CIVL 335 Surveying
Chapter 1
Part 1 - Introduction to Surveying
Mwafag Ghanma, Ph.D.
Geomatics Engineering
Chapter 1
Part 1 - Introduction to
Surveying
Definition for Surveying
In short, SURVEYING:
• Science, art, and technology of determining the
relative positions of points above, on, or
beneath the earth’s surface.
• A discipline which includes all methods for
measuring and collecting information about the
physical earth and our environment, processing
that information, and distributing a variety of
resulting products to a wide range of clients.
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What do we do in SURVEYING?
• Earth measurements:
• Distances: horizontal, slope, and vertical
• Angles: horizontal, vertical, and zenith
• Determination of relative position of points
located on, above or below the Earth’s surface:
• Determination of the position is achieved by
mathematical processing of the field measurements
• Final output is positional information:
• Maps: digital or paper
• Coordinates
• Features
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Why Surveying is Important to CE
• The planning and design of all Civil Engineering
projects such as construction of highways,
bridges, tunnels, dams etc. are based upon
surveying measurements.
• Moreover, during execution, project of any
magnitude is constructed along the lines and
points established by surveying.
• Thus, surveying is a basic requirement for all
Civil Engineering projects.
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Why Surveying is Important to CE
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Types of Surveying
• Land, Boundary and Cadastral Surveying
Deals with demarcating and mapping property boundaries and rights of land
• Construction and Route Surveying
Are surveying works for planning, design, implementation, and monitoring of construction
projects such as roads, buildings, bridges, communication and infrastructure networks, etc.
• Quantity Surveying
Field works and computations related to determination of project quantities such as earth works
(cut and fill), building materials, etc.
• Plane Surveying
(our course)
Surveying suitable for projects occupying small areas i.e., where earth curvature can be (and is)
ignored or neglected.
• Geodetic Surveying
Part of geodesy (study and representation of size and shape of the earth). This surveying deals
with projects occupying large areas i.e., earth curvature is considered.
• Topographic Surveying
Deals with determining locations and elevations of natural and artificial features on the ground.
This surveying is for making maps.
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Course Organization and Contents
• Basics of Surveying
•
•
•
•
Arithmetic and Measurements: percentages, ratio and proportion.
Geometry: angles types, polygons, triangles, circles.
Angles in surveying: bearing and azimuth of a line.
Theory of Errors: definitions, types and sources of errors, measures of
precision.
• Measurements and Field Practice
• Distance measurement (slope, horizontal and vertical) using tapes,
electronic distance measurement instruments, and leveling and errors in
such measurements.
• Direction and angle measurement using theodolites and total stations.
• Applications
• Topographic Surveying and Mapping: Contour lines and their
characteristics, construction of contour maps, interpreting contour maps.
• Traversing: uses, open and closed traverses, latitudes and departures,
errors of closure and corrections.
• Areas and Volumes: area of traverse, profile, cross-section using different
methods, volumes of earthworks using grids or contour maps.
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Lecture Notes Table of Contents
Chapter 1: Part 1 - Introduction to Surveying
Chapter 1: Part 2 - Basic Surveying Math
Chapter 2: Basics of Surveying
Chapter 3: Distance Measurement
Quiz 1 (15%)
Chapter 4: Leveling
Midterm (20%)
Chapter 5: Leveling Applications: Profiles and Cross-Sections
Chapter 6: Leveling Applications: Contouring
Quiz 2 (15%)
Chapter 7: Control Surveying Applications: Traversing
Chapter 8: Surveying Applications: Areas and Volumes
Final (30%)
Fieldwork & Reports = 15% + Lab Final Exam = 5%
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Lecture Notes
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Textbook and References
Any other book in surveying will do!
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Chapter 1
Part 2 - Basic Surveying
Math
Subjects
• Percentages
• The Pythagorean Theorem
• Ratio and proportion
• Types of Angles
• Polygons
• Triangles
• Rectangles and squares
• Trapezoids
• Circles and length of arc
• Perimeter
• Solution of oblique triangles
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Percentages
The word "percent" comes from a Latin word meaning by the hundred. The symbol
"%" is used for the word percent. A numerator in a fraction having 100 as a
denominator expresses a percent.
Examples:
1. Convert fraction or decimals to percent
0.005 = 5/1000= 5/1000x100% = 0.5%
2. Convert percent to fraction or decimals
a. 0.7% = 0.7/100 =7/1000= 0.007
b. 150% = 150/100 = 1.50
More examples
a.
1% of 7823 =7823x(1/100)= 78.23
b.
68% of 300 =300x(68/100)= 204
c.
15 is what percent of 750?
d.
If 30 is 75% of some number Y, to find Y solve 30 = (75/100)  Y; Y = 40
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(15/750)x100% = 2%
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Ratio and Proportion
• A ratio is a comparison of two values or quantities.
Formats:
• The ratio of 2 to 5,
• 2:5
• 2 ÷ 5, or
• 2 / 5,
are all expressions of the same ratio.
• In surveying applications ratios are expressed in the form of:
•
•
•
•
1 to x
1:x
1 ÷ x, or
1/x
• A proportion is a statement of equality between two ratios.
The same proportion can be expressed as 2:5 = 4:10,
2 ÷ 5 = 4 ÷ 10, or 2/5 = 4/10.
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Types of Angles
Acute Angle
Complementary Angles
Alternate Interior Angles
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Obtuse Angle
Straight Angle
Supplementary Angles
Alternate Exterior Angles
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Types of Angles
What is this angle called?
?
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Types of Angles
Name the pointed angles.
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Polygons
• A closed figure bounded by straight lines lying in the
same plane is known as a polygon.
• The sum of the interior angles of a closed polygon is
equal to:
(n - 2) (180)
n is the number of sides.
Examples
• sum of the interior angles of a triangle is 180°,
• of a rectangle 360°,
• of a five-sided figure 540°, and so on.
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Polygons
• The sum of the interior angles = (n - 2) (180) with n is
the number of sides (nodes).
• Derive a similar formula for the sum of exterior angles
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Polygons
+
(n-2)*180
+
=
X
=
n*2*180
X = n*2*180 - (n-2)*180
X = (2n – n + 2) * 180
X = (n + 2) * 180
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Polygons
Common polygons
Polygon
Number of Sum of interior
sides
angles (n - 2) x 180°
If regular, size of EACH
interior angle, ° ‘ “
Sum of exterior If regular, size of each
angles (n + 2) x 180° exterior angle, ° ‘ “
Triangle
3
180°
60° 0' 0"
900°
300° 0' 0"
Square
4
360°
90° 0' 0"
1080°
270° 0' 0"
Pentagon
5
540°
108° 0' 0"
1260°
252° 0' 0"
Hexagon
6
720°
120° 0' 0"
1440°
240° 0' 0"
Heptagon
7
900°
128° 34' 17.14"
1620°
231° 25' 42.86"
Octagon
8
1080°
135° 0' 0"
1800°
225° 0' 0"
Nonagon
9
1260°
140° 0' 0"
1980°
220° 0' 0"
Decagon
10
1440°
144° 0' 0"
2160°
216° 0' 0"
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Triangles (smallest polygon)
Right Triangle
Isosceles triangle
Equilateral triangle
Oblique triangle (Scalene)
Similar triangles (same shape, but different sizes)
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Triangles
Exercise:
Find the measure of angle x
T/F: If a triangle is equilateral, then it is isosceles.
T/F: If a triangle is isosceles, then it is also equilateral.
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Triangles
Exercise:
Which of the following triangles are always similar?
Right Triangle
Isosceles triangle
Equilateral triangle
Exercise:
The sides of a triangle are 5, 6 and 10. Find the length of the
longest side of a similar triangle whose shortest side is 15.
T/F:
Similar triangles are exactly the same shape and size?
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Solution to Right Triangles
The Pythagorean Theorem
In a right triangle, the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
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Solution of Oblique Triangles
• Any triangle has six parts: 3 angles, and 3 sides
• An oblique triangle can be solved if three of its parts, at least one of
which is a side, are known.
• Oblique triangles can be solved by the use of formulas of law of sines
or law of cosines
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Solution of Oblique Triangles
General Cases:
• SSS - Side, Side, Side:
1. Law of Cosines → Find any angle
2. Law of cosines or law of sines → Find
another angle
3. Law of cosines or law of sines or
summation of angles → Find the last
angle
• SAS - Side, Angle, Side
1. Law of Cosines → Find the third side
2. Law of cosines or law of sines → Find
one unknown angle
3. Law of cosines or law of sines or
summation of angles → Find the last
angle
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Solution of Oblique Triangles
General Cases:
• ASA - Angle, Side, Angle:
1. Summation of angles → Find the third
angle
2. Law of sines → Find another side
3. Law of cosines or law of sines → Find
the last side
• SAA = AAS - Angle, Angle, Side
1. Summation of angles → Find the third
angle
2. Law of sines → Find the 2nd side
3. Law of cosines or law of sines → Find
the last side
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Solution of Oblique Triangles
• ASS or SSA - Side, Side, Angle:
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Solution of Oblique Triangles
Example
Solve for the unknowns: A, a, b.
This is a SAA or AAS case
Start with summation of angles
A = 180-(83 + 61) = 36
Continue with the law of sines
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Solution of Oblique Triangles
Example
Solve for the unknown side and two angles.
This is a SAS case
Start with the law of cosines then continue with the law of sines
MN = 60 2 + 50 2 − 2  60  50  cos120 
= 3600 + 2500 − 6000  0.50 = 95m
50  sin 120 
sin M =
= 0.45580
95
M = 27 
60  sin 120 
sin N =
= 0.54696
95
N = 33 
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Solution of Oblique Triangles
Example
Solve triangle ABC with sides a = 3.0, b = 5.0, and c = 6.0
This is an SSS case
Start with the Law of Cosines and continue with either with law of
cosines or law of sines.
5 .0 2 + 6 . 0 2 − 3 .0 2
cos A =
2  5 . 0  6. 0
25 + 36 − 9
=
60
A = 30 
3.0 2 + 6.0 2 − 5.0 2
cos B =
2  3.0  6.0
9 + 36 − 25
=
36
B = 56 
3.0 2 + 5.0 2 − 6.0 2
cosC =
2  3.0  5.0
9 + 25 − 36
=
= −0.067
30
C = 94 
The negative value of cos C indicates that the angle is greater than 90°
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Solution of Oblique Triangles
Example
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Solution of Oblique Triangles
Example
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Solution of Oblique Triangles
Example
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Solution of Oblique Triangles
Example
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Solution of Oblique Triangles
Example
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Solution of Oblique Triangles
Example
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Rectangles and Squares
A rectangle is a four-sided polygon whose angles are right angles. A
square is a rectangle whose sides are equal.
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Trapezoids
A trapezoid is a four-sided polygon that has two parallel sides and two
nonparallel sides.
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Parallelograms and Rhombi
A parallelogram is a four-sided polygon with pairs of parallel sides. A
rhombus (plural – rhombi) is its special case with all sides equal
(equilateral).
Parallelogram
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Rhombus
Rhombus
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Circles
A circle is a closed plane curve, all points on which are equidistant from
a point within called the center.
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Length of an Arc
The length of an arc (L) of a circle is proportional to its central angle
(). A central angle of 90 (one-fourth of 360°) subtends an arc that is
one-fourth the circumference in length.
L=r
 is in radians here.
Example
Find the length of an arc of a 100 m circle that has a central angle of
36°.
Arc Length =
Surveying for Engineers – Dr. Mwafag Ghanma
36   100   100 
=
= 31.42m
360 
10
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Perimeter
It is a path that surrounds a two-dimensional shape.
The sum of the lengths of the sides of a polygon is called the perimeter of
the polygon.
Perimeter = 2L + 2W
Perimeter = 4S
Perimeter = a + b + c
Example
Triangle
Hypotenuse = 2.25 2 + 6.15 2 = 42.885 = 6.55cm
Perimeter = 2.25 + 6.15 + 6.55 = 14.95 cm
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Circumference
It is the perimeter of a circle or an ellipse.
The sum of the lengths of the sides of a polygon is called the perimeter
of the polygon.
Circumference = 2r
Approximation 1
Approximation 2
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Straight Line Equation
Equation of the line is 𝒚 = 𝒃 + 𝒎𝒙
b is the y-intercept
m is the slope of the line
𝒎=
∆ 𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍
∆ 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
=
∆𝒚
∆𝒙
Example
Find the equation of a straight line that goes through two
coordinates (-1, 5) and (5, -1).
Solution
−𝟏−𝟓
m = 𝟓−−𝟏 = −𝟏
b = 𝒚𝟏 − 𝒎𝒙𝟏 = 𝑦𝟐 − 𝒎𝑥𝟐 = −𝟏 − (−𝟏) × 𝟓 = 𝟒
The equation is 𝒚 = 𝟒 − 𝒙
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