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Geodetic Surveying and Plane Surveying
Surveying
has
been
traditionally
defined
as
the
art
and
science
of
determining
the
position
of
natural
and
artificial
features
on,
above
or
below
the
earth’s
surface;
and
representing
this
information in analog form as a
contoured map, paper plan or chart, or as figures
in report tables,
or in digital form as
a three dimensional mathematical model stored in
the computer. As such, the
surveyor/geodesist dealt with the
physical and mathematical aspect of measurement.
The accurate
determination
and
monumentation
of
points
on
the
surface
of
the Earth
is
therefore
seen
as
the
major task.
Though
these
surveys
are
for
various
purposes,
still
the
basic
operations
are
the
same---they
involve measurements and computations
or, basically, fieldwork and office work. There
are many
different types of surveys
such as land surveys, route surveys, city surveys,
construction surveys,
hydrographic
surveys, etc., but generally speaking, surveying
is divided into two major categories:
geodetic and plane surveying.
Surveys will either take
into account the true shape of the
Earth
（
Geodetic
surveys
）
or treat the
earth
as
a
flat
surface(Plane
surveys).
Additionally,
surveys
are
conducted
for
the
purpose
of
positioning
features
on
the
ground(Horizontal
surveys),
determining
the
elevation
or
heights
of
features(Vertical surveys) or a
combination of both.
Geodetic Surveying
The
type
of
surveying
that
takes
into
account
the
true
shape
of
the
earth
is
called
geodetic
surveying.
This type of survey is
suited for large areas and long lines and is used
to find the precise location
of basic
points needed for establishing control for other
surveys. In geodetic surveys, the stations
are
normally
long
distances
apart,
and
more
precise
instruments
and
surveying
methods
are
required for this type
of surveying than for plane surveying.
Widely
spaced,
permanent
monuments
serve
as
the
basis
for
computing
lengths
and
distances
between
relative
positions.
These
basic
points
with
permanent
monuments
are
called
geodetic
control
survey
points,
which
support
the
production
of
consistent
and
compatible
data
for
surveying
and
mapping
projects.
In
the
past,
ground-based
theodolites,
tapes,
and
electronic
devices were the
primary geodetic field measurements used. Today,
the technological expansion of
GPS has
made it possible to perform extremely accurate
geodetic surveys at a fraction of the cost.
A
thorough
knowledge
of
the
principles
of
geodesy
is
an
absolute
prerequisite
for
the
proper
planning and execution of geodetic
surveys.
In Geodetic
Surveys, the shape of the earth is thought of as a
spheroid, although in a technical
sense, it is not really a spheroid.
Therefore, distances measured on or near the
surface of the earth
are
not
along
straight
lines
or
planes,
but
on
a
curved
surface.
Hence,
in
the
computation
of
distances in geodetic surveys,
allowances are made for the earth’s minor and
major diameters from
which a spheroid
of reference is developed. The position of each
geodetic station is related to this
spheroid.
The
positions
are
expressed
as
latitudes(angles
north
or
south
of
the
Equator)
and
longitudes(angles east or west of a
prime meridian) or as northings and eastings on a
rectangular
grid.
A geodetic survey establishes the
fundamentals for the determination
of
the surface and gravity
field of a
country. This is realized by coordinates and
gravity values of a sufficiently large number
of
control
points,
arranged
in
geodetic
and
gravimetric
networks.
In
this
fundamental
work,
curvature and the gravity field of the
earth must be considered.
The type of surveying in which the mean
surface of the earth is considered a plane, or in
which the
curvature
of
the
earth
can
be
disregarded
without
significant
error,
generally
is
called
plane
surveying. The term is used to
designate survey work in which the distances or
areas involved are
of
limited
extent.
With
regard
to
horizontal
distances
and
directions,
a
level
line
is
considered
mathematically
straight, the direction of the plumb line is
considered to be the same at all points
within
the
limits
of
the
survey,
and
all
angles
are
considered
to
be
plane
angles.
