Lecture 2 Methods of Providing Control Networks for Engineering Projects II.pdf

Kwame Nkrumah University of Science &
Technology
METHODS OF PROVIDING CONTROLS FOR
ENGINEERING SURVEYS
A. Arko-Adjei
Department of Geomatic Engineering
KNUST, Kumasi, Ghana
arkoadjei@hotmail.com
July 2022

Kwame Nkrumah University of Science &
Technology
2
VERTICAL CONTROL SURVEYS

Kwame Nkrumah University
Of Science & Technology
▪ Reference Surface
– Geoid: an equipotential surface
▪ Measurement:
– Height difference between two points
▪ Datum
– Mean sea level
BASIC CONCEPTS

▪ Different orders
(K is the distance in kilometers between points)
Classification (Standard Error)
First - Order, Class I 0.5 mm K1/2
First - Order, Class II 0.7 mm K1/2
Second - Order, Class I 1.0 mm K1/2
Second - Order, Class II 1.3 mm K1/2
Third - Order 2.0 mm K1/2
ACCURACY REQUIREMENTS

▪ Ordinary Levelling
▪ Precise Levelling – more in Year III
▪ Trigonometric levelling
▪ GPS heighting or levelling
TYPES OF MEASUREMENTS

▪ Requirements (applications and accuracy)
▪ Network design
– Reference frames
– Network configuration
– Measurement scheme
▪ Surveying point Selection, Surveying Mark
▪ Observation
▪ Computation
▪ Accuracy Assessment
PROCEDURES FOR ESTABLISHING VERTICAL CONTROLS

▪ A measurement process whereby the difference in height
between two or more points can be determined
BS FS
Difference in height
H=BS-FS
SPIRIT LEVELLING

▪ Level
▪ Tripod
▪ Staff
▪ Change plate
▪ Staff bubble
▪ 50 m tape measure (sometimes)
SPIRIT LEVELLING
EQUIPMENT

▪ Level surface
– A surface over which water will not flow
– The direction of gravity is always normal to a level
surface
▪ Horizontal surface
– A horizontal surface will be tangent to a level surface
– Over short distances (<100 m) the horizontal surface and
the level surface will coincide
SPIRIT LEVELLING
TERMINOLOGY

limit of practical
coincidence (~100 m)
direction of gravity
level surface
horizontal
surface
SPIRIT LEVELLING
TERMINOLOGY

▪ Datum
– A reference surface to which the heights of all points
in a survey or on a site are referred
– May be arbitrary or a national height datum
– In Ghana we have the Ghana Height Datum (GHD)
– The surface which defines the GHD is
(approximately) Mean Sea Level (MSL)
SPIRIT LEVELLING
TERMINOLOGY

▪ Reduced Level (RL)
– The height of a point above the datum
▪ Benchmark (BM)
– A stable reference point of known RL
– Usually used as the starting and finishing point when
levelling
▪ Temporary Bench Mark (TBM)
– A point placed (e.g. peg, nail, spike) to provide a
temporary reference point
SPIRIT LEVELLING
TERMINOLOGY

▪ Backsight (BS)
– Always the first reading from a new instrument
station
▪ Foresight (FS)
– Always the last reading from the current instrument
station
▪ Intermediate sight (IS)
– Any sighting that is not a backsight or foresight
SPIRIT LEVELLING
TERMINOLOGY

▪ Height of the instrument
– It is the reduced level (R.L.) of the plane of sight when
the levelling instrument is correctly levelled.
– It is also called the "height of the plane of the
collimation" or the collimation.
– The line of collimation will revolve in a horizontal
plane known as plane of collimation or the plane of
sight.
SPIRIT LEVELLING
TERMINOLOGY

▪ Change point (CP)
– Location of the staff when the level is moved
– Change points should be...
– Stable
– Well defined
– Recoverable
– e.g. sharp rock, nail, change plate, etc...
SPIRIT LEVELLING
TERMINOLOGY

▪ There are three types of levels:
– Dumpy level
– Tilting level
– Automatic level
▪ The differences between the three types of levels
are the way in which the instruments are designed
to be adjusted to give a horizontal line.
SPIRIT LEVELLING
LEVEL INSTRUMENTS

