An Introduction to

Horizontal Control
Survey Techniques

J. Paul Guyer, P.E., R.A.

Editor

Paul Guyer is a registered civil engineer,

mechanical engineer, fire protection engineer and
architect with 35 years of experience designing
buildings and related infrastructure. For an
additional 9 years he was a principal staff advisor
to the California Legislature on capital outlay and
infrastructure issues. He is a graduate of Stanford
University and has held numerous national, state
and local offices with the American Society of Civil
Engineers, Architectural Engineering Institute and
National Society of Professional Engineers. He is
a Fellow of ASCE, AEI and CABE (U.K.).
 An Introduction to
Horizontal Control Survey
Techniques

J. Paul Guyer, P.E., R.A.

Editor

The Clubhouse Press

El Macero, California
 CONTENTS

1. INTRODUCTION
2. TRADITIONAL HORIZONTAL CONTROL SURVEY TECHNIQUES
3. SECONDARY OR TEMPORARY HORIZONTAL CONTROL
4. BEARING AND AZIMUTH DETERMINATION
5. ELECTRONIC DISTANCE MEASUREMENT
6. COORDINATE COMPUTATIONS
7. TRAVERSE SURVEYS
8. TRAVERSE SURVEY GUIDELINES
9. TRAVERSE COMPUTATIONS AND ADJUSTMENTS
10. TRAVERSE ADJUSTMENT (COMPASS RULE)
11. TRIANGULATION AND TRILATERATION SURVEYS

(This publication is adapted from the Unified Facilities Criteria of the United States government which are
in the public domain, have been authorized for unlimited distribution, and are not copyrighted.)

(Figures, tables and formulas in this publication may at times be a little difficult to read, but they are the
best available. DO NOT PURCHASE THIS PUBLICATION IF THIS LIMITATION IS UNACCEPTABLE
TO YOU.)
1. INTRODUCTION

1.1 PURPOSE AND SCOPE. Control surveys are performed to establish a

monumented reference system for a facility mapping project. These fixed horizontal
control points and vertical benchmarks are then used as starting points for supplemental
topographic site plan mapping.

1.2 HORIZONTAL CONTROL SURVEY METHODS. Horizontal positions of permanent

monuments around a facility or project site can be established by a number of survey
techniques. These include traditional traverse, triangulation, or trilateration surveys from
an established geodetic network on an installation or region (e.g., NSRS). Alternatively,
GPS methods can be performed to extend control from an established network to the
project site. Since most modern day survey crews or firms possess both GPS and total
station equipment, there would be little justification for running lengthy (and costly)
traverses or triangulation/trilateration networks to bring in control to a local site.
Therefore, this discussion will focus on current practices for performing "traditional"
horizontal control surveys--i.e. control being established using total station traverse
methods. (This discussion does contain some background on older survey methods for
use in basic surveying courses). Triangulation and trilateration methods will only be
briefly addressed.

1.3 VERTICAL CONTROL SURVEY METHODS. As with horizontal control

densification, a number of survey methods can be used to bring vertical control from an
established datum into a project site. These include trigonometric leveling (e.g., a total
station), differential (spirit) leveling, and differential GPS techniques. Since most facility
mapping projects require fairly accurate elevations relative to a local network, traditional
differential leveling is still the most effective and reliable method of transferring
elevations. GPS elevation transfer methods are reliable over short distances; however,
they are not as accurate as differential leveling methods.

© J. Paul Guyer 2017 1

2. TRADITIONAL HORIZONTAL CONTROL SURVEY TECHNIQUES

2.1 GENERAL OVERVIEW

2.1.1 PURPOSE. Horizontal control is established to serve as a basic framework for

large mapping projects, to establish new horizontal control in a remote area, or to
further densify existing horizontal control in an area.

2.1.2 INSTRUMENTS. Minimum instrument requirements for the establishment of

primary control will typically include a repeating theodolite having an optical micrometer
with a least-count resolution of six seconds (6") or better; a directional theodolite having
an optical micrometer with a least count resolution of one arc-second; an EDM capable
of a resolution of 1:10,000; or a total station having capabilities comparable to, or better
than, any of the instruments just detailed. A calibrated 100-ft steel tape may also be
used for measuring short distances.

2.1.3 MONUMENTATION. Primary project horizontal control points not permanently

monumented in accordance with appropriate criteria and guidance should meet the
following minimum standards:

2.1.3.1 MARKERS. Project horizontal control points should be marked with semi-
permanent type markers (e.g., re-bar, railroad spikes, or large spikes). If concrete
monuments are required, they will be set prior to horizontal survey work.

2.1.3.2 INSTALLATION. Horizontal control points should be placed either flush with the
existing ground level or buried a minimum of one-tenth of a foot below the surface.

2.1.3.3 REFERENCE MARKS. Each primary control point should be referenced by a

minimum of two points to aid in future recovery of that point. For this reference, well-
defined natural or manmade objects may be used. The reference point(s) can be either
set or existing and should be within 100 ft of the control point.

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2.1.3.4 SKETCHES. A sketch should be placed in a standard field survey book or on a
standard form, such as Figures 3-1 and 3-2. The sketch, at minimum, will show the
relative location of each control point to the reference points and major physical features
within 100 ft of the point.

