Department of Geomatics

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451 - 201 Geomatics for Engineers
The University of Melbourne Department of
Geomatics Lecture 3 - Plane Surveying 2
Establishing Vertical Control Dr Allison Kealy
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What you should know by the end of this
lecture.

• The equipment and measurements used for
  establishing vertical control
• The two different techniques for computing height
  differences between points
• Vertical datums
• The nature of errors in levelling measurements

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What is levelling and vertical control?
Levelling is the name given to the process of
measuring the difference in elevation between two
or more points.
Similar to horizontal control networks, vertical
control seeks to establish a network of
benchmarks from which heights can be transferred.
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Levelling Terminology
A height is the vertical distance of a point
above or below a datum surface.
A datum surface or datum line is a level surface
or line from which heights are measured or to
which heights are referred.
A level line is defined as a line along which all
points are the same height relative to mean sea
level, and is normal to the direction of gravity
at all points
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Levelling terminology
A horizontal line is one which is normal to the
direction of gravity at a point. It is
tangential to level lines.
A reduced level (RL) is the calculated height of
a point above or below a datum, as deduced from
field measurements.
A level is the equipment used to measure height
difference. When set up correctly a level
defines a horizontal line.
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Datums and benchmarks

• Similar to control networks in horizontal control
• A level line to which all elevations are related
• Mean sea level/Australian height datum
• The height of a point relative to a datum is its
  reduced level
• Bench marks are permanent marks, the reduced
  level of which has been determined precisely by
  levelling

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Types of levelling

• Geodetic
• Simple
• Concept of class and order

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This is the highest order of levelling work, with
readings generally observed and recorded to
decimals of millimetres. This form is used for
the basic framework of a country, such as the
establishment of fundamental benchmarks.
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Ordinary or simple levelling may be categorised
by its purpose eg. Section levelling,
construction etc. Readings taken at best to 1mm.
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The principle of levelling
In all forms of levelling, the typical problem is
that the height of one point above the datum is
known and it is required to find the reduced
levels of other points with respect to the same
datum.
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Simple arithmetic
Level line
1m
2m
4m
5m
Benchmark 120.0m
120 5 - 4 121
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Establishing a level line

• Level lines vs horizontal lines
• Levelling equipment

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Levelling fieldwork
Backsight the first reading taken from an
instrument position Foresight the last reading
taken from any instrument position Intermediate
sights readings which are neither the first nor
last to be taken from an instrument
position. Change point a staff position on
which first a foresight reading from one
instrument position and then a backsight
reading from a different instrument position are
taken. Collimation height the calculated
height of the line of collimation above or below
the datum.
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More definitions
Rise and fall the vertical distance between two
consecutive staff positions is either a rise or
a fall, a rise being a positive difference (the
second point being higher than the first) and a
fall being a negative distance.
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Simple Calculations
The whole circle bearing (WCB) of a line is
measured in a clockwise direction in the range 0o
to 360o from a specified north direction.
To establish the direction of a line between two
points on the ground, its bearing has to be
determined.
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Polar Coordinate System
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Worked Example - Computation of Rectangular
Coordinates
The coordinates of a point A are 311.617m E,
447.245m N. Calculate the coordinates of point B
where qAB 37o 11 20 and sAB 57.916m.
The coordinates of a point A are 311.617m E,
447.245m N. Calculate the coordinates of point C
where qAC 205o 33 55 and sAC 85.071m

Answer EC 274.906m NC 370.503m
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Inverse Calculations
180o
qAB 222o 12 19
Problem with quadrants!
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Inverse Calculations
1
4
DE -ve DN ve 360o
DE ve DN ve
90o
270o
DE ve DN -ve 180o
DE -ve DN -ve 180o
2
3
180o
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Inverse Calculations
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So how do we establish control?

• Traversing
• Intersection
• Resection
• Angles
• Distances

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Linear Measurement
AB slope distance AB horizontal distance
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Distance Measurement
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Direct Distance Measurement

• flat
• stepping
• catenary

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Steel Tapes

• 100m, 20m, 30m
• zero point
• measure their nominal length at a particular
  tension and temperature - printed on the tape
• fibreglass, invar

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Steel Taping - Field Procedure

• ranging rods set up between points A and B
• from A to B, set zero of tape at A
• tape unwound towards B
• ranging rod removed from A, and a third range rod
  ranged in at C
• tape straightened, held taut and read at rod C
• C marked with an arrow
• for next bay, tape moved from A and zero set at C
  and so on

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Steel Taping - Corrections

• Slope - reduced to horizontal
• standardisation - calibration over time
• tension - manufactured and calibrated at a set
  tension
• temperature - manufactured and calibrated at a
  set temperature
• sag - in catenary the tape will sag under its own
  weight

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Slope Measurement and correction
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Standardisation

• tape has a nominal length under certain
  conditions
• over time a tape stretches
• standardisation needs to be carried out
  frequently
• use reference tape or baseline
• L recorded length of line
• l nominal length of field tape (eg 30m)
• l standardised length of field tape (say
  30.011m)
• sign of correction depends on the values of l and
  l

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Standardisation

• baseline consists of two fixed points
• length of field tape compared to length of
  baseline
• lB length of baseline
• lF length of field tape on baseline

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Tension

• tape length varies with applied tension
• steel tapes manufactured and calibrated to 50N
• use of standardisation tension better
• spring balance
• TF tension applied to the tape (N)
• TS standard Tension (N)
• A cross sectional area of the tape (mm2)
• E modulus of elasticity for the tape material
• sign of the correction depends on TF and TS

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Temperature Variations

• steel tapes expand and contract with temperature
• calibrated at a standard temperature of 20o C
• temperature should be recorded for improved
  precision
• allow tape and thermometer to attain stable
  conditions
• a the coefficient of expansion of the tape
  material
• tF mean field temperature (oC)
• tS temperature of standardisation (20oC)

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Catenary - Sag

• on irregular surfaces, might need to suspend the
  tape above the ground between the points
• use tripods or wooden stakes
• for long lines, need to align tripods or stakes
• tape will sag under its own weight in the shape
  of a catenary curve

length required
A
L
B
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Catenary - Sag

• q the angle of slope between the tape supports
• w the weight of the tape per m
• TF the tension applied to the tape

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Combined Formula

• corrections computed separately
• For horizontal measurements

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Steel Taping - Precision and Applications

• for a maximum precision of 1 in 5000 (6mm in 30m)
  can be achieved by only applying standardisation
  and slope corrections
• 1 in 10000 if tension and temperature corrections
  applied
• 1 in 20000 - all corrections

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Distance Measurement - EDM

• Total station
• reflector

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EDM error sources

• Atmospheric
• Scale
• Additive constant
• Cyclic

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Due to a difference between the mechanically
defined centres of the instrument and reflector
and their electrical (optical) centres. The
error when present and not allowed for, produces
an effect akin tomiscentering of the instrument
by the operator and is independent of range.
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The modulation frequency does not corespond
exactly with the design value. This error
originates mainly in the crystal controlled
oscillator and produces errors on measurement
directly proportionaly to distances.
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electrical coupling between the reference signal
and the measurement signal optical crosstalk
between transmitter and receiver optics in EDMs
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Angular Measurements

• electronic theodolites/total station
• vertical and horizontal angles
• setting up a total station
• measurements

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Errors in survey measurements

• Gross
• Systematic
• Random

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Simple Statistics
30.615 30.618 30.614 30.615 30.616 30.614 30.613 3
0.614 30.616 30.618
Difference between precision and accuracy