surveying- lecture notes for engineers

SURVEYING
By Prof. N.I. Kihupi
Department of Engineering Sciences and Technology
Sokoine University of Agriculture
MOROGORO, TANZANIA

SURVEYING
Course Outline
The course comprises:
30 lecture hours
60 practical hours
Prerequisites: None
Learning Outcomes:
1. Apply appropriate equipment to obtain linear and
angular measurements and be able to analyse and
adjust those measurements.
2. Apply a variety of survey methods to map out features
on the earth’s surface.
3. Interpret survey information for setting out works.
4. Demonstrate ability to handle survey equipment
competently and safely.
2

SURVEYING
Course Contents:
Introduction; Linear measurements; Analysis
and adjustment of measurements, Survey
methods: coordinate systems, bearings,
horizontal control, traversing, triangulation,
detail surveying; Orientation and position;
Areas and volumes; Setting out; Curve
ranging; Global Positioning system (GPS);
Photogrammetry.
3

SURVEYING
Practicals:
1. Determination of areas and volumes using
different methods.
2. Conduct detail surveying of an area using a
variety of equipment and techniques.
3. Carry out leveling of an area using a level.
4. Use direct and indirect methods of
contouring to produce a topographic map.
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SURVEYING
Assessment:
According to SUA examination regulation 18.5
1 Students’ reports on practical work shall carry
10% of the assessment;
2 Practical test(s) conducted each semester shall
carry 25% of assessment;
3 Tests, essays and assignments, and quizzes
which will be given at appropriate stages
during the semester session shall carry 25% of
the assessment;
4 The final written semester examination shall
account for 40% of the final mark
5

SURVEYING
References:
1. Wilson, R.J.P. 1963. Land Surveying (3rd Ed.).
Macdonald & Evans Ltd. Plymouth. 480pp.
2. Clancy, J. 1981. Site Surveying and Levelling.
Edward Arnold Ltd. London. 244pp.
3. Mahajan, S.K. 1983. Elementary Surveying.
Dhanpat Rai & Sons. Delhi. 390 pp.
4. Bannister, A.B. Raymond, S. and Baker, R. 1977.
Surveying. Longman. 482pp.
5. Bannister, A. and Baker, R. 1989. Solving
Problems in Surveying. Longman, Harlow. 332p
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SURVEYING
6. Wishing. J.R. and Wishing. R.H. 1985.
Introductory Surveying. McGraw Hill Inc.
360pp.
7. Schofield, W. and Breach, M. 2007.
Engineering Surveying. Butterworth –
Heinemann.
Recommended Readings:
1. Kihupi, N.I. Lecture notes on Land Surveying.
2. Wilson, R.J.P. 1963. Land Surveying (3rd
Ed.). Macdonald & Evans Ltd. Plymouth.
3. Bannister, A.B. Raymond, S. and Baker, R.
1977. Surveying. Longman. 482pp.
7

SURVEYING
INTRODUCTION
Definition:
 Surveying has traditionally been defined as the
science and art of determining relative positions of
points above, on, or beneath the surface of the
earth, or establishing such points.
 In a more general sense, however, surveying can
be regarded as that discipline which encompasses
all methods for gathering and processing
information about the physical earth and the
environment.
 Therefore, the process of surveying would entail
taking a general view of; by observation and
measurement, determining the boundaries, size,
position, quantity, condition, value, etc., of land,
estates, buildings, farm, mines, etc. and
presentation in a suitable form. 8

SURVEYING
Purpose of Surveying:
 The measurement of existing land,
buildings, and other man-made
features; and
 The setting-out of works - i.e.
translating information given on the
drawing into fact on the ground.
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SURVEYING
Stages of Surveying:
 `Taking a general view' - i.e.
reconnaissance before actual work starts;
 `Observation and measurement' - to
determine the relative position and sizes of
natural and artificial features on the land;
 Presentation. In land surveying, maps and
plans showing the features on the ground
in graphic miniature are the end products.
10

SURVEYING
Plane and Geodetic Surveying:
 Geodetic surveying involves large
areas of the earth’s surface and the
curvature of the earth must be taken
into account.
 Plane surveying involves relatively
small areas, and it is taken that the
earth’s surface is flat, i.e. it gives a
horizontal plane.
11

SURVEYING
Measurements plotted will represent
the projection on the horizontal plane
of the actual field measurements.
For example, if the distance between
two points A and B on a hillside is l,
the distance to be plotted will be l cos
θ, where θ is the angle line AB makes
with the horizontal, assuming a
uniform slope.
12

SURVEYING
Branches of Surveying:
Topographic surveys
 Topographic surveys produce maps and
plans of the natural and man-made
features.
 Plans tend to be used for engineering
design and administration purposes only,
but maps have a multitude of uses –
navigational, recreational, geographical,
geological, military, exploration – their
scales ranging from 1:25 000 to, say, 1:1
000 000.
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SURVEYING
Engineering or site surveys
 These embrace all the survey work required
before, during and after any engineering
works.
 Especially for the design and construction
of new routes, e.g. roads and railways, but
in many other aspects of surveying, it is
often required to calculate the areas and
volumes of land
14

SURVEYING
Typical scales are as follows:
 Architectural work, building work, location
drawings: 1:50, 1:100, 1:200.
 Site plans, civil engineering works: 1:500,
1:1 000, 1:1 250, 1:2 000, 1:2 500.
 Town surveys, highway surveys: 1:1 250,
1:2 000, 1:2 500, 1:5 000, 1:10 000, 1:20
000, 1:50 000.
15

SURVEYING
Cadastral surveys
These are undertaken to produce
plans of property boundaries for legal
purposes.
In many countries the registration of
ownership of land is based on such
plans.
16

SURVEYING
The Reliability of a Survey
 Since every technique of measurement is
subject to unavoidable error, surveyors
must be aware of all sources and types of
error and how they combine.
 There are several types of error that occur
and a knowledge of their importance and
characteristics is essential in the
understanding of the limitations of the
techniques of measurement.
17

SURVEYING
Systematic, cumulative or constant errors:
 Systematic errors arise from sources which
act in a similar manner on observations.
 The method of measurement, the
instruments used and the physical
conditions at the time of measurement
must all be considered in this respect.
18

SURVEYING
Gross errors
 These are more appropriately referred to as
blunders or mistakes.
 These types of mistakes can occur at any
stage of a survey, when observing,
booking, computing or plotting, and they
would obviously have a very damaging
effect on the results if left uncorrected.
19

SURVEYING
Compensating, accidental or random errors
 Compensating, accidental or random errors
are really all those discrepancies remaining
once the blunders and systematic errors
have been removed.
 Even if a quantity is measured many times
with the same instrument in the same way,
and if all sources of systematic error have
been removed, it is still highly unlikely that
all results will be identical.
20

SURVEYING
Principles of Surveying
Understanding the errors that limit the accuracy of the
measurement techniques is but one step to ensuring
specifications are achieved. The following principles of
surveying are important in this respect:
 The survey area is always totally covered with the
simplest possible framework of high quality
measurements. If the rest of the survey work is
carried out within this control the possible
damaging accumulation of errors can be contained.
This is often termed “working from the whole to
the part”.
21

SURVEYING
 Observing procedures are designed so that (i) most
mistakes that occur are discovered immediately, and
(ii) possible sources of systematic errors eliminated.
 Additional, or redundant, observations are taken so
that all data can be checked for the mistakes,
systematic errors and random errors that do occur.
For example, the three angles of a triangle would be
observed although only two are required to define the
shape. The third angle could be deduced but, when
measured, acts as a check.
 Many quantities are observed several times. These
repeated measurements and the observation of
redundant data serve both as checks and to improve
on the precision of the final results.
22

SURVEYING
SURVEYING EQUIPMENT
For Linear Measurements
23

SURVEYING
(i) Chain
Chains are normally either
20m or 30m long made of
tempered steel wire with
links measuring 200 mm
from centre to centre of
each connecting ring as
shown in the Figure (1).
(ii)Steel band
It is made of steel strip,
some 6 mm in width and
30 m or 50 m long but
may go up to 100 m long
(figure 2)
Figure 1
Figure 2 24

