COMPASS SURVEY

INTRODUCTION TYPES OF COMPASS

The compass has been used by navigators and Prismatic Compass

others for many centuries. The surveyor's
1. Broad needle
compass is an instrument for determining
difference indirection between any horizontal 2. Ring moves with needle
line and a magnetic needle, the needle pointing
towards the magnetic north. Magnetic
compasses, though of limited .accuracy, hove 4. Whole circle bearings
the advantage of giving reading directly in terms
of directions or bearings referred to magnetic 5. Numbering inverted
north. Prismatic compasses can either be used 6. Eye vane and prism used to read
independently or in conjunction with other
angle measuring instruments in orienting a mop 7. Reading taken at south end
or plane table and making a surveyor traverse. 8. Can be used hand-held
PRINCIPLE OF COMPASS 9. Sighting and reading simultaneous
The earth acts as a powerful magnet and like Surveyor’s Compass
any magnet forms field of magnetic force which
exerts a directive action on a magnetized bar of 1. Edge-bar needle
steel or iron. A freely suspended magnetic
2. Ring fixed to box
needle will align itself in a direction parallel to
the lines of magnetic force of the earth at that 3. 0°at N and S to 90° at E and W in four
point and indicate the magnetic north. The quadrants; E and W interchanged.
imaginary line on the surface of the earth
4. Measures RB
joining a point and the true North and South
geographical poles indicate. The true north or 5. Numbering erect
Astronomical North. The horizontal angle
between true north and magnetic north is 6. Eye vane not used for reading
known as declination. The earth's magnetic 7. Reading taken at north end
force not only aligns a freely suspended
magnetic needle along magnetic north and 8. Has to be used with tripod
south but also pulls or dips one end of it below 9. Object sighted first; then move around to
the horizontal position. The angle of dip varies take reading
from 0" near the equator to 90° at the magnetic
poles. To overcome this dip a small weight is
placed on one side of the needle so that it can (Reference Book: Page 173-176, Fundamentals of
be adjusted until the needle is horizontal. Surveying by S.K. Roy)
Azimuth and Bearing of a Line whichever applies. The directions due east and
due west are, of course, perpendicular to the
The direction of any line may be described
north–south meridian. A line may fall in one of
either by its azimuth angle or by its bearing.
four quadrants: northeast (NE), southeast (SE),
Azimuth directions are usually preferred by
southwest (SW), or northwest (NW), as shown
surveyors; they are purely numerical and help
in Figure 6-7. A bearing may be measured either
to simplify office work by allowing a simple
in a clockwise or in a counter clockwise
routine for computations. Bearings, on the
direction, depending on which quadrant the line
other hand, require two letter symbols as well
is in. A bearing angle is always an acute angle,
as a numerical value, and each bearing
that is, less than 90°. It must always be
computation requires an individual analysis with
accompanied by the two letters that indicate
a sketch. But because they are easy to visualize,
the quadrant of the line. For example, a line
bearings are almost always used to indicate the
may have a bearing of N 42°30W; this is read as
direction of boundary lines in legal land
“north 42 degrees 30 minutes west,” or
descriptions (deeds) and on most official survey
“northwest 42 degrees 30 minutes.” It is
plats or subdivision maps.
important to remember that the numerical
Azimuths value of a bearing never exceeds 90°. It is often
necessary to convert directions from azimuths
The azimuth of a line is the clockwise horizontal to bearings, or vice versa. Although a systematic
angle between the line and a given reference set of rules can be used for this, it is usually best
direction or meridian. Usually, north is the to first make a sketch of the line and its
reference direction; south is sometimes used as meridian. In the NE quadrant, the numerical
a reference for geodetic surveys that cover values of bearing and AzimN are always
large areas. An azimuth angle should be identical. In the other quadrants, the conversion
identified as being measured from the north involves either a simple addition or subtraction
(AzimN) or from the south (AzimS); north is with 180°or 360°, whichever applies, as shown
generally assumed if no specific identification is in Figure 6-8.
given. Any azimuth angle will have a positive
value between 0 and 360° (see Figure 6-6). Line
AB, for example, has an azimuth of 125°.

