# 451-102 Surveying for Builders

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```					CE-209 Fundamentals of
Surveying
Lecture 4 Angle Measurement
Maps and Plans
Background                    Basic Computations
Geometrical Concepts
Errors and Statistics
Distances                coordinates
Angles
Measurements                                           heights
Height differences

Mid Semester examination
New Technologies           GPS

Practical Surveying           Setting Out

Analysis                      Geographical Information Systems

Computer assisted surveying
Why do we need to measure
angles?
• The location of points and orientation of
lines frequently depend on the measurement
of angles and directions.
What do we need to measure an
angle?

Direction of turning (+)
Reference or starting line

Angular distance
Units of angle measurement
• Sexagesimal system

eg 90o 20’ 35” = 90.343o = 1.577rads
Types of angles
Z              S
MLN – Horizontal angle
SLM – Vertical angle
TLN – Vertical angle
ZLS – Zenith angle
L              M   ZLT – Zenith angle

R
N

T
Angles, bearings and azimuths
• The bearing, direction or azimuth of a line is the
horizontal angle between it and an arbitrarily
chosen reference line called a north point.
• ‘True’ north – reference line through the north and
south poles
• Magnetic north – defined by a freely suspended
magnetic needle
• Assumed or arbitrary north.
How do we measure angles?
• Compass
• Theodolite
• Total Station
The compass
• No longer used for survey work
• Consists of a magnetised steel needle mounted on
a pivot at the centre of a graduated circle
• Points towards magnetic north unless disturbed by
local attraction.
• 0o near the equator to 90o near the poles
The theodolite
• Main components - sighting telescope, two
axes and level vials.

Trunnion or transit axis

Line of collimation
Vertical axis
Axis of plate level vial
Components of a theodolite
•   Telescope
•   Trunnion axis
•   Horizontal vernier plate
•   Vertical circle
•   Horizontal/vertical clamp
•   Horizontal/vertical slow motion screws
•   Plate bubble
•   Horizontal circle/lower plate
• Direct
• Micrometer
• Automatic
Setting up a theodolite
• Centring
• Levelling
• Elimination of parallax
• Clockwise angles
• Face left/right
• Rounds of angles
Measuring horizontal angles
• Select RO
• Set reading on horizontal circle
• Swing telescope to sight other points and record
‘face left’ directions
• Transit telescope to ‘face right’ and read direction
for all points including the RO
• One round of angles completed
• Change zero and repeat.
Reducing horizontal observations
• Method
• Checks
Measuring vertical angles
• Horizontal hair used for sighting targets
• Automatic compensator or index level vial
Reducing vertical angles
• Method
• Checks
In Figure 1, the horizontal angle was measured at B to C and A.
Following is an extract from the field book showing the
directions measured. Reduce the observations and compute the
value of the angle CBA.               [4 marks]
Station at     Station to       Face left    Face Right
deg min sec      deg    min                sec
B              C            00    03   50    180       04              30
B              A            83    58   50    264       00              00

A

B

C

Figure 1
Total stations
• Three basic components – EDM, electronic
digital theodolite, microprocessor
• No micrometer – resolves angles directly
Errors in Angle Measurement
• Gross – reading, pointing, setting up over the
wrong point, booking
• 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.
– Vertical index error

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