building stock survey section01_fundamentals

Geographical Information Systems (GIS)and

Building Stock Survey

Prof. Dr.-Ing. Willfried Schwarz

Bauhaus-Universität Weimar

Fakultät Bauingenieurwesen

winter semester 2013/2014

Building Stock Survey WS 2013/2014, Section 1: Fundamentals 1

Professur Geodäsie und Photogrammetrie

Marienstraße 9

99423 Weimar

Tel.: 03643/584530

Fax: 03643/584534

E-Mail: [email protected]

Homepage:

http://www.uni-weimar.de/de/bauingenieurwesen/ prof essuren/geodaesie-und-photogrammetrie/

Course program:Natural Hazards and Risks in Structural Engineering (NHRE)

Bau

haus

-Uni

vers

ität

Wei

mar

Contents of the lecture

1. Fundamentals

2. Three-Dimensional Positioning

3. Fundamentals of Photogrammetry

4. GIS/Cartography

5. Landmanagement/Cadastre

6. Monitoring of Structures


6. Monitoring of Structures

Literature[Bauer, M. 2003 ] Vermessung und Ortung mit Satelliten. 5., neubearb. u. erw. Aufl., 62,00 EUR, Wichmann Verlag 2003, ISBN 3-87907-360-0..[Baumann, E. 1999 ] Vermessungskunde, Band 1: Einfache Lagemessung und Nivellement. 5., bearb. u. erw. Aufl., 22,40 EUR, Dümmler Verlag, Bonn 1999,

ISBN 3-427-790444 (nicht mehr lieferbar).[Baumann, E. 1998 ] Vermessungskunde, Band 2: Punktbestimmung nach Höhe und Lage. 6., bearb. u. erw. Aufl., 24,10 EUR, Dümmler Verlag, Bonn 1998,

ISBN 3-427-790568[Deumlich, F.; Staiger 2002 ] Instrumentenkunde der Vermessungstechnik. 9., neubearb. Aufl., 86,00 EUR, Wichmann Verlag 2002, ISBN 3-87907-305-8.[Fröhlich, H. 1995 ] Vermessungstechnische Handgriffe. 4., neubearb. Aufl., 11,20 EUR, Dümmler Verlag 1995 (nicht mehr lieferbar).[Gelhaus, R.; Kolouch, D. 1997 ] Vermessungskunde für Architekten und Bauingenieure. 2. Aufl., 21,00 EUR, Werner Verlag, Düsseldorf 1997, ISBN 3-804-17937-7,

(momentan nicht lieferbar, Verlag plant Nachdruck).[Hennecke, F.; Meckenstock, H.; Pollmer, G. 1993 ] Vermessung im Bauwesen – Grundlagen, Techniken, Beispiele. 11., überarb. u. erw. Aufl., 19,90 EUR,

Dümmler Verlag 1993.[Kahmen, H. 2006 ] Vermessungskunde. 20., neu bearb. Aufl., 49,95 EUR , Gruyter Verlag 2006, ISBN 3-11-018464.[Matthews, V. 2003 ] Vermessungskunde Teil 1. 29., neubearb. Aufl., 24,90 EUR, Teubner Verlag 2003, ISBN 3-519-25252-x.[Matthews, V. 1997 ] Vermessungskunde Teil 2. 17., neubearb. Aufl., 24,90 EUR, Teubner Verlag 1997, ISBN 3-519-15253-3.[NN 1996 ] DIN–Taschenbuch Nr. 111 Vermessungswesen. Neuaufl., Beuth–Verlag 1996, in Bibliothek.[Prasuhn, K.–B. 1995 ] Vermessungstechnik im Gartenbau und Landschaftsbau. 6., neubearb. Aufl., 44,95 EUR, Blackwell Wissenschafts–Verlag 1995,

(nicht mehr im Buchhandel).

Literature


[Resnik, B.; Bill, R. 2003 ] Vermessungskunde für den Planungs–, Bau– und Umweltbereich. 29,80 EUR, 2. neubearb. u. erw. Aufl., Herbert Wichmann Verlag,Heidelberg 2003, ISBN 3-87907-399-6.

