1

UNIT 1: INTRODUCTION TO SURVEYING

1.0. Intended Learning Outcomes

At the end of this chapter, you shall be able to describe the direction of lines in terms
of their interior angles, deflection angles, angles to the right, bearings, azimuths and
magnetic declinations.

1.1. Introduction

One of the oldest arts practiced by man is surveying. The purpose of conducting
surveys is to gather information about the physical Earth. It includes measurement of
distances (e.i. horizontal and vertical distances) and locating and establishing points on or
beneath the surface of the Earth. In civil engineering, the data collected from the surveys are
used in planning, design and construction of complex structures like bridges, highways,
canals, dams, railroads, etc. Therefore, we can say that the efficiency and stability of
structures aforementioned are highly affected by the accuracy of the data collected during
the surveys - the reason why civil engineering practitioners should study the basic theory
and concepts of surveying.
In this chapter, you will be introduced to surveying. You will also learn the relevance
of this art to your chosen field which is civil engineering. In addition, you will get to know
the important qualities of a good surveyor that you should be possessing especially that you
will be conducting surveys (supposedly) in this course. Furthermore, you will be able to
identify the roles of the people in a survey party and you will be introduced to the
conventional instruments that are used in surveying.

1.2. Topics/Discussion (with Assessment/Activities)

1.2.1. History of Surveying
According to Rayner and Schimdt,

Surveying has two functions: (1) to

determine of the relative horizontal and vertical positions of points like what is presented in
maps, and (2) to establish control marks that are used in construction and in the
establishment of land boundaries. This science of gathering data has always been a part in
the development of human civilizations which started thousands of years ago. Surveying
was used by our ancestors especially in the fields of transportation, construction,
apportionment of lands and communication.

The beginning of surveying can be traced back to 2700 B.C.E. in ancient Egypt when
large-scaled pyramids were constructed across its region. The near-perfect dimensions of
these pyramids, as well as their north-south orientation, suggest that ancient Egyptians have
pioneered the use of the principles of surveying in construction.
 2

Great Pyramid of Khufu at Giza, Egypt. Retrieved from

https://www.sciencenews.org/article/mystery-void-discovered-great-
pyramid-giza

In 300 A.D., the Romans considered land surveying as a profession. Concepts of

surveying were used by the Romans in this era for measuring the lands that have been
conquered by the Roman Empire.

Europeans have developed the method called triangulation in the 16 th century. This
method, which relied mainly on angles, was used to build a hierarchy of networks to allow
point positioning within a country.

19th Century - Triangulation network for the

triangulation of Rhineland-Hesse. Retrieved from
https://upload.wikimedia.org/wikipedia/commons/2/2d/L-
Triangulierung.png

In 1620, English mathematician Edmund Gunter developed a surveying chain, called

used in measuring land parcels for the purpose of
apportioning land holdings to the settlers.

The study of astronomy resulted in the development of angle-reading devices that

were based on arcs of large radii, making such instruments too large for field use. With the
publication of logarithmic tables in 1620, portable angle-measuring instruments came into
use. They were called topographic instruments or theodolites. They included pivoted arms
for sighting and could be used for measuring both horizontal and vertical angles. Magnetic
compasses may have been included on some.

The Vernier (1631), the micrometer microscope (1638), telescopic sights (1669) and
spirit levels (1700) were all incorporated in theodolites in 1720. Stadia hairs were first applied
by James Watt in 1771.
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Modern surveying came into the picture in the late 18th century. During this era, two
French engineers by the name of Jean Delambre and Pierre Méchain, have measured the
meridian from Barcelona, Spain to Dunkirk, France which then led to the establishment of
the basic unit for metric system.
In the 19th century, further improvements and modifications were incorporated to the
previously developed surveying instruments. Photogrammetry or mapping of aerial
photographs and electronic distance measurement (EDM) that used laser for alignment
purposes were both introduced in this era. These two developments have increased the speed
and accuracy of the methods or operations that were conducted in the field.

1860) by James Wallace Black the first aerial photo shot in the
United States. Retrieved from https://petapixel.com/2019/10/16/a-
look-back-at-the-first-aerial-photo-shot-in-the-united-
states/Triangulierung.png

Important technological advancements starting in the late 20 th century included the

use of satellites as reference points for geodetic surveys and electronic computers to speed
the processing and recording of survey data.

It can be observed that during the earlier part of the history, surveying activities have
been limited only in gathering data on or near the surface of the Earth. However, as time
passed by, technological advancements have come into the picture which allow the experts
in the field to develop modern surveying techniques that can be applied in space exploration
and mapping of extraterrestrial bodies like stars, moon, planets and other heavenly bodies
in the solar system.

1.2.2. Types of Surveying and Their Importance

Surveying is not only intended for civil and geodetic engineers who need to gather
information about a land parcel that will be used in planning, design and construction of
structures needed by humankind. It is also suited for the practitioners in the fields of
architecture, forestry, agriculture and others who have a need to learn the basic concepts,
theory and practice of surveying that are greatly used in their respective fields of
specialization. Surveying is very important to all the fields aforementioned for the following
concerns:
mapping of the Earth below, on and above sea level
preparing navigational charts for the use on air, land and sea
establishing property boundaries of private and public lands
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developing data banks of land use to manage environment

determining some facts about the size, shape and magnetic fields of the Earth
preparing charts of some heavenly bodies like moons and planets

Generally, surveys are divided in two major classifications:

1. Plane Surveying. In here, the
Earth is considered as a flat
surface. In addition, measurement
of distances and areas are limited
due to the fact that the real shape
of the Earth is disregarded. It is
assumed in this classification of
survey that the level line is
considered as mathematically
straight. The direction of the
Plane surveying - a common method in calculating land
plumb line (vertical line) is composition and topography that involves considering a
assumed to be the same at all set expanse of land as a flat plane. Retrieved from
https://www.wisegeek.com/what-is-plane-surveying.htm
point. Moreover, the angles that
are taken in this classification of surveys are considered to be plane angles.
Plane surveying is commonly used in professional land surveys where details
about topography are collected which help the builders to estimate
distances,densities and land depths with a great deal of precision.
2. Geodetic Surveying. In here,
surveyors consider the spheroidal
shape of the Earth. In geodetic
surveying, the principles of
geodesy, which mainly deals with
geometric shape,
orientation in space and
gravitational field, that are of high
precision, are used. Calculations
in this classification of survey Students
conduct
on the University of California Davis field camp
a TLS survey. Retrieved from
involve solving equations derived https://www.unavco.org/education/resources/modules-and-
activities/field-geodesy/field-geodesy.html
from advanced mathematics
especially in spherical trigonometry, calculus and theory of least squares.
Typically, geodetic surveys are usually undertaken by the government
agencies for the production of accurate base and topographic maps.
Surveys can be further divided according to their purpose. The following are some of
the types of survey that are commonly executed:

1. Cadastral Surveys. This type of survey is conducted to determine and define

property lines, boundaries, corners and areas. This survey is also performed to
fix the boundaries of municipalities, towns and provincial jurisdictions.
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2. Construction Surveys. Sometimes called as stake-out, lay-out or setting-out

which is performed to establish reference points and markers to guide the
construction.
3. Hydrographic Surveys. This type of survey is initiated to map streams, lakes,
reservoirs, harbors, oceans and other bodies of water. Another purpose of
hydrographic surveys is to map the shorelines the areas underlying the water
surface and to measure the flow of streams.
4. Industrial Surveys. Sometimes called optical tooling that is used in industries
that require accurate dimensional layouts like ship building, construction and
assembly of aircrafts, layout and installation of heavy and complex
machineries, etc.
5. Mine Surveys. This type of survey is performed to measure and map on-
ground or underground points for the purpose of exploiting and utilizing
mineral deposits.
6. Photogrammetric Surveys. A type of survey which uses photographs, usually
taken in aerial or terrestrial perspective, to obtain reliable spatial information.
7. Route Surveys. This type of survey results in provides data about the
alignments, grades, earthwork quantities and location of natural and artificial
objects that are used in the planning, design and construction of highways,
railroads, pipelines and other linear projects.
8. Topographic Surveys. A survey that determines the shape of the ground and
the location and elevation of the natural and man-made features on it.

