Far Eastern University

Institute of Architecture and Fine Arts

MODULE 1: INTRODUCTION

Module Information

Module Overview
The module is an introductory lesson on surveying. It includes knowledge and insights to different
surveying terminologies and the importance of surveying. The module will also provide an insight on the
different types of surveys which generally requires different field procedure and the essential components
of field notes.

Module Coverage
The module will be covered for a duration of 1 week (see course outline schedule). It is scheduled on the
week 2 of the semester.

Module Objective
• The module aims to help the student understand what surveying is all about and its importance.
• The module aims to provide an insight to the different types of surveys.
• The module aims to help the student to become familiar with the difference between plane and
geodetic surveying
Module Learning Outcomes
By the end of this module the student should be able to:
• Define surveying and recognize its importance to every project that requires actual construction.
• Recognize and describe the different types of surveys.
• Differentiate plane surveying from geodetic surveying.
Module Interdependencies
The module serves as an introductory lesson that will reinforced by Module 2:
Module Learning Materials
Under this module the students are provided with the following materials:
• Lecture Note:
Title: Introduction to Surveying
The lecture discusses the classification of surveying and different types of surveys It also
includes a brief discussion on the components of field survey party and the different information
found in field notes.
• PowerPoint Presentation:
The presentation provided in pdf file are the slides used for the presentation of the mentor.

Additional Readings and Materials

Students may refer to the given lectures under this module. Nevertheless, should the student like to study
beyond the given materials, they may refer to the books listed below:
• Ghilani, C. (2012). Elementary Surveying: an Introduction to Geomatics
• Lee, Sandra Jean. Willis's elements of quantity surveying. Chichester, West Sussex, United
Kingdom: John Wiley & Sons Inc., 2014 IARFA 0140 Cir TH 435 L4 2014
• Surveying. UAE 3G Elearning, 2015. Cir TA 545 S9 2015
Module Output-base Work
References
 Far Eastern University
Institute of Architecture and Fine Arts

• Basak, N N. Surveying and Levelling. Second Edition. New Delhi: McGraw-Hill Education (India) Private
Limited, 2014. Cir TA 545 B3 2014
• Johnson, Aylmer. Plane and Geodetic Surveying. Second Edition. Boca Raton: CRC Press, Taylor &
Francis Group, 2014. Cir TA 545 J6 2014
• La Putt, Judy Pilapil. Higher Surveying, 2nd Edition. Mandaluyong City: National Bookstore, 1990. Fil TA
545 L3 1990
• Kavanagh, Barry F. Surveying: Principles and Applications. 6th ed. Upper Saddle River, NJ:
Prentice Hall, c2003. Cir TA 545 K3 2003

WEEK 2: LECTURE READING 1

 Far Eastern University
Institute of Architecture and Fine Arts

Definition of Plane Surveying

• The art of measuring horizontal and vertical distances between objects, of measuring angles
between lines, of determining the direction of lines, and of establishing points by predetermined
angular and linear measurements.

Importance of Surveying
Surveying plays an essential role in planning, design, layout and construction of our physical environment
and infrastructure. The term infrastructure is commonly used to represent all the constructed facilities and
systems which allows human communities to function and thrive productively.

Surveying is the link between design and construction. Roads, bridges, buildings, water supply, sewerage,
drainage systems, and many other essential public works projects could never be built without surveying
technology.

The figure shows a bird’s eye view of urban area which depends on accurate
surveying for its existence. Nearly every detail seen on that photograph was
positioned by surveying methods.

In addition to its customary applications in construction and land-use projects, surveying is playing an
increasingly important role in modern industrial technology. Some activities that would be nearly
impossible without accurate surveying methods include testing and installing accelerators for nuclear
research and development, industrial laser equipment, and other sensitive precision instruments for
manufacturing or research. The precise construction of rocket launching equipment and guiding devices
is also dependent on modern surveying.

Without surveying procedures, no self-propelled missile could be built to the accuracy necessary for its
operation; its guiding devices could not be accurately installed; its launching equipment could not be
constructed; it could not be placed in position or oriented on the pad; and its flight could not be measured
for test or control. Moreover, its launching position and the position of its target would be a matter of
conjecture. Surveying is an integral part of every project of importance that requires actual construction.
 Far Eastern University
Institute of Architecture and Fine Arts

CLASSIFICATIONS

Plane surveying

It is the type of surveying in which the earth is considered to be a flat surface, and where distances and
areas involved are of limited extent that the exact shape of the earth is disregarded.

Geodetic surveying
These are surveys of wide extent which take into account the spheroidal shape of the earth.

TYPES OF SURVEYS based on the following:

1. Nature of Survey Field
2. Object of Survey
3. Instruments Used
4. Methods Employed

TYPES OF SURVEYS BASED ON NATURE OF SURVEY FIELD:

Land survey- it involves measurement of various objects on land.

Topographic Survey
It is meant for plotting natural features like rivers, lakes, forests and hills as well as manmade
features like roads, railways, towns, villages and canals.

Cadastral Survey
It is for marking the boundaries of municipalities, villages, districts, states etc. Also comes the
survey made to mark properties of individuals.

City Survey
The survey made in connection with the construction of streets, water supply and sewage lines
fall under this category.

Route Surveys
Involves the determination of the alignment, grades, earthwork quantities, location of natural and
artificial objects in connection with planning, design, and construction of highways, railroads,
pipelines, canals, transmission lines, and other linear projects.

Marine or hydrographic survey

Survey conducted to find depth of water at various points in bodies of water like sea, river and
lakes fall under this category. Finding depth of water at specified points is known as sounding.

These surveys are made to map shorelines, chart the shape of areas underlying water surfaces,
and measure the flow of streams. They are of general importance in connection with navigation,
development of water supply and resources, flood control, irrigation, production of hydroelectric
power.
 Far Eastern University
Institute of Architecture and Fine Arts

Astronomical survey
Observations made to heavenly bodies like sun, stars etc., to locate absolute positions of points
on the earth and for the purpose of calculating local time.

TYPES OF SURVEYS BASED ON OBJECT OF SURVEY:

Engineering survey

The objective of this type of survey is to collect data for designing civil engineering projects like roads,
railways, irrigation, water supply and sewage disposals. These surveys are further sub-divided into:
• Reconnaissance Survey for determining feasibility and estimation of the scheme.
• Preliminary Survey for collecting more information to estimate the cost of the project.
• Location Survey to set the work on the ground.

Military survey
• This survey is meant for working out plans of strategic importance.

Mine survey
• This is used for exploring mineral wealth.
• This is survey which performed to determine the position of all underground excavations and
surface mine structures, to fix surface boundaries of mining claims, determine geological
formations, to calculate excavated volumes and establish lines and grades for other related
mining work.

Geological survey
• This survey is for finding different strata in the earth’s crust.

Archeological survey
• This survey is for unearthing relics of antiquity.

TYPES OF SURVEYS BASED ON INSTRUMENTS USED:

• Chain Survey
• Compass Survey
• Plane Table Survey
• Theodolite Survey
• Tacheometric Survey
• Modern Survey using Electronic Distance Meters and Total Station
• Photographic and Aerial Survey

TYPES OF SURVEYS BASED ON METHODS EMPLOYED:

Triangulation
In this method control points are established through a network of triangles.
 Far Eastern University
Institute of Architecture and Fine Arts

Traversing
In this scheme of establishing control points consists of a series of connected points established
through linear and angular measurements.

SURVEYING FIELD NOTES

Surveying field notes constitute the only reliable and permanent record of actual work done in
the field. These notes are then always kept for future references.

TYPES OF NOTES
• 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.
• Tabulations. A series of numerical values observed in the field are best shown in a tabulated
format.
• Explanatory Notes. Explanatory notes provide a written description of what has been done in
the field.
• Computations. Calculations or one kind or another form a large part of the work of surveying.
• Combination of The Above. The practice used in most extensive surveys is a combination of
the above types of notes.

INFORMATION FOUND IN FIELD NOTEBOOKS

• Title of the Field Work or Name of Project
• Time of Day and Date – These entries are necessary to document the notes and furnish the
timetable, as well as to correlate different surveys.
• Weather Conditions – Temperature, weather, velocity and other weather conditions have a
decided effect upon accuracy in survey operations. An instrument-man making precise
observations is unlikely to perform the best possible work during extremes in temperature
conditions. It is for these reasons that the details related to the weather play an important part
when reviewing field notes.
• Names of Group Members and their Designations – From this information, duties and
responsibilities can easily be pinpointed among the survey party members.
• 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 aids in isolating errors
in some cases.

THE FIELD SURVEY PARTY

• Chief of Party – the person who is responsible for the overall direction, supervision, and
operational control of the survey party.
• Instrumentman – the person whose duty is to set up, level, and operate surveying instruments.
• Technician – the person who is responsible for use and operation of all electronic instruments.
• Computer – the person whose duty is to perform all computations of survey data and works out
necessary computational checks required in the field work operation.
• Recorder – the person whose duty is to keep a record of all sketches, drawings, measurements,
and all observations taken and needed for a field work operation.
• Head Tapeman – the person responsible for the accuracy and speed of all linear measurements
with tape.
• Rear Tapeman – the person whose duty is to assists the Head Tapeman during taping operations
and in other related work.
 Far Eastern University
Institute of Architecture and Fine Arts

MODULE 2: MEASUREMENT OF HORIZONTAL DISTANCES

Module Information

Module Overview
The module begins with a discussion on the different types of mistakes and errors that a surveyor must
eliminate or minimize. It includes knowledge and insights to different methods of measuring the horizontal
distance. Moreover, the module discusses the rough distance measurement by pacing and by taping. Taping
has been the traditional surveying method for horizontal distance measurement. Furthermore, the module
provides knowledge on the application of correction in laying out and measuring distance by taping.

Module Coverage
The module will be covered for a duration of 3 weeks with 2 work outputs(see course outline schedule for
submission). It is scheduled on the week 3, 4, and 5 of the semester.

Module Objective
• The module aims to help the student recognize the different types and sources of errors and mistakes
in surveying.
• The module aims to provide an insight to the different methods of measuring horizontal distance
• The module aims to provide knowledge in the determination of errors and corrections in taping
• The module aims to provide knowledge in the determination of individual pace factor to be used in
measuring horizontal distance.
Module Learning Outcomes
By the end of this module the student should be able to:
• Discuss errors and mistakes
• Utilize the steel tape in measuring and laying out distances with precision.
• Analyze errors in measuring horizontal distances and apply corrections or adjustments for precision
• Measure an unknown distance of level and non-level by pacing and taping.
Module Learning Materials
Under this module the students are provided with the following materials:
• Lecture Note:
Title: Errors in Surveying
Methods of Measuring Horizontal Distance
Taping and Taping Correction
Measurement of Distance by Pacing
• PowerPoint Presentation:
The presentation provided in pdf file are the slides used for the presentation of the mentor.

Additional Readings and Materials

Students may refer to the given lectures under this module. Nevertheless, should the student like to study
beyond the given materials, they may refer to the books listed below:
• Ghilani, C. (2012). Elementary Surveying: an Introduction to Geomatics
 Far Eastern University
Institute of Architecture and Fine Arts

• Lee, Sandra Jean. Willis's elements of quantity surveying. Chichester, West Sussex, United
Kingdom: John Wiley & Sons Inc., 2014 IARFA 0140 Cir TH 435 L4 2014
• Surveying. UAE 3G Elearning, 2015. Cir TA 545 S9 2015
Module Output-base Work
To complete this module the student shall submit Formative Assessment 1 and 2. The details of the
assessment can be found in the Assessment Module.
References
• Basak, N N. Surveying and Levelling. Second Edition. New Delhi: McGraw-Hill Education (India) Private
Limited, 2014. Cir TA 545 B3 2014
• Johnson, Aylmer. Plane and Geodetic Surveying. Second Edition. Boca Raton: CRC Press, Taylor &
Francis Group, 2014. Cir TA 545 J6 2014
• La Putt, Judy Pilapil. Higher Surveying, 2nd Edition. Mandaluyong City: National Bookstore, 1990. Fil TA 545
L3 1990
• Kavanagh, Barry F. Surveying: Principles and Applications. 6th ed. Upper Saddle River, NJ: Prentice
Hall, c2003. Cir TA 545 K3 2003
 Far Eastern University
Institute of Architecture and Fine Arts

WEEK 3-4

LECTURE READING 2

ERRORS IN SURVEYING

ERRORS
An error is defined as the difference between the true value and measured value of a quantity. It is a deviation
of an observation or a calculation from the true value and is often beyond the control of the one performing
the operation.

MISTAKES
These are inaccuracies in measurements, which occur because some aspect of surveying operation is
performed by the surveyor w/ carelessness, inattention, poor judgment and improper execution.
Misunderstanding of the problem, inexperience, or indifference of the surveyor also causes mistakes. Large
mistake is referred to as blunder. Mistakes and blunder are not classified as errors because they usually are
so large in magnitude when compared to errors.

TYPES OF ERRORS

Systematic Errors
Systematic error is a type of error w/c always have the same sign and magnitude as long as field conditions
remain constant and unchanged. In a changing field condition, there is a corresponding change in magnitude
of error, however, the sign remains constant. A systematic error repeats itself in other measurements, still
maintaining sign, and thus will accumulate. It is for this reason that this type of error is also called a cumulative
error
For instance, in making a measurement w/ a 30-m tape w/c is 5 cm too short, the same error is made each
time the tape is used. If a full length is used six times, the error accumulates and totals six times the error (or
30 cm) for the total measurement.

Accidental Errors
These errors are purely accidental in character. The occurrence of such error 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.

SOURCES OF ERRORS

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. Surveying instruments just like any other
instruments are never perfect; proper corrections and field methods are applied to bring the measurements
w/in certain allowable limits of precision. Moreover, w/ time and continuous usage, the wear and tear of the
instrument will likely be a cause for errors.
 Far Eastern University
Institute of Architecture and Fine Arts

Examples of instrumental errors are:

• Measuring w/ a steel tape of incorrect tape.
• Using leveling rod w/ painted graduations not perfectly spaced.
• Determining the difference in elevation between two points w/ an instrument whose line of sight is
not in adjustment.
• Sighting on rod that is warped.
• Improper adjustment of the plate bubbles of transit or level.

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. Natural errors are beyond the
control of man. However, in order to keep the resulting errors w/in allowable limits, necessary precautions can
be taken.
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 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 measurement of a line w/ a tape being blown sidewise by a strong wind.
• Error in the measurement of a horizontal distance due to slope or uneven ground.

Personal Errors
These errors arise principally from limitations of the senses of sight, touch and hearing of the human observer
w/c are likely to be erroneous or inaccurate. This type of fallibility differs from one individual to another and
may vary due to certain circumstances existing during a measurement. Some personal errors are constant,
some are compensating, while others may be erratic. It is significantly reduced or eliminated as skills are
developed in surveying operations through constant practice and experience. It can also be eliminated by
employing appropriate checking of procedures in the taking and recording of measurements.

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
 Far Eastern University
Institute of Architecture and Fine Arts

MEASUREMENT OF HORIZONTAL DISTANCES

DISTANCE BY TAPING
The use of graduated tape is probably the most common method of
measuring or laying out horizontal distances. It consists of stretching
a calibrated tape between two points and reading the distance
indicated on the tape. It is a form of direct measurement which is
widely used in the construction of building, dams, bridges, canals and
many other engineering as well as non-engineering activities.

DISTANCE BY PACING
Pacing is measuring distance by counting the number of steps or
paces in a required distance. Pace is defined as the length of a step-in walking that is measured from heel to
heel or from toe to toe. Pacing means moving with measured steps; and if the steps are counted, distances
is calculated by multiplying the number of paces by the individual’s pace factor.
➙ the length of one’s pace is referred to as the pace factor.
Ø Advantages
• Simple
• Low Tech
• No specialized equipment

Ø Disadvantages
• Topography affects accuracy
• requires practice to take a consistent pace
• Only measures slope distance

DISTANCE BY TACHYMETRY

Tachymetry (Tacheometry) is another procedure of obtaining horizontal

distances. It is based on the optical geometry of the instruments employed
and is an indirect method of measurement.
A transit or theodolite is used to determine subtended intervals and
angles on a graduated rod or scale form w/c distances are computed by
trigonometry. Tachymetric measurements are performed either by the
stadia method or the sub tense bar method.