[Witte, B.; Schmidt, H. 2006 ] Vermessungskunde und Grundlagen der Statistik für das Bauwesen. 6., überarb. Aufl., 29,80 EUR, Konra d Wittwer Verlag,Stuttgart 2006, ISBN 3-87907-418-6.

[Konecny, G.; Lehmann, G. 1984 ] Photogrammetrie. 4., neubearb. Aufl., 42,95 EUR, Gruyter Verlag 1984 (nicht mehr im Buchhandel).[Luhmann, Th. 2003 ] Nahbereichsphotogrammetrie; Grundlagen, Methoden und Anwendungen. 88,00 EUR, Herbert Wichmann Verlag, Heidelberg 2003,

2. überarb. Aufl., ISBN 3-87907-398-8.[Regensburger, K. 1990 ] Photogrammetrie – Anwendungen in Wissenschaft und Technik. 1. Aufl. 1990, Wichmann Verlag 1990, in Bibliothek.[Rüger, W u.a. 1987 ] Verfahren und Geräte zur Kartenherstellung. 5., bearb. Aufl., Wichmann Verlag 1987, in Bibliothek.[Schwidefsky, K.; Ackermann, F. 1976 ] Photogrammetrie – Grundlagen, Verfahren. 7., neubearb. u. erw. Aufl., Teubner Verlag 1976, in Bibliothek.[Hake, G.; Grünreich, D. 2002 ] Kartographie. 8., neubearb. u. erw. Aufl., 42,95 EUR, Gruyter Verlag 2002, ISBN 3-11-016404-3.

[Kahmen, H.; Gaig, W. 1988] Surveying. Walter de Gr uyter 1988, ISBN 3-11-008303-5.[Bird, R. G. 1989] EDM TRAVERSES: Measurement, Com putation and Adjustment. Longman Scientific@Technic al, ISBN 0-582-02379-3.

Internet:http://www.uni-weimar.de/de/bauingenieurwesen/profe ssuren/geodaesie-und-photogrammetrie/

Internet


Internet


Motivation

fallen buildings, e. g. in Haiti � earthquakes 12 of January 2010

Methods of surveying

• Polar Surveys

• Terrestrical Laserscanning

• Photogrammetry


• Photogrammetry

• …

Ruined cathedral in Port-au-Prince

Definition of Geodesy

Friedrich Robert Helmert (1843 – 1917):

Surveying or Geodesy is the teaching to take themeasurements of the surface of the earth with allchanges and their presentation in registers, mapsand plans.


GEOA earth

DASEI share

from Greek:to share the earth.

History of Surveying

Cheops pyramid near Gizeh, about 2500 before Christ (B. C.)

Babylonia and Egypt


Quelle: Bachmann (1965)

City map of Nippurabout 1500 B. C.

ll



Quelle: Bachmann (1965)

Engineering Surveys in antiquity

Hiskia-Tunnel near Jerusalem705-701 B. C.

Supply of water of JerusalemTunnel construction of two sites

holy graves

Eupalinos-Tunnel at Samos6th century B. C.


Quelle: Grewe (1998)

World map ofEratosthenes, 240 B. C.



Map of Thuringia by Mellinger (1580)

Magnification of the cutout


Quelle: Vom Königreich der Thüringer zum Freistaat Thüringen. Verlagshaus Thüringen 1999.