Bearings
Computing Angles, Azimuths, and Bearings
A bearing of a line is the angle from the north Many types of surveying problems involve the
(N) or the south (S) end of the meridian, computation of the azimuths or bearings of
whichever is nearest, to the line; it has the adjoining lines, given a starting direction and a
added designation of east (E) or west (W), series of measured angles. These computations
are particularly important for traverse surveys, establishing true north is not a routine task for
as demonstrated in Chapter 7.Another common most surveyors in private practice. For this
type of problem involves the computation of an reason, the National Geodetic Survey (NGS) has
angle at the intersection of two lines of known established reference lines of known true
direction. For problems involving angles and direction throughout the United States. It is
bearings, it is always best to start with a neat, always best to reference new surveys to the
clearly labelled sketch of the lines. Although true meridian, if possible and convenient.
azimuth computations can be systematized with
Magnetic Meridian
a formula or rule, it is also advisable to use a
sketch as an aid in their computation. The A magnetic meridian is the direction taken by a
following examples serve to illustrate a basic pivoted, freely swinging magnetic needle,
visual approach to solving problems with suspended in a device called a compass. The
angles, azimuths, and bearings. At each point, compass needle aligns itself with the horizontal
the sketch includes a reference meridian line component of the earth’s magnetic field. The
representing the direction of due north–due magnetic field of the earth can be
south. Later, in Section 6-3, a distinction will be approximately described as the field that would
made between directions referenced to a “true” result if a huge bar magnet were embedded
meridian and those referenced to a magnetic within the earth, with one end located far
meridian. below the surface in the Hudson Bay region and
the other end in a corresponding position in the
MAGNETIC DECLINATION
southern hemisphere. The lines of magnetic
At the very beginning of this chapter, a meridian force follow somewhat irregular paths, running
was defined as a horizontal reference line for from the south magnetic pole to the north
measuring direction. In the example azimuth magnetic pole. They are approximately parallel
and bearing problems given, a “north–south” with the earth’s surface at the equator and dip
meridian was used as the reference direction. downward toward each of the poles.
At this time, it is necessary to be more specific
Magnetic Declination
with regard to reference meridians. In
particular, we must distinguish between a true The earth’s magnetic poles are not at the same
meridian and a magnetic meridian. location as the true geographic poles; they are
separated by a significant distance. In addition,
True Meridian
the field slowly changes in general direction
A true meridian at a point is an imaginary line over time, and it is slightly affected by the
that passes through that point and the position of the sun and changes in radiation
geographic north and south poles of the earth; from the sun. Consequently, the magnetic
the poles, of course, lie on the axis of rotation meridian is not necessarily parallel to the true
of the earth. At any given point, the direction of meridian. A magnetic needle will therefore
the true meridian is fixed; it does not change point exactly true north only by chance. At any
over time. True north may be established in the given time, at any point on the earth’s surface,
field by precise instrument observations and the true geographic bearing of a freely
angular measurements of the sun, the North suspended magnetic needle is called the
Star (Polaris), or any other bright star of known magnetic declination or, simply, the declination.
position. A special gyroscope theodolite may In other words, the declination is an angle east
also be used to obtain true north. But or west of the true meridian.
Changes in Declination afternoon. During some of the magnetic
disturbances associated with sunspots, there
At a given location, the magnetic declination
may also be significant irregular variations of
changes with time. Changes in the earth’s
declination. Generally, the annual and daily
magnetic field cause the following four types of
variations are too small to be detected in the
variations in declination: secular variation,
field with a magnetic compass. Overall, the
annual variation, diurnal variation, and irregular
secular variation is the most important type of
variation.
variation for the purposes of surveying and it
Secular Variation must be accounted for with appropriate
adjustments to past records of direction.
The secular variation is a long-term change in
declination, with a cycle of approximately 300 Adjustments for Declination
years. Its cause is not well understood and
It is sometimes necessary to convert magnetic
there is no precise law or formula to predict it
bearings or azimuths to true directions or to
exactly. But average observations over periods
convert past magnetic directions to magnetic
of time at different locations on the earth allow
directions at the present or some other point in
approximate predictions of its value and
time. This may be the case when using a
direction using tables and charts. In the United
magnetic compass to obtain an estimate for the
States, the maximum rate of secular variation is
direction of a line, or when resurveying a tract
about 7.5 minutes of arc per year. This amounts
of land that was originally surveyed using
to several degrees over the years, and over the
compass directions. An isogonic chart may be
300-year cycle, the declination at a given
used to obtain data regarding past and present
location may vary as much as 35°from east to
declinations. As demonstrated in the following