To
make
computations
in
plane
surveying,
you
will
use
formulas
of
plane
trigonometry,
algebra,
and
analytical
geometry.
For
small
areas,
precise
results
may
be
obtained
with
plane
surveying
methods,
but
the
accuracy
and
precision
of
such
results
will
decrease
as
the
area
surveyed
increases in size. For example, the
length of an arc 18.5 km long lying in the earth’s
surface is
only 7mm greater than the
subtended chord and, further, the
difference between the sum of the
angles in a plane triangle and the sum
of those in a spherical triangle is only 0.51
second for a
triangle at the earth’s
surface having an area of
100km
2
. It will be
appreciated that the curvature
of the
earth must be taken into consideration only in
precise surveys of large areas.
A great number of surveys are of the
plane surveying type.
Surveys
for
the
location
and
construction
of
highways,
railroads,
canals,
and
in
general,
the
surveys necessary for
the works of human beings are plane surveys, as
are the surveys made to
establish
boundaries,
except
state
and
national.
However,
with
the
increasing
size
and
sophistication of
engineering and other scientific projects,
surveyors who restrict their practice to
plane surveying are severely limited in
the types of surveys in which they can be engaged.
The
operation of determining elevation
usually is considered a division of plane
surveying. Elevations
are referred to
the geoid. The geoid is theoretical only.
It is the natural extension of the mean
sea level surface under the landmass. We could
illustrate
this
idea
by
digging
an
imaginary
trench
across
the
country
linking
the
Atlantic
and
Pacific
we allowed the
trench to fill with seawater, the surface of the
water in the trench would
represent he
geoid. So for all intents and purposes, the geoid
is the same as mean sea level. Mean
sea
level is the average level of the ocean surface
halfway between the highest and lowest levels
recorded.
We
use
mean
sea
level
as
a
datum
or,
curiously
and
incorrectly,
a
datum
plane
upon
which we can reference or describe the
heights of features on, above or below the ground.
Imagine
a true plane tangent to the
surface of mean sea level at a given point. At
horizontal distances of
1km from the
point of tangency, the vertical distances(or
elevations) of the plane above the surface
represented by mean sea level are
7.8cm. Obviously, curvature of the earth’s surface
is a factor
that cannot be neglected in
obtaining even rough values of elevations. The
ordinary procedure in
determining
elevations, such as balancing backsight and
foresight distance in differential leveling,
automatically
takes
into
account
the
curvature
of
the
earth
and
compensates
for
earth
curvature
and refraction, and elevations referred
to the curved surface of reference are secured
without extra
effort by the surveyor.
There is close cooperation
between geodetic surveying and plane surveying.
The geodetic survey
adopts the
parameters determined by measurements of the
earth, and its own results are available
to those who measure the earth. The
plane surveys, in turn, are generally tied to the
control points
of the geodetic surveys
and serve particularly in the development of
national map series and in the
formation of real estate cadastres.
Below we are about measure
distance, Angle and Direction Measurement and
Traversing.
Distance
Measurement
One
of
the
fundamentals
of
surveying
is
the
need
to
measure
distance.
Distances
are
not
necessarily linear, especially if they
occur on the spherical earth. In this subject we
will deal with
distances in Euclidean
space, which we can consider a straight line from
one point or feature to
another.
Distance between two points can be horizontal,
slope, or vertical. Horizontal and slope
distances
can
be
measured
with
lots
of
techniques
of
measurement
depending
on
the
desired
quality
of
the
result.
If
the
points
are
at
different
elevations,
then
the
distance
is
the
horizontal
length between plumb lines at the
points. Here gives a brief summary of relevant
techniques and
their respective
accuracies:
Pacing and
Odometer
Pacing is a very
useful form of measurement though it is not
precise, especially when surveyors
are
looking
for
survey
marks
in
the
field.