Surveying about 1800


Main area of work

higher geodesydetermination of the figure of the earthand of the outside gravity field

governmental surveycreation of horizontal networks and of the official maps


detail surveyplane survey and mappingcadastral surveying (real-estate surveying)

engineering surveyssurveying for buildingsadjustments for industry

Perception of the surveying tasks

• as sovereign tasks by the German statesCreation and monitoring of the networksEditing of the offical mapsSurvey and continuance of the cadastre

• AdministrationsFederal Agency of Cartography and Geodesy = BKGState Survey OfficesLand registries


Land registries

• Chartered Surveyor or Registered Land Surveyor (ÖbVI)

• other official surveying administrationsland consolidation authoritymanagement of state forestsroad building administrationsDeutsche Bahn AG (railway organisation)Waterways- and shipping administrations

Principles of work

Principle of neighbourhood„from great to little“protection of proximity principle

Principle of reliabilityall measurements and calculations are to ensure


all measurements and calculations are to ensure by independent checkings

Principle of economy„As accurately as possible,but not more accurate as required!“

Shape of earth

plain

sphere

Newton

Eratosthenes


ellipsoid of rotation

geoid

GaußListing

obelisk inAlexandria

well in Syene

bR

αααα

αααα

north pole

Circumference of the earth by Eratosthenes (250 B.C.)

sun


Determination of the circumference of the earthby Eratosthenes 250 B.C.

well in Syene

bottom of the well was illuminated

αααα

b = 5 000 Stadien (1 Stadie = 148.5 m)α = 1/50 of the full circle

circumference u = 50 * s = 37 125 km

radius R = 5 909 km

Quelle: Resnik/Bill (2000)

Eratosthenes(284 – 202 v. Chr.)

Geoid

Geoid

The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the earth, if the oceans were in equilibrium, at rest, and extended through the continents (such as with very narrow canals).


Quelle: www.google.deli

Quelle: GFZ Potsdam

Topographie(Bergmassiv)

Niveaufläche

sichtbareErdober-Fläche

Geoid

Lotlinien

R

R

R

R

RR

R

R = Rechter Winkel

Gravity field of the earth

actual earth surfacebig mountain

plumb line

equipotential surface

actualearthsurface

R = right angle


Meer Meer

Ellipsoid

GeoidLotabweichungLotabweichung

wahreLotrichtungEllipsoid-

normale Ellipsoid-normale

Stör-masse

ocean ocean

deflection to the verticaldeflectionto the vertical

actualplumb line perpendicular

to the ellipsoid

perpendicularto the ellipsoid

bigmass

Reference surfaces for positioning

Ellipsoid of rotation (mean ellipsoid)Mathematical surface of the whole earth.Axis of rotation is identical with axis of the earth.Deviations between „IUGG 1980“ und Geoid maximal 100 m.A local ellipsoid replaces only a limited area of the surface of the earth.

dimensions of semi-major axis semi-minor axisthe earth by a b

geometric flattening f of the earth:1 : 298.257

comparison :

a bf

a

−=


the earth by a bBessel 1841 6 377 397 m 6 356 079 mHayford 1924 6 378 388 m 6 356 912 mKrassowskij 1944 6 378 245 m 6 356 863 mIUGG 1980 6 378 137 m 6 356 752 m

Sphere (osculating sphere)For an area with a circumcircle of about 100 km.

Plain (tangent plane)For an area with a circumcircle of about 10 km.

comparison :By a globe with an equator radius of3.00 m the distance from the poles tothe equator plane is only 2.99 m.

Influence of earth curvature--> see black board

Shape of the earth

-120 m(maximal geoidundulation

plain

sphere


geoid

sphere



drawing: without scale!

exercise:

circumference: 40 000 km

rope with a length of40 000 km + 1 m

undulationbest shape of earth:

ellipsoid of rotationwith a

geometric flattening of 1: 300

actualplumb line

Regional and world-wide Ellipsoids

NorthAmerica

NorthAmericaEuropa Europa


Quelle: Landkarten verstehen und richtig nutzen www.brk.nrw.de

The geodetic datum defines the orientation of the ellipsoid of rotation to the body of the earth.