SURVEYING
(iii)Tapes
These may be made of
synthetic material, glass
fibre being typical, or
coated steel or plain steel.
Lengths of 10 m, 20 m and
30 m are common (Fig. 3).
(iv)Arrows or pins
These are 300 mm or 375
mm long made of steel
wire. They are used for
marking off chain lengths
as they are measured (Fig.
2).
Figure 3
25

SURVEYING
(v)Ranging rods or poles
These are steel or wooden
poles of circular section
about 25 mm in diameter
and 2 m, 2.5 m or 3 m long,
painted with characteristic
red and white bands which
are usually 0.5 m long, and
tipped with a pointed steel
shoe to enable them to be
driven into the ground (Fig.
4). On hard or paved ground
a tripod is used to support
the rods.
Figure 4
26

SURVEYING
(vi)Pegs
Points which require to be
more permanently marked,
such as the intersection
points of survey lines, are
marked by nails set in the
tops of wooden pegs driven
into the ground by a mallet.
A typical size is 40 mm x
40mm x 0.4 m long (Fig.5).
(vii)Plumb bob or dropping
arrow (Fig. 6)
A plumb bob is used to
check if objects are vertical.
Figure 5
Figure 6
27

SURVEYING
(viii)Spirit level (Fig. 6)
A spirit level is used to
check if objects are
horizontal or vertical.
Within a spirit level there
are one or more curved
glass tubes, called level or
bubble tubes.
(ix)EDM (Fig. 7)
Electromagnetic Distance
Measuring (EDM)
equipment is a more
sophisticated method of
measuring linear distances.
Figure 6
Figure 7
28

SURVEYING
For Angular Measurements and 90˚
Angle Setting-out and Slope
Measurement
29

SURVEYING
(i)Theodolite (Fig. 8)
Used to measure
horizontal and vertical
angles.
(ii)Cross staff and
optical square (Fig. 9)
Used for setting out
right angles.
Figure 8
Figure 9
30

SURVEYING
(iii)Clinometers (Fig.
10)
Used for measuring
angles of inclination.
Figure 10
31

SURVEYING
For Orientation and Positioning
32

SURVEYING
(i)Compass (Fig. 11)
Used for the
determination of
magnetic bearings
(ii)Global positioning
systems (GPS) (Fig.
12)
Used for measuring
coordinates.
Figure 11
Figure 12
33

SURVEYING
For Measuring the Difference in Height
Between Points
34

SURVEYING
(i)level (Fig. 13)
Various types of level are
used for measuring
elevations of points on the
earth’s surface.
(ii)GPS (Fig 12)
Apart from establishing
coordinates of points, GPS
can also be used for the
determination of altitude. Figure 13
35

SURVEYING
(iii)Levelling staff (Fig. 14)
Levelling staffs are
graduated rods used along
with a level for measuring
heights of points. These
may be either telescopic or
folding type, extending to a
length usually of 4 m. Most
modern designs are
manufactured in aluminium
alloys. They have a
centimetre graduation and
readings from the staff can
be estimated at 1 mm. Figure 14
36

SURVEYING
MEASURING AREAS
Measuring Areas from the Survey Plot
Areas can be calculated from the survey plot
in three ways:
 Use of geometrical figures
 Use of ordinates along with either the
trapezoidal rule or Simpson's rule.
 Use of a planimeter.
37

SURVEYING
Areas from geometrical figures:
 Triangles
 Squares
 Parallel strips
Areas from ordinates
The trapezoidal rule
 This rule assumes that the short lengths of
boundary between the ordinates are
straight lines, so that the area is divided
into a series of trapezoids (Fig. 15).
38

SURVEYING
Thus the total area is equal
to the common distance
apart multiplied by the sum
of half the first and last
ordinates, plus all the
others.
d
OO
trapezoidofArea st
×
+
=
2
1 21
d
OO
trapezoidlastofArea nn
×
+
= −
2
1






+++++= −
2
...
2
)1(32
1 n
n
O
OOO
O
dArea
Figure 15
39

SURVEYING
Simpson's rule.
Simpson’s rule assumes
that the short lengths of
boundary between
alternate ordinates are
parabolic curves. Thus,
referring to the Fig. 16
the area of each pair of
sections forms the area of
a trapezoid plus two
parabolic segments.
Figure 16
40

SURVEYING
Areas of first two sections:
Area of next two sections:
d
OO
Od
OO
2
23
2
2
2
31
2
31
×




 +
−+×
+
=
( )321 4
3
OOO
d
++=
d
OO
Od
OO
2
23
2
2
2
53
4
53
×




 +
−+×
+
=
( )543 4
3
OOO
d
++=
41

SURVEYING
and so on until the last pair of sections, ending
with the nth ordinate, the area of which
Summing up, the total area
( )nnn OOO
d
++= −− 12 4
3
( )nnn OOOOOOO
d
+++++++= −− )1()2(4321 42...424
3
42

SURVEYING
Simpson's rule states that the area equals one-third
the common distance apart multiplied by the sum of
the first and last ordinates, plus twice the sum of
the other odd ordinates, plus four times the sum of
the even ordinates.
Note:
 Simpson's rule requires an even number of
divisions of the area, i.e. the total number of
ordinates must be odd.
 To calculate an area with an even number of
ordinates by Simpson's rule, omit the final
ordinate, calculate, then add back the last
sectional area calculated as a simple trapezium.
43

SURVEYING
Areas by planimeter
This instrument (Fig.
17) is used to
measure areas
mechanically on
plans.
Figure 17
44

SURVEYING
Measuring areas from field notes or survey
data
In most surveys the area is divisible into
two parts (Fig.18):
 Rectilinear areas enclosed by survey
lines
 Irregular areas of strips between these
lines and the boundary.
45

SURVEYING
Rectilinear areas
(a)Chain surveying
The areas of the triangles forming the survey
network are calculated from the field dimensions
from the formula:
where: a,b, and c are the lengths of the
triangles' sides and
( ) ( ) ( )csbsassArea −−−=
2
cba
s
++
=
47

SURVEYING
(b)Traversing
 This is the technique of
measuring the lengths
of connected lines and
the angles between
successive lines.
 If the survey stations
are co-ordinated, the
computed co-ordinates
are used in the area
calculation
Figure 19
48

SURVEYING
Co-ordinate systems
(i) Plane rectangular cartesian co-ordinates
 In all but the simplest surveys covering
small areas, the relative positions of the
control points are calculated in a co-
ordinate system rather than directly plotted
by scale and protractor.
 In plane surveying a system of plane
rectangular cartesian co-ordinates is used
to define the positions of points in plan.
 It is usual in practice to adopt north and
east directions as axes of such a system
49

SURVEYING
The north-south axis is the principal direction, or
reference meridian, to which bearings are related.
This axis can be chosen from one of the following:
 The true meridian, or true north
 Magnetic north
 National Grid north which is related to true
north
 An arbitrary direction, e.g. one selected survey
line which is in a convenient direction
50

SURVEYING
 The grid co-ordinates of
a point A within this
system are given by the
perpendicular distances
EA (eastings) and NA
(northings) from the
two principal exes, at
whose intersection the
origin O of the system
is located (Fig.20).
 If in the figure the
eastings of A are shown
to be 221.2 m and the
northings 473.9 m, this
is recorded as
A:221.2m E, 473.9m N. Figure 20
51

SURVEYING
Most surveys are however more
concerned with the relative position of
points than with their position referred
to an unmarked point of origin. In the
figure, point B has co-ordinates of EB
and NB.
 EB – EA = ΔE, the co-ordinate difference in
eastings between A and B.
 NB – NA = ΔN, the co-ordinate difference in
northings between A and B.
52

SURVEYING
Thus if the co-ordinates of A are known and
the co-ordinate differences of the line AB are
also known, then the co-ordinates of B are
simply obtained:
 EB = EA + ΔE
 NB = NA + ΔN
53

SURVEYING
 ΔE is the same as the term departure and
ΔN is the same as the term latitude. The
latitude and departure of a line therefore
refer to the co-ordinate differences of the
ends of the line.
 The actual co-ordinates are termed total
latitudes and total departures under this
convention.
 By convention, latitudes are always
recorded before departures.
54

SURVEYING
(ii)Polar co-ordinates
In Figure 21, if O is an
origin chosen at a
convenient position and
OR is a chosen reference
direction, then P1 can be
located by its polar co-
ordinates d1 and θ1, where
d1 is the distance from the
origin and θ1 is the
clockwise angle between
OR and OP1. Figure 21
55

