Practical Approach to Understanding and Using Grid Coordinates · 7 12 Projections ! To have a...
Transcript of Practical Approach to Understanding and Using Grid Coordinates · 7 12 Projections ! To have a...
Practical Approach to Understanding and Using Grid
Coordinates !!!!
New$Jersey$Society$of$!Professional+Land+Surveyors!
SurvCon(2014!!!!
Presented by !!
Joseph Paiva – CEO
February 2014
1
New Jersey Society of Professional Land Surveyors
SurvCon 2014
Atlantic City
Practical Approach to Understanding and
Using Grid Coordinates
Joseph V.R. Paiva – CEO
Introduction
Overview of concepts Projection, scale differences How the mathematics operates rather than the mathematics itself Practical applications in the field, in the office, in communications Stress understanding of theory and mathematics used in the system
© 2013 GeoLearn, LLC 1
2
2
The grid headache
! Why do we have it anyway? ! Is it those darn software
manufacturers? ! Why can’t we have the good old
“ground” days?
3
Topics
! Surveys: limited scope vs. large extent; plane vs. geodetic surveys
! Projections—the concept and the math for surveyors
! SPCS Calculations ! Strategies for dealing with the grid/
ground “thing”
3
4
Introduction
! Most small-area surveys assume the earth is flat (plane surveys)
! For large areas, Earth’s curvature has to be considered
! This usually involves determining geodetic positions (latitude and longitude) of survey stations
5
State Plane Coordinate System
! SPCS was designed in the early 1930s by the Coast and Geodetic survey to solve the problem of surveys of large extents for the “local” surveyor
! In addition to allowing plane survey concepts to be used, it delivers several additional benefits
4
6
SPCS benefits
! Simplifies calculations for surveys over large distances
! Provides common datum of reference for all surveys (if tied in)
! Well suited for engineering projects of large extent, i.e. highways, but also photogrammetry, large scale cadastral surveys, etc.
! Supplies vital grid for GIS (other options exist)
7
SPCs
! When surveys are tied into the SPCS, their locations become (potentially) indestructible
! With GPS, the problem of what coordinates to use once geocentric coordinates of GPS have been transformed in geodetic coordinates makes SPCs a natural choice
5
8
Projections
! The basic problem with plane surveying is that it assumes the earth is flat
! Some problems…
9
Problems
! meridians converge
Parallel is curved
except at equator
6
10
Problems
! On the Earth, “straight lines” are not straight except for meridians (or the equator) and the difference gets larger as you extend them
N
11
Problems
! Changes in elevation cannot be ignored, that is why all geodetic distances are at “sea level”
7
12
Projections
! To have a plane coordinate system, it is necessary to distort the curved surface of the earth to a fit on a plane
! Orange peel analogy ! This process of flattening must be
systematic in order to have accuracy ! In surveying this process is called a
projection
13
Projections / 2
! Distortions inevitable (but systematic)
! Different projections are used because each minimizes distortion in some properties at the expense of others
! Different mathematical treatments are given to projections depending on the result desired
8
14
Developable surface
! A shape that can be made into a plane • Cone • Cylinder • Plane (of course)
General Classes
! Cylindrical
© 2013 GeoLearn, LLC 15
Tangent
Secant
9
16
© 2013 GeoLearn, LLC
Developing the surface
17
10
© 2013 GeoLearn, LLC
Transverse Mercator
18
Developed transverse cylinder - distortions
19
Distorted east-west distances
(Rel
ativ
ely)
un
dist
orte
d no
rth-
sout
h di
stan
ces
11
© 2013 GeoLearn, LLC
Transverse Mercator (cutting through center)
20
Cylinder
Ellipsoid (Earth)
© 2013 GeoLearn, LLC
General Classes
21
Secant
• Conic
12
© 2013 GeoLearn, LLC
Developed Cone - distortions
22
(Relatively) undistorted east-west distances D
isto
rted
nor
th-
sout
h di
stan
ces
Developed transverse cylinder - distortions
23
Distorted east-west distances
(Rel
ativ
ely)
un
dist
orte
d no
rth-
sout
h di
stan
ces Re
-visit
ing…
13
© 2013 GeoLearn, LLC
Lambert Conformal
! Varying central apex angle of cone changes section of ellipsoid that is intersected
24
© 2013 GeoLearn, LLC
Secant cone
25
14
Topography to ellipsoid to grid
26
Cylinder radius
Radius of
ellipsoid “slice”
Cylinder (grid)
Surface
Cylinder
Ellipsoid (Earth)
Topography to ellipsoid to grid
27
Ellipsoid (Earth)
Cone (grid)
Surface
Cone
15
“Lagrange” projection
28
Notice that this projection here shows the whole world in a circle! Interested in the concepts of projections? See more at http://www.progonos.com/furuti/MapProj/Normal/ProjConf/projConf.html
29
Next step
! Once developable surface parameters are picked, plane is created
! Because a developable surface is used, while there are distortions in converting coordinates on the earth to the developable surface, there is no further distortion of shape or size when it is unrolled or “developed”
16
30
Most common surfaces in SPCS
! Lambert conformal (conic) ! Transverse Mercator (cylinder) ! Also…skewed (or oblique) Mercator
31
State Plane Coordinate Systems (83)
! System for specifying geodetic stations using plane rectangular coordinates
! Over 120 zones for U.S. ! Long N-S states use Transverse
Mercator ! Long E-W states use Lambert ! If square, use either
17
32
SPCS (83)
! Alaska, Florida and New York use both types of projections
! In addition Alaska has an oblique projection for the southeastern part of the state
33
http://www.mapsfordesign.com/images/P/bj_NewYork-ppt.gif
18
34
http://i.infoplease.com/images/mflorida.gif
35
http://alaskafisheries.noaa.gov/maps/images/nmfs_reporting_areas.gif
19
36
SPC83 vs. SPC27
! Coordinate values changed (N and E) ! Meters ! Types of projections changed for
some states ! Zones different in some ! Numbers of zones per state changed
in some ! Check implementing statutes in your
state for details!