Geodetical Reference System ITRSxx/ITRFxx

Global system with an accuracy of a few centimeter

Definition (ITRS.xx)

• 3D-coordinate axisgeocentricaxis

Realization (ITRF.xx)

• measurement methodsVLBI, SLR, GPS and other

• problem: registration

ITRS = International Terrestrial Reference SystemITRF = International Terrestrial Reference Frame


axis

• Parametersemi-major axis ageometric flattening of the earthGMω

• Reduction of the observationsto the model earthpolar motionsdeformations

• problem: registrationof the changes

e. g. continental drift

One set of coordinates per year or frequently.

plate tectonics:2 cm to 10 cm per year

Quelle: Augath, W.: Beiträge des Vermessungs-wesens zur Ortung und Navigation im Wandel.

Quasars emit radio signals

VLBI = Very Long Baseline Interferometry


The geodetic datum defines the orientation of the ellipsoid of rotation to the body of the earth.

Geodetic datum, ETRS89

Current reference system in Germany:

ETRS89 (= European TerrestrialReference-System 1989)

The ERTS89 is a geocentric reference system which is based on the


The ERTS89 is a geocentric reference system which is based on the global International Terrestrial Reference System (= ITRS).

ellipsoid of rotation: GRS80 = IUGG 1980

fixing: fundamental stations of the global ITRF-Netin Europe, for example in Wettzell

projection: UTM

band size: 6°

Measuring methods: VLBI (= Very Long Baseline Interferometry),SLR (= Satellite-Laser-Ranging) undGPS (= Global Positioning System)

Current global reference system in Europa

• Reference System of the EuropeanState Survey Offices

• identical with ITRS89/ITRF89Status of the ITRF89 will fixedfor the date 01.01.1989

ETRS = European Terrestrial Reference SystemETRF = European Terrestrial Reference Frame

Changes of the ITRF

Geodetical Reference System ETRS89/ETRF89

continental drifts


for the date 01.01.1989

• transformation parameters for latent epochs are existing

• advantage: Europa is situated predominanton the solid eurasian plate

• realization with delimited points(EUREF)

• realization with the positioning servicesEUREF – Permanentin Gemany: SAPOS Quelle: Augath, W.: Beiträge des Vermessungs-

wesens zur Ortung und Navigation im Wandel.

Changes of the ETRF89

Geodetical Reference System WGS84

Current global Reference System

• WGS84 as Reference System of the GPS-Satellitesand of the points on the earth

• determination of the WGS84-coordinates

a) coordinates of the Tracking-Stations

WGS = World Geodetic System 1984


a) coordinates of the Tracking-Stations(12 fundamental stations distributed over the earth)

b) GPS-observations + algorithm(inclusive the global gravity field of the earth model)

c) coordinates of the GPS-Satellites

d) absolut positioning with GPS-observations

Quelle: Augath, W.: Beiträge des Vermessungs-wesens zur Ortung und Navigation im Wandel.

Fundamentals of horizontal geodetic networks

TP-Net brief description distancein km

1. order TP(1) 30-702. order TP(2) 10-203. order TP(3) 3-54. order TP(4) 1-2

Assembly of the horizontal geodetic network with triangles.


German first-order horizontal network DHDN 90


Quelle: Landesvermessungsamt Nordrhein-Westfalen http://www.lverm.nrw.de

Station monuments

granite stone with protecting pillar



granite stone with signal

Under the influence of gravity only geopotential numbers are determinable without any hypotheses.

potential = geopotential number= gravity * ∆H (differential levelling)

dimension of geopotential number = [m²]/[s²]

Geopotential number

Quelle: Normalhöhen in Nordrhein-Westfalen http://www.lverm.nrw.de

actual earth surface


To have the geopotential number in the dimension meter, it has to be divided the geopotential number by a gravity value.

orthometric height = geopotential numb er / actual gravity (mean value)normal orthometric height = normal height = geopotential n umber / normal gravity

normal gravity = gravity of the reference ellipsoid

Σ(∆Η * gravity) = geopotential number of P

Water gauge of Amsterdam and mean sea level (Normal Null)

• 1879: Levelling from the datum point of Amsterdam to Berlin (cue at observatory of Berlin = normal heights point )

• normal null point = 37.000 m under the normal heights point measured along the plumb line

• level surface in the normal null point is be termed as normal null (NN) .