0.3
0.33
0.339
READING AN “E-FACE”
STAFF
SPIRIT LEVELLING
LEVEL INTRUMENTS

▪ Rules for levelling
– Always commence and finish a level run on a
Benchmark (BM or TBM)
– Keep foresight and backsight distances as equal as
possible
– Keep lines of sight short (normally < 50m)
– Never read below 0.5m on a staff (refraction)
– Use stable, well defined change points
SPIRIT LEVELLING
PRINCIPLES OF LEVELLING

▪ First reading (B.S), is taken on the established
benchmark BM
▪ Place levelling staff on benchmark
▪ Set up the level anywhere in-between the
benchmark and the change point TP1 such that the
two are visible (not necessarily in the same line).
▪ Take staff reading at BM
▪ Instrument remains in its position, move staff to TP1
▪ Turn instrument to read fore sight (F.S.) at TP1
▪ TP1 is the change point
SPIRIT LEVELLING
OBSERVATION PROCEDURES

Back Inter Fore Rise Fall RL Comment
1.32 50.00 BM A
2.56 3.98 CP 1
1.25 Kerb
3.65 Post
3.49 0.67 CP 2
2.58 Kerb
2.64 1.54 CP 3
3.79 BM A


2.66
2.40
1.31
2.98
0.91
1.04
10.01
1.15
6.24
9.98 6.21
47.34
(0.03)
48.65
(0.03) (0.03)
49.23
50.14
51.18
50.03
46.25
SPIRIT LEVELLING
REDUCTION OF LEVELS – RISE AND FALL METHODS

Back Inter Fore Height of
Collimation
RL Comment
1.32 50.00 BM A
2.56 3.98 CP 1
1.25 Kerb
3.65 Post
3.49 0.67 CP 2
2.58 Kerb
2.64 1.54 CP 3
3.79 BM A


50.03
Height of Collimation = RL + BS
49.23
46.25
48.65
47.34
49.90
51.32
53.82 51.18
50.14
52.72
9.98
10.01
(0.03)
(0.03)
SPIRIT LEVELLING
REDUCTION OF LEVELS – HEIGHT OF COLLIMATION

▪ Misclosure
– The amount by which the measured height difference
(∆Hmeas) differs from the known height difference
derived from the RLs of the starting and finishing
benchmarks (∆Hknown)
Misclosure = ∆Hmeas - ∆Hknown
SPIRIT LEVELLING
REDUCTION OF LEVELS – LOOP MISCLOSURE

▪ Small misclosure in closed level loops are
expected because of the accumulation of errors
▪ If the misclosure is small, it can be adjusted
▪ If the misclosure is large, the loop (or part of it)
must be repeated
▪ Misclosure can also result from errors in published
BM levels and from BM instability
SPIRIT LEVELLING
REDUCTION OF LEVELS – ACCEPTABLE MISCLOSURES

▪ The amount of misclosure we are prepared to
accept depends on the accuracy we are hoping to
achieve
▪ For routine levelling, the third order levelling
standard is adopted…
misclosure  12k mm
where k is the length of the loop in km
misclosure  5n mm
where n is the number of instrument set up
SPIRIT LEVELLING
REDUCTION OF LEVELS – TESTING THE MISCLOSE

▪ Collimation
▪ Parallax
▪ Change point instability
▪ Instrument instability
▪ Staff instability
▪ Benchmark instability
▪ Refraction
SPIRIT LEVELLING
ERRORS IN LEVELLING

▪ Staff reading and interpolation errors
▪ Staff verticality
▪ Instrument shading
▪ Temperature on staff
▪ Booking errors (e.g. using just 1 benchmark)
▪ Earth curvature
▪ Magnetic field effects on auto level
SPIRIT LEVELLING
ERRORS IN LEVELLING

▪ Occurs when the line of sight (as defined by the
cross-hairs) is not horizontal
▪ Leads to an incorrect staff reading
horizontal line
error
▪ Generally collimation error in differential levelling is
removed as long as backsight and foresight distances
are balanced.
SPIRIT LEVELLING
ERRORS IN LEVELLING – COLLIMATION ERROR