1.2.3. Qualities of a Good Surveyor

Generally, a surveyor measures, maps, assesses, collects and interprets information
about specific pieces of land. These pieces of information are collected during field survey
operations with the aid of the necessary surveying instruments. According to the Holland
Code framework, surveyors are typically interested in the following areas: Building,
Thinking and Organizing. The Building interest area indicates a focus on working with tools
and machines and making or fixing practical things. The Thinking interest area indicates a
focus on researching, investigating and increasing the understanding of natural laws. The
Organizing interest area indicates a focus on working with information and processes to keep
things arranged in orderly systems.

Specifically, surveyors should possess the following qualities to guarantee the

success of the field survey operations they are undertaking.

a. Communication skills. Surveyors must provide clear instructions to the other

members of the survey party to ensure the fluidity in the execution of tasks during
field survey operations. They must also be able to receive instructions accurately
from the architects and construction managers. Moreover, they must be able to
explain the progress of the operation to the concerned people like the developers,
lawyers, financers and government authorities.
b. Detail oriented. The information collected by the surveyors in the field must be
reliable enough to provide accurate data that will be used by the technical groups
for planning, design and construction of the project. Aside from that, they must
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also need to work with precision and accuracy due to the legal nature of the
documents they produce.
c. Physical stamina. Surveyors traditionally work outdoors, often in rugged terrain.
Therefore, they must be able to walk long distances and stand still for several
hours.
d. Problem-solving skills. Surveyors must figure out discrepancies between
documents showing property lines and current conditions on the land. If there
were changes in previous years, they must figure out the reason for the changes
so that property lines can be reestablished.
e. Technical skills. Surveyors use sophisticated technologies like total stations and
GPS devices to collect land survey data.
f. Time-management skills. Surveyors must be able to plan their time and their
during field survey operations which is critical especially
when dealing with deadlines.
g. Visualization skills. Surveyors must be able to envision new buildings and
distances.

1.2.4. Surveying Field Notes

Surveying field notes are the permanent record
of the actual work done in the field. It includes
lengths, angles, sketches, descriptions and other
data collected in the field. Field notes can either
be handwritten or computer-generated and
they are compiled in a field notebook. They are
very important to any surveying activity for the
fact that they keep the only record of the work
done in the field. Aside from that, if these notes
are lost, the time and money invested in
gathering these data will be put in waste. For
property surveys, the status of the field
notebook must be preserved because it will
serve as the evidence or proof in court reviews
which is common when dealing with properties
and land boundaries. Furthermore, the
information that are kept in the field notebook
will be used for making drawings and
Example of a field note for closed traverse. Retrieved from
calculations, thus, the field notes must be https://www.engineersdaily.com/2017/11/overview-open-and-
complete, legible, concise, comprehensive and closed-traverses-in-surveying.html
logically arranged according to the recognized
practice. The following are the five (5) types of notes that are commonly kept in practice:
1. Sketches. They provide visual features of what can be seen in the field. In most
cases, sketches are made approximately in scale (because they are drawn in the
field) and are incorporated with conventional symbols for better understanding
of the other important details in the drawing.
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2. Tabulations. Numerical values that are collected in the field must be organized
in a simple and definite manner. This can be done by tabulating these values.
This format allows one to easily check the data that are presented in the field
notebook.
3. Explanatory Notes. They provide a written description of what has been done
in the field. Explanatory notes are used to make clear some details that cannot
be explained further by tabulations and sketches.
4. Computations. They include simple calculations of the data collected in the
field using simple arithmetical steps and trigonometric functions.
Computations in the field notebook should be clear and arranged in an orderly
manner so that they can be easily understood by the people other that the one
who made the computations.
5. Combination of the Above. Commonly used in most extensive surveys where
the combination of the four (4) other types of notes is suitable in presenting in
details the data collected in the field.

Aside from the technical details of the work done in the field, basic information must
be included in the field notebook for documentation purposes. This includes the title of
project or name of the project, time of day, date and the weather condition during the conduct
of survey, as well as the names of the group members and their respective designations and
the list of equipment used in a survey operation.

As a civil engineering practitioner, most of the time, you will be conducting field
survey operations. Thus, it is must for you to prepare accurate, comprehensive and organized
field notes that will be used in different purposes. You should always remember the
important information that should be included in the field notebook. Moreover, you should
take note that it is essential that notes are intelligible to others without further verbal
explanations.

1.2.5. The Field Survey Party

The conduct of a survey operation in the field is not a one-man show. It involves a
group of people that compose a field survey party. It should be noted that each member of a
survey party is given with a designation with distinct duties and responsibilities compared
to the other members. The designations in a field survey party aims to eliminate the
possibilities of overlapping tasks of one member to the other individuals in the group which
can disrupt the fluidity and organization of the field survey operation. In most cases, it
should be realized that the principle of flexibility is adapted. In other words, the duties and
responsibilities of members of a survey party should not always be fixed but should be
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modified depending on the prevailing work requirements and conditions, problems in the
field operations and the availability and usage of surveying equipment.

Surveyor Team by Underwood Archives. Retrieved from

https://fineartamerica.com/featured/surveyor-team-underwood-archives.html

The table below shows the designations of the members of a survey party and their
respective duties and responsibilities.
DESIGNATION DUTIES AND RESPONSIBILITIES
1. Chief of the Party responsible for the overall direction, supervision and
operational control of the survey party
responsible for the logistical and technical requirements
and problems of a field survey operation
consults or confers with the superiors regarding the
project to be undertaken
submits survey reports and records
checks survey reports and records if complete, accurate
and adhere to the prescribed technical standards and
specifications
prepares cost and estimates of survey projects
receives and disburses all cash expenses of the survey
party
acts as an expert witness in court on matters relating to
technical description of land and other surveying matters
2. Assistant Chief of Party assists the chief of party in the accomplishment of the
tasks assigned to the survey party
takes over the duties of the chief of the party during the
absence of the chief
conducts ground reconnaissance and investigates sites of
a proposed project to collect necessary data before the
start of a survey work
responsible for the employment of surveying equipment,
instruments and accessories used in the survey operation
prepares field and office reports and survey plans for
submission to the chief of the party
3. Instrumentman sets up, levels and operates surveying instruments
 9
1 | Fundamentals of Surveying
secures if the instruments to be used in a survey
operation are in good condition and in proper
adjustment
assists the technician in the operation of electronic
surveying equipment
4. Technician responsible for the use and operation of all electronic
instruments required in a field work operation
secures if the electronic instruments are functioning well
and are regularly calibrated and are in proper
adjustment
responsible for the establishment of a two-way
communication link using radio
5. Computer performs all computations of survey data and works out
necessary computational checks required in a field work
operation
responsible for the utilization of electronic calculators,
pocket or microcomputers
assists in the operation of computerized surveying
systems or equipment
6. Recorder keeps a record of all sketches, drawings, measurements
and observations taken or needed for a field work
operation
keeps the table of schedules of all phases of work and
employment of the members of the survey party
does clerical tasks related to surveying
undertakes limited cartographic jobs
7. Head Tapeman responsible for the accuracy and speed of all linear
measurements with tape
directs the marking of stations to be occupied by the
surveying instruments
directs the clearing out of obstructions along the line of
sight
inspects and compares tapes for standard length prior to
the use in taping operations
responsible for eliminating or reducing possible errors or
mistakes in taping
8. Rear Tapeman assists the head tapeman during taping operations and
in other related works.
9. Flagman holds the flagpole or range pole at selected points as
directed by the instrumentman
helps the tapeman in making measurements
assists the axeman in cutting down branches and in
clearing other obstructions to the line of sight
sets up reflectors or targets when electronic distance
measurements are used
10. Rodman holds the stadia or leveling rod when sights are to be
taken on it
 1 | Fundamentals of Surveying
10

11. Pacer checks all linear measurements made by the tapeman

assists the tapeman in securing that mistakes in linear
measurements are either reduced or eliminated
performs the job of a rodman, if needed
12. Axeman/Lineman clears the line of sight of obstructions
responsible for the security and safety of the members of
the survey party at the survey site
13. Aidman renders first aid treatment to members of the survey
party who are involved accidents and other cases
involving their health, safety and well-being
assists the instrumentman, if needed
14. Utilitymen render other forms of assistance needed by the survey
party or as directed by the chief of party
designated as driver when a survey vehicle is needed in
the field survey operation
responsible for setting up the camp site and its facilities
when the survey party needs to camp out in the field
prepare and serve meals
look after the security of the camp site
transport surveying equipment, accessories and supplies
lay-out concrete monuments, markers and signals at
designated points

The size of a survey party depends upon the survey requirements, the equipment
available, the method of operation and the number of personnel needed to do the required
tasks. The United States Naval Construction Battalions, better known as Seabees, commonly
used three (3) survey parties as enumerated below:
1. Level Party. The minimum number of members of a level party is two (2) which
includes an instrumentman and a rodman. In this set-up, the instrumentman
acts as the note keeper or recorder. To improve the efficiency of the leveling
operations, the party may add a recorder and rodmen. The level party may
combine with other survey parties when the leveling operations take place
alongside with other control surveys. In here, the personnel of the level may
assume dual roles depending on the work requirements or the direction of the
chief of the party.
2. Transit Party. This survey party is composed of at least three (3) members: an
instrumentman, head chainman and the chief of the party. The chief of the party
directs the survey operation and at the same time, acts as the note keeper or
recorder. The instrumentman operates the transit and the head chainman
measures the horizontal distance.
3. Stadia Party. This survey party is comprised of at least three (3) members: an
instrumentman, a note keeper or recorder and a rodman. The note keeper
records the data observed by the instrumentman in the field and makes the
necessary sketches. In case the distance between the points required in the
survey operation is too long, the stadia party may add another rodman.
 1 | Fundamentals of Surveying
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1.2.6. Conventional Surveying Instruments

Surveyors use instruments that enable precise and reliable measurements during field
survey operations. Most of the surveying instruments nowadays are product of extensive
enhancements from centuries of technological advancements and developments. The
following are some of the basic instruments and field equipment and supplies that are mostly
used in survey operations.

A. Basic Surveying Instruments

Magnetic Compass
It consists of a magnetized steel needle mounted on
a pivot at the center of graduated circle. The needle
continues to point towards the magnetic north and
gives a reading which is dependent upon the
position of the graduated circle. Magnetic compass
is used to determine the direction of lines and to
calculate angles between lines.

Magnetic compass

Retrieved from https://www.amazon.in/WTH-Magnetic-Compass-50-mm/dp/B07G8DGNLT

Theodolite
It consists of a telescope that is mounted on a
tripod. The purpose of this telescope is to sight and
align the target in the field. A theodolite has also a
focusing knob that is used to make the object being
sighted as clear as possible. The telescope contains
an eyepiece to locate the target being sighted. An
objective lens is also located in the telescope to sight
the object and with the help of the mirrors inside
the telescope, enables the sighted image to be
magnified. A theodolite can be either non-digital or
digital. Non-digital theodolites are rarely seen in
survey operations nowadays. Theodolites, in
general, are used to measure both the horizontal
and vertical angles. Modern theodolite

Retrieved from https://free3d.com/3d-model/theodolite-on-tripod-base-5872.html

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1 | Fundamentals of Surveying
Automatic Level
A special leveling instrument used in surveying
which contains an optical compensator which
maintains line of sight or line of collimation even
though instrument is slightly tilted. This
surveying instrument is used in reading elevations
and determining differences in elevation between
two points. Automatic levels are typically used
together with level or stadia rods and tripod.

Automatic level

Retrieved from https://www.alfaplanhold.com/AL124_Precision_Automatic_Level_24X_p/9361240.htm

Transit
It is also known as the universal surveying
instrument. It is an optical instrument with spirit
level that is mounted on a tripod. It is commonly
used in field survey operations especially in
determining relative positions of lines and objects.
In addition, a transit can be used to establish a
reference line and read angles. It is typically set-up
in conjunction with a tripod, measuring tape and
calibrated rod.

Transit level

Retrieved from https://www.lot-art.com/auction-lots/American-Engineers-Transit-Theodolite-by-

Eugene/693-american_engineer-26.5.18-team

Total Station
A lightweight, compact and fully integrated
electronic instrument with the capability of an EDM
and an angular measuring instrument such as wild
theodolite. Total station is a modern surveying
instrument that is used in measuring distances and
angles, processing data, digitally displaying point
details and storing data in an electronic field book.

Total Station

Retrieved from http://hydrolandbd.com/product/total-station/

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Global Positioning System (GPS)

GPS stands for global positioning system. It uses
signals from satellites to pinpoint a location on the

about velocity and time synchronization for

various forms of travel. GPS uses at least 24
separate satellites in a system that consists of six
Earth-centered orbital planes, each having four
satellites. In surveying, GPS is used to provide the
latitude and longitude position of a point without
determining the horizontal and vertical angles. It
is also used in mapping points in the area of
interest. GPS tracker

Retrieved from https://www.pinterest.ph/pin/737253401469906294/

B. Field Equipment include all devices, tools and instrument accessories used in field
survey operations
Field Tools
Types of tools that are used in clearing
obstructions from the line of sight during survey
operations in the field. This set of tools includes
machete, brush hook, single-bit belt and single bit
axes, half hatchet, long-handled shovel, double-
faced sledgehammer and pick axe.

Set of field tools

Retrieved from https://siamblades.com/collections/all/hand_made_knife

Surveying Tapes
Tapes that are used in measuring horizontal,
vertical and inclined distances. They may be
made of a ribbon or a band of steel, an alloy of
steel, cloth reinforced with metal or synthetic
materials.

Tapes used in surveying

Retrieved from https://civilsnapshot.com/types-of-measuring-tapes-in-surveying/

Surveying Accessories
Equipment, tools and other devices that are not an integral part of the surveying
instrument itself. Surveying accessories include the following:
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Tripod
The base that supports the surveying instrument
and keeps it stable during observations. It consists
of a head to which the instrument is threaded into,
three (3) wooden or metal legs that are hinged at the
head and pointed metal shoes that are pressed to
the ground to have a firm and steady setup.

Tripod

Retrieved from https://surveyequipment.com/leica-ctp104-aluminium-tripod/

Range Pole
A wooden or metal pole that is held vertically to on
a point that is part of the observation which acts
as a sighting rod for linear or angular
measurements. It is also used as a reference point
for the chainmen to keep the proper alignment
during measurements. A range pole runs about
eight (8) feet long and about 1/2 to 1 inch in
diameter. It has a steel point or shoe and is painted
with bands of alternating red and white to increase
its visibility.
Range poles

Retrieved from https://lasersurveyingequipment.com.au/product/range-pole-a-b-rp3/

Plumb Bob
A pointed, tapered brass or bronze weight that is
suspended using a cord that is used in determining
the plumb line or true vertical line from a point on
the ground.

Plumb bob

Retrieved from https://www.bobvila.com/articles/495-the-plumb-bob//

 15

Chaining Pin
Also called as taping arrow that is used as
temporary markings of the points included in the
observation. Chaining pins are frequently used in
keeping the count of tape increments in chaining of
long measurements. A chaining pin is a metal
about 1 foot long with a circular eye at one end and
the other one is a pointed end that is pushed into
the ground.

Set of chaining pins

Retrieved from https://www.engineersupply.com/Seco-Marking-Pins-2183-00.aspx

Leveling Rod
A tape that is supported vertically that is used in
in measuring the difference in elevation between a
line of sight and a point on the ground directly
above or below it.

Examples of leveling rod or staff

Retrieved from https://civiltoday.com/surveying/186-stadia-rod

Prisms and Reflectors

Surveying accessories that are used to secure
control points at a comfortable and accessible
height for pinpoint accuracy. These devices can be
mounted on surveying poles and are used in
conjunction with electronic distance measuring
(EDM) instruments for improved accuracy.

Prism and reflector

Retrieved from https://www.nsscanada.com/prisms.php

 16

Magnifying Glass
A tool used by the instrumentman to read
graduations on a Vernier like what is seen in the
horizontal and vertical circles of the transit.

Magnifying glass
Retrieved from https://www.indiamart.com/excellent-traders-roorkee/surveying-instrument.html

C. Field Supplies variety of materials used to mark the locations of points in the field
Survey Point Markers
Materials that are used to mark the points included
in the observation. They can be temporary, semi-
permanent or permanent.

US Coast and Geodetic Survey marker

Retrieved from https://www.pinterest.ph/pin/345440233890475899/instrument.html

Marking Materials
Materials that are used to mark stakes and other
surfaces.

Lumber crayons

Retrieved from https://surveysupplyinc.com/keson-hard-lumber-crayons-red-box-of-12/

 17

Flagging
These are used for identification purposes. They
are made up of either colored cloth bunting or
plastic tape.

Stake flags

Retrieved from https://www.uline.com/BL_7132/Stake-Flags

Note-Keeping Materials
Materials wherein field notes are recorded and
kept.

Field Notebooks

Retrieved from http://northingeasting.blogspot.com/2011/03/field-notebooks.html

Personal Protective and Safety Equipment

Necessary items that are brought with by the
survey party during field survey operations to
supply the basic necessities of the members and to
store emergency supplies in case of accidents and
other circumstances that might happen during
survey operations.

Set of personal protective and safety equipment

Retrieved from https://fic-services.com/what-personal-protective-equipment-ppe-should-you-have-onsite/

Accuracy is always the main concern when doing field survey operations. One way to
achieve precise and accurate observations is to maintain the surveying instruments and tools
 18

properly. Generally, these instruments and tools should be kept and organized inside a
storage room to maintain their normal conditions. Use carrying cases for storing and
transporting these instruments. Always check the site conditions prior to any survey
operations. Before using instruments like theodolite and total station, always check first if
the calibration is on-point and in proper adjustments. It should be noted that if the instrument
is not calibrated properly, it will give inaccurate or even false data. Always handle all the
instruments with care. Moreover, it is advisable for the instruments like total station to be
serviced regularly. The software of some electronic surveying instruments should always be
kept updated to function properly. After using them in survey operations, tools like tapes
and rods must be cleaned first before storing them. Stacking of instruments in the storage
room after using should be avoided.

ASSESSMENT Score:
Name: Year & Section:
 19

Instructor: Date Finished:

General Instructions: Answer all the items of this assessment by following the set of guidelines
indicated for each item. Use the back page/s of the questionnaire to answer some of items. You may add
extra paper (any size), if necessary. Avoid erasures. Do not mutilate this paper.
1. Make a timeline of milestones in the practice of surveying. You may add information that
are not presented in the discussion.
Points System: Presentation 2 points max.
Validity of the information provided 3 points max.

2. Identify which type of survey must be initiated/directed to realize the given objectives
below. Write your answer on the space provided. (1 point each)
a. gathering information needed to prepare as-built drawings
for a completed project
b. determining drainage areas for ditches and culverts
c. re-establishing an old property boundary from missing
d. locating natural and man-made features that may be
required by the survey
e. gathering information needed to make a bathymetric
contour map

3. What makes a good surveyor? Explain briefly. (maximum of 100 words)

Points System: Ideas 3 points max.
Organization 2 points max.

4. Explain (one-by-one) why the following information must be included in the field
notebook
Points System (each item):
Ideas 2 points max.
Organization 1 point max.
a. Title of the field work or name of the project
b. Time of the day and date
c. Weather condition
d. Names of the group members and their designations
e. List of equipment used during the survey operation

5. Cite the importance of designating the members of a survey party in field survey
operations. (maximum of 100 words)
Points System: Ideas 3 points max.
Organization 2 points max.

6. The following are some of the supplemental tools, equipment or supplies used in field
survey operations. Give the technical name of each tool, equipment or supply illustrated
below (1 point each) and describe its purpose or uses (1 point each). Write your answer on
the space provided.
 20

Name:

Purpose or Uses:

Name:

Purpose or Uses:

Name:

Purpose or Uses:

Name:

Purpose or Uses:
 21

Name:

Purpose or Uses:

End of Assessment - -

1.3. References
Baseline Equipment Company. (n.d.). How to Use GPS for Land Surveying.
https://www.baselineequipment.com/gps-land-surveying-equipment
Baseline Equipment Company. (n.d.). Types of Surveying Equipment & Their Uses.
https://www.baselineequipment.com/surveying-equipment-types
Bayogo, J.G. The Art of Civil Engineering (vol. 1, 2nd ed.). Juncel Garces Bayogo.
ICSM ANZLIC Committee on Surveying & Mapping. (n.d.). Evolution of surveying and
surveying technology. https://www.icsm.gov.au/education/fundamentals-land-ownership-
land-boundaries-and-surveying/surveyors-and-surveying-0
La Putt, J. P. (2007). Elementary Surveying (3rd ed.). Baguio Research & Publishing Center.
Mishra, G. (n.d.). Modern Surveying Instruments and Their Uses. The Constructor.
https://theconstructor.org/surveying/modern-surveying-instruments-uses/16/
Mitchell C. (23 July 2020). What is Plane Surveying?. wisegeek.
https://www.wisegeek.com/what-is-plane-surveying.htm
NavyBMR. (n.d.). Surveying: Elements and Equipment. [Ebook].
http://www.navybmr.com/study%20material/14069a/14069A_ch12.pdf
Rogers, K. (07 May 2018). 10 Tips for Maintaining Your Surveying Equipment. Onsite Installer.
https://www.onsiteinstaller.com/online_exclusives/2018/05/10-tips-for-maintaining-
your-surveying-equipment
Truity. (n.d.). Surveyor. https://www.truity.com/career-profile/surveyor
Wright, J.W. (n.d.). Surveying civil engineering. Encyclopaedia Britannica.
https://www.britannica.com/technology/surveying