Quelle: Heyde, H. (1999): Die Höhennullpunkte der amtlichen Kartenwerke europäischer Staaten und ihre Lage zu Normal-Null. Schriftenreihe des Förder-kreises Vermessungstechnisches Museum e. V. Band 28, Dortmund 1999.

be termed as normal null (NN) .

Normal heights point(be lacking)

Reference system for heights

Old german statesBetween 1912 und 1956: German levelling base network 1912 (DHHN12) is because of inhomogeneous calculation methods and of network differences involved absolute insufficient.

1980-1985: renewal of the whole levelling base network first order (DHHN85)

base: normal orthometric height referring to Amsterdam water gauge. The reference system is termed as mean sea level (NN-heights ).

New german statesSince 1979 normal heights of the national levellings base network 1976 (SNN76) referring to the water gauge of Kronstadt near St. Petersburg). The reference system is termed as hight zero (HN-heights ).

Mean sea level of Kronstadt is about 15 cmhigher than the mean sea level of Amsterdam.


termed as mean sea level (NN-heights ).

Federal Republic of Germany (after 1992)In October 1993 the AdV-plenum (AdV = Working Committee of the Surveying Authorities of the States of the Federal Republic of Germany) decided to establish a uniform reference system for heights for the whole area of the new Federal Republic of Germany. Levellings between the both levelling base networks were taken out. Description: Deutsches Haupthöhennetz 92 (DHHN92). Point of attachment: church Wallenhorst near Osnabrück. The new heights will be calculated as normal heights with measured gravity values . The reference system is termed as normal heights zero (NHN-heights ). Introduction of the NHN-heights in 2002.

Water gauges of the national reference systems in Europe

Reference systems in Europe

Water gauges and reference systems in Europe


Quelle: Normalhöhen in Nordrhein-Westfalen; http://www.lverm.nrw.de

Example:city church in Weimar, side datum post,east side, 0.7 m above road pavement

217.339 m über NN (Old System)217.404 m über NN (New System/System 1912)217.387 m über NN (56)217.244 m über HN (56)217.238 m über HN (76)217.374 m über NHN (92)

Neighbouring countries:Averaged heights neighbouring countries in relation to NN-system

Water gauges


217.374 m über NHN (92) relation to NN-system

Denmark -0.09 m (North Sea)Netherlands +0.02 m

Eastern neighbours +0.16 m (Baltic Sea)

France -0.25 m(Mediterranean Sea)

Austria -0.31 mSwitzerland -0.30 m

In the pipeline: United EuropeanLevelling Network (REU)

Bridge near Laufenburg

Classification of the levelling networks:

levelling brief diameternetwork description of the meshes

in km

1. order NivP(1) 30 - 50

2. order NivP(2) 15 - 20

3. order NivP(3) 2 - 10

German first-order levelling network (DHHN 92


Renewal of the DHHN 2006 - 2011

Monument at the Herder church in Weimar

Touchdown point for the levelling rod:

the highest point of the bolt

Station monuments for geodetic points


granite stone

bolt in a wall

(diameter:20 mm - 55 mm)


What is the height of a point?

mean sea level (geoid)

orthometric heightellipsoidical height

geoid height

actual earth surface


mountain hight above sea distance from the geocenterin m in km

Chimborazo 6 267 6 384.557 (Ecuador)Nevado Huascaran 6 768 6 384.552 (Peru)Cotopaxi 5 897 6 384.190 (Ecuador)Kilimandscharo 5 895 6 384.134 (Tansania)Cayambe 5 796 6 384.094 (Ecuador, Vulkan)Mount Everest 8 850 6 382.414 (Nepal/Tibet)

Gravity networks in the states

gravity= resulting from gravity and centrifugal acceleration

direction of gravity = plumb line

measurement of gravity: with gravimeter

reference system: Potsdamer gravity system


measurement precisionabsolut gravimeter: 20 - 30 nm/s²

= 2 - 3 µGal

superconducting gravimeter: < 0.1 nm/s²

g (mean value) = 9.81 m/s²

g at pole = 9.84 m/s²

g at equator = 9.78 m/s²

1 Gal = 1 cm / s²

decrease of g with height:

0,3 ‰ / 1000 m

Coordinate systems

three-dimensional cartesian coordinates: X, Y, Z

geographical coordinatesgeographic latitude: Bgeographic longitude: L

ellipsoidic height: h

earth surface

north poleGreenwich meridian

geocentre


Quelle: Witte u. Schmidt (2004)

ellipsoidic height: hell

astronomic coordinatesastronomic latitude: Λastronomic longitude: Φ

equator

geocentre

geographic coordinates

sphere ellipsoid

geographic longitude λ L

geographic latitude φ B

Ellipsoid(e. g. by Bessel)


The geographic longitude λλλλ of a point P is the angle between the plain of the zero meridian (e.g. Greenwich meridian) and the meridian plain at the point P.

The geographic latitude ϕϕϕϕ is the angle between the normal of the ellipsoid at P and the equator plain.

The angle between a curve of the surface on the ellipsoid and the meridian in point P is termed out as azimuth A (from the Greenwich meridian (north pole) clockwise).

Centre point of Europe

geographic coordinates of the centre point of europe:

northern latitude: 54°51´ 54´´

eastern longitude: 25°19´ 00´´


Quelle: Weih, W. (2005): Noch einmal: „Europas centras“. In VDV 56(2005)4, Seite 305.

Centre point of Europe is in Lithuania about 26 km northern of Vilnius.

x

P

0

s

x

x

0

y

y

P

polare coordinates (s, ϕϕϕϕ)cartesian coordinates (x, y)

Plain coordinate systemes

ϕϕϕϕ


0y

x

y0

A

B

tAB

grid bearing (tAB)

∆y

∆x

quadrant I

quadrant IIquadrant III

quadrant IVTable of sign

∆y ∆x Quadrant+ + I+ - II- - III- + IV

tBA

cone projectionazimuthal projection cylinder projection

Projection of the surface of earth in the plainMathematical congruence cannot be obtained because the ellipsoid cannot be mapped onto a plane without distortions.


cone projectionazimuthal projection cylinder projection

normal position transversal position inclined position


Gauss-Krüger-coordinate system

Projection of the surface of the ellipsoid to the H

Johann Carl Friedrich Gauss (1777-1855)


Projection of the surface of the ellipsoid to the boundary surface of the touches cylinder from the centre point M (contact of the main meridian).

Sheet blank of the cylinder in the plain.

To have small distortions the width of the meridian strap will be limited to 3°.

The declaration of the meridian strap takes place with a code number in the R-value (y = easting).

Translation of the H-Axis (x = northing) in each case at 500 km to west to avoid negativ R-values.

H

R

equatoroffset 500 km

mai

n m

erid

ian

scal

e fa

ctor

= 1

.000

0

Distortions by Gauß-Krüger

2 2(1 / 2 )GK gem ms s y r= ⋅ +

mean y-coord. ym [km] 10 20 40 60 80 100

correction [cm] -0.1 -0.5 -2.0 -4.4 -7.9 -12.3(for s = 1 km)

ym = (y1 + y2)/2

r = 6381 km (radius of the earth)

Reduction of distances


Reduction of areas

2 2(1 / )UTM Ell mF F y r= ⋅ +

Distortions in the directions:

are negligible

mean y-coordinate = 100 kmscale factor for area = 1.000246

FEll = area onto the ellipsoid

Lüneburg

Michaelis-church in Lüneburg

in system of 9. longitude:

H = 59 02 863.21 m

R = 35 93 571.20 m

code number 3 (= 9°)The church is situated eastward of the 9. longitude and the Gauß ordinate is

Gauß-Krüger-coordinate system


9. longitude and the Gauß ordinate is +93 571.20 m.

in system of 12. longitude:

H = 59 03 137.40 m

R = 43 93 360.64 m

code number 4 (= 12°)

In the system of the 12. longitude the church is situated westward of the 12. longitude and the Gauß ordinate is -106 639.36 m.

