Transcript Shape of Networks

Geodetic Control Network
Lecture 2.
The determination of the geometry and the size of 1st order
triangulation networks.
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
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)
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;
Shape of Networks – Network Design
The 1859
triangulation network
(1859-1864)
Adjustment took 4
years!
The 1948
triangulation network
(1949-1952)
6 baselines
Shape of Networks – Network Design
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.
Checking the intervisibility
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.)
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).
Point marking and constr. of network
Temporary and permanent marking
Simple pyramid
Wooden observation tower
Point marking and constr. of network
Illés observation tower
Point marking and constr. of network
Wooden tripod and mark
Steel observation platform
Point marking and constr. of network
Point marking and constr. of network
Monuments
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;
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)
k
2
k
 1
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:
p angle  s 
s
2
k  2  
sk
2
The weight depends on the
number of directions!
Observation Techniques
Schreiber angular observations
The weight of a direction is predefined:
p dir  p i  sk  const
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.
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
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
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
The scale factor of baseline extension nets
The scale factor is the ratio between the measured length
and the extended baseline length.
B
 N
b
Note: the error of the length observations are multiplied!
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)
Thank You for Your Attention!