1.4. Acknowledgment
The images, tables, figures and information contained in this module were taken from
the references cited above.
 22

UNIT 2: MEASUREMENT OF DISTANCE

2.0. Intended Learning Outcomes

At the end of this chapter, you shall be able to:
a. Convert one unit of measurement of distance (used in surveying) to the other;
b. Apply the principles of pacing and taping in determining the distance between
two points;
c. Determine the errors in the observations;
d. Apply necessary corrections to tape measurements to obtain more accurate
data;

2.1. Introduction

Distance is one of the three elements of space, together with direction and elevation,

surveying, distance is described as the as the horizontal distance or length between two
points. However, considering the actual topography of the Earth, points may have different
elevations. In here, the distance is taken as the horizontal length of the plumb lines (used to
determine verticality) of the points. The accurate determination of the distance between two
distant points is indeed one of the basic operations in plane surveying that surveyors, in
general, need to deal with. In surveying, there are several methods in determining the
distance between two points. The choice of the method to be employed depends on the
purpose for which the measurement is intended for, the required precision, the cost and other
considerations. However, in this chapter, only two methods of linear measurement are
introduced; pacing and taping. The other methods will be discussed thoroughly in the latter
parts of the course.

In this chapter, you will learn the basic units of linear and areal measurement that are
commonly used in surveying. Aside from that, you will be able to measure distances using
the method called pacing. Furthermore, you will get know how to determine the possible
errors in the observations using the theory of probability and you will learn how to correct
them by applying necessary adjustments.

2.2. Topics/Discussion (with Assessment/Activities

2.2.1. Units of Measurement Used in Surveying
In present time, surveyors use the combination of traditional and modern
systems of units in measuring distances and areas. As a civil engineering practitioner,
you need to familiarize these units of measurement for the fact that you will be
conducting field works not only for the compliance of the requirements for this course
but also for future endeavors which require the practice of surveying. The conversion
table for some units used in surveying is presented below.
 23

For Linear Measurement

1 chain 100 links = 4 rods = 66 ft.
1 cubit 18 in.
1 furlong 40 rods
1 knot 6,080 ft. = 1 nautical mile
1 link 0.66 ft.
1 mile (nautical mile) 6,080 ft. = 8 furlongs
1 mile (statute mile) 5,280 ft.
1 military pace 2.5 ft.
1 perch 1 pole = 1 rod = 25 links
1 pin 100 links = 1 tape length
1 tally 10 pins
1 vara 33 in.
1 yard 3 ft.

For Areal Measurement

1 acre 4,047 m2
1 section 640 acres
1 township 36 sections

EXAMPLE 1. Units of Measurement Used in Surveying

A line was measured with 50-m tape. There were 10 tallies, 16 pins and the distance from
the last pin to the end of the line was found to be 2.5 meters. Find the length of the line in
meters.
SOLUTION:
Using the table presented above, convert each unit of measurement to meters. Note that
the length of one full-stretched tape is 50 m.

Sum up all the three (3) measurements to determine the length of the line, L.
L = 5000 + 800 + 2.5
L = 5,802.5 m.

2.3.2. Distance by Pacing

Pacing is one of the oldest and simplest methods of measuring distances. It involves
counting the number of steps in a given distance. There are two (2) units that are commonly
used in pacing: pace and stride.

A pace is simply the length of a step. It can either be measured on a heel-to-heel or toe-
to-toe basis. A stride is a double step. It is equivalent to two (2) paces.
 24

1 pace 1 stride
(toe-to-toe) (toe-to-toe)

1 pace 1 stride
(heel-to-heel) (heel-to-heel)

Illustration of pace and stride.

There are two (2) steps involved in determining the horizontal distance using pacing.
First, you need to determine your pace factor. Pace factor is the distance covered by one pace.
It should be noted that the length of a pace differs from person to person. It can be determined
by establishing a line of known length (taped distance) and pacing it back and forth (at least
5 trials). The mean or average number of paces for this line must be computed for the
determination of the pace factor. The pace factor P.F. can be computed using the equation:

After determining your pace factor, you can now estimate the unknown distance of
any line described by two points. Just like in the previous step, you need also to pace this line
back and forth (at least 5 trials) and compute for another mean or average number of paces.
The unknown distance between two given points (paced distance) is given by the equation:

It should be noted that the horizontal distance determined using pacing is just an
approximation. Pacing is suitable for situations like small-scale mapping and reconnaissance
surveys where low precision is already sufficient. When determining your pace factor, it is
important for you to walk naturally. Inconsistency in the speed of stepping or walking may
affect the accuracy of pacing. Other factors that might affect the reliability of pacing include
the roughness of the ground, the weight of the clothing and shoes used, fatigue on the part
of the pacer, slope of the terrain, as well as the age and sex of the pacer. In general, the length
of the pace decreases when any of these factors increases, except for the speed.

EXAMPLE 2. Distance by Pacing

A line 100 m. long was paced by a surveyor for five (5) times with the following number
of strides: 71, 72, 68, 70 and 71. Another line was paced five (5) times again with the
following number of paces: 634, 631, 632, 635 and 637.
1. Determine the pace factor.
2. Determine the distance of the new line.
 25

SOLUTION:
Considering the 100-m line, convert first the given data into number of paces.
71 strides = 142 paces
72 strides = 144 paces
68 strides = 136 paces
70 strides = 140 paces
71 strides = 142 paces
Solve for the mean or average number of paces for the 5 trials on the 100-m line.

Obtain the pace factor using the equation:

Considering the new line, solve for the mean or average number of paces for the 5 trials.

Determine the paced distance using the equation:

2.3.3. Distance by Taping

Taping is the process of directly measuring distances using a calibrated tape. It is
probably the most common method of determining horizontal distances. The process of
taping involves the stretching of the calibrated tape between two points and reading the
distance indicated on the tape. In a typical taping operation, the party is composed of the
following individuals: head tapeman, rear tapeman, recorder and flagman. Taping
operations are carried out by following the following steps:
1. Aligning the tape. Prior to the taping process, both ends of the line being
considered must be marked first. Range poles which are held by the flagmen at
both ends serve as guides for the alignment of the tape during the measurement.
The tapemen should secure that the tape being laid out aligns to the straight line
described by the two range poles at both ends before reading the measurement.
They should also make sure that the tape is not looped or twisted to avoid possible
errors.
2. Stretching the tape. A steady and firm pull must be exerted on both ends of the
tape. It should be noted that a standard pull is required to obtain the correct
measurement. If the tape is stretched less, the measurement that will be obtained
 26

is larger in value compared to the correct measurement. In contrast, if the tape is

stretched more, a smaller value of measurement is obtained.
3. Plumbing. As a practice, when there are irregularities and obstacles on the ground
surface, the tape is held above the ground. In this case, a plumb bob is dropped
on the ground to mark the turning points of the taping process. These marks are
then staked with pins to make the points more visible.
4. Marking full tape lengths. When dealing with long distances, measurement is
carried out by chains of full tape lengths. In simplistic approach, when one full
tape length is already laid out on the ground, its one end must be marked to chain
the next full tape length. This is done repeatedly until the entire distance of the
line being considered is already covered. These marks must be staked with pins
for tallying purposes.
5. Tallying Taped Measurements. It should be noted that 1 pin is equivalent to 1
tape length. As a common practice, the recorder only counts the number of pins
along the line being measured. The number of pins is then multiplied by the length
of the tape to determine the distance covered by these pins.
6. Measuring fractional lengths. There are cases that the measurement from the last
pin to the endpoint of the line does not describe one tape length. This fractional
length must be recorded for the fact that it completes the entire distance of the line
being considered. This length is added to the distance obtained in Step 5 to
determine the full distance of the taped line.

