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ECE 2218- ENGINEERING SURVEYING I NOTES
INTRODUCTION TO SURVEYING
1
...

It is the art of measuring slope, horizontal and vertical distances between objects, measuring
angles between lines, determining the direction of lines and establishing point locations by
predetermined angular and linear measurements
...
The third dimension
(height) is shown on the plan in various ways
...
g
...
Horizontal plane is the plane tangent
to a level surface
...
Vertical plane is normal to the horizontal plane
...
2 Principal classifications of surveying (size)
a)

b)

Geodetic surveying – where measurements cover such a large part of the surface of the
earth that the curvature of the earth cannot be ignored if discrepancies are to be
eliminated
...


1
...

b) Topographic surveying – the location of the main natural and artificial features of the
earth
...

d) Engineering surveying – preparatory to, or in conjunction with, the carrying out of
engineering or building works
...


1
...
4
...

1
...
2 Purpose of Engineering Surveying:
i)
-

At the conception stage (Planning &design)
to provide topographical surveys and other measurements upon which projects are
designed
...
Levelling is done for purposes of design and earth works computations
...

- The control network established for these topographic and property surveys contain many
of the horizontal and vertical control points which will eventually form the subsequent
construction surveys
...

-Setting out of engineering constructions e
...
roads, buildings , pipelines etc such that they are
correctly positioned in all the three dimensions
...

-Also include deformation monitoring of engineering works

•
•

2
...

Mostly Slope distance is measured then reduced to horizontal distance for purposes of
mapping
...
1 Methods of Linear Measurements
i)

Pacing

ii)

Chaining

iii)

Taping

iv)

Electronic Distance Measurement- Indirect method of measuring distance where
electromagnetic waves are used
...


vi)

Sonic Distance measurement- Indirect measurement of distance by use of sound
waves
...


2
...
They measure the
number of whole wavelengths of the generated signal, and any fractional part of the
wavelength between the instrument and the target
...

2
...
4
...

a) Correction of chain for standardization
Checking the chain frequently is necessary for the correction to be effective as the chain changes
in length due to wear and tear
...
If used in its incorrect condition a correction needs to be applied

 
   


 
    
   

   

Example: a line is measured with a chain believed to be 20 m long which gives a length of 365
...
on checking, the chain is found to measure 20
...
what is the correct length of the line?

 
   



365
...
03
 365
...

All measurements in surveying must be in the horizontal plane or be corrected to give the
projection on the plane
...

Step Chaining
On ground of variable slope this is the best method and needs no calculation
...

measuring the angle of the slope
Applicable where the ground runs in regular long slopes
...

 
   
  cos  
!

C

Correct length = L cosѲ

Ground slope

When applied as a correction

A

"  #$1 # cos &!

Ѳ

Horizontal

Where L = measured length and θ is the slope angle
...

c) Other corrections

B

When using the steel band, in addition to standardization correction, the following factors may
have to be considered for especially higher order survey work
...

• Slope
• Height above mean sea level
• Sag
Therefore in addition to standardization and slope corrections, the following corrections must be
done especially for catenary measurements
...
If it is not applied, then a correction needs to be made since the length of the
tape will change

(  $ ·

* # *"
+·,

Where: T, Ts = field and standard tension respectively ( N)
A = cross sectional area of band (mm2)
E = Young's modulus of elasticity for the band (N/mm2)
L = Length measured
ii)

Temperature correction

A correction is required if the tape temperature, t is not equal to the standard temperature, ts
...
$ # " !

where α = coefficient of linear expansion of the band per °C

iii) sea level correction
The length of the line measured needs to be reduced to the
equivalent length at mean sea level
...
In this
case, a correction for sag in the tape needs to be applied if the tape has been standardized on the
flat
...


4  #

5 ' $6
24* '

Where: w = weight per unit length of tape (N/m ); L = length under suspension and T = tension
applied to the tape (N), expressed in the same units as w

B) When using EDM
All EDMs use some form of radiations which are propagated through the atmosphere
...
Some of the corrections applied to the measured distance
are:i)

Curvature of signal path
Where long ranges are involved, the signal path is curved and not a straight line due to the
linear refractive index gradient ( variation of refractive index along the path) ,since the
signal passes through different layers of air exhibiting different refractive indices
...

ii)

iii)

Sea level correction
This is similar to the one in catenary measurements
...
H/R
Arc to chord correction
In the derivation of sea level and slope corrections, assumption is made of two similar
triangles with common vertex at the centre of the earth
...

