INTRODUCTION TO SURVEYING
BACELOR OF SCIENCE IN CIVIL ENGINEERING | 2ND YEAR
Surveying is described as the art and science of 2) Accidental Errors - are beyond the control of the
determining positions through measurements in distance, surveyor and persist even after mistakes and systematic
direction, and elevation. errors have been eliminated.
ex. In a distance measurement using a tape, the
TYPES OF SURVEYING tape man may accidentally misread a marking,
leading to a slightly incorrect measurement.
1) Plane Surveying - the horizontal distances are
considered straight. B. SOURCES OF ERRORS
2) Geodetic Surveying - the horizontal distances
considers the spheroidal shape of the Earth. 1) Instrumental Errors - result from imperfections in
the instrument.
A. TYPES OF SURVEYS 2) Natural Errors - errors arise from natural
phenomena.
1) Cadastral Surveys - focus on defining and delineating 3) Personal Errors - result from limitations in the
land ownership boundaries. observer’s senses.
2) City Surveys - involve mapping and planning within
urban areas. C. ACCURACY VS PRECISION
3) Construction Surveys - provide precise measurements
Accuracy - refers to how close a measurement is to the
and layout for construction projects.
true value.
4) Forestry Surveys - deal with mapping and assessing Precision - refers to the consistency and refinement of
forested areas. repeated measurements.
5) Hydrographic Surveys - map underwater features and
study bodies of water.
6) Industrial Surveys - applied in industrial settings for
layout and planning.
7) Mine Surveys - involve mapping and planning for
mining activities. a b c d
8) Photogrammetric Surveys - use aerial photography
for mapping and measurements. a) good precision but poor accuracy
b) good accuracy but poor precision
9) Route Surveys - plan and map transportation routes
c) good precision and good accuracy
such as roads or railways. d) poor precision and poor accuracy
10) Topographic Surveys - create detailed maps
representing the natural and man-made features of a D. THEORY OF PROBABILITY
region.
Probability measures the likelihood of occurrences.
MEASUREMENT OF DISTANCE
The Residual - also called as deviation, represents the
1) Direct Measurements - involve comparing the difference between a measured value and its most
measured quantity with a standard measuring unit. probable value.
2) Indirect Measurements - are made when it’s not Residual = MV - MPV
feasible to apply a measuring instrument directly to the
quantity being measured. Most Probable Value - or the mean. That value of a
quantity which is mathematically determined from a
Error - in surveying, is defined as the difference series of observations.
between the true value and measured value.
MPV = ∑x / n
Err = TV - MV
Relative (error) Precision - indicates the degree of
Mistakes - are inaccuracies that occur due to refinement in measurements.
carelessness, inattention, poor judjment, Weighted Observations - measurements may have
improper execution, or misunderstanding of a different degrees of reliability.
problem. The Probable Error - defines a range w/in which there
is a 50% chance that the true value of a measured
Blunders - considered as large mistakes.
quantity lies.
A. TYPES OF ERRORS
∑v 2 probable error of a
PEs = +
- 0.6745 _____
1) Systematic Errors - consistently have the same sign n - 1 single measurement
and magnitude under constant and unchanged field
conditions. It is also known as cumulative errors.
∑v 2
ex. Imagine using a measuring tape with 1 cm longer PEm = +
- 0.6745 _____ probable error of
than the standard length, as long as the tape n(n-1) the mean
remains unchanged, this systematic error will
persist in all measurements.
, EXAMPLE SURVEYING INSTRUMENTS
A quantity was measured ten times with the following
results; 34.630, 34.626, 34.634, 34.628, 34.629, A. Basic Tools
34.626, 34.627, 34.633, 34.625, and 34.624 meters. 1. Tape Measure - measures distances on the ground.
Determine the most probable value, the residual of each 2. Compass - determines direction.
measurement, the probable error of single measurement, B. Modern Instruments
the probable error of the mean and the relative 1. Total Station - electronic device combining
precision of the mean. theodolite and distance measuring capabilities.
2. Global Positioning System (GPS) - satellite-based
system for accurate positioning.
SOLUTION: 3. Theodolite - measures horizontal and vertical
angles.
Let x = measured length
v = residual C. Leveling Instruments
RP = relative precision of the mean 1. Level and Rod - measures height differences.
2. Automatic Level - self-leveling instrument for
precise leveling.
MPV = ∑x / n
= ( 34.630 + 34.626 + 34.634 + 34.628 + 34.629
+ 34.626 + 34.627 + 34.633 + 34.625 + 34.624) / 10
= 346.
MPV = 34.6282 m
v = x - MPV
= 34.630 - 34.6282 = 0.0018
= 34.626 - 34.6282 = -0.0022
= 34.634 - 34.6282 = 0.0058
= 34.628 - 34.6282 = -0.0002
= 34.629 - 34.6282 = 0.0008
= 34.626 - 34.6282 = -0.0022
= 34.627 - 34.6282 = -0.0012
= 34.633 - 34.6282 = 0.0048
APPLICATIONS IN CIVIL ENGINEERING
= 34.625 - 34.6282 = -0.0032
= 34.624 - 34.6282 = -0.0042
A. Site Planning and Design
1. Utilizing survey data for optimal project layout.
Solving for the summation of the square of the residual, 2. Minimizing environmental impact and maximizing
efficiency.
∑v² = (0.0018)² + (-0.0022)² + (0.0058)² + (-0.0002)² +
(0.0008)² + (-0.0022)² + (-0.0012)² + (0.0048)² B. Construction and Infrastructure
+ (-0.0032)² + (-0.0042)² 1. Setting out precise locations for structures.
∑v² = 0.0000996 2. Monitoring construction progress and quality.
C. Environmental Monitoring
1. Assessing and managing natural resources.
∑v 2
_____
PEs = +
- 0.6745 2. Mitigating the impact of engineering projects
n-1 on the environment.
0.0000996
= +
- 0.6745 _________ A. PURPOSE
10 - 1
+ 1. To create accurate maps and plans.
PEs = - 0. 0022438 m
2. To establish boundaries for construction projects.
3. To measure and monitor land changes over time.
+ ∑v 2
_____
PEm = - 0.6745
n(n-1)
ETHICAL CONCERNS IN SURVEYING
0.0000996
= +
- 0.6745 _________ A. Professional Integrity:
10(10 - 1) 1. Adhering to ethical standards in data collection.
PEm = +
0. 0007092 m 2. Avoiding misrepresentation of survey results.
-
B. Privacy Concerns:
1. Respecting individuals' privacy rights.
PE m
RPm = _____ 2. Proper handling of sensitive information.
MPV
C. Environmental Impact:
0.0007092 m/ 1. Minimizing the impact of surveying activities on
= ____________
34.6282 m
/ the environment.
1 2. Implementing sustainable surveying practices.
= ________
48 827 D. Informed Consent:
1. Obtaining consent from property owners or
1
RPm = ________ individuals affected by surveys.
49 000 2. Ensuring transparency in surveying processes.
BACELOR OF SCIENCE IN CIVIL ENGINEERING | 2ND YEAR
Surveying is described as the art and science of 2) Accidental Errors - are beyond the control of the
determining positions through measurements in distance, surveyor and persist even after mistakes and systematic
direction, and elevation. errors have been eliminated.
ex. In a distance measurement using a tape, the
TYPES OF SURVEYING tape man may accidentally misread a marking,
leading to a slightly incorrect measurement.
1) Plane Surveying - the horizontal distances are
considered straight. B. SOURCES OF ERRORS
2) Geodetic Surveying - the horizontal distances
considers the spheroidal shape of the Earth. 1) Instrumental Errors - result from imperfections in
the instrument.
A. TYPES OF SURVEYS 2) Natural Errors - errors arise from natural
phenomena.
1) Cadastral Surveys - focus on defining and delineating 3) Personal Errors - result from limitations in the
land ownership boundaries. observer’s senses.
2) City Surveys - involve mapping and planning within
urban areas. C. ACCURACY VS PRECISION
3) Construction Surveys - provide precise measurements
Accuracy - refers to how close a measurement is to the
and layout for construction projects.
true value.
4) Forestry Surveys - deal with mapping and assessing Precision - refers to the consistency and refinement of
forested areas. repeated measurements.
5) Hydrographic Surveys - map underwater features and
study bodies of water.
6) Industrial Surveys - applied in industrial settings for
layout and planning.
7) Mine Surveys - involve mapping and planning for
mining activities. a b c d
8) Photogrammetric Surveys - use aerial photography
for mapping and measurements. a) good precision but poor accuracy
b) good accuracy but poor precision
9) Route Surveys - plan and map transportation routes
c) good precision and good accuracy
such as roads or railways. d) poor precision and poor accuracy
10) Topographic Surveys - create detailed maps
representing the natural and man-made features of a D. THEORY OF PROBABILITY
region.
Probability measures the likelihood of occurrences.
MEASUREMENT OF DISTANCE
The Residual - also called as deviation, represents the
1) Direct Measurements - involve comparing the difference between a measured value and its most
measured quantity with a standard measuring unit. probable value.
2) Indirect Measurements - are made when it’s not Residual = MV - MPV
feasible to apply a measuring instrument directly to the
quantity being measured. Most Probable Value - or the mean. That value of a
quantity which is mathematically determined from a
Error - in surveying, is defined as the difference series of observations.
between the true value and measured value.