37
Feet!
! U.S. Survey foot = [m] x 3937/1200 ! International foot = [m] / 0.3048 ! 2 PPM! ! [0.01 ft in a mile] ! [but with a coord value of 500,000 m,
difference is 1 m!]
20
38
NOAA/NGS document
! NOAA Manual NOS NGS 5 State Plane Coordinate System of 1983
! http://www.ngs.noaa.gov/ [www.ngs.noaa.gov/PUBS_LIB/ManualNOSNGS5.pdf]
39
Distortions
! Scale is exact where cone or cylinder intersects ellipsoid surface
! Scale is less than one between lines of true scale (i.e. length on ellipsoid is greater than length on plane)
! Scale is more than one outside lines of true scale (i.e. length on ellipsoid is smaller than length on plane)
21
Scale less or greater than one…where?
40
41
Zone size
! Where the zone intersects the Earth, and whether it is tangent or secant controls the distortions
! By strategic placement, distortions are minimized, scale differences can be kept to 1:10,000 or less
! Done by keeping zone size to <158 mi and keeping zone width such that two-thirds of the zone is between lines of true scale (secant lines)
22
42
More on zone size
! Zones are designed to overlap each other considerably
! Thus a survey done near a zone boundary can be done in either zone
43
Transverse Mercator projection
! Scale varies east to west but not north to south
! Scale is true at the secant line ! All geodetic meridians are curved,
converging at the pole
23
44
Transverse Mercator projection / 2
! All parallels (of latitude) are curved ! CM is assigned to a meridian line ! All lines on the plane parallel to the
CM are grid north ! East-west lines on the plane are
perpendicular to the CM
45
Transverse Mercator
A
B
C
D
24
TM edge view
46
Cylinder
Ellipsoid
47
When developed… A
B
C
D
Scale greater
than true
Scale greater
than true
Scale less than true
25
…or
48
View perpendicular to axis of cylinder
Scale less than true
Scale greater than true Cylinder
49
Mapping angle
! Also called grid declination or variation
! Greek letter - γ [gamma] for Mercator
! θ Theta for Lambert
26
Grid overlaid on developed surface - Mercator
50
New York SPCS constants Item Value Zone New York E (3101) also NJ Type Transverse Mercator Central Meridian 74° 30’ W Grid origin latitude 38° 50’ N Grid origin longitude 74° 30’ W Grid origin X coordinate -easting 150,000 m Grid origin Y coordinate- northing 0 m Scale at central meridian 1:10,000
51
27
New York SPCS constants Item Value Zone New York C (3102) Type Transverse Mercator Central Meridian 76° 35’ W Grid origin latitude 40° 00’ N Grid origin longitude 76° 35’ W Grid origin X coordinate -easting 250,000 m Grid origin Y coordinate- northing 0 m Scale at central meridian 1:16,000
52
New York SPCS constants (be careful!)
Item Value Zone NY (LI) - Lambert (3104) Type Lambert Conformal Central Meridian 74° 00’ W Standard parallel N 41° 02’ N Standard parallel S 40° 40’ N Grid origin latitude 40° 10’ N * Grid origin longitude 74° 00’W Grid origin X coordinate -easting 300,000 m Grid origin Y coordinate- northing 0 m
53
28
Pennsylvania SPCS constants Item Value Zone PA North - Lambert (3701) Type Lambert Conformal Central Meridian 77° 45’ W Standard parallel N 41° 57’ N Standard parallel S 40° 53’ N Grid origin latitude 40° 10’ N Grid origin longitude 77° 45’W Grid origin X coordinate -easting 600,000 m Grid origin Y coordinate- northing 0 m
54
Pennsylvania SPCS constants Item Value Zone PA South - Lambert (3702) Type Lambert Conformal Central Meridian 77° 45’ W Standard parallel N 40° 58’ N Standard parallel S 39° 56’ W Grid origin latitude 39° 20’ N Grid origin longitude 77° 45’ W Grid origin X coordinate -easting 600,000 m Grid origin Y coordinate- northing 0 m
55
29
Delaware SPCS constants Item Value Zone DE - (0700) Type Transverse Mercator Central Meridian 75° 25’ W Grid origin latitude 38° 00’ N Grid origin longitude 75° 25’ W Grid origin X coordinate -easting 200,000 m Grid origin Y coordinate- northing 0 m Scale at central meridian 1:200,000
56
Ellipsoid, Geoid, Topography
57
Mass Excess
Mass Deficiency
Geoid
Ellipsoid
Local topography
30
Reducing surface distance to geodetic distance
Rm = 20,906,000 ft or 6,372,000 m ! Approximate SLF can be
calculated for project where relief is small
! In high relief areas need to calculate individually using average elevation of the line
....
...
..
DistSurfSLFDistGeod
DistGrndElevRR
DistGeodm
m
×=
×+
=
58
Reducing geodetic distance to grid distance
! k is sometimes called SF (scale factor)
! k is calculated from equations or interpolated from tables in state or NOAA documents
kDistGeodDistGrid ×= .
59
31
Scale factor (Mercator)
! “k” based on longitude (sometimes, k is calculated using EP’, which is the distance away from the C.M.)
! A single Scale Factor (SF), can be picked for projects that are not large (under ~8 km)
60
Direct conversion from surf. dist. to grid dist.
Grid Dist = Surf Dist x SLF x SF ! If average elevation and E for the
project are being used, multiply SLF and SF and use it as the Grid Factor (GF)
! Grid factor also sometimes called “Combined Scale Factor” (CSF)
! SF converts from geodetic to grid ! GF converts from ground to grid
61
32
Grid Azimuth
62
Grid Az = Geod Az - γ + Second Term ! For most surveys Second Term can
be ignored (lines under 8 km)
Why second term?
63
33
How to apply mapping angle?
64
Mapping angle gamma
).sin()..( StaLatStaLongCMLong ×−=γ
65
! Varies with longitude but can use same γ for many surveys
LaPlace correction may need to be added if using astro-azimuths
34
General Pattern
66
! adjust traverse ! determine SLF using elevation (either for
project or dist. by dist.) ! determine SF using dist. from CM (either
for project or dist. by dist.) ! calc. GF if desired ! convert all distances to grid distances
using GF ! convert all azimuths to grid azimuths
General pattern / 2
! Assuming one of the traverse points has a known SPC, calculation of the coordinates (SPC) of the other points is straightforward
! Always multiply distances ! NEVER multiply coordinates by scale
or grid factor!
67
35
Lambert conformal conic projection
! Scale varies north to south but not east to west
! Secant lines, where scale is true, are called standard parallels
! All geodetic meridians are straight, converging at the pole
68
Lambert / 2
! All parallels (of latitude) are arcs of concentric circles have their center at the cone’s axis
! CM is assigned to a meridian line ! All lines on the plane parallel to the
CM are grid north ! East-west lines on the plane are
perpendicular to the CM 69
36
70
Lambert conformal
! Varying central apex angle of cone changes section of ellipsoid that is intersected
71
Standard parallels Pr
ojec
tion
limits
37
Grid overlaid on developed surface - Lambert
72
73
Mapping angle
! Also called grid declination or variation
! Greek letter - θ [theta]
38
74
Calculations (Lambert)
! Same as for Transverse Mercator except…
! Tables for the zone have the value
of the long. of the CM and l ! General pattern for calcs is the
same
lStaLongCMLongAzGeodAzGrid
×−=
−=
.)..(....
θθ
75
Typical calculations
! Elevation 0 m; ground dist = 1000 m
! Elevation 1,000 m; ground dist = 1000 m
....
...
..
DistSurfSLFDistGeod
DistGrndElevRR
DistGeodm
m
×=
×+
=
39
76
Scale factor
! Assume distance from CM is 30,000 m (doesn’t matter whether east or west)
! Enter table and pick off value for 30,000 m: 0.9999444
! If distance from CM is not a round number, will have to interpolate!