Universal-Transversale-Merkator-system (UTM-system)

Projection of the surface of the ellipsoid to the boundary surface of the cylinder from the centre

N

Ecent

ral m

erid

ian

scal

e fa

ctor

= 0

,999

6

Gerhard Kremercalled:

Gerardus Mercator(1512-1594)

lines of true scale


boundary surface of the cylinder from the centre point M (contact of the two intersection meridians).

Scale factor in the central meridian = 0.999 600.

Sheet blank of the cylinder into the plain.

The width of the meridian strap is be limited to 6°.

The declaration of the meridian strap takes place with the number of zone in the E-value (y).

Translation of the N-Axis (x) in each case at500 km to west to avoid negativ E-values (y).

E

equatoroffset 500 km

UTM-Zonenbildung

Distortions by UTM

2 20.9996 (1 / 2 )UTM gem ms s y r= ⋅ ⋅ +

mean y-ordinate ym [km] 10 40 80 120 160 200

correktion [cm] +39.9 +38.0 +32.1 +22.3 +8.6 -9.1(für s = 1 km)

ym = (y1 + y2)/2

r = 6381 km (earth radius)

UTM-StreckenreduktionUTM-Reduction of distances


UTM-Reduction of areas2 2 20.9996 (1 / )UTM Ell mF F y r= ⋅ ⋅ +

Distortions in the directions:

are negligible

mean y-ordinate = 0 kmscale factor for areas = 0.999 200 160

FEll = area on the ellipsoid

Reductions of distances in GK- and UTM-Projection


Quelle: Europäisches Terrestrisches Re-ferenzsystem 1989. Landesamt für Ver-messung und Geoinformation, Erfurt 2007.

GK-system UTM-systemwidth of zones 3° 6°

zones in Germany 2, 3, 4, 5 31, 32, 33

central meridian 6°, 9°, 12°, 15° 3°, 9°, 15°

cylinder touch cylinder intersection cylinder

scale factor 1,0000 0,9996

ellipsoid Bessel GRS80

Differences between GK- and UTM-system


Coordinates of the well on the market place in Weim ar

coordinate system geod.Datum Long./R/East Lati./H/North

geograhical coordinates WGS84 11°19´ 47´´ 50°58´ 46´´GK-System Potsdam-Datum 44 53 032 m 56 4 9 570 mUTM-System ETRS89 32:663 539 m 56 50 123 m

Coordinate transformations


AllTrans 2.321GEOTRANS 3.0TRANSDAT 13.43

Height reduction

All distances measured at an elevation h have to be reduced onto the surface of the rotation ellipsoid.

lgem

m r

m r r r

m r r r

l l

r h rl l l l

r h r r hr h

l l l l lr

=+− = −+ +

+∆ = − = ⋅ −lm


Rotationsellipsoidbzw. Geoid

r = E

rdra

diu

s

h hlred

example:

radius of the earth r = 6380 km

lm = 1 km, h = 500 m ∆l = 7.8 cm

lm = 10 km, h = 1000 m ∆l = 1.57 m

m

rh

l lr

∆ ≈ ⋅lr

rotation ellipsoid or geoid

geographic north, grid north, magnetic north


In TK25 the annually changes are registered.

http://geo.phys.uit.no/articl/roadto.html

Definition of the meter1792: arc measurementArc measurement between Barcelona and Dünkirchen to define the meter.Geometric flattening of 1 : 334Quadrant of the earth:5 130 740 Toisen = 10 000 000 m!

�Archive Meter

Problem: The length of the quadrant of the earth was 2288 m too long and therefore the Archive Meter is 0.2 mm too short.


the Archive Meter is 0.2 mm too short.

20.10.1983: 17. General Conference for Measure and Weight1 Meter has been defined as the distance light travels through a vacuum in 1/299 792 458 of a second.

