Types of Maps Mercator Projections Conic Projections Gnomonic Projections Topographic Maps.
Projections and Reference Local Systems in Engineering Survey · Projections and Reference Local...
Transcript of Projections and Reference Local Systems in Engineering Survey · Projections and Reference Local...
Projections and Reference Local Systems in Engineering Survey
OVIDIU COSARCA, CONSTANTIN COSARCA, ALEXANDRU CALIN
Technical University of Civil Engineering Bucharest
122-124, Bvd. Lacul Tei, Sector 2, Bucharest
ROMANIA
[email protected], [email protected], [email protected]
http://geodezie.utcb.ro
Abstract: - Usually, the engineering survey applications are carried on in all the realization stages which
concern construction objectives based on a local three-dimensional geodetic network. When these networks are
lying on a small surface, the problem is treated trivially, but correctly, by choosing a local coordinate system
which widely meets the requirements regarding the accuracy and the configuration of these projects. Another
problem for the geodetic specialist appears in case of large range works and especially in case of works that are
developing, mainly, in one cardinal direction. In this situation it is necessary to choose and adopt a specific
projection system, so that the deformation coefficient of the linear values induced by the chosen projection
system tends to the value of 1. To reach this desideratum it is necessary to develop a local projection system,
chosen in such way that in the points of the extended line barycentre, the linear deformations induced by the
system are null.
Key-Words: - engineering measurements, survey geodetic network, cartographic projections, local projection
plan, linear deformation coefficient
1. Purpose of the research In this paper is approached the issue of
design, implementation and use of geodetic
networks that should stand as a basis for
construction / rehabilitation / modernization projects
of the railways. It is noted that these works show a
very important feature being that they are carried
out predominantly on a dimension and require very
high precision. Such a work can be carried out over
distances of hundreds of kilometres and accuracies
required in the Technical Specifications usually are
of the order of a few millimetres. Premises for
achieving this work are determined by the
requirements of production practices and are
intended to clarify issues that appear in such cases
and that should be solved by geodetic engineers.
The ultimate aim of this paper is to identify ways of
generating a local projection plan that would
conform to the requirements of conserving linear
deformation.
2. Work content The paper is based on a real situation, which
required the realization of a survey geodetic network
used in the rehabilitation of the railway Brasov -
Arad - Hungarian border. The entire project covers a
distance of about 400 km and covers practical more
than half of Romanian territory, predominantly on
the East – West direction.
In order to realize this work, has been
considered the inclusion of the following theoretical
considerations and the following stages:
- Brief overview of geodetic reference systems
used in Romania;
- Theoretical study of cartographic projections
and descriptive elements that can lead us to
choosing a particular projection;
- Reduction of observations to the reference
surface. Calculations and relationships
principles;
- Conceiving of the case study in which is solved
problems related to:
o choosing an appropriate cartographic
projections;
o adoption of a local projection plane, that -
correspond to the declared aspirations of
this work;
o reduction of the field observations measured
by using classical technology (total station)
to the adopted projection plane;
o creating the possibility to automatically
make the reduction calculations, by writing
a program (in MATLAB) with various
options and the possibility of using the final
data in an adjustment program;
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ISBN: 978-960-474-335-3 15
o calculations and adjustment of
measurements made in the network, in order
to obtain the final coordinates of all the
geodetic network points, using dedicated
software components (HANNA);
o validation of the final results, to confirm
that the linear deformation coefficient tends
to the value 1;
3. General information about the
work On this particular section, the field works
were performed in order to create a survey geodetic
network that will ensure all the necessary surveying
data for its design and execution. Measurements
were performed using combined methods - GNSS
technology, measurements performed with total
station (for polygonal traverses between the points
determined with GNSS technology) and geometric
levelling measurements performed with digital
levelling instruments for survey of heights.
3.1 Measurements carried out using GNSS
technology
On this section, there were determined a
total of 30 points, materialized in areas with easy
access and which qualify for the use of GNSS
technology.
The network measurements were processed
with specialized software, such as free network by
imposing restraints, the inner accuracy of the
network, wasn’t negatively affected. Finally, the
network has ellipsoidal coordinates in the WGS84
system that was defined at that time (when
measurements were made).