Distance by stadia requires an instrument with stadia cross hairs

 Far Eastern University
Institute of Architecture and Fine Arts

𝐻𝑜𝑟. 𝐷𝑖𝑠𝑡. = (𝑆𝐼)(𝑆𝐹)

𝑆𝐼 = Stadia Interval
= TSR - BSR
𝑆𝐹 = Stadia Factor

DISTANCE BY GRAPHICAL and MATHEMATICAL METHOD

By graphical or mathematical methods, unknown distances may be determined through their relationship w/
known distances geometrically.

DISTANCE BY MECHANICAL DEVICES

Odometer
Odometer is a simple device that can be attached to a wheel for
purposes of roughly measuring surface distances. It measures
distance based upon the number of revolutions of the wheel.

The wheel is rolled over the distances to be measured and the

number of revolutions of the wheel is directly registered by the
device. Since the circumference of the wheel is known, the
relationship between revolution and distance could then be
established.
Multiplying the number of revolutions with the circumference of the wheel gives you the distance covered by
the odometer.

Measuring Wheel (Surveyor’s wheel)

This is very similar in operation to an odometer except that it is a more portable and
self-contained measuring device. It is also called a clickwheel, hodometer, waywiser,
trundle wheel or perambulator.

Optical Rangefinder

An optical instrument for measuring distance, usually from its position to a target point, by measuring the
angle between rays of light from the target, which enter the rangefinder through the windows spaced apart,
the distance between the windows being termed the baselength of the rangefinder; the two types are
coincidence and stereoscopic.
 Far Eastern University
Institute of Architecture and Fine Arts

It operates on the same principle as a rangefinder on a single-lens reflex camera.

DISTANCE BY ELECTRONIC DISTANCE MEASUREMENT INSTRUMENT

Electronic Distance Measurement (EDM)

EDM is a term used as a method for distance measurement by electronic means. In this method, instruments are
used to measure distance that rely on propagation, reflection and reception of electromagnetic waves like radio,
visible light or infrared waves.

Laser Distance Meter

A Laser Distance Meter sends a pulse of laser light to the target and
measures the time it takes for the reflection to return. For distances up
to 30m, the accuracy is ±3𝑚𝑚. On-board processing allows the
device to add, subtract, calculate areas and volumes and to
triangulate. You can measure distances at a distance.

Total Station(TS) or Total Station Theodolite (TST) is an electronic/optical

instrument used for surveying and building construction. It is an
electronic transit theodolite integrated with electronic distance
measurement (EDM) to measure both vertical and horizontal angles
and the slope distance from the instrument to a particular point, and an
on-board computer to collect data and perform triangulation
calculations.
 Far Eastern University
Institute of Architecture and Fine Arts

DISTANCE BY PHOTOGRAMMETRY

Photogrammetry
Photogrammetry is the science of making measurements from photographs. This includes calculating
distances and lengths, objects heights and area measurements. Photogrammetry has been around since the
development of modern photography techniques. If the scale of an image is known, distances or lengths of
objects can be easily calculated by measuring the distance on the photo and multiplying it by the scale factor.
Remember that scale is the ratio of the size or distance of a feature on the photo to its actual size. Scale for
aerial photos is generally expressed as a representative fraction (1 unit on the photo equals "x" units on the
ground). If the scale is known distances on the photograph can easily be transformed into real-world ground
distances.

𝑃ℎ𝑜𝑡𝑜 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑆𝑐𝑎𝑙𝑒 =
𝐺𝑟𝑜𝑢𝑛𝑑 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
 Far Eastern University
Institute of Architecture and Fine Arts

TAPING AND TAPING CORRECTION

TAPING: Applying the known length of a graduated tape directly to a line a number of times.

Taping operations could either be of the following: (Measuring) taping to determine an unknown length, or
(Laying Out) taping for the purpose of laying out a required or specified length. Regardless of which of these
two categories is involved, there are some corrections, which are applied to the original measurements to
determine the correct and more accurate length.

TAPING ERROR

1. Instrumental Error – a tape may have different length due to defect in manufacture or repair or as the result
of kinks
2. Natural Error – length of tape varies from normal due to temperature, wind and weight of tape (sag)
3. Personal Error – tape person may be careless in setting pins, reading the tape, or manipulating the equipment

Note: Instrumental and natural error can be corrected mathematically, but personal error can only be
corrected by repeating the measurement. When a tape is obtained, it should either be
standardized or checked against a standard.

CORRECTIONS in TAPING

CORRECTIONS TO TAPING ARE APPLIED BY THE USE OF THE FOLLOWING RULES:

1ST RULE: When a line is measured with a tape that is “ too long”, the corrections are applied to the observed length
by adding.
2ND RULE: When a specified or required length is to be laid out with a tape that is “too long”, the corrections are
subtracted from the known length to determine the corrected length to be laid out.
3 RULE: When measuring or laying out lengths with a tape that is “too short”, the corrections are applied opposite
RD

to those stated in the first two rules.

Laying Out a Line: Measuring a Line:

Tape Too Long – (-) Tape Too Long – (+)
Tape Too Short – (+) Tape Too Short – (-)

1. CORRECTION DUE TO TEMPERATURE.

𝑪𝒕 = 𝒌𝑳(𝑻 − 𝑻𝒔 )

Where:
𝒌 = coefficient of linear expansion or the amount of change in length per unit length
per degree change in temperature, ( 0.0000116 per degree Celsius).
𝑳 = the length of the tape or length of the line measured
𝑻 = the observed temperature of the tape at the time of the measurement
𝑻𝒔 = the temperature at which the tape was standardized
 Far Eastern University
Institute of Architecture and Fine Arts

2. CORRECTION DUE TO TENSION or PULL.

(𝑷𝒎 %𝑷𝑺 )𝑳
𝑪𝑷 = 𝑳𝑪 = 𝑳𝑴 ± 𝑪𝑷
𝑨𝑬

Where:
𝑪𝒑 = total elongation in tape length due to pull or the correction due to incorrect pull applied on the tape (m)
𝑷𝒎 = pull applied to the tape during measurement. (m)
𝑷𝒔 = standard pull for the tape or pull for which the tape is calibrated (kg)
𝑳𝑴 = measured length of line (m)
𝑨 = cross-sectional area of the tape (sq. cm)
𝑬 = modulus of Elasticity of steel (kg/sq. cm)
𝑳𝑪 = corrected length of the measured line (m)

𝑾
𝑨=
𝑳(𝜸)

Where:
𝑨 = cross-sectional area of the tape
𝑾 = total weight of the tape
𝑳 = length of the tape
𝜸 = Unit Weight of steel = 7.866 x 10-3kg/cm3

3. CORRECTION DUE TO SLOPE.

𝒉𝟐
𝑪𝒉 =
𝟐𝒔
Where:
𝒔 = measured slope distance between points A and B
𝒉 = difference in elevation between A and B.
𝒅 = equivalent horizontal distance AC
𝑪𝒉 = slope correction

𝒅 = 𝑺 − 𝑪𝒉

4. CORRECTION DUE TO SAG.

𝒘𝟐 𝑳𝟑 𝑾𝟐 𝑳
𝑪𝑺 = 𝑪𝑺 =
𝟐𝟒𝑷𝟐 𝟐𝟒𝑷𝟐
Where:
𝑪𝑺 = correction due to sag or the difference between the tape reading and the horizontal distance between
supports (m)
𝒘 = weight of tape per unit length (kg/m)
𝑾= total weight of tape between supports (kg)
𝑳 = interval between supports or the unsupported length of tape (m)
𝑷 = tension or pull applied on tape (kg)
 Far Eastern University
Institute of Architecture and Fine Arts

SAMPLE PROBLEMS:

1. CORRECTION DUE TO CHANGE IN TEMPERATURE. A steel tape with a coefficient of linear expansion
of 0.0000116/°C is known to be 50 m long at 20°C. The tape was used to measure a line which was found
to be 532.28-meter long when the temperature was 35°C. Determine the following:

a. Temperature correction per tape length

b. Temperature correction for the measured line
c. Correct length of the line

Solution:
𝑪𝒕 = 𝒌𝑳(𝑻 − 𝑻𝒔 )

a) Correction per tape length due to temperature

C1 = kL(T − T2 ) = 0.0000116/℃(50)(35℃ − 20℃)
C1 = +0.0087m (The positive sign indicates that tape is too long)

b) Correction for measured line due to temperature

C3 = kL(T − T2 ) = 0.0000116/℃(532.28)(35℃ − 20℃)
C3 = +0.0926m

Or
C3 C1
=
532.28 50

532.28C1 532.28(0.0087)
C3 = = = +0.0926m
50 50

c) Correct length of measured line

L4 = L5 ± C3 = 532.28 + 0.0926
L4 = 532.37 m
(Measuring - The correction is added since
the tape is too long)

2. CORRECTION DUE TO CHANGE IN TEMPERATURE. A steel tape, known to be of standard length at

20°C, is used in laying out a runway 2,500.00m long. If its coefficient of linear expansion is 0.0000116/°C,
determine the temperature correction and the correct length to be laid out when the temperature is 42°C.

𝑪𝒕 = 𝒌𝑳(𝑻 − 𝑻𝒔 )
Given:
TS = 20 0 C LM = 2500.00m
k = 0.0000116 0
0
T = 42 C
C
a) Correction per tape length due to temperature
C1 = kL(T − T2 ) = 0.0000116/℃(2,500)(42℃ − 20℃)
C1 = +0.638m (The positive sign indicates that tape is too long)
 Far Eastern University
Institute of Architecture and Fine Arts

b) Correct length to be laid out

L4 = L5 ± C3 = 2,500 − 0.638
L4 = 2,499.36 m
(Laying Out - The correction is subtracted
since the tape is too long)

3. CORRECTION DUE TO TENSION OR PULL. A heavy 50-m tape having a cross-sectional area of 0.05cm2
has been standardized at a tension of 5.5 kg. If E = 2.10 x 106kg/cm2, determine the elongation of the tape if
a pull of 12kg is applied.
(𝑷𝒎 − 𝑷𝑺 )𝑳
𝑪𝑷 =
𝑨𝑬
(12𝑘𝑔 − 5.5 𝑘𝑔)50𝑚
𝐶6 = = +0.003 𝑚 Positive means tape is too long
0.05(2.10𝑥107 )

4. CORRECTION DUE TO TENSION OR PULL A 30-m steel tape weighing 1.45kg is of standard length under
a pull of 5kg, supported for full length. The tape was used in measuring a line 938.55m long on smooth level
ground under a steady pull of 10kg. Assuming E = 2.0 x 10-3kg/cm2, determine the following:
a) cross-sectional area of the tape
b) correction for increase in tension
c) correct length of the line measured

Solution:
a) cross-sectional area of the tape
𝑊 1.45 𝑘𝑔
𝐴= = = 0.06 𝑐𝑚9
𝐿(𝛾) 100 𝑐𝑚 7.9𝑥10%8 𝑘𝑔
30𝑚 g 1 𝑚 h i j
𝑐𝑚8

b) correction for increase in tension

( Pm − PS ) L (10kg − 5kg) 30m

Cp = =
" 2.0x10 6 kg % = +0.00125 m
AE 0.06cm 2 $ ' tapelength
# cm 2 &
(Correction per tape length. The positive sign
indicates that tape is too long)

CT CP CT 0.00125 0.00125 ( 938.55)

= = CT =
LM LTapeLength 938.55 30 30

C3 = +0.04 m
(Total correction for measured line. The
positive sign indicates that tape is too long)
c) Correct length of the line measured
L4 = L5 ± C3 = 938.55 + 0.04
L4 = 938.59 m
(Measuring - The correction is added since
the tape is too long)
 Far Eastern University
Institute of Architecture and Fine Arts

5. CORRECTION DUE TO SAG. A 30-m tape is supported only at its ends and under a steady pull of 8 kg. If
the tape weighs 0.91kg, determine the sag correction and the correct distance between the ends of the tape.
𝒘𝟐 𝑳𝟑 𝑾𝟐 𝑳
𝑪𝑺 = 𝑪𝑺 =
𝟐𝟒𝑷𝟐 𝟐𝟒𝑷𝟐
Given:
L = 30m (Nominal length of the tape)
P = 8 kg (Pull applied on ends of tape)
W = 0.91 kg (Total weight of tape)

a) Correction due to sag between the ends of the tape

𝑊 9 𝐿 (0.91)9 (30)
𝐶: = = = 0.016 𝑚
24𝑃9 24(8)9
For Sag – always tape too short
b) Correct distance between the ends of the tape
L4 = L5 − C; = 30 − 0.0162
L4 = 29,9838 m

6. CORRECTION DUE TO SAG. A 50-m steel tape weighs 0.04 kg/m and is supported at its end points and at
the 8-m and 25-m marks. If a pull of 6kg is applied, determine the following:
a) Correction due to sag between the 0-m & 8-m marks, 8-m & 25-m marks and the 25-m & 50-m marks.
b) Correction due to sag for one tape length
c) Correct distance between the ends of the tape
d) If the tape was used to measure a 578.5m line, determine the correct length of the line.

Given:
L = 30m (total length of the tape)
L1 = 8m (length of 1st span)
L2 = 17m (length of 2nd span)
L3 = 25m (length of the 3rd span)
P = 6 kg (pull applied on ends of tape)
ω = 0.04 kg/m (unit weight of tape)

𝒘𝟐 𝑳𝟑
𝑪𝑺 =
𝟐𝟒𝑷𝟐
Solution:

a) Determining Correction Due to Sag for each Span

𝑤 9 𝐿= 8 (0.04)9 (8)8
𝐶:= = = = 0.0009 𝑚 (correction due to sag bet. the 0m and 8m marks)
24𝑃9 24(6)9
𝑤 9 𝐿9 8 (0.04)9 (17)8
𝐶:9 = = = 0.0091 𝑚 (correction due to sag bet. the 8m and 25m marks)
24𝑃9 24(6)9
𝑤 9 𝐿8 8 (0.04)9 (25)8
𝐶:8 = = = 0.0289 𝑚 (correction due to sag bet. the 25m and 50m marks)
24𝑃9 24(6)9
 Far Eastern University
Institute of Architecture and Fine Arts

b) Determining Total Sag Correction for one Tape Length

𝐶: = 𝐶:= + 𝐶:9 + 𝐶:8
𝐶: = 0.0009 + 0.0091 + 0.0289
𝐶: = 0.0389 𝑚

c) Determining Correct Distance Between Tape Ends

𝐿> = 𝐿? ± 𝐶6
𝐿> = 50 − 0.0389 = 49.9611 𝑚

d) If the tape was used to measure a 578.5m line, determine the correct length of the line.
𝑚
𝐶: = 0.0389
𝑡𝑎𝑝𝑒 𝑙𝑒𝑛𝑔𝑡ℎ

Number of times using the whole tape

578.5
n= = 11.57 LT =11( 50) + 28.5 = 578.5m
50

Total Correction:
For 550m (11-full tape length): 𝐶!! = 11(0.0389) = 0.4279 𝑚

For 28.5m: 𝐶@# = 𝐶:= + 𝐶:9 + 𝐶:A

𝑤 9 𝐿A 8 (0.04)9 (3.5)8
𝐶:A = = = 0.00008 𝑚
24𝑃9 24(6)9
(sag correction between the 25m and 28.5m marks)

𝐶@# = 𝐶:= + 𝐶:9 + 𝐶:A = 0.0009 + 0.0091 + 0.00008 = 0.01008𝑚

𝐶@ = 𝐶@= + 𝐶@9 = 0.4279 + 0.01008 = 0.43798 𝑚

Correct Length: 𝐿> = 𝐿? − 𝐶@

𝐿> = 578.5 − 0.43798 = 578.06202

7. CORRECTION DUE TO SLOPE. Slope distance AB and BC measured 330.49m and 660.97m, respectively.
The difference in elevation are 12.22m for points A and B, and 10.85m for points B and C. Using the approx.
slope of line ABC. Assume that line AB has rising slope and BC a falling slope, determine the horizontal
distance ABC.

Given: s1 = 330.49m (slope length of AB)

h1 = 12.22m (difference in elevation between A and B)
s2 = 660.97m (slope length of BC)
 Far Eastern University
Institute of Architecture and Fine Arts

h2 = 10.85m (difference in elevation between B and C)

Solution:
Horizontal Length of line AB
ℎ= 9 (12.22)9
𝑑= = 𝑆= − = 330.49 − = 330.49 − 0.23 = 330.26 𝑚
2𝑆= 2(330.49)
Horizontal Length of line BC
ℎ9 9 (10.85)9
𝑑9 = 𝑆9 − = 330.49 − = 660.97 − 0.09 = 660.88 𝑚
2𝑆9 2(660.97)
Horizontal Length of line ABC
𝑑BC> = 𝑑= + 𝑑9 = 330.49 + 660.88 = 991.14 𝑚

8. CORRECTION DUE TO SLOPE. A line AB cannot be measured directly because of an obstruction along the
line. Accordingly, the two lines AC and CB were measured as 2,400.850m and 1,320.420m, respectively.
Point C was set at a perpendicular distance 155m from point D on line AB, using the approximate slope
correction formula for steep slopes, determine the length of AB.

Solution:
Horizontal Length of line AD
ℎ= 9 (155)9
𝑑= = 𝑆= − = 2,400.85 − = 2,400.85 − 5.003 = 2,395.847 𝑚
2𝑆= 2(2,400.85)
 Far Eastern University
Institute of Architecture and Fine Arts

Horizontal Length of line DB

ℎ9 9 (155)9
𝑑9 = 𝑆9 − = 1,320.42 − = 1,320.42 − 9.097 = 1,311.323 𝑚
2𝑆9 2(1,320.42)
Horizontal Length of line ADB
𝑑BDC = 𝑑= + 𝑑9 = 2,395.847 − 1,311.323 = 3,707.17 𝑚

9. COMBINED CORRECTION. A line was determined to be 2395.25m when measured with a 30-m steel tape
supported throughout its length under a pull of 4kg and at a mean temperature of 35°C. Determine the correct
length of the line if the tape is of standard length at 20°C under a pull of 5kg. The cross-sectional area of the
tape is 0.03sq.cm, its coefficient of linear expansion is 0.0000116/°C, and the modulus of elasticity of steel is
2.0x106 kg/cm2.

GIVEN:
L = 2395.25m T = 35°C A = 0.03cm2
Lt = 30m Ts = 20°C C = 0.0000116/°C
Pm = 4kg Ps = 5kg E = 2.0x106kg/cm2

SOLUTION:

a) Temperature Correction for Measured Length

C1 = kL(T − T2 ) = 0.0000116/℃(2,395.25)(35℃ − 20℃)
C1 = +0.42m (The positive sign indicates that tape is too long)

b) Tension Correction for Measured Length

(𝑃? − 𝑃: )𝐿 (4𝑘𝑔 − 5 𝑘𝑔)2,395.25𝑚
𝐶E = = = −0.04 𝑚
𝐴(𝐸) 9 2.0𝑥107 𝑘𝑔
0.03 𝑐𝑚 i j
𝑐𝑚9
(The negative sign indicates
that tape is too short)
c) Length of measured line corrected for effects of temperature and pull
𝐿> = 𝐿? ± 𝐶F ± 𝐶6
𝐿> = 2,395.25 + 0.42 − 0.04 = 2,395.63 𝑚
(Measuring - The correction is added if tape is too long
and is subtracted if tape is too short
Far Eastern University
Institute of Architecture and Fine Arts
 Far Eastern University
Institute of Architecture and Fine Arts

WEEK 5

LECTURE READING 3

MEASUREMENT OF DISTANCE BY PACING

Pacing is measuring distance by counting the number of steps or paces in a required distance. Pace
is defined as the length of a step-in walking that is measured from heel to heel or from toe to toe.
Pacing means moving with measured steps; and if the steps are counted, distances is calculated by
multiplying the number of paces by the individual’s pace factor.

Sample Problems:

PROBLEM 1. A 45-m course, AB, on level ground was paced by a surveyor for the purpose of determining
his pace factor. The no. of paces for each trial taken are shown in accompanying tabulation.

Requirements.
a) Determine his pace factor.
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?
c) Assuming that the taped length of line CD is 667.0m, determine the relative precision of the
measurement performed.

PACING DATA

TRIAL LINE TAPED DIST NO. OF MEAN

PACES
1 AB 50
2 BA 53
3 AB 45.0 51
4 BA 53
5 AB 52
6 BA 53

a) Determine Pace Factor

L1 = 45m (length of line AB)
n1 = 6 (no. of trials taken on line AB)

Sum1 = (50 + 53 + 51 + 53 + 52 + 53) = 312 paces

M1 = Sum1 / n1 = 312 / 6
= 52 paces (mean no. of paces to walk line AB)

PF = L/M1 = 45m / 52 paces

= 0.865 m/pace (pace factor of the surveyor)

b) Determining Unknown Distance

n2 = 6 (no. of trials taken on line CD)

Sum2 = (771 + 770 + 768 + 770 + 772 + 769)

= 4620 paces
 Far Eastern University
Institute of Architecture and Fine Arts

M2 = Sum2 / n2 = 4620 / 6
= 770 paces (mean no. of paces to walk line CD)

PD = M2(PF)
= 770 paces (0.865m/pace)
= 666.1 m (paced length of line CD)

c) Determining Relative Precision

TD = 667.0m (taped distance)
PD = 666.1m (paced distance)

RP = (PD – TD)/TD = (666.1 – 667.0)/667.0

=- 0.9/667.0
= 1/741 say 1/700 (relative precision of the measurement)

PROBLEM 2. In five trials of walking along a 90-m course on fairly level ground, a pacer for a survey
party counted 51, 52.5, 51.5, 52.5 and 51.5 strides respectively. He then started walking an unknown
distance XY in four trials w/c were recorded as follows: 88.5, 89, 88 and 87 strides. Determine the following:
a) Pace factor of the pacer
b) Length of line XY
c) Percentage of error in the measurement of the taped length of XY is 150.5 meters.

a) Determining Pace Factor

L = 90.0 m (length of course)
n1 = 5 (no. of trials taken)

Sum1 = (51 + 52.5 + 51.5 + 52.5 + 51.5)

= 259 strides or 518 paces. (NOTE: 1 stride = 2 paces)

M1 = Sum1 / n1 = 518 / 5
= 103.6 paces (mean no. of paces to walk the course)

PF = L/M1 = 90m / 103.6 paces

= 0.869 m/pace (pace factor of pacer)

b) Determining Unknown Distance

n2 = 4 (no. of trials taken on line XY)

Sum2 = (88.5 + 89 + 88 + 87)

= 352.5 strides or 705 paces

M2 = Sum2 / n2 = 705 / 4
= 176.25 paces (mean no. of paces to walk line XY)

PD = M2(PF)
= 176.25paces (0.869m/pace)
 Far Eastern University
Institute of Architecture and Fine Arts

= 153.2 m (paced length of line XY)

MEAN
TAPED NO. OF MEAN NO. PACED
TRIAL LINE NO. OF
DISTANCE STRIDES OF STRIDES DISTANCE
PACES

1 XY 88.5

2 YX 89.0
150.5 m 88.125 176.25 153.16 m
3 XY 88.0

4 YX 87.0

c) Determining Relative Precision

TD = 150.5 m (taped distance)
PD = 153.16 m (paced distance)

Percentage of Error = (PD – TD) (100%) = (153.16 –150.5)(100%)

TD 150.5
= 1.77 %

FIELD EXERCISE: PACING

Objectives: a) To determine individual pace factor.

b) To measure distance by pacing.

1. OUTLINE

A. INSTRUMENT & ACCESSORIES: Steel Tape, Markers (hubs, paint, chalk or crayons)

B. PROCEDURE:

1. Determining the Pace Factor.

a) Select a straight and level course and on both ends establish markers at least
10 meters apart. Designate these end points as A and B.
b) Walk over the course at a natural pace or gait starting with either heel or toe
over point A and count the number of paces to reach point B.
c) For succeeding trials, walk from B to A, then A to B, until 10 trials are completed,
and the number of paces recorded accordingly.
d) Refer to the accompanying sample format for the recording of observed field
data.
 Far Eastern University
Institute of Architecture and Fine Arts

TRIAL LINE TAPE NUMBER OF MEAN PACE FACTOR

DIST (m) PACES NO. OF (m/pace)
PACES
1 AB
2 BA
3 AB
4 BA
5 AB
6 BA
7 AB
8 BA
9 AB
10 BA

2. Measuring Distance by Pacing

a) Define or establish the end points of another level course whose length is to be
determined by pacing. Designate these end points as C and D.
b) For the first trial, walk over the course form C to D at a natural pace and record
the number of paces. Then, walk from D to C and again record the number of
paces.
c) Repeat the above procedure until all five trials are completed.
d) After the field data is recorded, make an actual taping of the course CD to
determine the taped distance.
e) Refer to the accompanying sample format for the recording of observed field
data.

LINE NO. OF MEAN PACED TAPED RELATIVE

TRIAL PACES DIST DIST PRECISION
1
2
3
4
5

C. COMPUTATIONS:

1. Computing Pace Factor (PF).

a) Get the sum of the number of paces for the five trials performed on course AB
then compute the mean number of paces.
b) Divide the known or taped length of course AB by the mean number of paces for
AB to determine the pace factor.
2. Computing Paced Distance (PD).
a) Get the sum of the number of paces for the five trials performed on course CD
and compute the mean number of paces.
b) Multiply the mean number of paces for CD by the pace factor to obtain the
paced distance.
3. Computing Relative Precision (RP).
Far Eastern University
Institute of Architecture and Fine Arts

a) Determine the difference between the taped distance of CD and the paced
distance of CD.
b) Divide the difference by the taped distance of CD and reduce the numerator to
unity to determine the relative precision.
 Far Eastern University
Institute of Architecture and Fine Arts

___________________________________________________________________________

MODULE 3: MEASUREMENT OF VERTICAL DISTANCES

Module Information

Module Overview
The module covers the fundamentals of leveling, including types and proper use of leveling equipment,
leveling field procedures and field notes. The module also provides an insight on the different methods of
measuring vertical distances and determining the elevations of points. Moreover, the module discusses the
determination of elevation of points and difference in elevation between two points by reciprocal leveling,
differential leveling, and profile leveling. It also provides knowledge on plotting the profile of the ground.

Module Coverage
The module will be covered for a duration of 3 weeks with 2 work outputs(see course outline schedule for
submission). It is scheduled on the week 6, 7, and 8 of the semester.

Module Objective
• The module aims to help the student understand the fundamentals of leveling
• The module aims to help students to recognize different leveling equipment and understand its
usage.
• The module aims to provide insights on different leveling methods of measuring vertical distances
• The module aims to provide knowledge in the determination of elevation of point and difference in
elevation between two points
• The module aims to provide knowledge in plotting the profile of the ground surface.

Module Learning Outcomes

By the end of this module the student should be able to:
• Understand the principle and concept of leveling in surveying
• Familiarize with different leveling instruments
• Compute the elevation between two inter-visible point by reciprocal leveling
• Compute the elevation of points and difference in elevation between two points by differential leveling
• Compute the elevation of points and difference in elevation between points along the line to be
profiled
• Plot the vertical section of the ground surface
Module Learning Materials
Under this module the students are provided with the following materials:
• Lecture Note:
Title: Measurement of Elevation
Reciprocal Leveling
Differential Leveling
Profile Leveling
• PowerPoint Presentation:
The presentation provided in pdf file are the slides used for the presentation of the mentor.

Additional Readings and Materials

Students may refer to the given lectures under this module. Nevertheless, should the student like to study
beyond the given materials, they may refer to the books listed below:
• Ghilani, C. (2012). Elementary Surveying: an Introduction to Geomatics
 Far Eastern University
Institute of Architecture and Fine Arts

___________________________________________________________________________
• Lee, Sandra Jean. Willis's elements of quantity surveying. Chichester, West Sussex, United
Kingdom: John Wiley & Sons Inc., 2014 IARFA 0140 Cir TH 435 L4 2014
• Surveying. UAE 3G Elearning, 2015. Cir TA 545 S9 2015
Module Output-base Work
To complete this module the student shall submit Formative Assessment 3 and 4. The details of the
assessment can be found in the Assessment Module.
References
• Basak, N N. Surveying and Levelling. Second Edition. New Delhi: McGraw-Hill Education (India) Private
Limited, 2014. Cir TA 545 B3 2014
• Johnson, Aylmer. Plane and Geodetic Surveying. Second Edition. Boca Raton: CRC Press, Taylor &
Francis Group, 2014. Cir TA 545 J6 2014
• La Putt, Judy Pilapil. Higher Surveying, 2nd Edition. Mandaluyong City: National Bookstore, 1990. Fil TA 545
L3 1990
• Kavanagh, Barry F. Surveying: Principles and Applications. 6th ed. Upper Saddle River, NJ: Prentice
Hall, c2003. Cir TA 545 K3 2003
 Far Eastern University
Institute of Architecture and Fine Arts

WEEK 6

LECTURE READING 4

Vertical distances are measured in order to determine the elevations of points. The determination of
elevations constitute a fundamental operation in surveying and engineering projects. Leveling provides data
for determining the shape of the ground. The elevations of new facilities such as roads, structural foundations,
and pipelines can then be designed. The designed facilities are laid out and marked in the field by the
construction surveyor. The surveyor’s elevation marks serve as reference points from which building
contractors can determine the proper slope of a road, the first floor elevation of a building, the required cutoff
elevation for foundation piles, the invert elevation for a storm sewer, and so on. The importance of leveling
cannot be overestimated, it must always be considered in every form of design and construction

MEASUREMENT OF ELEVATION

LEVELING - is the process of directly or indirectly measuring vertical distances to determine the elevation of points or
their differences in elevation.

Basic Leveling Terms:

1. Level Surface – a curved surface that at every point is perpendicular to the plumb line.
2. Level Line – a line in a level surface equidistant from the center of the earth
3. Horizontal Plane – a plane perpendicular to the direction of gravity that is tangent to the level surface
4. Horizontal Line – a line in a horizontal plane
5. Vertical Line – a line parallel to the direction of gravity.
6. Mean Sea Level – is an imaginary surface of the sea which is midway between high tide and low tide
7. Datum – any convenient level surface coincident or parallel with mean sea level to which elevations of a
particular area are referred.
8. Elevation – is the vertical distance above or below mean sea level or any other selected datum
9. Difference in Elevation- is the vertical distance between the two level surfaces in which points lie.

EQUIPMENT for LEVELING

1. Level Instrument
a) Dumpy Level
b) Tilting Level
c) Automatic Level
d) Digital level
 Far Eastern University
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e) Electronic Laser Level

f) Hand Level
2. Tripod
3. Staff/Pole/Rod
4. Pole
5. Staff Bubble

EQUIPMENT: LEVEL INSTRUMENT

Automated Levels

Parts of Automatic Level Use of Leveling Screw

Parts of Tilting Level

 Far Eastern University
Institute of Architecture and Fine Arts

Digital Levels Hand Level

EQUIPMENT: TRIPOD
Wooden design or aluminum - Leveling instrument are all mounted in a tripod

EQUIPMENT: STAFF/POLE/ROD
Wooden design or aluminum Invar type for high precision leveling
 Far Eastern University
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READING the Staff / Rod

Read the (m), (dm) & (cm)

EQUIPMENT: STAFF BUBBLE (Keep the pole upright)

BASIC RULES for LEVELING

1. Always start and finish a leveling run on a Benchmark (BM) and close the loops
2. Keep fore sight and back sight distances as equal as possible
3. Keep lines of sight short (normally < 50m)
4. Never read below 0.5m on a staff (refraction)
5. Use stable, well defined change points
6. Beware of shadowing effects and crossing waters

LEVELING METHODS

Methods of Determining Differences in Elevation

 Far Eastern University
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1. Differential Leveling - commonly employed method of determining the elevation of points some distance
apart by a series of set ups of a leveling instrument along a selected route

2. Barometric Leveling – involves the determination of differences in elevation between points by measuring
the variation in atmospheric pressure at each point by means of a barometer.

3. Trigonometric Leveling - difference in elevation between two points can be determined by measuring:
@ inclined or horizontal distance between them
@ vertical angle between the points.

4. Reciprocal Leveling - leveling used across topographic features such as rivers, lakes and canyons when it
is difficult or impossible to keep plus and minus sights short and equal

5. Profile Leveling - used to determine differences in elevation between points at designated short measured
intervals along an established line to provide data from which a vertical section of the ground surface can be
plotted.
 Far Eastern University
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6. Grid Leveling - method for locating contours by staking an area in squares and determining the corner
elevations by differential leveling
Grid size depends on:
• Project extent
• ground roughness
• required accuracy

7. Cross-Section or Borrow-Pit Leveling - employed on construction jobs to ascertain quantities of earth,

gravel, rock or other material to be excavated or filled

SOURCES OF ERRORS IN LEVELING

1. Instrumental Errors
o Instrument out of adjustment
o Rod not standard length
o Defective tripod

2. Personal Errors
o Bubble not centered
o Parallax
o Faulty rod readings
o Rod not held plumb
o Unequal Backsight and Foresight distances

3. Natural Errors
o Curvature of the earth
o Atmospheric Refraction
o Wind
o Settlement of the Instrument
o Faulty Turning Poin

Effect of Earth’s Curvature

Effect of Refraction
 Far Eastern University
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Collimation Error
Occurs when the line of sight (as defined by the lens axis and cross-hairs) is not horizontal
Leads to an incorrect staff reading

COMMON LEVELING MISTAKES

² Misreading the Rod. Unless the instrument-man is very careful, he or she may occasionally read the rod
incorrectly. This mistake most frequently occurs when the line of sight to the rod is partially obstructed by
leaves, limbs, grass, rises in the ground.
² Moving Turning Points. A careless rodman causes serious leveling mistakes if he or she moves the turning
points.
² Incorrect Recording
² Mistakes on Extended Rod. When readings are taken on the extended portion of the level rod, it is absolutely
necessary to have the two parts adjusted properly. If they are not, mistakes will be made.
² Erroneous Computation

Reducing Errors and Eliminating Mistakes

a) Careful Adjustment of Instrument and Rod
b) Establishment of Standard Field Methods and Routines
Ø Check the bubble before and after each reading
Ø Use a rod level
Ø Keep the horizontal lengths of plus and minus sights equal
Ø Make the usual field-book arithmetic check

Balancing plus and minus sight distances cancels errors caused by curvature and refraction
 Far Eastern University
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RECIPROCAL LEVELING:

RECIPROCAL LEVELING – is a process of accurately determining the difference in elevation between two
intervisible points located at a considerable distance apart and between which points leveling could not be
performed in the usual manner.

Illustrative problem:
In leveling across a wide river, reciprocal level readings were taken between two points A and B as shown in the
accompanying tabulation. Determine the following:
a) Difference in elevation between two points.
b) Elevation of B if the elevation of A is 951.750 m.

INSTRUMENT SET-UP NEAR A

STATION BS FS
1.283
1.284
a
1.286
1.283
0.675
0.674
0.677
b
0.674
0.677
0.678
SUM
MEAN
 Far Eastern University
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INSTRUMENT SET-UP NEAR B

STATION BS FS
1.478
1.480
b’
1.476
1.478
2.143
2.140
2.145
a’
2.142
2.143
2.146
SUM
MEAN

Solution:
a) Determining Mean Rod Readings and Difference in Elevation.

am = (1.283 + 1.284 + 1.286 + 1.283)/4 = 1.284m

bm = (0.675 + 0.674 + 0.677 + 0.674 + 0.677 + 0.678)/6
= 0.676m

a’m = (2.143 + 2.140 + 2.145 + 2.142 + 2.143 + 2.146)/6

= 2.143m
b’m = (1.478 + 1.480 + 1.476 + 1.478)/a = 1.478m

DE1 = (am - bm) = (1.284 – 0.676)

= +0.608 m (Difference in elevation between A and B w/ instrument set-up near A)
DE2 = (a’m – b’m) = (2.143 – 1.478)
= +0.665 (Difference in elevation between A and B w/ instrument set up near B)

TDE = (DE1 + DE2)/2 = (0.608 + 0.665)/2

= +0.637m (True difference in elevation between the two bench-marks)
Far Eastern University
Institute of Architecture and Fine Arts

INSTRUMENT SET-UP NEAR A

STATION BS FS
1.283
1.284
a
1.286
1.283
0.675
0.674
0.677
b
0.674
0.677
0.678
SUM 5.136 4.055
MEAN 1.284 0.676

INSTRUMENT SET-UP NEAR B

STATION BS FS
1.478
1.480
b’
1.476
1.478
2.143
2.140
2.145
a’
2.142
2.143
2.146
SUM 12.859 5.912
MEAN 2.143 1.478
 Far Eastern University
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a) Elev. of B = Elev A ± TDE

= 951.750 + 0.637
= 952.387m

Note: The TDE is added to the elevation of A since B is higher than A. In the solution for DE1 and DED2
above, a positive value is determined w/c shows that B is higher than A. If the value were negative, B would
have been lower than A.
 Far Eastern University
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WEEK 7

LECTURE READING 5

DIFFERENTIAL LEVELING

The different terms commonly used in differential leveling work are graphically illustrated. A cursory look at the
figure may imply that the points along the leveling route all lie in a straight line. It is important to understand that
is not always the case in actual leveling work. The points and the instruments station may in fact be the
positioned in plain along the zigzag pattern.

1. Bench Mark (BM) – is the fixed point of reference whose elevation is either known or assumed. They
may be permanent or temporary.
2. Back sight (BS)– is the reading taken on a rod held on a point of known or assumed elevation. It is
a measure of vertical distance from the established line of sight to the point sighted, and is always the
first rod reading taken after the instrument has been set up and leveled.
3. Foresight(FS) – a reading taken on a rod held on point whose elevation is held to be determined is
called foresight. It is represented as a vertical distance from the line of sight of the instruments to the
point observed.
4. Back sight Distance(BD) – the back sight distance is measured from the center of the instrument to
the rod on which the back sight is taken.
5. Foresight Distance(FD) – the horizontal distance from the center of the instrument to the rod on which
a foresight is taken is referred to as foresight distance.
6. Turning Points(TP) – a turning point is an intervening point between two bench marks upon which
point foresight and back sight rod readings are taken to enable leveling operation to continue from a
new instrument position.
7. Height of Instrument(HI) – the height of instrument is the elevation of the line of sight of an instrument
above or below the selected reference datum. It is be adding the rod reading on the back sight to the
elevation of the point on which the sight is taken.

PROCEDURES OF DIFFERENTIAL LEVELING

The procedure followed in determining the difference in elevation between two points is illustrated in Figure 1
in which a line of levels, is run from BMa to BMb. There should be at least 2 persons to undertake differential
leveling; the Rodman who carries and holds the rod, and the instrument man who sets up the level and
determines the required rod readings. The instrument man can record the data recorder. If a bigger leveling
party could be formed, a chief of party, a pacer, an axe man, and utility men may be added to complete the
team.

The leveling instrument is set up at any convenient location along the level route and a back sight is taken on a
leveling rod held vertically on BMa. The back sight reading added to the known or assumed elevation of the initial
bench mark gives the height of instrument above datum or

HI = Elev BMa + BS

The rod man moves forward along the general direction of BMb and holds the rod at the convenient
turning point (TPl ). The instrument man takes a foresight on the rod. This foresight reading subtracted from the
height of instrument gives the elevation above datum of the turning point or

Elev TP1 = HI – FS
 Far Eastern University
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The level is the transferred and set up at another convenient location beyond TP1, but still in the general
direction of BMb and a foresight rod readings can be made. A backsight is then taken on TP1 to establish a new
height of instrument (HI2). The rodman finally moves forward to the location of BMb and a foresight is taken on
the rod held on it. Since the new HI has already been determined, the elevation of BMb is computed by
subtracting the foresight reading from height of instrument.

If the terminal point BMb is still some distance away such that more turning points have to be
established before it could be foresighted, the procedure of reading a backsight, the rodman moving ahead to
establish another turning point, and the reading of the foresight is repeated. This is done as many times as
necessary until the elevation of BMb is finally obtained. The illustrative problems given in this lesson should
provide the student a clearer idea as to how differential leveling is undertaken, how the notes are kept, and how
the customary arithmetic check is made.

FS= 1.2’, since

rod reading is Elev = HI - FS
HI = Elev + BS taken from an
unknown
elevation
BS= 8.42’,
since rod
reading is
taken from a
known
elevation

1)
STATION BS(ft) HI (ft) FS (ft) ELEV (ft)

BM Rock 8.42 820.00

x 1.2

2) HI = Elev + BS HI = 820 + 8.42 = 828.42 ft

 Far Eastern University
Institute of Architecture and Fine Arts

3) Elev = HI – FS Elev(X)= 828.42 – 1.20 = 827.22 ft

When both benchmarks cannot be reached from one instrument position, turning points are used.
Because a turning point is a temporary benchmark, it must be stable.

Figure 1

Note: A cursory look at the figure may imply that the points along the leveling route all lie in a straight line. It is
important to understand that is not always the case in actual leveling work. The points and the instruments
station may in fact be positioned in plain along a zigzag pattern.

STATION BS HI FS ELEV

BM1 1.33 2053.18

TP1 0.22 8.37
TP2 0.96 7.91
TP3 0.46 11.72
BM OAK 8.71
 Far Eastern University
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SOLUTION:
 Far Eastern University
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SAMPLE PROBLEM: The level rod readings are given in the order in which they were taken on BM-1 and the
last reading is taken on BM-2, the point whose elevation is desired. Set-up and complete differential
level notes and include the customary math check. The elevation is given under each problem number

SOLUTION:
Far Eastern University
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Negative means downhill

 Far Eastern University
Institute of Architecture and Fine Arts

PROBLEM 3: Plan-view sketches of differential leveling runs as shown. Along each line representing a sight is
the value of the rod reading for that sight. The numbering of TPs shows the direction of the level run. Place the
data in the form of field notes. Include the arithmetic check. Assume that the average length of each BS and FS
is 40m.

SOLUTION:
 Far Eastern University
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WEEK 8

LECTURE READING 6

PROFILE LEVELING

The process of determining differences in elevation along a fixed line at designated short measured
intervals is referred to as profile leveling. It is executed to provide data from which a vertical section of the
ground surface can be plotted. A profile is necessary for the design and construction of roads, railroads,
canals, culverts, bridges, sewer lines and others. The fieldwork involved is identical to differential leveling since
it also requires the establishment of turning points in which foresight and backsight readings are taken before
the terminal point is reached. The main difference between these two methods of leveling lies in the number of
foresights taken from each setup of the instrument.

DEFINITION OF TERMS.

1. Profile. The profile is a curved line, which graphically portrays the intersection of a vertical plane with
the surface of the earth. It depicts ground elevations of selected critical points along a surveyed line
and the horizontal distances between these points.
2. Stationing. A numerical designation given in terms of horizontal distance any point along a profile line
is away from the starting point. Each stake used is marked with its station and plus.
3. Intermediate Foresights. These sights, which are also known as ground rod readings, are taken
along the centerline of the proposed project to provide an accurate representation of the ground
surface. Intermediate foresights are observed at regular intervals and at points where sudden changes
in elevation occur.
4. Full Stations. Are points which are established along the profile level route at uniformly measured
distances. These points are usually made in multiples of 100, 50, 30, 20 or 10 meters.
5. Plus Stations. Any other intermediate point established along a profile level route which is not
designated a full station is called a plus station.
6. Vertical Exaggeration. Is a process of drawing the vertical scale for a profile much larger than the
horizontal scale in order to accentuate the differences in elevations.

Stationing - A numerical designation given in terms of horizontal distance any point along a profile line away
from the starting point.

I LLUSTRATIVE PROBLEMS.

1. LOCATING STATIONS. Work out the following problems regarding points and stations along
a profile level route.

a) A turning point along a profile level route measures 126.44m beyond station 8 + 24.50.
Determine the stationing of this turning point
 Far Eastern University
Institute of Architecture and Fine Arts

Solution:

dtp = 126.44m (distance of turning point beyond station 8 + 24.50 )

dsta = 8 + 24.50 or 824.50m (distance of the reference station from station 0 + 00
)
D = dsta + dtp = 824.50 + 126.44 = 950.94m (distance of the turning point from station 0 + 00 )

Therefore, Stationing of Turning Point = 9 + 50.94

b) For the illustrated problem given above, determine the stationing of the turning point if
it is instead located 83.45m before the given reference station.

Solution:
dtp = 83.45 m (distance of turning point beyond station 8 + 24.50
)
dsta = 8 + 24.50 or 824.50m (distance of the reference station from station 0 +
00 )
D = dsta - dtp = 824.50 – 83.45 = 741. 05m (distance of the turning point from station 0 + 00 )

Therefore, Stationing of Turning Point = 7 = 41.05

c) Determine the distance between station 3 + 345.02 and station 2 + 662.75

Solution:
d1 = 3 + 345.02 or 3,345.02 m (distance of one of the stations from beginning point
of the survey)
d2 = 2 + 662.75 or 2,662.75 m (distance of the other station from beginning point
the survey)
D = d1 – d2 = 3345.02 – 2662.75 = 682.27m (distance between the two stations)

PROFILE LEVEL

• fieldwork involved is identical to differential leveling since it also requires the establishment of turning
points in which foresight and back sight readings are taken before the terminal point is reached
• main difference between these two methods of leveling lies in the number of foresights taken from
each setup of the instrument.
 Far Eastern University
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PROBLEM: Complete the following set of profile level notes and show the customary check. Draw the profile.
Far Eastern University
Institute of Architecture and Fine Arts
 Far Eastern University
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a) Complete Profile Level Notes

 Far Eastern University
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b) Profile
 Far Eastern University
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___________________________________________________________________________

MODULE 4: MEASUREMENT OF ANGLES AND DIRECTIONS

Module Information

Module Overview
The module begins with a discussion of different types of meridian and their respective designation of north
points and with the units of angular measurements. The module focuses on horizontal angles and the various
ways in which angles and directions of lines are defined and computed. The module provides insight on the
different kinds of horizontal angles and how they are being measured.

Module Coverage
The module will be covered for a duration of 1 week with 1 work output(see course outline schedule for
submission). It is scheduled on the week 11 of the semester.

Module Objective
• The module aims to help the student understand the types of meridian used as reference in
identifying the direction of lines.
• The module aims to provide insights on different kinds of horizontal angles that describes the
direction of lines.

Module Learning Outcomes

By the end of this module the student should be able to:

• Use and take care of compass in determining directions

• Discuss the meridians and designation of north points, and units of angular measurement,
• Determine direction of lines such as interior angles, bearings, azimuths, and magnetic declination.
• Discuss the adjustment of a closed compass traverse.
Module Interdependencies

This module serves as an introductory lesson that will be reinforced by Module 5: Traverse and Traversing

Module Learning Materials

Under this module the students are provided with the following materials:
• Lecture Note:
Title: Measurement of Angles and Direction
• PowerPoint Presentation:
The presentation provided in pdf file are the slides used for the presentation of the mentor.

Additional Readings and Materials

 Far Eastern University
Institute of Architecture and Fine Arts
___________________________________________________________________________

Students may refer to the given lectures under this module. Nevertheless, should the student like to study
beyond the given materials, they may refer to the books listed below:
• Ghilani, C. (2012). Elementary Surveying: an Introduction to Geomatics
• Lee, Sandra Jean. Willis's elements of quantity surveying. Chichester, West Sussex, United
Kingdom: John Wiley & Sons Inc., 2014 IARFA 0140 Cir TH 435 L4 2014
• Surveying. UAE 3G Elearning, 2015. Cir TA 545 S9 2015

Module Output-base Work

To complete this module the student shall submit Formative Assessment 5 . The details of the assessment
can be found in the Assessment Module.

References
• Basak, N N. Surveying and Levelling. Second Edition. New Delhi: McGraw-Hill Education (India) Private
Limited, 2014. Cir TA 545 B3 2014
• Johnson, Aylmer. Plane and Geodetic Surveying. Second Edition. Boca Raton: CRC Press, Taylor &
Francis Group, 2014. Cir TA 545 J6 2014
• La Putt, Judy Pilapil. Higher Surveying, 2nd Edition. Mandaluyong City: National Bookstore, 1990. Fil TA 545
L3 1990
• Kavanagh, Barry F. Surveying: Principles and Applications. 6th ed. Upper Saddle River, NJ: Prentice
Hall, c2003. Cir TA 545 K3 2003
 Far Eastern University
Institute of Architecture and Fine Arts
___________________________________________________________________________

WEEK 11

LECTURE READING 7

Meridians. The direction of a line is usually defined by the horizontal angle it makes with a fixed reference line or
direction.

Four Types of Meridian:

1.True meridian. The true meridian is the sometimes known as the astronomic or geographic meridian It is generally
adapted reference line in surveying practice. This line passes through the geographic north and south
poles of the earth and the observer’s position.
2. Magnetic meridian. A magnetic meridian is a fixed line of reference, which lies parallel with the magnetic lines of
force of the earth. It is not parallel to the true meridian since they converge at a magnetic pole, which
is located some distance away from the true geographic poles.
3. Grid meridian. A grid meridian is a fixed line of reference parallel to the central meridian of a system of plane
rectangular coordinates.
4. Assumed meridian. An assumed meridian is an arbitrarily chosen fixed line of reference, which is taken for
convenience.

UNITS OF ANGULAR MEASUREMENT.

1. Degree. The sexagesimal system is used in which the circumference of a circle is divided into 360 parts or
degrees. The angle of one degree is defined as the angle, which requires 1/360 of the rotation
needed to obtain one complete revolution. The basic unit is the degree , which is further subdivided
into 60 minutes and the minute into 60 seconds.
2. Grad. The grad is the unit of measure in the centesimal system. In this system the circumference of a circle is
divided into 400 parts called grads.
3. Mil. The circumference is divided into 6400 parts called mils, or 1600 mils is equal to 90 degrees. It is commonly
used in military operations as in fire direction of artillery units.
4. Radian. The radian is another measure of angles used frequently for a host of calculations. One radian is
defined as angle subtended at the center of a circle by an arc length exactly equal to the radius of
the circle. One radian equals 180/π .

DESIGNATION OF NORTH POINTS.

There is always a starting or reference point to define directions. Map users are primarily concerned with the north
point for the determination of directions and the following are the commonly used reference points.

1. True North – is the north point of the true meridian. A star, an asterisk, or the letters TN symbolizes it.
2. Magnetic north – a north point that is established by means of a magnetized compass needle when there
are no local attractions affecting it. The point is usually symbolized by a half arrowhead or the letters MN.
3. Grid North – a north point, which is established by lines on a map, which are parallel to a selected central
meridian. A full arrowhead or the letters GN symbolizes it.
4. Assumed North – is used to portray the location of any arbitrarily chosen north point. A small blackened
circle or the letters AN symbolizes it.
 Far Eastern University
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___________________________________________________________________________

DIRECTION OF LINES
The direction of a line is defined as the horizontal angle the line makes with an established line of reference. In
surveying practice, directions maybe defined by means of interior angles, deflection angles, angles to the right ,
bearings, or azimuths.

Basic Requirements in Determining an Angle

KINDS of HORIZONTAL ANGLES

INTERIOR ANGLES
• the angles between adjacent lines in a closed polygon.

ANGLES TO THE RIGHT

• angles to the right are measured clockwise from the preceding line to the
succeeding line.

Closed Polygon: Clockwise Interior Angles (ANGLES TO THE RIGHT)

 Far Eastern University
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___________________________________________________________________________

Closed Polygon: Counterclockwise Interior Angles (ANGLES TO THE LEFT)

DEFLECTION ANGLES
• the angle between a line and the prolongation of the preceding line.
• always accompanied either by R (clockwise) or L (counter-clockwise)

BEARINGS
Ø The bearing of a line is the acute horizontal angle between a reference meridian and the line
Ø A quadrantal system is used to specify bearings such that a line may fall under one of the following quadrants:
NE, NW, SE, and SW.
Ø Each quadrant is numbered from 0 to 90° from either the north or south end of the meridian to the east or
west end of the reference parallel
 Far Eastern University
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___________________________________________________________________________

BEARING ANGLES from either north or south of the meridian to the east or west end of the reference parallel.

Forward and Back Bearings

PROBLEM: Compute the angles AOB,COD, EOF, and GOH from the following set of lines whose magnetic lines are
given:
1. OA, N 39 ° 25' E and OB, N 75°50' E
2. OD, N 34 ° 14' E and OC, N 53°22' W
3. OE, S 15°04' E and OF, S 36°00' W
4. OG, N 70°15' W and OH, S 52°05' W
 Far Eastern University
Institute of Architecture and Fine Arts
___________________________________________________________________________

SOLUTION:

1. OA, N 39 °25' E and OB, N 75°50' E

2. OD, N 34 °14' E and OC, N 53°22' W

3. OE, S 15°04' E and OF, S 36°00' W

4. OG, N 70°15' W and OH, S 52°05' W

 Far Eastern University
Institute of Architecture and Fine Arts
___________________________________________________________________________

AZIMUTHS. The azimuth of a line is its direction as given by the angle between the meridian and the line measured in
a clockwise direction from either the north or south branch of the meridian. It may range from 0 to 360
degrees and letters are not required to identify quadrants.

AZIMUTH observed from NORTH (always clockwise either from South or North)

PROBLEMS:

1) Determine the azimuths of lines AB, BC, and CD.

 Far Eastern University
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___________________________________________________________________________

a) AZIMUTH of AB

b) AZIMUTH of BC

c) AZIMUTH of CD

2) Compute the angles APB, CPD, and EPF from the following set of lines whose azimuths are
given.
a) AZIMN of Line PA = 39°48' ; AZIMN of Line PB = 115°29'
b) AZIMS of Line PC = 320°22' ; AZIMS of Line PD = 62°16'
 Far Eastern University
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Solution:

a) AZIMN of Line PA = 39°48' ; AZIMN of Line PB = 115°29

b) AZIMS of Line PC = 320°22' ; AZIMS of Line PD = 62°16'

COMPARISON of AZIMUTHS and BEARING

AZIMUTHS BEARINGS

Ø Vary from 0 to 360° Ø Vary from 0 to 90°

Ø Require only a numerical value Ø Require two letters and a numerical value
Ø May be geodetic, astronomic, magnetic, grid, Ø Same as Azimuths
assumed, forward or back
Ø Are measured clockwise only Ø Are measured clockwise and counterclockwise
Ø Are measured either from North only, or from South Ø Are measured from North and South
only on a particular survey
 Far Eastern University
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CONVERSION OF AZIMUTH TO BEARING

Computation of Bearings BC and CD

BEARING of AB = 𝑵𝟒𝟏°𝟑𝟓! 𝑬
 Far Eastern University
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Computation of Azimuth (from the South) of BC and CD

Compute the rest of the bearings and azimuths and complete the table below.
 Far Eastern University
Institute of Architecture and Fine Arts

MAGNETIC DECLINATION

Magnetic declination, or magnetic variation, is the angle on the horizontal

plane between magnetic north (the direction the north end of a
magnetized compass needle points, corresponding to the direction of the Earth's
magnetic field lines) and true north (the direction along a meridian towards the
geographic North Pole). -wikipedia

Ø Deflection of the needle may be eastward or westward of the true meridian.

Sample Problem 1:
Assume the magnetic bearing of a property line was recorded as S 43°30' E in 1862. At that time the
magnetic declination at the survey location was 3°15’ W. What true bearing is needed for a
subdivision property plan?

Sample Problem 2:
Assume the magnetic bearing of line AB read in 1878 was N 26°15' E . The declination at the time
and place was 7°15’W. In 2000, the declination was 4°30' E . The magnetic bearing in 2000 is
needed.
 Far Eastern University
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MODULE 5: TRAVERSE AND TRAVERSING

Module Information

Module Overview

The module begins with the discussion of the different kinds of traverse and terminologies in traversing.
It focuses on the traverse computation and the adjustment of angular measurement to ensure the
geometric condition of the traverse is met. Moreover, the module covers the discussion on the common
types of omitted measurements and how it can be determined. The discussion is further focusses on
the adjustment of the traverse to ensure its closure.

Module Coverage
The module will be covered for a duration of 2 weeks with 1 work output(see course outline schedule
for submission). It is scheduled on the week 12 and 13 of the semester.

Module Objective
• The module aims to provide insights on the kinds of traverse and the possible sources of
errors that may be committed during traversing.
• The module aims to provide knowledge on traverse computation to ensure the geometric
condition of the traverse being fulfilled.
• The module aims to develop the skills of solving the omitted measurements that may occur
due to site condition.

Module Learning Outcomes

By the end of this module the student should be able to:
• Apply the principle of traversing and its adjustment during surveying exercises
• Compute latitude and departure of a line and error of closure of a traverse
• Analyze and determine the missing data or omitted measurement of a closed traverse
• Evaluate and apply the adjustment in the traverse using compass rule and transit rule

Module Interdependencies
The output of the module will be reinforced by Module 6: Area Computation and Lot Plan

Module Learning Materials

Under this module the students are provided with the following materials:
• Lecture Note:
Title: Traversing
Missing Data (Omitted Measurement)
Traverse Adjustment
• PowerPoint Presentation:
The presentation provided in pdf file are the slides used for the presentation of the mentor.
 Far Eastern University
Institute of Architecture and Fine Arts

Additional Readings and Materials

Students may refer to the given lectures under this module. Nevertheless, should the student like to
study beyond the given materials, they may refer to the books listed below:
• Ghilani, C. (2012). Elementary Surveying: an Introduction to Geomatics
• Lee, Sandra Jean. Willis's elements of quantity surveying. Chichester, West Sussex, United
Kingdom: John Wiley & Sons Inc., 2014 IARFA 0140 Cir TH 435 L4 2014
• Surveying. UAE 3G Elearning, 2015. Cir TA 545 S9 2015

Module Output-base Work

To complete this module the student shall submit Formative Assessment 6 . The details of the
assessment can be found in the Assessment Module.

References
• Basak, N N. Surveying and Levelling. Second Edition. New Delhi: McGraw-Hill Education (India)
Private Limited, 2014. Cir TA 545 B3 2014
• Johnson, Aylmer. Plane and Geodetic Surveying. Second Edition. Boca Raton: CRC Press, Taylor &
Francis Group, 2014. Cir TA 545 J6 2014
• La Putt, Judy Pilapil. Higher Surveying, 2nd Edition. Mandaluyong City: National Bookstore, 1990. Fil
TA 545 L3 1990
• Kavanagh, Barry F. Surveying: Principles and Applications. 6th ed. Upper Saddle River, NJ:
Prentice Hall, c2003. Cir TA 545 K3 2003
 Far Eastern University
Institute of Architecture and Fine Arts

WEEK 12

LECTURE READING 8

TRAVERSING
It is the act of marking the lines.
A means of determining the relative locations of points.

Commonly Used Terms in Traversing

1. Traverse is a series of lines connecting successive points whose lengths and directions have been
determined from field measurements.
2. Traversing is a process of measuring the lengths and directions of the lines of a traverse for the
purpose of locating the position of certain points.
3. Traverse Station is any temporary or permanent point of reference over which the instrument is set up.
4. Traverse Lines are lines connecting traverse stations and whose lengths and directions are
determined.

KINDS OF TRAVERSE:

A. CLOSED TRAVERSE
It is said to be closed traverse when the lines return to the
starting point, thus forming a closed figure.
It provides checks on the observed angles and distances and
used extensively in control, construction, property and
topographic surveys

B. OPEN TRAVERSE
It consists of a series of lines that are connected but do not
return to the starting point or close upon a point of equal or
greater order accuracy
This should be avoided because they offer no means of
checking for observational errors and mistakes

SOURCES OF ERROR IN TRAVERSING

a) Poor selection of stations, resulting in bad sighting conditions caused by

§ alternate sun and shadow
§ visibility of only the rod’s top
§ line of sight passing too close to the ground
§ Lines that are too short
§ Sighting into the sun
b) Errors in observations of angles and distances
c) Failure to observe angles an equal number of times direct and reversed
 Far Eastern University
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MISTAKES IN TRAVERSING

§ Occupying or sighting on the wrong station

§ Incorrect orientation
§ Confusing angles to the right and left
§ Mistakes in note taking
§ Misidentification of the sighted station

TRANSVERSE COMPUTATION

For any closed traverse the first step taken by the surveyor should always be to check if the observed
angles fulfill the geometric conditions of the figure. Should there be an angular error of closure it must be
corrected to give series of preliminary adjusted directions. All linear distances should then be corrected since
errors in measured lengths will alter the shape of traverse.

Latitude and Departure

The latitude of a line is its projection onto the reference meridian or

a north-south line. Latitude are sometimes referred to as northings or
southings. Latitude of lines with northerly bearings are designated as being
north (N) or positive (+); those in a southerly direction are designated as
south (S) or negative (-).

On the other hand, the departure of a line is its projection onto the
reference parallel or an east-west line. Departures are east (E) or positive
(+) for lines having easterly bearings and west (W) or negative(-) for lines
having westerly bearings.

When the direction of a line is given in terms of azimuth from

north, the proper signs of the latitudes and departures are
automatically generated in the calculator or electronic digital
computer.
 Far Eastern University
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PROBLEM: Determine the latitude and departure of each course(line).

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SOLUTION:

a) LATITUDES:

b) DEPARTURES

PROBLEM: Determine the latitude and departure of each course(line).

 Far Eastern University
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Compute the rest of the latitudes and departures and fill up the table completely.

ERROR OF CLOSURE.

There is no such thing as a mathematically perfect survey. Small errors in both distances and angles will
always be present even in closed traverses observed using instruments and methods of high precision. In all
probability a surveyed closed traverse would not satisfy the geometry requirements of a closed polygon. Until
adjustments are made these observed quantities it will always expected that the traverse will not
mathematically close.

The linear error of closure (LEC) is usually a short line of unknown length and direction connecting the initial
and final stations of the traverse.

When latitudes are added together, the resulting error is called the error
in latitudes (CL).
The error resulting from adding departures together is called the error in
departure (CD).

Where:
LEC = linear error of closure
CL = closure in latitude or the algebraic sum of north and south latitudes
CD = closure in departure or the algebraic sum of the east and west departures
Ǿ = bearing angle of the side of error
 Far Eastern University
Institute of Architecture and Fine Arts

RELATIVE PRECISION is defined as the ratio of the linear error of closure to the perimeter or total length of
the traverse.

Where:
RP = relative precision
LEC = linear error of closure
D = total length or perimeter of the traverse

ADJUSTMENT OF CLOSED COMPASS TRAVERSE:

The method of compass surveying is one of the most basic and widely practiced methods of
determining the relative location of points where high degree of precision is not required.
As mentioned earlier, closed traverse consists of series of lines of known lengths and bearings which
forms a closed loop. It provides checks on measured angles and distances. It is customary to begin
at some convenient corner when making a survey enclosing an area, and to take bearings and
measure distances in a particular order (clockwise or counterclockwise) around the field. An
excellent advantage of a closed traverse over an open traverse is the available check on angular
measurements. The sum of the interior angles of a closed traverse is exactly equal to (𝑛 − 2)180° ,
where 𝑛 is the number of sides of the traverse.

Steps during Adjustment

1. Compute and adjust the interior angles
2. select the best line or the line in the traverse which is unaffected by local attraction
3. adjust the observed bearings of successive lines.
 Far Eastern University
Institute of Architecture and Fine Arts

WEEK 12

LECTURE READING 9

MISSING DATA (OMITTED MEASUREMENT)

Sometimes it is impossible to determine the length or direction of a line within a closed traverse. The
values of these missing quantities can be determined as long as they do not exceed two in number.
The practice of omitting measurements for one or more sides and solving for them is not desirable and
should be avoided. The trouble with such calculations is that it tends to throw all possible errors and mistakes
into the computation of the lengths or directions. Also, it eliminates the check on the precision of the field
measurements that were made. There is no choice but to assume that the measurements taken are all correct
and without error. Since the observed and omitted measurements are part of a closed traverse, the algebraic
sum of all the latitudes and of all the departures are both zero.
It is not justifiable, however, to say that such a practice should never be attempted or employed. There
are various circumstances where this method can be used to advantage. There are several other reasons why
measurements are omitted in the field and are computed later in the office.

The following are some of the more common types of omitted measurements:

I. Omitted Measurements are in One Side

Case 1: Length and Bearing of One Side Unknown

II. Omitted Measurements involving Two Adjoining Sides

Case 2: Length of One Side and Bearing of Another Side Unknown
Case 3: Lengths of Two Sides Unknown
Case 4: Bearings of Two Sides Unknown

III. Omitted Measurements involving Two Non-Adjoining Sides

Case 5: Length of One Side and Bearing of Another Side Unknown
Case 6: Lengths of Two Sides Unknown
Case 7: Bearings of Two Sides Unknown

Case I: Length and Bearing of One Side Unknown

In determining the length and direction of a closed traverse is the same as that of computing the
length and direction of the side of error in any closed traverse. It is necessary to compute first the latitude and
departure of lines having known directions and lengths. Since only one latitude and one departure are
unknown, the algebraic sum of the north and south latitude (taken with opposite sign) will yield the latitude of
unknown side; while, the algebraic sum of the east and west departure (also taken with opposite sign) will be
the departure of the unknown side.
It can also be noted that condition of a closed traverse can be applied. The algebraic sum of all
latitudes and of all the departures of a closed traverse must be zero.
 Far Eastern University
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PROBLEM: Given the accompanying tabulation for a closed traverse in which the length and bearing of line
2-3 unknown. Determine the values of the unknown quantities.

Compute the latitude and departure of the known lines

𝒍𝒂𝒕 = (𝒅𝒊𝒔𝒕)(𝐜𝐨𝐬 𝑩𝒆𝒂𝒓𝒊𝒏𝒈)

Lat is (-) if Southerly, ex. S 49° 35’ E, and (+) if Northerly,

ex. N 51° 44’ W

𝑙𝑎𝑡!"# = (27.89)(cos 49° 35% ) = − 18.15𝑚

𝑙𝑎𝑡&"' = (5.95)(cos 86° 15% ) = − 0.39𝑚

𝑙𝑎𝑡'"( = (24.01)(cos 51° 44% ) = +14.87𝑚

𝑙𝑎𝑡("! = (21.99)(cos 45° 07% ) = +15.52𝑚

𝒅𝒆𝒑 = (𝒅𝒊𝒔𝒕)(𝒔𝒊𝒏 𝑩𝒆𝒂𝒓𝒊𝒏𝒈)

Dep is (+) if Easterly, ex. S 49°35’ E, and (-) if Westerly,

ex. N 51°’ W
𝑑𝑒𝑝!"# = (27.89)(𝑠𝑖𝑛 49° 35% ) = +21.31𝑚

𝑑𝑒𝑝&"' = (5.95)(𝑠𝑖𝑛 86° 15% ) = −5.94𝑚

𝑑𝑒𝑝'"( = (24.01)(𝑠𝑖𝑛 51° 44% ) = −18.85𝑚

𝑑𝑒𝑝("! = (21.99)(𝑠𝑖𝑛 45° 07% ) = +15.58𝑚

 Far Eastern University
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Solve for the latitude and departure of line 2-3 by applying the condition of a closed traverse that the
sum of latitudes and departures must be zero.

B 𝑙𝑎𝑡 = 0 −18.15 + 𝒍𝒂𝒕𝟐"𝟑 − 0.39 + 14.87 + 15.52 = 0

𝒍𝒂𝒕𝟐"𝟑 = +18.15 + 0.39 − 14.87 − 15.52
𝒍𝒂𝒕𝟐"𝟑 = −11.85 𝑚

B 𝑑𝑒𝑝 = 0 +21.31 + 𝒅𝒆𝒑𝟐"𝟑 − 5.94 − 18.85 + 15.58 = 0

𝒅𝒆𝒑𝟐"𝟑 = 5.94 + 18.85 − 15.58 − 21.31
𝒅𝒆𝒑𝟐"𝟑 = −12.10

Therefore, distance of line 2-5 is:

𝑑𝑖𝑠𝑡#"& = F𝑙𝑎𝑡 # + 𝑑𝑒𝑝# = F(−11.85)# + (−12.10)#

𝒅𝒊𝒔𝒕𝟐"𝟑 = 𝟏𝟔. 𝟗𝟒 𝒎

Bearing of line 2-5 is:

𝑑𝑒𝑝
𝐵𝑒𝑎𝑟𝑖𝑛𝑔#"& = 𝑡𝑎𝑛"! Q R
𝑙𝑎𝑡
12.10
𝐵𝑒𝑎𝑟𝑖𝑛𝑔#"& = 𝑡𝑎𝑛"! Q R = 45° 36%
11.85

𝑩𝒆𝒂𝒓𝒊𝒏𝒈𝟐"𝟑 = 𝑺 𝟒𝟓° 𝟑𝟔% 𝑾

OMITTED MEASUREMENTS INVOLVING TWO ADJOINING SIDES

Case 2: Length of One Side and Bearing of Another Side Unknown

PROBLEM: Determine the bearing of 1-2 and length 0f 2-3

 Far Eastern University
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Step 1: Separate known sides from unknown side by a dividing line drawn from point 1 to point 3.

Step 2: Determine the length and bearing of the dividing line 1-3 by considering traverse 1-3-4-5-1.

Compute the latitude and departure of the known lines

B 𝑙𝑎𝑡 = 0 −0.39 + 14.87 + 15.52 + 𝑙𝑎𝑡!"& = 0

𝑙𝑎𝑡!"& = −14.87 − 15.52 + 0.39 = −30

B 𝑑𝑒𝑝 = 0 −5.94 − 18.85 + 15.58 + 𝑑𝑒𝑝!"& = 0

𝑑𝑒𝑝!"& = +5.94 + 18.85 − 15.58 = +9.21

𝑑𝑖𝑠𝑡!"& = F𝑙𝑎𝑡 # + 𝑑𝑒𝑝#

= F30# + 9.21#

= 31.38 𝑚

𝑑𝑒𝑝
𝐵𝑒𝑎𝑟𝑖𝑛𝑔!"& = 𝑡𝑎𝑛"! Q R
𝑙𝑎𝑡
9.21
𝐵𝑒𝑎𝑟𝑖𝑛𝑔!"& = 𝑡𝑎𝑛"! Q R = 17° 04%
30

𝑩𝒆𝒂𝒓𝒊𝒏𝒈𝟏"𝟑 = 𝑺 𝟏𝟕° 𝟎𝟒% 𝑬

 Far Eastern University
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Step 3: Determine the bearing of line 1-2

Solve ∅ based on the given bearings of lines 2-3 and 3-1

∅ = 17° 04% + 45° 36%
∅ = 62° 40 %

Using sine law, solve for angle 𝛼

27.99 31.38
=
sin ∅ sin 𝜶

sin 𝜶 31.38
=
sin 62° 40 % 27.99

31.38
sin 𝜶 = sin 62° 40 %
27.99
31.38
𝜶 = 𝑠𝑖𝑛"! Q sin 62° 40 % R
27.99
𝛽 = 180° − (𝜶 + 45° 36% ) 𝜶 = 84° 50 %

𝛽 = 180° − (84° 50% + 45° 36% )

𝛽 = 49° 34%

Bearing of line 1-2

Bearing angle must be measured at point 1
𝑩𝒆𝒂𝒓𝒊𝒏𝒈𝟏"𝟐 = 𝑺 𝟒𝟗° 𝟑𝟒% 𝑬

Step 4: Determine the length of line 2-3

𝜃 = 180° − (∅ + 𝜶)
𝜃 = 180° − (62° 40% + 84° 50% )
𝜃 = 32° 30%

Using sine law, solve for angle 𝛼

27.99 𝑑𝑖𝑠𝑡#"&
=
sin ∅ 𝑠𝑖𝑛 𝜃

27.99 𝑑𝑖𝑠𝑡#"&
° %
=
sin 62 40 𝑠𝑖𝑛 32° 30%
27.99 𝑠𝑖𝑛 32° 30%
𝑑𝑖𝑠𝑡#"& =
sin 62° 40 %

𝒅𝒊𝒔𝒕𝟐"𝟑 = 𝟏𝟔. 𝟗𝟑 𝒎
 Far Eastern University
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OMITTED MEASUREMENTS INVOLVING TWO ADJOINING SIDES

Case 3: Lengths of Two Sides Unknown

PROBLEM: Determine the bearing of 1-2 and length 0f 2-3

Step 1: Separate known sides from unknown side by a dividing line drawn from point 1 to point 4.

Step 2: Determine the length and bearing of the dividing line 4-1 by considering traverse 1-2-3-4-1.

Compute the latitude and departure of the known lines

B 𝑙𝑎𝑡 = 0 𝑙𝑎𝑡'"! − 18.15 − 11.86 − 0.39 = 0

𝑙𝑎𝑡'"! = +18.15 + 11.86 + 0.39 = +30.40
B 𝑑𝑒𝑝 = 0 𝑑𝑒𝑝'"! + 21.31 − 12.11 − 5.94 = 0
𝑑𝑒𝑝'"! = −21.31 + 12.11 + 5.94 = −3.26

𝑑𝑒𝑝
𝑑𝑖𝑠𝑡'"! = F𝑙𝑎𝑡 # + 𝑑𝑒𝑝# 𝐵𝑒𝑎𝑟𝑖𝑛𝑔'"! = 𝑡𝑎𝑛"! Q R
𝑙𝑎𝑡
= F30.4# + 3.26# 3.26
𝐵𝑒𝑎𝑟𝑖𝑛𝑔'"! = 𝑡𝑎𝑛"! Q R = 17° 04%
30.4
= 30.57 𝑚
𝑩𝒆𝒂𝒓𝒊𝒏𝒈𝟒"𝟏 = 𝑵 𝟎𝟔° 𝟎𝟕% 𝑾
 Far Eastern University
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Step 3: Determine lengths of lines 1-2 and 2-3

∅ = 180° − (45° 07% + 51° 44% )

∅ = 83° 09 %
𝜽 = 51° 44% + 06° 07%
𝜽 = 45° 37 %

𝜶 = 180° − (45° 37% + 83° 09% )

𝜶 = 51° 14 %

Use Sine Law: 𝑑𝑖𝑠𝑡("! 30.57 𝑑𝑖𝑠𝑡'"(

= =
sin 𝜽 sin ∅ sin 𝜶

𝑑𝑖𝑠𝑡("! 30.57 𝑑𝑖𝑠𝑡'"(

° %
= ° %
=
sin 45 37 sin 83 09 sin 51° 14 %

30.57 sin 45° 37 %

𝑑𝑖𝑠𝑡("! = = 22 m
sin 83° 09 %
30.57 sin 51° 14 %
𝑑𝑖𝑠𝑡'"( = = 24.01 m
sin 83° 09 %
 Far Eastern University
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OMITTED MEASUREMENTS INVOLVING TWO ADJOINING SIDES

Case 4: Bearings of Two Sides Unknown

PROBLEM: Determine the bearings of 5-1 and 1-2

Step 1: Separate known sides from unknown side by a dividing line drawn from point 2 to point 4.

Step 2: Determine the length and bearing of the dividing line 5-2 by considering traverse 2-3-4-5-2.

Compute the latitude and departure of the known lines

B 𝑙𝑎𝑡 = 0 𝑙𝑎𝑡'"! − 18.15 − 11.86 − 0.39 = 0

𝑙𝑎𝑡'"! = +18.15 + 11.86 + 0.39 = +30.40
B 𝑑𝑒𝑝 = 0 𝑑𝑒𝑝'"! + 21.31 − 12.11 − 5.94 = 0
𝑑𝑒𝑝'"! = −21.31 + 12.11 + 5.94 = −3.26
 Far Eastern University
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𝑑𝑒𝑝
𝐵𝑒𝑎𝑟𝑖𝑛𝑔("# = 𝑡𝑎𝑛"! Q R
𝑑𝑖𝑠𝑡("# = F𝑙𝑎𝑡 # + 𝑑𝑒𝑝# 𝑙𝑎𝑡
36.90
= F2.62# + 36.90# 𝐵𝑒𝑎𝑟𝑖𝑛𝑔("# = 𝑡𝑎𝑛"! Q R = 85° 56%
2.62
= 36.99 𝑚
𝑩𝒆𝒂𝒓𝒊𝒏𝒈𝟓"𝟐 = 𝑺 𝟖𝟓° 𝟓𝟔% 𝑬

Step 3: Determine bearings of lines 5-1 and 1-2

Use Cosine
L
(𝑑𝑖𝑠𝑡'"( )' = (𝑑𝑖𝑠𝑡(") )' + (𝑑𝑖𝑠𝑡)"' )' − 2(𝑑𝑖𝑠𝑡(") )(𝑑𝑖𝑠𝑡)"' )(cos 𝜶 )
a
w '
(36.99) = (21.99)' + (27.99)' − 2(21.99)(27.99)(cos 𝜶)

(21.99)' + (27.99)' − (36.99)'

cos 𝜶 =
2(21.99)(27.99)
𝜶 = 𝟗𝟒° 𝟒𝟔%

Use Sine Law

27.99 36.99
=
𝑠𝑖𝑛 𝛽 𝑠𝑖𝑛 𝛼

27.99 36.99
=
𝑠𝑖𝑛 𝛽 𝑠𝑖𝑛 94° 46%

27.99Qsin 94° 46% U

𝑠𝑖𝑛 𝛽 =
36.99

𝜷 = 𝟒𝟖° 𝟓𝟕%
 Far Eastern University
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Take Note: The sum of interior angles of triangle is equal to 180°

180° = 𝜃 + 𝛽 + 𝜶
180° = 𝜃 + 48° 57% + 94° 46%
𝜃 = 180° − (48° 57% + 94° 46% )
𝜃 = 36° 17%

𝐵𝑒𝑎𝑟𝑖𝑛𝑔("' = 𝑆 85° 56% 𝐸

Bearing of 5-1:
180° = 𝐵𝑒𝑎𝑟𝑖𝑛𝑔(") + 𝜷 + 85° 56%
𝐵𝑒𝑎𝑟𝑖𝑛𝑔(") = 180° − 𝜷 − 85° 56%

𝐵𝑒𝑎𝑟𝑖𝑛𝑔(") = 180° − 48° 57% − 85° 56%

𝐵𝑒𝑎𝑟𝑖𝑛𝑔(") = 45° 07%
𝑩𝒆𝒂𝒓𝒊𝒏𝒈𝟓"𝟏 = 𝑵 𝟒𝟓° 𝟎𝟕% 𝑬

Bearing of 1-2:

𝜶 = 𝐵𝑒𝑎𝑟𝑖𝑛𝑔)"' + 45° 07% 45° 07% 𝐵𝑒𝑎𝑟𝑖𝑛𝑔)"'

𝐵𝑒𝑎𝑟𝑖𝑛𝑔)"' = 𝜶 − 45° 07%

𝐵𝑒𝑎𝑟𝑖𝑛𝑔)"' = 94° 46% − 45° 07%

𝜶
𝑩𝒆𝒂𝒓𝒊𝒏𝒈𝟏"𝟐 = 𝟒𝟗° 𝟑𝟗% = 𝑺 𝟒𝟗° 𝟑𝟗% 𝑬
 Far Eastern University
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WEEK 13

LECTURE READING 10

TRAVERSE ADJUSTMENT

Adjusting a traverse, also known as balancing a traverse, is used to distribute the closure error back into the
angle and distance measurement.
The condition of adjusted traverse is that sum of adjusted latitudes and departures are zero.

Methods of traverse adjustment:

1. Compass Rule
2. Transit Rule
3. Arbitrary Adjustment– placing error in one or more measurements

COMPASS (Bowditch) RULE

may be stated as follows:

The correction to be applied to the latitude (or departure) of any course is equal to the total closure in latitude
(or departure) multiplied by the ratio of the length of the course to the total length or the perimeter of the
traverse. These corrections are given by the following equations:

Cl = correction to be applied to the latitude of any course.