2.1.4 REDUNDANCY. A minimum of two repeated angle measurements (i.e. positions

or sets) should be made for establishing project control points. With EDM distance
measurements, a minimum of two readings should be taken at each setup and recorded
in a standard field book (or data collector). The leveled height of the instrument and the
height of the reflector should be measured carefully to within 0.01 ft and recorded. Each
measured slope distance (taped or EDM) should be reduced to a horizontal distance
using either reciprocal vertical angle observations or the known elevation of each point
obtained from differential leveling. Duplicate distances should be observed over each
line by remeasuring backsight lines at each traverse point set up. Depending on the
accuracy requirements, additional sets of angle measurements or EDM distances may
be specified.

© J. Paul Guyer 2017 3

 Figure 3-1.
Form -- Description or Recovery of Horizontal Control Station

© J. Paul Guyer 2017 4

 Figure 3-2
Blank Form 1959 -- Description or Recovery of Horizontal Control Station

© J. Paul Guyer 2017 5

2.1.5 REPEATING THEODOLITE. If a repeating theodolite (e.g., a Wild T1) is used for
the horizontal angles, the instrument will be pointed at the backsight station with the
telescope in a direct reading position, and the horizontal vernier set to zero degrees. All
angles should then be turned to the right, and the first angle recorded in a field book.
The angle should be repeated a minimum of four times (i.e. two sets) by alternating the
telescope and pointing in the direct and inverted positions. The last angle will also be
recorded in the field book. If the first angle deviates more than five seconds (5") from
the result of the last angle divided by four, the process should be repeated until the
deviation is less than or equal to five seconds. Multiples of 360 degrees may need to be
added to the last angle before averaging. The horizon should be closed by repeating
this process for all of the sights to be observed from that location. The foresight for the
last observation should be the same as the backsight for the first observation. If the sum
of all the angles turned at any station deviates more than ten seconds (10") from 360
degrees, the angles should be turned again until the summation is within this tolerance.

2.1.6 DIRECTIONAL THEODOLITE. If a directional theodolite (e.g., Wild T2 or Wild

T3) is used for the horizontal angles, the instrument should be pointed at the backsight
station with the telescope in a direct reading position and the horizontal scales set to
within ten seconds (10") of zero degrees. The scales should be brought into coincidence
and the angle read and recorded in the field book. The angles (directions) should then
be turned to each foresight in a clockwise direction, and the angles read and recorded
in a field book. This process will continue in a clockwise direction and should include all
sights to be observed from that station. The telescope should then be inverted and the
process repeated in reverse order, except the scales are not to be reset, but will be read
where it was originally set. The angles between stations may then be computed by
differencing the direct and reverse readings. This process of observing a "set" should be
repeated two or more times, depending on the survey specification. It is difficult to set
the angle values precisely on the plates of an optical theodolite. Angles are determined
by reading the initial and the final directions, and then determining the angular
difference between the two directions. Optical theodolites are generally very precise--a
Wild T2 optical theodolite reads directly to 1". If several sets are required for precision

© J. Paul Guyer 2017 6

purposes, distribute the initial settings around the plate circle to minimize the effect of
circle-graduation distortions.

2.1.7 HORIZONTAL DISTANCES. To reduce EDM slope distances to horizontal, a

vertical angle observation must be obtained from each end of each line being
measured. The vertical angles should be read in both the direct and inverted scope
positions and adjusted. If the elevations for the point on each end of the line being
measured are obtained by differential leveling, then this vertical angle requirement is not
necessary.

2.1.8 TARGETS. All targets established for backsights and foresights should be fixed
and centered directly over the measured point. Target sights may be a reflector or other
type of target set in a tribrach, a line rod plumbed over the point in a tripod, or
guyed/fixed in place from at least three positions. Artificial sights (e.g., a tree on the hill
behind the point) or hand held sights (e.g., line rod or plumb bob string) should not be
used to set primary control targets.

2.1.9 CALIBRATION. All theodolites, total stations, EDM, and prisms used for
horizontal control work should be serviced regularly and checked frequently. Tapes and
EDMs must be periodically calibrated over lines of known length, such as NGS
calibration baselines. Instrument calibrations should be done at least annually.
Theodolite instruments should be adjusted for collimation error at least once a year and
whenever the difference between direct and reverse reading of any theodolite deviates
more than thirty seconds from 180 degrees. Readjustment of the cross hairs and the
level (plate) bubble should be done whenever misadjustments affect the instrument
reading by more than the least count of the reading scales of the theodolite. Forced
centering type tribrachs should be periodically (monthly) checked to ensure the optical
plumb line is correct. Circular or "bulls eye" bubbles on tribrachs, total stations, rods,
etc. should be periodically checked and adjusted. Tribrach or total station optical
plummets (visual or laser) must be periodically checked.

© J. Paul Guyer 2017 7

2.1.10 HORIZONTAL DIRECTION RECORDING. Procedures for recording horizontal
directions are the same for all orders of accuracy. Record horizontal directions in a
bound field survey book (see Figure 3-3 below), or any equivalent electronic recording
form. Each time a point is occupied, the following information should be recorded--either
on the Title Page or entry page, as appropriate:

Title Page:
• Instrument make, model, and serial number.
• Instrument operator’s name.
• Recorder’s name.
• Weather description.
o Temperature.
o General atmospheric condition.
o Wind.
Entry Page:
• Designation of the occupied station.
o Full station name.
o Year established.
o Name of the agency on the disk.

The field book or recording form should include the above information for each station
observed. If an instrument, signal, or target is set eccentric to a station (not plumbed
directly over the station mark), that item should be sketched on the recording form. The
sketch should include the distance and the directions that the eccentric item is from the
station. When intersection stations are observed, the exact part of the point observed
must be recorded and shown on the sketch.