The obtained ellipsoidal geodesic
coordinates were converted, transferred into a local
own projection plane, where a mapping projection
was applied (Transverse Mercator, for example,
with a corresponding scale factor, calculated as the
ratio between the measured distance and reduced to
the ellipsoid distance) and plane coordinates were
obtained. Therefore, besides that the coordinates
obtained in the projection plane were not affected by
any restraint, they were not obtained through
coordinate transformations, but through conversion.
All software components for processing the
measurements made by GNSS technology offer
these opportunities.
3.2 Measurements carried out using classical
technology
For the other points of geodetic network
(about 120 points) the measurements were
performed using classical technology, respectively
total stations. The measurements were constituted in
horizontal directions, vertical angles and slope
distance. It is necessary for these measurements
(horizontal directions and slope distances) to be
reduced to the same local projection plane,
generated under the condition of a null coefficient of
linear deformations. Preliminary processing of this
type of measurements (for example choosing
appropriate cartographic projection and the
reduction of the measured distances at the local
projection plane) was performed using a MATLAB
application that was developed.
Final processing (adjustment of the
measurements performed in geodetic network) was
also achieved during the training stage, using
appropriate software components.
For the determination of the heights of the
geodetic network points it was used the method of
geometric precision levelling, using digital levelling
instruments. Finally, the point’s heights resulted in a
unique system, respectively “normal heights system
with zero fundamental point Black Sea 1975”, which
is the official system in Romania. Points from
National Altimetry Network were used for this
purpose.
In order to achieve the ultimate goal of this
work was used as initial elements:
- geodetic coordinates B, L, h, results from
measurements performed with of GNSS
technology;
- slope distances ("GPS vectors");
- slope / horizontal distance, results from
measurements performed with classical
technology;
- horizontal directions;
- point’s heights.
4. Reference ellipsoids / Coordinate
systems (Datum used in Romania) In Geodesy, a reference ellipsoid is a
mathematically-defined surface that approximates
the geoid, the truer figure of the Earth, or other
planetary bodies. Because of their relative
simplicity, reference ellipsoids are used as a
preferred surface on which geodetic network
computations are performed and point coordinates
such as latitude, longitude, and elevation are
defined.
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Krassovsky 1940 - The size and shape of a rotation
ellipsoid are currently defined throughout two
geometrical parameters, from which one of them
must be one of the semi-axes. For example, one
needs the value of the major semi
flattening.
Since 1951 the official reference ellipsoid
used in Romania is the Krasovsky (1940) ellipsoid
and its corresponding parameters.
WGS 1984 - The World Geodetic System is a
standard for use in cartography, geodesy
navigation. It comprises a standard coordinate frame
for the Earth, a standard spheroid reference surface
(the datum or reference ellipsoid) for raw altitude
data and a gravitational equipotential surface (the
geoid) that defines the nominal sea level.
coordinate origin of WGS 84 is meant to be locate
at the Earth's center of mass.
The WGS 84 originally used the GRS 80
reference ellipsoid, but has undergone some minor
refinements in later editions since its initial
publication. Most of these refinements are important
for high-precision orbital calculations for satellites
but have little practical effect on typical
topographical uses.
GRS 80 - The GRS 80 reference system was
originally used by the World Geodetic System 1984
(WGS 84). The reference ellipsoid of
differs slightly due to its later refinements (see
WGS84).
Fig. 0- WGS84 reference frame
The Stereographic Projection
Romania's official mapping projection
geodetic works on Romanian territory are executed
using the Stereographic Projection 1970
70” for cadastral maps, topographical maps, etc..
This cartographical projection was introduced as
official projection around 1970 (hence the name
“Stereo 70”), replacing the old Gauss
projection that represented the territory of
on spindles of 3 or 6 degrees. Pulkovo 1942(58)
geodetic datum first defined in 1956 and is suitable
The size and shape of a rotation
ellipsoid are currently defined throughout two
geometrical parameters, from which one of them
axes. For example, one
needs the value of the major semi-axes and the
reference ellipsoid
used in Romania is the Krasovsky (1940) ellipsoid
The World Geodetic System is a
cartography, geodesy and
navigation. It comprises a standard coordinate frame
reference surface
llipsoid) for raw altitude
and a gravitational equipotential surface (the
geoid) that defines the nominal sea level. The
coordinate origin of WGS 84 is meant to be located
The WGS 84 originally used the GRS 80
reference ellipsoid, but has undergone some minor
refinements in later editions since its initial
publication. Most of these refinements are important
ions for satellites
but have little practical effect on typical
reference system was
originally used by the World Geodetic System 1984
). The reference ellipsoid of WGS 84 now
differs slightly due to its later refinements (see
WGS84 reference frame
tereographic Projection 1970 is
ion. All the topo-
geodetic works on Romanian territory are executed
rojection 1970 or “Stereo
cadastral maps, topographical maps, etc..
