directional angles of the sides of the network and direction to reference points are determined.
On the ground, these points are fixed with geodetic signs. These signs are called trigopoints and each of you has seen them somewhere in a field or in a forest in the form of wooden or iron pyramids. If you stand near one of these points and carefully look around, then another or several of the same points will surely come into view. This is the network of mutually visible points of the HS.
Depending on the accuracy of determining the coordinates, geodetic networks of 4 accuracy classes are distinguished. Data on HS points are placed in catalogs of coordinates, which indicate:
Item name
Type of geodetic sign and its height
Item class
Its full rectangular coordinates
Directional angles to neighboring points visible and invisible from it
Distances to neighboring points
B) By solving the inverse geodetic problem on the coordinates of the GGS points
The solution of the inverse geodesic problem (IGZ) on the plane is reduced to the calculation of the directional angle from one point to another, the distance between them according to the rectangular coordinates of these points.
The principle of the solution is to determine the direction factor (Kn) and the range factor (Kd) which depend on the magnitude of the increment (i.e. change) of the difference between the DC and DU coordinates.
For certain values of DC ,DU there will be a certain value of the directional angle a . With a constant range value (AB), the greater the value of DC, the smaller the value of DU and the greater the value of the angle a and vice versa. This can be seen from the figure.
Knowing the values of DC and DU, by dividing them, i.e. through tg determine the value of the angle a and then determine the value of (AB) using trigonometric functions, i.e. distance from one point to another.
To avoid working with trigonometric functions, a special table has been compiled for determining Kn and Kd called table Kravchenko .
Let's consider the work with the table and its structure using the example of solving the OGZ.
Given: Map M 1:50 000 Sheet N-37-119-B
X 1 \u003d 63490 otm. 122.1 X 2 \u003d 65290 Ot.157.6
Y 1 = 66660 Y 2 = 62060
Define: Directional angle (a) with elev. 122.1 at elevation 157.6.
1. Find the difference in coordinates by subtracting the coordinates of the point With which it is necessary to determine the angle, from the coordinates of the point ON THE which you want to determine the angle. It's easier to remember the rule subtract legs from eyes .
X 2 \u003d 65290 Y 2 \u003d 62060
X 1 = 63490 Y 1 = 66660
DC=+1800 DU=-4600
Big difference of coordinates - BRK - DU=-4600
Smaller coordinate difference - MRK - DC=+1800
2. Find the coefficient of direction Kn. To do this, it is necessary to divide the smaller difference of coordinates by the larger one.
Kn \u003d MRK + DC 1800 \u003d 0.391
BRK - DU 4600
3. It is necessary to find the range coefficient Kd from the Kravchenko table. The input to the table is the ratio of the differences in coordinates i.e. DC and DU with their signs and the value of Kn itself. We enter the table and by the coefficient
Kn = 0.391 and find the range coefficient Kd = 1.074. Next in relation
signs "+" DC and "-" DU we find the value of the directional angle a = 48-56 with el. 122.1 at el. 157.6.
4. Determine the distance between the points according to the formula:
D \u003d 4600 0.074 \u003d 4940m.
5. Let's check roughly with the help of a ruler and AK-3 on the map the correctness of the calculations.
Positive properties of the method:
1. Pretty high accuracy.
2. Lack of appliances
Disadvantages:
1. Dependence on the catalog of coordinates and geodetic network
According to the known directional angle a n and by corrected horizontal angles b correct the directional angles of the remaining sides of the theodolite traverse are calculated according to the formulas for the right horizontal angles:
– the directional angle of the next side is equal to the directional angle of the previous side plus 180° and minus the corrected horizontal angle right along the way.
The directional angle cannot exceed 360° and be less than 0°. If the directional angle is greater than 360°, then 360° must be subtracted from the calculation result (see example).
Control of calculation of directional angles. In a closed theodolite traverse, the calculation results in the directional angle of the original side.
An example of calculating directional angles:
Directional angle of the original side a 1-2 equals 45°45¢.
When calculating the directional angle, the value obtained was 405°45 ¢. Subtracted from the resulting value 360°.
The control of the calculation of directional angles turned out.
All calculation results are entered in the table "Statement of calculation of coordinates" (Table 2).
1.3 Calculation of coordinate increments
Coordinate increments are calculated using the formulas:
where d– horizontal laying (length) of the line; a is the directional angle of this line.
Coordinate increments are calculated with an accuracy of two decimal places.
An example of calculating coordinate increments:
All calculation results are entered in Table. 2. An example of calculating trigonometric functions on a calculator is given in a separate file.
1.4 Adjustment of linear measurements
The difference between the sum of the calculated increments of coordinates and the theoretical sum is called the linear residual of the stroke and is denoted f X and fY. Adjustment of linear measurements is performed along the axes X and Y.
The linear discrepancy is calculated by the formulas:
The theoretical sum of the coordinate increments depends on the traverse geometry. In a closed theodolite traverse, it is equal to zero, then the discrepancy is equal to
Before distributing residuals into coordinate increments, it is necessary to make sure that they are admissible. What is the absolute discrepancy of the course calculated for? f abs
and relative
where R- perimeter of the course (the sum of the lengths of the sides), m.
The relative discrepancy is compared with the allowable 
.
In the case when the resulting relative discrepancy is acceptable, i.e. , then corrections to increments of coordinates are calculated in proportion to the lengths of the sides . The residuals are distributed with the opposite sign. If , then the calculations in Sections 3.3 and 3.4 are verified.
Corrections to increments of coordinates d X and d Y calculated by formulas rounded to 0.01 m:
,
where d X and d Y – incremental correction along the X and Y axes, respectively, m; f X and f Y are residuals along the axes, m; Р – perimeter (sum of sides), m; d i – measured length (horizontal distance), m.
The sign of the correction is opposite to the sign of the residual. The corrections are recorded in the "Sheet for calculating coordinates". In the example (Table 6), the corrections are shown in red.
After calculating the corrections, a check should be made, i.e. add up all the adjustments. If their sum is equal to the residual with the opposite sign, then the distribution of the residual is performed correctly. I.e:
Corrected increments are calculated.
The resulting corrections are algebraically added to the corresponding increments and corrected increments are obtained:
Control: the sum of the corrected increments in a closed traverse must be zero, i.e. equality must hold:
An example of calculating a linear residual:
.
An example of calculating corrections to coordinate increments:
