Field Geology

&
Geological Survey
 Field Geology & Plane Surveying Chapter One

Chapter One

1. Introduction
Surveying can be regarded as that discipline that encompasses all
methods for measuring and collecting information about the physical
Earth and our environment, processing that information, and
disseminating a variety of resulting products to a wide range of clients.
Surveying has been important since the beginning of civilization.
However, engineering works such as buildings, bridges, roads, pipelines
and tunnels require very precise dimensional control during their
construction. Buildings must be vertical, long tunnels must end at the
correct place, and foundations must often be constructed in advance to
accommodate prefabricated structural sections. To achieve this,
surveying work is required to determine the relative positions of fixed
points to high accuracy, and also to establish physical markers at (or very
close to) predetermined locations.
Its earliest applications were in measuring and marking boundaries of
property ownership. Throughout the years its importance has steadily
increased with the growing demand for a variety of maps and other
spatially related types of information, and with the expanding need for
establishing accurate line and grade to guide construction operations.

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2. Definition
Survey defined as the science, art, and technology of determining the
relative positions of points above, on, or beneath the Earth’s surface, or
of establishing such points.
Also, surveying may be defined as the science of determining the
position, in three dimensions, of natural and man-made features on or
beneath the surface of the Earth. These features may be represented in
analogue form as a contoured map, plan or chart, or in digital form such
as a digital ground model (DGM).

3. History of Surveying
It is recorded that the oldest historical records in existence today that
bear directly on the subject of surveying state that this science began in
Egypt. They use the cubit, palm and finger for measurements. The cubit
length was the essential distance measurements. Herodotus recorded
that Sesostris (about 1400 b.c.) divided the land of Egypt into plots for
the purpose of taxation. Annual floods of the Nile River swept away
portions of these plots, and surveyors were appointed to replace the
boundaries. These early surveyors were called rope-stretchers, since
their measurements were made with ropes having markers at unit
distances.

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Ancient Egyptian Units

Cubit = 52.4 cm
Palm = 7.48 cm
Finger = 1.87 cm

As a consequence of this work, early Greek thinkers developed the

science of geometry. Their advance, however, was chiefly along the lines
of pure science. Heron stands out prominently for applying science to
surveying in about 120 b.c. He was the author of several important
treatises of interest to surveyors, including The Dioptra, which related
the methods of surveying a field, drawing a plan, and making related
calculations.

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Figure 1: Historical surveying instruments: (a) the diopter and (b) the groma.

4. Classification of Surveys

Surveys are conducted for many different purposes, which will

determine the types of instruments which are used, the measurements
which are taken, and the subsequent processing of those measurements
to produce the required results. It is useful to know the names of the
principal types of surveys, and the nature of the work which is involved.

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4.1. Classification by Purpose

4.1.1. Geodetic
To determine the shape of the earth, or to provide an accurate
framework for a big survey, whose size means that the curvature of the
earth must be taken into account.

4.1.2. Topographic
To produce ordinary medium-scale maps for publication and general use.
Topographic surveys record all the features of the landscape which can
be shown on the scale of the map. Topographic maps are usually
produced by means of aerial or satellite photogrammetry.

4.1.3. Cadastral
To establish and record the boundaries of property or territory. Cadastral
surveys are concerned only with those features of the landscape which
are relevant to such boundaries.

4.1.4. Engineering
To choose locations for, and then set out markers for, engineering
construction works. Engineering surveys are concerned only with the
features relevant to the task in hand, and usually have two phases.

The first phase typically involves collecting an amount of topographic

information, to allow the project to be planned in detail. When the
planning is complete;

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The second phase consists of setting out the necessary markers for
earthmoving and construction to begin.

4.2. Classification by the Type of Measurements Taken

4.2.1. Triangulation
Finding the size and shape of a network of triangles by measuring their
angles and (since about 1980) the lengths of their sides. Used in
conventional surveying when each station can see three or more other
stations.