west. Because of its large magnitude, secular
examples, a large and clear sketch is essential
variation is of particular significance to the
for solving these problems without blunder.
surveyor. The lines on an isogonic chart are the
lines of equal annual change in declination.
They give the yearly rate and direction of (Reference Book: Pages 116-123, Surveying Fundamentals
movement of the north end of a compass and Practices 6th Edition, by Jerry Natbanson, Michael T.
needle. These data, along with the isogonic Lanzafama, and Philip Kissam)
lines of the chart, provide the surveyor a means
for estimating the declination at any time as
well as at any point in the United States. This ROUTE SURVEYS
may be necessary when surveying land
Route surveying includes the field and office
described in old deeds.
work required to plan, design, and lay out any
Other Variations “long and narrow” transportation facility. Most
of the basic surveying concepts and methods
The annual variation is a magnetic meridian described in the previous chapters apply to
swing of at most 1 minute (01) of arc, back and route surveying. Horizontal distances,
forth, during the year. The diurnal or daily elevations, and angles must be measured, maps
variation is a swing of approximately 4–10 must be drawn, and profile and cross-section
minutes of arc, depending on the locality. At views of the route must be prepared. Route
night the needle is quiescent in its mean surveying operations, however, typically include
position. It swings east 2–5 minutes in the a reconnaissance, a preliminary, and a location
morning and west 2–5 minutes in the
survey. The reconnaissance survey involves an the horizontal alignment of the route without
examination of a wide area, from one end of the curves. Distances along the traverse are
the proposed route to the other. It is the first marked as stations and pluses and run
step in selecting alternative routes. For most continuously from the beginning point of the
projects, this would be done using existing route. The angles at intersection points where
small-scale maps and aerial photographs, the baseline tangents change direction are
although ground reconnaissance surveys may carefully measured by double centering. Data
be used for the relocation of short sections of for drawing a profile of the traverse line are also
existing routes. In some cases, a complete obtained. The design of the horizontal curves
topographic survey may be conducted so that that connect the tangent sections of the
an appropriate map can be prepared. Matching baseline depends on several factors, including
up aerial photos to form a strip mosaic is done the topography and the maximum speed of
frequently to prepare the required map. For vehicles using the route. After the curve
preliminary reconnaissance and planning, this computations have been made and appropriate
can be an uncontrolled mosaic, that is, one in field notes prepared, the horizontal alignment
which reference to ground control stations has of the route can be laid out on the ground in a
not been made. In relatively flat areas, a location survey. This includes setting stakes
planimetric map is usually sufficient for this along the tangents and the curves of the route
stage. Reconnaissance maps are used for centerline (and often along an offset line as
comparing alternative “paper routes” before well). Because the stations and pluses of the
the actual survey or layout on the ground. Map final centerline run along the curves as well as
scales range from 1 in =2000 ft. (1:24,000) to 1 the tangents, new stations have to be
in =200 ft. (1:2400). The preliminary survey may computed for points on the final alignment. This
be conducted on the ground with surveying is explained further and illustrated in Section
instruments, or in the office, using aerial 10-2. As the staking of the centerline
photogrammetry. Modern transportation progresses, topographic data are collected, and
routes are usually located using low-altitude property corners within the route boundaries or
photogrammetric maps at a scale of 1 in = 50 ft. right-of-way (ROW) are located. Profile and
(1:600) and 2-ft (0.5-m) contours. The maps cross-section data are obtained for final design,
generally cover about 1300 ft. (400 m) in width, for preparation of engineering drawings, and for
primarily along the alternate route corridor final estimates of earthwork quantities. The
selected in the reconnaissance survey final grade line (vertical alignment) is
operation. In effect, conducting the preliminary established to balance cut-and-fill (excavation
survey using photogrammetry is a refinement of and embankment) quantities, as explained in
the reconnaissance effort. The state of the art Section 10-7. On the engineering drawings, the
of modern photogrammetry and computer final horizontal alignment is shown in plan view,
applications is such that even the required above the profile view of the vertical alignment.
earthwork (cut-and-fill) computations for The plan view should include the bearings of
roadway design can be done using data from the tangents, angles of intersection, stationing,
aerial photography. The basic product of the and geometric data for each horizontal curve. It
preliminary survey is the location of a baseline should also include topographic data within and
or connecting traverse. This is a series of adjacent to the ROW lines and any existing
straight lines that run along or near what will be structures affected by the project. The profile
the centerline of the final route. It is essentially view should include the existing ground surface,
proposed route grade line, grades (slopes) of all (Reference Book: Pages 227-232, Surveying Fundamentals
and Practices 6th Edition, by Jerry Natbanson, Michael T.
the tangent sections, vertical curve data, and
Lanzafama, and Philip Kissam)
other pertinent information.