2.1.11 HORIZONTAL ABSTRACTS OF DIRECTIONS. An abstract of horizontal

directions should be compiled for every station at which horizontal directions have been
observed. An appropriate form or equivalent field book abstracts should be completed
before leaving the point. If a horizon closure is specified, the corrected station angle and

© J. Paul Guyer 2017 8

the corrected explement angle should be recorded in the field book before leaving the
point. If a form is used, readings will be entered opposite the proper circle position, as
indicated in the field notes. The degrees and minutes for each direction are entered one
time at the top of each column, and the seconds are entered for each circle position.

Figure 3-3
Sample horizontal field book recording--Directional Theodolite

© J. Paul Guyer 2017 9

3. SECONDARY OR TEMPORARY HORIZONTAL CONTROL

3.1 GENERAL. Secondary horizontal control is established to determine the location of

structure sections, cross sections, or topographic features, for construction control, or to
pre-mark requirements for small to medium scale photogrammetric mapping. These
points are often temporary in nature and can easily be reset from the permanent
primary control points.

3.2 REQUIREMENTS. Secondary horizontal control requirements are identical to that

described for primary horizontal control with the following exceptions.

3.2.1 MONUMENTATION. It is not required for secondary horizontal control points to

have two reference points. Wooden hubs, PK nails, or other similar markings are
adequate. Descriptions or sketches are usually not required.

3.2.2 WHEN A TOTAL STATION OR EDM IS USED, a minimum of two readings

should be taken at each setup and recorded in a standard field book or electronic data
collector.

3.2.3 IF A REPEATING THEODOLITE is used for the horizontal angles, the angle
measurement should be repeated a minimum of two times by alternating the telescope
and pointing in the direct and inverted positions.

3.2.4 IF A DIRECTIONAL THEODOLITE is used for the horizontal angles, the process
(described for primary control) should be repeated two times--for a total of two data set
collections.

© J. Paul Guyer 2017 10

4. BEARING AND AZIMUTH DETERMINATION. Horizontal angles are usually turned
(or deflected) to the right or left. The three types of angle measurements are as follows:

 Interior angles. If angles in a closed figure are to be measured, the interior angles
are normally read. When all interior angles have been recorded, the accuracy of
the work can be determined by comparing the sum of the abstracted angles with
the computed value for the closed loop (Figure 3-4 below).
 Deflection angles. In an open traverse (Figure 3-4), the deflection angles are
measured from the prolongation of the backsight line to the foresight line. The
angles are measured either to the left or to the right. The direction must be
shown along with the numerical value.
 Vertical angles. Vertical angles can be referenced to a horizontal or vertical line
(Figure 3-5).

Optical-micrometer theodolites measure vertical angles from the zenith (90° or 270°
indicate a horizontal line). Zenith and nadir are terms describing points on a sphere. The
zenith point is directly above the observer, and the nadir point is directly below the
observer. The observer, the zenith, and the nadir are on the same vertical line.

© J. Paul Guyer 2017 11

 Figure 3-4
Interior angles on a closed traverse (top) and deflection angles
on an open traverse (bottom)

© J. Paul Guyer 2017 12

 Figure 3-5
Reference directions for vertical angles--Horizontal, Zenith, and Nadir

4.1 BEARING TYPES. The bearing of a line is the direction of the line with respect to a
given meridian. A bearing is indicated by the quadrant in which the line falls and the
acute angle that the line makes with the meridian in that quadrant. Observed bearings
are those for which the actual bearing angles are measured, while calculated bearings
are those for which the bearing angles are indirectly obtained by calculations. A true
bearing is made with respect to the astronomic north reference meridian. A magnetic
bearing is one whose reference meridian is the direction to the magnetic poles. The
location of the magnetic poles is constantly changing; therefore the magnetic bearing
between two points is not constant over time. The angle between a true meridian and a
magnetic meridian at the same point is called its magnetic declination. An assumed
bearing is a bearing whose prime meridian is assumed. The relationship between an
assumed bearing and the true meridian should be defined, as is the case with most
SPCS grids.

© J. Paul Guyer 2017 13

4.2 BEARING DETERMINATION GUIDELINES. All bearings used for engineering
applications should be described by degrees, minutes, and seconds in the direction in
which the line is progressing. Bearings are recorded with respect to its primary direction,
north or south, and next the angle east or west. For example, a line can be described as
heading north and deflected so many degrees east or west. Alternatively, a line also can
be described as heading south and deflected so many degrees east or west. A bearing
will never be listed with a value over 90 degrees (i.e. the bearing value always will be
between over 0 degrees and 90 degrees. Bearing angles are computed from a given
azimuth depending on the quadrant in which the azimuth lies. When the azimuth is in
the first quadrant (0° to 90°), the bearing is equal to the azimuth. When the azimuth is in
the second quadrant (90° to 180°), the bearing is equal to 180° minus the azimuth.
When the azimuth is in the third quadrant (180° to 270°), the bearing is equal to
the azimuth minus 180°. When the azimuth is in the fourth quadrant (270° to 360°), the
bearing is equal to 360° minus the azimuth. Since the numerical values of the bearings
repeat in each quadrant, the bearings must be labeled to indicate which quadrant they
are in. The label must indicate whether the bearing angle is measured from the north or
south line and whether it is east or west of that line. For example, a line with an azimuth
of 341° 12' 30" falls in the fourth or northwest (NW) quadrant and its bearing is N 18° 47'
30" W.