4.2.2. Traverse
Proceeding from one point to another by ‘dead reckoning’, using
measured distances and angles to calculate bearings. Used when the
construction work is long and narrow, such as a motorway or tunnel.

4.2.3. Resectioning
Establishing the precise position of a single station by measuring
distances and angles to a number of other nearby stations whose
positions are already known.

4.2.4. DGNSS (differential GNSS)

Measuring the relative three-dimensional (3-D) positions of two stations
by simultaneously recording satellite observations at each one, and
comparing the results.

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4.3. Classification by the Equipment Used

4.3.1. Tape
For direct linear measurement. Cheap and robust. Still occasionally used
for small detailed surveys, but now largely supplanted by
electromagnetic distance measurement devices.

4.3.2. Compass
To observe bearings. Used mainly in preliminary reconnaissance.

4.3.3. Theodolite
A telescopic sight pivoted horizontally and vertically, with two graduated
protractors (called ‘circles’) for measuring angles.

4.3.4. Electromagnetic distance measurement (EDM)

Devices—typically used for measurements of lengths from, say, 5 m to 5
km, though some instruments have ranges up to about 25 km.

4.3.5. Total station

Essentially a theodolite with a built-in EDM. Total stations usually have
facilities for recording and processing measurements electronically, and
have largely replaced conventional theodolites.

4.3.6. LiDAR
Acronym which stands for light detection and ranging, and refers to a
class of surveying instruments which can measure distances and angles
to solid surfaces to a reasonable accuracy at a very high rate.

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4.4. Geodetic and Plane Surveys

Two general classifications of surveys are geodetic and plane. They differ
principally in the assumptions on which the computations are based,
although field measurements for geodetic surveys are usually performed
to a higher order of accuracy than those for plane surveys.

In geodetic surveying, the curved surface of the Earth is considered by

performing the computations on an ellipsoid (curved surface
approximating the size and shape of the Earth.

In plane surveying, except for leveling, the reference base for fieldwork
and computations is assumed to be a flat horizontal surface. The
direction of a plumb line (and thus gravity) is considered parallel
throughout the survey region, and all observed angles are presumed to
be plane angles. For areas of limited size, the surface of our vast ellipsoid
is actually nearly flat.

5. Importance of Surveying

Surveying is one of the world’s oldest and most important arts because,
as noted previously, from the earliest times it has been necessary to
mark boundaries and divide land. Surveying has now become
indispensable to our modern way of life. The results of today’s surveys
are used to;

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• Map the Earth above and below sea level;

• Prepare navigational charts for use in the air, on land, and at sea;
• Establish property boundaries of private and public lands;
• Develop data banks of land-use and natural resource information;
• Determine facts on the size, shape, gravity, and magnetic fields of
the earth;
• Prepare charts of our moon and planets.
6. Units and Significant Figures
Five types of observations, illustrated in Figure 2.1, form the basis of
traditional plane surveying: (1) horizontal angles, (2) horizontal
distances, (3) vertical (or zenith) angles, (4) vertical distances, and (5)
slope distances.

In the (figure, 2), OAB and ECD are horizontal planes, and OACE and ABDC
are vertical planes. Then as illustrated, horizontal angles, such as angle
AOB, and horizontal distances, OA and OB, are measured in horizontal
planes; vertical angles, such as AOC, are measured in vertical planes;
zenith angles, such as EOC, are also measured in vertical planes; vertical
lines, such as AC and BD, are measured vertically (in the direction of
gravity); and slope distances, such as OC, are determined along inclined
planes.

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Figure 2: Kinds of measurements in surveying.

6.1. Units of Measurements

Magnitudes of measurements (or of values derived from observations)
must be given in terms of specific units. In surveying, the most commonly
employed units are for length, area, volume, and angle. Two different
systems are in use for specifying units of observed quantities, the English
and metric systems. Because of its widespread adoption, the metric
system is called the International System of Units, abbreviated SI.

