The most common procedure in engineering geodesy is the construction of a theodolite traverse - a system of broken lines and angles measured between them. It is called closed if it rests on only one starting point, and its sides form a polygonal figure. Let's take a closer look at how a closed-type theodolite traverse is created and what its features are.
Moves can form entire networks, intersecting with each other and covering large areas, and their shape is determined by the characteristics of the area. They are usually divided into:
– closed (polygon);
– open;
– hanging;
– diagonal (laid inside other passages). If you need to photograph a flat area, like a construction site, best choice there will be a testing ground. On elongated objects, such as roads, it is customary to use an open path, and a hanging one - for shooting closed areas, such as back streets.
A closed move is essentially a polygonal figure and is based on only one base point with established coordinates and directional angle. The vertices of the side are the points fixed on the ground, and the segments are the distance between them. It is most often created for shooting construction sites, residential buildings, industrial buildings or land plots.
Work order
Like other geodetic activities, this procedure is carried out with preliminary preparation to obtain accurate metric data. Their mathematical processing also plays an important role. The work itself is carried out according to the principle from general to specific and consists of the following stages:
- Reconnaissance of the area. Assessment of the territory being photographed, study of its features. At this stage, the location of the points to be photographed is determined.
- Field photography. Work directly on site. Carrying out linear and angular measurements, drawing up outlines, preliminary calculations and making changes if necessary.
- Cameral processing. The final stage of work, which consists of calculating the coordinates of a closed theodolite traverse and subsequent drawing up a plan and technical reference.
Reconnaissance and field measurements are carried out directly at the site and are the most labor-intensive and costly activities. However, the further result depends on the quality of their implementation.
Data processing is already carried out indoors. Today it is carried out using a special software, although manual calculations still remain relevant and can be used by a surveyor for verification purposes.
Data processing
Processing the measurement results of a closed theodolite traverse will allow you to evaluate the quality of the work done and make corrections to the obtained geometric values. To ensure that angular and linear measurements are within tolerance, initial calculations are performed during field work.
To calculate the coordinate values of closed traverse points, use the following data:
– coordinates of the starting point;
– initial directional angle;
– horizontal angles;
– lengths of the sides.
Field measurements, even if all rules and requirements are followed, will have inaccuracies. They are caused by systematic and technical errors, as well as human factors.
Calculations are carried out in a certain sequence, which we will consider below.
Equalization
At the beginning of the calculations, the theoretical sum of the angles is determined, and then they are linked, distributing the angular discrepancy between them.
\(\sum \beta _(theor)=180^(\circ)\cdot (n-2)\)
n - number of polygon points;
\(f_(\beta )=\sum \beta _(measured)-180^(\circ)\cdot (n-2)\)
\(\sum \beta _(measured)\) – the value of the measured angular quantities;
To obtain \(f_(\beta )\), it is necessary to calculate the difference between \(\beta _(measured)\), which contains errors, and \(\sum \beta _(theor)\).
In the equation, \(f_(\beta )\) acts as an indicator of the accuracy of the measurement work performed, and its value should not be higher than the limit value determined from the following formula:
\(f_(\beta 1)=1.5t\sqrt(n)\)
t-accuracy of the measuring device,
n – number of angles.
The adjustment ends with a uniform distribution of the resulting discrepancy between the angular values.
Determination of directional angles
With a known value of the directional angle (\(\alpha \)) of one side and the horizontal angle (\(\beta \)), we can determine the value of the next side:
\(\alpha _(n+1)=\alpha _(n)+\eta \)
\(\eta =180^(\circ)-\beta _(pr)\)
\(\beta _(pr)\) – the value of the right angle along the direction, from which it follows:
\(\alpha _(n+1)=\alpha _(n)+180^(\circ)-\beta _(pr)\)
For the left (\(\beta _(lion)\)) these signs will be opposite:
\(\alpha _(n+1)=\alpha _(n)-180^(\circ)+\beta _(lion)\)
Since the value of the directional angle cannot be greater than \(360^(\circ)\), then \(360^(\circ)\) is subtracted from it, accordingly. In the case of a negative angle, it is necessary to add \(180^(\circ)\) to the previous \(\alpha \) and subtract the value \(\beta _(correct)\).
Calculation of directions
There is a relationship between rhumbs and directional angles, and they are determined by the quarters, which are called the four cardinal directions. As can be seen from Table 1. calculations are carried out according to the established scheme.
Table 1. Calculations of the rumba depending on the limits of the directional angle.
