MODULE 1

Subject: CE 214 – Fundamentals of Surveying

1. Topic

1. Introduction to Surveying

• What is surveying
• Functions of surveying
• Importance of surveying
• Objectives of surveying
• Uses of surveying
• General principles of surveying

2. Introduction
This module introduces the basics of surveying, its origin, concepts and
principles, thus, giving the students a foresight of the subject.
3. Learning Outcome
1. Students will be able to understand the importance of surveying.
2. Students will know the usage of surveying in real life.
3. Students will know the different disciplines and practices on different types
of survey.
4. Learning Content
What is surveying
Surveying
Surveying is the art and science of determining angular and linear measurements to
establish the form, extent, and relative position of points, lines, and areas on or near
the surface of the earth or on other extraterrestrial bodies through applied mathematics
and the use of specialized equipment and techniques. (Juny Pilapil La Putt)
Surveying is the art and science of civil engineering that determines the relative
(comparable) position of points on, above or beneath the surface of the Earth by
measuring the horizontal and vertical distances, angles, elevations and taking the
details of these points and by preparing a map or plan to any suitable scale.
(civilplanet.com)

For instance, if we are talking about our position in a hill station, we say we are at 3000
feet above mean sea level (vertical distance). When talking about our position in a city,
we refer to some landmarks near us (Horizontal distance).
Likewise, surveying identifies the position of points on or below the Earth’s surface by
referring to known points, such as benchmarks.

According to the American Congress on Surveying and Mapping (ACSM), Surveying is

the technique, profession, art, and science of determining the two-dimensional or three-
dimensional positions of points and the distances and angles between them on or below
the Earth’s surface.

Surveying has two functions:

 The determination of existing relative horizontal and vertical position such as
that used for the process of mapping.
 The establishment of marks to control construction or to indicate land
boundaries. (britannica.com)
 Importance of Surveying
Any civil engineering project starts with surveying measurements or techniques to
determine the boundaries between properties (land), the location of existing
infrastructure, and the topography and slopes of a land. (civilplanet.com)

Knowledge of surveying is important in the planning and execution of any construction

project. The surveying is the crucial initial step (plan) of a project execution which helps
to manipulate the project without errors.

The Importance of surveying in civil engineering is listed below:

 The data measurements gathered from surveying helps establish the plan
and design of all civil engineering projects such as tunneling, irrigation,
dams, reservoirs, waterworks, sewerage works, building, roads, bridges,
railways, irrigation canals, reservoirs etc.
 During the project execution, any proposed structure is constructed along
the lines and points established by surveying (boundaries).
 Surveying helps calculate the project’s possible alignment and the required
amount of earthwork. Example is in alignment of roads in cuts and backfills
in mountains and depressions and in the design of super elevation.
 Surveying helps to assess the high-risk areas and hazards of a project.
Example is in identification and mapping of high-risk areas and hazards
(hazard maps).
 Surveying helps to prepare the measurement data such as topography of
the site, adjacent structures, locations and sources available to kick-start the
architectural design conceptualization. (Project proposals and feasibility
studies)
 Surveying helps to know the accurate soil profile, establish drainage paths,
and prepare contour surveys.
 Surveying prepares the plan and map of an area occupied by the project,
also known as boundaries (legal boundaries).
 Surveying helps to establish control points (benchmark)
 Surveying helps to determine the economic feasibility by avoiding errors
during execution, saving time and money for an efficient project.
 Surveying helps to fix national and state boundaries.
 Surveying determines the required land acquisition.
 Surveying helps to chart coastlines, navigable streams and lakes.
 Surveying helps prepare a topographic map of the Earth’s land surface.
 Surveying in road construction helps to identify the right location for the road
works along with optimal curve placements, materials, and methods to be
used.
  Surveying in town planning determines the flexible land zone that is easy to
build in the construction, roads, railways, cable, drinking water plans, etc.
 Even though the result of surveying supports the execution of the project,
we can quickly identify the hindrances at the earliest. (civilplanets.com)

What is the main objective of surveying?

The main objective of surveying is to show all the features of the earth’s surface (larger
area) prepared as a plan or map in a horizontal plane. The scale of the area describes
the difference between the plan & map. If the range represents a small area, then it is
called a map at the same time if the scale denotes a more substantial space that is
called a plan. (civilplanet.com)

Objective of surveying

 To determine the relative position of any objects or points of the earth.

 To determine the distance and angle between different objects.
 To prepare a map or plan to represent an area on a horizontal plan.
 To develop methods through the knowledge of modern science and the technology
and use them in the field.
 To solve measurement problems in an optimal way. (civiltoday.com)

Uses of surveying
Before starting any civil engineering work, regardless of branches, horizontal, vertical,
and angular measurements of the project (plan or map) is required.
Surveying is used in many branches according to the need. The following are the
primary uses of surveying.
 Surveying is used to prepare Topographic maps, which represent the
accurate graphic representations of features on the Earth, such as rivers,
streams, lakes, woods, valleys, hills, towns, villages, forests, contours and
cliffs, and depressions.
 Surveying is used to prepare Engineering maps representing the details of
engineering works such as dams, buildings, railways, road work, irrigation
canals, reservoirs, and transmission lines.
 Surveying is used to prepare Cadastral maps representing the land
boundaries (property lines) and houses for legal purposes.
 Surveying is used to prepare Military maps representing the road and
railway communications with different parts of a country and different
strategic points essential for the defense of a country.
 Surveying is used in Urban Planning which helps to plan/locate the large-
scale extensions of the existing facilities such as streets, water supply,
sewer systems, and the layout of new roads.
  Surveying is used to prepare Contour Maps representing the capacity of
reservoirs and the best possible transportation routes.
 Surveying prepares Hydrographic Maps, which help plan navigation routes
on water bodies, water supply, and harbors or determine mean sea level.
 Surveying is used to prepare Geological Maps, which help to determine the
different strata in the Earth’s crust.
 Surveying is used to prepare Archaeological Maps, which help unearth
relics of antiquity.
 Surveying is used in Astronomical Survey, which helps to determine the
latitudes and longitudes of any points on the Earth. It helps study planets’
movements and calculates local and standard times.
 Surveying is used in Mining which helps to explore the minerals under the
Earth. (civilplanet.com)

General principle of surveying

The general principles of surveying are:

1. To work from the whole to the part
2. Locating new points by measurement of minimum two reference points

Working from the whole to the part

The main principle of this method is establishing the survey work from the whole to the
part.
For example, if you are going to take surveys for vast land, first, you have to fix
systematic control points with high precision around the area—a boundary line formed
by connecting the points which are the main skeleton drawing of the survey.
The survey points are established by triangulation or traverse around the area. Then the
triangles are broken into small areas and can be measured by less workmanship.
The primary purpose of work from the whole to the part survey is to avoid the error. In
case the survey works are established by part to whole, then we have to face many
mistakes in the surveying.

Locating new points by measurement of minimum two reference points

Two different independent processes have to do to fix a new point. The two different
methods can cross-check together.

From the above picture, C is new, which has to be fixed & point A, B are the given
point.
 Now the point C can be fixed by measuring the distance of AC & BC; it is
one method of process.
  A perpendicular line may be drawn from point C to baseline AB. Now we
have got two different possibilities to locate point C by the line CD.
(civilplanet.com)

Types of surveying methods

The primary methods of surveying are
 Plane Surveying
 Geodetic Surveying

Plane Surveying

In surveying, when the earth’s surface is assumed to be a plane, and the curvature of
the earth is omitted, it is called Plane Surveying.

 The line connecting any two points is considered a straight line, and the
angle between any two lines is viewed as the plane’s angle. Any triangle
made by the plane survey is also called a plane triangle.
  The Plane surveying method is suitable for surveying up to 250 km2 area.
The plane surveying methods are used in the construction of dams, bridges
& road work.

Geodetic Surveying
The earth’s surface is not considered as plane and curvature of the planet also taken
into account for measurement is called Geodetic Surveying.

 The government department of surveying will carry the Geodetic Surveying

under the direction of survey general.
 The geodetic survey method gives high accuracy compared to the plane
survey method because the earth’s curvature is also measured.
 The line connecting any two points is considered as an arc, so the angle
between the two arcs is considered as a spherical angle.
 Precious knowledge has been required in trigonometry to carry out this
method of surveying. The geodetic surveying covers the area above 250
Km2.
Difference between the Plane and Geodetic Surveying
Plane Surveying Geodetic Surveying

Earth is considered as a sphere (Curved

Earth is considered as a plane. Surface).

The line joining 2 points will be The line joining 2 points will be
considered as a straight line. considered as a curved line.

The triangle formed by 3 points will be The triangle formed by 3 points will be
considered as a plane triangle. considered as a spherical triangle.

Suitable for an area of less than 250

Km2. Suitable for the area more than 250 km2.

Classification of Surveying
The classification of surveying is dependent on the nature of the field, objective &
instruments.

Based on Nature of the Field

 Land Survey – The land surveying is the investigation of the terrain like the
river, falls, or maybe a town, village.
 Marine Survey – The marine survey involves discovering the sea level,
mean sea level, and planning, preparing of harbor construction.
 Astronomical Survey – To find out the fixed point of any location of the
earth’s surface. This survey also deals with knowing the position or distance
of the planet like sun, stars, etc.,

Based on the Objective

 Engineering Survey – The engineering survey is used to determine the
data used in engineering works in buildings, bridges, and roads.
 Defense Survey – Preparation of the map for military areas.
 Mine Survey – This survey shall be carried out to explore mineral wealth
below the earth’s surface.
 Geological survey – The geological survey is carried out by the
government to develop the map of the natural resources of a country.
  Archaeological survey – To prepare a map of the ancient area location of
a country.

Based on the Survey Method

 Triangulation Survey – The basis of the triangulation survey is
trigonometry, mostly it is carried out in the hills area. By the data of the
baseline & angle of other points, we can determine the length of the other
sides. The execution of the triangulation survey is a little critical, but the
result of the study gives high accuracy.

 Traverse Survey – The traverse survey contains a series of connected

lines. In this survey, the length and direction of the lines have been
measured by the tape. The angle between the lines is also noted for
calculating the survey area. The traverse survey has been further classified
as closed traverse and open traverse, as shown in the pictures below.
 Based on the Surveying Instruments
Chain Surveying
The chain survey is the conventional method of surveying, which is used to survey
small land. The survey areas are divided into a number triangle and can be calculated.
The chain of length is around 20m to 30m. This survey method has been suitable for
minor uneven surface land.
Compass Surveying
The compass survey principles are traversed.
The survey points are connected as a series of lines and measured by the compass
instrument’s magnetic bearing. The angle between the lines is measured, and the chain
measures the length of the lines.

Two different types of instruments are used in compass surveying.

 Prismatic Compass
 Surveyor Compass

Plane Table Surveying

The plane table survey is suitable where the area is not larger & does not require high
accuracy.
The fieldwork points are simultaneously plotted on the drawing, which is placed over the
plane table. The plotted points are correlative with each other.
Theodolite Surveying
Theodolite surveying used where high accuracy of results required.
The telescope, which is mounted on the theodolite instrument, can rotate 360
degrees in both horizontal & vertical directions, so the measurement can be taken
both horizontally & vertically. The vertical & horizontal angle can calculate the length
of the survey points.
Theodolite Surveying is used in all types of construction, roads, bridges, dam &
pipeline projects.

Tacheometric Surveying
The tachymetric survey is used mainly in contour surveying.
The measurement of the distance can be taken in both horizontal & vertical
directions. The stadia distance and reduced level will be calculated for the distance
of the points.
Dumpy Level or Auto Level

The dumpy level or auto level instrument survey is mostly used where the earth’s
surface is uneven. The measurement can be measured in a 360-degree horizontal
direction.
The reduced level points are calculated by the height of the collimation or by the rise
and fall method.

Aerial Surveying
To discover the overview of an area, aerial surveying is carried out from the aeroplane
or helicopter. The photographs will be taken from an elevated position to identify the
object clearly from the top angle.

Total Station
The technology improvement of theodolite is a total station.
The total station is an electronic instrument that is mostly preferred for surveying at
present. The measurement of distances and angles are recorded in the device and can
quickly get the result through a computer. (civilplanets.com)

DEVELOPMENT OF SURVEYING INSTRUMENT

Surveying instruments were developed gradually. It is believed that, an extensive use of surveying
instruments came about during the early days of the Roman Empire. This remarkable engineering
ability of Romans is clearly demonstrated by their extensive construction of structures and buildings
which continue to exist even up to this modern era. It will be noted that many surveying instruments
and devices evolved from those which were earlier used in astronomy. The following instruments
were the early forerunners of our present-day surveying instruments.

 1. Astrolabe. The astrolabe of Hipparchus is considered to be one of the best known of the
measuring instruments that have come down from ancient times. It was developed sometime in
 140 B.C., and further improved by Ptolemy. The instrument had a metal circle with a pointer
hinged at its center and held by a ring at the top, and a cross staff, a wooden rod about 1.25
meters long with an adjustable cross arm at right angles to it. The known length of the arms of the
cross staff allow distances and angles to be determined by proportion. It was originally designed
for determining the altitude of stars.

 2. Telescope. The invention of the telescope in. 1607 is generally accredited to Lippershey. In
1609, Ga1ileo constructed a refracting telescope for astronomical observations. However, it was
only when cross hairs for fixing the line of sight were introduced, that the telescope was fixed in
early surveying instruments.
 3. Transit. The invention of the transit is credited to Young and Draper who worked
independently from each other sometime in 1830. Both men were able to put together in one
instrument the essential parts of what has long been known as the universal surveying
instrument.
 4. Semicircumferentor. An early surveying instrument which was used to measure and layoff
angles, and establish lines of sight by employing peep sights.

 5. Plane Table. One of the oldest types of surveying instruments used in field mapping. It
consists of a board attached to a tripod in such a way that it can be leveled or rotated to any
desired direction.
 6. Dioptra. The dioptra, which was perfected by Heron of Alexandria, was used in leveling and for
measuring horizontal and vertical angles. It consists essentially of a copper tube supported on a
stand and could be rotated in either a horizontal or vertical plane. For measuring horizontal
angles, a flat circular disc with graduations in degrees is used. An arm containing sighting
apertures at either end could be rotated to any desired position on the disc.
 7. Roman Groma. The Roman surveyors used the groma instrument for aligning· or sighting
points. It consisted basically of cross arms fixed at right angles and pivoted eccentrically upon a
vertical staff. Plumb lines were suspended from the ends of the arms. By employing the groma
two lines at right angles to each other could be established on the ground where it is set up.
 8. Libella. The Assyrians and Egyptians are believed to be the first users of the libella. The
instrument had an A-frame with a plumb line suspended from its apex and was used to determine
the horizontal. Archeologists are of the belief that the horizontal foundations of the great pyramids
of Egypt were probably defined by this device.
 http://blog.oldwolfworkshop.com/2011/04/exploring-libella.html

 9. Vernier. The vernier is a short auxiliary scale placed alongside the graduated scale of an
instrument, by means of which fractional parts of the smallest or least division of the main scale
can be determined precisely without having to interpolate. It was invented in 1631 by a
Frenchman name Pierre Vernier. Surveying instruments employ either a direct or retrograde
vernier.

