Geodetic Control Network Lecture 2. The determination of the geometry and the size of 1st order

1. Geodetic Control Network Lecture 2. The determination of the geometry and the size of 1st order triangulation networks.

2. Outline • The determination of theshapeoftriangulationnetworks • network design; • reconnaisance; • point marking, constructingthenetwork; • permanent marking of points, monuments; • observationtechniques. • The determination of thesizeofthenetwork • thedetermination of principalbaselines; • baselinedevelopingmethods; • baselinedevelopmentsin Hungary; • angularobservations. • Trilaterations

3. 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)

4. 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;

5. Shape of Networks – Network Design The 1859 triangulation network (1859-1864) Adjustment took 4 years! The 1948 triangulation network (1949-1952) 6 baselines

6. 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.

7. Checking the intervisibility

8. 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.)

9. 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).

10. Point marking and constr. of network Temporary and permanent marking Simple pyramid Wooden observation tower

11. Point marking and constr. of network Illés observation tower

12. Point marking and constr. of network Wooden tripod and mark Steel observation platform

13. Point marking and constr. of network

14. Point marking and constr. of network Monuments

15. 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;

16. 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) 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: The weight depends on the number of directions!

17. Observation Techniques Schreiber angular observations 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.

18. Outline • The determination of theshapeoftriangulationnetworks • network design; • reconnaisance; • point marking, constructingthenetwork; • permanent marking of points, monuments; • observationtechniques. • The determination of thesizeofthenetwork • thedetermination of principalbaselines; • baselineextensionmethods; • baselineextensionsinHungary; • angularobservations. • Trilaterations

19. 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

20. 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

21. The scale factor of baseline extension nets The scale factor is the ratio between the measured length and the extended baseline length. Note: the error of the length observations are multiplied!

22. 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)

23. Thank You for Your Attention!