Because the English system has long been the officially adopted standard
for measurements in the United States, except for geodetic surveys, the

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linear units of feet and decimals of a foot are most commonly used by
surveyors.

6.1.1. Length units

1 m = 10 Decimeter = 100 centimeter = 1000 millimeter
1 kilometer = 10 Hectometer = 1000 meter
Inch = 2.54 Centimeter = 25.4 millimeter
Feet = 12 Inch = 30.48 Centimeter
6.1.2. Area units
1 m2 = 106 mm2
104 m2 = 1 hectare (ha)
106 m2 = 1 square kilometre (km2)
6.1.3. Volume units
For volumes, litter, m3 and mm3
7. Errors in Survey
All the results of surveying are based on measurements, and all
measurements are subject to errors. Because surveying involves high
degrees of accuracy (most surveying measurements are accurate to
within 10 parts per million and some are within 1 or 2 parts per million),
it is relatively easy to make significant errors, and relatively hard to
detect them.

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7.1. Types of Errors

Surveying errors fall into three categories:

7.1.1. Gross errors

Gross errors are due to mistakes or carelessness, such as misreading by
a meter or a degree. A proper routine of checks should detect them. A
surprisingly common source of error is the manual transcription of
readings from one place to another.

7.1.2. Systematic errors

Systematic errors are cumulative and due to some persistent cause—
generally in an instrument, but sometimes in a habit of the observer.
They can be reduced by better technique but not by averaging many
readings, as they are not governed by the laws of probability. Thus all
distances measured with an inaccurate tape or electromagnetic distance
measurement (EDM) device will, from that cause, have the same
percentage or absolute error, whatever their lengths and however many
times they are measured; the only remedy is to calibrate the device more
carefully.

7.1.3. Random errors

Random errors are due to a number of small causes beyond the control
of the observer. Their magnitude depends on the quality of the

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instrument used and on the skill of the observer, but they cannot be
corrected.
8. Source of Errors

All leveling measurements are subject to three sources of error: (1)

instrumental, (2) natural, and (3) personal. However, all measurements,
no matter how carefully executed, will contain error, and so the true
value of a measurement is never known. These are summarized in the
subsections that follow.

• Natural errors caused by variation in or adverse weather

conditions, refraction, unmodelled gravity effects, etc.
• Instrumental errors caused by imperfect construction and
adjustment of the surveying instruments used.
• Personal errors caused by the inability of the individual to make
exact observations due to the limitations of human sight, touch and
hearing.

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Field Geology & Geological Survey Chapter Two

Chapter Two

Measuring Distance

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 Field Geology & Geological Survey Chapter Two

1. Introduction

Distance measurement is generally regarded as the most fundamental of all

surveying observations. In traditional ground surveys, even though many
angles may be read, the length of at least one line must be measured to
supplement the angles in locating points. In plane surveying, the distance
between two points means the horizontal distance. If the points are at
different elevations, the distance is the horizontal length between vertical
lines at the points.

2. Distance Measurements

In surveying, linear measurements have been obtained by many different

methods. These include (1) pacing, (2) odometer readings, (3) optical
rangefinders, (4) tacheometry (stadia), (5) subtense bars, (6) taping, (7)
electronic distance measurement (EDM).

2.1. Pacing
Distances obtained by pacing are sufficiently accurate for many purposes in
surveying, engineering, geology, agriculture, forestry, and military field
sketching. Pacing is also used to detect blunders that may occur in making
distance observations by more accurate methods.

Pacing consists of counting the number of steps, or paces, in a required

distance. The length of an individual’s pace must be determined first. This

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is best done by walking with natural steps back and forth over a level course
at least 300 ft long, and dividing the known distance by the average number
of steps.