projection was introduced as
official projection around 1970 (hence the name
), replacing the old Gauss-Kruger
that represented the territory of Romania
Pulkovo 1942(58) is a
d in 1956 and is suitable
for use in Onshore Albania, Bulgaria, Czech
Republic, Germany (former DDR), Hungary,
Poland, Romania, and Slovakia.
1942(58) references the Krassowsky 1940 ellipsoid
and the Greenwich prime meridian.
The European Terrestr
1989 (ETRS89) is an ECEF
Fixed) geodetic Cartesian reference frame, in which
the Eurasian Plate as a whole is static. The
coordinates and maps in Europe based on
are not subject to change due to the continental drift
The development of
the global ITRS geodetic datum, in which the
representation of the continental drift is balanced in
such a way that the total apparent angular
momentum of continental plates is about 0.
In Romania, the reference system used to
determine the altitudes, is called the system of
normal heights with fundamental zero point Black
Sea 1975. Fundamental zero Point of this system is
considered the fundamental benchmark ty
Military Chapel of Constanta. The altitude of this
point was determined by means of repeatedly
geometric leveling works and gravimetric
measurements. The Studies were performed after
this period led to the idea of creating a new
fundamental zero point, in an area geologically
'stable'. The site was chosen at about 53 km from
Constanta, between localities Tariverde and
Cogealac.
5. Cartographical ProjectionsCartography is an ancient art and
methods to project / mathematically transform all or
part of the surface of a sphere (e.g., the earth) onto a
two-dimensional, flat surface or plane. The process
of map projection introduces distortions of the data
and/or its geometry. The choice of a specific
projection method in visualization is very important
for the proper communication of information.
map projection is a systematic representation of all
or part of the surface of a round body, especially the
Earth, on a plane [5].
Fig. 3 - From ellipsoid or sp
(right)
for use in Onshore Albania, Bulgaria, Czech
Republic, Germany (former DDR), Hungary,
Poland, Romania, and Slovakia. Pulkovo references the Krassowsky 1940 ellipsoid
and the Greenwich prime meridian.
errestrial Reference System
ECEF (Earth-Centered, Earth-
ixed) geodetic Cartesian reference frame, in which
the Eurasian Plate as a whole is static. The
coordinates and maps in Europe based on ETRS89
are not subject to change due to the continental drift.
The development of ETRS89 is related to
geodetic datum, in which the
representation of the continental drift is balanced in
such a way that the total apparent angular
inental plates is about 0.
In Romania, the reference system used to
is called the system of
normal heights with fundamental zero point Black
Fundamental zero Point of this system is
considered the fundamental benchmark type I from
Military Chapel of Constanta. The altitude of this
point was determined by means of repeatedly
geometric leveling works and gravimetric
The Studies were performed after
this period led to the idea of creating a new place for
ntal zero point, in an area geologically
'stable'. The site was chosen at about 53 km from
Constanta, between localities Tariverde and
Cartographical Projections Cartography is an ancient art and science of
mathematically transform all or
part of the surface of a sphere (e.g., the earth) onto a
dimensional, flat surface or plane. The process
of map projection introduces distortions of the data
and/or its geometry. The choice of a specific
d in visualization is very important
for the proper communication of information. A
map projection is a systematic representation of all
or part of the surface of a round body, especially the
From ellipsoid or sphere (left) to flat map
(right)
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A projection is required in any case. Since
this cannot be done without distortion, the
cartographer must choose the characteristic which is
to be shown accurately at the expense of others, or a
compromise of several characteristics. Map
projections allow us to represent some or the Earth’s
entire surface, at a wide variety of scales, on a flat,
easily transportable surface, such as a sheet of
paper. Map projections also apply to digital map
data, which can be presented on a computer screen.
Each map projection has advantages and
disadvantages; the appropriate projection for a map
depends on the scale of the map, and on the
purposes for which it will be used. The properties of
a map projection may also influence some of the
design features of the map. Some projections are
good for small areas, some are good for mapping
areas with a large east-west extent, and some are
better for mapping areas with a large north-south.
5.1 Reduction of the distances – General situation
The first step is the reduction to the chord,
second to the ellipsoid and last, to the projection
plane. Reducing the distance to the chord:
���� � ���� � ��∆�� � ���������������� (1)
where:
Dc - is the distance reduced to the chord;
Df – is the distance measured on the field
and physically reduced;
DH – is the level difference between the
points;
H – provisory elevation.
Reducing the distance to the ellipsoid: ��� � 2�� �� �!" �#$%� (2)
where:
S – the distance reduced to the ellipsoid;
Dc – the distance reduced to the chord.
Reducing the distance to the projection plane ���& � ��� �1 ( )* �+* ,%� ( ) �+ ,-%� � (3)
where:
S – the distance reduced to the ellipsoid;
c – scale factor.
For the local Transverse Mercator
projection plane: ���& � ���./�1 ( +* $%� ( + $,%� � (4)
Fig. 4 – Reduction of distances (general case)
6. Local Projection Systems and
Reference Systems in Survey
Engineering. Overview Survey engineering applications are usually
carried on in all the creation stages which concern
some construction objectives, based on a local
three-dimensional network. When the networks are
lying on a small surface, the problem is handled
trivially, but correctly, by choosing a local
coordinate system which widely meets the
requirements regarding the accuracy and the
configuration of these projects.
The problem regarding the accuracy
requirements of the engineering projects becomes
complicated when the networks are lying on bigger
surfaces. In these types of situations, a three-
dimensional approach using conventional
measurements makes sense only if the vertical
deviations in the network points are known, and this
occurs very rarely.
Depending on the requirements, there are
some solutions of solving this problem, of which we
mention only three:
- The measurement of the vertical deviation, an
operation that is very laborious. However, in
plain terrain, the variation of the vertical
deviation usually remains under the
measurement precision;
- The continuous separation between the
reference systems for the planimetric
determinations and those for the altimetric
determinations;
- Adoption of some mixed measurement and
processing solutions.
Another problem encountered by the
geodetic specialist appears in case of large range
works and especially in case of works developing,
mainly, to one cardinal direction.
In this situation it is necessary to choose and
adopt a specific projection system, so that the
Recent Advances in Geodesy and Geomatics Engineering
ISBN: 978-960-474-335-3 18
coefficient of deformation for the linear values
induced by the chosen projection system tends to the
value of 1.
This approach leads to an increased ease for
the stake-out works in the execution stage and also
to the elimination of some supplementary reduction
calculus for the adopted projection system. An
eloquent example is represented by the design /
execution and rehabilitation works of the
communications ways. These stages must be
considered in the design stage, because executing
the works in the national projection systems is out
of discussion by reason of the deformation induced
by these projection systems
To reach this desideratum it is necessary to
develop a local projection system, chosen in such a
way that, in the barycentre points of the extended
course, the linear deformations induced by the
system will be null. In this way, the variation of the
distance deformation coefficient has minimum
values (close to value of 1) to the end of the course.
6.1 Theoretical considerations
This concept was tested on a rehabilitation
(modernization) work of the Bucharest – Arad
railway, on the Micasasa – Coslariu section. The
section between the railway stations Micasasa and
Coslariu, extends approximately on 40 km, on the
East – West direction (on an almost perpendicular
direction on the deformation circles of the
Stereographic 1970 projection – cartographic
projection commonly used in Romania).
To guarantee the accuracy requirements
imposed by the customer along the whole railway
line, a mixed measuring and processing solution was
adopted by using GNSS technology combined with
conventional technologies. In order to monitor the
linear deformation, one can imagine various
mathematical models using the projection mapping
properties. For the present study I imagined two
situations which correspond to the hypotheses layed
down above:
a. Generating a local stereographic projection plan
(having essential features of a stereographic
plan), tangent to the WGS 84 ellipsoid, with the
projection pole approximately in the middle of
the work.
One reason for the choice of stereographic
projection contact or secant plane is that the
coordinate system axes concur with those of the
national system axis and especially for the fact that
many production specialists who will use the points
of this network in the execution period, are
familiarized with this system.
b. For the network of points from the section CF
Micasasa - Coslariu a local cylindrical
projection – was adopted and tested -
respectively Transverse Mercator projection.
