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TBA4231 APPLIED GEOMATICS
Time: 0900 – 1300
Solution, version 12.1.2011.
For the theory questions check also the curriculum. For some of the questions the answers are in
keyword form (some more text is required to obtain the top score).
Grades, included the project assignment counting 30% of the final grade: 3A-3B-13C-3D-1E.
Question no 1: Total station etc
Explain what a bearing is.
See the textbook, chapter 6 (2010). The horizontal angle from the
northern part of a parallel of the north axis going through a point
(G2 on the figure) to the vector from the same point to another
point (T1). Clockwise. Numerical value between 0 and 400 gon
Verify with your own calculations that the bearing from G2 to T1 is
= +47,6998 gon
From the signs of
(and looking at the figure) we find the bearing to be in the 3.rd
= 247,6998 gon
Calculate the bearing from T1 to T2,
, by using all the measurements in point T1
towards the known control points.
NB: Two of the bearings, those to G1 and G3, were given in the exam text. Some of the students
did not see that, and they did some unnecessary calculations.
Remember to ”turn” the bearing from G2 to T1 which is calculated in (b),:to the bearing from T1
to G2 :
, see the table below.
Bearing to the Gi point
Bearing to T2
= 77,5524 gon
= 239,035 gon
2 or 1
= 47,6998 gon
= 268,891 gon
2 or 1
= 117,8638 gon
= 198,727 gon
4 or 2
The weights are relative numbers, the weights 1, 1 and 2 are used here. The observation of unit
weight is therefore an angle measured 2 times.
3 suggestions in the table above, where one of the horizontal angles (
is measured 4 times
compared with 2 times for the other 2
Therefore: Weighted mean must be used
calculate the mean value of the measurements, where measurement/suggestion no 3 have the
double weight compared with the 2 others.
(316,5908 1 316,5874 1 316,5908 2) / 1 1 2
(316,5874 316,5908 316,5908) / 3