SURVEYING
(iii)Geographical co-ordinates
 The geographical co-ordinates of latitude and
longitude are never used in plane surveying but
they are sometimes needed in geodetic work.
 Even then they are usually converted to plane
rectangular co-ordinates for computation
purposes.
 Maps often show selected meridians and parallels
and the network of lines produced is referred to
as a graticule.
 It is seldom square or rectangular and must not
be confused with a grid.
56

SURVEYING
Areas from co-
ordinates
The area of figure
1234 = area of
trapezoid 1AD4 -
trapezoid 1AB2 -
trapezoid 2BC3 -
trapezoid 3CD4. Figure 22
( )( ) ( )( ) ( )( ) ( )( )343423232121414
2
1
2
1
2
1
2
1
1
NNEENNEENEENNEEA N −+−−+−+−−+= −
57

SURVEYING
 By altering the signs to suit the convention of
signs in the co-ordinate system:
 Twice the area of a figure equals the algebraic
sum of the products of the latitudes (or ΔN's)
of each line and the sum of the eastings of
each end of that line.
 The above expression may be expanded to
produce another form of area calculation:
( )( ) ( )( ) ( )( ) ( )( )34342323121241142 NNEENNEENNEENNEEA −++−++−++−+=−
( ) ( )112113221 ......2 −+++−+++= nnnn ENENENENENENA
58

SURVEYING
 This can be tabulated
(Fig. 23) for ease of
calculation, which for
a triangle results in
the following with
initial co-ordinates
being repeated at the
end:
 The oblique full lines
are multiplied and the
products added and
the oblique pecked
lines are multiplied
and the products
added. The difference
between the two is
twice the area.
Figure 23
59

SURVEYING
Irregular areas
 The areas of the irregular strips are either
positive or negative to the rectilinear area and,
since they are divided up by offsets between
which the boundary is supposed to run
straight, they are computed as a series of
tropezoids.
 The mean of each pair of offsets is taken and
multiplied by the chainage between them.
 Where the offsets are taken at regular intervals
the trapezoidal rule or Simpson's rule for areas
is used.
60

SURVEYING
Volumes of Earthworks
Methods of estimation:
 By cross-sections: Generally used for long,
narrow works such as roads, railways,
pipelines, etc.
 By contours: Generally used for larger areas
such as reservoirs, landscapes, redevelopment
sites, etc.
 By spot heights: Generally used for smaller
areas such as underground tanks, basements,
building sites, etc.
61

SURVEYING
Volumes from cross-sections
In order to compute the volumes it is first
necessary to evaluate the cross-sectional
areas, which may be obtained by the following
methods:
 By calculating from formulae or from first
principles the standard cross-sections of
constant formation widths and side slopes.
 By measuring graphically from plotted cross-
sections drawn to scale, areas being obtained
by planimeter, or division into triangles or
squares as previously described. 62

SURVEYING
Calculating the cross-sectional
areas of embankments and cuttings
from formulae
With reference to Figures (a) and (b)
overleaf it can be shown that the formulae
for calculating the cross-sectional area of
an embankment or cutting are the
following:
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SURVEYING
Example:
 Formation width AB
= b = 16 m
 Height at centre = h
= 4 m
 Side slopes
= 1: s = 1:2
 Ground slope
= 1:g = 1:12
65

SURVEYING
Calculating the cross-sectional areas of
embankments and cuttings from first
principles
With reference to previous figure, calculation of
the required area involves calculating the area of
the trapezium DCXY and subtracting from it the
area of the two triangles DYA and CBX.
Using the same data as in the previous example,
the unknowns x and y, the projections of the side
slopes needed for the Area calculation, are
obtained as follows:
66

SURVEYING
In the figure GC = 12GM because the ground
slope is 1:12. But GC = 8 + 2x and GM = x – 4.
Thus 8 + 2x = 12(x – 4)
10x = 56
x = 5.600 and 2x = BX = 11.200 m
Also DH = 12MH as before
But DH = 8 + 2y and MH = 4 – y
Thus 8 + 2y = 12(4 – y)
14y = 40
y = 2.857 and 2y = AY = 5 714 m
67

SURVEYING
The geometry of calculating the cross-sectional area of a
cut and fill section
69

SURVEYING
The prismoid
 In order to calculate the volume of a substance, its geometrical
shape and size must be known.
 A mass of earth has no regular geometrical shape, but it may
be assumed to take the form of a prismoid, the geometrical
figure it most nearly approaches.
 A prismoid is a solid consisting of two ends which form plane,
parallel figures, not necessarily of the same number of sides,
which can be measured as cross-sections. The faces between
the parallel ends are plane surfaces between straight lines
which join all the corners of the two end faces.
 A prismoid can be considered to be made up of a series of
prisms, wedges and pyramids, all having a length equal to the
perpendicular distance between the parallel ends.
75

SURVEYING
 Prism, in which the end polygons are
equal and the side faces are
parallelograms.
 Wedge, in which one end is a line, the
other end is a parallelogram, and the
sides are triangles and parallelograms.
 Pyramid, in which one end is a point, the
other end is a polygon and the side
faces are triangles.
76

SURVEYING
The prismoidal formula
 Let D = the perpendicular distance between the
parallel end planes
 A1 and A2 = the areas of these end planes
 M = the mid-area, the area of the plane
parallel to the end planes and midway between
them.
 V = the volume of the prismoid and
 a1, a2, m, v = the equivalent for any prism,
wedge or pyramid forming the prismoid
77

SURVEYING
Volumes from contour lines
 Contour lines may be used for volume calculations and
theoretically this is the most accurate method. However,
as the small contour interval necessary for accurate
work is seldom provided, owing to cost, high accuracy is
not often obtained.
 Requires contour interval of less than 1 or 2 m at most
for the assumption that there is an even slope between
the contours to be valid, otherwise volume calculations
from contours become unreliable.
 The end areas formula or Simpson’s rule for volumes can
be used for volume calculation; the distance d in the
formulae being the contour interval.
92

SURVEYING
 The area enclosed by each contour line is
measured, usually by planimeter, and these
areas A1, A2, etc. are used in the formulae as
shown previously.
 If the prismoidal method is used either each
alternate contour line is assumed to enclose a
mid-area or the outline of the mi-area can be
interpolated between the existing contour
intervals.
93

SURVEYING
Intersection of surfaces
Figure shows the contour
plan of an area with a dam
wall 10 m wide on top at a
level of 67 m and an access
road, also 10 m wide and
rising at a gradient of 1:10
from the wall. The dam has
side slopes of 1:1 upstream
and 1:2 downstream. The
road runs through a cutting
with side slopes of 1:2.
94

SURVEYING
 The outline of the area of fill is obtained by drawing
the contours of the dam. As the top is level the
contours along the side slope run parallel to it.
 The first contour on the upstream side at 65 m lies 2
m in plan from the edge as the slope is 1:1.
 The next at 60 m lies 5 m from the 65-m contour for
the same reason.
 Similarly the other contours are drawn, those
downstream being drawn 10 m apart because the
slope is 1:2.
 By joining the intersection of each set of contours the
outline of the area of fill required to form the dam
wall can be drawn.
95

SURVEYING
 The outline of the cutting is obtained in a
similar fashion.
 The 70-m contour will cross the road at right-
angles 30 m away from the level section
because the rise of 3 m from 67 m to 70 m at a
gradient 1:10 takes 30 m horizontally.
 Similarly the next contour across the road at
75 m is now 50 m away from the previous one
because the rise is 5 m at a gradient of 1:10.
96

SURVEYING
 The contours on the cutting slope deviate from
the road gradient in plan by 10 m in 50 m
because the cutting slope contours are 10 m
apart for 5-m rise at 1:2 and the gradient must
go to 50 m to rise these 5 m.
 They can therefore be plotted, their
intersection with the ground contours allowing
the outlines of the cutting to be drawn.
97

SURVEYING
Calculating volumes from spot heights
This is a method of volume calculation frequently used on
excavations where there are vertical sides covering a fairly
large area, although it can be used for excavations with
sloping sides.
The site is divided into squares or rectangles, and if they
are of equal size the calculations are simplified.
The volumes are calculated from the product of the mean
length of the sides of each vertical truncated prism (a prism
in which the base planes are not parallel) and the cross-
sectional area.
The size of the rectangles is dependent on the degree of
accuracy required.
100

SURVEYING
Example
Figure shows the
reduced levels of a
rectangular plot
which is to be
excavated to a
uniform depth of 8
m above datum.
Calculate the mean
level of the ground
and the volume of
earth to be
excavated.