The variants with tangent or secant plane to
WGS 84 ellipsoid having the projection pole
approximately in the "middle" of the work were
tested.
The differences obtained in the processing
of the polygonal network in these two local
projection systems were very small.
The final goal is to avoid such deformations
induced by the national geodetic system
(Stereographic 1970), which in this area their values
are between -10 to -20 cm / km.
This aspect will also be observed in the
results (standard deviations) of the polygonal
network compensation. Having as a base the points
from the geodesic network performed with GNSS
technologies, this network was completed
afterwards.
6.2 Theoretical Basis of the Local Stereographic
Projection Plane
From the beginning, we must determine the
coordinates φ0 and λ0 of the central point for the
representation of a point with φ and λ coordinates
from the ellipsoid in the projection plane with the x
and y coordinates [3]. With the notations:
2
0
2
0
1 η+=
b
aN (5)
- curvature mean radius for φ0; 2
0
22
0 cos'e=η
00 tan=t (6)
0ϕϕϕ −=∆
- latitude deference between central point, in arc
units:
0λλ −=l (7)
- longitude difference between central point, in arc
units.
An accuracy of a few millimeters for the
plane coordinates x and y is ensured by this
relations, for ∆φ = ±1,5° latitude differences and ∆l
= ±2° longitude differences. Taking into account
these notations, the transformation relations have
the form:
Recent Advances in Geodesy and Geomatics Engineering
ISBN: 978-960-474-335-3 19
........)105510(cos240
1
)1010(cos240
1)2(
240
1)62(cos
24
)1869(cos24
)3(24
)6663(cos12
1)429641(
12
1
cos2
)63(2
)1(
44
0
2
00
4
0
232
00
2
0
5
0
42
0
2
00
4
00
222
0
2
0
2
00
2
0042
000
24
0
2
0
2
0
2
0
2
00
2
0
34
0
2
0
4
0
2
00
2
00
2
0
2
0024
0
2
0006
0
4
0
2
00
+⋅∆+−+
⋅∆−−+∆++⋅+−+
⋅∆−−−+∆−+
⋅∆−+−+∆+−−++
⋅+∆⋅−+∆⋅−+−⋅=
lttN
ltNNltNt
ltNt
Nt
ltttNttN
lNt
Nt
Nx
ϕϕ
ϕϕϕηϕ
ϕηηϕϕη
ϕηηϕϕηηηη
ϕϕηηϕηηη
..........)2112(cos240
1
)7020(cos240
1)10(cos
240
1
)41648(cos24
)12102(cos24
)21(cos12
1
)3631833(cos12
1
)222(cos2
cos
54
0
2
00
5
0
322
00
3
0
4
00
32
0
2
0
2
0
2
00
3
00
32
0
2
0
2
000032
0
2
00
3
0
24
0
2
0
4
0
2
0
2
0
2
000
4
0
2
0000
00
+⋅+−+
⋅∆+−+⋅∆−+
⋅∆−−+−+
⋅∆+−−+⋅+−+
⋅∆+−−+−+
⋅∆⋅−+−+⋅=
lttN
ltNlN
lttNt
ltNt
ltN
lttN
lNt
lNy
ϕ
ϕϕϕϕ
ϕηηϕ
ϕηηϕηϕ
ϕηηηηϕ
ϕηηϕϕ
(8)
6.3 Theoretical Basis of the Local Transverse
Mercator Projection Plan
The transverse Mercator map projection is
an adaptation of the standard Mercator projection.
The transverse version is widely used in national
and international mapping systems around the
world, including the UTM. When paired with a
suitable geodetic datum, the transverse Mercator
delivers high accuracy in zones less than a few
degrees in east-west extent.
Some of the features of the Transverse Mercator
Projection are:
− Near the central meridian (Greenwich in the
above example) the projection has low
distortion and the shapes of Africa, Western
Europe, Britain, Greenland and Antarctica
compare favorably with a globe.
− The central regions of the transverse
projections on sphere and ellipsoid are
indistinguishable on the small scale
projections shown here.
− The meridians at 90° east and west of the
chosen central meridian project to
horizontal lines through the poles. The more
distant hemisphere is projected above the
North Pole and below the south pole.
