GEODETIC SURVEYING
1. INTRODUCTION
Geodesy is the science of the measurement and representation of the shape, size and distribution of
the earth and its gravity field in three-dimensional time-varying space. It is the branch of earth
science that deals with determining:
1. precise positions on the surface of Earth,
2. the size and shape of Earth,
3. the motions of Earth in space, and
4. the gravity field of Earth.
Scientists known as geodesists create networks of accurately measured points on Earth’s surface.
They measure the angles, distance, and gravity differences between these points, and then compute
their latitude, longitude, and height. The sets of accurately measured points that geodesists create are
known as control networks. These control networks are used to construct accurate maps and charts.
They also provide reference grids for surveys made in building roads, bridges, pipelines, tunnels, and
many other structures.
On the other hand, geodetic surveying is the science of locating and relating the position of objects
on the earth relative to each other, while taking into account the size, shape and gravity of the earth.
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. Horizontal and vertical networks that
span the country form the primary spatial reference system used in mapping, boundary demarcation,
and other applications.
Differences between Plane surveying and Geodetic Surveying
Plane surveying is a specific type of surveying where the surface of the earth is considered as plane
and the curve of the earth is taken into account. The line connecting any two points is a straight line
and the angles of the polygons are plane angles. The type of surveying is suitable for small and flat
areas, and its degree of accuracy is comparatively low. The limit of treating a surface as a plane is
about 250km2; while geodetic surveying is a particular type of surveying where the curvature of the
earth is taken into account. Since the earth is a spherical shape, the line connecting any two points on
the earth’s surface is curved or an arc. Hence, it involves spherical trigonometry. In geodetic
surveying, long distances and large areas are measured and its degree of accuracy is comparatively
high. In other words, geodetic surveying is the type of surveying that takes into account the true
shape of the earth. These surveys are of high precision and extend over large areas; while Plane
Surveying is the type of surveying in which the mean surface of the earth is considered as a plane, or
in which its spheroidal shape is neglected, with regard to horizontal distances and directions. The
major differences between plane surveying and geodetic surveying are tabulated below in table 1.
1
,Table 1
SN Plane surveying Geodetic surveying
1 Effect of the curvature of the earth surface is Effect of the curvature of the earth surface is
ignored. included.
2 The earth surface is assumed to be plane, The earth surface is assumed to be spherical,
i.e. two dimensional. i.e. three dimensional
3 Involves smaller areas less than about 250 This survey is done on large area greater than
km2. 250 km2
4 Lower degree of accuracy. Higher degree of accuracy.
5 Done locally by the individual organization Done by the concerned state or government
department.
6 Simple methods and instruments can be used Very refined methods and instruments are
as the required accuracy is low. used.
7 In plane Surveying, line joining any two In geodetic surveying line joining two points
points of triangle formed by any three points of triangle formed by three points is
is considered as straight line and plane considered as curved line of spherical triangle
triangle are assumed to be plane angles. and angles of triangle are considered as
spherical angles.
2. REDUCTION OF EARTH-SURFACE MEASUREMENTS INTO THE REFERENCE
ELLIPSOID
To compute and record positions and directions on or above the earth’s surface, some coordinates
systems are necessary. Geodetic latitude, ø, and longitude, λ, on an arbitrary ellipsoid are often used
for such computation. Measurements taken on the earth’s surface are reduced to the ellipsoid after
the removal of the blunders and the systematic errors; and the spherical trigonometry applied.
Basic Geodetic reference surfaces
There are three basic geodetic surfaces; these are the geoid, the earth (topographic surface) and the
ellipsoid. The relationship between these surfaces is shown in figure 1. Reference ellipsoid may be
defined as a surface whose plane sections are all ellipses. Ellipsoid defines mathematical surface
approximating the physical reality while simplifying the geometry. Ellipsoid is a good approximation
to the shape of the earth but not an exact representation. It is the only regular surface among the three
geodetic surfaces; hence it has a regular shape which made it possible to be represented
mathematically, and therefore enables computation to be carried on it.
2
,Fig. 1: The Three Geodetic Surfaces and their Pictorial Representations
Fig. 2: The Three Geodetic Surfaces and the offset of vertical datum with respect to the geoid
Spirit levelling is the dominant technique for providing elevation above MSL. The equipment are
inexpensive and the method is highly accurate. However, it is labour intensive over long distances
and the field procedures are tedious and prone to human, systematic and random errors. In some
areas, it is often impossible to perform spirit levelling due to weather and terrain conditions.
Ellipsoidal height is fast, easy and convenient to obtain from GPS and is equally useful. To make full
use of the three-dimensional potentials of GPS, one needs to determine the separation between the
ellipsoid and the geoid. This separation is known as geoidal undulation (N) (Fig. 2).