4.3 AZIMUTH TYPES. The azimuth of a line is its direction as given by the angle
between the meridian and the line, measured in a clockwise direction. Azimuths can be
referenced from either the south point or the north point of a meridian. (Geodetic
azimuths traditionally have been referenced to the south meridian whereas grid
azimuths are referenced to the north meridian). Assumed azimuths are often used for
making maps and performing traverses, and are determined in a clockwise direction
from an assumed meridian. Assumed azimuths are sometimes referred to as "localized
grid azimuths." Azimuths can be either observed or calculated. Calculated azimuths
consist of adding to or subtracting field observed angles from a known bearing or
azimuth to determine a new bearing or azimuth.

© J. Paul Guyer 2017 14

4.4 AZIMUTH DETERMINATION GUIDELINES. Azimuths will be determined as a line
with a clockwise angle from the north or south end of a true or assumed meridian. For
traverse work using angle points, the traverse closure requirements outlined in Chapter
4 will be followed.

4.5 ASTRONOMIC AZIMUTH. In order to control the direction of a traverse, an

astronomic azimuth must be observed at specified intervals and abrupt changes of
direction of the traverse. Astronomic azimuth observations can be made by the well-
known hour angle or altitude methods. Azimuth observations should be divided evenly
between the backsight and foresight stations as reference objects. Using the rear
station, turn clockwise to forward station then to star, reverse telescope on star, then
forward station and back to rear station. Then using forward station, turn clockwise to
rear station then to star, reverse telescope on star, then rear station and back to forward
station. The number of position repetitions will depend upon the order of accuracy
required. Since GPS has effectively eliminated the need for lengthy traverse networks,
astronomic azimuth observations are rarely ever required. Exceptions may involve
boundary surveys originally referenced from solar azimuth observations. Procedures for
observing astronomic azimuths can be found in the references listed at Appendix A-2.
(Note that GPS azimuths determined relative to WGS 84 must be corrected to the
reference orientation of the local datum).

© J. Paul Guyer 2017 15

5. ELECTRONIC DISTANCE MEASUREMENT. The distance between two points can
be horizontal, slope, or vertical. A tape measure or an EDM device (such as a total
station) can measure horizontal and slope distances. A distance measured on a slope
can be trigonometrically converted to its horizontal equivalent by using the slope angle
or vertical difference of elevation (DE). Figure 3-6 below illustrates a basic example of
the geometry used to determine the horizontal distance of a measurement over uneven
ground.

Figure 3-6
Geometry of an EDM measurement

Alternatively, the elevations of the occupied hubs (Stations A and B in Figure 3-6 above)
may have been determined by differential levels. Applying the measured HI and HT
yields the absolute elevation of the instrument and target. The measured slope distance
"S" can then be reduced to a horizontal distance "H" given the delta elevation between
the instrument and target. A meteorological correction is applied to the observed slope
distance before reducing it to horizontal. Subsequently, the horizontal distance is
corrected for grid scale and sea level. A traditional field book example of a horizontal
slope distance observation is shown in Figure 3-7 below. In this example, slope
distances are manually recorded along with meteorological data. A series of 10 slope

© J. Paul Guyer 2017 16

distances were observed and averaged. A meteorological correction is applied along
with a constant instrument/system constant. The resultant slope distance "T" (76.106 m)
is reduced to horizontal, then to a grid distance (Hg in Figure 3-7). No sea level
correction was applied since this project was set on an arbitrary datum (PICES). Note
that Figure 3-7 illustrates the internal computations now automatically performed in a
total station/data collector system.

Figure 3-7
Horizontal distance observations and reductions--manual computations in field book

5.1 ERRORS. Distances measured using an EDM are subject to the same errors as
direction measuring equipment. The errors also include instrumental component errors.
Instrumental errors are usually described as a number of millimeters plus a number of
ppm. The accuracy of the infrared EDM is typically ± (5 millimeters + 5 ppm). The ppm
© J. Paul Guyer 2017 17
accuracy factor can be thought of in terms of millimeters per kilometer, as there are 1
million millimeters in 1 kilometer. This means that 5 ppm equals 5 millimeters per
kilometer. Errors introduced by meteorological factors must be accounted for when
measuring distances of 500 meters or more. Accurate ambient temperature and
barometric pressure must be measured. An error of 1 degree Celsius (C) causes an
error of 0.8 ppm for infrared distances. An error of 3 millimeters of mercury causes an
error of 0.9 ppm in distance.

5.2 INSTRUMENT CONSTANTS. Although manufacturers provide instrument and

prism constants, it is essential that instrument constants be verified under actual
operating conditions, especially for precise surveys. The following factors must be
considered:

• The use of a prism typically provides an indicated distance longer than the true
value. Applying a negative correction will compensate for this effect. Each prism
should have its own constant or correction determined individually, and a master
file should be maintained.
• An instrument constant can be either positive or negative and may change due to
the phase shifts in the circuitry. Therefore, a positive or a negative correction
may be required.
• The algebraic sum of the instrument and the prism constants are referred to as
the total constant. The correction for the total constant (equal in magnitude but
opposite in sign) is referred to as the total constants correction, from which the
instrument or prism constant can be computed if one or the other is known.