SURVEYING
NOTE
 The mean or average level of the ground is
that level of the ground which would be
achieved by smoothing the ground off level,
assuming that no bulking would take place.
 The mean level of the ground is the mean of
the mean heights of each prism. It is not the
mean of all the spot heights.
102

SURVEYING
TAPE AND OFFSET SURVEYING (CHAIN
SURVEYING
 In tape and offset surveying only linear
measurements are made in the field.
Hence the items of equipment required are
limited to those used for linear
measurements.
 Other items of equipment may also be
required for setting out right angles and
measuring ground slope.
107

Figure 24 Basic terminology in chain surveying
108

SURVEYING
Procedures in Tape and Offset Surveying
The following principles must be adhered to in
tape and offset surveying:
 The survey must be so arranged that the area
can be plotted by triangles. The term used
when all the sides are measured is trilateration
as opposed to triangulation where all the
angles and one side are measured.
 Check or proof lines must also be measured to
check or prove that the plotted figure is
correct.
109

SURVEYING
 Chain lines must be placed as close as is
practical to the boundaries
 Offsets should be kept as short as
possible and are measured at right
angles to the chain line. Oblique offsets
are the exception
 Ties are usually used in pairs to locate
some point of detail, e.g. a corner of a
building, from two known points on the
line.
110

SURVEYING
Setting out straight lines
 A straight line is the shortest distance
between two points on a map, plan or
between two points on the field.
 Long lines in the field have to be
ranged out to facilitate chaining.
 This is done using ranging rods or
poles as will be demonstrated during
practical session.
111

SURVEYING
(a)Setting out a
straight line over
a short distance
 Poles (A), (B),
(C) and (D)
are in line if
the observer,
standing 1 or 2
metres behind
pole (A), sees
pole (A) only,
while the other
poles are
hidden behind
pole (A). Figure 25
112

SURVEYING
Setting out straight lines over a ridge or hill
Figure 26113

SURVEYING
Figure 27
Setting out straight lines over a ridge or hill – Step 1114

SURVEYING
Figure 28

SURVEYING
Figure 29

SURVEYING
Figure 30

SURVEYING
Figure 31
Field signals 118

SURVEYING
Setting out right angles
This is an important operation in
connection with the measurement of
offsets. There are two cases to consider:
(a) dropping a perpendicular from a point
to a line; and
(b) setting out a line at right angles to the
survey line from a given point on the
steel band.
119

SURVEYING
Figure 32
Setting out right angles with a tape 120

SURVEYING
Figure 33
Setting out a right angle with an optical square 121

SURVEYING
Measuring the length of a line
Figure 34
Procedure of measuring a line 122

SURVEYING
Offsetting procedures
Figure 35
A chained network showing offsets 123

SURVEYING
Field Work
Reconnaissance
A rough sketch is made in the field book,
showing the survey stations and the routes of
the main and other chain lines.
Choice of stations
A survey station is a point of importance at
the beginning or end of a chain line, or at the
junction of one line with another, and is
usually marked by the insertion into the
ground of a vertical ranging pole, wooden peg
or nail depending on ground conditions.
124

SURVEYING
 The number of survey lines should be kept
to a minimum.
 The base line, which is normally the longest
of the chain lines forming the pattern of
triangles should, if possible be positioned
right across the site. A compass bearing
should be taken to fix its direction.
 NOTE: all survey drawings require a drawn
north point.
125

SURVEYING
 All triangles should be well-
conditioned.
 Obstacles should be avoided as far as
possible.
 Extension lines are important as it is
often convenient to position a station
on the extension of a check line or a
triangle side.
126

SURVEYING
Figure 36
A sketch showing an area to be surveyed 127

SURVEYING
A good layout of survey lines is shown in Fig. 37.
Figure 37
A chained network showing properly placed stations128

SURVEYING
Field notes
 These are made in a field-book
usually with a double red line ruled up
the middle of each page.
 Booking is usually done from the back
and continued towards the front of
the book starting at the bottom of
each page.
129

SURVEYING
The following should be included to
complete the field record:
 The name and location of the survey.
 The description and reference number
of the tapes and other instruments
used.
 The date of the survey.
 The names of the survey party
members.
130

SURVEYING
 A sketch of the layout of the survey lines made
during the reconnaissance which includes:
(i) the names or letters designating stations;
(ii) the line numbers;
(iii)the arrows indicating the direction of
survey.
 The witnessing and description of station
marks.
 An index of lines and/or stations.
 The weather at the time of the survey and any
other feature likely to affect the accuracy of the
work.
131

SURVEYING
Booking field notes
 The following points should be borne in mind:
 Booking should be accurate and clear.
 Nothing other than the changes should be written
between the double red lines which represent the
chain/band.
 The chainage of stations should be ringed for
clarity.
 Always book in metres or millimetres with or
without a decimal point respectively
 Leave nothing to memory.
 Use an H or 2H pencil.
132

SURVEYING
Figure 38
An example of line booking 133

SURVEYING
Figure 39
Correct and incorrect way of booking features crossing the survey line134

A simple case of line booking showing details for lines CD and DA
135

SURVEYING
When booking and making sketches of
the survey area, use of recommended
symbols is imperative. Figure 40 shows
suggested symbols for representing
different features.
136

SURVEYING
Figure 40
Some conventional symbols used on maps and plans137

SURVEYING
Running the survey line
This consists of chaining the line and the
survey or picking up nearby detail. It
includes:
(a)Ranging the tape or chain along the survey
line (see Sect. 4.2.3);
(b)With the tape/chain left lying on the
ground, the leader runs back to the zero
end to assist the follower in offsetting;
138

SURVEYING
(c)The chainages along the line at which
fences, streams, kerbs and other
survey lines intersect the chain line
are also recorded;
(d)Offset measurements as with all
other linear measurements must be
horizontal and should be booked in
order of their chainage.
139

SURVEYING
 All measurements in surveying must
either be in the horizontal plane, or
be corrected to give the projection on
this plane.
 Lines measured on sloping land must
be longer than lines measured on the
flat, and if the slope is excessive,
then a correction must be applied.
There are two methods.
140

SURVEYING
(a)The process of step chaining or
stepping
Step chaining
Figure 41
141

SURVEYING
(b) Measuring the angle of slope with a
clinometer
 By measuring the angle of slope θ
(Fig. 42), the horizontal distance, s,
can be calculated from the slope
distance l from the formula:
θcosls =
142

SURVEYING
(a) (b)
Use of the clinometer
Figure 42
θcosls =
143

SURVEYING
Plotting the survey
The plotting is carried out in exactly the same
sequence as the measurements in the field.
(i) Select an appropriate scale.
(ii)Position the base line on the drawing sheet in
such a way that the whole area will be
contained within the limits of the paper.
(iii)Plot all the triangles off the base line using a
beam compass.
(iv)Draw in the positions of the check lines, then
confirm that they agree with the field
measurements.
144

SURVEYING
(v) Plot the detail in the same order in which
the measurements were taken in the field.
(vi)Draw in the details carefully (i.e. lining-in)
using conventional symbols.
(vii)`Title up' the drawing and print additional
information on the sheet in the bottom
right-hand corner.
(viii)Finally, include a north point and this can
be parallel to the side of the sheet, i.e.
north is at the top of the sheet, although
this is not obligatory.
145

SURVEYING
A properly finished survey drawing
Figure 43
146

SURVEYING
PLANE TABLE SURVEYING
Advantages of the Plane Table Technique:
(a) The plan is produced directly in the field, with
a minimum of measurement and booking of
field notes
(b) There is little chance of important features
being omitted.
(c) Very rapid work is possible.
(d) A good field technique and is fairly easily
acquired by the beginner in a relatively short
period of time.
147