Stationing Along a Route

Stadia Tacheometry / Stadia Survey
One of the goals of route design is to establish
the stations of all the PCs and the PTs. The In stadia tacheometry, a levelling staff is held
station of a PC is computed by simply vertically at one end of the line being measured
subtracting T from the station of the PI. But to and a level or theodolite is set up above the
compute the station of the PT, the arc length L other. The staff is read using the stadia lines
must be added to the station of the PC. This is engraved on the telescope diaphragm as shown
because the final stationing along the route in figure 4.13. The vertical angle along the line
runs continuously along the tangents and the of sight is also recorded. If a level is used, the
curves. The stations indicate the true centerline line of sight will be horizontal assuming that the
distances from the beginning point of the level has no collimation error. If a theodolite is
project. The following expressions summarize used, the line of sight can be either horizontal
the method for stationing along a simple curve: or inclined as shown in figure 4.13. The vertical
compensating system of the theodolite must be
Station PT = station PC + L
in correct adjustment since vertical angles are
Station PC = station PI – T read on one face only.

Deflection Angles

For a 100-ft arc, the central angle is, by

definition, equal to the degree of curve, Da. The
deflection angle that corresponds to an interval
of one full station (100ft) on the curve, then,
must be equal to half the degree of curve, Da/2.
Likewise, the deflection angle for a half-station
(50-ft) interval on the curve is Da/4, and for a
quarter-station interval it is Da/8. A useful
formula for computing the deflection angle of
any given length of arc, expressed in minutes of With reference to figure 4.13
arc, may be written as follows:

arc length
a= ×1718.87
R
Where a = deflection angle, minutes of arc
R=radius of curve, ft. Where,
The deflection angle to any point on the curve is K-is the multiplying constant of the instrument,
equal to the sum of the incremental deflection usually 100
angles for each subdivision of the arc.
C-is the additive constant of the instrument,
usually 0
s-is the staff intercept, that is, the difference (2) Non-verticality of the staff can be a serious
between the two stadia readings source of error. This and poor accuracy of staff
readings form the worst two sources of error.
θ -is the vertical angle along the line of sight
The error in distance due to the non-verticality
Hi-is the height of the trunnion axis above point
of the staff is proportional to both the angle of
P
elevation of the sighting and the length of the
m-is the middle staff reading at X sighting. Hence, a large error can be caused by
steep sightings, long sightings or a combination
+V is used if there is an angle of elevation of both. It is advisable not to exceed () = ± 10°
-V is used if there is an angle of depression for all stadia tacheometry.

