Chapter 1.
Principles of Land Measurement and Surveying
An example of the art of surveying is being
able to reconnoiter a site and determine the
“best” instruments and methods to use to
collect the desired data.
Introduction
Land is all around us. We walk on it, build
houses and commercial buildings on it, drive
on it, fence it, dig trenches in it, and farm it.
Life as we know it would not exist without
land. Its presence permeates our lives to the
point that we seldom think about it.
Best is a very subjective term. What is best
for one individual, crew or site may not be
best if any changes are made. The best
instruments and methods produce the required
data with the least consumption of resources.
This includes determining what data needs to
be collected, the most appropriate surveying
method to use, the best location of the
instruments, etc.
Many of our uses of the land require us to
measure, mark, or locate points on, above or
below the surface. We often do this without
thinking about the principles we are using.
Property is located and marked before a fence
is built. A carpenter carefully marks the
corners of a building before starting
construction. Engineers may spend days
marking the course of a road. The surface of
an area must be measured before a pond is
built or a drainageway constructed. The
property corners of a parcel of land are located
and marked during the transfer of ownership.
For professional surveyors, and for
commercial construction operations, time is
money. An experienced surveyor can look at a
site and determine the best method for
collecting the necessary data. This ability is
an art because it cannot be learned from a
textbook or in a classroom. This "art" is
developed through natural abilities and from
experience.
The principles of surveying are used in all of
the examples mentioned above. Surveying
may be as simple as taking a few minutes and
two sticks to lay out a 90o corner, or as
complex as spending several days with
thousands of dollars worth of equipment
establishing a road or power line right-of-way.
In many cases, standards and procedures have
been developed to provide guidance in this
area. For example, if the purpose of a survey
is to establish the legal description of a parcel
of land, then standard procedure requires an
instrument that measures angles with extreme
accuracy be used.
Distances must be
measured accurately and a procedure called
“balancing the traverse” should be used.
What is surveying?
Surveying is the art and science of measuring
and locating points and angles on, above and
below the surface of the earth.
Surveying is also a science. Webster defines
science as, “knowledge covering general
truths or the operation of general laws esp. as
obtained and tested through scientific
method”.
In this definition, the term’s “art” and
“science” are used because good surveying is
both. Webster defines art as “skill acquired
by experience, study, or observation” and,
“the conscious use of skill and creative
imagination esp. in the production of aesthetic
objects”.
This definition is appropriate for many aspects
of surveying. One example of the science of
1
2
surveying is the principles and practices that
have been developed to collect accurate data.
Accurate data is a necessity of surveying.
Inaccurate data is worse than no data because
it can result in design errors.
Procedures have been developed and tested
over time that, if followed, control errors.
These include procedures to set up and use the
instruments, data recording methods and
specific mathematical procedures used to
complete surveying calculations.
Evidence exists that many early cultures built
water collection devices, irrigation canals,
large buildings, and complex road systems.
For years, archeologists were not able to
determine how these feats were accomplished
without surveying instruments.
There is sufficient evidence for one
archeologist to suggest, based on the pieces of
pottery he has found, that at least one early
South American culture developed a clay
bowl level for this purpose.
History of surveying
A complete bowl has not
been discovered, so the
illustration is the author's
best guess as to what this
instrument actually looked
like based on the description
of the pottery pieces that
have been found.
The bowl had two holes
opposite each other, the same
vertical distance from the
bowl rim. It is surmised that
it was filled with water up to
a mark, and if it were
mounted on a tripod or
suspended, it could be tilted.
The
bowl
would
be
positioned at the bottom of a
slope and tilted. Water levels
at different marks on the
opposite side would represent
Evidence of measuring land
and marking boundaries is
almost as old as civilization.
Hunter-gatherer societies had
no need to measure or mark
land because they where
nomadic and did not have a
concept of land ownership.
As cultures evolved from
"hunting-gathering”
to
farming, they developed the
desire to mark out and claim
ownership of the land.
The basis
of
modern
techniques can be traced to
ancient Egypt. In Egypt, the
most fertile farmland was
located along the Nile River
and each year the river would flood,
completely covering this prime farmland.
The flood would erase many if not all of the
boundary markers. The Egyptians developed
methods to replace the field corners after each
flood so each family could identify their area.
Certain individuals identified as surveyors
were responsible for this task.
History indicates that the primary concern was
not the assurance that each family farmed the
same land every year, but that the correct
taxes were collected.
different slopes.
Surveying also played an important role in the
early development of the United States. The
first Europeans who came to North America
during the European migration chose to ignore
land rights established by the American
Indians. They justified this position based on
the assumption that American Indians were
heathens, sub-humans and therefore had no
rights to the land.
3
Having a tradition of land ownership, they set
about establishing a system of boundaries and
land ownership.
The first land descriptions were modeled after
the system that was used in Europe.
The King of England, who never visited North
America, gave large grants of land and
charters for land to many different individuals
and groups.
These land grants and charters were described
with very rudimentary boundary descriptions.
Some of the boundary descriptions
overlapped, and to make matters worse, some
individuals interpreted the grant and charter
land boundary lines to give them the best land
and exclude land that they did not want. This
resulted in many boundary conflicts.
By the Revolutionary War, many boundaries
where in dispute and lawyers spent a large
portion of their time settling these conflicts.
The number of land disputes expanded
dramatically after the Revolutionary War.
The Continental Congress increased the
number of land boundary problems because it
did not have sufficient funds to pay soldiers
after the war, so they granted them land
instead of wages. The land grants did not
cause the problem; the land boundary
problems arose because a good plan for
assigning the land did not exist.
The soldiers were told to identify their claim
by staking the corners and filing a written
description of the corner marker locations at a
local land office established for that purpose.
This type of land identification is called metes
and bounds.
Individuals naturally set their stakes to claim
the best land with no regard to direction and
location of other stakes. This caused a sudden
rash of land disputes. These land disputes
added fuel to the desire for a better system.
Consequently, the Continental Congress
formed a committee charged with the task of
determining a better method for measuring
and identifying land.
The result was the adoption of the Rectangular
System of Land Description (RSLD). The
goal of the RSLD system was to provide a
method of giving each parcel of land a unique
description of its location. The RSLD was
first applied in the Ohio River valley. The
RSLD was modified further and applied to
land as they where opened for settlement. The
last major revision occurred in time to be
applied to the Louisiana Purchase. The
system has remained unchanged since then.
The RSLD established a multiple level grid
system based on an initial point. Latitude and
longitude located the initial point.
The
smallest unit of the grid was a section, which
is one square mile. The adoption of the RSLD
required that all land must be surveyed.
During these surveys, every section corner,
and in most cases half section corners, were
located and marked with a permanent marker.
Most of these markers still exist and continue
to be used as starting points for modern
surveys.
Surveying terms
To understand the methods and techniques of
any subject it is important to understand the
terminology used. This is especially true for
surveying because the meaning of some terms
is different from common usage.
A good understanding of the following terms
and definitions is essential for understanding
surveying.
Oblate spheroid
Oblate Spheroid is the term used to describe
the shape of the Earth. It is a solid obtained
by rotating an ellipse on its shorter axis.
4
This means the distance between the poles
through the center of the earth (P) is less than
the diameter at the equator (E).
Figure 1.3 Disk or bulls eye spirit level
A spirit level by itself is not a useable tool. It
is usually incorporated within a frame or as
part of another tool. An example is a
carpenter’s level, Figure 1.4, or a survey level,
Figure 1.5.
Figure 1.1 Oblate spheroid
Because the earth is not a standard geometric
shape mathematical equations representing the
shape of the earth are best estimates. This
complicates the Global Positioning System
(GPS) and other electronic measuring
systems.
Figure 1.4 Carpenter’s level
Level
The term level is used to compare the relative
position of an object with the horizon or the
relative position of two or more objects.
Objects that are level are parallel with the
horizon and at the same elevation with each
other. Objects are also level if they are
perpendicular (at a 90o angle) to a vertical
line.
The condition of being level is usually
determined by a tool called a spirit level or
just level. An air bubble in a small container
of liquid moves as the level is tilted, Figure
1.2. When the air bubble is in the middle, the
tool is level. The container is usually a
tube/cylinder, Figure 1.2, or disk Figure 1.3.
Figure 1.2 Tubular spirit level
Figure 1.5 Dumpy level
Vertical line
A vertical line is a line that follows the
direction of gravity. At any point on the
Earth’s surface, a string with an attached
weight will always point toward the center of
the earth forming a vertical line Figure 1.7.
Vertical lines are perpendicular to the earth’s
surface. They also radiate out from the center
of the earth like the spokes on a wheel.
5
Figure 1.7 Vertical lines
A carpenter’s level can
also be used to establish
a vertical line because
they have spirit levels
that
are
mounted
perpendicular to the long
dimension of the frame.
These spirits levels are
used to establish if
objects are “plumb”
vertical. See Figure 1.8.
Figure 1.8 Vertical planes
Horizontal line
A horizontal line is formed when a line is
established perpendicular to a vertical line, or
when a line is established parallel with the
horizon. At any one point, there are an
unlimited number of horizontal lines.
Vertical plane
A plane is defined as a
flat surface. Therefore, a
vertical plane is a flat
surface that is vertical. A
Figure 1.6
vertical
plane
will
Establishing a
incorporate a vertical
vertical line
line. For any vertical
line, there are an infinite
number of vertical planes. The walls of a
building are usually vertical planes.
Figure 1.9 Horizontal lines
Horizontal plane
A horizontal plane is a plane that is
perpendicular to a vertical line or parallel with
the horizon.
6
For a small area, the difference between a
level surface and a horizontal plane is
indistinguishable.
The difference between a horizontal plane and
a level surface is the primary difference
between the two types of surveying methods,
plane surveying and geodetic surveying.
Figure 1.10 Horizontal planes
Every vertical line has only one horizontal
plane with a given elevation above or below
the surface, but an infinite number of planes
with different elevations may exist at a point
Figure 1.11.
Plane surveying assumes the earth is a flat
plane. As long as the distances are short, this
is a good assumption. Geodetic surveying
does not use this assumption. All elevations
are adjusted for the curvature of the earth.
Horizontal distance
A distance is the amount of separation
between two points, lines, surfaces, or objects
measured along the shortest path joining them.
A horizontal distance is a distance measured
on a horizontal line or plane.
Figure 1.11 Multiple horizontal planes
Level surface
A level surface is a continuous surface that is
at all points perpendicular to the direction of
gravity. A level surface is not a flat surface or
a plane. A level surface is a surface that
follows the curvature of the Earth. A large
body of still water, such as a lake, best
illustrates a level surface.
Figure 1.13 Horizontal Distance
If a distance is measured by laying surveyor’s
tape on the surface of the earth, the distance
measured is not a horizontal distance. This is
called slope or surface distance.
Angle
An angle is formed by the intersection of two
lines. An angle has three parts: a base line,
vertex, and second line, Figure 1.14.
Figure 1.12 Level Surface
7
Figure 1.14 Parts of an angle
In surveying, both horizontal and vertical
angles are used.
Horizontal angle
A horizontal angle is an angle measured on a
horizontal plane. A horizontal angle is the
angle between two vertical planes.
Figure 1.16 Horizontal zero vertical angles
When zenith zero angles are used, zero
degrees is vertically overhead and 180 degrees
is vertically down.
Figure 1.15 Horizontal angle
Vertical Angle
A vertical angle is an angle measured in a
vertical plane.
When measuring vertical
angles in surveying, two different base lines
can be used, horizontal zero, Figure 1.16, and
zenith zero, Figure 1.17.
If horizontal zero is used, angles measured
upward from a horizontal line or plane are
referred to as plus angles, and angles
measured downward from a horizontal line or
plane are referred to as minus angles. Note:
this is not a negative angle. The (-) sign is
used to indicate the direction.
Figure 1.17 Zenith zero vertical angle
Bench mark
A benchmark (BM) is a point of known or
assumed elevation.
To be considered a
benchmark, the point should be identified by a
permanent or semi-permanent structure that
will not be affected by frost heave, traffic
vibrations or environmental changes.
Surveying standards have very specific
guidelines on the appropriate structure for
benchmarks.
The United States Geological Service (USGS)
has established a series of benchmarks
throughout the United States. These are used
to establish additional local bench marks.
8
It is common practice to establish a
benchmark at a construction project. This
becomes the reference point during
construction. These benchmarks may be
removed when construction is complete, or if
they meet the standards for a benchmark, they
may be left in place and used for additional
projects.
Elevation
Elevation (EL) is the distance above or below
a reference level surface.
The most
commonly used reference level surface in the
U.S. is the National Geodetic Vertical Datum
of 1929. It was established by connecting 26
tidal benchmarks along the Atlantic, Gulf of
Mexico, and Pacific Coasts. This datum is the
zero elevation reference point used for
surveying.
For many construction surveys the true
elevation is not important, so a local
benchmark is established and used as the
reference point. This type of benchmark may
use any assumed elevation.
When an assumed elevation is used for the
benchmark, it is common practice to use an
elevation of 100.00 feet. Any elevation can be
used for a benchmark as long as it does not
result in negative elevations.
Difference in elevation
A difference in elevation is the vertical
distance between two level surfaces or planes.
Figure 1.18 Difference in elevation
If the elevation of each of the level surfaces
(1, 2 & 3) in Figure 1.18 is known, then the
difference in elevation can be calculated
between the Earth (1) and surface 2 or
between the Earth and surface 3 and also
between surface 2 & 3.
Back sight
A backsight (BS) is a rod reading taken on a
point of known or assumed elevation. The
elevation of the point would be known or
assumed if it was a benchmark. A backsight
is the vertical distance from the top of the
object that the rod is resting on to the line of
sight established by the instrument.
The backsight is added to the elevation at the
point the rod is resting on to determine the
height of the instrument.
Foresight
A foresight is a rod reading taken on a point of
unknown elevation. It is used to calculate the
elevation of the point where the measurement
is taken.
In surveying two different types of foresights
are used, intermediate (IFS), and true (FS).
An intermediate foresight is a rod reading on a
point that will not be used as a turning point or
benchmark. Extra care and procedures must
be used when recording these rod readings
because the checks for error will not catch a
mistake in these readings. This is discussed in
more detail in the chapter on differential
leveling.
A true foresight is a rod reading on an
unknown point that will be used for a turning
point or for a benchmark. The person on the
instrument must also be careful when
recording these readings. The error checks
will catch a mistake in the rod reading of a
true foresight, which prevents the use of data
that has errors.
The problem is that the errors cannot be
corrected. If the error is excessive, the data is
destroyed and the survey must be repeated.
Turning point
A turning point (TP) is a station along a
survey that is established as a temporary
9
benchmark. The purpose of the turning point
is to provide a point of known elevation that
can be used to reestablish the height of the
instrument after it has been moved. The
turning point should be a stake or other
durable structure that has a constant elevation.
The elevation of the turning point is recorded
in the notes, but it should not be used for
design work unless you know that it is the
elevation of the earth at that point.
instruments use a straight reference plane, this
requires all instrument readings of elevation to
be adjusted for the curvature of the earth.
Geodetic surveys are used when a high degree
of accuracy is needed or when the survey will
cover long distances and large areas.
Figure 1.20 Geodetic Surveying
Figure 1.19 Turning point
In Figure 1.19, the instrument would be set up
at instrument position one (IP1); a backsight
would be taken on benchmark one (BM1) and
a foresight on the turning point (TP). Adding
the value of the backsight to the elevation of
BM1 results in the height of the instrument.
Subtracting the value of the foresight from the
height of the instrument results in the
elevation of the turning point. The TP
becomes a new station that can be used as a
reference elevation. It is not considered a
benchmark unless the appropriate type of
structure is used. Turning points are intended
to be temporary. After the foresight on the TP
is recorded, the instrument would be moved to
IP2, and the process repeated until the second
bench mark was reached. There is no limit on
the number of turning points that can be used
to complete a survey.
Common Surveying Methods
Professional surveyors complete many
different types of surveys, but most can be
categorized into two methods, geodetic and
plane.
The primary difference between
geodetic and plane surveying is the approach
used to account for the curvature of the earth.
Geodetic surveying
Geodetic surveying measures all elevations
from a level surface, and because all
Geodetic surveys are much more technical and
time consuming, and they are only used for
surveys that require the highest degree of
accuracy.
Plane surveying
Plane surveying assumes the earth is flat and
that all rod readings are measurements from a
flat surface (plane). We know that the surface
of the earth is a level surface, not a flat
surface. Therefore, in plane surveying every
rod reading has a small amount of error. For
general construction and for all surveys that
use short distances and small areas, this error
can be ignored.
Common types of surveys
Many different types of surveys are used and
can be completed either as a geodetic or as a
plane survey. Eight common surveys are:
1. Distance measurement
2. Angle measurement
3. Differential
4. Profile
5. Topographic
6. Traverse
7. Construction
8. Property
These types of surveys will be briefly
discussed in the following sections.
10
Additional information on the first six is
included in subsequent chapters.
% Slope
Error (ft/ft)
Error (ft/100 ft)
1
0.00015
0.01522
Construction and property surveys are beyond
the scope of this text. Information on these
two types of surveys can be found in texts
written for civil engineering. These texts will
also include more information on the six types
of surveys included in the subsequent chapters
of this text.
2
0.00061
0.06086
3
0.00137
0.13691
4
0.00243
0.24335
5
0.00380
0.38014
6
0.00547
0.54726
Distance measurement
7
0.00745
0.74463
Many activities involving land require
measuring distance. Many different methods
are available. The best method to use will
depend on the accuracy required and the
resources available.
Common distance
measuring methods are:
1. Pacing
2. Chaining
3. Stadia
4. Odometer wheel
5. Optical range finder
6. Electronic distance measuring (EDM)
7. Laser
8
0.00972
0.97221
9
0.01230
1.22992
10
0.01518
1.51769
A distance can be measured as either a slope
(surface) distance or true horizontal distance.
The methods and techniques used will depend
on which type of distance is required. If the
slope is less than five percent, the difference
between slope distance and horizontal distance
is relatively small, Table 1.1. At 5% slope,
the amount of error in one hundred feet is
0.38014 feet or 4 1/2 inches. The difference
can be ignored for surveys that do not require
a high level of accuracy.
Table 1.1 Difference between percent slope
and horizontal distance
It is important to know when horizontal
distance is required and when slope distance is
sufficient.
Additional information on methods and
principles of measuring distance is included in
Chapter Four.
Angle measurement
An angle has three parts, the base line, vertex,
and second line.
Angles can be accurately measured with a
survey instrument in degrees-minutes-seconds
(DMS) or decimal degrees (DD). There are
also applications in which the accuracy
requirements allow angles to be measured or
laid out without using an instrument.
Common methods of measuring angles
without using a surveying instrument are:
 Chord
 3-4-5
 Tape-sine
Factors to consider when choosing the best
method are available resources, degree of
accuracy and precision required, and the use
of the data.
Addition information on
11
measuring angles can be found in Chapter
Seven.
100
Differential Surveys
Differential surveys are used to determine or
establish the difference in elevation between
two or more points. A common use of
differential surveys is to establish a new
benchmark. The process of determining if
concrete forms are at the correct elevation,
and are level, is also a use of differential
surveying. Differential surveys are covered in
more depth in Chapter Five.
Profile surveys
A profile is a side view of an object. A profile
survey is used to establish a side view of the
Earth’s surface. Once the data is collected, it
is plotted, and the plot can then be used to
make decisions about the slope, depths of cuts,
cuts and fills, etc. A profile survey is usually
done before constructing routes, such as
roadways, sidewalks, pipelines, and drains.
99.5
99
98.5
98
97.5
97
96.5
A
96
C
95.5
E
1
2
3
G
4
5
6
7
I
8
9
10
Figure 1.22 Plot of topographic data.
Topographic maps are very useful for
planning and preliminary design work. On
topographic maps each line connects points of
constant elevation.
The two common methods used to collect the
required data for topographic maps are the
grid method and the angle and distance
method.
Figure 1.23 Example topographic map.
Figure 1.21 Example plot of profile survey
More information on conducting profile
surveys can be found in Chapter Six.
Topographic survey
Topographic surveying is used to collect the
data required to draw a topographic map. A
topographic map is a three-dimensional
drawing of the Earth’s surface.
Chapter Eight includes additional information
on conducting topographical surveys and
drawing topographic maps.
Property Surveys
Property surveys are used either to establish
property lines when subdividing a parcel of
land or to check existing property lines. A
property survey should be completed before
starting any construction or before buying
property. Property lines can become confused
as land transfers through owners. Corner
markers may be destroyed or moved. For
these reasons, it is not safe to rely on the
memories of landowners. If the area has been
surveyed using the RSLD, the property survey
12
will start with the RSLD description. If the
parcel size is less than a section, or has an
irregular shape, then accurately measured
angles and distances are used to define the
property lines.
If the location of a property line is in dispute,
a property survey may not resolve the issue. It
is natural for an individual to think that with
modern equipment and techniques it would be
possible to locate a property line very
accurately. This is not necessarily true. Many
factors may cause inaccuracies. The surveyor
may be working with old, incomplete or
inaccurate information.
If two different
surveyors attempt to locate a property line but
use different starting points, they may not
agree on the location of the property line. For
this reason, many states have passed fence
laws that determine property lines. Although
states differ, in principle, if a fence has existed
for a prescribed number of years and has been
the recognized property line, then it becomes
the legal property line even if a property
survey shows the fence is not on the property
line. The "fence property line" can be moved
if both property owners agree to accept the
survey and move the fence.
balanced. The process of balancing a traverse
calculates the best fit of angles and distances,
forming a geometrically correct shape. Figure
1.24 is an illustration of the measured angles
and distances recorded for a five-sided area.
Figure 1.24 Measured traverse.
If you were to plot this figure with the angles
and distances given, it would not be a
complete figure. Figure 1.25 shows the
balanced angles and distances.
Construction surveys
A construction survey is used to either lay out
a proposed construction project, or to evaluate
a project after it is built. Construction surveys
may be relatively simple or very complex,
depending on the size and the type of project.
Traverse
A traverse is a survey establishing the
circumference of a property. A traverse
requires very careful measurements of
distances and angles. Once data is collected,
mathematical procedures are used to balance
the traverse. A traverse must be balanced
because there is only one possible
combination of angles and distances that will
form a geometric shape. If errors occur in
measuring angles or distances, the measured
shape is not geometrically possible. Errors
always occur; therefore, the traverse must be
Figure 1.25 Balanced traverse
Additional information concerning traverses is
included in Chapter Nine.
Data use
Measurements are collected for many different
purposes. The intended use of data must be
considered when determining the equipment
and methods to use. For example, if the
13
purpose of a job is to determine the lengths of
water pipe required to lay a water line,
measurements to the nearest 10-feet are
probably sufficient. If the purpose of a job is
to locate the legal boundaries for a piece of
property, the instruments and methods
measure angles to the nearest minute and
distances to the nearest 0.001-feet. The
surveyor must use appropriate equipment and
methods to collect the desired information.
Accuracy and precision
Accuracy and precision are two important
concepts to keep in mind when taking any
measurements. The level of accuracy and
precision needed to determine how many rolls
of barbed wire are required to build a fence is
different from the
level of accuracy
and
precision
needed to build a
dam.
Some standards and
common practices
have
been
developed
to
provide a guide in
this area but in
many
cases,
decisions are based
on experience.
The principles of
accuracy
and
precision can be
illustrated
graphically
by
using
the
distribution of shots
at a target. Four
different situations
can exist. They can
be neither precise
nor
accurate,
precise but not
accurate, accurate
but not precise, and
both accurate and precise.
Mathematically, accuracy is defined as the
number of decimal places included in a
measurement, and precision is defined as the
unit of measure. A measurement of 12.45 feet
is more accurate that a measurement of 12.4
feet.
The measuring tool determines
mathematical accuracy.
All measuring devices are accurate to only
plus or minus one of the smallest units. To
illustrate this point, consider a one-foot ruler
graduated in eighths of an inch. The accuracy
of all measurements made with the ruler is
accurate to 1/8 inch. Therefore, if a higher or
lower level of accuracy is required, then a
measuring tool that has the capability to
measure at the required level must be used.
Mathematical precision, or unit of measure,
defines the increments of the measurement.
The smaller the increment used, the more
precise the measurement. A measurement in
units of inches is more precise that a
measurement with units of feet. Ounces are
more precise than pounds.
The measuring tool determines the precision
of the measurement. If a carpenter is working
with a precision of 1/8 inch, the quality of the
work will suffer if the smallest graduation on
the tape being used is 1/4 inch.
Before measurements are taken, decisions
must be made regarding the appropriate level
of accuracy and precision for the job. The
selection of the most appropriate equipment
also depends on the required accuracy and
precision. These decisions should be made
before any measurements are recorded.
Field notes
Surveying and land measurement require the
collection and recording of information.
Traditional methods of recording information
have been developed to provide a systematic,
accurate way of recording data. The purpose
of these methods is to improve the ease of
using the information and to reduce the chance
14
of errors. Incorrect information is worse
than no information because it can lead to
wrong decisions. Wrong decisions can cause
very expensive mistakes.
In addition, field data collected by a surveyor
can become public documents and used as
evidence in court cases.
Field books
Surveyors have traditionally used a specific
type of book to record data. Field books are
made up of very high quality paper that is also
weather resistant.
Surveyors have developed specific guidelines
for putting information in the field book.
collected, should be able to find the same spot,
conduct the same survey, and get the same
results.
To achieve this result it is important that the
writing be very legible and that the
information be spread out on the page. Paper
is cheap compared to an error caused by
reading scrunched up, illegible data.
Error and error control
Surveying data must be accurate to be useful.
To insure the data is accurate the surveyor
must understand the types of errors that can
occur and learn how to control the factors that
cause errors.
Common errors for each type of survey will
be included in the appropriate section. In
general, errors can be divided into two
categories-random and systematic.
Random error
Figure 1.26 Field book page.
The uses of a field book will vary with the
project.
For example, on large projects
professional surveyors will use a new book for
every survey. The original book is kept in a
safe and copies of the information are use for
daily use. If a surveyor is surveying small
projects, he/she may use one book for several
different projects. The customer and the
complexity of the job dictate the use. In either
case, the original information should be stored
in a safe and copies made for daily use.
There is one fundamental principle governing
field book information. A person, who was
not there when the original data was
A random error is an error that does not occur
with a predictable pattern. Random errors are
very hard to control because the surveyor does
not always know the cause. If the cause is
unknown, it is very difficult, if not impossible;
to use any means to control the errors that are
generated. The primary method of control of
random errors is to follow or adopt the
appropriate
methods
and
techniques
commonly used to complete a particular type
of survey. Examples of random errors include
an instrument reader who switches two
numbers when recording a rod reading or an
individual who reads the rod incorrectly.
Several different methods, such as double
reading, and three wire reading have been
developed over the years to prevent these
types of errors. When double reading, the
instrument reader calls out the rod reading and
the note keeper writes it down. Then the
instrument person rotates the instrument away
from the rod and back again and reads the rod
a second time. Double reading provides dual
protection against the possible errors of
15
reading the rod wrong and recording the data
incorrectly.
Three wire reading utilizes all three horizontal
crosshairs in the instrument, if they are
available. In this method all three crosshairs
are read and recorded in the field book and
then averaged. The averaged value is used as
the measurement.
Systematic errors
Systematic errors are errors that are
predictable. They are often associated with
the limitations of, or problems associated
with, measuring instruments.
Systematic errors are easier to account for.
Once the error for an instrument or condition
is known, a correction factor can be calculated
and the appropriate adjustments can be made.
An example is temperature correction for a
surveyor's tape. The amount of error is
predictable for the temperature because the
expansion or contraction of the steel is
predictable. An equation is used to determine
the amount of correction needed.
This
number is added to or subtracted from each
measurement.
16
Chapter 2.
Equipment
Introduction
Surveying is heavily dependent on the use of
instruments and equipment. Proper selection,
use, and care of this equipment will greatly
influence the quality of data collected and the
amount of resources that will be required. The
instruments and equipment used may be as
simple as two tree branches or as complex as
an electronic total station costing several
thousand dollars.
In this section, we will discuss the common
equipment used for land measurement and
surveying.
One of the most important principles to
remember is that surveying instruments are
precision instruments and rough use or
improper care easily damages them.
Instruments can be easily damaged by being
dropped, stored improperly, or the having the
movements "forced" without being unlocked.
A damaged instrument may function correctly,
but the data it produces will be wrong, and the
operator may not know the instrument is
damaged.
Categories of equipment
Surveying equipment can be divided into three
categories: distance measuring equipment,
instruments for measuring angles and
elevations and accessories.
Distance measuring equipment includes:
1.
2.
3.
4.
5.
Tapes and chains
Odometer wheel
Levels (stadia)
Optical range finders
Electronic Distance Measuring (EDM)
Instruments for measuring angles and
elevations include:
1. Hand level
2. Dumpy/farm Level
3. Automatic level
4. Laser level
5. Transit
6. Theodolite
7. Construction transit
8. Total stations
Common accessories include:
1. Pins
2. Field books
3. Rods and targets
4. Range poles
5. Stakes/flags
6. Nails
7. Plumb bobs
8. Paint
Surveying equipment, instruments and
accessories are available with different
features and capabilities.
The following
sections will discuss some of these.
Equipment for measuring distance
Distance measuring equipment ranges in
technology from steel tapes to EDM
equipment that uses microwaves or lasers.
One of the arts of measuring distance is
determining the best equipment to use. The
best equipment for measuring distance is
primarily dependent on the topography, the
skill of the surveyor, and the use of the data.
If a high degree of accuracy is required, then
chaining or EDM should be used. If a low
level of accuracy is acceptable, then an
odometer wheel or even pacing can be used.
Regardless of the equipment used, the
surveyor must insure it is in proper working
order and that it is used correctly.
17
Tapes and chains
In the United States, the Gunter’s Chain was
the standard chain for many years. A Gunter’s
chain is 66 feet long, comprised of 100 links,
with each length being 7.92 inches. The links
were made of heavy wire and connected by
rings. The handle was threaded and was used
to adjust the length of the chain to compensate
for wear.
If a high level of accuracy is required and the
atmospheric temperature is not at standard,
then a temperature correction must be
calculated.
The other difference between a surveyor’s
chain and a standard tape is the graduations.
An individual must be careful when using a
surveyor’s chain because several different
graduations are used.
A standard carpenter’s tape uses a scale of feet
and inches and fractional graduations for each
inch. Fractions of 1/2, 1/4, 1/8 and 1/16 of an
inch are common. A surveyor’s chain/tape
divides a foot into tenths (0.1) and hundredths
(0.01) of a foot.
Figure 2.1 Handle and two links of early
surveyors chain.
The Gunter’s chain was primarily used for
land surveying because of its relationship to a
mile, 80 chains = 1 mile. The link size made
the chain difficult to use when distances were
less than a full chain.
In the United States the Gunter’s chain was
replace by the engineer’s chain. Engineer’s
chains are composed of links also, but it was
designed to be 100 feet long and each link was
one foot. The modern 100-foot steel tape
eventually replaced engineer’s chains.
Modern surveying tapes may look like a
carpenter’s tape, but they are designed
specially for surveying. They have two
unique characteristics. One difference is their
construction. They are constructed of a steel
alloy that has a known coefficient of
expansion due to temperature.
This is
necessary because steel expands when heated
and contracts when cooled. The designed
accuracy of a steel surveyor’s chain is only
true if it is at standard temperature, usually 72
o
F, and has a standard tension applied, usually
15 pounds.
Another difference between carpenter’s tapes
and surveyor’s chains is that several styles of
surveyor’s tape do not have graduations
between each foot mark. Surveyor’s chains
are designed for measuring long distances.
Several styles will only have one graduated
foot at each end of the tape. This feature
defines the three common styles of tapes that
are used, Figure 2.2
1. First Foot Graduated
2. Extended Foot Graduated
3. Fully Graduated
In addition to the three styles of chains,
manufactures also place the zero footmark at
different points on the chain. For some styles
of chains the zero mark is at the end of the
chain. For others, it will be several inches in
from the end of the chain. It is very important
for the measuring team to inspect the chain
and determine which style of tape they are
using before they start measuring. Errors up
to 18 inches per 100 feet of travel can result if
the chain is not read correctly.
There are two common errors when using
surveyor’s chains: failure to use the correct
reference point for zero, and failure to read a
partial foot correctly. The partial foot error
occurs when chains that are not fully
graduated, first foot and extended foot, are
used to measure a distance that is less than a
18
full chain and less than a whole foot. When a
partial foot is being measured, the person at
the head of the chain holds the chain so that
the pin is aligned with a foot mark on the
chain. The person at the rear of the chain
applies the correct tension and reads the chain.
If an extended foot chain is used the chance
for error is less, but if a first foot chain is used,
the person reading the chain must remember
that the distance is one foot less than the foot
mark aligned with the pin at the head of the
chains. This is explained in more detail in the
next section and in Figure 2.2.
measured is less than the footmark at the head
of the chain. The distance from zero to one
foot is used to measure the partial foot.
Extended foot tape
The extended foot tape is similar to a first foot
tape, except that an additional foot has been
added to each end for the graduated foot. With
this style of tape there is less chance for the
one-foot error associated with the first foot
graduated tape. However, the user must be
careful to select the zero point of the chain,
and not the beginning of the extended foot as
this will cause an error of
one foot in the reading.
Fully Graduated tape
A fully graduated tape is
more similar to a
standard carpenter’s tape
than either the first foot
or extended foot tape.
The primary differences
are that it is constructed
from steel and the scale
is in decimal feet,
hundredths of a foot,
instead of feet and
fractional inches.
Figure 2.2 Common types of tapes
First foot graduated tapes
First foot graduated tapes have graduations
only within the first (0 & 1) and last foot (99
& 100). When this style of tape is used, it is
very easy to make an error of one foot when a
partial chain is used. Figure 2.2 illustrates this
problem.
When reading a first foot graduated tape, the
head person holds the tape on the nearest foot
mark and the rear person reads the partial foot.
The error occurs because the distance being
It is very important for
the user to understand
the style of tape being
used before starting to
record
measurements.
Failure to do so may
result in incorrect information.
Using surveyor’s tapes
Surveyors’ chains must be used carefully.
These chains break easily if a loop is pulled
tight. The surveyor chain should always be
wiped clean and oiled after each use. Chains
can be hand rolled, but a chain holder, as
shown in Figure 2.3, is very handy and
reduces the chance of breaking the tape.
19
Figure 2.4 Odometer wheel
Figure 2.3 Modern tape holder
Until the adoption of EDMs, chaining was the
most accurate method of measuring distance.
A reasonable attention to detail will produce
accurate measurements to 0.01 foot. With the
appropriate chain and procedures, accuracy of
0.001 foot are possible.
To measure a distance with an odometer
wheel the odometer is set to zero. Then the
wheel is placed at the starting point, and the
operator "walks the distance".
Optical range finder
An optical range finder is a useful instrument
for estimating distances to an object.
Chains are still very useful, especially for
short distances. Electronic distance measuring
has replaced chains for long distances. Today
the terms chaining and taping are
synonymous.
Odometer wheel
The odometer wheel is a very common
instrument for measuring distance. As the
name implies, it is a combination of the
odometer and wheel. An odometer is a
mechanical revolution counter that can be
designed by the manufacturer so that the dial
reads with one of several different standard
units of measure. For example, the odometer
on an automobile is designed to read in miles
and tenths of a mile.
Odometer wheels are available in many
different sizes, with different types of handles,
wheels, units of measure, and precision.
Surveying odometer wheels can be purchased
that read in whole feet, feet and tenths of a
foot, or in feet and inches.
Figure 2.5 Optical range finder
These instruments are commonly used for
hunting, but they can also be used for land
measurement when a low level of precision is
acceptable.
Optical range finders use a splitting mirror and
a tilting mirror. When you look through the
eyepiece, the view is split into two images.
One image is looking straight ahead. The
other image is a shadow image produced by
the mirror offset to the side.
Using an optical range finder
The instrument is used by focusing the
instrument on a well-defined object. If the
instrument is not set at the correct distance, a
20
shadow image will be visible. The distance is
determined by rotating the adjustment wheel
until the shadow image is superimposed on the
original image.
When the images are
superimposed, the distance can be read from
the scale on the instrument.
The principle of optical range finders is based
on trigonometric function. If you know the
length of one side and one angle of a right
triangle, then you can calculate the length of
any remaining sides. The range finder does
this using a mechanical linkage and a
calibrated wheel.
For the example in Figure 2.5, if the distance
between the splitting mirror and the tilting
mirror is one foot, then the distance from the
range finder to the object is:
opp
Tan  =
adj
adj =
=
opp
Tan 
1.0 ft.
= 301 ft.
Tan 0.19
The biggest limitations of optical range
finders are measuring range, accuracy, and
precision. For example, the useable range
may only be between 20 and 400 yards or 50
and 1,000 yards. The accuracy may be as low
is 1/100 and the precision as large as one yard.
An accuracy of 1/100 for a range finder with a
precision of one yard means that the
maximum error for any measurement is one
yard for every 100 yards measured.
Electronic Distance Measuring (EDM)
One of the newer methods of measuring
distance is by using EDM.
Electronic
Distance Measuring instruments use
microwaves or invisible light to determine the
distance between itself and an object or
between two instruments. These instruments
measure distance by rearranging the equation
for velocity. In the standard equation, velocity
equals distance divided by time.
D
V=
D = VT
T
Rearranged, distance equals velocity times
time. EDMs determine distance by using a
signal of known velocity and then recording
the time it takes the signal to reach the object
and return. This is accomplished by locating
the EDM over one point and either a prism or
a return unit over the second point. When the
distance measuring function of the EDM is
activated, it sends a signal to the prism or
second unit. The signal is either reflected
back, by the prism, or sent back, by the second
unit, to the EDM. When the EDM receives
the return signal, it can determine the amount
of time that elapsed between when the signal
was sent and when it returned.
Time
multiplied by velocity equals distance. The
distance is displayed on a screen and/or stored
in the memory.
The onboard CPU determines the amount of
time that elapsed between when the signal was
sent and when it returned. The instrument
must know the number of complete cycles and
the point on a partial cycle when the signal
returns to the instrument. If a single beam is
used, the instrument can determine the point
in a cycle when the beam returns, but not the
number of complete cycles.
Therefore,
instruments use multiple beams with different
wavelengths. Each wavelength will reach the
sending unit at a different point in the cycle.
Comparing the return point on the cycle, for
beams with different frequencies, provides the
CPU program with the information it needs to
determine the number of cycles and the point
on the partial cycle that occurred between
when the signal was sent and when it was
received.
21
1. Some models must be calibrated for air
density.
2. They are electronic instruments and may
be more restricted by environmental
conditions.
3. They use microprocessors: no electricity =
no measurement.
4. High quality instruments are expensive.
Equipment for measuring angles and
leveling
All of the instruments listed can be used for
leveling, but only dumpy levels, automatic
levels, transits, theodolites and total stations
can be used for measuring angles.
Figure 2.6 Comparison of wave lengths
With this information, the EDM can determine
the elapsed time and the distance between
itself and the prism or the second unit.
The categories of EDM’s range from hand
held units that cost as little as $150.00 and are
not very precise or accurate to instruments that
cost tens of thousands of dollars and can be
used with the highest order of surveying.
Advantages and disadvantages of EDM's
1. Electronic distance measuring has several
advantages:
2. The operator doesn’t need to walk the
distance.
3. Distances can be taken across obstacles
such as water, trees, and rough terrain.
The only requirement is that a signal can
reach the second point and return.
4. Instruments can be purchased which have
the capability of downloading the data into
a computer, thereby eliminating the errors
associated with manually recording data.
5. Once leveled, EDM instruments can
produce a reading every few seconds.
6. They require fewer individuals to take
measurements.
7. They will measure short or long distances.
Disadvantages of EDM’s include:
Within a given type of instrument there are
many different models available based on
options, focal length, and accuracy. The best
source of information for a specific instrument
is the owners’ manual or a manufacturer's
catalogue. This section will discuss the
common categories of surveying levels.
Hand levels
Hand levels are the simplest style of level.
They have a spirit level and a single cross
hair. This style of hand level is used to insure
that chains are level when measuring
horizontal distance with plumb bobs, and
estimating slope and changes in elevation.
The common magnification is from zero to 5x.
The more sophisticated hand levels will
include stadia hairs for measuring horizontal
distance.
Figure 2.7 Hand level
The hand level illustrated uses an external
spirit level for controlling the location of the
instrument. With this type, you must be able
to hold the instrument horizontally while
22
looking through the lens. An alternative
design includes an internal level. This style
uses a split viewing area. When looking
through the eyepiece you can see on one side
the bubble for the spirit level and on the other
half the cross hair. It is easier to hold this
style of instrument in a horizontal position.
Hand levels are primarily used for estimating
slope. This is accomplished by standing at the
bottom of the slope, and while holding the
level in a horizontal position, making note of a
landmark where the line of sight strikes the
ground. Using the distance to this point and
the user’s eye height above the ground, the
slope can be determined.
Rise
% Slope =
x 100
Run
Figure 2.8 Stadia cross hairs
An explanation of measuring distance by
stadia method is included in Chapter 4.
Most Abney Levels have adjustments for both
focusing and magnification. When used with
a rod and target they provide sufficient
accuracy for preliminary surveying.
Rise is the eye height of the user, and run is
the distance from the observation point to
where the line of sight strikes the ground.
Abney level
Abney levels are a more sophisticated type of
hand level. They will usually have a direct
reading scale for vertical angles and slope,
stadia hairs, and better magnification and
optics. Stadia crosshairs are visible when
looking through the eyepiece. They are
mounted inside the telescope and allow the
instrument to be used for measuring distance.
Horizontal stadia cross hair is located an equal
distance above and below the elevation cross
hair, Figure 2.8.
Figure 2.9 Abney level
Using an Abney level
Abney levels use a split viewing area. When
the user looks through the eyepiece, half of the
area is used to view the spirit bubble and the
remaining area is for viewing the target.
To measure vertical angles or slope, the tilting
lock is loosened and the instrument is aligned
on a target the same height as
the user’s eye. While holding
the instrument on the target, the
level is tilted until the bubble is
centered. Once the tilting lock
is secured, the angle or slope
can be read from the scale.
The accuracy of both hand
levels and Abney levels is
improved if they are used in
conjunction with a stick or rod
of known height. For example,
Figure 2.10 Dumpy level
23
if the centerline of the level is held on the 5.0foot mark on a stick, the instrument height is
five feet. Any difference in the rod reading at
the unknown station from five feet is a
difference in elevation. The use of a stick will
also make it easier to hold the level steady.
Dumpy Level
The dumpy level is one of the simplest types
of levels commonly mounted on a tripod. The
use of a tripod improves the accuracy of the
instrument and provides a reference for
horizontal angles.
A dumpy level consists of a telescope with a
spirit level mounted in parallel. The telescope
will have at least one horizontal crosshair,
mounted inline with the line of sight, and may
have a vertical crosshair and two stadia
crosshairs.
The telescope and spirit level are mounted on
a mechanism (leveling plate) that rotates in a
360o horizontal circle. The entire mechanism
is mounted on a plate that can be leveled and
attached to a tripod. Accuracy is insufficient
for precise surveying, but is acceptable for
general work such as leveling forms for
concrete and shooting profiles for drainage
work. A dumpy level will also contain a
horizontal scale for measuring horizontal
angles. The precision of the angle scale will
vary because different manufacturers use
different systems. It is usually limited to the
nearest degree.
Using the Dumpy level
The first step in using the level is to set up the
tripod. The legs of the tripod should be spread
until the tripod is stable and the head of the
tripod is a good height for the operator. The
points of the legs should be planted firmly in
the ground. During this process, the head of
the tripod should be as close to horizontal as
possible. This will reduce the amount of time
that will be required to level the instrument
after it is mounted.
When the tripod is set, the instrument is
mounted on the head. All instruments are
attached by either a large diameter threaded
cap or a smaller diameter threaded bolt.
During attachment to the tripod, the base of
the instrument should be loosened so it can be
turned without releasing the instrument.
Once the instrument is mounted on the tripod,
the next step is to level the instrument (set the
telescope horizontal).
Turning the four
leveling screws in the correct sequence levels
the instrument. This process requires several
hours of practice before an individual can
level an instrument quickly.
Leveling a four legged instrument
Figure 2.11 Leveling an instrument
The first step in leveling the instrument is to
align the telescope over any two of the
adjusting screws. These two screws are
turned in opposite directions until the bubble
is between the lines on the spirit level vial.
The direction the leveling screws should be
turned depends on which way the instrument
must be tilted to make it level. In Figure 2.11,
the right hand screw is turned clockwise and
the left-hand screw is turned counter
clockwise because the right side of the
telescope needs to be lowered to level the
instrument. The opposite rotation of the
leveling screws would be used if the opposite
movement were desired.
24
The second step is to rotate the telescope 90
degrees and repeat the leveling process. These
two steps may need to be completed several
times before the instrument remains level as it
is rotated. The instrument is level when the
bubble of the spirit level stays within the lines
as the telescope is rotated 360 degrees.
minimized because the instrument can
compensate for slight movement in the tripod.
Reading an instrument
Before a reading is taken, it is necessary to
adjust the instrument for parallax. Parallax
occurs when the line of sight of the eye is not
aligned with the line of sight of the telescope.
Parallax is removed by adjusting the eyepiece
until the crosshairs are the darkest. Note: on
some instrument, the eyepiece is adjusted by
rotating the outer lens and on others, it is
adjusted by sliding the lens. If more than one
individual is reading the instrument, the
eyepiece must be adjusted each time a
different person reads the instrument.
Once the instrument is leveled and the
eyepiece adjusted for parallax, the focusing
knob is adjusted to bring the rod and/or target
into focus.
When using any surveying instrument, never
force any movement. If a part is designed to
move, but will not, do not try to force it.
Instead, check to be certain the locks have
been released.
Automatic Level
An automatic level has all the features of a
dumpy level but is easier to use. The term
“automatic” does not mean the instrument
levels itself. Instead, with the combination of
three leveling screws instead of four, and a
bull’s eye spirit level instead of a tube level,
the user can set the level much quicker. Once
the instrument is nearly level, an internal
compensator completes the leveling process
and maintains the telescope in a level position.
The compensator also prevents the instrument
from being knocked out of adjustment by
slight bumps. The effect of the wind is also
Figure 2.12 Automatic level
Automatic levels are available in several
different models. They are more accurate and
more precise than dumpy levels, but less
accurate and precise than transits or total
stations.
Laser levels
Laser levels are one of the newest types of
instruments. Laser levels can be divided into
four categories: (1) single beam invisible, (2)
single beam visible, (3) circular beam visible
and (4) circular beam invisible. Circular beam
lasers can also be categorized as rotating or
non-rotating.
A single beam laser will produce a single dot
or a short line. A circular beam laser produces
a 360-degree beam.
If an invisible beam laser is used, a detector is
mounted on the surveyor’s rod to indicate
when the detector encounters the laser beam.
Some detectors will beep and/or flash a light
when in contact with the light beam.
One distinct advantage of laser levels is that a
single person can operate them. The laser
level is mounted on a tripod and leveled.
Once turned on, the laser does not require any
supervision. The surveyor can walk around
the area and record rod readings anywhere
within the range of the beam.
25
angle. This is a handy feature when installing
drains and grading land.
Transits
Figure 2.13 Non-rotating, circular beam laser
level and detector
Figure 2.14 Transit
This is accomplished by sliding the detector
up and down a surveying rod and recording
the rod reading aligned with the pointer when
the detector beeps.
Another advantage of this system is that
multiple detectors can be used with a single
laser. This allows more than one person to
record data simultaneously.
Some lasers have the ability to establish a
beam that is not horizontal. The advantage of
this ability is being able to establish a
reference line or reference plane at a desired
Transits are the most complicated and precise
surveying instrument. Consequently, they can
be used for the widest variety of surveying
jobs. Features of transits include a telescope
that can be rotated 360 degrees horizontally
and vertically, higher power telescopes, and a
magnetic compass for bearings.
Transits are capable of measuring both
horizontal
and
vertical
angles
with a high degree
of precision. Even
though
total
stations
have
replaced transits
as the primary
surveying
instrument, they
are still very
useful when a
high degree of
accuracy
and
precision
are
required or when
a total station is
not available.
Using a transit
The process of
setting up a transit
is identical to that
of a dumpy level. Before any readings can be
taken it must be leveled, using the four
leveling screws, the eyepiece must be adjusted
for parallax and the telescope must be focused
on the rod.
The primary difference is the higher level of
care required to insure the transit is level.
Transits have more capabilities than laser or
dumpy levels, but they also have greater
possibility of error.
26
One common error is failing to set the
telescope at zero vertical degrees when using
it for horizontal measurements. Another
common problem is reading vernier scales
correctly.
(DD). In this example, each ten degrees is
labeled and each degree is not divided. The
vernier scale goes from 0 to 10. The smallest
measurement is one divided by ten or 0.1 of a
degree.
Vernier Scales
Transits and other instruments use a vernier on
the angle scales to provide a higher level of
precision. A vernier is a smaller scale
mounted to the side of the main scale.
Figure 2.15 Vernier scale
Verniers are a mechanical means of increasing
the physical size of the last unit on the main
scale so an additional level of precision is
available.
When reading a vernier the first step is to
determine the smallest possible reading,
commonly called least count.
This is
accomplished by determining the smallest
reading on the main scale and then
determining the precision of the vernier.
Figure 2.16 is an example of a double vernier,
and the degree-minute-second (DMS) angle
scale that is commonly found on transits. The
angle scales are labeled at every 10 degrees
and each degree is divided into three parts.
The precision of the angle scale is 20 minutes;
1 degree (60 minutes) ÷ 3 = 20 minutes. The
vernier has lines numbered from 0 to 20 with
no additional graduations.
The smallest
reading, least count, for this vernier is one
minute.
Figure 2.16 Double DMS vernier
Figure 2.17 is an example of a single vernier,
angle scale that reads in decimal degrees
Figure 2.17 Single DD vernier
The steps for reading a vernier are included in
Chapter 7.
The lines on vernier scales are very fine and
the scale is usually small. Some type of hand
held magnification is useful.
Other instruments
Manufacturers of surveying equipment often
develop instruments based on new technology
or for specialized uses. Examples of these are
electronic transits, transit levels, Theodolites,
and total stations.
Electronic transits
Transits are distinguished by their ability to
measure both horizontal and vertical angles
and bearings.
Transits also have the
reputation of being hard to use because of the
difficulty in reading the vernier scales. The
electronic transit has the same angle
capabilities, but it has been improved to
provide the angle readings on a digital
readout. This reduces reading errors and
speeds up the process of collecting data.
Construction transit
The terms construction transit and transit level
refers to a group of instruments that have
characteristics of both transits and levels.
They consist of a dumpy level with a
telescope having a few degrees of vertical
movement. This increases their capabilities,
but they are not considered a transit because
the telescope cannot be rotated in a full
vertical circle.
27
Theodolite
A Theodolite is very similar to a transit. It
differs primarily in the level of precision in
measuring angles. A good quality transit will
measure angles to the nearest minute. A good
quality Theolodite is capable of measuring
angles to the nearest second.
Total Station
Total stations are the instruments of choice for
modern professional surveyors. A total station
is a combination of an electronic transit and an
EDM. They can still be used visually with a
rod like a transit, but they also have the ability
to take readings electronically. They do not
use verniers, and they have either a built-in or
an attachable EDM. This allows multiple
measurements, such as horizontal angle,
vertical angle and distance to be recorded
simultaneously. When the EDM is used, the
total station uses one or more prisms to return
the beam to the instrument. With the built-in
microprocessor, readouts of horizontal
distance, vertical distance, slope distance and
angles are all possible.
Accessories
Pins
Land surveyors have traditionally used special
pins when measuring distances with a chain.
A surveying pin is usually constructed from
heavy gauge wire and painted in white and red
alternating stripes. A set consists of eleven
pins. When chaining, the individual at the
rear of the chain places one pin at the starting
point and gives the remaining ten pins to the
person at the head of the chain. The chain is
stretched out and the head person places a pin
in the ground at the 100-foot mark. The chain
is moved 100 feet and the process repeats until
the head person reaches the destination. As
the chain is moved the rear person pulls the
pins set by the head person. When the head
person is out of pins, the survey party has
traveled 10 x 100 feet or 1,000 feet. If the
distance to be measured is greater than 1,000
feet, A notation is made in the notes that the
pins have been transferred, the 10 pins are
transferred to the head person and the process
continues.
During the measurement, the appropriate
notations are recorded in the field book.
Surveying pins should not be used to mark
stations or for other purposes. If the number
on the ring is incorrect, it could cause and
error the next time they are used for chaining.
Flags or stakes should be used to mark
stations.
Field book
The field book is used to record information
from surveys. It is important to note that
when the book is opened up one sees the left
half and the right half of a page, not two pages
as in a normal book. It is very important that
the information be identified, well organized,
complete and legible.
To meet these
requirements, a standard form of organization
and locating information on the page has been
developed.
The front cover or first page in a field book is
used for the owner’s identification. The next
page(s) contain the index. The remaining
pages are used for survey information. The
information pages use a standard form to
reduce the opportunity for making mistakes
with using the data and to aide the reader in
finding information, Figure 2.18.
The purpose of identification is to provide a
means of returning the book in case it is lost
or misplaced. A set of survey data can
represent many hours of work and thousands
of dollars in expenses, all of which would
have to be repeated if the book was lost.
Figure 2.18 Organization of information in a
field book
The index should be located in the front of the
book and it should include:
1. Survey title
2. Date of survey
3. Page number(s)
If a book is used for several surveys, a page or
series of pages are used for each survey. The
pages for individual survey should include:
1. Title
2. Location
3. Data
4. Equations
5. Error checks
6. Page number
7. Weather information
8. Party names
9. Party jobs
10. Equipment list
11. Equipment identification
12. Sketch of survey
13. Benchmark description and location
14. Note keeper’s signature
Standards of practice for different disciplines
may require some differences in the location
and methods of recording information.
Some individuals prefer icons be used for the
party jobs. For example:
28
29
Rod holder
Note keeper
Chaining crew
Instrument reader
Modern professional surveyors may not use
field books because microprocessor based
electronic equipment stores data on disk that
can be loaded directly into a computer.
Printouts of this data may substitute for a field
book.
Even when data is collected
electronically, it is important to collect
weather data and party names, and to sketch
the area.
Targets are used when the distance between
the instrument and the rod are so great that the
numbers on the rod are too small to read, or
when precision to the 0.001 of a foot are
required. The target is red and white and
includes a clamp to secure it to the rod.
A surveyor’s rod is read differently than a
carpenter’s tape. When reading a carpenter’s
tape the measurement is taken from the closest
line on the tape. When reading a surveyor’s
rod, the number of transitions from black to
white must be noted. The edge of each black
line is one unit, Figure 2.20.
Rods and Targets
Surveying rods are used to measure the
distance from the ground to the optical plane
established by the level. Standard surveying
rods are essentially a 13-foot wooden ruler.
The primary difference is in the scale used to
record the measurements.
Rods can be read to the nearest 1/100th (0.01)
of a foot directly and to the nearest 1/1,000th
(0.001) when the target is used. Traditionally
rods are made of wood with a vinyl scale.
Figure 2.20 Reading a rod
Common errors in using rods include incorrect
rod reading, transposing numbers and failing
to hold the rod vertical.
Practice is the best method of controlling
reading errors, and non-vertical rods can be
eliminated by using a rod level or by rocking
the rod.
The practice of slowly rocking the rod is
based on characteristics of right triangles. As
the illustration in Figure 2.21 shows, the
shortest rod reading occurs when the rod is
vertical.
Figure 2.19 Rod and target
30
surveying. Stakes are commonly used when
establishing a turning point or when a semipermanent known elevation is needed.
Figure 2.21 Rocking a surveying rod
The person at the instrument watches the rod
readings as the rod is rocked. As the rod is
moved from vertical, the rod reading increases
and as the rod moves toward vertical, the
readings decrease. The correct reading is the
minimum reading. It will take some practice
for a survey team to determine the best speed
to rock the rod and the optimum distance to
move the top of the rod.
Range Poles
Range poles are five to six foot steel tubes
with a solid, sharp point on one end. They are
painted in alternate red and white wide stripes.
Range poles are used to provide a visual
reference for a line of travel or to locate
stations.
Stakes are usually 1-1/2 inch to 2 inches
square and 18 to 24 inches long. It is a
common practice to sharpen one end of stakes
to aid in driving them in the ground. Different
colors of paint can be used to indicate a
specific class of stakes, for example, the
centerline or grade line.
Flags are commonly used to show the route of
the survey or stations where rod readings were
taken on the ground. Flags of various colors
can be used to identify different routes.
It is also common practice to use both a stake
and a flag at each station. The stake can be
used to provide or establish a known elevation
or turning point and the flag is used to make
the spot more visible.
Nails
Surveyors have traditionally used special nails
to accurately mark a station when turning
horizontal angles and measuring distances
accurately by chaining. The nails have a
cupped head which increase the accuracy of
aligning plumb bobs with the nail.
Figure 2.23 Surveyor’s nail
Plumb bobs
Figure 2.22 Range pole
Stakes/Flags
Stakes, flags or other means of establishing
stations are necessary accessories for
Plumb bobs are used to establish a vertical
line.
Vertical lines are useful when
transferring a point vertically from the earth to
the chain when chaining horizontally and for
setting an instrument over the vertex of an
angle.
31
Good quality plumb bobs are constructed of
brass, have replaceable points, and, if cared
for properly, should last several lifetimes.
Figure 2.24 Plumb bob and string
Chapter 4.
Chapter 5.
Differential Leveling
In Chapter 1, the term level was defined as "a
comparison of the relative position of an
object with the horizon or with another
object."
into another tool or object, it can be used to
level the object. Spirit levels are attached to
or built into surveying instruments so they can
be set level.
If an object is parallel to the horizon, it is said
to be "level". This is not a new concept.
When a picture is hung on the wall, care is
taken to insure that it hangs straight--level.
Kitchen appliances are “leveled” when they
are installed. As a carpenter builds forms for
placing concrete, they are leveled, or checked
to see if they are parallel with the horizon.
This concept of “level” is also used in land
measurement and surveying. This chapter will
explain the principles of leveling and how
these principles are used in differential
leveling.
Some of the confusion surrounding the term
“level” occurs because it has multiple uses.
Not only is it used to describe the position of
two or more objects, but it is also used to
identify a group of tools. Both uses have one
commonality—they both use a spirit level.
Figure 5.1 Spirit level
A spirit level is a tube of liquid with an air
bubble. The air bubble is in the center of the
tube when the tube is horizontal, “level”.
When the spirit level is attached to or built
Leveling
Leveling is the process of determining if an
object is parallel with the horizon or if two or
more objects are at the same elevation. A
person can attach two objects to the wall and
be satisfied that they are at the same height,
but there is a good chance that another person
will not agree. It is very difficult to tell if two
or more objects are level without the use of a
tool or instrument.
The principles of leveling can be illustrated
with a simple type of level--a garden hose.
Two clear, vented, graduated tubes are
attached to a garden hose. When the hose and
tubes are filled with water and the tubes are
held in a vertical position, the water will be at
the same elevation at both ends of the hose.
32
We would say that a straight line between the
top of the water at each end of the hose is
level.
The distance over which the hose level can be
used is only limited by the length of hose the
operators are willing to manipulate.
Leveling with an instrument
Try to visualize an instrument set up so the
centerline of the instrument is at the same
level as the top of the water at one end of the
hose in Figure 5.4. If the horizontal crosshair
of the instrument telescope is at the same
elevation as the water in the first tube, then the
line of sight through the instrument will strike
the second tube at the height of the water. The
line of sight through the telescope of the
instrument establishes a level reference line.
Figure 5.2 Garden hose level
If the tubes are held near different objects, the
top of the water will indicate if the objects are
level, or at the same elevation.
Figure 5.4 Comparison of hose and instrument
Figure 5.3 Using a hose level
A hose level can also be used to determine the
difference in elevation between two points.
Figure 5.3 is an illustration of a hose level
being used to determine the difference in the
height at two ends of a wall. In this case, the
difference in height is 2.9 feet.
The hose level is not practical for surveying
large areas, nor does it have the appropriate
precision for many surveying jobs. It is useful
for demonstrating the principles of leveling
and for rough measurements.
Note: the water level as described establishes
a level surface, not a plane, but for short
differences, the difference between a level
surface and a plane can be ignored.
Because the line of sight is horizontal, if the
instrument is set up correctly, it can be used to
compare the relative elevation of two or more
objects. The rod is placed on one object, or
station, and the center crosshair is read on the
rod. The rod is then placed on the second
object, or station, and the center crosshair is
read for the second time. Subtracting the rod
readings results in the difference in elevation
between the two objects. The rod simply
measures the distance from the line of sight,
the reference line, to the top of the object the
rod is resting on. If the same reference line is
used, then the rod readings can be compared.
If the first rod reading is greater than the
second is, then the first object is at a lower
elevation than the second object.
The opposite is also true. If the first rod
reading is less than the second is, the first
object is higher than the second is. If the
difference between the rod readings is zero,
then the two objects are at the same elevation.
This is the principle of leveling used for
differential and other types of surveys. As
33
long as the instrument is set up correctly, the
line of sight through, the telescope establishes
a horizontal reference line that can be used to
compare the elevations of two or more
objects/stations.
Reference line
Figure 5.6 Line of sight
As the name implies, a reference line is a line
used as the reference, or the basis, for
measurements. A reference line may be
visible, as a line on the floor, or invisible, as
the line of sight through a surveying
instrument.
If the instrument is level, the reference line is
level. When a horizontal reference line is
established, points on, above, and below the
line can be located and compared to each
other.
For example, consider the process for laying
floor tile. The tile layer will establish a
straight line down the center of the floor
(reference line) and then start by placing the
tiles along the reference line and then move
out to the walls.
In Chapter 1, a plane was defined as a flat
surface. A reference plane is established
whenever a surveying level is rotated in a
horizontal or vertical circle.
Reference Line
Reference plane
When a horizontal reference plane is
established, the elevation of points on, above,
or below the plane can be located. The
elevations of these different points can be
compared although they are not located on the
same vertical plane.
When a horizontal plane is used, the points
being measured do not need to be in a straight
line. They can be scattered randomly above,
below or on the plane.
Figure 5.5 Reference line
The reference line establishes a line that can
be used to compare the location of all of the
floor tiles to insure they are properly aligned
and spaced.
A similar, though invisible, line is established
when using a surveying instrument. As an
individual looks through the eyepiece of the
telescope and across the center crosshair, the
line of sight establishes a reference line.
Figure 5.7 Random points on a reference
plane
Figure 5.7 is an illustration of several points
above and below a reference plane. If point A
is 5.0 feet above the horizontal plane and point
C is 7.5 feet below the plane, then the vertical
distance between point A and point C is 5.0
feet plus 7.5 feet, or 12.5 feet. In addition,
because point B is 3.5 feet above the plane,
then the difference in height between point A
34
and point B must be 5.0 feet - 3.5 feet, or 1.5
feet.
The term vertical distance was used to
describe the 12.5 foot distance between points
A & C because the distance would not be 12.5
feet if a tape were stretched between points A
and C.
The distance between the two
horizontal planes that contain points A and C
is 12.5 feet. Points A and C are not on a
vertical line; therefore, if the distance were
measured from point to point, it would be
greater than 12.5 feet.
Figure 5.9 Balancing the sights
Differential leveling
Differential leveling uses these principles of
leveling to accomplish two common tasks;
determining if objects are level and
establishing new benchmarks.
Figure 5.8 Distance point to point
In surveying, the instrument is used to
establish a reference line or reference plane.
The surveying rod is used to measure the
vertical difference between the reference line
or plane and the points being surveyed.
Comparing objects
Differential leveling is used to compare the
top of the forms before placing concrete. The
instrument is set up and leveled. A rod is used
to determine the elevation of the tops of the
forms at several locations.
As long as the reference line or plane is
horizontal, all of the points measured from the
reference line or plane can be compared.
Balancing the sights
Whenever a surveying instrument is used, it
should be, if possible, set up halfway between
the two points being measured. This is called
balancing the sights.
Establishing the instrument position halfway
between the two stations will reduce the
chance of an error caused by the instrument
not being level. See Figure 5.9.
Figure 5.10 Using differential leveling
If the three different rod readings in Figure
5.10 are the same, then the top of the form is
level.
Establishing benchmarks
The second common use of differential
leveling is establishing the elevation of a new
benchmark. If the existing benchmark and the
location of the new benchmark can be seen
from one instrument position, then the
procedure is very simple.
The instrument is set up halfway between the
points and leveled. A rod reading is taken on
35
the existing benchmark, this is called a
backsight, and on the new benchmark, the
foresight. The backsight reading is added to
the elevation of the existing benchmark to
establish the height of the line of sight,
reference line.
This is also called the
instrument height (IH), or height of instrument
(HI). Then foresight is subtracted from the
instrument height. The result is the elevation
of the new benchmark.
Turning points
As defined in Chapter 1, a turning point is a
temporary benchmark. They are used to
extend the survey along the route when both
benchmarks can not be seen from one
instrument position. Three primary factors
cause this condition; the line of sight running
into the ground, blocked view and instrument
limitations.
Figure 5.11 Turning point
One example of the use of benchmarks is
illustrated in Figure 5.11. In this example, the
line of sight at IP1 will run into the ground
before reaching BM2. The use of a turning
point allows the instrument to be moved and
reset at a higher elevation.
Turning points are also used when the line of
sight is blocked by trees, structures, and other
objects. The third use of turning points is
because of the limitations of the instrument.
The potential for error increases as the
distance between the rod and the instrument
increases. Optics of instruments are designed
with a maximum recommended distance. If
the two stations being used are greater than
two times the maximum recommended
distance, then a turning point must be used.
The elevation of turning points is calculated as
if they where benchmarks. A backsight is
recorded for the benchmark and a foresight is
recorded for the turning point. With this
information, the elevation of the turning point
can be determined.
When the elevation of the turning point is
known, then the instrument can be moved to
IP2 and the process is repeated. When the
instrument is at IP2 the backsight on the
turning point and the foresight on BM2 is used
to calculate the elevation of BM2.
The example in Figure 5.11 is completed by
used only one turning point. There is no limit
on the number of turning points that can be
used, but part of the art of differential leveling
is being able to complete the survey with the
fewest number of turning points. As the
number of turning points used increases, the
amount of time required to complete the
survey increases and the opportunity for error
increases.
Note: The elevation of the turning points is
used to complete the survey and check for
errors. They do not provide data that is used
for design or calculations.
The purpose of differential leveling is to
compare the elevation of two or more points.
The data collected will not allow the user to
define or draw the topography between the
two points. The primary influence of the
topography is the difficulty it presents for
completing the survey.
It is much easier to complete a differential
leveling survey on a flat open field, than if the
survey must traverse hills, forests, creeks etc.
The time and resources required to establish a
new benchmark will depend on the distance
between the existing and new benchmark, and
the hazards of the terrain between the two
points.
36
Differential example
In this example we want to determine the
elevation of Station B when the elevation of
Station A is 100.00 feet.
Figure 5.12 Differential example backsight
The instrument is set up halfway between
Station A and Station B. The instrument is
leveled and a backsight of 8.47 feet is
recorded at Station A, Figure 5.12
of this table helps organize the data, making it
easier to read. It also reduces errors in
recording and completing calculations.
Differential data table
The table used for differential leveling data
uses columns and rows. Columns are used for
the different types of numbers and rows are
used for the stations. For the example in
Figure 5.12 and Figure 5.13, the rod reading
of 8.47 feet is a backsight on Station A;
therefore, it is placed in row A, column BS.
STA
A
B
BS
8.47
HI
108.47
FS
6.11
ELEV
100.00
102.36
STA = Station
BS = Backsight
HI = Height of instrument
FS = Foresight
ELEV = Elevation
Table 5.1 Differential leveling table
Figure 5.13 Differential example foresight
The instrument is rotated to align on Station B
and a foresight of 6.11 feet is recorded, Figure
5.13. Because station A and station B are both
visible from one instrument position, the
survey is complete. Sufficient data has been
collected to determine the elevation of Station
B.
100.00 +8.47 =108.47
108.47 - 6.11 =102.36
If the elevation of benchmark one (Station A)
is 100.00 feet, then the elevation of
benchmark two (Station B) is 102.36 feet.
This example is simple and therefore the
amount of data generated is small and easy to
manage. For surveys that are more complex,
the amount of data will be much larger and
more difficult to manage.
To reduce the chance of random errors in
managing differential data, a standard style of
table has been developed, Table 5.1. The use
The rod readings are recorded in the columns
labeled BS and FS. The numbers in the
columns labeled HI and ELEV are
calculations. The calculations are governed
by two equations.
HI = ELEV + BS
ELEV = HI - FS
In this example, Table 5.1, the elevation of
102.36 feet for station B is only correct if no
errors were made during the survey. It is not
safe to assume there were no errors.
Data collected by differential surveying is not
used until it is checked for errors.
A good way to begin checking data is the eye
ball test. Look at the data. See if everything
looks correct.
For example, differential
surveying notes should have the same number
of backsights as foresights and the FS column
of row A should be blank.
37
Three checks for error
Three standard checks for error have been
developed. These are closing the loop, the
note check, and allowable error of closure.
Closing the loop
Closing the loop means surveying back to the
starting point. It may or may not follow the
same route. When closing the loop one
assumes that, the difference in elevation
between station A & B has not been
determined. Another differential survey is
completed, but this time the starting point is
station B and the survey is conducted to
station A.
The first step is to move the instrument from
the position used to record the foresight on
station B. The instrument is leveled and a
backsight recorded on Station B.
STA
A
B
A
BS
8.47
6.21
HI
108.47
108.57
FS
6.11
8.58
ELEV
100.00
102.36
99.99
Table 5.2 Completed differential table
The calculations in Table 5.2 show that the
elevation of Station A was 100.00 feet at the
start of the survey, but only 99.99 feet at
closing. An error of 0.01 occurred sometime
during the survey. If there is an error in the
survey, then the calculated elevation of Station
B (102.36) must be questioned.
Benchmarks by definition are structures that
are stable and have a constant elevation. If the
elevation of station A was 100.00 feet at the
start of the survey, then it should be 100.00
feet at the end of the survey. Any difference
in the elevation of BM1 from the start of the
survey to the elevation determined during the
closing loop is caused by error.
The second check for error, note check, is
used to determine if the error is caused by a
math mistake in the data table.
Figure 5.14 Closing backsight
The purpose of moving the instrument is to
insure that the backsight rod reading for
closing is different from the previous foresight
reading.
Then the instrument is rotated and a foresight
reading is recorded for Station A.
Figure 5.15 Closing foresight
These numbers are recorded in the table in the
appropriate spot and the math completed.
Note check
The data is checked for math errors through a
procedure called the note check. The purpose
of the note check is to determine if an addition
or subtraction error was made during the
calculations. It also may indicate if a number
was transposed when recorded. The note
check is based on the following equation:
| FS- BS | = | BM1 i - BM1c |
This equation reads, “absolute value of the
sum of the foresights minus the sum of the
backsights equals the absolute value of the
elevation of benchmark one initially minus the
elevation of benchmark one at closing”. If
this equation is true, the error in the notes is
not caused by an error in the calculations. If
this equation is not true, there is a math error
in the notes and they must be refigured.
38
In this example the note check results in:
|14.68 -14.69 | = | 100.00 - 99.99 |
0.01 = 0.01
The statement is true. The difference in
elevation for Station A is not caused by a math
error in the notes.
The source of the error could be in an
incorrect reading of the rod, the rod not being
plumb, instrument not level, etc.
Although there is an error in the survey, the
data may still be useable. One additional
check is completed to determine if the data is
useable.
Allowable error of closure
The third check for error is determining the
allowable error of closure.
The concept of allowable error developed
because engineers and surveyors realized that
it is not realistic to expect surveys to be
completed without any error. Some surveys
may travel many miles. The characteristics of
the environmental and topography may make
surveying very difficult. Therefore, a system
was developed that determines an allowable
error.
This was accomplished by establishing classes
of survey with an allowable error for each
class. The higher the class of survey, the less
error is acceptable.
The allowable error (AE) of closure is
determined by the equation:
AE = K M
The allowable error is equal to the constant K
times the square root of M. The variable M is
the total distances traveled during the survey,
in miles. The value for K can range from 1.00
to 0.001, depending on the class of survey. A
K value of 0.1 or 0.01 is appropriate for most
general construction work. A K value of 0.01
to 0.001 is used for boundary surveys, and for
projects, that have very stringent error
requirements.
If we assume the distance in the previous
example between Station A and Station B is
524.2 feet and the appropriate value for K is
0.1, then the allowable error is:
AE = 0.1 524.1 ft. x 2 5280 ft.
= 0.04
In this example because the actual error, 0.01,
is less than the allowable error, 0.04, the
correct conclusion is that the survey is
acceptable. Note: this doesn't mean that the
survey is correct. It only means that if the
individuals involved will accept a survey done
with a K value of 0.1, the results are
acceptable. The value for K must be agreed
upon before the survey is conducted.
Differential leveling example
The following figure illustrates a more
complicated differential survey.
Figure 5.16 Differential survey requiring a
turning point.
In this example, a single setup of the
instrument is not workable, as the instrument
line of sight strikes the ground before station
B. This situation requires the use of at least
one turning point.
The first step is to determine the best location
for the turning point. The best location is one
that is in view from IP1 and IP2, and provides
a stable structure.
Next, the instrument is set up halfway
between Station A and the turning point, and
then leveled. The first rod reading is a
backsight on Station A.
39
recorded to reestablish the height of the
instrument.
Figure 5.17 Backsight on station A
This rod reading (8.19 ft.) is recorded in the
Station A row of the backsight column and is
used to determine the height of the instrument
(108.19). In this example, the elevation of
Station A is assumed to be 100.00 feet.
STA
A
B
BS
8.19
HI
108.19
FS
ELEV
100.00
Figure 5.19 Backsight on turning point one
The reading of 10.97 ft. is recorded in the TP1
row of the backsight column and is used to
establish the height of the instrument (112.63
ft.).
STA
A
TP1
Table 5.3 Differential example with backsight
and height of instrument
The next step is to rotate the instrument and
record the foresight on the turning point.
BS
8.19
10.97
HI
108.19
112.63
FS
6.53
ELEV
100.00
101.66
Table 5.5 Differential example with elevation
of turning point
The last step is to rotate the instrument and
record the foresight reading for Station B.
Figure 5.18 Foresight on turning point
The rod reading of 6.53 ft. is recorded in the
turning point one (TP1) row of the foresight
column and used to determine the elevation of
turning point one.
STA
A
TP1
BS
8.19
HI
108.19
FS
6.53
ELEV
100.00
101.66
Table 5.4 Differential example with foresight
and turning point elevation
Next, the instrument is moved to a location
approximately halfway between turning point
one and Station B. Each time the instrument
is moved, it must be leveled and a backsight
Figure 5.20 Station B foresight
The reading of 2.22 feet is recorded in the data
table and used to determine the elevation of
Station B (110.41 ft.).
STA
A
TP1
B
BS
8.19
10.97
HI
108.19
112.63
FS
6.53
2.22
ELEV
100.00
101.66
110.41
Table 5.6 Differential example with elevation
of Station B
The elevation of Station B has been
determined, but the survey is not acceptable
until the three checks for error are completed.
40
TP1
B
TP2
A
10.97
2.53
6.55
112.63
112.94
108.75
6.53
2.22
10.74
8.74
∑
28.24
28.23
|28.24-28.23| = |100.00-100.01|
.01 =.01
Notes acceptable
101.66
110.14
102.20
100.01
Figure 5.21 Closing loop
In this example of closing the loop, all of the
information is included in one figure. In the
field, each reading would be recorded in the
backsight-foresight sequence as in the first
portion of this example.
Table 5.7 includes this information with the
note check and check for allowable error.
STA
A
BS
8.19
HI
108.19
FS
ELEV
100.00
AE = K M
= 0.1 1091.4 5280
= 0.04
0.01 < 0.04
Error of closure is acceptable
Table 5.7 Differential example completed
The principles of leveling discussed in this
example problem are also used for profile and
topographic surveys. These will be discussed
in the following chapters.