SURVEYING
(e)Office work is cut to an absolute
minimum, i.e. making the field
plotting presentable.
(f) Since complex calculations are
unnecessary, the work may be
carried out by relatively unskilled
technicians.
148

SURVEYING
Disadvantages of the Technique
(a) Work is impossible in persistently wet
and/or windy climatic conditions, and it is
impracticable in heavily wooded or densely
bushed areas.
(b) The scale of the map or plan must be
known before work is started, since the
actual plotting takes place on site.
(c) The absence of field notes may prove a
disadvantage on some jobs, especially
where areas and volumes need to be
calculated.
149

SURVEYING
Basic plane table surveying equipment (left to right from top):
board and tripod; Indian-pattern clinometer; trough compass;
microptic or telescopic alidade; alidade rule; and plumbing fork
Figure 44
150

SURVEYING
Plane tabling methods
(a)Radiation
(b)Triangulation or intersection
(c)Traversing
(d)Resection
151

SURVEYING
Radiation
 This is a method whereby a
complete survey may be carried
out with one set-up of the table.
 Point p is marked on the
drawing sheet to represent P on
the ground by means of a
plumbing fork
 Sights are then taken with the
alidade from this point to each
of the points A,B,C,D,E in turn
 The distances PA, PB, PC, etc.
are measured by tape, and
plotted to scale.
 The survey is completed by
drawing in the features such as
the boundary lines ab, bc, etc. Figure 45
152

SURVEYING
Triangulation or intersection
 Most used method of
plotting detail.
 Points to be fixed by
intersection must form the
apex of well-conditioned
triangles. Rays
intersecting at less than
30° or more than 150° are
unacceptable in the fixing
of any point. Figure 46
153

SURVEYING
 Triangulation is
also a method by
which a small area
can be completely
surveyed without
measurement
except for the base
line of the survey.
Figure 47
154

SURVEYING
Traversing
 This is a graphic method
of making a traverse.
 It is rather tedious and is
therefore seldom used
unless restricted visibility
prevents the use of other
techniques.
 The method is best used
for fixing survey lines and
stations on the plan so
that the filling-in of the
detail can be done by
radiation and/or
intersection. Figure 48
155

SURVEYING
The graphical adjustment
 E' should be at E and
must be moved the
distance EE' in the
direction shown. The
effect of this
movement will be to
move the plotted
position of the other
points proportionally
along parallel
directions.
Figure 49
156

SURVEYING
Resection or the "three-point problem"
 This is a process whereby the position of an
occupied station may be plotted if its position has
not previously been fixed.
 The need for this arises when a position suitable
for plane table detailing has not previously been
observed to and delay would arise in occupying a
previously fixed point in order to establish the
required position by forward intersection.
 The problem here is one of orientation because
the table cannot be oriented in the same way as
under normal circumstances as there is now no
ray drawn on the sheet towards the occupied
station.
157

SURVEYING
Solution of the three-point problem:
(a) Collins' point solution
(b) Plane table resection
(i) Tracing paper method.
(ii)Trial and error method.
(iii)Intersection of loci method.
158

SURVEYING
LEVELLING
Introduction
 Levelling is the process of measuring the
difference in height between points on the
surface of the earth.
 A level surface or a level line is a surface or
line, all points of which are normal or at
right angles to the pull of gravity. The
surface of a still lake is an example of a
level surface, which tends to follow the
curve of the earth's surface.
162

SURVEYING
 A horizontal surface or a horizontal line is a
plane, flat surface or straight line which passes
through a point at right-angles to the pull of
gravity at that point. It is therefore a tangent to
the curve of a level surface.
 A datum surface is any level surface to which the
elevations of points may be referred.
 The reduced level of a point is its height or
elevation above the surface adopted as a datum.
 Bench-marks are stable reference points, the
reduced levels of which are accurately
determined by spirit levelling.
163

SURVEYING
The basic items of equipment necessary are:
 An instrument capable of giving a truly
horizontal line of sight - e.g. a level
 A graduated staff for reading the vertical
height from the ground or object to this
horizontal line - e.g. a levelling staff.
 A special book in which to note the
readings from which calculations can be
made - e.g. a level book.
165

SURVEYING
Types of level
There are three basic types of level in
common use:
a)Dumpy levels.
b)Tilting levels of which the quickset and
precise levels are particular kinds.
c)Automatic levels, some of which can also be
considered as precise levels.
The common factor between all these levels is
the telescope, which when levelled defines a
horizontal line of sight.
166

SURVEYING
Procedure in levelling:
 Consider two points A and B
as shown in the figure.
 Referring to the figure, the
instrument is set up at a
convenient spot which is
roughly equidistant between
the points with the staff held
on each point in turn.
 The two readings on the staff
are noted and the difference
between them gives the
required difference in height,
viz. 2.515 m. Figure 54
167

SURVEYING
Series levelling
When it is necessary to set up the level
in several positions and so work in
stages by means of change points, the
system employed is called either series
levelling or continuous levelling.
168

SURVEYING
Plan and sectional view of series levelling
Figure 55
169

SURVEYING
B.S. I.S. F.S.
2.390
1.985
1.318
0.988 1.612
1.502
1.415
2.420 0.316
0.532
170

SURVEYING
Reduction of observations
The field or level book is reduced in either
one of two ways:
(a)By the height of instrument (or height
of collimation) method;
(b)By the rise and fall method.
171

SURVEYING
Reduction of observations using the height of instrument method172

SURVEYING
Reduction of observations using the rise and fall method173

SURVEYING
Checking the levels
 The difference between the sum of
the B.S.s and F.S.s should equal the
known difference in height between
the starting and finishing points.
 The sum of B.S.s minus the sum of
F.S.s when positive indicates a rise
and when negative indicates a fall.
174

SURVEYING
 Taking the figures from the examples
above, this difference is +3.338 which is a
rise. However the difference between the
known and observed rise is 0.007. This
indicates a small acceptable error due to
minor compensating errors of observation.
 The permissible error in levelling on
ordinary site surveys may be taken as ± 20
√K mm, where K is the total distance
levelled over in kilometres. In precise work
the permissible error is generally reduced
to ± 5 √K mm or even less.
175

SURVEYING
The inverted staff
 When the level of a point which is above
the line of collimation has to be found, such
as the underside level of a bridge, the staff
may be held upside down with the base on
the high point.
 The inverted staff may also be usefully
employed in carrying a line of levels over a
high wall, where the level of the top of the
wall is used as a change point
176

SURVEYING
Levelling over an obstruction, e.g. a wall
Figure 56
177

SURVEYING
Booking example depicting the case where the inverted staff is employed178

SURVEYING
Reciprocal levelling
 In order to obtain the true level difference
between points the instrument is normally
set up midway between them so as to
eliminate instrumental errors.
 In some cases, such as when levelling
across a wide river, it may not be possible
to set up midway between the points.
 The system of reciprocal levelling is
adopted under such circumstances.
179

SURVEYING SURVEYING
Reciprocal levelling
Figure 57
180

SURVEYING
Observations from station X:
on to staff held at A = 1.470
on to staff held at B = 3.562
observed difference in level = 2.092
Observations from station Y:
on to staff held at A = 0.516
on to staff held at B = 2.620
observed difference in level = 2.104
= 2.098 m.