Accuracy and Sources of Error in Stadia (3) A further source of error is in reading the
Tacheometry vertical circle of the theodolite. If the line of
sight is limited to ± 10°, errors arising from this
The accuracy of basic stadia tacheometry source will be small. Usually, it is sufficiently
depends on two categories of error, accurate to measure the vertical angle to ± 1'
instrumental errors and field errors. and, although it is possible to improve this
Instrumental Errors reading accuracy, it is seldom worth doing so
owing to the magnitude of all the other errors
These include previously discussed.
(1) An incorrectly assumed value for K, the Considering all the sources of error, the overall
multiplying constant, caused by an error in the accuracy expected for distance measurement is
construction of the diaphragm of the theodolite 1 in 500 and the best possible accuracy is only 1
or level used. in 1000.
(2) Errors arising out of the assumption that K The vertical component, V, is subject to the
and C are fixed when, strictly, both K and C are same sources of error described above for
variable. distances, and the accuracy expected is
approximately ± 50 mm. The precision of stadia
The possible errors due to (1) and (2) above
tacheometry is also discussed in section 6.1 0.
limit the overall accuracy of distance
measurement by stadia tacheometry to 1 in Applications of Stadia Tacheometry
1000.
Vertical staff tacheometry is ideally suited for
Field Errors detail surveying by radiation techniques. This is
discussed fully in section 9. 7. Since the best
These can occur from the following sources.
possible accuracy obtainable is only 1 in 1000,
(1) When observing the staff, incorrect readings the method is best restricted to the production
may be recorded which result in an error in the of contoured site plans and should not be used
staff intercept, s. Assuming K = 100, an error of to measure distances where precisions better
± I mm in the value of s results in an error of ± than this are required.
100 mm in D. Since the staff reading accuracy
decreases as D increases, the maximum length
of a tacheometric sight should be 50 m. (Reference Book: Pages 144-148, Surveying for Engineers
by J. Uren and W.F. Price 3rd Ed.)
FORMULA DERIVATION Formulas for Inclined Sights.

In practice it is customary to hold the rod plumb rather

than perpendicular to the line of sight, because the former
position can be readily and accurately judged, while it is
not easy to determine when the rod is perpendicular to
the line of sight. On inclined sights, when the rod is plumb,
the vertical and horizontal distances evidently cannot be
found by solving a single right triangle. In Fig. 94 let AB he
the intercept on the rod when it is held vertical, A'B' the
intercept when the rod is perpendicular to the line of sight,
i.e., A’B’ is perpendicular to CO.

The formula just derived applies to a horizontal

sight on a vertical rod, or to an inclined sight on
a rod held perpendicular to the direction of
view. It is not easy to hold a rod perpendicular
to the line of sight, so it is held accurately
vertical. If s is the intercept on a vertical rod,
then s cos α would be the intercept,
The difference in elevation between the center of the
approximately, if the rod were held instrument and the point O on the rod is derived as
perpendicular to the line of sight. The slant follows:
distance is, then, D' = ks cos α = (f + c). Now it is
easy to find the horizontal distance D = D' cos α DO=CO sin a
and the vertical distance V = D' sin α. At one
time, tables were prepared for performing
these calculations, but with pocket calculators
¿ { Fi A B +(F +C) }sina
' '

they are no longer necessary. A pocket F

¿ AB sin a cos a+ ( F +C ) sin a
calculator can reduce the data quickly and i
accurately, including the correction (f + c)
F AB∗1
without any approximation. ¿ sin 2 a+ ( F+ C ) sin a
i 2
For the horizontal distance from the transit point to the
(Reference Book: Page 108, C. B. Breed and G. L. rod we have:
Hosmer, The Principles and Practice of Surveying, 11th ed.)
CD=COcos a

¿ { Fi A B +( F+C ) }cos a
' '

F
¿ AB cos2 a+ F+ C ¿ cos a
i
(Reference Boook: Pages 195-197, C. B. Breed and G. L.
Hosmer, The Principles and Practice of Surveying)
REFERENCE BOOKS: