# Decoding the Mystery of Coordinates

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1 Decoding the Mystery of Coordinates NHLSA TOWN MONUMENT LOCATION WORKSHOP UNH DURHAM, N.H PART 1: THE DIFFERENT COORDINATE SYSTEMS Bob Moynihan UNH - TSAS Coordinate Systems 1

2 Decoding the Mystery of Coordinates Objective of Presentation: To introduce and discuss the common Surveying and Mapping Coordinate Systems used to establish the position of monuments Coordinate Systems 2

3 PRESENTATION OUTLINE 4 SURFACES 3 HEIGHTS 2 DATUMS 4 COORDINATE SYSTEMS 3 DISTANCES 5 NORTHS Coordinate Systems 3

4 FOUR SURFACES

5 FOUR SURFACES 1- Earth - Topographic surface 2- Geoid - Sea Level or equipotential surf. 3- Ellipsoid - Mathematical surface 4- Grid - Projection, flat surface Coordinate Systems 5

6 Coordinate Systems 6

7 1. Earth s Topographic Surface Coordinate Systems 7

8 1. Earth s Topographic Surface Coordinate Systems 8

9 2. Earth s Sea Level Surface THE GEOID: Equipotential, or gravity surface Current Model is Geoid 03 Gravity Recovery and Climate Experiment (GRACE) Center for Space Research Univ. of Texas Coordinate Systems 9

10 3. Earth s Mathematical Surface THE ELLIPSOID: World Geodetic System 84 WGS 84 a = 6,378,137 meters b = 6,356, meters f = 1 / For a circle, flattening = 0 Coordinate Systems 10

11 Coordinate Systems 11

12 4. Earth s Flat, Map Surface THE GRID Coordinate Systems 12

13 Creating The GRID: 1 A Mathematical Surface 2 Reduce the Scale 3 Project on a surface 4 Unroll the surface Coordinate Systems 13

14 THREE HEIGHTS 1. ORTHOMETRIC (elevation) 2. ELLIPSOID 3. GEOID

15 In Search of the Geoid Coordinate Systems 15 Courtesy of Natural Resources Canada

16 THREE HEIGHTS Monument Coordinate Systems 16

17 Ellipsoid, Geoid, and Orthometric Heights H = Orthometric Height (NAVD 88) h = Ellipsoidal Height (NAD 83) N = Geoid Height (GEOID 03) h =H +N h TOPOGRAPHIC SURFACE Ellipsoid GRS80 Geoid H N GEOID99 Coordinate Systems 17

18 Ellipsoid, Geoid, and Orthometric Heights STATION DURHAM 1943 : Has THREE Heights Coordinate Systems 18

19 TWO DATUMS 1. HORIZONTAL 2. VERTICAL

20 TWO DATUMS A Datum: Any numerical or geometrical quantity or set of such quantities which serve as a reference or base for calculation of other quantities. (GMS) 1. Horizontal Geodetic Datum: : An Ellipsoid 2. Vertical Geodetic Datum: Mean Sea Level Geoid Coordinate Systems 20

21 1. Horizontal Control Datum A Geodetic Datum specifying the coordinate system in which horizontal control points are located. Defined by 8 Constants 3 specify the location of the origin of the coordinate system. 3 specify the orientation of the coordinate system. 2 specify the dimensions of the reference ellipsoid. NAD 27, NAD 83 *Definition from the Geodetic Glossary, September 1986 Coordinate Systems 21

22 THE GEOID AND TWO ELLIPSOIDS GRS80-WGS84 CLARKE 1866 Earth Mass Center Approximately 236 meters GEOID Coordinate Systems 22

23 Comparison of Horizontal Datum Elements NAD 27 NAD 83 ELLIPSOID CLARKE 1866 GRS80 a = 6,378,206.4 m a = 6,378,137. M 1/f = /f = DATUM POINT Triangulation Station NONE MEADES RANCH, KANSAS EARTH MASS CENTER ADJUSTMENT 25k STATIONS 250k STATIONS Several Hundred Base Lines Appox. 30k EDMI Base Lines Several Hundred Astro Azimuths 5k Astro Azimuths Doppler Point Positions VLBI Vectors BEST FITTING North America World-Wide Coordinate Systems 23

24 NAD 27 and NAD Position ~ 40 meters ( (131 ft.) SW of 27 position Coordinate Systems 24

25 2. Vertical Control Datum A set of fundamental elevations to which other elevations are referred Coordinate Systems 25

26 Vertical Control Datum A Geodetic Datum specifying the system in which vertical control points are located. A set of fundamental elevations to which other elevations are referred NGVD 29, NAVD 88 Orthometric, Sea Level Others Cairo, Local Tidal *Definitions from the Geodetic Glossary, September 1986 Coordinate Systems 26

27 VERTICAL DATUMS MEAN SEA LEVEL DATUM OF 1929 NATIONAL GEODETIC VERTICAL DATUM OF 1929 (As of July 2, 1973) NORTH AMERICAN VERTICAL DATUM OF 1988 (As of June 24, 1993) Coordinate Systems 27

28 COMPARISON OF VERTICAL DATUM ELEMENTS NGVD 29 NAVD 88 DATUM DEFINITION 26 TIDE GAUGES FATHER S POINT/RIMOUSKI IN THE U.S. & CANADA QUEBEC, CANADA BENCH MARKS 100, ,000 LEVELING (Km) 102,724 1,001,500 GEOID FITTING Distorted to Fit MSL Gauges Best Continental Model Coordinate Systems 28