In the following decades, several countries adopted the system. In 1875 these nations formed the International Metric Convention to spread international recognition of the metric system. The nations also agreed on the formation of an International Bureau for Measure and Weight in Paris. As the first major project, the Bureau produced a new meter prototype of platinum-iridium with an x-shaped cross section. This prototype was designed to define the metre more exactly than the Archive Meter, and it was accepted by the first general conference in 1889 as the new International Meter prototype.

Later on different definitions of the meter were given.

Measurements to define the metersince 1792

Job for the two scientists Delambre und Méchain:

To determine one ten millionth of the earth meridian between north pole and equator.

1075

km

51°02´


Delambre(1749 - 1822)

Méchain (1744 - 1804)

1075

km

41°21´

Dimension units

From unit of length Meter [m] derived measures of l ength:kilometer 1 km = 1000 mhektometer 1 hm = 100 mdekameter 1 dam = 10 mdecimeter 1 dm = 0.1 mcentimeter 1 cm = 0.01 mmillimeter 1 mm = 0.001 mmicrometer 1 µm = 0.000001 mnanometer 1 nm = 0.000000001 m


From unit of area square meter [m²] derived measure s of area:square kilometer 1 km² = 1000000 m²hectare 1 ha = 10000 m²are 1 a = 100 m²square decimeter 1 dm² = 0.01 m²square centimeter 1 cm² = 0.0001 m²square millimeter 1 mm² = 0.000001 m²

From unit of volume cubic meter [m³] derived measur es of volume:cubic decimeter 1 dm³ = 0.001 m³ = 1 Litercubic centimeter 1 cm³ = 0.000001 m³

Units of angles

Radiant-SystemThe derived SI-unit of a plain angle is Radiant [rad].1 Radiant equates to the angle at centre, where the radius is re = 1 m and the arc of the circle is also be = 1 m.

Gon-System

0°360°400 gon

90°100 gon270°

1 rad5 rad

6 rad57,29578°63,66198 gon

αr = 1

e

b= 1e


Gon-SystemFull circle = 400 gonDecigon 1 dgon = 0.1 gonCentigon 1 cgon = 0.01 gonMilligon 1 mgon = 0.001 gon

Grad-SystemFull circle = 360 Grad (°)arc minute 1´ = (1/60)°arc second 1´´ = (1/60)´

100 gon

180°200 gon

270°300 gon 2 rad

3 rad

4 rad

Conversion from Grad to gon

1 gon = 0.9°

Example:

36° 12´ 37´´ = ? gon


36° 12´ 37´´ = ? gon

36°+ (12 + (37/60))/60

= 36.210278°

= 40.2336 gon

Radian measure

b / r = α / ρ

ρ [gon] = 200 gon / πρ = 63.66197 gonρ = 6366.197 cgon

ρ [°] = 180°/ πρ = 57.2957795 °ρ = 3437.74677 ´

with ρ as conversion factor


ρ = 6366.197 cgonρ = 63661.97 mgon

ρ = 3437.74677 ´ρ = 206264.806 ´´

Application: estimation of small angles

r = 100 m r = 100 m

b = 1 cm α = 1 cgon

α = 6.3 mgon b = 1.6 cm

Ratios of scales

Distance in the map or in the plan Distance in nature = M = 1 / m

M = scale

m = dimensional ratio = number of scale


Example:

10 cm100 m

= 0.001 = 1 : 1000

Measure for inclination

opposite leg

100

p

h

en

1αααα

tan α = 1 / n = h / e = p [%] / 100


adjacent leg

100en

α = angle of inclination

1 : n = gradient of slope

p = percent- or per mill declaration(to 100 m) (to 1000 m)

h : e = ratio of slope

Example:

h : e = 4.75 / 75.50α = 4 gon = 3.6°1 : n = 1 : 15.89p = 6.29 %

building stock survey section01_fundamentals

Documents

dmmler verlag

gruyter verlag

teubner verlag

werner verlag

herbert wichmann verlag

konrad wittwer verlag

bauwesen grundlagen

grundlagen der statistik