− The equator bisects Africa, crosses South
America and then continues onto the
complete outer boundary of the projection;
− Distortion increases towards the right and
left boundaries of the projection but it does
not increase to infinity.
− The map is conformal. Lines intersecting at
any specified angle on the ellipsoid project
into lines intersecting at the same angle on
the projection. In particular parallels and
meridians intersect at 90°.
− The point scale factor is independent of
direction at any point so that the shape of a
small region is reasonably well preserved.
− The choice of central meridian greatly
affects the appearance of the projection.
Used notations and relations: � Semi-major axis of reference ellipsoid 0 Ellipsoidal flattening 1/ Origin latitude
λ/ Origin longitude 2/ False Northing 3/ False Easting ./ Central meridian scale factor 1 Latitude of computation point
λ Longitude of computation point 2 Northing of computation point 3 Easting of computation point
and:
ω � λ 4 λ/ ; 5 � 5�"1
(10)
6 � ��1 4 7$��1 4 7$ sin$ 1�;
< � �=�1 4 7$ sin$ 1�
> � ?@ ; A/ � 0
N�N/(k/Em-m/(Term1(Term2(Term3(Term4M (11)
where: N7�A1 � O$2 < sin 1 cos 1
N7�A2 � O,24 < sin 1 cosR 1 �4ø$ ( > 4 5$�
N7�A3 � OT720 < sin 1 cosV 1 W�8>,�11 4 245$�4 28>R�1 4 65$� ( >$�1 4 325$�4 >�25$� ( 5,Z N7�A4 � O-40320 < sin 1 cos[ 1 �1385 4 31115$( 5435, 4 5T� A � ��]/1 4 ]$ sin 21 ( ], sin 41 4 ]T sin 61� (12)
where: ]/ � 1 4 �7$4 � 4 �37,64 � 4 �57T256�
]$ � 38 �7$ ( 7,4 ( 157T128 �
], � 15256 �7, ( 37T4 �
]T � 357T3072
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ISBN: 978-960-474-335-3 20
3 � 3/ ( ./< O cos 1 �1 ( N7�A1 ( N7�A2 ( N7�A� (13)
where: N7�A1 � O$6 cos$ 1 �> 4 5$�
N7�A2 � O,120 cos, 1 W4>R�1 4 65$�( >$�1 ( 85$� 4 >25$ ( 5,Z N7�A3 � OT5040 cosT 1 �61 4 4795$ ( 1795,4 5T�
7. Description of the practical
application The geodetic works represent the first stage
within the studies related to the rehabilitation of the
railway line on the Bucharest – Arad thoroughfare,
sections Sighisoara – Alba Iulia (Fig. 5 and 6).
In order to ensure the suitable reference
system for the detailed surveying in the design
phase and further on during the execution period
according to the specialty designer requirements,
constructing a proper geodesic network was
necessary from the accuracy and easy access
viewpoint.
Fig. 5 – Romanian railway map
Fig. 6 – Map detail
Considering the high requirements of
accuracy (standard deviation in the horizontal plane
of +/- 5 mm and standard deviation in level plane of
+/- 2 mm) and the special characteristic of such kind
of work it was considered that a new network was
necessary to be designed and executed.
The design of the planimetry and altimetry
geodetic network, as well as the processing of the
data resulted from measurements are performed
according to the precision requirements of the
beneficiary.
7.1 Project of Geodetic Network. General
Concept
The design of the geodetic network aimed
to ensure a mean density of about 2 points / km in
the main network, completed by 3 points / km in the
polygonal network, ensuring in this way the
possibility to use the entire network for developing
the needed polygonal traversing for the detailed
surveying works.
Taking into account the beneficiary’s
request and in view of eliminating the deformations
induced by the national projection system right from
the design stage, a local projection system
completion for railway section has been considered.
In order to set up the leveling reference
system it has been established that this should
correspond with the national reference system
(Black Sea 1975).
7.2 The Network Establishment Methods
Considering the hierarchic character of the
planimetric network and the accuracy required by
the beneficiary, in the design stage, the use of two
methods for defining the coordinates of the points:
− GPS technology for main network points,
taking into account its advantages:
− Accurate polygon traversing method by
using total performing stations.
