Download - Geodetic Control Network Lecture 2. The determination of the geometry and the size of 1st order
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Geodetic Control Network
Lecture 2.
The determination of the geometry and the size of 1st ordertriangulation networks.
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Outline
The determination of the shape of triangulation networks
• network design;
• reconnaisance;
• point marking, constructing the network;
• permanent marking of points, monuments;
• observation techniques.
The determination of the size of the network• the determination of principal baselines;
• baseline developing methods;
• baseline developments in Hungary;
• angular observations.
Trilaterations
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Shape of Networks – Network Design
Design criteria:
• creating a frame with a low number of approx. equilateral triangles with approx. same size;
• bigger triangles -> less needed -> decreases the propagation of error• smaller triangles -> more needed -> cheaper to measure one point (smaller marks, faster)• on plains big triangles should be avoided due to the fact that the line of sight is close to the surface -> meteorological effects
In Hungary: • average point distance is approx. 30 km (in other countries up to 50 km)
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Shape of Networks – Network Design
Design criteria:
• the shape of triangles:• angles must be larger than 30°;• stations must on the highest topography in the area (hill tops)
• the structure of the network:• homogeneous, or chains + fills (size of the country, computational facilities);• in case of chains we must decide on the location of astronomical observations (twin points in a distance of 120-150 km, located at the junction and breaks of chains) -> decrease the effect of angular distortions in the network;• in case of chains the location of baselines (to determine the size of the network) should also be chosen;• the location of suitable places have an impact on the location of chains.
•The 2nd order network:• at the centroid of the triangles, intervisible with all the three adjacent 1st order point and the adjacent 2nd order points;• when the above criteria is too tight, then more 2nd order point is established in the triangle;
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Shape of Networks – Network Design
The 1859 triangulation
network (1859-1864)
Adjustment took 4 years!
The 1948 triangulation
network (1949-1952)
6 baselines
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Design criteria:
• intervisibility:• in the 1st order network it is a must, in 2nd and 3rd order network it is preferable.
• maintenance of network:• high-order-points must be permanently marked:
• long observation period (many years);• must create a consistent frame for the network.
• checking the intervisibility / determining the size of the marks:
• the line of sight must not intersect the topography, building, vegetation, etc;• graphical and mathematical methods, which include the effect of Earth curvature.
Shape of Networks – Network Design
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Checking the intervisibility
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Reconnaisance
To check the network design on the field. Is the designed network feasible?
• reconnaisance to check the network design in previously mapped areas;• checking the status of existing network points in case of remeasurement of existing networks (usually vegetation is checked and the existence of intervisibility);• reconnaisance and planning of network in previously unmapped areas (planes, helicopters, aerial photos).• Are the points suitable for the observations?• Is there a better location in the vicinity?• How high the observation tower or the mark should be?• Additional approval is needed (natural reserves, local authorities, military authorities, etc.)
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Reconnaisance
Checklist:
• point should be located at the highest points of the topography;
• the point should be stable and prevail for a long period;
• good visibility;
• the vicinity should be suitable for building high marks (observation towers);
• good transportation (car, truck);
• suitable location for densification of the network;
• intervisibility with the adjacent points (preliminary coordinates are needed to check with WCBs).
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Point marking and constr. of network
Temporary and permanent marking
Simple pyramid
Wooden observation tower
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Point marking and constr. of network
Illés observation tower
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Point marking and constr. of network
Wooden tripod and mark Steel observation platform
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Point marking and constr. of network
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Point marking and constr. of network
Monuments
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Observation Techniques
• Direction observations
• deformation of tripods have an impact;• all the stations should be intervisible;
• Angle observations
• directly measured angles have the same weight -> indirect angles have different weights -> different methods • pair of targets should be visible;• moderate effect of the deformation of tripods;
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Observation Techniques
Angle observations in all combinations:• all the angles are measured which can be formed between the k number of tagets (but not the complementer angles)
12
kk combinations -> increased number of observations
For each angle (k-1) values can be computed, one is a direct observation, the others are indirect ones, thus the weight of one angle is:
2
22
skk
sspangle
The weight depends on the number of directions!
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Observation Techniques
Schreiber angular observations
constskpp idir
The weight of a direction is predefined:
Since pi depends on the number of repetitions, the number of repetitions depend on the number of directions.
Angles can be measured in arbitrary sequence ->only two directions should be visible at one time.
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Outline
The determination of the shape of triangulation networks
• network design;
• reconnaisance;
• point marking, constructing the network;
• permanent marking of points, monuments;
• observation techniques.
The determination of the size of the network• the determination of principal baselines;
• baseline extension methods;
• baseline extensions in Hungary;
• angular observations.
Trilaterations
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The Det. of the size of the Network
The scale of the network must be determined.
Distances must be determined
- length observations + baseline extensions- distance observations
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Baseline extension methods
Rhombus networks• contains one or more rhombus inserted into each other;• usually the shorter diagonal is measured;
Triangular networks• formed by equilateral triangles;• one side of the triangle is measured (at the edge, or in the middle);
Various baseline extension networks
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The scale factor of baseline extension nets
Nb
B
The scale factor is the ratio between the measured length and the extended baseline length.
Note: the error of the length observations are multiplied!
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Angular observations in baseline ext. nets.
The scale factor depends on the geometry of the network.
Rhombus networks: • when N>3 then usually 2 rhombus are better than 1. More than 3 rhombus are not necessary.• more economical (less observations)
Triangle networks: • when the measured side is in the middle and perpendicular to the extended baseline, the triangle networks are better than the rhombus networks.
• when the measured length is at the edge, the rhombus network outperforms the triangle network (with the same N)
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Thank You for Your Attention!