The procedure presented above is only applicable for taping over a level ground. To
determine the horizontal distance of a sloping ground, the method called breaking tape is
initiated. This procedure involves measuring shorter distances at a time to allow the tape to
be held horizontally. The procedure starts by marking the endpoints of the line being
considered. Then, range poles are positioned on these points to serve as guide in aligning the
tape during the measurement. A 10-m tape length is commonly used to measure the line
from the starting point to the end. It should be noted that this procedure goes downslope
always and is repeated for at least 5 trials. For the measurement of the first tape length, the
rear tapeman holds the 10-m mark over the starting point and the head tapeman holds the 0-
m mark with a plumb bob suspended on this point. Other members of the party make sure
that the tape is properly aligned and is in horizontal position. Once the suspended tape is set
in proper alignment, the head tapeman drops the plumb bob (at 0-m mark) which leaves a
mark on the ground. This mark is replaced with a pin, signifying the end of the first tape
length. The rear tapeman, the, moves to the newly set pin as the head tapeman advances to
mark the next tape length. This same process previously is repeated until the end point of
the line being considered is reached.

10 m 10 m 8m
Breaking tape procedure.
 27

2.3.4. Errors in Observations

Errors are inevitable in all surveying measurements. An error is defined as the
difference between the observed value and the true value of a measurement. Errors may
come from the instruments used, variations in the environmental condition during the
measurement and personal limitations of the observer. In surveying, errors are classified into
two (2) in terms of the behavior of their signs and magnitudes and the conditions prevailing
during the measurement.
1. Systematic Errors. These errors include the instrument factor, natural causes and
human limitations of the observer. The sign and magnitude of this type of error
remains the same as long as the field conditions remain constant and unchanged.
There is a corresponding change in the magnitude of the error for changing field
conditions, however, the sign remains the same.
2. Accidental Errors. These are errors beyond the control of the observer. They occur
as a matter of chance or probabilistic in nature and they are likely to be positive or
negative. There is no absolute way of determining or eliminating them since the
error for a measurement is not likely to be the same for the next measurements.
Accidental errors are still present even after eliminating all the possible mistakes
and systematic errors in the measurement.

In determining the possible errors in the measurements, two terms are commonly
used interchangeably: precision and accuracy. Precision refers to the degree of consistency of
a group of observations. Accuracy, on the other hand, refers to the closeness of a measurement
to its true value. The set of figures on the next page shows the difference between accuracy
and precision.

Low Accuracy Low Accuracy High Accuracy

Low Precision High Precision High Precision

Precision versus accuracy.

2.3.5. Theory of Errors in Observations

Probability is defined as the number of times something will probably occur over the
range of possible occurrences. The theory of probability is based upon the following
assumptions relative to the occurrences of errors:
Small errors occur more often than large ones and that they are more probable.
Large errors happen infrequently and are therefore less probable; for normally
distributed errors, unusually large ones may be mistakes than accidental errors.
Positive and negative errors of the same size happen with equal frequency; that is,
they are equally probable.
The mean of an infinite number of observations is the most probable error.

In surveying, the magnitude and frequency of the accidental errors are governed by
the principles of probability. In other words, accidental errors in measurements can be
 28

adjusted by applying the theory of probability. The following are the simpler applications of
the laws of probability in determining the errors in the observations:
a. Most Probable Value (mpv). It is the representation of the true value of an
observation. It is assumed that the most probable value is the closest value to the
true value of the measurement. It given by the equation:

where: x = individual measurement or observation

n = total number of observations made

b. Error/Residual/Deviation (v). The difference between the individual measurement

or observation and the most probable value.

c. Standard Deviation of Any Single Observation (Sx). It is the measure of

spread/variation/dispersion/scatter of a distribution. It is also called the root-mean
square.

d. Standard Error of the Mean ( ). It is the deviation of the sample mean from the
actual mean of the population. It is given by the equation:

e. Probable Error. It is the quantity in which when added or subtracted from the most
probable value, defines a range within which there is a 50% chance that the true
value of the measured quantity lies inside (or outside) the limits set.
Probable Error of Any Single Observation (PEs)

Probable Error of the Mean (PEm)

f. Relative Error/Precision. It the ratio of the magnitude of the error to the magnitude
of the measured value. It should be noted that when expressing the relative error
or precision, the numerator of the fraction must be 1 in order to provide an easy
comparison to other measurements.

Many surveying measurements are made under different circumstances and

conditions which lead to different degrees of reliability. Therefore, it is necessary to estimate
the degree of reliability (weight) for each measurement prior to the determination of the most
probable value. The relative weights of the different measurements are based upon the
judgment of the surveyor and the number of measurements taken for a particular quantity.
The following are some of the rules applied for weighted measurements:
 29

1. The weight is directly proportional to the number of observations or measurements.

2. The weight is inversely proportional to the square of the probable errors.
3. The weight is inversely proportional to the distance.
4. The weight is inversely proportional to the number of set-ups.

Note: When dealing with closed traverses, the weight is inversely proportional to the number of
number of measurements.

To understand the propagation of errors in measurements, two principles of the

theory of errors are applied. The two principles show the algorithm used when values with
known errors are added or multiplied.
1. Summation of Errors. If several measured quantities are added, each of which is
affected by accidental errors, the probable error of the sum is given by the square
root of the sum of the squares of the separate probable errors arising from the
several sources, or in equation form:

where: PESUM = probable error of the sum

PE1, PE2, 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 Q 1 and Q2 (with their
corresponding probable errors), the probable error of the product is given the
equation:

where: PEPRODUCT = probable error of the product

Q1 & Q2 = measured quantities
PE1 & PE2= probable error corresponding to each quantity
measured

EXAMPLE 3. Theory of Errors in Observations

Given the following data in measuring the distance of a certain line.
Distance No. of Measurements
47.23 3
47.21 2
47.19 4
47.27 2

1. Determine the most probable value of the measurements.

2. Calculate the standard deviation of any single observation
3. Calculate the standard error of the mean.
4. Calculate the probable error of any single observation.
5. Calculate the probable error of the mean.
6. Determine the relative error or precision of the mean.
 30

SOLUTION:
Take note that the given data in the problem can be treated as weighted observations since
the number of measurements for each distance is given. In weighted measurements, the
data (x) must be multiplied first by the frequency to determine the value of . Note: The
number of measurements corresponds to the frequency.
Data (x) Frequency
47.23 m. 3 141.69
47.21 m. 2 94.42
47.19 m. 4 188.76
47.27 m. 2 94.54
n = 11 = 519.41
Compute the most probable value of the measurements using the equation:

Tabulate the given data.

Data (x) Deviation (v) v2 Frequency
47.23 47.23 47.2191 = + 0.0109 0.000119 3 0.000357
47.21 47.21 47.2191 = - 0.0091 0.000083 2 0.000166
47.19 47.19 47.2191 = - 0.0291 0.000847 4 0.003388
47.27 47.27 47.2191 = + 0.0509 0.002591 2 0.005182
n = 11 = 0.009093
Calculate the standard deviation of any single observation.