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6. COORDINATE COMPUTATIONS. If the coordinate of a point and the azimuth (or
bearing) and distance from that point to a second point are known, the coordinate of the
second point can be computed. In Figure 3-8 below, the azimuth and distance from
Station A to Station B are determined by measuring the horizontal angle ( β ) from the
azimuth mark to Station B and the distance from Station A to Station B.

Figure 3-8
Forward Position Computation

The azimuth (or bearing) from A to B ( α ) is determined by reducing the observed

azimuth to the relative quadrant. For example, in Figure 3-8, if the azimuth from Point A
to the Azimuth Mark is 320°, and observed angle "β" from Station A between the
reference azimuth point and Point B is 105°, then the azimuth of the line from Point A to
Point B "α" is computed from:

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The computation of the difference in northing (dN) and the difference in easting (dE)
requires the computation of a right triangle. The distance from Station A to Station B ("s"
in Figure 3-8--reduced to horizontal, sea level, corrected for grid scale, etc.) is the
hypotenuse of the triangle, and the bearing angle (azimuth) is the known angle. The
following formulas are used to compute dN and dE:

If the traverse leg falls in the first (northeast [NE]) quadrant, the value of the easting
increases as the line goes east and the value of the northing increases as it goes north.
The product of the dE and the dN are positive and are added to the easting and
northing of Station A to obtain the coordinate of Station B, as shown in Figure 3-8.
When using trigonometric calculators to compute a traverse, enter the azimuth angle,
and the calculator will provide the correct sign of the function and the dN and the dE. If
the functions are taken from tables, the computer provides the sign of the function
based on the quadrant. Lines going north have positive dNs; lines going south have
negative dNs. Lines going east have positive dEs; lines going west have negative dEs.
The following are examples of how to compute the dN and the dE for different
quadrants:

© J. Paul Guyer 2017 20

© J. Paul Guyer 2017 21
7. TRAVERSE SURVEYS. A traverse survey is defined as the measurement of the
lengths and directions of a series of straight lines connecting a series of points on the
earth. Points connected by the lines of a traverse are known as traverse stations. The
measurements of the lengths and directions are used to compute the relative horizontal
positions of these stations. Traversing is used for establishing basic area control where
horizontal positions of the traverse stations, and elevations of the stations, must be
determined. If reference azimuth marks or features are not available, astronomic
observations and/or GPS-derived azimuths are made along a traverse at prescribed
intervals to control the azimuth alignment of the traverse. The interval and type of
controlling azimuth observation will depend upon the order of accuracy required and the
traverse methods used; and the availability of existing control.

7.1 TRAVERSE TYPES. There are two basic types of traverses, namely, closed
traverses and open traverses.

7.1.1 CLOSED TRAVERSE. A traverse that starts and terminates at a station of known
position is called a closed traverse. The order of accuracy of a closed traverse depends
upon the accuracy of the starting and ending known positions and the survey methods
used for the field measurements. There are two types of closed traverses.

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 Figure 3-9
Closed Traverse--Looped (Station A fixed) or Connecting (Stations A and B fixed)

7.1.1.1 LOOP TRAVERSE. A loop traverse starts on a station of known position and
terminates on the same station--e.g., Station A in Figure 3-9 above. An examination of
the position misclosure in a loop traverse will reveal measurement blunders and internal
loop errors, but will not disclose systematic errors or external inaccuracies in the control
point coordinates. In a loop traverse, the measured angular closure is the summation of
the interior or exterior horizontal angles in the traverse. If there are "n" sides in a loop
traverse, and interior angles were measured, the true angular closure should equal (n-2)
· 180º. If exterior angles were measured when performing a loop traverse, the true
angular closure should equal (n+2) ·180º. In Figure 3-9 above, the starting azimuth from
Station "A" is not shown. This initial azimuth might have been taken from a GPS,

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magnetic, or astronomic observation--or even an arbitrary (assumed) value might have
been used.

7.1.1.2 CONNECTING TRAVERSE. A connecting traverse starts on a station of known

position and terminates on a different station of known position. An example would be
Stations "A" and "B" in Figure 3-9 above--if these two points have fixed coordinates (and
azimuth A-B between them). When using this type of traverse, the systematic errors and
position inaccuracies can be detected and eliminated along with blunders and
accidental errors. The ability to correct measurement error depends on the known
accuracy of the control point coordinates, and related azimuth references used at each
end of the traverse.

7.1.2 OPEN TRAVERSE. (Figure 3-10 below). An open traverse starts on a station of
known position and terminates on a station of unknown position. With an open traverse,
there are no checks to determine blunders, accidental errors, or systematic errors that
may occur in the measurements. The open traverse is very seldom used in topographic
surveying because a loop traverse can usually be accomplished with little added
expense or effort.

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 Figure 3-10
Open traverse

7.2 RIGHT-OF-WAY TRAVERSE. A right-of-way traverse normally starts and ends on

known points. This type of traverse can be run with a transit and steel tape, EDM, or
total station. The style of notes is similar to most traverses with the only difference being
the type of detail shown. Fences can be of particular importance in determining right-of-
way limits, especially when working in an area not monumented. Notes for right-of-way
traverses should be especially clear and complete for many times this type of traverse is
the basis for legal or court hearings regarding true property corners. If a search for a
corner is made and nothing is found, a statement should be written in the field book to
this effect. Property title searches and deed research will generally be required to obtain
appropriate existing descriptions, plans, and other documents, which are generally
available in the public record.

7.3 STADIA TRAVERSE. Uses of stadia traverses include rough or reconnaissance

type surveys, checking on another traverse for errors, and control for a map being made
by stadia methods on a very large scale. Stadia traverses are rarely performed given
the availability of total stations today.

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7.4 COMPASS TRAVERSE. A compass traverse is made to establish the direction of a
line by magnetic compass measurements (i.e. no angles are turned). Distances are
usually measured by stadia or paced. These types of surveys are rarely performed.

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8. TRAVERSE SURVEY GUIDELINES. Several basic steps are required to plan and
execute a traverse survey:

• research existing control in the project area

• design survey to meet specifications
• determine types of measurements
• determine types of instruments
• determine field procedures
• site reconnaissance and approximate surveys
• install monuments and traverse stations
• data collection
• data reduction
• data adjustment
• prepare survey report

8.1 THE FOLLOWING GENERAL GUIDELINES are recommended in performing

traverse surveys:

8.1.1 PREPARATION. For most applications, it is recommended that permanent points

be established at intervals of one mile or less, starting at a known point--preferably a
NGS published control point on the NSRS. Plan the traverse to follow a route that will
be centered as much in the project area as possible, and avoiding areas that will be
affected by construction, traffic, or other forms of congestion. The route should provide
a check into other known points as often as practicable. After determining the route, it is
best to set temporary or permanent monuments (e.g., wooden hubs, PK nails, iron rods,
brass caps in concrete, or some other suitable monument) at each angle point on the
traverse. Ensure there is a clear line of sight from angle point to angle point and
determine an organized numbering or naming system to mark all points when set.

8.1.2 ACCURACY REQUIREMENTS. Control traverses are run for use in connection
with all future surveys to be made in the area of consideration. They may be of Second,

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Third, or Fourth-Order accuracy, depending on project requirements. Most project
requirements will be satisfied with Second- or Third-Order accuracies. The order of
accuracy for traversing may also be determined by the equipment and methods used to
collect the traverse measurements, by the final accuracy attained, and by the coordinate
accuracy of the starting and terminating stations of the traverse. The point closure
standards indicated in Chapter 4 must be met for the appropriate accuracy classification
to be achieved.

8.1.3 POSITION AND AZIMUTH ORIENTATION. If it is impossible to start or terminate

on stations of known position and/or azimuth, then a GPS or astronomic observation for
position and/or azimuth must be conducted. Astronomic position or azimuth
observations are no longer practical given the ease of GPS for these requirements. Two
GPS static points can be established at the ends of a traverse, from which a starting
position and azimuth is available. The GPS azimuth point should be 500 to 1,000 ft
distant from the initial point. Extreme care should be taken not to mix up astronomic,
geodetic, GPS, magnetic, and grid azimuths--they are all different.

8.1.4 TRAVERSE ROUTE. The specific route of a new traverse should be selected with
care, keeping in mind its primary purpose and the flexibility of its future use. Angle
points should be set in protected locations if possible. Examples of protected locations
include fence lines, under communication or power lines, near poles, or near any
permanent concrete structure. It may be necessary to set critical points below the
ground surface. If this is the case, reference the traverse point relative to permanent
features by a sketch, as buried points are often difficult to recover at future dates. Select
sites for traverse stations as the traverse progresses. Locate the stations in such a way
that, at any one station, both the rear and forward stations are visible. The number of
stations in a traverse should be kept to a minimum to reduce the accumulation of
instrument errors and the amount of computing required. Short traverse legs (courses or
sections) require the establishment and use of a greater number of stations and may
cause excessive errors in the azimuth. Small errors in centering the instrument, in

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station-marking equipment, and in instrument pointings, can be magnified over short
courses and can result in abnormally high azimuth closures.

8.1.5 TEMPORARY HUBS. Temporary station markers are usually 2x2-inch wooden
hubs, 6 inches or more in length. These hubs should be driven flush with the ground,
especially in maintained areas or where the hubs could present a hazard. The center of
the top of the hub is marked with a surveyor’s tack or an "X" to designate the exact point
of reference for angular and linear measurements. To assist in recovering a station, a
reference stake (e.g., a flagged 1 x 2 inch wood stake) may be set near the hub. The
reference stake should be marked with the traverse station designation, stationing,
offset, etc.—as applicable.

8.1.6 MEASUREMENTS. Follow manufacturer instructions for operation of theodolites,

EDM, or total stations. When using an EDM or total station, a minimum of two
redundant readings should be made before moving to the next occupation point. Special
care should be taken with the type of sights used for angle measurement--fixed rigid
sights should be used, not hand held targets on poles. For directional theodolite or total
station angle measurements, at least two sets (positions) of angles should be made.
Always measure horizontal angles at the occupied station by sighting the instrument at
the rear station and measuring the clockwise angles to the forward station. A horizon
closure may be performed as a check.

8.1.7 FIELD DATA REDUCTIONS. All survey field notes should be carefully and
completely reduced; with the mean angle calculated in the field and recorded along with
the sketch. All traverse adjustments should be made in the office unless this capability
is available on the data collector in the field. A sketch of the permanent monument
locations should be made in the field and a detailed description on how to recover them
should be recorded in writing. This information can be used for making subsequent
record of the survey monument and survey report. Temporary monuments need only be
briefly described in the field notes

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9. TRAVERSE COMPUTATIONS AND ADJUSTMENTS. There are a number of
methods available for adjusting traverses. The most common are listed below.