2.2. Odometer
An odometer converts the number of revolutions of a wheel of known
circumference to a distance. Lengths measured by an odometer on a vehicle
are suitable for some preliminary surveys in route-location work. They also
serve as rough checks on observations made by other methods. Other types
of measuring wheels are available and useful for determining short
distances, particularly on curved lines. Odometers give surface distances,
which should be corrected to horizontal if the ground slopes.

2.3. Tacheometry (stadia)

Tacheometry (stadia is the more common term in the United States) is a
surveying method used to quickly determine the horizontal distance to, and
elevation of, a point. stadia observations are obtained by sighting through
a telescope equipped with two or more horizontal cross wires at a known
spacing. The apparent intercepted length between the top and bottom

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wires is read on a graduated rod held vertically at the desired point. The
distance from telescope to rod is found by proportional relationships in
similar triangles.

2.4. Subtense bars

The distance-measuring procedure involves using a theodolite to read the
horizontal angle subtended by two targets precisely spaced at a fixed
distance apart on a subtense bar. The unknown distance is computed from
the known target spacing and the measured horizontal angle. Prior to
observing the angle from one end of the line, the bar is centered over the
point at the other end of the line, and oriented perpendicular to the line
and in a horizontal plane.

2.5. Taping
Tapes come in a variety of lengths and materials. For engineering work the
lengths are generally 10 m, 30 m, 50 m and 100 m. Linen or glass fibre tapes
may be used for general use, where precision is not a prime consideration.
The linen tapes are made from high quality linen, combined with metal
fibres to increase their strength. They are sometimes encased in plastic
boxes with recessed handles. These tapes are often graduated in 5-mm
intervals only.

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More precise versions of the above tapes are made of steel and graduated
in millimetres. For high-accuracy work, steel bands mounted in an open
frame are used. They are standardized so that they measure their nominal
length at a designated temperature usually 20◦C and at a designated
applied tension usually between 50 N to 80 N. This information is clearly
printed on the zero end of the tape.

For the most precise work, invar tapes made from 35% nickel and 65% steel
are available. The singular advantage of such tapes is that they have a
negligible coefficient of expansion compared with steel, and hence
temperature variations are not critical. Their disadvantages are that the
metal is soft and weak, whilst the price is more than ten times that of steel
tapes.

2.5.1. Tapping Accessories

Chaining pins or taping pins are used to mark tape lengths. Most taping pins
are made of number 12 steel wire, sharply pointed at one end, have a round
loop at the other end, and are painted with alternate red and white bands.

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Range poles (lining rods) made of wood, steel, or aluminum are about 1 in.
thick and 6 to 10 ft long. They are round or hexagonal in cross section and
marked with alternate 1-ft long red and white bands that can be used for
rough measurements

Plumb bobs for taping [see Figure 6.1(f)] should weigh a minimum of 8 oz
and have a fine point. However, most surveyors use 24-oz plumb bobs for
stability reasons. At least 6 ft of good-quality string or cord, free of knots, is
necessary for convenient work with a plumb bob.

2.6. Electronic distance measurement (EDM)

A major advance in surveying instrumentation occurred approximately 60

years ago with the development of electronic distance measuring (EDM)

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instruments. These devices measure lengths by indirectly determining the

number of full and partial waves of transmitted electromagnetic energy
required in traveling between the two ends of a line. In practice, the energy
is transmitted from one end of the line to the other and returned to the
starting point; thus, it travels the double path distance. Multiplying the total
number of cycles by its wavelength and

dividing by 2, yields the unknown distance.

3. Horizontal Measuring on Slope Ground

In taping on uneven or sloping ground, it is standard practice to hold the
tape horizontally and use a plumb bob at one or perhaps both ends. It is
difficult to keep the plumb line steady for heights above the chest. Wind
exaggerates this problem and may make accurate work impossible. On
steeper slopes, where a 100-ft length cannot be held horizontally without
plumbing from above shoulder level, shorter distances are measured and
accumulated to total a full tape length. This procedure, called breaking
tape.

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4. Slope Measurements
In measuring the distance between two points on a steep slope, rather than
break tape every few feet, it may be desirable to tape along the slope and
compute the horizontal component. This requires measurement also of
either the altitude angle α or the difference in elevation d.

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In the case of altitude angle is determined, the horizontal distance between

points A and B can be computed from the following equation;

𝐻 = 𝐿 cos ∝

where H is the horizontal distance between points, L the slope length

separating them, and the altitude angle from horizontal.

In the case of the difference in elevation d between the ends of the tape is
measured, which is done by leveling, the following equation can be used;

𝐻 = √𝐿2 − 𝑑2

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5. Area Measurements
There are a number of important reasons for determining areas. One is to
include the acreage of a parcel of land in the deed describing the property.
Other purposes are to determine the acreage of fields, lakes, etc., or the
number of square yards to be surfaced, paved, seeded, or sodded. In plane
surveying, area is considered to be the orthogonal projection of the surface
onto a horizontal plane.

5.1. Methods of Area Measurements

Both field and map measurements are used to determine area. Field
measurement methods are the more accurate and include (1) division of
the tract into simple figures (triangles, rectangles, and trapezoids), (2)
coordinates, and (3) double-meridian distances.
Methods of determining area from map measurements include (1) counting
coordinate squares, (2) dividing the area into triangles, rectangles, or other
regular geometric shapes, (3) digitizing coordinates, and (4) running a
planimeter over the enclosing lines.

5.1.1. Division into Simple Figures

A tract can usually be divided into simple geometric figures such as
triangles, rectangles, or trapezoids. The sides and angles of these figures

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can be observed in the field and their individual areas calculated and
totaled.

Figure 3: Area determination by triangles.

Formulas for computing areas of rectangles and trapezoids are well known.
The area of a triangle whose lengths of sides are known can be computed
by the formula;

𝐴𝑟𝑒𝑎 = √𝑠(𝑠 − 𝑎)(𝑠 − 𝑏)(𝑠 − 𝑐)

Where a, b, and c are the lengths of sides of the triangle and 𝑠 =

1⁄ (𝑎 + 𝑏 + 𝑐) , another formula for the area of a triangle is;
2

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1
𝐴𝑟𝑒𝑎 = 𝑎𝑏 sin 𝐶
2

Where C is the angle included between sides a and b.

5.1.2. Regularly Spaced Offsets

Offsets at regularly spaced intervals are shown in Figure 12.2. For this
case, the area is found by the formula;

ℎ0 ℎ𝑛
𝐴𝑟𝑒𝑎 = 𝑏( + ℎ1 + ℎ2 + ⋯ + )
2 2

Where b is the length of a common interval between offsets, and are the
offsets. The regular interval for the example of below Figure is a half-
station, or 50 m.

Figure 4: Area by offsets.

Solution
2.8
𝐴𝑟𝑒𝑎 = 50(0 + 5.2 + 8.7 + 9.2 + 4.9 + 10.4 + 5.2 + 12.2 + )
2
= 2860 m2

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5.1.3. Area by Coordinates

Computation of area within a closed polygon is most frequently done by the
coordinate method. In this procedure, coordinates of each angle point in
the figure must be known. They are normally obtained by traversing,
although any method that yields the coordinates of these points is
appropriate.

The coordinate method is easily visualized; it reduces to one simple

equation that applies to all geometric configurations of closed polygons and
is readily programmed for computer solution.

In terms of coordinate values, the area E'EDD'E' is;

𝑋𝐸 + 𝑋𝐷
𝐴𝑟𝑒𝑎𝐸′ 𝐸𝐷𝐷′ 𝐸′ = × (𝑌𝐸 − 𝑌𝐷 )
2

Which can be expressed also as,

1
𝐴𝑒𝑎 = (𝑋𝐴 (𝑌𝐸 − 𝑌𝐵 ) + 𝑋𝐵 (𝑌𝐴 − 𝑌𝐶 ) + 𝑋𝐶 (𝑌𝐵 − 𝑌𝐷 ) + 𝑋𝐷 (𝑌𝐶 − 𝑌𝐸 ) + 𝑋𝐸 (𝑌𝐷 − 𝑌𝐴 ))
2

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Figure 5: Area computation by the coordinate method.

5.1.4. Area by Measuring from Map

A planimeter measures the area contained within any closed figure that is
circumscribed by its tracer. There are two types of planimeters: mechanical
and electronic. Because of its ease of use, the electronic planimeter (Figure
12.9) has replaced its mechanical counterpart. An electronic planimeter
operates similarly to the mechanical type, except that the results are given
in digital form on a display console.

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Figure 6: Electronic planimeter.

5.1.5. Area using software

There are several methods of determining the area of a parcel or figure. The
method of area by coordinates is most commonly used in practice. Software
typically uses the method of area by coordinates. For example, a computer-
aided drafting (CAD) software package and GIS and other can use the
coordinates of an irregularly shaped parcel to quickly determine its area by
the coordinate method.

5.2. Source of errors in determining area

Some sources of error in area computations are:
1. Errors in the field data from which coordinates or maps are derived.

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2. Making a poor selection of intervals and offsets to fit irregular

boundaries.

3. Making errors in scaling from maps.

4. Shrinkage and expansion of maps.

5. Using coordinate squares that are too large and therefore make
estimation of areas of partial blocks difficult.

6. Making an incorrect setting of the planimeter scale bar.

7. Running off and on the edge of the map sheet with the planimeter drum.

8. Using different types of paper for the map and planimeter calibration
sheet.

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Field Geology & Plane Surveying Chapter Three

Chapter Three

Angles, Azimuth, and Bearing

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 Field Geology & Plane Surveying Chapter Three

Angles, Azimuth, and Bearing

1. Introduction
Determining the locations of points and orientations of lines frequently
depends on the observation of angles and directions. In surveying,
directions are given by azimuths and bearings. Angles are most often
directly observed in the field with total station instruments, although in
the past transits, theodolites, and compasses have been used. The
sixagesimal system used in the United States, and many other countries,
is based on degrees, minutes, and seconds, with the last unit further
divided decimally.

Figure 7: Basic requirements in determining an angle..

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2. Azimuth
Azimuths are horizontal angles observed clockwise from any reference
meridian. In plane surveying, azimuths are generally observed from
north, but astronomers and the military have used south as the
reference direction. Azimuths can be read directly on the graduated
circle of a total station instrument after the instrument has been
oriented properly. Azimuths are used advantageously in boundary,
topographic, control, and other kinds of surveys, as well as in
computations.

Figure 8: Azimuths.

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3. Bearing
Bearings are another system for designating directions of lines. The
bearing of a line is defined as the acute horizontal angle between a
reference meridian and the line. The angle is observed from either the
north or south toward the east or west, to give a reading smaller than
90°. The letter N or S preceding the angle, and E or W following it shows
the proper quadrant. Thus, a properly expressed bearing includes
quadrant letters and an angular value; an example is N80°E.

Figure 9: Bearing angles.

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4. Compass and Earth magnetic field

The compass instrument consists of a metal baseplate (A) with two sight
vanes (B) at the ends. The compass box (C) and two small level vials (D)
are mounted on the baseplate, the level vials being perpendicular to
each other. When the compass was set up and the bubbles in the vials
centered, the compass box was horizontal and ready for use. A single leg
called a Jacob staff supported early compasses. A ball-andsocket joint

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and a clamp were used to rotate the instrument and clamp it in its
horizontal position.