MPV = ∑x / n
Err = TV - MV
Relative (error) Precision - indicates the degree of
Mistakes - are inaccuracies that occur due to refinement in measurements.
carelessness, inattention, poor judjment, Weighted Observations - measurements may have
improper execution, or misunderstanding of a different degrees of reliability.
problem. The Probable Error - defines a range w/in which there
is a 50% chance that the true value of a measured
Blunders - considered as large mistakes.
quantity lies.
A. TYPES OF ERRORS
∑v 2 probable error of a
PEs = +
- 0.6745 _____
1) Systematic Errors - consistently have the same sign n - 1 single measurement
and magnitude under constant and unchanged field
conditions. It is also known as cumulative errors.
∑v 2
ex. Imagine using a measuring tape with 1 cm longer PEm = +
- 0.6745 _____ probable error of
than the standard length, as long as the tape n(n-1) the mean
remains unchanged, this systematic error will
persist in all measurements.
, EXAMPLE SURVEYING INSTRUMENTS
A quantity was measured ten times with the following
results; 34.630, 34.626, 34.634, 34.628, 34.629, A. Basic Tools
34.626, 34.627, 34.633, 34.625, and 34.624 meters. 1. Tape Measure - measures distances on the ground.
Determine the most probable value, the residual of each 2. Compass - determines direction.
measurement, the probable error of single measurement, B. Modern Instruments
the probable error of the mean and the relative 1. Total Station - electronic device combining
precision of the mean. theodolite and distance measuring capabilities.
2. Global Positioning System (GPS) - satellite-based
system for accurate positioning.
SOLUTION: 3. Theodolite - measures horizontal and vertical
angles.
Let x = measured length
v = residual C. Leveling Instruments
RP = relative precision of the mean 1. Level and Rod - measures height differences.
2. Automatic Level - self-leveling instrument for
precise leveling.
MPV = ∑x / n
= ( 34.630 + 34.626 + 34.634 + 34.628 + 34.629
+ 34.626 + 34.627 + 34.633 + 34.625 + 34.624) / 10
= 346.
MPV = 34.6282 m
v = x - MPV
= 34.630 - 34.6282 = 0.0018
= 34.626 - 34.6282 = -0.0022
= 34.634 - 34.6282 = 0.0058
= 34.628 - 34.6282 = -0.0002
= 34.629 - 34.6282 = 0.0008
= 34.626 - 34.6282 = -0.0022
= 34.627 - 34.6282 = -0.0012
= 34.633 - 34.6282 = 0.0048
APPLICATIONS IN CIVIL ENGINEERING
= 34.625 - 34.6282 = -0.0032
= 34.624 - 34.6282 = -0.0042
A. Site Planning and Design
1. Utilizing survey data for optimal project layout.
Solving for the summation of the square of the residual, 2. Minimizing environmental impact and maximizing
efficiency.
∑v² = (0.0018)² + (-0.0022)² + (0.0058)² + (-0.0002)² +
(0.0008)² + (-0.0022)² + (-0.0012)² + (0.0048)² B. Construction and Infrastructure
+ (-0.0032)² + (-0.0042)² 1. Setting out precise locations for structures.
∑v² = 0.0000996 2. Monitoring construction progress and quality.
C. Environmental Monitoring
1. Assessing and managing natural resources.
∑v 2
_____
PEs = +
- 0.6745 2. Mitigating the impact of engineering projects
n-1 on the environment.
0.0000996
= +
- 0.6745 _________ A. PURPOSE
10 - 1
+ 1. To create accurate maps and plans.
PEs = - 0. 0022438 m
2. To establish boundaries for construction projects.
3. To measure and monitor land changes over time.
+ ∑v 2
_____
PEm = - 0.6745
n(n-1)
ETHICAL CONCERNS IN SURVEYING
0.0000996
= +
- 0.6745 _________ A. Professional Integrity:
10(10 - 1) 1. Adhering to ethical standards in data collection.
PEm = +
0. 0007092 m 2. Avoiding misrepresentation of survey results.
-
B. Privacy Concerns:
1. Respecting individuals' privacy rights.
PE m
RPm = _____ 2. Proper handling of sensitive information.
MPV
C. Environmental Impact:
0.0007092 m/ 1. Minimizing the impact of surveying activities on
= ____________
34.6282 m
/ the environment.
1 2. Implementing sustainable surveying practices.
= ________
48 827 D. Informed Consent:
1. Obtaining consent from property owners or
1
RPm = ________ individuals affected by surveys.
49 000 2. Ensuring transparency in surveying processes.