S
3

2

Cr= (S-C)= C /24R
where;
Cr= correction
S=arc distance
C=Chord distance
R=radius of the earth
iv)

C

R

Variation in refractive index
Refractive index of light wave and microwaves in air is a function of temperature,
atmospheric pressure, partial pressure of water vapour which depend on temperature
and relative humidity
...
Since
distance is a function of velocity a correction is therefore applied
...


3
...
The transmitted wave is compared to the received wave and the instrument is able to
compute and display the required distance
...

The EDM equipment utilises the electromagnetic waves to measure distances
...
The type of electromagnetic wave generated
depends on the nature of the electromagnetic wave generated
...

The wave completes a cycle when moving between identical points on the wave and the number
of times in one second the wave completes a cycle is termed the frequency of the wave
...

The wavelength is the distance which separates two identical points on the wave or is that length
traversed in one cycle by the wave and is denoted by λ metres
...

The speed of an electromagnetic wave in a vacuum is termed the speed of light and is given the
symbol C
...
0 × 108 m/s
...
Another usage is the fraction of the wave cycle which has
elapsed relative to the origin )
The phase provides a convenient method of identifying fractions of wavelengths or cycle
...
The
electromagnetic spectrum is continuous from visible light with frequencies of the order of 1014

Hz, corresponding to a wave length of 10-6 m, to long radio waves of frequencies 104 or 105 Hz,
corresponding to wavelength of order 104 m
...
In the
former case the following three categories exist:
i
...

iii
...

However, for marine and air navigation and for much hydrographic work, long range is vital,
accuracy requirements are comparatively low and permanent or semi permanent transmitters are
appropriate
...

For practical field instruments for engineering and land surveying the higher frequencies are the
most useful as the instruments can be made smaller and transportable and the propagation
through the atmosphere more stable
...
The solution adopted is to modulate the high

frequency carrier with low frequency wave and use the modulated wave for measurement
purpose
...
The carrier signal does not have to be at precisely
determined frequency but it must be produced efficiently and in such a form that it can be
modulated easily
...

Some instruments use an amplitude modulation, whilst other uses a frequency modulation, the
difference being indicated in the figure below;

In amplitude modulation the amplitude of the carrier wave is varied above and below its unmodulated value by an amount proportional to the amplitude of the modulated signal and the
frequency of the signal
...

Phase modulation refers to indirect frequency modulation of the carrier wave, the amplitude
remains the same
...


In the pulse transit time case, the unmodulated carrier is usually a pulse train or series of pulse,
and not the continuous wave previously
...
01 m or better is required usually the phase difference system
is adopted, being based on the relationship between the transmitted and received signal
...

Where the two signals are touching, then the transmitted and the received signal would be in
phase, but as the receiver moves away from the transmitter the received signal will lag behind
the transmitted due to the time of travel of that signal
...
When that distance is equal
to the wavelength the phase difference will be equal to 2A and the signals will be in phase, as in
fact they will be each time the distance apart is an integral wavelength
...

It’s not possible to compare instantaneously the phase of the signal at a transmitter and distant
receiver
...
Thus it’s always a double phase that is measured
...
e
...

v0 = velocity of electromagnetic wave in vacuum
µ = refractive index
f = frequency
Cλ

=            5=
 = @>  5=
2π
Generally n is unknown and d can be found by repeating the measurements of phase difference at
frequencies differing from a ‘fine’ measuring frequency
...
This process is referred to as resolving ambiguity
...
An operator is required at each, inter communication
being possible by means of built in radio telephones
...
The display
is calibrated to read directly in metres
...
e
...
03 m)and the measurement
is carried out using a frequency modulation of about 7
...
The effective modulation
wavelength is typically 10 m and, with a phase resolution of 0
...
This gives a basic
precision of about 0
...
The length of the modulated wave is given by:

λ=

Vr
f

With λ = wavelength; Vr = velocity of the microwave through the atmosphere and f = modulating
frequency
...

Effect of atmospheric conditions
The conditions of the atmosphere that have an effect on the velocity of light and microwaves are
the air temperature, atmospheric pressure and relative humidity
...
Knowledge of these conditions allow the determination of the

refractive index of the air which must be known to compute the velocity of light or microwaves
under given meteorological conditions
...
8864 0
...
604 +
+
 10
λc2
λc4 

Where λc = wavelength of the light carrier in micrometers

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