▪ For tilting levels, when the bubble of the level vial is
centered, the line of sight should be horizontal (e.i.
the axis of the level vial and the line of sight must be
parallel. If they are not, a collimation error exists. For
the automatic levels, collimation error occurs when
the automatic compensator defining a horizontal line
of sight is out of adjustment.
24/07/2022
SPIRIT LEVELLING
ERRORS IN LEVELLING – COLLIMATION ERROR

▪ Identifies whether the level has a collimation error and
allows the collimation error to be determined
▪ To determine the collimation error, stake out four
points spaced equally, each about 100m apart on
approximately level ground as shown in Figure.
▪ Set up level at point 1, level and take staff reading rA at
A, and RB at B.
▪ Next, move the instrument to point 2, relevel and take
readings RA at A, and rB at B.
29
SPIRIT LEVELLING
TWO-PEG TEST

30
Horizontal collimation test
SPIRIT LEVELLING
TWO-PEG TEST

▪ Assume that a collimation error  exists in the staff
readings of the two shorter sights, then the error
caused by this source would be 2 in the longer
sights because their length is double that of the
shorter ones.
▪ Whether or not there is a collimation error, the
difference between the staff readings at 1 should
equal the difference of the two readings at 2.
31
SPIRIT LEVELLING
TWO-PEG TEST

▪ Trigonometric leveling is the process of determining the
difference in elevations ( ∆𝑯 ) between two points from
observed vertical angles ( 𝜶 ) and measured horizontal
distance (𝑫).
▪ The vertical angles are measured by means of theodolite.
▪ The horizontal distance may either measured or computed
trigonometrically.
▪ Relative heights are calculated using trigonometric formula.
▪ Difference in elevation between two points is determined
by measuring:
o the inclined or horizontal distance between them and
o
o the zenith angle or the altitude angle to one point from the
other.
32
TRIGONOMETRIC LEVELLING

▪ Difference in elevation between two points is determined by
measuring:
o the inclined or horizontal distance between them and
o the zenith angle or the altitude angle to one point from the
other.
❖ Zenith and altitude angles are measured in vertical
planes.
❖ Zenith angles are observed downward from vertical
❖ Altitude angles are observed up or down from
horizontal.
33

▪ Depending upon the horizontal distance between stations,
trigonometrical levelling, may be classified into two categories :
i. Observations of heights and distances as plane surveys.
▪ If the distance between the instrument station and
object is small, correction of earth curvature and
reflection is not required.
ii. Observations of heights and distances as geodetic surveys.
▪ If the distance between the instrument station and
object is large the combined correction = 0.0673 𝐃𝟐
,
for earth’s curvature and reflection is required, were D
= distance in Km.
▪ If the vertical angle is positive (+ve), the correction is
taken as +ve.
▪ If the vertical angle is negative (–ve), the correction is
taken as –ve.
34

24/07/2022
Trigonometric levelling for short lines
▪ Observations of heights and distances as plane surveys

▪ Short lines
– S = slope distance and zenith angle z or altitude angle between
C and D are observed
– H = measured horizontal distance between C and D
– V = elevation difference between C and D
– Δelev = difference in elevation between points A and B
24/07/2022
If slope distance (S) is measured
V = S cos z;
V = S sin α
If horizontal distance (H) is
measured
V = H cot z;
V = H tan α

▪ Short lines
– Δelev = difference in elevation between points A and B
– hi = height of the instrument above point A
– r = reading on the rod held at B when zenith angle z or altitude
angle is read
– RLB and RLA are reduced level at points A and B respectively
Δelev = hi + V – r
RLB = RLA + hi + V – r

▪ Long lines
– For longer lines Earth curvature and refraction
become factors that must be considered.
24/07/2022 Trigonometric levelling for long lines
▪ Observations of heights and distances as geodetic surveys

Of Science & Technology 39
Note: (c+r) are curvature and refraction corrections
▪ Observations of heights and distances as geodetic surveys

▪ Trigonometric leveling is not as accurate as direct/spirit
levelling but can be used for topographic work or where direct
levelling is not possible.
▪ In these techniques after setting the instrument at any location,
first, back sight reading is taken, then angle of elevation is
measured to the target.
40

