ELEMENTARY SURVEYING
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Introduction
Surveying is one of the oldest arts practiced by man. The practice of surveying is indispensable to
all branches of engineering and architecture. Today, surveying has become an important profession. The
introduction to the principles and practices of surveying has become an integral part of engineering and
architecture education and training. Surveys are required prior to (preparation) and during the planning
and construction of projects.
“Surveying is the starting point for any engineering and architecture project”
SURVEYING
It is defined as an art or science to determine the relative positions of points on, above or beneath
the surface of the earth, with respect to each other, by measurements of horizontal and vertical distances,
angles and directions.
It also includes the computation of areas, volumes and other quantities and the preparation of
maps.
General Classification
Plane Survey – it is a type of surveying in which the earth is considered to be a flat surface and
where distances and areas involved are of limited extent and that the exact shape of the earth
is disregarded. Plane surveys are done for engineering projects and also for establishing
boundaries.
Geodetic Survey – A survey in which the shape or the curvature of the earth’s surface is taken
into account and a higher degree of precision is exercised in linear an angular measurements.
Geodetic surveying deals in fixing control points, which may afterwards be used for plane
surveys.
Types of Surveys
a. Based on Instrument Used
a.1. Chain Survey – Measurements are done with chain and tape. This is a type of surveys which
consists of linear measurements only.
a.2. EDM – Electronic distance measuring instruments rely on propagation, reflection and
subsequent reception of either light or radio waves and displays in some form of the result of
the measurement.
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a.3. GPS - GPS or the Global Positioning System was invented by the U.S. Department of Defense
(D.O.D). It utilizes a constellation of at least 24 medium Earth orbit satellites that transmit
precise microwave signals, the system enables a GPS receiver to determine its location, speed,
direction, and time.
a.4. Leveling – This method of surveying in which the relative vertical heights or elevations of
points are determined by employing a level and a level rod.
a.5. Plane Tabling – I is a graphical method of surveying in which fieldwork and plotting are
done simultaneously with the use of plane table.
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a.6. Traverse Survey – After the linear measurements are done with the chain and tape, the
directions or angles are measured with a compass a transit, and this survey is called traverse
survey.
a.7. Tacheometry – This method of surveying in which both the horizontal and vertical distances
are determined by observing a stadia or level rod with an instrument equipped with a
telescope having stadia wires.
b. Based on Purpose of Survey
b.1. Archeological Survey – These surveys are done to unearth or excavate the relics of
civilizations, towns, etc. that were buried due to earthquakes or other calamities. This will lead
us to the remains, which reflect the history, culture and development of the era that will
provide vital links on understanding of the present civilization.
b.2. Cadastral Surveys – are usually closed surveys which are undertaken in urban and rural
locations for the purpose of determining and defining property lines and boundaries, corners
and areas.
b.3. City Surveys – are surveys of areas in and near a city for the purpose of planning
expansions or improvements, locating property lines, fixing reference monuments,
determining the physical features and configuring of land and preparing maps.
b.4. Construction Surveys – these surveys are undertaken at a construction site to provide data
regarding grades, reference lines, dimensions, and the location and elevation of structures
which are of concern to engineers, architects and builders. It is also known as engineering
surveys.
b.5. Defense Survey – Surveys that provide important and critical application in the military. It
provides strategic information that can decide the cause of war. The information gathered
may be used for preparing tactical and strategic plans both for defense and attack.
b.6. Forestry Survey – a type of survey executed in connection with forest management and
mensuration, and the production and conservation of forest lands.
b.7. Geological Survey – both surface and sub-surface surveying is required to determine
location, extent and reserves of different minerals and rock types. Different types of geological
structures like folds and faults may help to locate the possibility of the occurrence of minerals,
oils, etc.
b.8. Geographical Surveys - These are conducted to provide data for the preparation of
geographical maps that depicts the land use efficiency, sources, intensity of irrigation, slope
profile and contours.
b.9. Industrial Survey – it is sometimes known as optical tooling and it refers to the use of
surveying techniques in ship building, construction and assembly of aircraft, lay-out and
installation of heavy machineries and in other industries where very accurate dimensional layouts are required.
b.10. Mine Surveys – are surveys which are performed to determine the position of all
underground excavation and surface mine structures, to fix surface boundaries of mining
claims, to calculate excavated volumes, and establish lines and grades for other related mining
work.