Pacing
can
be
performed
at
an
accuracy
level
of
1/100~1/500
when
performed
on
horizontal
land,
while
the
accuracy
of
pacing
can
’
t
be
relied
upon
when pacing up or down steep hills. The odometer
is a simple device that can be attached to
any vehicle and directly registers the
number of revolutions of a wheel. With the
circumference of
the wheel known, the
relation between revolutions and distance is
fixed.
Ordinary Taping and
Precise Taping
Taping
is
a
very
common
technique
for
measuring
horizontal
distance
between
two
points.
Ordinary
taping
refers
to
the
very
common
tapes
that
we
can
buy
them
in
stores,
such
as
the
plastic tapes or poly
tapes. Such tapes have low precision in distance
measurements with about
1/3000~1/5000.
The precise taping refers to the steel tapes and
which are much more expensive
than
the
plastic
tape
and
have
higher
precision
of
1/10000~1/30000.
Invar
tapes
are
composed
35% nickel and 65%
steel. This alloy has a very low coefficient of
thermal expansion, making the
tapes
useful in precise distance measurement. Many tapes
are now graduated with foot units on
one side and metric units on the
reverse side. Metric units are in meters,
centimeter and minimeter
with the total
length of 20 m, 30 m, 50 m and 100 m.
If we want to measure the horizontal
distance between the two points A and B, we can do
like this:
With zero of the tape to the
higher point B and tape going along the point A,
we can measure the
horizontal distance
by using the plumb bob with pump line entering to
the point A. To judge the
exact
horizontal line, we should move the tape up and
down along the pump line and we will find
the changes of reading in the tape. The
shortest reading of the tape is the horizontal
distance.
If the distance is longer
than the length of tape, then we can divide the
long distance into several
segments
and
get
the
total
distance
by
plus
each
segment
together.
Since
different
tapes
have
different starts of
zero of the tapes, it is very important to judge
where the zero of the tape begins.
Tacheometry and Stadia
Tacheometry is an optical solution to
the measurement of distance. The word is derived
from the
Greek
Tacns,
meaning
“
swift
”
,
and
metrot,
meaning
“
a
measure
”
.
Tacheometry
involves
the
measurement
of
a
related
distance
parameter
either
by
means
of
a
fixed-angle
intercept.
Theodolite
tacheometry is an example of stadia system.
The theodolite is directed
at the level staff where the staff is held
vertically and the line of sight of
the
telescope is horizontal.
By reading the
top and bottom stadia hairs on the telescope view
and then the horizontal distance
from
center of instrument to rod can be obtained by
multiplying the stadia interval factor K by the
stadia interval and plus the distance C
which is from the center of instrument to
principal focus, i.e.
D=Ks
+
C.
Usually
the
nominal
stadia
interval
factor
K
equals
100
which
is
a
constant
for
a
particular
instrument
as
long
as
conditions
remain
unchanged,
but
it
may
be
determined
by
observation in practice.
The value of C is determined by the manufacturer
and stated on the inside
of
the
instrument
box.
For
external-focusing
telescopes,
under
ordinary
condition,
C
may
be
considered as 1 ft without error of
consequence. Internal-focusing telescopes are so
constructed
that C is 0 or nearly
so; this is an advantage of
internal-focus telescopes for stadia
work. Most
instruments now used for
stadia are equipped with internal-focusing
telescopes.
Applications of
tacheometry include traversing and leveling for
the topographic surveys, location
of
detail
surveys,
leveling
and
field
completion
surveys
for
the
topographic
mapping,
and
hydrographic mapping.
The relative precision is 1:1000 to 1:5000.
Stadia
is
a
form
of
tacheometry
that
uses
a
telescopic
cross-hair
configuration
to
assist
in
determining distances.
A
series of rod readings is taken with a theodolite
and the resultant intervals are used to determine
distances.
Electronic Distance Measurement(EDM)
The
Electronic
Distance
Measurement(EDM)
was
first
introduced
in
1950s
by
the
founders
of
Geodimeter
Inc.
The
advent
of
EDM
instrument
has
completely
revolutionized
all
surveying
procedures,
resulting
in
a
change
of
emphasis
and
techniques.
Distance
can
now
be
measured
easily, quickly and
with great accuracy, regardless of terrain
conditions.
EDM instruments
refer to the distance measurement equipments using
light and radio waves. Both
light waves
and radio waves are electromagnetic. They have
identical velocities in a vacuum (or
space) to
299,792.458
±
0.001km/sec.
These velocities, which are
affected by the air
’
s
density, are reduced and need to be recalculated
in
the atmosphere. The basic principle
of EDM instruments is that distance equals time
multiplied by
velocity.
Thus
if
the
velocity
of
a
radio
or
light
wave
and
time
required
for
it
to
go
from
one
point
to
another are known, the distance between
the two points can be calculated.
The
EDM
instruments
may
be
classified
according
to
the
type
and
wavelength
of
the
electromagnetic energy generated or
according to their operational range. EDM
instruments use
three different
wavelength bands: (1)Microwave systems with range
up to 150km, wave length 3
cm, not
limited to line of sight and unaffected by
visibility; (2)Light wave systems with range up
to 5 km (for small machines), visible
light, lasers and distance reduced by visibility;
(3)Infrared
systems
with
range up to 3
km, limited to line of
sight
and limited by rain, fog, other
airborne
particles.
Although
there
is
a
wide
variety
of
EDM
instruments
available
with
different
wavelengths, there
are basically only two methods of measurement
employed which may divide
the
instruments
into
two
classification
as
electro-optical
(light
waves)
and
microwaves
(radio
waves)
instruments.
These
two
basic
methods
are
namely
the
pulse
method
and
more
popular
phase different
method. They function by sending light waves or
microwaves along the path to be
measured
and
measuring
the
time
differences
between
transmitted
and
received
signals,
or
in
measuring
the
phase
differences
between
transmitted
and
received
signals
in
returning
the
reflecting light wave to source. Modern
EDM instruments are fully automatic to such an
extent
that,
after
the
instruments,
set
up
on
one
station,
emits
a
modulated
light
beam
to
a
passive
reflector
set
up
on
the
other
end
of
the
line
to
be
measured.
The
operator
need
only
depress
a
button, and the slope distance is
automatically displayed. More complete EDM
instruments also
have
the
capability
of
measuring
horizontal
and
vertical
or
zenith
angles
as
well
as
the
slope
distance. These
instruments referred to as total station
instruments.
Angle and
Direction Measurement
Horizontal and
vertical angles are fundamental measurements in
surveying. It is necessary to be
familiar
with
the
meanings
of
certain
basic
terms
before
describing
angle
and
direction
measurement. The terms discussed here
have reference to the actual figure of the earth.
Basic Terms
A vertical line
at any point on the earth
’
s
surface is the line that follows the direction of
gravity at
that point.
It is the direction that a string will
assume if a weight is attached at that point and
the string is
suspended freely at the
point.
At a given point
there is only one vertical line.
A horizontal line at a point is any
line that is perpendicular to the vertical line at
the point.
At any point
there are an unlimited number of horizontal lines.
A
horizontal
plane
at
a
point
is
the
plane
that
is
perpendicular
to
the
vertical
line
at
the
point.
There is only one horizontal plane
through a given point.
A vertical plane
at a point is any plane that contains the vertical
line at the point.
There
are an unlimited number of vertical planes at a
given point.
Horizontal Angle and Vertical Angle
A horizontal angle is the angle formed
in a horizontal plane by two intersecting vertical
planes, or
a
horizontal
angle
between
two
lines
is
the
angle
between
the
projections
of
the
lines
onto
a
horizontal plane. For
example, observations to different elevation
points B and C from A will give
the
horizontal angle
∠
bac which
is the angle between the projections of two lines
(AB and AC)
onto the horizontal plane.
It follows that, although the points observed are
at different elevations,
it
is
always
the
horizontal
angle
and
not
the
space
angle
that
is
measured
(Figure
1).
The
horizontal
angle
is
used
primarily
to
obtain
relative
direction
to
a
survey
control
point,
or
topographic detail points, or to points
to be set out.
A vertical
angle is an angle measured in a vertical plane
which is referenced to a horizontal line by
plus (up) or minus (down) angles, or to
a vertical line from the zenith direction. Plus
and minus
vertical angles are sometimes
referred to as elevation or depression angles,
respectively. A vertical
angle thus
lies between 0
°
and
±
90
°
.
Zenith is the term describing points on a
celestial sphere
that is a sphere of
infinitely large radius with its center at the
center of the earth. The zenith is an
angle measured in a vertical plane
downward from an upward directed vertical line
through the
instrument. It is thus
between 0
°
and
180
°
. Obviously the zenith
angle is equal to 90
°
minus
the vertical angles.
Vertical
angles or zeniths are used in
the correction of slope distance to the
horizontal or in height determined. For
the most part, the instrument used in the
measurement of
angles is called a
transit or theodolite, although angles can be
measured with clinometers, sextants
(hydrographic surveys), or compasses.
The theodolite contains a horizontal
and vertical circles of either glass or silver.
The
horizontal
and
vertical
circles
of
theodolite
can
be
linked
to
circular
protractors
graduated
from
0
°
to
360
°
in
a
clockwise
manner
set
in
horizontal
and
vertical
plane.
The
horizontal
circle
is
used
when
measuring
or
laying
off
horizontal
angles
and
the
vertical
circle
is
used
to
measure
or
lay
off
vertical
angles
or
zenith
angles.
Usually
the
units
of
angular
measurement
employed
in
practice
are
degrees,
minutes,
and
seconds,
the
sexagesimal
system.
Angle
Measurement
A
horizontal angle in surveying has a direction or
sense; that is, it is measured or designed to the
right or to the left, or it is
considered clockwise or counterclockwise. In the
above figure, the angle
at A from B to
C is clockwise and the angle from C to B is
counterclockwise. With the theodolite
set
up,
centered,
and
leveled
over
at
station
A,
then
a
simple
horizontal
angle
measurement
between
surveying point B, A and C would be taken as
follows:
⑴
Commencing on, say,
“
face
left
”
, the target set at
survey point B is carefully bisected and the
reading on horizontal scale is
25
°
.
⑵
The upper plate clamp is
released and telescope is turned
clockwise
to
survey
point
C.
The
reading
on
horizontal
circle
is
75
°⑶
The
horizontal
angle
is
then
the
difference
of
the
two
directions,
i.e.
(75
°
< br>-25
°
)
=50
°（⑷
Change
face
and
observe
point
C
on
“
face
right
”
,
and
note
the
reading=255
°
⑸
< br>Release
upper
plate
and
swing
counterclockwise to point B and note
the reading =205
°⑹
The
reading or the direction must be
subtracted in the same order as 255
°
-205
°
=50<
/p>
°⑺
The mean of two values
would be accepted
if
they
are
in
acceptable
agreement.
Modern
electronic
digital
theodolites
contain
circular
encoders
that
sense
the
rotations
of
the
spindles
and
the
telescope,
convert
these
rotations
into
horizontal
and
vertical
(or
zenith)
angles
electronically,
and
display
the
value
of
the
angles
on
liquid
crystal
displays
(LCDs)
or
light-emitting
diode
displays
(LEDs).
These
readouts
can
be
recorded in a conventional field book
or can be stored in a data collector for future
printout or
computation.
The
instrument
contains
a
pendulum
compensator
or
some
other
provision
for
indexing the vertical circle readings
to an absolute vertical direction.
The
circle can be set to zero readings by a simple
press of a button or initialized to any value on
the instrument.
Azimuth is the horizontal angle
measured in a clockwise direction from the plane
of the meridian,
which is a line on the
mean surface of the earth joining the north and
south poles. Azimuth ranges
in
magnitude from 0
°
to 360
°
, values
in excess of 360
°
, which are
sometimes encountered in
computations,
are simply reduced by 360
°
before final listing.