10. Diopter. An instrument developed by the Greeks sometime in 130 B.C., and known to be their
most famous surveying instrument. The diopter was used for leveling, laying off right angles, and
 for measuring horizontal and vertical angles. Since the telescope was not yet invented during the
time the diopter was used, peep sights were employed for sighting and in aligning the device.

https://en.wikipedia.org/wiki/Dioptra

 11. Compass. The magnetic compass came into wide use during the 13th century for
determining the direction of lines and in calculating angles between lines. It was first introduced
for use in navigation. The compass consists of a magnetized steel needle mounted on a pivot at
the center of a graduated circle. The needle continues to point toward magnetic north and gives a
reading which is dependent upon the position of the graduated circle.
 12. Gunter"s Chain. The Gunter's chain, which was invented by Sir Edmund Gunter in 1620,
was the forerunner of instruments used for taping distances. It is 66 ft long and contains 100
links, so that distances may be recorded in chains and in decimal parts of the chain. Each part,
called a link, is 0.66 ft or 7.92 inches long.

13. Chorobates. This instrument was designed for leveling work. It consisted of a horizontal
straight-edge about 6 meters long with supporting legs, and a groove 2.5 cm deep and,
1.5m long on top. Water is poured into the groove and when the bar is leveled so that
water stood evenly in the groove without spilling, a horizontal line is established.
 http://www.romanaqueducts.info/aquasite/foto/lijntekchorobates.jpg

 14. Merchet. The merchet was a device for measuring time and meridian. It was first used by the
Chaldeans in about 4,000 B.C. It consisted of a slotted palm leaf through which to sight and a
bracket from which a plumb bob was suspended. -By sighting through the 'slot and past the
plumb bob string, a straight line could be projected.
 http://surveytypes.blogspot.com/2008/01/surveying-instruments-were-developed.html

Surveying measurements
A measurement is the process of determining the extent, size or dimensions of a
particular quantity in comparison to a given standard. In surveying, measurements may
be made directly or indirectly.
1. Direct measurements. A direct measurement is a comparison of the
measured quantity with a standard measuring unit or units employed for
measuring a quantity of that kind.
2. Indirect measurements. When it is not possible to apply a measuring
instrument directly to a quantity to be measured an indirect measurement
is made.

The meter
The international unit of linear measurement is the meter. This was proposed sometime
in 1789 by French scientists who hoped to establish a system suitable for all times and
all peoples, and which could be based upon permanent natural standards. Originally,
the meter was defined as 1/10 millionth of the earth’s meridional quadrant. In May 20,
1875, the meter was defined as the distance between two lines engraved across the
surface (near the ends) of a bar with an X-shaped cross-section, composed of 90%
platinum and 10% iridium, when the temperature of the bar is 0 degree Celsius.
In October 1960, the meter was redefined as a length equal to 1,650,763.73
wavelengths of the orange-red light produced by burning the element krypton (with an
atomic weight of 86) at a specified energy level in the spectrum.

International system of units (SI)

Effective January 1, 1983 the English System was officially phased out in the
Philippines and only the modern metric system was allowed to be used. Metric
conversion or change-over was signed into law on December 1978 by former Pres.
Ferdinand E. Marcos. Examples of units for measurements are meter for linear
measurements, square meters for areas and cubic meters for volumes. Degrees,
minutes, and seconds are acceptable for plane angles.

Units of measurement
Common prefixes in SI units are listed below;
Mega- = 1,000,000 kilo- = 1,000 hecto- = 100 deca- = 10
Deci- = 0.1 centi- = 0.01 milli- = 0.001 micro- = 0.000 001
Nano- = 0.000 000 001

1. Linear, Area, and Volume Measurements.

1 kilometer (km) = 1,000 meters
1 meter (m) = 1,000 millimeters
1 millimeter (mm) = 1,000 micrometers
1 millimicrometer (mu) = 1,000 million micrometers
1 meter (m) = 10 decimeters
1 decimeter (dm) = 10 centimeters
1 centimeters (cm) = 10 millimeters

2. Angular Measurements.
The SI unit for plane angles is the radian. The radian is defined as an
angle subtended by an arc of a circle having a length equal to the radius
 of the circle. 2 rad = 360 degrees, 1 rad = 57 degrees 17 minutes and
44.8 seconds or 57.2958 degrees.
a. Sexagesimal units – the sexagesimal units of angular measurement
are the degree, minute, and second. The unit of angle used in
surveying is the degree which is defined as 1/360 th of a circle. One
degree equals 60 minutes, and 1 minute equals 60 seconds.
b. Centesimal units – in this system, the circumference of a circle (360
degrees) is divided into 400 grads. The grad is divided into 100
centesimal minutes or 0.9 degrees and the minutes is subdivided
into 100 centesimal seconds or 0 deg 00 minutes 32.4 seconds.
Grads are usually expresses in decimals, for example, 194g 45c
82cc is expressed as 194.458 2 grads.

Significant Figures
By definition, the number of significant figures in any value includes the number of
certain digits plus one digit that is estimated and, therefore, questionable or
uncertain. For example, a line that is measured with a scale graduated in one
meter increments and recorded as 3.6 meters, the value has two significant
figures, 3 is the certain number and 6 is the estimated. If the same line is again
measured with a scale graduated in tenths of a meter and recorded with three
significant figures as 3.65 meters, the 3 and 6 are certain whereas 5 is estimated
or uncertain.

General rules regarding significant figures:

Rule 1. Zeroes between other significant figures are significant. For example,
12.03, 35.06 and 4009 have 4 significant figures.

Rule 2. For values less than one, zeroes immediately to the right of the decimal
are not significant, they merely show the position of the decimal such as in the
following values which contain three significant figures; 0.00325, 0.000468, and
0.0230.

Rule 3. Zeroes placed at the end of decimal numbers are significant such as
169.30, 366.00, and 11.000. These values all have five significant figures.
 Examples:
1. One significant figure
 100 9 0.001
 400 8000 0.000005
2. Two significant figures
 24 0.020 0.0024
 0.24 0.000065 3.6
3. Three significant figures
 365 3.65 0.000249
 12.3 10.1 0.0120
4. Four significant figures
 7654 0.8742 0.00006712
 32.25 15.00 364.0
5. Five significant figures
 12345 100.00 40.000
 0.86740 46.609 155.28

Rounding off numbers

The following procedures of rounding off values are generally accepted:
1. Digit is less than 5. When the digit to be dropped is less than 5, the
number is written without the digit. Thus, 24.244, rounded off to the
nearest hundredth, becomes 24.24. Rounded off to the nearest tenths
would become 24.2.
2. Digit is equal to 5. When the digit to be dropped is equal to 5, the nearest
even number is used for the preceding digit. Thus, 26.175, rounded off to
the nearest hundredth becomes 26.18 and 156.285 becomes 156.28.
3. Digit is greater than 5. When the digit to be dropped is greater than 5,
the number is written with the preceding digit increased by one. Thus,
226.276, rounded off to the nearest hundredth becomes 226.28 and
226.28 becomes 226.3.

Surveying Field Notes

Surveying field notes constitute the only reliable and permanent record of actual work
done in the field. The notekeeper should always put himself in the place of one who is
not in the field at the time the survey is made. Field work observations should be
recorded directly in the notebook at the time observations are made. In court, field notes
may be used as evidence.
The field notebook
In practice the field notebook should be of good quality rag paper, with stiff board or
leather cover made to withstand hard usage, and of pocket size. Treated papers are
available which will shed rain; some of these can be written on even wet. In some
technical schools, students are asked to use bond paper instead of field notebooks
when preparing and submitting their field notes.

Types of notes
1. Sketches. A good sketch will help to convey a correct impression.
Sketches are rarely made to exact scale, but in most cases they are made
approximately to scale. They are drawn freehand and of liberal size. Many
features may be readily shown by conventional symbols. Special symbols
may be adapted for the particular organization or job. The student should
note that a sketch crowded with unnecessary data is often confusing.
2. Tabulation. A series of numerical values observed in the field are best
shown in tabulated format. Tabular forms prevents mistakes, allows easy
checking, saves time, makes the calculation legible to others, and
simplifies the work of the person checking the field notes.
3. Explanatory notes. Explanatory notes provide a written description of
what has been done in the field. These are employed to make clear what
the numerical data and sketches fail to do. Usually, they are placed on the
right- hand page of the field notebook in the same line with the numerical
data that they explain. If sketches are used, the explanatory notes are
placed where they will not interfere with other data and as close as
possible to that which they explain.
4. Computations. The portrayal of calculations should be clear and orderly
in arrangement in order that these will easily be understood by persons
other than the one who made the computations.
5. Combination of the above. The practice used in most extensive surveys
is a combination of the above types of notes. The surveyor should be able
to determine which type of combination would be most logical to use in
portraying the type of data gathered in the field.
Information found in the field notebooks
1. Title of the field work or name of project. The official name of the
project or title of the field work should always be identified. The location of
the survey and preferably its nature or purpose should always be stated.
2. Time of day and date. These entries are necessary to document the
notes and furnish a timetable as well as a reference for precision,
problems encountered and other factors affecting the survey.
3. Weather conditions. Temperature, wind velocity, typhoons, storms and
other weather conditions such as fog, sunshine and rain have an effect on
accuracy in surveying operations.
4. Name of group members and their designations. The chief party,
instrumentman, tapeman and other members of the survey party must be
identified. This information will be necessary for documentation purposes
and other future reference. From this information, duties and
responsibilities can easily be pinpointed among the survey party
members.
 5. List of equipment. All survey equipment used must be listed, including its
make, brand, and serial number. The type of instrument used and its
adjustment all have a definite effect on the accuracy of a survey. Proper
identification of the particular equipment used helps in isolating errors in
some cases.

The field survey party

1. Chief of party. The person who is responsible for the overall direction,
supervision and operational control of the survey party.
2. Assistant chief of party. The person whose duty is to assist the chief of party
in the accomplishment of the task assigned to the survey party. He takes over
the duties of the chief of party during the absence of the chief. He prepares
field and office reports and survey plans for submission to the chief of party.
3. Instrumentman. The person whose duty is to set up, level, and operate
surveying instruments such as the transit, engineer’s level, theodolite, sextant,
plane table, alidade and etc.
4. Technician. The person who is responsible for use and operation of all
electronic instruments required in a field work operation.
5. Computer. The person whose duty is to perform all computation of survey data
and works out necessary computational checks required in a field work
operation. He is responsible for the utilization of electronic calculators, pocket
or microcomputers, and assists in the operation of computerized surveying
systems or equipment.
6. Recorder. The person whose duty is to keep a record of all sketches,
drawings, measurements and observations taken or needed for a field work
operation. He keep table of schedules of all phases of work and the
employment of the members of the survey party. He does clerical tasks related
to surveying in the office and undertakes limited cartographic jobs.
7. Head tapeman. The person responsible for the accuracy and speed of all
linear measurements with tape. He determines and directs the marking of
stations to be occupied by the surveying instruments and directs the clearing
out of obstructions along the line of sight. He inspects and compares tapes for
standard length prior to their use in taping operations and is responsible for
eliminating or reducing possible errors and mistakes in taping.
8. Rear tapeman. The person whose duty is to assist the head tapeman during
taping operations and in other related work.
9. Flagman. The person whose duty is to hold the flagpole at selected points as
directed by the instrumentman. He helps the tapeman in making
measurements assists the axeman in cutting down branches and in clearing
other obstructions to line of sight. When electronic distance measuring
instruments are used, he is responsible for setting up reflectors or targets.
 10. Rodman. The person whose primary duty is to hold the stadia or levelling rod
when sights are to be taken on it.
11. Pacer. The person whose duty is to check all linear measurements made by
the tapeman. He assists the tapeman in seeing to it that mistakes and blunders
in linear measurements are either reduced or eliminated. In addition the pacer
may also perform the job of a rodman.
12. Axeman/ lineman. The person whose duty is to clear the line of sight of trees,
brush and other obstructions in wooded country. He is also responsible for the
security and safety of the members of the survey party at the survey site. The
axeman is usually provided not only with an ax but a rifle or a sidearm as well.
13. Aidman. The person whose duty is to render first aid treatment to members of
the survey party who are involved in snake and insect bites, accidents and
other cases involving their health, safety and well-being. In addition, he may be
designated as an assistant instrumentman.
14. Utilitymen. The person whose duties are to render other forms of assistance
needed by the survey party or as directed by the chief of party.

Errors
An error is defined as the difference between the true value and the measured value of
a quantity. Errors are inherent in all measurements and result from sources which
cannot be avoided. They may be caused by the type of equipment used or by the way in
which the equipment is employed. It may also be caused by the imperfections of the
senses of the person undertaking the measurement or by natural causes. The effects of
errors cannot be entirely eliminated; they can, however, be minimized by careful work
and by applying corrections.

Mistakes
Mistakes are inaccuracies in measurements which occur because some aspect of a
surveying operation is performed by the surveyor with carelessness, inattention, poor
judgement and improper execution. Mistakes are also caused by a misunderstanding of
the problem, inexperience, or indifference of the surveyor. A large mistake is referred to
as a blunder. Mistakes and blunders are not classified as errors because they usually
are so large in magnitude when compared to errors.
Among students of surveying mistakes which are frequently committed include; reading
the wrong graduation on the tape, omitting whole length of tape, transposition of figures,
reading a scale backward, misplacing a decimal point, incorrect recording of field notes,
adding a row or column of numbers incorrectly, etc.

Types of errors
 1. 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. For instance, in making a measurement with a 30m tape
which is 5 cm too short, the same error is made each time the tape is
used. If a full tape length is used six times, the error accumulates and
totals six times the error (or 30 cm) for the total measurement. It is for this
reason that this type of error is also called a cumulative error. Such errors
can be computed and their effects eliminated by applying corrections,
employing proper techniques in the use of instruments, or by adopting a
field procedure which will automatically eliminate it.
2. Accidental errors. These errors are purely accidental in character. The
occurrence of such errors are matters of chance as they are likely to be
positive or negative, and may tend in part to compensate or average out
according to laws of probability. There is no absolute way of determining
or eliminating them since the error for an observation of a quantity is not
likely to be the same as for a second observation. An example of such an
error is the failure of the tapeman to exert the correct amount of pull on the
ends of a tape during measurement. Another example is in the reading of
an angle with a transit. Since the instrumentman cannot read it perfectly,
there would be times when he would read a value which is too large and in
another instance he may read a value too small.
In comparison to systematic errors, accidental errors are usually of minor
importance in surveying operations since they are variable in sign and are
of a compensating nature.

Sources of errors.
1. Instrumental errors. These errors are due to imperfections in the
instruments used, either from faults in their construction or from improper
adjustments between the different parts prior to their use. Examples of
instrumental errors are;
 Measuring with a steel tape of incorrect length.
 Using a leveling rod with painted graduations not perfectly spaced.
 Determining the difference in elevation between two points with an
instrument whose line of sight is not in adjustment.
 Sighting on a rod which is warped.
 Improper adjustment of the plate bubbles of a transit or level.
2. Natural errors. These errors are caused by variations in the phenomena
of nature such as changes in magnetic declination, temperature, humidity
wind refraction, gravity and curvature of the earth. The surveyor may not
be able to totally remove the cause of such errors but he can minimize
their effects by making proper corrections of the results and using good
judgment. Common examples are;
 The effect of temperature variation on the length of a steel tape.
  Error in the readings of the magnetic needle due to variations in
magnetic declination.
 Deflection of the line of sight due to the effect of the earth’s
curvature and atmospheric refraction.
 Error in the measurement of a line with a tape being blown sidewise
by a strong wind.
 Error in the measurement of a horizontal distance due to slope or
uneven ground.
3. Personal errors. These errors arise principally from limitations of the
senses of sight, touch and hearing of the human observer which are likely
to be erroneous or inaccurate. Typical of these errors are;
 Error in determining a reading on a rod which is out of plumb during
sighting.
 Error in the measurement of a vertical angle when the cross hairs of
the telescope are not positioned correctly on the target.
 Making an erroneous estimate of the required pull to be applied on
a steel tape during measurement.

Accuracy and precision.

Accuracy indicates how close a given measurement is to the absolute or true
value of the quantity measured. The difference between the measured value of a
quantity and its actual value represents the total error in the measurement.

Precision refers to the degree of refinement and consistency with which any
physical measurement is made.
https://www.antarcticglaciers.org/glacial-geology/dating-glacial-sediments-2/
precision-and-accuracy-glacial-geology/

Theory of probability.
Probability is defined as the number of times something will probably occur over
the range of possible occurrences. In dealing with probability, it is assumed that
we refer principally only to accidental errors and that all systematic errors and
mistakes have been eliminated.

The theory of probability is based upon the following assumptions relative to the
occurrence of errors:
1. Small errors occur more often than large ones and that they are more
probable.
2. Large errors happen infrequently and are therefore less probable; for
normally distributed errors unusually large ones may be mistakes rather
than accidental errors.
3. Positive and negative errors of the same size happen with equal
frequency; that is, they are equally probable.
4. The mean of an infinite number of observations is the most probable
value.

Most Probable Value.

Most probable value refers to a quantity which, based on available data, has more
chances of being correct than has any other. From the theory of probability, a
basic assumption is that the most probable value (mpv) of a group of repeated
measurements made under similar conditions is the arithmetic mean or average.

x
mpv=Σ
n
where mpv is the most probable value, Σ x is the sum of the individual
measurements, and n is the total number of observations made.

Illustrative examples:
1. A surveying instructor sent out six groups of students to measure a
distance between two points marked on the ground. The students came
up with the following six different values: 250.25, 250.15, 249.90, 251.04,
250.50, and 251.22 meters. Assuming these values are equally reliable
and that variations result from accidental errors, determine the most
probable value of the distance measured. (250.51 m)
2. The angles about a point Q have the following observed value.
130º15’20”, 142º37’30”, and 87º07’40”. Determine the most probable
value of each angle. (130º15’10”, 142º37’20”, and 87º07’30”)

3. The observed interior angles of a triangle are A= 35º14’37”, B= 96º30’09”,

and C= 48º15’05”. Determine the discrepancy for the given observation
 and the most probable value of each angle. (35º14’40”, 96º30’12”,
48º15’08”)
4. Measurement of three horizontal angles (see accompanying figure) about
a point P are: APB = 12º31’50”, BPC = 37º29’20”, and CPD = 47º36’30”. If
the measurement of the single angle APD is 97º37’00”, determine the
most probable values of the angles. (12º31’40”, 37º29’10”, 47º36’20”,
97º37’10”

Residual.
The residual is referred to as the deviation, is defined as the difference between
any measured value of a quantity and its most probable value.

v=x−X
where v is the residual in any measurement, x is a measurement made of a
particular quantity, and X is the most probable value of the quantity measured.
Residuals and errors are theoretically identical. The only difference is that
residuals can be calculated whereas errors cannot because there is no way of
knowing true values.
Probable error.
The probable error is a quantity which, when added to and subtracted from the
most probable value, defines a range within which there is a 50 percent chance
that the true value of the measured quantity lies inside (or outside) the limits thus
set.
If errors are arranged in order of magnitude, it will be possible to determine the
probable error. This is the error that would be found in the middle place of the
arrangement, such that one half of the errors are greater than it and the other half
are less than it.

PEs =±0.6745
√ ∑ v2
(n−1)
PEm=± 0.6745
√ ∑ v2
n(n−1)

Where: PEs = probable error of any single measurement of a series

PE m= probable error of the mean
2
∑ v = summation of the squares of the residuals
n = number of observations

The determination and use of the probable error in surveying is primarily to give an
indication of the precision of a particular measurement. For example, if 235.50 m
represents the mean or most probable value of several measurements and 0.10 m
represents the probable error of the mean value, the chances are even that the
true value lies between 235.40 m and 235.60 m, as it is also probable that the true
value lies outside of these limiting values. To express the probable limits of
precision for this particular case, the quantity should be written as 235.50 ±0.10 m.

Relative (error) Precision.