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b.11. Route Surveys – involves the determination of alignment, grades, earthwork quantities,
location of natural and artificial objects in connection with the planning, design and
construction of highways, railroads, pipelines, canals, transmission lines and other linear
projects.
b.12. Topographic Survey – are those surveys made for determining the shape of the ground,
and the location of natural and artificial features upon it.
c. Based on Place of Survey
c.1. Aerial Survey – it is a survey which is carried out by taking photographs with a camera fitted
in an airplane. It is also known as Photogrammetric Survey.
c.2. Land Survey – surveys that consists of re-running old land lines to determine their lengths
and directions, subdividing the land into predetermined sizes and shapes and calculating their
areas and setting monuments and locations their positions.
c.3. Hydrographic Survey – Surveys that deals with bodies of water and consists in acquiring
data to chart the shorelines of water bodies. It will also determine the shape of the underlying
water surface to assess the factors affecting navigation.
c.4. Underground Survey – This is referred to as preparation to underground plans that consists
in transferring bearings and coordinates from the surface baseline to the underground
baseline.
Character of Work
The work of a surveyor consists mainly of making measurements and can be divided into two
parts:
Fieldwork – for true representation of the field conditions, sufficient data should be obtained
from the fieldwork. It consists of adjusting and care of the instruments, making measurements and
recording these measurements.
Office work – it consists of making necessary calculations or computations for transforming the
field measurements into a form suitable for plotting.
Observation VS Measurements
An observation is a single, unadjusted determination of a linear or angular value. A single reading
of an angle or a single reading of an instrument is an observation. An observed value is a quantity that is
obtained by instrumental measurement of the quantity. A direct observation is an observation of the
desired quantity while an indirect observation is a quantity computed from direct observations. For
example, rod readings in leveling are direct observations and the elevation difference between two points
that is computed from these rod readings is an indirect observation.
A measurement is the entire process of obtaining a desired quantity. A measurement entails
performing a physical operation that usually consists of several more elementary operations such as
preparations (instrument calibration and setup), pointing, matching, and comparing (reading). The result
of these physical operations renders a numerical value that is called a “measurement”.
Surveys should be considered as measurements not as observations. With the advent of electronic
readouts of linear or angular quantities everyone can make an observation. It requires a surveyor to make
a measurement.
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Surveying Measurements
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Measurement – it is the process of determining or comparing an unknown quantity with a known
standard.
In surveying, measurements may be made directly or indirectly:
Direct Measurements – A direct measurement is a comparison of the measured quantity with a
standard measuring unit or units employed for measuring quantity of that kind.
Indirect Measurements –The observed value is determined by its relationship to some other
known values.
Principles of Surveying
Surveying is concerned with measurement of quantities whose exact or true values may not be
determined. Thus a basic principle of surveying is that “no measurement is exact and the true value
of the quantity being measured is never known”. Exact or true values exist but they can never be
determined.
Before measured data can be utilized, whether for surveying and mapping projects, they must be
processed. Every observed quantity contains errors of unknown magnitude, due to a variety of causes and
consequently a measurement is never exact.
Error – it is defined as the difference between the true value and the measured value of a quantity. It is a
deviation of an observation or a calculation from the true value and is often beyond the control of the one
performing the operation.
Mistakes – it is an unintentional fault or conduct arising from poor judgment or from confusion in the
mind of the observer. These are inaccuracies in measurements which occur because some aspects of
surveying operation are conducted with carelessness, inattention, and improper execution. Large mistakes
are referred to as blunders.
Types of Errors
Systematic Errors – this type of error is one which will always have the same sign and
magnitude as long as field conditions remain constant and unchanged. A systematic error will
repeat itself in other measurements, still maintaining the same sign, and thus will accumulate,
thus it is called Cumulative Error. These are associated with a flaw in the equipment or in
the design of the experiment
Random or Accidental Errors – These errors are purely accidental in nature. These are caused
by factors beyond the control of the surveyor and are present in all surveying measurements.
An important characteristic of the random error is that if we repeat the same measurement
many times, the sum of all these errors tends to be zero.
Sources of Errors
Instrumental Errors – These errors are due to the imperfections in the instruments used, either
from their construction or from improper adjustments.
Natural Errors – These are caused by the variations in the phenomena of nature.
Personal Errors – these errors arise from limitations of the senses of sight, touch and hearing.
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ACCURACY and PRECISION
Accuracy and precision are two terms which are constantly used in surveying.
Accuracy – it indicates how close a given measurement is to the absolute or true value of the
quantity measured.
Precision – it refers to the degree of refinement and consistency with which any physical
measurement is made. It is portrayed by the closeness to one another in a set of
observation.
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By applying the theory of probability, redundant measurements containing errors could be adjusted.
The most probable value of a set of observations could then be determined and expected
discrepancies are eliminated. It must be understood, however, the results of such adjustments are not
the true values.
Most Probable Value (of a group of repeated measurements) is the average or arithmetic mean. It
refers to a quantity which has more chances of being correct than has any other.
MPV
 X 
X
n

X 1
Where: MPV = most probable value
X = average or mean
X = observed value
n = number of observations
 X 2  ...  X n 
n
Sample Problem
1. The following values were obtained in measuring line XY for 6 times of equal reliability; 99.93 m,
100.06 m, 100.10 m, 99.9 m, 100.12 m and 100.08 m. Determine the most probable value of the
distance measured.