Relationship Between Ellipsoidal and Orthometric Heights
The relationship between the ellipsoid and the geoid can be represented mathematically by:
h - H = N…………………………………………… 1
In (1), h is the ellipsoidal height, H is the Orthometric height, and N is the geoidal undulation,
Equation (1) can be stated as
h – H - N = 0…………………………………………2
However, equation (2) may not be valid because of the offset of the vertical datum with respect to
the geoid. This offset of the vertical datum with respect to the geoid may be represented by Q and
hence equation 2 becomes: h – H -N = Q……………3
3
, Q can be represented diagrammatically in figure 2.
The offset of the vertical datum with respect to the geoid (Q) is very small and always neglected in
low order surveys.
The earth is a “closed” surface ¾ of which is covered with water, while the remainder is dry land
(terrain). The determination of the size and shape of the earth has been always been one of the major
tasks of Geodesy. A number of surfaces have been used or proposed to model the geometry of the
earth’s surface. These include the Terrain (the physical surface of the earth); Geoid; the sphere and
Ellipsoidal surfaces.
The physical surface of the earth may be described as the topographical surface on which
observations are carried out for purposes of determining coordinates of terrain points as well as the
geometrical relationship between such points. The terrain is a topographical surface characterized by
hills and valleys. The surface is very irregular and cannot be represented by a simple mathematical
relation, and therefore not ideal reference surface.
The geoid is an equipotential surface corresponding to the undisturbed mean sea level underneath the
continents. Although a much smoother surface than earth’s terrain, the geoid is still too complicated
for use as a computational surface for surveying and mapping purposes. It, however, serves as a
reference datum to which vertical measurements and astronomical observations may be reduced. By
far the most mathematically suitable geodetic surfaces are the ellipsoidal surfaces which include the
sphere, biaxial ellipsoid and triaxial ellipsoid.
Other complex mathematical surfaces have also been used and these include the telluroid and the
hydrostatic ellipsoid. The telluroid approximates the physical surfaces of the earth and is defined as
the surface whose height above a geocentric ellipsoid is the same as the height of the terrain above
the geoid. The height telluroid above the ellipsoid is called normal height, usually denoted as HN,
while the height of the earth’s surface is height anomaly.
Fig. 3: Geodetic Reference Surfaces
In geophysical studies, the hydrostatics equilibrium has been suggested as a reference system. It is
supposed to depict mass anomalies within the earth by assuming the earth as fluid and laterally
homogeneous so that the shape of the earth’s surface in hydrostatic equilibrium would be the
4
1. INTRODUCTION
Geodesy is the science of the measurement and representation of the shape, size and distribution of
the earth and its gravity field in three-dimensional time-varying space. It is the branch of earth
science that deals with determining:
1. precise positions on the surface of Earth,
2. the size and shape of Earth,
3. the motions of Earth in space, and
4. the gravity field of Earth.
Scientists known as geodesists create networks of accurately measured points on Earth’s surface.
They measure the angles, distance, and gravity differences between these points, and then compute
their latitude, longitude, and height. The sets of accurately measured points that geodesists create are
known as control networks. These control networks are used to construct accurate maps and charts.
They also provide reference grids for surveys made in building roads, bridges, pipelines, tunnels, and
many other structures.
On the other hand, geodetic surveying is the science of locating and relating the position of objects
on the earth relative to each other, while taking into account the size, shape and gravity of the earth.
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. Horizontal and vertical networks that
span the country form the primary spatial reference system used in mapping, boundary demarcation,
and other applications.
Differences between Plane surveying and Geodetic Surveying
Plane surveying is a specific type of surveying where the surface of the earth is considered as plane
and the curve of the earth is taken into account. The line connecting any two points is a straight line
and the angles of the polygons are plane angles. The type of surveying is suitable for small and flat
areas, and its degree of accuracy is comparatively low. The limit of treating a surface as a plane is
about 250km2; while geodetic surveying is a particular type of surveying where the curvature of the
earth is taken into account. Since the earth is a spherical shape, the line connecting any two points on
the earth’s surface is curved or an arc. Hence, it involves spherical trigonometry. In geodetic
surveying, long distances and large areas are measured and its degree of accuracy is comparatively
high. In other words, geodetic surveying is the type of surveying that takes into account the true
shape of the earth. These surveys are of high precision and extend over large areas; while Plane
Surveying is the type of surveying in which the mean surface of the earth is considered as a plane, or
in which its spheroidal shape is neglected, with regard to horizontal distances and directions. The
major differences between plane surveying and geodetic surveying are tabulated below in table 1.
1
,Table 1
SN Plane surveying Geodetic surveying
1 Effect of the curvature of the earth surface is Effect of the curvature of the earth surface is
ignored. included.
2 The earth surface is assumed to be plane, The earth surface is assumed to be spherical,
i.e. two dimensional. i.e. three dimensional
3 Involves smaller areas less than about 250 This survey is done on large area greater than
km2. 250 km2
4 Lower degree of accuracy. Higher degree of accuracy.
5 Done locally by the individual organization Done by the concerned state or government
department.