4.1. Magnetic Declination

Magnetic declination is the horizontal angle observed from the geodetic
meridian to the magnetic meridian. Navigators call this angle variation of
the compass; the armed forces use the term deviation. An east
declination exists if the magnetic meridian is east of geodetic north; a
west declination occurs if it is west of geodetic north. East declinations
are considered positive and west declinations negative. The relationship
between geodetic north, magnetic north, and magnetic declination is
given by the expression

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geodetic azimuth = magnetic azimuth + magnetic declination

5. Mistakes
Some mistakes made in using azimuths and bearings are:

1. Confusing magnetic and other reference bearings.

2. Mixing clockwise and counterclockwise angles.
3. Listing bearings with angular values greater than.
4. Failing to include both directional letters when listing a bearing.
5. Failing to change bearing letters when using the back bearing of a
line.
6. Using an angle at the wrong end of a line in computing bearings—
that is, using angle A instead of angle B when starting with line AB
as a reference.
7. Not including the last angle to recompute the starting bearing or
azimuth as a check—for example, angle A in traverse ABCDEA.
8. Subtracting as though it were instead of or using 90° instead of 180°
in bearing computations.
9. Adopting an assumed reference line that is difficult to reproduce.
10. Reading degrees and decimals from a calculator as though they
were degrees, minutes, and seconds.

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11. Failing to adjust traverse angles before computing bearings or

azimuths if there is a misclosure.

6. Volumes
The most common unit of volume is a cube having edges of unit length.
Cubic feet, cubic yards, and cubic meters are used in surveying
calculations, with cubic yards and cubic meters being most common for
earthwork. The acre-foot (the volume equivalent to an acre of area, 1-ft
deep) is commonly used for large quantities of water, while cubic feet
per second (ft3/sec) and cubic meters per second are the usual units for
water flow measurement.

6.1. Methods of Volumes Measurements

Direct measurement of volumes is rarely made in surveying, since it is
difficult to actually apply a unit of measure to the material involved.
Instead, indirect measurements are obtained by measuring lines and
areas that have a relationship to the volume desired. Three principal
systems are used: (1) the cross-section method, (2) the unit area (or
borrow-pit) method, and (3) the contour-area method.

6.1.1. Cross-section method

The cross-section method is employed almost exclusively for computing
volumes on linear construction projects such as highways, railroads, and

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canals. In this procedure, after the centerline has been staked, ground
profiles called cross sections are taken (at right angles to the centerline),
usually at intervals of full or half stations if the English system of units is
being used, or at perhaps 10, 20, 30, or 40 m if the metric system is being
employed. Cross-sectioning consists of observing ground elevations and
their corresponding distances left and right perpendicular to the
centerline. Readings must be taken at the centerline, at high and low
points, and at locations where slope changes occur to determine the
ground profile accurately.

Figure 10: Section of roadway illustrating excavation (cut) and embankment (fill).

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6.1.2. Contour-area method

Volumes based on contours can be obtained from contour maps by using
a planimeter to determine the area enclosed by each contour.
Alternatively, CAD software can be used to determine these areas. Then
the average area of the adjacent contours. The contour-area method is
suitable for determining volumes over large areas, for example,
computing the amounts and locations of cut and fill in the grading for a
proposed airport runway to be constructed at a given elevation. Another
useful application of the contour-area method is in determining the
volume of water that will be impounded in the reservoir created by a
proposed dam.

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Figure 11: Determining the volume of water impounded in a reservoir by the

contour-area method.

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Chapter Four
Traversing

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1. Introduction
A traverse is a series of consecutive lines whose ends have been marked
in the field and whose lengths and directions have been determined from
observations. In traditional surveying by ground methods, traversing, the
act of marking the lines, that is, establishing traverse stations and making
the necessary observations, is one of the most basic and widely practiced
means of determining the relative locations of points.

Figure 12: Close Traverse.

2. Traverses
There are two kinds of traverses: closed and open.
2.1. Close Traverse
Two categories of closed traverses exist: polygon and link.

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2.1.1. Link traverse

The below figure illustrates a typical link traverse commencing from the
precisely coordinated point Y and closing onto point W, with terminal
orienting bearing to points X and Z. Generally, points X, Y, W and Z would
be part of an existing precisely coordinated control network, although
this may not always be the case.

