Types of angles

A

M

N

B

R

L

Z MLN – Horizontal angleALM – Vertical angleNLB – Vertical angleZLA – Zenith angleZLB – Zenith angle

The theodoliteMeasure: vertical and horizontal angles

• Main components - sighting telescope, horizontal and vertical circles and leveling system.

Horizontal (Trunian) axis

Line of sight

Axis of plate level

Vertical axis

In a well condition theodolite

• 1- Line of sight axis + H-H axis• 2-H-H axis + V-V axis• 3- V-V axis + L-L axis• If these axis are not perfectly perpendicular

, errors in angles will occur• To reduce these errors the mean of the

face left and face right reading is taken

Types of theodolite

• 1- Optical reading theodolite• 2- Digital reading theodolite

• The total station : Digital reading theodolite• +EDM( electronic distance measurement device )• + processor and memory

Major Components of a theodolite

• Telescope• Vertical circle+ horizontal circle • Horizontal/vertical clamp• Horizontal/vertical slow motion screws• Plate bubble (Level tube)

Optical reading theodolite

Setting up a theodolite

• Centering• Levelling• Elimination of parallax• Sighting the target• Reading the angle

Measuring horizontal angles

• Sight point A on face left• Set reading on horizontal circle ( e.g. 00 00´ 00˝)• Direct the telescope to point B and record ‘face

left’ directions (e.g. 35 26´ 20˝)• Reverse the telescope to ‘face right’ and read

direction to point B ( 215 26 40˝)• Back to point A on face right and record the

reading (180 00 20)

In the figure, the horizontal angle was measured at B to C and A. Compute the angle CBA.

Station at Station observed Face left Face Right deg min sec deg min sec

B C 00 03 20 180 03 50A 83 50 10 263 50 40

A

C

B

Errors in Angle Measurement• Mistakes –pointing, setting up over the wrong

point, booking, reading • Random – settling of tripod, wind, temperature,

refraction• Systematic/instrumental

– Horizontal axis not perpendicular to the vertical axis– Axis of sight not perpendicular to the horizontal axis– Axis of the plate bubble not perpendicular to the

vertical axis.

Total station

ZA (Line of Sight / Collimation Axis)

SA (vertical axis :Standing Axis)

KA (Trunian Axis)

V (Zenith Angle)

VK (Vertical Circle)

Hz (Horizontal Angle)

HK (Horizontal Circle)

HEIGHT OF REMOTE POINT

SD (Slope Distance)

HD (Horizontal Distance)

dH (Difference of Height)

hr (Height of Reflector)

hi (Height of Instrument)

E0 (Easting of Station)

N0 (Northing of Station)

H0 (Height of Station)

E (Easting of Target Point)

N (Northing of Target Point)

H (Height of Target Point)

Vertical angles

(zenith angle ) .

V%.

The vertical angle

• Is the angle above or below a horizontal plane through the point of observation

• The angle above the horizontal plane is +ve vertical angle (angle of elevation)

• The angle below the plane is –ve angle (angle of depression)

Measuring vertical angles

Point observed

F.L F.R Reduced F.L

Reduced F.R

Mean vertical angle

A 85 36´ 274 28´ 4 24´ 4 28´ 4 26´

B 98º 48´ 261 08´ -8 48´ -8 52´ -8 50´

Theodolite is set over point P the following vertical angles circle readings were recorded on targets at points A and B. Calculate the vertical angles to points A and B