Starting from the accuracy criteria for the
leveling position required by the beneficiary it has
been estimated that the corresponding method for
determining the levels of the network points is:
− Accurate geometric levelling traversing
method by using professional leveling
instruments.
7.3 Generating the Local Projection System
For this Micasasa – Coslariu section,
considering that it is approximately 40 km long, a
local Transverse Mercator projection plan has been
generated, secant to the ellipsoid WGS 84, having
the centre point approximately at the middle of the
distance, B=46°08`30``; L=23°52a30aa. It has been tested several versions of
generating local project plan, considering that the
scale coefficient ko (the ratio between the horizontal
Recent Advances in Geodesy and Geomatics Engineering
ISBN: 978-960-474-335-3 21
distance determined from measurements
distance and the ellipsoid – true distance) to have a
small influence on the linear deformations, meaning
that the deformation value tends toward the value of
1.
Fig. 7 - Paramenters of the local projection system
The table below shows the differences
between the distances obtained from the coordinates
(determined with GNSS technology) in the local
system selected and horizontal distances measured.
The results justify choosing the scale factor of
1.000046.
Table 1 – Diferences between Grid Distances and
Ground Distances for scale factor 1.000046
From To
True
Dist.
(m)
Ell.
Dist.
(m)
Grid
Dist.
(m)
402 403 221.418 221.403 221.412
402 613 159.808 159.771 159.777
402 614 3505.845 3505.662 3505.833
539 547 1431.275 1431.213 1431.283
624 546 415.279 415.258 415.278
624 623 1635.219 1635.148 1635.229
625 546 660.458 660.429 660.460
625 547 463.628 463.608 463.629
625 623 1884.086 1884.004 1884.098
625 624 265.109 265.097 265.110
7.4 Measurements reduction
Are briefly presented the obtained values of
the data set before the reduction to the projection
plane and the final values that have been
by using the software developed.
The complete comparison will be detailed
after the data adjustment.
The following tables present
the data used in the MATLAB program, as input
data, and the final results – the reduced distances
that were finally used in the adjustment.
present the data used for scale factor: 1.000046
Table 2 – Reduced measurements for scale factor
1.000046
measurements – ground
true distance) to have a
all influence on the linear deformations, meaning
that the deformation value tends toward the value of
Paramenters of the local projection system
The table below shows the differences
between the distances obtained from the coordinates
(determined with GNSS technology) in the local
system selected and horizontal distances measured.
The results justify choosing the scale factor of
Grid Distances and
for scale factor 1.000046 Ground
Dist.
(m)
Diff.
(mm)
221.414 -2
159.779 -2
3505.835 -2
1431.275 9
415.275 3
1635.218 11
660.457 3
463.628 1
1884.085 12
265.108 2
the obtained values of
the data set before the reduction to the projection
have been obtained
The complete comparison will be detailed
The following tables present a small part of
the data used in the MATLAB program, as input
the reduced distances
that were finally used in the adjustment. The tables
scale factor: 1.000046.
Reduced measurements for scale factor
Pt.
No.
Provisional coordinates
N (m) E (m)
403 43848.487 416311.798
404 43863.933 416075.929
405 43911.398 415810.242
406 43936.869 415557.831
407 44010.418 415301.836
408 44124.811 415066.485
409 44309.284 414846.163
410 44455.069 414679.350
The Matlab program simplifies the
calculation process of reducing the distances to the
projection plane. The program uses raw date, gives
the user the possibility to select the transformation
parameters and exports the final results, comparing
them to the calculated distances.
Fig. 8 Main window of the Matlab program
7.5 Adjustment of Measurements Carried out in
the Planimetric Network
The measurements executed with
conventional technology in the planimetric network
were carried out according to t
the beneficiary, respectively 3 series of
measurements in each station point.
The distances measured with the total
station were then reduced to the defined local
projection plane. The values of the horizontal
directions and of the measured distances (
the local projection plane) were the input data in
compensation.
The points determined with GNSS
technology, were considered in this phase
points, all the other points (determined by
conventional technologies)
The adjustment calculations were carried
out using appropriate software
The results obtained after compensation confirmed
Elev. Slope
distance
(GPS
vector)
(m)
Reduced
distance
(m) H (m)
274.094 221.418 221.415
272.359 236.388 236.383
270.905 269.905 269.903
268.701 253.710 253.702
267.544 266.361 266.360
266.983 261.688 261.689
268.273 287.365 287.364
266.237 221.557 221.549
The Matlab program simplifies the
calculation process of reducing the distances to the
projection plane. The program uses raw date, gives
ibility to select the transformation
parameters and exports the final results, comparing
them to the calculated distances.