Cd = correction to be applied to the departure of any course.
CL = total closure in latitude or the algebraic sum of the north and south latitudes (∑NL+ ∑SL)
CD = total closure in departure or the algebraic sum of east and west departures (∑ED+ ∑WD)
D = length of any course.
D = total length of perimeter of the traverse

ADJUSTED LENGHTS AND DIRECTIONS.

Where: L’ = adjusted length of a course

Lat' = adjusted latitude of a course
Dep' = adjusted departure of a course
α = adjusted horizontal angle between the reference meridian and a course.
 Far Eastern University
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APPLICATION OF THE CORRECTION:

If the sum of the north latitudes exceeds the sum of the south latitudes, latitude corrections are
subtracted from north latitudes and added to corresponding south latitudes. However, if the sum
of the south latitudes exceeds the sum of the north latitudes, the corrections are applied in the opposite
manner. A similar procedure is used when adjusting the departures.

PROBLEM: Adjust the traverse using COMPASS RULE.

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Far Eastern University
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 Far Eastern University
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Corrected Distance and Corrected Bearing may be computed using the corrected latitude and
corrected departure
 Far Eastern University
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COMPASS RULE

TRANSIT RULE

may be stated as follows:

• The correction to be applied to the latitude (or departure) of any course is equal to the latitude (or
departure) of the course multiplied by the ratio of the total closure in latitude (or departure) to the
arithmetical sum of all the latitude (or departures) of the traverse. This corrections are given by the
following equations.

Where:
Cl = correction to be applied to the latitude of any course.
Cd = correction to be applied to the departure of any course
CL = total closure in latitude or the algebraic sum of the north and south latitudes (∑NL+ ∑SL)
CD = total closure in departure or the algebraic sum of the east and west departures (∑ED+ ∑WD)
∑NL = summation of north latitudes
∑SL = summation of south latitudes
∑ED = summation of east departures
∑WD = summation of west departures
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Adjust the traverse using TRANSIT RULE

Latitude Correction:

Departure Correction:
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 Far Eastern University
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Compute the corrected length:

Compute the Corrected Bearing

CORRECTED LENGTH/BEARING
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MODULE 6A:

Module Information

Module Overview
The module focuses on the preparation of the lot plan. It discusses on how to plot a lot plan based on
the technical description described on the Transfer Certificate of Title (TCT).

Module Coverage
The module will be covered for a duration of 1 week with 1 work output(see course outline schedule
for submission). It is scheduled on the week 14 of the semester.

Module Objective
• The module aims to help the student understand and interpret the technical description of the
lot.
• The module aims to develop skills in plotting the lot using the technical description on the
Transfer Certificate of Title (TCT)

Module Learning Outcomes

By the end of this module the student should be able to:
• Interpret the technical description on the TCT
• Plot a lot plan based on the technical description on the Transfer Certificate of Title (TCT) .
Module Interdependencies
This output of the module will be reinforced by Module 6B: Area Computation

Module Learning Materials

Under this module the students are provided with the following materials:
• Lecture Note:
Title: Lot Plan
• PowerPoint Presentation:
The presentation provided in pdf file are the slides used for the presentation of the mentor.

Additional Readings and Materials

Students may refer to the given lectures under this module. Nevertheless, should the student like to
study beyond the given materials, they may refer to the books listed below:
• Ghilani, C. (2012). Elementary Surveying: an Introduction to Geomatics
• Lee, Sandra Jean. Willis's elements of quantity surveying. Chichester, West Sussex, United
Kingdom: John Wiley & Sons Inc., 2014 IARFA 0140 Cir TH 435 L4 2014
• Surveying. UAE 3G Elearning, 2015. Cir TA 545 S9 2015

Module Output-base Work

To complete this module the student shall submit Formative Assessment 7 . The details of the
assessment can be found in the Assessment Module.
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References
• Basak, N N. Surveying and Levelling. Second Edition. New Delhi: McGraw-Hill Education (India)
Private Limited, 2014. Cir TA 545 B3 2014
• Johnson, Aylmer. Plane and Geodetic Surveying. Second Edition. Boca Raton: CRC Press, Taylor &
Francis Group, 2014. Cir TA 545 J6 2014
• La Putt, Judy Pilapil. Higher Surveying, 2nd Edition. Mandaluyong City: National Bookstore, 1990. Fil
TA 545 L3 1990
• Kavanagh, Barry F. Surveying: Principles and Applications. 6th ed. Upper Saddle River, NJ:
Prentice Hall, c2003. Cir TA 545 K3 2003
 Far Eastern University
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WEEK 14

LECTURE READING 11

Plotting of LOT Plan using the technical description from the TCT (Transfer Certificate of Title)

Sample of SUBDIVISION PLAN:

Subdivision plans are required for a parcel of land or a building that is to be divided into two or more lots whether
industrial, commercial or residential. A subdivision plan is produced after an initial survey of the property or land.
The survey determines the existing boundaries, and is used to understand the new proposed boundaries for
the subdivision. A subdivision plan outlines both existing boundaries and marks new boundaries. When you
want to subdivide, a compliant subdivision survey and plan is required before any other processes.

Steps in Subdivision Process:

1. Preparation of a plan by a licensed land surveyor.
2. Application for a planning permit and certification to local council
3. Referral to service authorities for consent and compliance
4. Registration with the Land Title office
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Sample of Relocation Plan:

Relocation surveys involve the precise identification of established land and its corners. The main purpose of
this kind of survey is to re-establish the boundaries of a tract for which a survey has previously been made
and to verify if existing location property overlaps to adjoining lots.

Requirements for Relocation Survey

1. Copy of Tax Declaration
2. Copy of Land Title

After Relocation Survey, owner will get:

1. Sketch plan signed and verified by a licensed geodetic engineer.
2. Placement of concrete monuments (mohon) on the corners of established boundaries.

Sample of Land Title (Transfer Certificate of Title – TCT)

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Prepare the Relocation Plan of Lot 29 Block 18 as described on the TCT- Transfer Certificate of Title
shown below.
Far Eastern University
Institute of Architecture and Fine Arts
 Far Eastern University
Institute of Architecture and Fine Arts

Plot the lot using protractor for the angles and specify the scale for the length.

1. From station 1,using protractor, measure an angle 30° 52’ from the
south end eastward since bearing is S30° 52’ E to establish line 1-
2. From station 1 along the line, measure a distance 13m (using the
specified scale) to establish station 2.

2. Move to station 2, layout the next line 2-3 using the

technical description for line 2-3.

3. Move to the next station , layout the next line

using the technical description for that line.
Follow the same steps above until you reach
the point of. Beginning.
Far Eastern University
Institute of Architecture and Fine Arts
 Far Eastern University
Institute of Architecture and Fine Arts

MODULE 6B: AREA COMPUTATION

Module Information

Module Overview
The module covers the presentation of different methods of computing the area of an enclosed land.
The presentation begins with the area by triangle, it is when the land is divided into series of triangles
and then taking the sum of the areas of all the triangles. Moreover, the module focusses on the area
computation by coordinates, double meridian distance (DMD) method, and double parallel distance
(DPD) method.

Module Coverage
The module will be covered for a duration of 3 weeks with 1 work output(see course outline schedule
for submission). It is scheduled on the week 14 to 16 of the semester.

Module Objective
• The module aims to help the student understand the different methods of finding the area of
enclosed land for deed description
• The module aims to develop student’s mathematical skills in computing the area of an
enclosed land using different methods.
Module Learning Outcomes
By the end of this module the student should be able to:
• Compute land area by triangles and by coordinates
• Determine the lot area using DMD and DPD method.
Module Learning Materials
Under this module the students are provided with the following materials:
• Lecture Note:
Title: Traversing and
Missing Data (Omitted Measurement)
Traverse Adjustment
• PowerPoint Presentation:
The presentation provided in pdf file are the slides used for the presentation of the mentor.

Additional Readings and Materials

Students may refer to the given lectures under this module. Nevertheless, should the student like to
study beyond the given materials, they may refer to the books listed below:
• Ghilani, C. (2012). Elementary Surveying: an Introduction to Geomatics
• Lee, Sandra Jean. Willis's elements of quantity surveying. Chichester, West Sussex, United
Kingdom: John Wiley & Sons Inc., 2014 IARFA 0140 Cir TH 435 L4 2014
• Surveying. UAE 3G Elearning, 2015. Cir TA 545 S9 2015

Module Output-base Work

To complete this module the student shall submit Formative Assessment 6 . The details of the
assessment can be found in the Assessment Module.
 Far Eastern University
Institute of Architecture and Fine Arts

References
• Basak, N N. Surveying and Levelling. Second Edition. New Delhi: McGraw-Hill Education (India)
Private Limited, 2014. Cir TA 545 B3 2014
• Johnson, Aylmer. Plane and Geodetic Surveying. Second Edition. Boca Raton: CRC Press, Taylor &
Francis Group, 2014. Cir TA 545 J6 2014
• La Putt, Judy Pilapil. Higher Surveying, 2nd Edition. Mandaluyong City: National Bookstore, 1990. Fil
TA 545 L3 1990
• Kavanagh, Barry F. Surveying: Principles and Applications. 6th ed. Upper Saddle River, NJ:
Prentice Hall, c2003. Cir TA 545 K3 2003
 Far Eastern University
Institute of Architecture and Fine Arts

WEEK 14

LECTURE READING 12

When the courses or sides of a loop travers represent boundary lines, it is usually necessary
to compute the enclosed land area for the deed description or plotted survey plat. The area is
expressed in terms of square feet (ft2), or acres (ac) for relatively large parcels; in SI metric units, area
is expressed in terms of square meters (m2), or hectares (ha).
When the tract of land is formed by straight lines only, it is possible to divide up the tract into
adjacent triangles, rectangles, trapezoids and take the sum of the areas of all those regular geometric
figures. Most surveyors, though, prefer to use either the double meridian distance(DMD) method or
the coordinate method in order to determine the enclosed area of a traverse. These methods will be
illustrated in this module.

AREA COMPUTATION
• Area by Triangles
• Area by Coordinates
• Area by Double Meridian Distance Method (DMD)
• Area by Double Parallel Distance Method (DPD)
• Area by Trapezoidal Rule
• Area by Simpson’s One-Third Rule

AREA BY TRIANGLES:

PROBLEM: Determine the area of the traverse.

SOLUTION:
a) Draw the traverse based on the technical
description given
 Far Eastern University
Institute of Architecture and Fine Arts

b) Divide the traverse into series of triangles

OPTION 1
OPTION 2

OPTION 3:

c) Compute the area of each triangle

HERON’S FORMULA:
a
b 𝑨 = )𝒔(𝒔 − 𝒂)(𝒔 − 𝒃)(𝒔 − 𝒄)
c
𝒂+𝒃+𝒄
𝒔=
𝟐
 Far Eastern University
Institute of Architecture and Fine Arts

Considering OPTION 3
LOT 1 (𝑨𝟏 )

To apply Heron’s formula, all sides must be known. Therefore, solve the length of line 2-5 based on
its latitude and departure.
𝒅𝒊𝒔𝒕𝟐"𝟓 = &𝒍𝒂𝒕 + 𝒅𝒆𝒑
𝟐 𝟐

Compute the latitude and departure of the known lines

5-1 & 1-2.
𝑙𝑎𝑡&"$ = (27.99)(cos 49° 35( ) = − 18.15𝑚
𝑑𝑒𝑝&"$ = (27.99)(𝑠𝑖𝑛 49° 35( ) = +21.31𝑚
𝑙𝑎𝑡%"& = (21.99)(cos 45° 07( ) = +15.52𝑚
𝑑𝑒𝑝%"& = (21.99)(𝑠𝑖𝑛 45° 07( ) = +15.58𝑚

Solve for the latitude and departure of line 2-5 by applying the condition of a closed traverse that
the sum of latitudes and departures must be zero.

6 𝑙𝑎𝑡 = 0 +15.52 − 18.15 + 𝑙𝑎𝑡$"% = 0

𝑙𝑎𝑡$"% = −15.52 + 18.15 = +2.63

6 𝑑𝑒𝑝 = 0 +15.58 + 21.31 + 𝑑𝑒𝑝$"% = 0

𝑑𝑒𝑝$"% = −15.58 − 21.31 = −36.89

Therefore, distance of line 2-5 is:

𝑑𝑖𝑠𝑡$"% = &𝑙𝑎𝑡 $ + 𝑑𝑒𝑝$ = &2.63$ + 36.89$ = 36.98 𝑚

Area of Lot 1 (𝑨𝟏 ) can now be computed:

𝑨 = &𝒔(𝒔 − 𝒂)(𝒔 − 𝒃)(𝒔 − 𝒄) 𝒂+𝒃+𝒄

𝒔=
𝟐
𝟐𝟕. 𝟗𝟗 + 𝟐𝟏. 𝟗𝟗 + 𝟑𝟔. 𝟗𝟖
𝑺= = 𝟒𝟑. 𝟒𝟖 𝒎
𝟐

𝐴& = &43.48(43.48 − 27.99)(43.48 − 21.99)(43.48 − 36.98)

𝐴& = &43.48(15.49)(21.49)(6.5)

𝐴& = 306.72 𝑚$
 Far Eastern University
Institute of Architecture and Fine Arts

Another Solution:
𝟏
Using 𝑨 = 𝒂𝒃 𝒔𝒊𝒏∅
𝟐

Solve for the included angle

∅ = 49° 35( + 45° 07(
∅ = 94° 42( 1
𝐴 = 𝑎𝑏 𝑠𝑖𝑛∅
2
&
𝐴 = (21.99)(27.99) 𝑠𝑖𝑛 94° 42(
$

= 𝟑𝟎𝟔. 𝟕𝟐 𝒎𝟐

By cosine law, length of line 2-5 can be solved.

𝑑𝑖𝑠𝑡$"% = &(21.99)$ + (27.99)$ − 2(21.99)(27.99)(cos 94° 42( )

𝑑𝑖𝑠𝑡$"% = 36.98𝑚

LOT 3 (𝑨𝟑 )

1
Solve for the included angle 𝐴* = 𝑎𝑏 𝑠𝑖𝑛∅
2
∅ = 51° 44( + 86° 15( &
𝐴* = $ (24.01)(5.95) 𝑠𝑖𝑛 137° 59(
° (
∅ = 137 59
𝑨𝟑 = 𝟒𝟕. 𝟖𝟏 𝒎𝟐

𝑑𝑖𝑠𝑡%"* = &(24.01)$ + (5.95)$ − 2(24.01)(5.95)(cos 137° 59( )

𝑑𝑖𝑠𝑡%"* = 28.71𝑚
LOT 2 (𝑨𝟐 )

Since all sides are known, Heron’s formula can be applied

𝑨 = &𝒔(𝒔 − 𝒂)(𝒔 − 𝒃)(𝒔 − 𝒄)
𝑎+𝑏+𝑐
𝑠=
2
16.95 + 28.71 + 36.98
𝑆= = 41.32 𝑚
2
𝐴$ = &41.32(41.32 − 16.95)(41.32 − 28.71)(41.32 − 36.98)
𝐴$ = &41.32(24.37)(12.61)(4.34)

𝑨𝟐 = 𝟐𝟑𝟒. 𝟕𝟓𝒎𝟐
𝑨𝑻 = 6 𝑨 = 𝑨𝟏 + 𝑨𝟐 + 𝑨𝟑

𝑨𝑻 = 6 𝑨 = 𝟑𝟎𝟔. 𝟕𝟐 + 𝟐𝟑𝟒. 𝟕𝟓 + 𝟒𝟕. 𝟖𝟏

𝑨𝑻 = 𝟓𝟖𝟗. 𝟐𝟖 𝒎𝟐
 Far Eastern University
Institute of Architecture and Fine Arts

WEEK 15
LECTURE READING 13

AREA BY COORDINATES:

Given the adjusted latitude and departure, solve for the area of the lot by coordinates. Take note, that area can
be computed when the traverse is already balanced or adjusted.