Bearing
is
the
traditional
way
of
stating
the
orientation
of
the
line.
It
is
actually
the
angle
measured from the
north or south.
The bearing, which can
be measured clockwise or counterclockwise from the
north or south end of
the meridian, is
always accompanied by letters that locate the
quadrant in which the line falls. For
example, bearing N32W indicates a line
trending 32
°
west
of the north. It is equal to an azimuth
of 328
°
.Bearing
S12W indicates a line trending
12
°
west of the
south. It is equal to an azimuth
of
192
°
. It is important to
state that the bearing and azimuth are respect to
true north..
Traversing
The purpose of the surveying is to
locate the positions of points on or near the
surface of the earth.
To determine
horizontal positions of arbitrary points on the
earth
’
s surface and
elevation of points
above or below a
reference surface are known as a control survey.
The positions and elevations of the
points make up a control network.
There are different types of control
networks depending on where and why they are
established.
A control network may have
very accurate positions but no elevations (called
a Horizontal Control
Network) or very
accurate elevations but no positions (called a
Vertical Control Network).
Some points
in a control network have both accurate positions
and elevations.
Control
networks
range
from
small,
simple
and
inexpensive
to
large
and
complex
and
very
expensive to establish.
A
control network may cover a small area by using a
“
local
”
coordinate system that allows you to
position the features in relation to
the control network but
doesn
’
t tell you where the
features are
on
the
surface
of
the
earth,
or
cover
a
large
area
by
consisting
of
a
few
well-placed
and
precise-established
control points, which is sometimes called the
primary control.
The
horizontal positions of points in a network can be
obtained in a number of different
ways.
（
The
generally used methods are triangulation,
trilateration, traversing, intersection, resection
and
GPS.
The main topic of
this text refers to the traversing.
Triangulation
The method of surveying called
triangulation is based on the trigonometric
proposition that if one
side and three
angles of a triangle are known, the remaining
sides can be computed by the law of
sines.
Furthermore,
if
the
direction
of
one
side
is
known,
the
direction
of
the
remaining
sides
can
be
determined.
And then
coordinates of unknown points can be computed by
application of trigonometry.
Trilateration
Since the
advent of long-range EDM instrument, a method of
surveying called trilateration was
adopted to combine with triangulation.
The trilateration is based on the
trigonometric proposition that if the three sides
of a triangle are
known, the three
angles can be computed by the law of cosines.
Trilateration
possesses
some
advantages
over
triangulation
because
the
measurement
of
the
distances with EDM
instrument is so quick, precise and economical
while the measurement of the
angles
needed for triangulation may be more difficult and
expensive. For some precise projects,
the combination of triangulation and
trilateration which is called triangulateration is
applied.
Traversing
A
survey
traverse
is
a
sequence
of
lengths
and
directions
of
lines
between
points
on
the
earth,
obtained by or from
field angle and distance measurements and used in
determining positions of
the
point.
The
angles
are
measured
using
transits,
theodolites,
or
total
stations,
whereas
the
distances can be measured using steel
tapes or EDM instruments. A survey traverse may
determine
the relative positions of the
points that if connects in series, and if tied to
control stations based on
some
coordinate
system,
the
positions
may
be
referred
to
that
system.
From
these
computed
relative positions, additional data can
be measured for layout of new features, such as
buildings
and
roads.
Since
the
advent
of
EDM
equipment,
traversing
has
emerged
as
the
most
popular
method to establish control networks
such as basic area control, mapping, control of
hydrographic
surveys and construction
projects.
In engineering surveying, it
is ideal way to surveys and dimensional control of
route-type projects
such as highway,
railroad, and pipeline construction. In general, a
traverse is always classified as
either
an open traverse or a closed traverse. An open
traverse originates either at a point of known
horizontal position with respect to a
horizontal datum or at an assumed horizontal
position, and
terminates at a station
whose relative position is not previously known..
The
open
traverse
provides
no
check
against
mistakes
and
large
errors
for
its
termination
at
an