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

ovidiu_cosarca@yahoo.com, constantin_cosarca@yahoo.com, alexcalin1975@yahoo.com

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;

Recent Advances in Geodesy and Geomatics Engineering

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.

Recent Advances in Geodesy and Geomatics Engineering

ISBN: 978-960-474-335-3 16

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)

Recent Advances in Geodesy and Geomatics Engineering

ISBN: 978-960-474-335-3 17

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

Recent Advances in Geodesy and Geomatics Engineering

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