 +
=
2
104.2092.2
elevationindifferenceTrue
181

SURVEYING
 Reciprocal levelling is a
second method of
finding the true level
difference between
points with a level
suspected of being out
of adjustment.
 The method of
reciprocal levelling is
often used instead of
the midway set-up to
find the true difference
in level when testing a
level.
182

SURVEYING
Flying levels
 Taking flying levels is a system of levelling without
intersights, where every point of ground levelled is
treated as a change point.
 Used when levelling between two points such as two
B.M.'s or from B.M. to T.B.M. which are well apart
from each other in terms of either distance or height.
 Used for quantifying the closing error which requires
that a line of levels be run back to the starting point
or to some other point of known height.
 In order to reduce errors to a minimum, the
backsight and foresight distances should be kept
equal.
183

SURVEYING
Sources of error
(a) Instrumental errors e.g. collimation error,
insensitivity of the bubble tube, structural
damage of tripod and incorrect staff
graduations.
(b) Errors in handling the equipment e.g. bubble
off centre and non verticality of staff.
(c) Errors due to displacement of the equipment
e.g. alteration of the H.I. due to settlement
especially on soft or marshy ground, unstable
change points and inexperienced operators.
184

SURVEYING
(d) Errors in reading and booking, e.g.
incorrect staff reading and booking
wrongly. Always read the staff, book the
observation and then check that the
recorded entry agrees with a second
reading through the telescope.
(e) Errors due to natural causes, e.g. vibration
caused by wind and sun, the latter being
due to uneven refraction.
185

SURVEYING
Sectioning
 Sectioning consists of surveying the variations
in height of the ground along any survey line
relating to any proposed construction so that
they may be represented to scale on a drawing.
Longitudinal sections
 Longitudinal sections or profiles are sections
which follow some particular line defining a part
of a new construction and are usually run along
the centre lines of the proposed work such as
new roads, pipe-lines, etc.
186

SURVEYING
Running a longitudinal section
 This is the term used to describe the field
work involved in surveying a longitudinal
section.
 The line of the section must first be set out
on the ground by ranging in sufficient poles
or pegs to define the straights and curves.
 Levels are then observed along the required
line by means of series levelling.
187

SURVEYING
 Observations are made with the staff at
regular intervals of horizontal distance (e.g.
20, 25, 50, 100 m, etc.) together with the
levels of any points where the profile is
disturbed, such as at a change of ground
slope, obstructions, etc.
 Work should be started and finished on a
B.M. or T.B.M., or be closed by means of
flying levels in the normal way.
188

SURVEYING
Plotting the profile
(a) Draw a datum line chosen to plot about 5 cm below
the lowest reduced level on the profile and being a
multiple of 5 m above datum. This line must be
clearly marked, e.g. datum line 35 m A.M.S.L.
(b) Scale off the chainages of the points at which the
levels were observed along the datum line to a
suitable scale and tabulate them.
(c) Erect ordinates at these points and scale off the
reduced levels of each and tabulate them as shown.
(d) The vertical scale is usually five to ten times greater
than the horizontal, the greater exaggeration being
used on flatter land.
189

SURVEYING
(e)Join each point of reduced level
plotted with a continuous line. The
latter comprises of a series of
straight lines.
(f) Represent on the profile the features
which intersected the line on the
ground. Include descriptive notes,
e.g. street names, property
designations, etc.
190

SURVEYING
Plot of a profile
Figure 58
191

SURVEYING
Cross-sections
 If the proposed construction work is of some width,
the longitudinal sections will need to be supplemented
by cross-sections.
 Such sections are at right angles to the longitudinal
profile line and are used primarily for the calculation
of the volume of earthworks.
 The cross-sections are taken at regular intervals from
20m on broken ground to perhaps 100 m where the
slope is gentle.
 Normal series levelling is used for this work, and it
may be done in concert with the longitudinal section
levelling or completely separate from it.
192

SURVEYING
Cross-sectioning field notes
Booking may take one of two forms:
(a) The sketch section, with the readings
noted thereon. This is usually adopted
where the cross-sections are to be scale
drawn only without a record of reduced
levels.
(b) The level book form, with three distance
columns to denote cross-sectional
distances to the right and left of the
longitudinal section line.
193

SURVEYING
Level book form for cross-sectioning field notes194

SURVEYING
Cross-sectional plotting
 Unlike longitudinal sections the
horizontal and vertical scales of
cross-sections are usually the same.
 They are plotted without vertical
exaggeration as this is more
convenient for showing new work and
for volume calculations.
195

SURVEYING
CONTOURING
Definitions
 A contour line or contour is an imaginary line on the
surface of the earth, every point on which is at the
same height or altitude.
 The vertical interval (V.I.) or contour interval is the
term used to denote the difference in height between
successive contour lines and it is usually constant on
any one drawing.
 The horizontal equivalent (H.E.) is the term used to
denote the shortest horizontal distance between
successive contour lines. H.E. will vary with the slope
of the ground.
196

SURVEYING
 The gradient is the slope of the
ground as determined by:
 Spot height or spot levels is the term
used for levels on a site which are
taken in a random manner on various
spots or points of ground.
..
..
EH
IV
Gradient =
197

SURVEYING
Contour Characteristics
 The direction of the
steepest slope is
indicated by the
normal to the
contour lines, thus
a water course or
water-shed will run
at right-angles to
the contours (Fig.
59).
Contours with an inverted “V” shape representing a valley
Figure 59
198

SURVEYING
 Contour lines which
are close together
indicate a steep
slope (Fig. 60)
are widely spaced
indicate a gentle
slope (Fig. 60)
are nearly equally
spaced represent a
fairly uniform slope
(Fig. 61)
Figure 60
Figure 61 199

SURVEYING
 A contour `island'
indicates either a hill
or a depression,
according to how the
levels are changing.
 Ascending contour
lines denote a hill
(Fig. 62a) while
descending contour
elevations denote a
depression (Fig. 62b).
Figure 62
200

SURVEYING
Two `islands' close
together will
indicate either:
Two hills with a
`pass' between
them (Fig. 63)
Two
depressions
with a `ridge'
between Figure 63
201

SURVEYING
 Contour lines can never cross.
 Contour lines must be continuous.
 A single contour line cannot split into two lines
of the same elevation.
 Only in the case of a vertical cliff can contour
lines join.
 A contour line cannot simply end - it must close
back on itself, though not necessarily on any
one map.
 A peak or summit will be indicated by a small
dot with the relevant spot height alongside.
202

SURVEYING
Use of Contoured Maps and Plans
 It may be used in reconnaissance work in
order to plan a preliminary route;
 Approximate ground profiles or sections can
be drawn to scale along any line which is
shown in plan to check intervisibility among
other functions;
 To calculate approximate volumes of
earthworks;
 To calculate the approximate capacity of
reservoirs, etc.
203

SURVEYING
Contouring Methods
The direct method
Direct contouring is a method whereby the
contour is found by means of ordinary levelling
technique, each point on the contour line being
pegged out in the field.
(a)Direct vertical control using a level
 Levelling is begun from any convenient B.M. or
T.B.M.
 Deduce the height of instrument and calculate
the readings to be observed for each contour.
204

SURVEYING
Example:
R.L. of T.B.M. = 21.736
B.S. to T.B.M. = 2.072
H.I. = 23.808
Reading on staff for 20-m contour = 3.81
205

SURVEYING
 Taking one contour at a time, mark the
required reading on the staff with a piece of
tape for speed of location and direct the
staffman uphill or downhill at the edge of the
site until the required reading is obtained.
 When he is signalled to mark, the staffman
places a peg marked with the contour height.
 The staffman then proceeds forward along
the same level and holds the staff where he
assumes the contour to have changed
direction and the previous process is
repeated.
206

SURVEYING
 Having pegged one complete contour
visible from the instrument the next one is
dealt with and pegged in the same way.
 When the whole area visible from the
instrument has been covered a foresight is
observed. The instrument is moved to
another position to cover more of the site
and the same process is repeated.
 This goes on until the whole site has been
pegged and a final foresight can be taken
back on to the T.B.M., thus completing the
level circuit.
207

SURVEYING
(b) Direct vertical control using simple
equipment
 The A-frame or N-frame level;
 Flexible tube water level; and
 Hand level.
208

SURVEYING
The N-level (Fig. 64):
(i) Testing the N-
frame level
 Before fixing the
carpenter level to
the frame, the
instrument must
be tested to make
sure that the
carpenter level is
in the correct
position.
Figure 64
209

SURVEYING
(ii) Setting out contour
lines and slopes
Setting out contour lines
 By turning the frame
around one leg (Fig.
65), a position of
the frame is found
such that the second
leg is on the ground
and the bubble of
the carpenter level
is in between the
marks.
Figure 65
210

SURVEYING
 The N-frame is
moved to the
newly-placed peg
and the
procedure is
repeated until the
end of the field is
reached (Fig.
66).
 All the pegs, thus
driven in the
ground, form a
contour line
Figure 66
211

SURVEYING
 Setting out
subsequent
contours (Fig. 67)
will require a
choice of an
appropriate
contour interval.
 In practice, the
height difference
will vary between
10 and 50 cm. Figure 67
212

