Position from Angles

1
Position from Angles

• Calculating a resection with Tienstras Formula

2
Tienstras Formula

• It is important to follow the angle labelling
  sequence as presented in the lecture notes

3
Known Data

• We know the MGA coordinates of the three targets
• More targets would give redundancies, hence
  greater precision
• But then Tienstras formula would not apply
• We calculate the angles between these points from
  the coordinates
• We observe 2 angles and computer the third

4
Draw a Diagram
5
?
?
?
North Melb Town Hall
B
REB
C
A
StPauls
6
Data

• For REB
• E 321422.165
• N 5813909.535
• For StPaul
• E 321102.389
• N 5812582.604
• For NMTH
• E 319510.547
• N 5814032.432

• Angle ?86º1612
• Angle ?42º3638
• Angle ?231º 0710
• See angle reduction demonstration

7
Tienstras Formula (Easting)
8
Other Formula
9
Calculating Angle A,B,C

• As we know the coordinates of A,B,C, we can
  derive the bearing (and distance) between the
  three points
• The angles (by definition) are the differences
  between the bearings
• WATCH the sense (direction) of the bearings
• The sketch map helps

10
North
North Melb Town Hall
B
REB
C
A
StPauls
11
Angles

• Angle C Brg CB Brg CA
• Angle B Brg BA Brg BC
• Angle A Brg AB (360) Brg AC
• Look at the diagram, these are NOT formula
• And remember the sense of the bearing

12
Calculations

• See the Bearing spreadsheet
• And guess what, see the Tienstras spreadsheet

13
Results

• We calculated coordinates for the instrument
  point
• These are compared with the known coordinates
• And we see how good we were!

14
Other Positioning

• It is also possible to use angles for surveying
  other than a resection
• For example, angle/angle or bearing/bearing
  intersection

15
Base-line
Base-line to scale
16
Understanding

• You must know the conversion between rectangular
  and polar coordinates
• This is a fundamental to all Geomatics,
  everything has a spatial attribute
• You should have some idea how to use a
  jigger/theodolite/total-station