2. From the given observed values for a five-sided closed polygon, determine the MPV. 1=6630’,
2=5925’, 3=9200’, 4=6002’ and 5=8705’.
Residual, v – it is sometimes referred to as deviation, is defined as the difference between any measured
quantity and its most probable value.
Where:
v = residual
v  X  X
X = observed value
X = mpv or average
Probable Error – it is a quantity which defines a range within which there is a 50% chance that the true
vale of the measured quantity lies inside or outside the limit thus set.
- it gives an indication of the precision of the measurement. It does not specify the
magnitude of the error. Note that the sign or direction of the probable error is not
known and therefore no correction can be made.
PE
PE
s
m
  0 . 6745
  0 . 6745
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v
2
Where:
n 1
v
2
n n  1 
PEs = Probable error of any single measurement
PEm = Probable error of the mean
v2 = sum of the squares of the residual
n =number of observations
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Relative (Error) Precision – it indicates the accuracy of measurement
RP 
PE
MPV
Sample Problems:
1. The elevation of a benchmark was determined by three groups of surveyors. The measurements
were made with equal reliability and are as follows; 2101.50 m, 12101.45 m, and 2101.62 m.
Determine the MPV, PEs, PEm, RPs and RPm.
2. The observed interior angles of a triangle are 9514’37”, 3630’09”, and 4805’15”. Determine the
MPV of each angle.
Weighted Observations – measurements that were made with different degrees of reliability.
Weights are assigned based upon the judgment of the one performing the operation.
Weights are inversely proportional to the square of the probable error.
Sample Problem:
1. Lines of levels to determine the elevation of a point were run over three different routes. The
observed elevation of the point with probable errors is tabulated below. Determine the MPV of the
elevation of that point.
Line
1
2
3
Obs. Elev. m
1284.18
1284.16
1284.22
PE
+ 0.06
+ 0.05
+ 0.04
2. Determine the most probable value of the measurements having different values based on the
number of measurements as tabulated in the shown below,
Distance
320.14
320.20
320.18
320.24
320.12
No. of Measurements
1
2
4
2
3
Interrelationship of Errors
 Sum of Errors
Es 
Where:
2
PE 1  PE
2
2
 ...  PE
2
n
 Product of Errors
Ep 
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Q 1
Es = Probable error of a sum of
measurements
PE = Probable error of the several
observations
Where:
 PE
2

2
  Q 2  PE 1 
2
EP = Probable error of a product of
measurements
PE = Probable error of the
observation
Q = Observed value
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Sample Problems:
1. Calculate the most probable value and the probable error of the area of a rectangular lot whose
sides are as follows:
a= 100.01+0.012m
b= 135.79+0.011m
2. The following observations were recorded for horizontal angles of a triangle
A = 20º10’ + 0.02
B = 100º40’ + 0.01
C = 59º10’ + 0.03
Determine the probable error of the sum of the interior angles.
Exercises
1. In three trials of measuring a certain distance, the following data were recorded. Find the most
probable value and the probable error.
Trials
1
2
3
Length, m
51.82
81.94
51.75
2. The following values were observed in a series of rod readings taken under similar conditions.
Determine the most probable value, probable error and relative precision.
Trial
1
2
3
4
5
6
7
8
9
10
Rod Readings on pt. A
3.187
3.182
3.179
3.181
3.184
3.176
3.183
3.178
3.181
3.188
3. After all systematic errors have been eliminated, the measured lengths of a line are: 1012.36,
1012.36, 1012.38, 1012.32, 1012.33 and 1012.30 meters. Determine the most probable value of
the length of the line, and the probable error of the mean.
4. The angles about a point have the following observed values: 13015’20”, 14237’30” and
8707’40”. Determine the most probable values of the three angles.
5. The following data are the observed elevation of a point by running a line of levels over four
different route. It is required to determine the most probable value of the elevation of the point.
Route
1
2
3
4
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Elevations
340.22
340.30
340.26
340.32
Probable Error
+ 0.02
+ 0.04
+ 0.06
+ 0.08
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6. The four approximately equal sides of a tract of land were measured and the measurements
included the following errors: + 0.085, + 0.014, + 0.175 and + 0.205 respectively. Determine the
probable error for the total length of the tract.
7. The dimensions of a five-sided tract of land are given by the following measurements and
corresponding probable errors: 221.63 + 0.004 m, 235.70 + 0.002m, 196.05 + 0.005m, 296.13 +
0.012m, and 303.18 +0.015m. Determine the most probable value of the perimeter.
8. The base and altitude of a triangular shaped lot were measured with certain estimated probable
errors as follows: b = 425.67 + 0.07m and h = 138.63 + 0.06m. Determine the area of the lot
and the probable error in the resulting calculation.
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