Determine the x and y coordinates

of all the points.
 Far Eastern University
Institute of Architecture and Fine Arts

x- coordinates of all the points. (you may assume the coordinates of the first point)

𝑥! = 𝑥" + 𝑑𝑒𝑝"#! = 50 + 21.31 = 71.31

𝑥$ = 𝑥! + 𝑑𝑒𝑝!#$ = 71.31 + (−12.11) = 59.20
𝑥% = 𝑥$ + 𝑑𝑒𝑝$#% = 59.20 + (−5.94) = 53.26
𝑥& = 𝑥% + 𝑑𝑒𝑝%#& = 53.26 + (−18.84) = 34.42
𝑥" = 𝑥& + 𝑑𝑒𝑝&#" = 34.42 + 15.58 = 50.00

!" = !$ + &'($)" = 50 + (−18.41) = 31.86

!5 = !" + &'(")5 = 31.86 + (−11.86) = 20.00
!7 = !5 + &'(5)7 = 20.00 + (−0.39) = 19.61
y- coordinates
!9 = of
!7 all the7)9
+ &'( points.
= 19.61 + 14.87 = 34.48
;$ = !9 + &'(9)$ = 34.48 + 15.52 = 50.00 𝑦! = 𝑦" + 𝑙𝑎𝑡"#! = 50 + (−18.41) = 31.86
𝑦$ = 𝑦! + 𝑙𝑎𝑡!#$ = 31.86 + (−11.86) = 20.00
𝑦% = 𝑦$ + 𝑙𝑎𝑡$#% = 20.00 + (−0.39) = 19.61
𝑦& = 𝑦% + 𝑙𝑎𝑡%#& = 19.61 + 14.87 = 34.48
𝑥" = 𝑦& + 𝑙𝑎𝑡&#" = 34.48 + 15.52 = 50.00

Use the determinant form as derived in analytic geometry

𝟏 𝒙𝟏 𝒙𝟐 𝒙𝟑 𝒙𝟒 𝒙𝟓 𝒙𝟏
𝑨= < <
𝟐 𝒚𝟏 𝒚𝟐 𝒚𝟑 𝒚𝟒 𝒚𝟓 𝒚𝟏

1
𝐴= @A 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠(𝑑𝑜𝑤𝑛 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡) − A 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠(𝑢𝑝 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡M
2

A 1 = A 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠(𝑑𝑜𝑤𝑛 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡)

A 1 = 𝑥" (𝑦!)+ 𝑥! (𝑦$)+ 𝑥$ (𝑦%)+ 𝑥% (𝑦& )+ 𝑥& (𝑦" )

A 2 = A 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠(𝑢𝑝 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡)

A 2 = 𝑦" (𝑥!)+ 𝑦! (𝑥$)+ 𝑦$(𝑥% )+ 𝑦% (𝑥& )+ 𝑦&(𝑥" )

 Far Eastern University
Institute of Architecture and Fine Arts

1
𝐴 = [7,737.52 − 8,915.79]
2
1
𝐴 = [−1,178.18] NOTE: The sign of the resulting quantity is immaterial and is disregarded.
2

𝑨 = 𝟓𝟖𝟗. 𝟎𝟗 𝒎𝟐

ANOTHER SOLUTION with different assumed coordinates of the first point

Far Eastern University
Institute of Architecture and Fine Arts

1
𝐴 = [−969.48 − 208.79]
2

1
𝐴= [−1,178.27]
2 NOTE: The sign of the resulting quantity is
𝑨 = 𝟓𝟖𝟗. 𝟏𝟑𝟓 𝒎𝟐 immaterial and is disregarded.
 Far Eastern University
Institute of Architecture and Fine Arts

WEEK 15

LECTURE READING 14

When the adjusted latitudes and departures of the traverse courses are known, the DMD method
and DPD method may be conveniently applied for area computation.

AREA COMPUTATION BY DOUBLE MERIDIAN DISTANCE (DMD)

Meridian Distance – is the distance of the midpoint of the line to the reference meridian (N-S line).
This method is an adaptation of the coordinates method and is convenient to use when the latitudes and
departures of the traverse are known.

RULES in COMPUTING DMD:

Rule 1: The DMD of the first course is equal to the departure of the course
Rule 2: The DMD of any other course is equal to the DMD of the preceding course, plus the departure of the
preceding course, plus the departure of the course itself.
Rule 3: The DMD of the last course is numerically equal to the departure of that course, but with the opposite
sign.

𝑫𝒐𝒖𝒃𝒍𝒆 𝑨𝒓𝒆𝒂, 𝑫𝑨 = 𝑫𝑴𝑫(𝑳𝒂𝒕𝒊𝒕𝒖𝒅𝒆)

𝟏
𝑨= (𝜮𝑵𝑫𝑨 + 𝜮𝑺𝑫𝑨)
𝟐

PROBLEM: Determine the area of the traverse using DMD method.

 Far Eastern University
Institute of Architecture and Fine Arts

a) Compute the DMD of each course.

RULE 1. The DMD of the first line is equal to the departure of that line.

The DMD of AB is equal to the departure of line AB.

𝑫𝑴𝑫𝑨𝑩 = 𝒅𝒆𝒑𝑨𝑩 = + 𝟖. 𝟕𝟔

RULE 2. The DMD of any other line is equal to the DMD of the preceding
line, plus the departure of the preceding line, plus the departure of the
line itself.

The DMD of line BC is DMD of line AB + departure of line AB + the departure

of line BC.

𝑫𝑴𝑫𝑩𝑪 = 𝑫𝑴𝑫𝑨𝑩 + 𝒅𝒆𝒑𝑨𝑩 + 𝒅𝒆𝒑𝑩𝑪

= 𝟖. 𝟕𝟔 + 𝟖. 𝟕𝟔 + 𝟏𝟏. 𝟑𝟎 = + 𝟐𝟖. 𝟖𝟐

RULE 2. The DMD of any other line is equal to the DMD of the preceding
line, plus the departure of the preceding line, plus the departure of the
line itself.

The DMD of line CD is DMD of line BC + departure of line BC + the

departure of line CD.

𝐷𝑀𝐷$% = 𝐷𝑀𝐷&$ + 𝑑𝑒𝑝&$

+ 𝑑𝑒𝑝$%
= 28.82 + 11.30 + 13.48
= +53.6
Far Eastern University
Institute of Architecture and Fine Arts

RULE 2. The DMD of any other line is equal to the DMD of the preceding
line, plus the departure of the preceding line, plus the departure of the
line itself.

The DMD of line DE is DMD of line CD + departure of line CD + the

departure of line DE.

𝐷𝑀𝐷%' = 𝐷𝑀𝐷%$ + 𝑑𝑒𝑝$%

+ 𝑑𝑒𝑝%'
= +53.6 + 13.48 − 27.19
= +39.89

RULE 2. The DMD of any other line is equal to the DMD of the preceding
line, plus the departure of the preceding line, plus the departure of the
line itself.

The DMD of line EA is DMD of line DE + departure of line DE + the departure

of line EA.

𝐷𝑀𝐷'( = 𝐷𝑀𝐷%' + 𝑑𝑒𝑝%' + 𝑑𝑒𝑝'(

= +39.89 − 27.19 − 6.35 = +6.35

RULE 3. The DMD of the last line is numerically equal to the

departure of the line but with opposite sign.
 Far Eastern University
Institute of Architecture and Fine Arts

b) Compute the DA of each course

𝑫𝒐𝒖𝒃𝒍𝒆 𝑨𝒓𝒆𝒂, 𝑫𝑨 = 𝑫𝑴𝑫(𝑳𝒂𝒕𝒊𝒕𝒖𝒅𝒆)

𝑫𝑨𝑨𝑩 = 𝑫𝑴𝑫𝑨𝑩 (𝒍𝒂𝒕𝑨𝑩 )

= (𝟖. 𝟕𝟔)(𝟏𝟎. 𝟒𝟗) = 𝟗𝟏. 𝟖𝟗

𝑫𝑨𝑩𝑪 = 𝑫𝑴𝑫𝑩𝑪 (𝒍𝒂𝒕𝑩𝑪 )

= (𝟐𝟖. 𝟖𝟐)(−𝟏𝟐. 𝟔𝟔) = −𝟑𝟔𝟒. 𝟖𝟔

𝑫𝑨𝑪𝑫 = 𝑫𝑴𝑫𝑪𝑫 (𝒍𝒂𝒕𝑪𝑫 )

= (𝟓𝟑. 𝟔𝟎)(−𝟏𝟓. 𝟐𝟑) = −𝟖𝟏𝟔. 𝟑𝟑

𝑫𝑨𝑫𝑬 = 𝑫𝑴𝑫𝑫𝑬 (𝒍𝒂𝒕𝑫𝑬 )

= (𝟑𝟗. 𝟖𝟗)(−𝟕. 𝟎𝟓) = −𝟐𝟖𝟏. 𝟐𝟐

𝑫𝑨𝑬𝑨 = 𝑫𝑴𝑫𝑬𝑨 (𝒍𝒂𝒕𝑬𝑨 )

= (𝟔. 𝟑𝟓)(𝟐𝟒. 𝟒𝟓) = 𝟏𝟓𝟓. 𝟐𝟔

c) Compute the Area, A :

𝟏
𝐀= (𝚺𝐄𝐃𝐀 + 𝚺𝐖𝐃𝐀)
𝟐

𝜮𝑵𝑫𝑨 + 𝜮𝑺𝑫𝑨 = 𝟗𝟏. 𝟖𝟗 − 𝟑𝟔𝟒. 𝟖𝟔 − 𝟖𝟏𝟔. 𝟑𝟑 − 𝟐𝟖𝟏. 𝟐𝟐 + 𝟏𝟓𝟓. 𝟐𝟔 = −𝟏, 𝟐𝟏𝟓. 𝟐𝟔

Disregard the sign after computing the ΣDA.

Always use positive value for the area.
𝟏 𝟏
𝑨= (𝜮𝑵𝑫𝑨 + 𝜮𝑺𝑫𝑨) = (𝟏, 𝟐𝟏𝟓. 𝟐𝟔) = 𝟔𝟎𝟕. 𝟔𝟑 𝒎𝟐
𝟐 𝟐

PROBLEM: Given the following data, adjust the traverse using transit rule and compute the area by DMD.
 Far Eastern University
Institute of Architecture and Fine Arts

LECTURE READING 15

AREA COMPUTATION BY DOUBLE PARALLEL DISTANCE (DPD)

Parallel Distance – is the distance of the midpoint of the line to the reference parallel(E-W line).

The double parallel distance method of area computation is similar to the double meridian distance method.

RULES in COMPUTING DPD:

Rule 1: The DPD of the first course is equal to the latitude of the course
Rule 2: The DPD of any other course is equal to the DPD of the preceding course, plus the latitude of
the preceding course, plus the latitude of the course itself.
Rule 3: The DPD of the last course is numerically equal to the latitude of that course, but with the
opposite sign.

FORMULAS:
Double Area, DA = DPD(Departure)

𝟏
𝐀= (𝚺𝐄𝐃𝐀 + 𝚺𝐖𝐃𝐀)
𝟐

PROBLEM: Determine the area of the traverse using DPD method.

 Far Eastern University
Institute of Architecture and Fine Arts

a) Compute the DPD of each course.

RULE 1. The DPD of the first line is equal to the latitude of that
line.

The DPD of AB is equal to the latitude of line AB.

𝐷𝑃𝐷!" = 𝑙𝑎𝑡!" = +10.49

RULE 2. The DPD of any other line is equal to the DPD of the
preceding line, plus the latitude of the preceding line, plus the
latitude of the line itself.

The DPD of line BC is DPD of line AB + latitude of line AB + the latitude of

line BC.

𝑫𝑷𝑫𝑩𝑪 = 𝑫𝑷𝑫𝑨𝑩 + 𝒍𝒂𝒕𝑨𝑩 + 𝒍𝒂𝒕𝑩𝑪

= 𝟏𝟎. 𝟒𝟗 + 𝟏𝟎. 𝟒𝟗 − 𝟏𝟐. 𝟔𝟔 = + 𝟖. 𝟑𝟐

RULE 2. The DPD of any other line is equal to the DPD of the preceding
line, plus the latitude of the preceding line, plus the latitude of the line
itself.

The DPD of line CD is DPD of line BC + latitude of line BC + the

latitude of line CD.
𝐷𝑃𝐷&' = 𝐷𝑃𝐷"& + 𝑙𝑎𝑡"& + 𝑙𝑎𝑡&'

= 8.32 − 12.66 − 15.23 = −19.57

Far Eastern University
Institute of Architecture and Fine Arts

RULE 2. The DPD of any other line is equal to the DPD of the preceding line,
plus the latitude of the preceding line, plus the latitude of the line itself.

The DPD of line DE is DPD of line CD + latitude of line CD + the

latitude of line DE.

𝐷𝑃𝐷'( = 𝐷𝑃𝐷'& + 𝑙𝑎𝑡&' + 𝑙𝑎𝑡'(

= −19.57 − 15.23 − 7.05 = −41.85

RULE 2. The DPD of any other line is equal to the DPD of the preceding line,
plus the latitude of the preceding line, plus the latitude of the line itself.

The DPD of line EA is DPD of line DE + latitude of line DE +

the latitude of line EA.

𝐷𝑃𝐷(! = 𝐷𝑃𝐷'( + 𝑙𝑎𝑡'( + 𝑙𝑎𝑡(!

= −41.85 − 7.05 + 24.45 = −24.45

RULE 3. The DPD of the last line is numerically equal to the latitude
of the line but with opposite sign.
 Far Eastern University
Institute of Architecture and Fine Arts

b) Compute the DA of each course

𝑫𝒐𝒖𝒃𝒍𝒆 𝑨𝒓𝒆𝒂, 𝑫𝑨 = 𝑫𝑴𝑫(𝑳𝒂𝒕𝒊𝒕𝒖𝒅𝒆)

𝑫𝑨𝑨𝑩 = 𝑫𝑷𝑫𝑨𝑩 (𝒅𝒆𝒑𝑨𝑩 )

= (𝟏𝟎. 𝟒𝟗)(𝟖. 𝟕𝟔) = 𝟗𝟏. 𝟖𝟗

𝑫𝑨𝑩𝑪 = 𝑫𝑷𝑫𝑩𝑪 (𝒅𝒆𝒑𝑩𝑪 )

= (𝟖. 𝟑𝟐)(𝟏𝟏. 𝟑𝟎) = 𝟗𝟒. 𝟎𝟐

𝑫𝑨𝑪𝑫 = 𝑫𝑷𝑫𝑪𝑫 (𝒅𝒆𝒑𝑪𝑫 )

= (−𝟏𝟗. 𝟓𝟕)(𝟏𝟑. 𝟒𝟖) = −𝟐𝟔𝟑. 𝟖𝟎

𝑫𝑨𝑫𝑬 = 𝑫𝑷𝑫𝑫𝑬 (𝒅𝒆𝒑𝑫𝑬 )

= (−𝟒𝟏. 𝟖𝟓)(−𝟐𝟕. 𝟏𝟗) = 𝟏, 𝟏𝟑𝟕. 𝟗𝟎

𝑫𝑨𝑬𝑨 = 𝑫𝑷𝑫𝑬𝑨 (𝒅𝒆𝒑𝑬𝑨 )

= (−𝟐𝟒. 𝟒𝟓)(−𝟔. 𝟑𝟓) = 𝟏𝟓𝟓. 𝟐𝟔
c) Compute the Area, A :

𝟏
𝐀= (𝚺𝐄𝐃𝐀 + 𝚺𝐖𝐃𝐀)
𝟐

𝜮𝑬𝑫𝑨 + 𝜮𝑾𝑫𝑨 = 𝟗𝟏. 𝟖𝟗 + 𝟗𝟒. 𝟎𝟐 − 𝟐𝟔𝟑. 𝟖𝟎 + 𝟏, 𝟏𝟑𝟕. 𝟗𝟎 + 𝟏𝟓𝟓. 𝟐𝟔 = 𝟏, 𝟐𝟏𝟓. 𝟐𝟕

Disregard the sign after computing the ΣDA.

Always use positive value for the area.

𝟏 𝟏
𝑨= (𝜮𝑵𝑫𝑨 + 𝜮𝑺𝑫𝑨) = (𝟏, 𝟐𝟏𝟓. 𝟐𝟕) = 𝟔𝟎𝟕. 𝟔𝟑 𝒎𝟐
𝟐 𝟐

PROBLEM: Given the following data, adjust the traverse using transit rule and compute the area by DMD.