Calculate the standard error of the mean.

Calculate the probable error of any single observation.

Calculate the probable error of the mean.

 31

Determine the relative error or precision of the mean.

EXAMPLE 4. Theory of Errors in Observations

From the following tabulated data, several lines of levels are run over different routes
from Benchmark 1 to Benchmark 2.
ROUTE DISTANCE DIFFERENCE IN ELEVATION
A 6 km. 25.012 m.
B 8 km. 24.958 m.
C 10 km. 25.135 m.
Determine the most probable value of the difference in elevation between BM1 and BM2.
SOLUTION:
From the problem, the observed data are the differences in elevations. Applying the rule,
the weight is inversely proportional to the distance, it can be concluded that the weight of each
observed value (difference in elevation) is equivalent to the reciprocal of its corresponding
distance.
Data (x) Weight Weight
25.012 m. 1/6 4.1687
24.958 m. 1/8 3.1198
25.135 m. 1/10 2.5135
n = 47/120 = 9.8020
Compute the most probable value of the difference in elevation between BM1 and BM2
using the equation:

EXAMPLE 5. Theory of Errors in Observations

The following interior angles of a triangular traverse were measured with the same
precision.
B

A C
ANGLE VALUE NO. OF MEASUREMENTS
A 5
B 6
C 2
Determine the most probable values of angles A, B and C, in sexagesimal form.
 32

SOLUTION:
In geometry, it can be recalled that the sum of the interior angles of a triangle must be

Sum of the interior angles o

Determine the total error in the given measurements.
Total error = True value Observed value
less compared to the true value
Applying the rule in closed traverses, the weight is inversely proportional to the number of
number of measurements, the angle measured the most frequent must have the least error.
Therefore, the weight for each measured angle is equivalent to the reciprocal of the
number of measurements taken in that angle.
Angle Value Weight of the Error
25.012 m. 1/5
24.958 m. 1/6
25.135 m. 1/2
= 13/15
The most probable value or true value of each angle measured is given by the equation:

Notes: Use (+) if the sum of the interior angles of a given traverse is less than the true value of
the sum of the interior angles of the shape of the traverse being described.
Use (-) if the sum of the interior angles of a given traverse is greater than the true value of
the sum of the interior angles of the shape of the traverse being described.
The equation presented above is applicable to all polygonal traverses.

EXAMPLE 6. Theory of Errors in Observations

The two sides of a rectangular lot were measured with certain estimated probable errors
as follows: and .
1. Determine the probable error in the area of the rectangular lot.
2. Determine the range where there is a 50% chance that the true area may lie.
SOLUTION:
Given: Q1 = 324.36 m PE1 = 0.075 m
Q2 = 568.15 m PE2 = 0.096 m
 33

It should be noted that when the area of a lot is analyzed, the product of the two
independently measured quantities (with their corresponding probable errors) must be
determined. It can be computed using the equation:

Determine the range where there is a 50% chance that the true area may lie.

Therefore, the true area of the given rectangular lot has a 50% chance of lying between
184,232.3578 m2 and 184,337.9102 m2.

2.3.6. Corrections to Tape Measurements

Generally, all tapes used in surveying are calibrated in standard conditions. In
standard conditions, a tape provides a value which is close to the true value of the
measurement. However, when employed in the field during actual survey operations, the
tape may provide a different value due to fact that it is exposed to some environmental
factors. The errors may be relatively small for short distances but when they are accumulated,
these errors become significant. Surveyors need to deal with these errors and it can be done
by applying corrections to the measurements done.

Tapes can either be too short or too long. To understand the difference between the
two, consider two fixed points that are 13 cm apart (true distance). If this distance is measured
under standard conditions, the tape will read an exact 13 cm.
Fixed points (13 cm apart)

Standard length tape

Tape too short

Tape too long

Illustration of a tape that is in standard length, tape that is too short and tape that is too long.

It can be seen from the figure that when the tape is too short, the error is negative and
thus, it is subtracted from the measured length. Consequently, when the tape is too long, the
 34

error is positive and it is added to the measured length. Given the measured distance and the
total error, the true distance of a certain measurement is obtained using the relation:
TD = MD + E
where: TD = true distance
MD = measured distance
Note: In measuring distances, the error is treated as positive when the tape is too long and negative
when the tape is too short.

The following are some of the corrections applied to tape measurements:

a. Temperature Correction. Applying the principle of physics, it can be observed that
the tape lengthens when the temperature rises and shortens when the temperature
falls. This type of correction is to be added or subtracted to or from the measured
distance depending on the sign obtained during the calculation. The correction
applied to the length of the tape due to change in temperature is given by the
formula:

where: CT = correction due to temperature

= coefficient of thermal expansion, 11.6 x 10-6
steel)
T1 = standard temperature or the temperature during the
calibration
T2 = temperature during the time of observation
L = length of the tape or length of the line measured

b. Pull Correction. The tape used in the field during a taping operation can also
elongate or shorten depending on the amount of pull applied to its ends. If the
applied pull is greater than the standard pull to the tape, the tape elongates and
becomes too long. Consequently, the tape stretches less when insufficient pull is
applied during the measurement compared to the standard pull, making it too
short. Just like the correction due to temperature, pull correction is to be added or
subtracted to or from the measured distance (depending on the sign obtained during
the calculation) and can be calculated using the formula:

where: CP = correction due to incorrect pull applied to the tape

P1 = standard pull or the pull during the calibration
P2 = applied pull
L = length of the tape or length of the line measured
A = cross sectional area of the tape
E = modulus of elasticity, 200 GPa (for steel)

c. Sag Correction. If the tape is not fully supported throughout its length and is
subjected to the pull that is not equal to the pull applied during the calibration
process, sagging of the tape is observable. This sag provides a reading of distance
between two points that is greater than the actual or horizontal distance, thus, this
correction is to be subtracted always from the measured distance.
 35

Apparent length of tape

P P

Sag

Suspended tape

Illustration of the sag produced when the tape is suspended.

The correction due to sag can be determined using the equation:

where: CSAG = correction due to sag

w = linear density or the weight of the tape per unit length
L = interval between supports or the unsupported length of the
tape
P = applied pull
Note: The value of L to be substituted to the given equation is the length between the
supports, not necessarily the total measured distance (can be used if the tape is supported at
both ends only). The total correction due to sag for a certain distance is the summation of
the sag corrections for each interval between the supported points of the tape. For instance,
if the tape is supported at mid-length and at the end points to measure a certain distance,
the total correction due to sag is equal to the summation of corrections due to sag for the two
intervals described by the three supports.

d. Normal Tension. It is the amount of pull required to make the end points of the
tape coincide with the marked points on a horizontal surface. Normal tension can
be solved by equating the elongation due to increased tension or pull to the
shortening due to sag or in equation form:

e. Slope Correction. Surfaces to which the tape is laid out during taping operations
are not always level, some are inclined. When dealing with inclined surfaces, the
inclined distance is mistakenly thought by surveyors as the horizontal distance
between two points. Recalling a principle on right triangles, the inclined distance
(hypotenuse) of a sloping surface is always greater than the horizontal distance,
therefore, slope correction is to be subtracted always from the inclined distance to obtain
the horizontal distance between the two points being observed. The illustration on
the next page shows the relationship between the inclined distance (S), horizontal
distance (H) and slope correction (Cslope).