6 Simple methods and instruments can be used Very refined methods and instruments are
as the required accuracy is low. used.
7 In plane Surveying, line joining any two In geodetic surveying line joining two points
points of triangle formed by any three points of triangle formed by three points is
is considered as straight line and plane considered as curved line of spherical triangle
triangle are assumed to be plane angles. and angles of triangle are considered as
spherical angles.
2. REDUCTION OF EARTH-SURFACE MEASUREMENTS INTO THE REFERENCE
ELLIPSOID
To compute and record positions and directions on or above the earth’s surface, some coordinates
systems are necessary. Geodetic latitude, ø, and longitude, λ, on an arbitrary ellipsoid are often used
for such computation. Measurements taken on the earth’s surface are reduced to the ellipsoid after
the removal of the blunders and the systematic errors; and the spherical trigonometry applied.
Basic Geodetic reference surfaces
There are three basic geodetic surfaces; these are the geoid, the earth (topographic surface) and the
ellipsoid. The relationship between these surfaces is shown in figure 1. Reference ellipsoid may be
defined as a surface whose plane sections are all ellipses. Ellipsoid defines mathematical surface
approximating the physical reality while simplifying the geometry. Ellipsoid is a good approximation
to the shape of the earth but not an exact representation. It is the only regular surface among the three
geodetic surfaces; hence it has a regular shape which made it possible to be represented
mathematically, and therefore enables computation to be carried on it.
2
,Fig. 1: The Three Geodetic Surfaces and their Pictorial Representations
Fig. 2: The Three Geodetic Surfaces and the offset of vertical datum with respect to the geoid
Spirit levelling is the dominant technique for providing elevation above MSL. The equipment are
inexpensive and the method is highly accurate. However, it is labour intensive over long distances
and the field procedures are tedious and prone to human, systematic and random errors. In some
areas, it is often impossible to perform spirit levelling due to weather and terrain conditions.
Ellipsoidal height is fast, easy and convenient to obtain from GPS and is equally useful. To make full
use of the three-dimensional potentials of GPS, one needs to determine the separation between the
ellipsoid and the geoid. This separation is known as geoidal undulation (N) (Fig. 2).
Relationship Between Ellipsoidal and Orthometric Heights
The relationship between the ellipsoid and the geoid can be represented mathematically by:
h - H = N…………………………………………… 1
In (1), h is the ellipsoidal height, H is the Orthometric height, and N is the geoidal undulation,
Equation (1) can be stated as
h – H - N = 0…………………………………………2
However, equation (2) may not be valid because of the offset of the vertical datum with respect to
the geoid. This offset of the vertical datum with respect to the geoid may be represented by Q and
hence equation 2 becomes: h – H -N = Q……………3
3
, Q can be represented diagrammatically in figure 2.
The offset of the vertical datum with respect to the geoid (Q) is very small and always neglected in
low order surveys.
The earth is a “closed” surface ¾ of which is covered with water, while the remainder is dry land
(terrain). The determination of the size and shape of the earth has been always been one of the major
tasks of Geodesy. A number of surfaces have been used or proposed to model the geometry of the
earth’s surface. These include the Terrain (the physical surface of the earth); Geoid; the sphere and
Ellipsoidal surfaces.
The physical surface of the earth may be described as the topographical surface on which
observations are carried out for purposes of determining coordinates of terrain points as well as the
geometrical relationship between such points. The terrain is a topographical surface characterized by
hills and valleys. The surface is very irregular and cannot be represented by a simple mathematical
relation, and therefore not ideal reference surface.
The geoid is an equipotential surface corresponding to the undisturbed mean sea level underneath the
continents. Although a much smoother surface than earth’s terrain, the geoid is still too complicated
for use as a computational surface for surveying and mapping purposes. It, however, serves as a
reference datum to which vertical measurements and astronomical observations may be reduced. By
far the most mathematically suitable geodetic surfaces are the ellipsoidal surfaces which include the
sphere, biaxial ellipsoid and triaxial ellipsoid.
Other complex mathematical surfaces have also been used and these include the telluroid and the
hydrostatic ellipsoid. The telluroid approximates the physical surfaces of the earth and is defined as
the surface whose height above a geocentric ellipsoid is the same as the height of the terrain above
the geoid. The height telluroid above the ellipsoid is called normal height, usually denoted as HN,
while the height of the earth’s surface is height anomaly.
Fig. 3: Geodetic Reference Surfaces
In geophysical studies, the hydrostatics equilibrium has been suggested as a reference system. It is
supposed to depict mass anomalies within the earth by assuming the earth as fluid and laterally
homogeneous so that the shape of the earth’s surface in hydrostatic equilibrium would be the
4