9.1 CRANDALL RULE. The Crandall rule is used when the angular measurements
(directions) are believed to have greater precision than the linear measurements
(distances). This method allows for the weighting of measurements and has properties
similar to the method of least squares adjustment. Although the technique provides
adequate results, it is seldom utilized because of its complexity. In addition, modern
distance measuring equipment and electronic total stations provide distance and
angular measurements with roughly equal precision. Also, a standard Least Squares
adjustment can be performed with the same amount of effort.

9.2 COMPASS RULE. The Compass Rule adjustment (also called the Bowditch
Method) is used when the angular and linear measurements are of equal precision. This
is the most widely used traverse adjustment method. Since the angular and linear
precision are considered equivalent, the angular error is distributed equally throughout
the traverse. For example, the sum of the interior angles of a five-sided traverse should
equal 540º 00' 00".0, but if the sum of the measured angles equals 540° 01' 00".0, a
value of 12".0 must be subtracted from each observed angle to balance the angles
within traverse. After balancing the angular error, the linear error is computed by
determining the sums of the north-south latitudes and east-west departures. The
misclosure in latitude and departure is applied proportional to the distance of each line
in the traverse.

9.3 LEAST SQUARES. The method of least squares is the procedure of adjusting a set
of observations that constitute an over-determined model (redundancy > 0). A least
squares adjustment relates the mathematical (functional model) and stochastic
(stochastic model) processes that influence or affect the observations. Stochastic refers
to the statistical nature of observations or measurements. The least squares principle
relies on the condition that the sum of the squares of the residuals approaches a
minimum.

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9.3.1 FUNCTIONAL MODEL. The functional model relates physical or geometrical
conditions to a set of observations. For example, if a surveyor measures the interior
angles of a five-sided figure, the sum of these angles should add up to 540º. If the
correct model is not determined, the adjusted observations will be in error.

9.3.2 STOCHASTIC MODEL. The stochastic model is the greatest advantage of the
least squares procedure. In least squares adjustment, the surveyor can assign weights,
variances, and covariance information to individual observations. The traditional
traverse balancing techniques do not allow for this variability. Since observations are
affected by various errors, it is essential that the proper statistical estimates be applied.

9.3.3 OBSERVATIONS. Observations in least squares are the measurements that are
to be adjusted. An adjustment is not warranted if the model is not over-determined
(redundancy = 0). Observations vary due to blunders and random and systematic
errors. When all blunders and systematic errors are removed from the observations, the
adjustment provides the user an estimate of the “true” observation.

9.3.4 BLUNDERS. Blunders are the result of mistakes by the user or inadvertent
equipment failure. For example, an observer may misread a level rod by a tenth of a
foot or a malfunctioning data recorder may cause erroneous data storage. All blunders

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must be removed before the least squares adjustment procedure. Blunders can be
identified by scrutinizing the data before they are input in the adjustment software.
Preliminary procedures like loop closures, traverse balancing, and weighted means are
techniques that can identify blunders before adjustment.

9.3.5 SYSTEMATIC ERRORS. Systematic errors are the result of physical or

mathematical principles. These errors must be removed before the adjustment
procedure. Systematic errors are reduced or eliminated through careful measurement
procedures. For example, when using a total station EDM, the user should correct the
distance for meteorological effects (temperature, pressure, relative humidity).

9.3.6 RANDOM ERRORS. Random errors are an unavoidable characteristic of the

measurement process. The theories of probability are used to quantify random errors.
The theory of least squares is developed under the assumption that only random errors
exist within the data. If all systematic errors and blunders have been removed, the
observations will differ only as the result of the random errors.

9.3.7 REFERENCES. Many field data collectors are capable of performing Least
Squares traverse adjustments; thus, simple traverses are more frequently being
adjusted by this method.

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10. TRAVERSE ADJUSTMENT (COMPASS RULE). The Compass Rule is a simple
method and is most commonly employed for engineering, construction, and boundary
surveys. It is also recognized as the accepted adjustment method in some state
minimum technical standards. The following sections only briefly describe traverse
adjustment techniques—detailed procedures and examples of traverse adjustments can
be found in many of the texts.

10.1 GENERAL. Traverse computations and adjustments require the following steps:

• Adjust angles and directions to fixed geometric conditions based on angular

misclosure
• Calculate latitudes (dY or dN) and departures (dX or dE) of the traverse
misclosure
• Distribute the misclosure latitudes and departures over the traverse
• Compute adjusted coordinates of the traverse stations
• Calculate final adjusted lengths and azimuths between traverse points

10.2 ANGLE COMPUTATIONS AND ADJUSTMENTS. The azimuth of a line is the

horizontal angle (measured clockwise) from a base direction to the line in question. To
compute a traverse, surveyors determine the azimuth for each traverse leg, starting with
the fixed azimuth at the known starting point. This fixed azimuth is typically that
computed between the fixed starting station and some azimuth reference point (another
monument, a known object, or astronomical), as was shown back on Figure 3-8. The
azimuth for each succeeding leg is then determined by adding the value of the
measured angle at the occupied station to the value of the azimuth from the occupied
station to the rear station. On occupation of each successive station, the first step is to
compute the back azimuth of the preceding leg (the azimuth from the occupied station
to the rear station). At the closing station, the azimuth carried forward is compared with
the computed azimuth from the closing station to the reference azimuth mark.