SURVEYING
Setting out slopes
 Suppose that the slope
of a ditch to be set out
on the field is 1%.
 A slope of 1% would
require one leg to be 2
cm (1% of 2 m) shorter
(Fig. 68);
 a slope of 1.5% would
require one leg to be 3
cm (1.5% of 2 m)
shorter; and a slope of
2% would require a 4
cm (2% of 2 m) shorter
leg.
Figure 68
213

SURVEYING
The shortest leg of
the N-frame is
placed close to the
starting peg (A)
(Fig. 69).
A position is found
such that the second
leg is on the ground
and the bubble of
the carpenter’s level
is centred
The spot thus found
is 2 cm lower than
the starting point
and is marked with
a new peg .
Figure 69
214

SURVEYING
 The N-frame is
moved and the
short leg is placed
near peg (B).
 The procedure is
repeated until the
end (Fig. 70).
 The line marked
would be, after
correction, the
centre line of a
ditch with a slope
of 1%.
Figure 70
215

SURVEYING
(c)Direct horizontal control
With the contours now pegged on the
ground the peg positions must be surveyed
to enable them to be plotted.
 With a chain survey.
 With a control traverse.
 With polars. The bearing and distance
from traverse stations or triangulated
control points can be observed to the
various peg positions.
216

SURVEYING
(d)Plotting
 The peg positions are plotted from
the data obtained from the horizontal
control survey and the heights of
each are recorded.
 Finally the contour lines are drawn as
curves running through the peg
positions denoting each contour.
217

SURVEYING
The indirect method
 In the indirect method the points
located do not necessarily fall on the
actual contours.
 The points surveyed are plotted and
their heights recorded and then the
points serve as a basis for the
interpolation of the contour positions
218

SURVEYING
Methods for obtaining height information:
Grid levelling
 Most systematic, and probably the most
commonly used method of obtaining the
information for indirect contouring.
 Operations involved:
(a) The area must first be surveyed;
(b) The area is then marked out with a grid;
(c) Spot levels are taken at the points of
intersection of the grid lines;
(d) The grid is plotted on the survey drawing
and the contours are found by
interpolation.
219

SURVEYING
 Setting out the grid
 The grid is set out
from the longest
chain line in such a
way that it can be
plotted accurately
on the survey
drawing or an
overlay (Fig. 71).
 The size of the grid
will depend on the
terrain but will
generally vary
between 5m and
20m.
Illustration showing the field book sketch
of a grid layout off a survey line T3– T4
Figure 71
220

SURVEYING
Contouring by sections
 Following the method
of section levelling, a
long line may be
ranged out through
the area and sections
of levels be taken left
and right of the
longitudinal line (Fig.
72).
 The points taken are
plotted on the plan
and the contours are
interpolated between
them in the normal
way.
Contouring by sections
Figure 72
221

SURVEYING
Contouring by radiating lines
 The level with a horizontal
circle of degrees is set up
over a fixed known spot in
the centre of the area
under consideration.
 A reference direction is
chosen, and levels and
distances on several lines
radiating from the
instrument position are
observed (Fig. 73).
 It is a useful method on a
small hill top or knoll to
enable the slopes of the
hillside to be contoured.
Figure 73 222

SURVEYING
Contouring by tacheometry
 Tacheometry is that branch of surveying where
heights and distances between ground marks are
obtained by optical means only, the slower process of
measuring by direct taping being entirely eliminated.
 A tacheometer (or tachymeter) is any theodolite or
level adapted, or fitted with an optical device, to
enable measurements to be made optically.
 Using such an instrument, levels can be taken where
they will best reflect the nature of the ground, rather
than in some predetermined pattern of say, a grid.
 The routine is the same as that used for direct
levelling when tacheometry is used.
223

SURVEYING
Interpolating contours
 Interpolation is the
process of locating
in plan any required
levels along a line
joining two known
levels.
 The method is to
plot the points of
intersection of each
contour with the grid
lines, then draw in
the contours as
smooth curves (Fig.
74).
Figure 74 224

SURVEYING
Faults of grid levelling
 A large number of levels are observed
simply to complete the grid, and some of
these may not be required for the
contouring.
 Time consuming especially so with laying
out of the grid.
 Changes of slope or features may exist
within the grid which if not dealt with will
go unrecorded.
 In built-up areas or in woodland, it may not
be possible to set up a grid.
225

SURVEYING
Comparison of methods
 Direct contouring is the most accurate
method, but because of the excessive
amount of field work, it is seldom adopted
except on small sites where accurate
contours are required.
 Indirect contouring is most commonly used
because it is the quicker method and
provides contours with sufficient accuracy
for most practical purposes.
226

SURVEYING
ORIENTATION AND POSITION
Introduction
 Orientation is synonymous with bearing
from the surveyor’s point of view, although
the term azimuth rather than bearing can
be encountered when referring to true
north.
 The bearing of a line is the angle formed
between the line, the direction of which is
required, and a line parallel to the
reference direction.
227

SURVEYING
 With reference to Fig.
75, the observer’s
terrestrial meridian is
indicated as the line
connecting the north
and south poles and
his station O.
 The true bearing of
line OY at O is thus
the horizontal
clockwise angle
between the direction
to true north along
the meridian at O and
line OY.
Figure 75
228

SURVEYING
Magnetic Declination and its Variation
 The angle between the direction of the magnetic
meridian and the true or geographical meridian
at any point is called the angle of declination or
simply declination.
 The angle of declination varies from place to
place.
 Lines on a map joining places of equal
declination are known as isogonals, isogons or
isogonic lines.
 The isogonic line of zero declination, along which
the direction of a compass indicates True North,
is known as an agonic line.
229

SURVEYING
 The positions of the magnetic poles are not
fixed and the north magnetic pole tends to
wander more than the south.
 This causes alterations in the positions of
the isogonic lines and new isogonic charts
have to be prepared from time to time.
 The angle of declination at any point is
therefore not constant, but is subject to a
number of variations:
230

SURVEYING
 Secular variation
 Diurnal variation
 Periodic variations
 Irregular variations
 Of these various effects, the diurnal variation
and magnetic storms are the most serious in
reducing the accuracy of compass bearings.
 In addition there can be interference with the
magnetic field caused by electric cables, small
masses of iron, or iron ore and this is known
as local attraction.
231

SURVEYING
Bearings
(a) Whole-circle bearings
 The whole-circle bearing
(αAB) of a line AB is defined
as the clockwise angle from
0˚ to 360˚ at A between the
direction to north and the
direction to B.
 The bearing of the line AB,
i.e. the bearing of B from A
(Fig. 76a), differs by 180˚
from the bearing of the line
BA (αBA), i.e. the bearing of A
from B (Fig. 76b).
Figure 76
232

SURVEYING
 Whole-circle bearings can be based on the
sexagesimal system or the centesimal system.
 In the the sexagesimal system the circle is divided
into four quadrants, each subdivided into 90˚,
giving a total of 360˚. Each degree is further
divided into 60’ and each minute into 60”.
 The centesimal system is the continental or metric
system where the whole circle is divided into four
quadrants as before, but each is divided into 100
grades, giving a total of 400 grades. The hundredth
part of a grade is known as a centigrade denoted by
the letter c.
233

SURVEYING
(b) Quadrantal bearings
 A quadrantal or reduced
bearing is the angle
between the main line
marking the direction to
which bearings are
referred (N-S lines which
need not necessarily lie
in the true meridian) and
the direction of the given
line measured from 0° to
90° only, the shortest
way east or west from
the north-south line (Fig.
77)
Figure 77
234

SURVEYING
True or Geographical North
(a) Determination of true bearing by gyroscope
 A bearing is the angle made relative to grid north
while an azimuth is in relation to true north.
 The gyroscope has been used in navigation as a
north-seeking device for a considerable period of
time.
 A gyrotheodolite is a north–seeking gyroscope
integrated with a theodolite.
 A gyroscopic azimuth is the azimuth determined
with a gyrotheodolite.
(b) Determination of true bearing by observation to
the sun
235

SURVEYING
Global Positioning Systems
Background
 The traditional method for the direct determination
of position has been by astronomical observation.
 The Global Positioning System (GPS) was developed
purely for military purposes.
 GPS is a worldwide radio-navigation system formed
from a constellation of 24 satellites and their
ground stations.
 GPS uses these "man-made stars" as reference
points to calculate positions accurate to a matter of
metres.
236

SURVEYING
Working principles of GPS
 The basis of GPS is "triangulation" from
satellites.
 To "triangulate," a GPS receiver measures
distance using the travel time of radio signals.
 To measure travel time, GPS needs very
accurate timing which it achieves with some
tricks.
 Along with distance, you need to know exactly
where the satellites are in space.
 Finally you must correct for any delays the
signal experiences as it travels through the
atmosphere.
237

SURVEYING
(a)Triangulating from satellites
 The whole idea behind GPS is to use satellites
in space as reference points for locations here
on earth.
 By very, very accurately measuring our
distance from three satellites we can
"triangulate" our position anywhere on earth.
First let’s consider how distance measurements
from three satellites can pinpoint you in space.
238

SURVEYING
Step One:
 Suppose distance from a
satellite = 17,702 km.
 Possible locations represented
by the surface of a sphere that
is centered on this satellite that
has a radius of 17,702 km (Fg.
78)
Step Two:
 Distance to a second satellite =
19,312 km.
 This tells us that we're also on
a sphere that is 19,312 km
from the second satellite
 Or in other words, we are
somewhere on the circle where
these two spheres intersect
(Fig. 79).
Figure 78
Figure 79239

SURVEYING
Step Three:
 Measurement from a third
satellite = 20,921 km
narrows our position down
even further, to the two
points where the 20,921
km sphere cuts through
the circle that is the
intersection of the first
two spheres (Fig. 80).
 Usually one of the two
points is a ridiculous
answer (either too far
from Earth or moving at
an impossible velocity)
and can be rejected
without a measurement.
Figure 80
240

SURVEYING
(b) Measuring distance from satellite
 In the case of GPS we are measuring a
radio signal so the velocity is going to be
the speed of light or 3 x 108
ms-1
(the speed
of light in vacuum).
 The difference in sync of the receiver time
minus the satellite time is equal to the
travel time.
TimexVelocityceDis =tan
241

SURVEYING
So in summary:
 Distance to a satellite is determined
by measuring how long a radio signal
takes to reach us from that satellite.
 To make the measurement we
assume that both the satellite and
our receiver are generating the same
pseudo-random codes at exactly the
same time.
242

SURVEYING
 By comparing how late the satellite's
pseudo-random code appears
compared to our receiver's code, we
determine how long it took to reach
us.
 Multiply that travel time by the speed
of light and you've got distance.
243

SURVEYING
(c) Getting perfect timing
 On the satellite side, timing is almost
perfect because they have incredibly
precise atomic clocks on board.
 Atomic clocks don't run on atomic energy.
They get the name because they use the
oscillations of a particular atom as their
"metronome."
 A fourth measurement, synchronizes our
receiver clocks with the atomic clocks on
board the satellites so that we are
perfectly synced with universal time.
244

SURVEYING
(d)Satellite positions
 The spacings of the satellites are
arranged so that a minimum of five
satellites are in view from every
point on the globe.
 The basic orbits are quite exact but
just to make things perfect the GPS
satellites are constantly monitored by
the Department of Defense.
245

SURVEYING
(e) Error correction
 There are several factors that may affect a GPS
signal
 To get the most out of the system, a good GPS
receiver needs to take a wide variety of possible
errors into account.
 As a GPS signal passes through the charged particles
of the ionosphere and then through the water vapor
in the troposphere it gets slowed down a bit, and this
creates the same kind of error as bad clocks.
 Even though the satellites positions are constantly
monitored, they can't be watched every second. So
slight position or "ephemeris" errors can sneak in
between monitoring times.
246

SURVEYING
 As hard as it may be to believe, the same
government that spent $12 billion to develop the
most accurate navigation system in the world
intentionally degraded its accuracy.
 The policy was called "Selective Availability" or "SA"
and the idea behind it was to make sure that no
hostile force or terrorist group can use GPS to make
accurate weapons.
 Basically the Department of Defense introduced
some "noise" into the satellite's clock data which, in
turn, added noise (or inaccuracy) into position
calculations.
 Military receivers used a decryption key to remove
the SA errors and so they're much more accurate.
247

SURVEYING
Differential GPS
 Basic GPS is the most accurate radio-based
navigation system ever developed, and for many
applications it is sufficiently accurate.
 The quest for excellence led to the development
of Differential GPS, as a way to correct the
various inaccuracies in the GPS system, pushing
its accuracy even farther.
 Differential GPS or "DGPS" can yield
measurements good to a couple of metres in
moving applications and even better in stationary
situations.
248

SURVEYING
 Differential GPS involves the cooperation of two
receivers, one that is stationary and another that
is roving around making position measurements.
 The stationary receiver is the key. It ties all the
satellite measurements into a solid local
reference.
 Differential GPS can eliminate all errors that are
common to both the reference receiver and the
roving receiver which include everything except
multipath errors (because they occur right
around the receiver) and any receiver errors
(because they're unique to the receiver).
249

SURVEYING
 That is the idea behind differential GPS:
 We have one receiver measure the
timing errors and then provide
correction information to the other
receivers that are roving around.
 That way virtually all errors can be
eliminated from the system, even the
pesky Selective Availability error that
the Department of Defense puts in on
purpose.
250

SURVEYING
 The reference receiver is placed on a point that has
been very accurately surveyed.
 This reference station receives the same GPS signals
as the roving receiver but instead of working like a
normal GPS receiver it attacks the equations
backwards.
 Instead of using timing signals to calculate its
position, it uses its known position to calculate timing.
 It figures out what the travel time of the GPS signals
should be, and compares it with what they actually
are. The difference is an "error correction" factor.
 The receiver then transmits this error information to
the roving receiver so it can use it to correct its
measurements.
 Many new GPS receivers are being designed to accept
corrections, and some are even equipped with built-in
radio receivers. 251

SURVEYING
Various levels of GPS accuracy:
 Using varying techniques, varying GPS
receivers and other equipment, a range of GPS
accuracies can be achieved:
 An autonomous GPS receiver with Selective
Availability 'on' will achieve a horizontal
accuracy of 50-lOO m, 95% of the time.
 An autonomous GPS receiver with Selective
Availability 'off' will achieve a horizontal
accuracy of 12-15 m, 95% of the time.
252

SURVEYING
 A code-phase GPS receiver using
differential correction techniques can
achieve accuracies of between 0.5 and 3
m, 95% of the time.
 A carrier-phase GPS receiver in
kinematic mode can achieve accuracies
of between 1 and 5cm, 95% of the time.
 A carrier-phase GPS receiver in static
mode can achieve reliable sub-cm
accuracy.
253

SURVEYING
 The important questions to ask, when
considering which GPS equipment is
suitable for a particular application, are:
 What level of accuracy do you really
need?
 Do you need this accuracy in the field,
in real-time, or do you just need this
accuracy when you return to the
office?
254

SURVEYING
Advanced concepts:
(a) Code-phase vs Carrier-phase
(b) Augmented GPS
 Wide Area Augmentation System
(WAAS)
 Local Area Augmentation System
(LAAS)
255

SURVEYING
Applications of GPS
(a) Location
 GPS is the first positioning system to offer highly
precise location data for any point on the planet, in
any weather.
(b) Navigation
 Using the GPS coordinates, appropriate software can
perform all manner of tasks, from locating the unit,
to finding a route from A to B, or dynamically
selecting the best route in real time.
(c) Tracking
 If navigation is the process of getting something
from one location to another, then tracking is the
process of monitoring it as it moves along.
256

SURVEYING
(d) Mapping
 Mapping is the art and science of using
GPS to locate items, then create maps and
models of everything in the world,
including natural features e.g. mountains,
rivers, forests and other landforms, and
man made features e.g. roads, routes, city
streets, buildings, etc.
 GPS can be used in conjunction with
geographical information systems (GIS) for
data capture and mapping.
257

SURVEYING
(e) Timing
 Time is a powerful commodity, and exact time is
more powerful still.
 GPS is used to disseminate precise time, time
intervals, and frequency (every GPS receiver is, in
essence, an atomic accuracy clock). Astronomers,
power companies, computer networks,
communications systems, banks, and radio and
television stations can benefit from this precise
timing.
 GPS makes the job of "synchronizing our watches"
easy and reliable.
258

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