Coordinate increments
For coordinate increments in closed course apply formulas used in solving a direct geodetic problem. Its essence is that from the known values of the coordinates of the starting point, directional angle and horizontal application, the coordinates of the next one can be determined. Based on this, the formula for increasing values will look like this:
\(\Delta X = d\cdot cos \alpha \)
\(\Delta Y = d\cdot sin \alpha \)
d-horizontal layout;
α-horizontal angle.
For a polygon that has the form of a closed geometric figure, the theoretical sum of the increments will be equal to zero for both coordinate axes:
\(\sum \Delta X_(theor)= 0\)
\(\sum \Delta Y_(theor)= 0\)
Linear discrepancy and discrepancy of increment of coordinate values
Despite the above, random errors do not allow the algebraic sums to go to zero, so they will be equal to other residuals of coordinate increments:
\(f_(x)\sum_(i=1)^(n)\Delta X_(1)\)
\(f_(y)\sum_(i=1)^(n)\Delta Y_(1)\)
Variables \(f_(x)\) and \(f_(y)\) are projections of the linear discrepancy \(f_(p)\) on the coordinate axis, which can be calculated using the formula:
\(f_(p)=\sqrt(f_(x)^(2)+f_(y)^(2))\)
In this case, \(f_(p)\), should not be more than 1/2000 of the share of the polygon perimeter, and the distributions of \(f_(x)\) and \(f_(y)\) are carried out as follows:
\(\delta X_(i)=-\frac(f_(x))(P)d_(i) \)
\(\delta Y_(i)=-\frac(f_(y))(P)d_(i) \)
In these formulas \(\delta X_(i)\) and \(\delta Y_(i)\) are the corrections for the coordinate increment.
i - point numbers;
In calculations, it is important not to forget about the values of the algebraic sum, in other words, the signs. When making corrections, they must be opposite to the signs of the residuals.
After increments and corrections are made to the measurement data, their corrected values are calculated.
Coordinate calculation
When the increments of the polygon points are linked, the coordinates are determined, which is carried out using the following formulas:
\(X_(pos)=X_(pr)+\Delta X_(sp)\)
\(Y_(pos)=Y_(pr)+\Delta Y_(sp)\)
The values \(X_(pos)\) \(Y_(pos)\) are the coordinates of subsequent points, \(X_(pr)\) and \(Y_(pr)\) - the previous ones.
\(\Delta X_(sp)\) and \(\Delta Y_(sp)\) are the corrected increments between these two values.
If the coordinates of the first and last points coincide, then the processing can be considered complete.
Based on the obtained coordinates and the outlines compiled during field measurements, a plan for the theodolite traverse is subsequently drawn up.
B. 1.2.1: Dividing the horizon into degrees and bearings relative to the centerline of the ship. How many degrees does one rhumb contain? Basic 8 directions.
A: The true horizon is divided into heading angles from the ship's DP to 180° of the left and right sides, and in bearings into 16 bearings of the left and right sides. One rhumb is equal to 11.25°. The horizon is divided into 360" or 32 points, the main 8 of them are called north (N), north-east (NE), east (E), south-east (SE), south (S), south-west (SW), west (W), north-west (NW).
B.1.2.2: Visual surveillance responsibilities. Dangerous sectors of the observation horizon.
A: While on the move, observation is carried out constantly over the entire horizon using binoculars; special attention is paid to the directions directly along the bow and to the beam (90°) of the starboard and port sides, while the sector along the starboard side is the most dangerous when diverging from ships. Upon detection of this or that object or lights (in the dark), it is necessary to take a bearing on it in degrees or determine the heading angle (the difference between the ship's course and the bearing or remove the CG along the azimuthal circle using the main navigation repeater) and report the result to the watch officer! observations. The observer should also scan the surface of the sea for possible sightings of life-saving craft containing persons in distress or persons fallen overboard.
B. 1.2.3: Form for the observer’s report to the watch officer about detected objects
ABOUT:
1st - what I see;
2nd - curo angle on volume;
3rd - distance in cables,
one cable = 0.1 miles = l85.3 meters.
B.1.2.4: Means of providing fog signals. Options for signal characteristics.
A: Fog signals are given by such means as a horn (whistle), bugle, ship's bell, gong, siren, etc. Possible signal characteristics:
one long (------)-4-6 sec;
two long (----- -----);
one long one followed by two short ones (--- * *);
one long and followed by three short ones (----- * * *);
one short, one long, one short (*----*);
four short sounds (* * * *);
with a bell - frequent strikes of the bell for 5 seconds or frequent strikes of the gong complementing it. Based on the observer's report, the watch officer determines the object giving these signals. However, it is also recommended that the observer independently identify objects giving fog signals based on their characteristics.