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10.2.1 AZIMUTH CORRECTION. The azimuth closure error is obtained by subtracting
the known closing azimuth from the computed closing azimuth, as described above.
This difference provides the angular closure error with the appropriate sign. By
reversing this sign, the azimuth correction (with the appropriate sign) is obtained. If the
angular error of closure is less than the allowable angular error of closure for the order
of traverse (see closure standards in Chapter 4), the azimuths of the traverse may be
adjusted. If the azimuth error is larger than the allowable closure error, then
reobservations may be necessary. The allowable error of closure (or misclosure)
depends on the instrument, the number of traverse stations, and the order of the control
survey.

10.2.2 AZIMUTH ADJUSTMENT. The Compass Rule is based on the assumption that
angular errors have accumulated gradually and systematically throughout the traverse.
The angular correction is then distributed systematically (equally) among the angles in
the traverse. Refer to the "Balanced Angle" column in the example at Figure 3-11 below
where a 4-second misclosure was distributed equally.

10.2.3 TRAVERSE POSITION COMPUTATIONS. After the angles are adjusted as

described above, compute the adjusted azimuth (or bearing) of each leg by using the
starting azimuth and the adjusted angles at each traverse station. Verify the computed
closing azimuth agrees with the computed fixed closing azimuth. Using the adjusted
azimuths (or bearings) for each leg, and the measured distances (as corrected to sea
level and grid scale), compute each traverse station X-Y (or N-E or departure-latitude)
position from the beginning to the closing station--e.g., the "Unadjusted Latitudes and
Departures" column in Figure 3-11. The linear misclosure at the closing station is
determined in both X (departure or easting) and Y (latitude or northing) coordinates-- ΔX

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and ΔY. The overall position misclosure ( √ [ ΔX 2 + ΔY 2] ) is then used to determine
the relative accuracy (or precision) of the traverse, and conformance with the minimum
closure standards in Table 4-1. The relative accuracy is obtained by dividing the
misclosure (as computed after adjusting the angles) by the sum of the overall traverse
length. This value is then inversed to obtain a ratio for comparison with Table 4-1, as
shown in Equation 3-5 below.

The position misclosure (after azimuth adjustment) can then be distributed among the
intermediate traverse station based on the adjustment rule being applied. For the
Compass Rule, the latitude and departure misclosures are adjusted in proportion to the
length of each traverse course divided by the overall traverse length. For any traverse
leg with length dX (departure) and dY (latitude) in each coordinate, and with a final
misclosure after azimuth adjustment of " ΔX " and " ΔY ", the corrections to the dX or dY
lengths are adjusted by:

Once the above corrections are applied to the latitudes and departures in each traverse
course, the adjusted length and direction of each course can be computed, along with
the final adjusted coordinates of each intermediate point. (These final computations are
not shown in Figure 3-11).

10.2.4 ADJUSTMENT TECHNIQUES. In the past, the above adjustment was performed
using a tabular form that was laid out to facilitate hand calculation of the angular and

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coordinate corrections and adjustments-- see sample at Figure 3-11 below. Today,
COGO software packages can perform this adjustment in the field or office and these
tabular computation forms are not necessarily needed.

Figure 3-11
Tabular computation format for a Compass Rule traverse adjustment

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11. TRIANGULATION AND TRILATERATION SURVEYS. Triangulation and
trilateration methods are now rarely used for expanding or densifying horizontal control.
Before GPS, they were extensively used for this purpose. In USACE, localized
triangulation and trilateration techniques (using Wild T3s and precise EDM) are still
used for accurate structural deformation monitoring work. However, these specialized
surveys are only performed around a lock, dam, or hydropower project.

11.1 GENERAL. A triangulation network consists of a series of angle measurements

that form joined or overlapping triangles in which an occasional baseline distance is
measured. The sides of the network are calculated from angles measured at the
vertices of the triangle. A trilateration network consists of a series of distance
measurements that form joined or overlapped triangles where all the sides of the
triangles and only enough angles and directions to establish azimuth are determined.

11.2 NETWORKS. When practicable, all triangulation and trilateration networks should
originate from and tie into existing coordinate control of equal or higher accuracy than
the work to be performed. An exception to this would be when performing triangulation
or trilateration across a river or some obstacle as part of a chained traverse. In this
case, a local baseline should be set. Triangulation and trilateration surveys should have
adequate redundancy and are usually adjusted using least squares methods.

11.3 ACCURACY. Point closure standards listed in Chapter 4 must be met for the
appropriate accuracy classification to be achieved. If project requirements are higher-
order, refer also to the FGCS "Standards and Specifications for Geodetic Control
Networks" (FGCS 1984).

11.4 RESECTION. Three-point resection is a form of triangulation. Three-point

resection may be used in areas where existing control points cannot be occupied or
when the work does not warrant the time and cost of occupying each station.
Triangulation of this type should be considered Fourth-Order, although Third-Order
accuracy can be obtained if a strong triangular figure is used and the angles are

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accurately measured. The following minimum guidelines should be followed when
performing a three-point resection:

11.4.1 LOCATION. Points for observation should be selected to give strong geometric
figures, such as with angles between 60 and 120 degrees of arc.

11.4.2 REDUNDANCY. If it is possible to sight more than three control points, the extra
points should be included in the figure. If possible, occupy one of the control stations as
a check on the computations and to increase the positioning accuracy. Occupation of a
control station is especially important if it serves as a control of the bearing or direction
of a line for a traverse that originates from this same point.

11.4.3 MEASUREMENTS. Both the interior and exterior angles should be observed and
recorded. The sum of these angles should not vary by more than three (3) arc-seconds
per angle from 360 degrees. Each angle should be turned not less than 2-4 times (in
direct and inverted positions).

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