Determination of the slope correction.

 36

The slope correction can be derived using Pythagorean Theorem. It can be obtained
using the following equations:
For Gentle Slopes (less than 20%)

For Steep Slopes (between 20% to 30%)

For Very Steep Slopes (greater than 30%)

where: Cslope = slope correction

h = difference in elevation between the ends of the measurement
S = inclined or sloping distance
H = horizontal distance
= angle of inclination

f. Mean Sea Level Correction. In surveying, it is assumed that the distance measured
along the mean sea level gives the measurement that is closest to the true value.
However, considering the natural topography of the Earth, the points being
observed may lie above or below the mean sea level, therefore, this correction is to
be added or subtracted to or from the measured distance.

Illustration of a distance measured along the mean sea level.

Mean sea level correction can be obtained using the equation:

where: Cmsl = mean sea level correction

L = length measured at the specified elevation
R =
estimated to be equal to radius of the Earth which is usually
taken as 6,400 km.
h = elevation of the location or place where the length is
measured
Note: This correction is subtracted if the line is measured above sea level and added if
the line is measured below sea level.
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To determine the total error of a certain measurement, just add up all the possible
errors or corrections obtained during the observation. It should be noted that the correction
to be applied to obtain the true distance is equal to the error observed during the
measurement. Signs of the individual corrections must be carried over in doing this
calculation.

EXAMPLE 7. Corrections to Tape Measurements

was used. Find the correction per tape length if the temperature at the time of
5

N/mm2 and coefficient of thermal expansion = 11.6 x 10-6 -sectional area of

tape is 8 mm2.
SOLUTION:
Given: T1 T2 E = 2 x 105 N/mm2
P1 = 80 N P2 = 150 N = 11.6 x 10-6
L = 30 m A = 8 mm2
There are two (2) corrections that are needed to be applied to the measurement based from
the problem: temperature and pull corrections. Determine first the temperature correction
per tape length using the equation:

Determine the pull correction per tape length using the equation:

To solve for the total correction per tape length, sum up all the corrections previously
calculated. Do not forget to include their respective signs for this calculation.

EXAMPLE 8. Corrections to Tape Measurements

A student is asked was to make a 345.43 m long line using a 25-m tape that is 0.0021 m too
long. What is the required measurement?
SOLUTION:
This problem is an example of laying out a distance. In tape measurements, measuring
and laying out a distance are two opposite procedures. When measuring a distance, MD
is given and by applying proper corrections, TD is obtained. However, when laying out a
distance, TD is already given and what is needed is to find the required measurement
(MD), considering the errors, that will be measured in the field. With this, we can say that
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in the problem, TD = 345.43 m. To solve this, calculate first the total error for the required
measurement (MD) using ratio and proportion because when measuring the distance of a
straight line, errors propagate linearly. It can be recalled that in a 25-m tape, there is an
error of 0.0021 m (too long). Let: E = total error for the required measurement.

To solve for the value of the required measurement (MD), use the equation:
TD = MD + E

Substitute the value of E to the equation presented above.

EXAMPLE 9. Corrections to Tape Measurements

Compute the sea level distance of a line which measures 324.45 m if it was measured in
Mount Apo (elevation is 2,954 m).
SOLUTION:
Given: L = MD = 324.45 m R = REarth = 6,400 km = 6,400,000 m
h = 2,954 m
Calculate the mean sea level correction using the equation:

(the line is measured above sea level)

Determine the sea level distance (TD) of the line using the equation:
TD = MD + E
Take note that the error in the measurement is equal to the correction to be applied.
TD = MD +
TD = 324.45 m + (-0.14975 m)
TD = 324.30025 m (sea level distance)

EXAMPLE 10. Corrections to Tape Measurements

A 50-m steel tape weighs 5 kg and is supported at its end points and at 8-m and 25-m
marks. If a pull of 6 kg is applied, determine the following:
1. Correction due to sag between the 0-m and 8-m marks, 8-m and 25-m marks, and 25-m
and 50-m marks.
2. Correction due to sag for one tape length.
3. Correct distance between the ends of the tape.
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SOLUTION:
Draw the figure.

Given: L = 50 m L2 = 25 8 = 17 m P = 6 kg
L1 = 8 m L3 = 50 25 = 25 m

Determine the linear density of the tape using the equation:

Compute the sag correction between 0-m and 8-m marks. It can be recalled that sag
corrections are always treated as negative.

Compute the sag correction between 8-m and 25-m marks.

Compute the sag correction between 25-m and 50-m marks.

Solve for the total correction due to sag for one tape length.

Determine the correct distance between the ends of the tape. Note: E = CSAG (TOTAL)
TD = MD + E
TD = MD + CSAG (TOTAL)
TD = 50 m + (-0.03898 m)
TD = 49.96102 m
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ASSESSMENT Score:
Name: Year & Section:
Instructor: Date Finished:

General Instructions: Read the questions carefully and answer all the items of this assessment. Use
the back page/s of the questionnaire for your illustrations and solutions. Round off your final answers
to the nearest ten-thousandths. You may add extra paper (any size), if necessary. Avoid erasures. Do
not mutilate this paper.
1. A distance was measured and recorded to have a value equivalent to 10 perches, 5 rods
and 50 varas. Compute the total distance in feet. (1 point)

2. A 45-m course, AB, on level ground was paced by a surveyor for the purpose of
determining his pace factor. The number of paces for each trial taken are shown in the
accompanying table.
PACING DATA
TRIAL LINE TAPED DISTANCE NO. OF PACES
1 AB 50
2 BA 53
3 AB 51
45.0 m
4 BA 53
5 AB 52
6 BA 53
a. Determine his pace factor. (1 point)
b. If the surveyor then took 771, 770, 768, 770, 772 and 769 paces in walking an unknown
distance CD, what is the length of the line? (2 points)
c. Assuming that the taped length of line CD is 667.9 m, determine the relative precision
of the measurement performed. (1 point)

3. The following data are the observed elevation of a point by running a line of levels over
four different routes.
ROUTE ELEVATION PROBABLE ERROR
1 28.89 m
2 28.40 m
3 28.63 m
4 28.23 m
Determine the most probable value of the elevation of the point. (2 points)

4. The following interior angles of a closed traverse A-B-C-D were measured with the same
precision. Draw the polygon described in the problem. (1 point)
NO. OF
ANGLE VALUE
MEASUREMENTS
A 5
B 6
C
D 7
 41

a. Determine the most probable value of angle A, in sexagesimal form. (1 point)

b. Determine the most probable value of angle B, in sexagesimal form. (1 point)
c. Determine the most probable value of angle C, in sexagesimal form. (1 point)
d. Determine the most probable value of angle D, in sexagesimal form. (1 point)

5. A civil engineer used a 30-m tape in measuring an inclined distance. The measured
length on the slope was recorded to be 459.20 m long. The difference in elevation between
the initial and the end point was found to be 1.25 m. The 30-m tape is of standard length

The cross-sectional area of the tape is 6.50 mm² and the modulus of elasticity is 200 GPa.
The tape has a linear density of 0.075 kg/m, = Draw the figure. (8 points)

End of Assessment -

2.3. References

Bayogo, J.G. The Art of Civil Engineering (vol. 1, 2nd ed.). Juncel Garces Bayogo.
La Putt, J. P. (2007). Elementary Surveying (3rd ed.). Baguio Research & Publishing Center.

2.4. Acknowledgment
The images, tables, figures and information contained in this module were taken from
the references cited above.
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