29 NGVD 29 and NAVD elevation is ~ 0.5 ft. less than 27 elev. Coordinate Systems 29

30 FOUR COORDINATE SYSTEMS

31 FOUR COORDINATE SYSTEMS (3D) 1. GEOCENTRIC COORDINATES: X,Y,Z 2. GEODETIC COORDINATES Φ,λ,h 3. CARTESIAN (PLANE) COORDINATES N,E,H (State Plane Coordinates., UTM coord.) 4. ASSUMED COORDINATES Y, X, Elevation Coordinate Systems 31

32 1. Geocentric Coordinates Conventional Terrestrial System (CTS) CIO Greenwich Meridian center of mass CIO Equator Coordinate Systems 32

33 2. Geodetic Coordinates LATITUDE: φ (PHI) LONGITUDE: λ (LAMBDA) Ellipsoid Height: h Coordinate Systems 33

34 2. Geodetic Coordinates The graticule Coordinate Systems 34

35 2. Geodetic Coordinates LATITUDE: φ The north-south position on the Globe A Parallel Coordinate Systems 35

36 2. Geodetic Coordinates LONGITUDE: λ The east - west position on the Globe A Meridian Coordinate Systems 36

37 Remember Ellipsoid Height (h)? Coordinate Systems 37

38 3. CARTESIAN (PLANE) COORDINATES STATE PLANE COORDINATES (SPC): Transverse Mercator States Lambert Conformal States 2 Issues Convergence/Mapping Angle Ground Geodetic Grid Distances UNIVERSAL TRANSVERSE MERCATOR COORDINATES (UTM): US National Grid (USNG) Coordinate Systems 38

39 3. CARTESIAN COORDINATES NORTHING: N (Y) EASTING: E (X) Orthometric Height: H (elevation) Coordinate Systems 39

40 3. CARTESIAN COORDINATES Two dimensional coordinates of a point: or X,Y N,E (Y,X) From Wikipedia Coordinate Systems 40

41 3. CARTESIAN COORDINATES ΔX ΔY L Coordinate Systems 41

42 3. CARTESIAN COORDINATES To obtain Cartesian (plane) coordinates from a round surface. We must Flatten the earth by MAP PROJECTION Coordinate Systems 42

43 The four steps in Map Projection 1 A Mathematical Surface 2 Reduce the Scale 3 Project on a surface 4 Unroll the surface Coordinate Systems 43

44 MAP PROJECTIONS: CONIC AND CYLINDRICAL Coordinate Systems 44

45 Globe Coordinate Systems 45

46 Flat Map Projection (Mercator) Coordinate Systems 46

47 3a. The Transverse Mercator Projection System New Hampshire State Plane Coordinates Based on the T M System: Offset of the Central Meridian: NAD27 System K = 500,000 ft. Xp K Central. Meridian. Secant Lines NAD83 System K = 300,000 m Coordinate Systems 47

48 3a. The N.H. State Plane Coordinate System CENTRAL MERIDIAN IN N.H. λ = BETWEEN SECANT LINES: Scale Factor less than 1 OUTSIDE SECANT LINES: Scale Factor greater than1 Scale factor constant in N -S direction Scale Factor varies in the E - W direction ALSO NOTICE:CONVERGENCE OF MERIDIANS CURVATURE OF PARALLELS Coordinate Systems 48

49 Cross-section view of projection Coordinate Systems 49

50 3b. Universal Transverse Mercator Projection System: 80 S to 72 N 6 wide Zones # d from 1 to 60 starting at 180 λ Coordinate Systems 50

51 3b. Universal Transverse Mercator (6 Zones) Projection System : Coordinate Systems 51

52 3b. Universal Transverse Mercator Projection UTM Zones in lower 48 states Coordinate Systems 52

53 3b. Universal Transverse Mercator Projection System (6 Zones) : Each zone has a Central Meridian with An Easting of 500,000 m Coordinate Systems 53

54 3b. Universal Transverse Mercator Projection System (6 Zones) : In Northern Hemisphere: Northing (Y) = 0 At the equator In Southern Hemisphere: Northing (Y) = 0 At the South Pole (equator given a false nothing of 10,000,000 meters) Coordinate Systems 54

55 Universal Transverse Mercator Projection NH in two different zones, 18 & 19 Coordinate Systems 55

56 THREE DISTANCES

57 THREE DISTANCES 1. GROUND DISTANCE Slope distance between two points 2. ELLIPSOID (GEODETIC) DISTANCE Curved distance on Ellipsoid between two points 3. GRID DISTANCE Horizontal distance on Plane between two points Coordinate Systems 57

58 Ground Ellipsoid - Grid Distances L SL = Sea Level (Geodetic) Dist. L M = Ground Dist. L G = Grid Dist. Durham, N.H. Coordinate Systems 58

59 FIVE NORTHS

60 FIVE NORTHS 1. Astronomic North Based on Earth s Rotation Axis 2. Geodetic North Based on Ellipsoid s Rotation Axis 3. Grid North Based in Central Meridian of System 4. Magnetic North Based on magnetic lines of force 5. Assumed North Based on any convenient axis Coordinate Systems 60

61 Geodetic Grid Magnetic North Coordinate Systems 61

62 Other Map Information: Norths Coordinate Systems 62

63 Assumed North Assumed Coordinate System Using any arbitrary direction (Building column line, center of pipeline, etc.) as a reference meridian from which directions (angles) will be measured. Coordinate Systems 63

64 RECAP OF PRESENTATION OUTLINE 4 SURFACES 3 HEIGHTS 2 DATUMS 4 COORDINATE SYSTEMS 3 DISTANCES 5 NORTHS Coordinate Systems 64

65 RECOMMENDED SYSTEM TO USE FOR MUNICIPAL BOUNDS N.H. STATE PLANE COORDINATES, NAD 83 (FEET OR METERS) OR LATITUDE(φ), LONGITUDE (λ), NAD 83 Coordinate Systems 65

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