The total amount of error in a given measurement should relate to the magnitude
of the measured quantity in order to indicate the accuracy of a measurement. In
surveying measurements, ratio of the error to the measured quantity is used to
define the degree of refinement obtained.
Relative error, sometimes called relative precision, is expressed by a fraction
having the magnitude of the error in the numerator and magnitude of a measured
quantity in the denominator. It is necessary to express both quantity in the same
units, and the numerator is reduced to unity or 1 in order to provide an easy
comparison with other measurements.
For example, if for a particular measurement, the most probable error of the mean
is 0.10 m and the most probable value of the measurement is 235.50 m, the
relative precision (RP) would be expressed as 0.10/235.50 or 1/2355, also written
as 1:2355.
Weighted observations.
It is not always possible to obtain measurements of equal reliability under similar
conditions. Many surveying measurements are made under different
circumstances and conditions and therefore have different degrees of reliability.
The problem often encountered is how to combine these measurements and
determine the most probable values. For such a situation it is necessary to
estimate the degree of reliability (or weight) for each of the measurements before
they are combined and the most probable values are determined. A measured
length obtained on a bright early morning could be considered as more reliable
than one measured on a cold and rainy day. Another example is in the case of
repeated measurements, if a quantity is measured in two repetitions by group A
and in four repetitions by group B, then the measurement taken by group B should
be given twice the weight of the measurement of group A.

Interrelationship of errors
In some instances it is required to determine how the final result is affected when a
computation involves quantities that are subject to accidental errors. Two
commonly applied principles of the theory of errors involve the summation of errors
and the product of errors. These principles are given to provide the student a
better understanding of the propagation of errors.
1. Summation of errors. If several measured quantities are added, each of
which is affected by accidental errors.
PEs =± √ PE21 + PE22+ PE 23+ ….. PE2n
Where: PEs = probable error of the sum
PE 1 , PE 2 , etc = probable error of each measurement
n= number of values added

2. Product of errors. For a measured quantity which is determined as the

product of two other independently measured quantities such as Q1 and
Q2 (with their corresponding probable errors), the probable error of the
product is;
PE p=± √ (Q ¿ ¿ 1 x PE2 )2+(Q ¿ ¿ 2 x PE1 )2 ¿ ¿
Where: PE p= probable error of the product
PE1∧PE2 = probable error corresponding to each quantity measured
Q1∧Q2 = measured quantities

Illustrative examples:
1. The following values were determined in a series of tape measurements of a
line: 1000.58 ,1000.40, 1000.38, 1000.48, 1000.40, and 1000.46 meters.
Determine the following:
a. Most probable value of the measured length (1000.45 m)
b. Probable error of a single measurement and probable error of the mean (
± 0.05029 ¿, (± 0.02053 ¿
c. Final expression for the most probable length (1000.45 ± 0.02053 ¿
d. Relative precision of the measurement ( RPs=0.05/1000.45 ¿, (
RP m=0.02 /1000.45 ¿

2. Four measurements of a distance were recorded as 284.18, 284.19, 284.22,

and 284.20 meters and given weights of 1, 3, 2, and 4, respectively. Determine
the weighted mean. (284.20 m)
3. It is desired to determine the most probable value of an angle which has been
measured at different times by different observers with equal care. The values
observed were as follows; 74º39’45” (in two measurements), 74º39’27” (in four
measurements), and 74º39’35” (in six measurements). (74º39’34”)
4. Lines of levels to establish the elevation of a point are run over four different
routes. The observed elevations of the point with probable errors are given
below. Determine the most probable value of the elevation of the point.
Line Observed Probable E2 W= Relative P=Elev(RW)
elevation error (E) 1/E2 weight
(RW)
1 219.832 m ±0.006 m 7509.375
2 219.930 ±0.012 1877.266
3 219.701 ±0.018 1201.62
4 220.021 ±0.024

Weighted mean = ∑P/∑RW = 219.847 m

5. The length of a line was measured repeatedly on three different occasions and
the probable error of each mean value was computed with the following results:
st
1 set of measurements = 1201.5 ±0.02 m
2nd set of measurements = 1201.45 ±0.04 m
3rd set of measurements = 1201.62 ±0.05 m
Determine the weighted mean of the three sets of measurements. (1201.50 m)

6. The three sides of a triangular-shaped tract of land are given by the following
measurements and corresponding probable errors: a = 162.54 ±0.03 m, b =
234.26 ±0.05 m, and c = 195.70 ±0.04 m. Determine the probable error of the
sum and the most probable value of the perimeter. (±0.07), (592.50 ±0.07 m)
 7. The two sides of a rectangular lot were measured with certain estimated
probable errors as follows: W = 253.36 ±0.06 m and L = 624.15 ±0.08 m.
Determine the area of the lot and the probable error in the resulting calculation.
(±42.58 square meters), (158134.64 ±42.58 square meters)

5. References
1. La Putt, J.P., Elementary Surveying (3rd Edition) 2013 Reprint
2. https://civiltoday.com/surveying/86-objectives-of-surveying
3. https://www.britannica.com/technology/surveying
4. https://civilplanets.com/uses-of-surveying

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Revision: 02
Effectivity: August 1, 2020