▪ Equipment
– Theodolite
– Staff or rod
– Tape
▪ Method
– Measure vertical angle
– Measure slope distance
– Measure instrument and target heights
▪ Calculation
41

▪ Methods of Observation
▪ There are two method of observation in trigonometric
leveling.
42

1. Direct Method
▪ This method is useful where it is not possible to set the
instrument over the station, whose elevation is to be
determine.
▪ Ex:To determine the height of the tower.
▪ In this method the instrument is set on the station on the
ground whose elevation is known.
▪ If the distance between two point is so large, combined
correction = 0.0673 𝐃𝟐
for earth curvature and refraction is
required. (D in Km)
43

2. Reciprocal Method
▪ In this method the instrument is set on each of the two
station alternatively and observation are taken.
▪ Difference in elevation between two station A and B is to
be determine.
▪ First set the instrument on A and take observation of B
then set the instrument on B and take the observation of
A.
44

▪ Method of determining the elevation of a point
by theodolite
▪ There are three main cases to determine the R.L of any
point.
• Case : 1 :- Base of Object accessible.
• Case : 2 :- Base of object inaccessible, instrument station
in the vertical plane as the elevated object.
• Case : 3 :- Base of the object inaccessible, instrument
stations not in the same vertical plane as the elevated
object.
45

• Case : 1 :- Base of Object accessible, i.e. The Two
Points are at a Known Distance
• When the two points are at a known horizontal distance then
we can find out the distance between them by taking the
vertical angle observations.
• If the vertical angle of elevation from the point to be observed
to the instrument axis is known we can calculate the vertical
distance using trigonometry.
• Vertical difference between the two = Horizontal distance ×
tangent(vertical angle)
• If the points are at a small distance apart then there is no need
to apply the correction for the curvature and refraction else
you can apply the correction as given below:
C= 0.06728* 𝐃𝟐
46

• Where D is the horizontal distance between the given two
points in Kilometers, but the Correction is in meters (m).
47

48

49

• Summary:
• Let B represent the base of any structure (like: tower, chimney,
etc.) that is accessible, and D be the horizontal distance the
instrument station A and the base B, which can be measured
using a tape. Let Q be the top of the structure whose elevation
is be calculated as shown in the figure below.
50

• Summary:
• Setup a theodolite over A. Take a backsight on the Bench
Mark (BM) and determine the height of instrument (s). RL of
the line of collimation = RL of BM+S
• If the line of collimation intersects the structure at Q, the
distance PQ’ is same the horizontal distance D.
• Sight the top of the chimney and measure the angle of
elevation (α).
• In the triangle PQQ’, QQ’ = h = D*tan(θ)
• RL of the top of the structure = RL of BM+s+Dtan(θ)
51

• Case : 2 :- Base of Object not accessible
• When it is not possible to measure the horizontal distance
between the instrument station and the base of the object, this
method is employed to determine the R.L of the object.
• In this case, instrument at two known locations and staff
reading are taken to the Benchmark (BM) and vertical angle is
measured to the target from both stations.
52

• There may be two case
A. Instrument axis at the same level
• When the Instrument is Shifted to the Nearby Place
and the Observations are Taken from the Same Level
of the Line of Sight(HI.)
B. Instrument axis at the different level
53

• In such a case, we have to take the two angular observations
of the vertical angles. The instrument is shifted to a nearby
place of known distance, and then with the known distance
between these two and the angular observations from these
two stations, we can find the vertical difference in distance
between the line of sight of the instrument and the top point
of the object.
54

55

56

57

∴RL of P = RL of BM + BS + h
58

B. Instrument axis at different level
• In the field it is difficult to keep the height of the instrument at
the same level.
• The instrument is set at the different station and height of the
instrument axis in both the cases is taken by back sight on
B.M.
• There are main two cases
1. Height of the instrument axis nearer to the object is lower.
2. Height of the instrument axis near to the object is higher.
59

A. Instrument axis at different level
1. Height of the instrument axis nearer to the object is
lower.
60

lower.
61

lower.
62

lower.
63

lower.
∴ RL of P = RL of BM + BS1 + h1
64

2. Height of the instrument axis near to the object is
higher.
65

higher.
66

higher.
67

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