Figure 13: Link traverse.

2.1.2. Polygonal traverse

The figure below illustrates the concept of a polygonal traverse. This type
of network is quite popular and is used extensively for peripheral control
on all types of engineering sites. If no external orientation is available,
the control can only be used for independent sites and plans and cannot
be directly connected to other survey systems.

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Figure 14: .Polygonal traverse

2.2. Open Traverse

An open traverse geometrically and mathematically open) consists of a
series of lines that are connected but do not return to the starting point.

Figure 15: Open Traverse.

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3. Observation of traverse angles or directions

The methods used in observing angles or directions of traverse lines vary
and include (1) interior angles, (2) angles to the right, (3) deflection
angles, and (4) azimuths.

3.1. Traversing by Interior Angles

Interior-angle traverses are used for many types of work, but they are
especially convenient for property surveys. Although interior angles
could be observed either clockwise or counterclockwise, to reduce
mistakes in reading, recording, and computing, they should always be
turned clockwise from the backsight station to the foresight station.

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3.2. Traversing by Angles to the Right

Angles observed clockwise from a backsight on the “rearward” traverse
station to a foresight on the “forward” traverse station are called angles
to the right. According to this definition, to avoid ambiguity in angle-to-
the right designations, the “sense” of the forward traverse direction
must be established. This is normally done by consecutive numbering or
lettering of traverse stations so that they increase in the forward
direction. Depending on the direction of the traversing, angles to the
right may be interior or exterior angles in a polygon traverse. If the
direction of traversing is counterclockwise around the figure, then
clockwise interior angles will be observed.

Figure 16: Traversing by Angles to the Right.

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3.3. Traversing by Deflection Angles

Route surveys are commonly run by deflection angles observed to the
right or left from the lines extended. A deflection angle is not complete
without a designation R or L, and, of course, it cannot exceed 180°. Each
angle should be doubled or quadrupled, and an average value
determined. The angles should be observed an equal number of times in
face left and face right to reduce instrumental errors.

3.4. Traversing by Azimuths

With total station instruments, traverses can be run using azimuths. This
process permits reading azimuths of all lines directly and thus eliminates
the need to calculate them. In Figure 9.3, azimuths are observed
clockwise from the north end of the meridian through the angle points.

Figure 17: Azimuth traverse.

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4. Observation of Traverse lengths

The length of each traverse line (also called a course) must be observed,
and this is usually done by the simplest and most economical method
capable of satisfying the required precision of a given project. Their
speed, convenience, and accuracy makes the EDM component of a total
station instrument the most often used, although taping or other
methods. A distinct advantage of traversing with total station
instruments is that both angles and distances can be observed with a
single setup at each station. Averages of distances observed both
forward and back will provide increased accuracy, and the repeat
readings afford a check on the observations.

5. Selection of traverse stations

Positions selected for setting traverse stations vary with the type of
survey. In general, guidelines to consider in choosing them include
accuracy, utility, and efficiency. Of course, intervisibility between
adjacent stations, forward and back, must be maintained for angle and
distance observations. The stations should also ideally be set in
convenient locations that allow for easy access. Ordinarily, stations are
placed to create lines that are as long as possible. This not only increases
efficiency by reducing the number of instrument setups, but it also

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increases accuracy in angle observations. However, utility may override

using very long lines because intermediate hubs, or stations at strategic
locations, may be needed to complete the survey’s objectives.

6. Source of errors in traversing

Some sources of error in running a traverse are:
• Poor selection of stations, resulting in bad sighting conditions
caused by (a) alternate sun and shadow, (b) visibility of only the
rod’s top, (c) line of sight passing too close to the ground, (d) lines
that are too short, and (e) sighting into the sun.
• Errors in observations of angles and distances.
• Failure to observe angles an equal number of times direct and
reversed.
7. Mistakes in traversing
Some mistakes in traversing are:
➢ 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.

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