Main window of the Matlab program
Adjustment of Measurements Carried out in
The measurements executed with
conventional technology in the planimetric network
were carried out according to the requirements of
the beneficiary, respectively 3 series of
measurements in each station point.
The distances measured with the total
station were then reduced to the defined local
The values of the horizontal
nd of the measured distances (reduced to
the local projection plane) were the input data in
The points determined with GNSS
technology, were considered in this phase old
, all the other points (determined by
becoming new points.
The adjustment calculations were carried
appropriate software program package.
The results obtained after compensation confirmed
Recent Advances in Geodesy and Geomatics Engineering
ISBN: 978-960-474-335-3 22
the precision of the measurement execution. It was
also confirmed that is demanded from the start.
The report between measured distances and
those obtained from coordinates tends toward the
value of 1.
8. Conclusions The planimetric and altimetric geodetic
network (bridging and survey geodetic network)
conceived and executed with the purpose to
complete the modernization works of railway line
corresponds, as point density and precision, to the
requirements expressed by the beneficiary and is
according to the regulations in force regarding this
type of works.
The execution of this geodetic network at
high quality parameters and precision will also
ensure the quality of the future topographical works
that will develop in the design and execution study
stage.
To achieve these quality criteria and also in
order to conserve the linear deformation coefficient,
was studied and solved a number of problems in the
present paper. Identifying suitable cartographical
projections for such work with special character and
choosing between a section plane and a contact
plane was the most important problem that was
treated in present paper.
It has analyzed and emphasized the
significant differences between the reduced
distances using different scale factors – considering
both a contact and a section plane and various
cartographical projection systems.
As a result of this study, our opinion is that -
if the geodetic networks are carried on long
distances of hundreds of kilometers and
predominant one direction and are intended for
engineering works - the solution is to adopt a local
projection plane using Transverse Mercator
projection (in present case), on sections between 20
to 30 km.
Conversion and transfer of the GPS points
coordinates (the obtained ellipsoidal geodetic
coordinates) to a certain local projection plane were
easy to accomplish by using certain GPS post-
processing applications.
But what happens in case of using combined
measurements (measurements carried out with
GNSS technology and classical technology - total
stations)?
We believe that it has filled the gap of
reducing the distances measured with other
instruments, as the total station. We have solved this
problem using MATLAB and creating a suitable
application. Having a graphical user interface, it is
now very easy to load your data, all the parameters
of the ellipsoid and projection plane and have in just
few seconds your reduced data. The program
already compares the calculated distances (from
local coordinates) with reduced distances and also
the calculated distances with measured horizontal
distances, therefore you will be able to see the
differences between them – all in matter of just a
few seconds. Finally, using the appropriate software
programs system, adjustment of the measurements
performed in network with reduced elements to
adopted projection plan and considering the points
determined with GNSS technology as “fixed points”
has led to the determination of the final coordinates
of the geodetic network.
References:
[1] Munteanu, C. Cartografie matematica,
Editura MATRIX ROM Bucuresti, 2003
(Mathematical Cartography, MATRIX ROM
Publishing House, Bucharest, 2003);
[2] Snyder, J.P. Map Projections – A
Working Manual, U.S.GEOLOGICAL
SURVEY PROFESSIONAL PAPER 1395,
Supersedes USGS Bulletin 1532;
[3] Cosarca, C., Neuner, J., Calin, A. Projection and
Reference Local Systems in Engineering Survey
– Scientific Bulletin of Technical University of
Civil Engineering, Bucharest, 2006;
[4] Moldoveanu, C., Geodezie – Editura
MatrixRom, Bucureşti, 2002 (Geodesy,
MATRIX ROM Publishing House, Bucharest,
2002);
[5] Lloyd A. Treinish - Correlative Visualization
Techniques for Disparate Data, 1996;
[6] Cosarca, O., Dissertation: Geodetic Networks in
Engineering Surveying works, Faculty of
Geodesy Bucharest, 2013.
Recent Advances in Geodesy and Geomatics Engineering
ISBN: 978-960-474-335-3 23