# Surveying lecture 1

Urban and Civil

Nov 15, 2013 (4 years and 5 months ago)

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A2.2NP1

Environmental Practical 1

TOPIC 1

TECHNIQUES IN

BASIC SURVEYING

Basic ideas

Surveying
-

the creation of a scale representation of
the ground surface
-

is a basic activity in many areas
of environmental management.

A survey will be one of of two types:

Primary survey

-

to establish the position of objects in three
dimensions when no previous information exists

Secondary survey

-

to add extra information to existing
data or to measure changes over an interval of time

Basic ideas

The task of three dimensional position fixing
is normally broken into two parts:

Determining
plan position

Determining
elevation

Basic ideas

Each of these determinations may be either:

absolute

-

made in terms of a fixed co
-
ordinate
system

relative

-

made in terms of local co
-
ordinates
which may later be converted to absolute co
-
ordinates if required.

The majority of surveys carried out for
environmental management are thus
secondary relative surveys

Plan Position Fixing

The plan position of a station can be
established in a number of ways:

By reference to the apparent positions
of astronomical objects when viewed
from that station

This method gives the absolute location of the
station in terms of latitude and longitude,
which can be converted to local systems such
as the National Grid.

By the measurement of the
angles

between lines
of sight
to

the unknown station
from

other known
positions

By the
intersection

of lines of sight
from

the
unknown station
to

other objects whose

These two methods both rely on the simple Euclidean
geometry of the plane. (Hence the term plane surveying).
The first procedure is termed
triangulation

and the
second
resection
.

Baseline

A

B

The basic principle of triangulation

Measured angle

Measured angle

Unknown position

The basic principle of resection

Measured

angle

Measured

angle

Known position

Known position

Known position

Measured

angle

By measurement of
distances

between
the unknown station and other objects
of known positions

This last method includes a number of
particular cases:

measurements of
offset

distances from
a base line.

trilateration

-

the distance equivalent of
triangulation.

tacheometry

-

an optical method of
distance measurement along a known
bearing

Baseline

A

B

The basic principle of trilateration

Measured side

Measured side

Plane Surveying: Theory

Plane surveying relies on the basic
concepts of Euclidean geometry, and in
particular the properties of triangles.

The most important (for our purposes)
of these are:

Plane Surveying: Theory

The internal angles of a triangle sum to 180

The sides of an
equilateral

triangle are equal
and the internal angles are all 60
°

The base angles and opposing sides of an
isosceles

triangle are equal

60º

60º

60º

The equilateral triangle

All sides equal in length

All angles equal (= 60º)

The isosceles triangle

Two sides equal in length

Two angles equal

a

a

Plane Surveying: Theory

If the respective angles in two triangles are
equal then the triangles are
similar

and their
sides are all in the same proportion

If two triangles have
two angles

and
one side

equal (or vice versa) then they are
congruent

and all their other respective angles and
sides are equal.

Two triangles are also congruent if all their
sides are equal.

Similar triangles have corresponding angles equal

but are of differing size

Conguent triangles are identical

two angles and one side equal

two sides and one angle equal

all three sides equal

Plane Surveying: Theory

Congruent triangles are
unique

-

you cannot
draw two different triangles from the same set
of measurements

This means that a
complete

set of survey
data must define the positions of objects
uniquely.

Plane Surveying: Theory

Any
closed polygon

can be subdivided into a
series of contiguous triangles

These properties are repeatedly used in the
procedure of
triangulation

in which stations
are surveyed in a pattern of contiguous
triangles.

Any closed polygon can be subdivided into contiguous triangles

These should be chosen to make as many of the triangles as

close to equilateral as possible

Plane surveying: practical aspects

In practice, most plane surveys are carried out
in a straightforward way following an
established sequence:

1. A
reconnaisance survey

will establish the
dimensions of the area, relative levels,
significant features, accessibility, obstacles etc

Plane surveying: practical aspects

2. Establish an accurate
baseline

by measurement
from existing survey points, natural features,
buildings etc. If none are available then the baseline
must be fixed by absolute methods.

3. Establish as required any further
control

points

by
triangulation or trilateration from the base
-
line.

Plane surveying: practical aspects

4. Incorporate detail by tacheometry, traversing, tape &
offset or whatever other method is appropriate.

5. The intermediate stations should where appropriate
be cross
-
checked with the control points by resection
and all traverses should be
closed

at a control point.

6. Inaccessible detail should be incorporated by
triangulation or plane tabling from the ends of the
baseline.

Baseline

ILLUSTRATION OF THE USE OF OFFSETS

Plane surveying: practical aspects

7. If a topographic survey is being undertaken, levelling
traverses should be carried out around the survey
stations and the baseline tied to the local benchmark
by a closed traverse.

8. The use of a theodolite or total station will enable
both the position and the elevation of stations to be
found simultaneously by combined tacheometry and
triangulation or by trilateration

THE “CHAIN” SURVEY

How to establish relative plan positions

Chain survey

Simplest of all survey techniques

Relies on linear measurements; slopes
>3
o

Usually requires a clear line of sight

The triangles used should be equilateral
or approximately so

Terminology

Trilateration

is the measurement of
sides of a triangle

whereas
triangulation

refers to the
measurement of the angles of the
triangle

Basic equipment

Ranging poles

Survey pegs and ‘arrows’

Chain & tape measure or other distance
measuring instrument

Plumb line

Compass

Chain survey components

Base line: the longest line

Chain /survey lines

Survey stations

Offset lines

Order of events

“Range out” survey stations with ranging rods

Establish base line and measure accurately

Measure remaining distances between other
survey stations

Measure offset lines whilst measuring
between survey stations

Sloping ground

If the ground slopes by more than about 3
°
,
this must be allowed for in the survey.

The measured distances are thus slant
distances and must be corrected to true
horizontal distances.

This requires that the vertical angle between
the stations is known

Ground distance determined

a

h

X

Sloping ground

For an approximate survey, it may be
sufficient to step up or downhill using a
series of horizontal and vertical lines

If the drop is measured at the same
time, some estimate of the slope profile
can be obtained

Chain surveying (“stepping”)

w

x

y

z

c

b

a

Sloping ground

If stepping is not appropriate, more
sophisticated methods must be used to
measure the slant distance and the
vertical angle simultaneously

Requires optical sighting equipment:
usually either a clinometer, Abney level
or theodolite

Basic levelling in chain surveys

a

h

h

Correcting for horizontal distance:

the “hypotenusal allowance”

a

h

z

correction factor = xy
-

yz

= xy(1
-

cos
a
)

y

x

LEVELLING

How to destermine relative
elevations

Levelling:

accounting for slopes

Unlike chain surveys, levelling surveys
account directly for slope and
incorporate this data into the whole
measurement exercise

AIMS:

to determine height differences between
two points

to determine elevations for sections

The elevation of a station can be
established by:

inclined line of sight from chain survey stations

levelling from another point of known height

by inclined tacheometry

Levelling is the more accurate method but is
also the slower. Modern instruments are
capable of cm accuracy under normal
conditions over distances of 100’s metres.

The keys to successful levelling lie in the
setting up of the instrument, in the closure of
the traverses and in the careful recording
(booking) of the results.

Inclined tacheometry relies on the combined
measurement, by theodolite, of the slant
distance to the new station and the angle
relative to the horizontal.

The elevation change and horizontal distance
can then be found by simple trigonometry.

The accuracy of the method, using normal
instruments, is around 10’s cms in 100’s
metres.

Direct levelling

Most typical form used

Relies upon:

a horizontal line of sight, also termed
“the line of collimation”

a fixed datum level

Measurements to be taken

Backsight

Foresight

Intermediate sights

The “rise and fall” method

This method records the relative change
in level between successive stations

The changes are converted to the
reduced level of each station

The reduced level is relative to the local
datum

Booking the results

The method relies on recording your
results in a survey book in a standard
format

This allows you to check your work and
to identify any errors systematically

Reduced levels

The change of level is 2.312m
-

2.533m =
-
0.221m

2.533m

Datum line: 100.522m

(from OS Benchmark)

2.312 m

The
reduced

level of point B is
100.301m

B

A

The absolute (datum) level of point A is
100.522m

IP 1

Backsight

Interm.

Foresight

Rise

Fall

R.L.

Distance

Remarks

2.312

100.522

0.221

100.301

1.2

Rise and fall booking

Point A

Point B

-

2.533

Transfer of level

The new change of level is 1.674m
-

1.631m = + 0.043m

1.631m

1.674 m

The absolute level of point C is
100.344m

C

B

At the next stage, B becomes the backsight and C is the new foresight

IP 2

Backsight

Interm.

Foresight

Rise

Fall

R.L.

Distance

Remarks

2.312

100.522

-

0.221

100.301

1.2

Rise and fall booking (cont)

Point A

Point B

-

2.533

1.674

1.631

+ 0.043

100.344

Point C

Continuing this process, suppose we
end up with a set of results as follows:

This will enable us to check our working

Backsight

Interm.

Foresight

Rise

Fall

R.L.

Distance

Remarks

2.312

100.522

-

0.221

100.301

Rise and fall booking (cont)

Point A

Point B

--

2.533

1.674

1.631

+ 0.043

100.344

Point C

2.504

3.010

2.413

0.956

2.016

2.718

--

--

--

--

+ 1.548

+ 0.994

-
0.305

101.892

102.886

--

--

--

--

102.581

11.913

9.854

9.854

2.585

-

0.526

-

0.526

102.581

-

100.522

2.059

2.059

2.059

CHECKS

OK

Using an intermediate sight

Sometimes we wish to include a specific
feature but it is not convenient to set up
a new instrument position for this

The solution is to take a sighting onto
the staff when it is placed on this feature
-

this is called an
intermediate

sight

Intermediate sight

The new change of level is 1.674m
-

2.988m =
-
1.314m

2.988m

The absolute level of the intermediate point C is
98.987m

C

B

The intermediate sight is taken at the base of the channel between B and C

IP 2

Intermediate sight

1.674m

Backsight

Interm.

Foresight

Rise

Fall

R.L.

Distance

Remarks

2.312

100.522

-

0.221

100.301

1.2

Rise and fall booking
(intermediate sight)

Point A

Point B

-

2.533

1.674

1.631

+ 0.043

100.344

Point C

2.988

channel

-
1.314

98.987

Next FS

Optical distance measurement

It is often convenient to use the levelling
instrument itself to calculate the distance
between the instrument and staff positions

This is done using the

that are
visible in the viewfinder

These are arranged such that the distance to
the staff is
100x

the

that is
read on the staff between the two lines

This procedure is known as
tacheometry

Tacheometry

The viewfinder:

lines

Multiply vertical

distance by 100

to obtain

horizontal distance

Inclined tacheometry

If the ‘level’ can be swung in a vertical
arc, the distance up an inclined sight
line can be obtained.

If the vertical angle is also measured,
the slant distance can be converted to
give both the change in height and the
true horizontal distance.

Inclined tacheometry

a

Change of height

Tacheometric distance

Measured angle

True horizontal distance

The theodolite

If such an instrument can also be swung in a
horizontal arc, and the angle of rotation can
be measured, we are able to determine the
angles of the sight lines between stations.

This allows both trilateration and triangulation
with the same instrument.

Such a versatile instrument exist and is called
a

theodolite
.

Summary

Chain surveys are suited to planimetric
surveys on low slopes. They rely upon
trilateration.

Levelling is used where terrain is more
uneven. Levelling surveys often use
tacheometry to fix station positions.

A theodolite survey permits levelling,
tacheometry or triangulation as required.