77
Grid factor
! GF = SLF x SF ! Also called Combined Scale Factor
(CSF)
40
78
Mapping angle calcs (Mercator)
! Sta. Long. = 93°00’00” ! CM = 92°30’00” ! Sta. Lat = 38°00’00”
).sin()..( StaLatStaLongCMLong ×−=γ
79
Which way to apply mapping angle?
41
80
Practical use
! Tie in to monuments with SPCs, therefore don’t need to calculate mapping angle
! Project coordinates sometime used—be careful!
! On plats show SPCs. If you must show ground distances, show grid distances also!
! Meta data!
81
Whew ! How to use? ! My suggestion: use all grid (coordinates)
or all ground (distances) ! If all ground distances, publish a table of
grid coordinates of all the points ! If all grid coordinates, publish a table of all
ground distances and, if desired, azimuths/bearings on non-grid basis
42
82
Grid vs. ground
! Many publish “ground coordinates.” If you do, be sure that the values don’t look anything like SPCs!
! DO NOT publish “ground coordinates” unless X and Y values are readily differentiable
! On the plat if you show ground values and grid values use a suffix or prefix (GRID & ground)
83
Grid vs. ground
! If you have to, use different fonts or different styles (regular vs. italics)
! But make sure they can be easily differentiated
! Do NOT use different colors to differentiate; remember that whatever you prepare may become monochrome
43
84
Keep in mind ! A point is a point ! It doesn’t matter whether it is on the
plane (grid), ellipsoid or surface ! Do some work on a survey nearby…
hand calculate grid or ground values…then see if your data collector and PC software handle correctly
! Need to have fairly long distances to see differences between grid and ground (figure PPM to know how long)
! Using a data collector do the math is OK, as long as it does it correctly
! Remember: GIGO
85
44
86
Closing note about transformations
E
X
X’
N
Y Y’
A
B
Given: A and B in N/E reference frame and X/Y reference frame. Determine the transformation equation to convert any point from the X/Y to N/E system
87
Transformation / 2
E
X
X’
NY Y’
A B
Three parts to the transformation:
1. Rotation
2. Scale
3. Translation
45
88
Transformation / 3
E
X
X’
NY Y’
A B
Rotation:
1. Determine azimuth of AB in XY and NE systems
2. Rotation = azimuth in XY minus azimuth in NE = θ
89
Transformation / 4
E
X
X’
NY Y’
A B
Scale:
1. Determine length of AB in XY and NE systems
2. Scale = length in NE system divided by length in XY system = s
46
90
Transformation / 5
E
X
X’
NY Y’
A B
Translation is done in two steps:
1. Calculate coordinates of A and B in X’Y’ system
2. Then determine translation by subtracting coordinates in X’Y’ system from coordinates in NE system
3. Result is Tx and TY
91
Determining coordinates in X’Y’ frame
θθ
θθ
cossin'sincos'
AAA
AAA
sXsXYsYsXX
+=
−=
Transforms from XY to X’Y’ coordinates
E
X
X’
NY Y’
A B
AAY
AAX
YNTXET''
−=
−=
47
92
Final equations for transformation
Y
X
TsYsXNTsYsXE++=
+−=
θθθθ
cossinsincos
The “your survey doesn’t check” problem
! When you have users of your data, provide a value they can use to multiply ground distances by for the project so they can get grid values
! Provide a value they can use to divide grid distances by for the project so they can get ground values
93
48
Helping your user base
! If possible, try to have one CSF for the project
! If you have more than one indicate boundaries for each factor
! Provide worked out solutions for calculating in both directions
94
Helping…
! If you know what instrumentation they will be using, provide specific instructions on how to set up their field equipment
! Make sure your own field and office personnel know “which end is up”
95
About&the&seminar&presenter& Joseph V.R. Paiva, PhD, PS, PE Joseph V.R. Paiva is CEO of GeoLearn, LLC (www.geo-learn.com), which is launching an online professional education business for the geospatial industry in early 2014. Joe started this business with his partner Bob Morris, whose most recent global industry position was President of Leica Mapping. Previously, Dr. Paiva was CTO of SADAR 3D and COO of Gatewing NV, a Belgian unmanned airborne systems company. Prior engagements in consulting were in the field of geomatics and general business, particularly to international developers, manufacturers and distributors of instrumentation and other geomatics tools. Dr. Paiva and Mr. Morris continue to be involved in consultancy through a separate partnership called GeoSpatial Associates, LLC will continue this consultancy. Joe’s career includes: managing director of Spatial Data Research, Inc., a GIS data collection, compilation and software development company; various assignments at Trimble Navigation Ltd. including senior scientist and technical advisor for Land Survey research & development, VP of the Land Survey group, and director of business development for the Engineering and Construction Division; vice president and a founder of Sokkia Technology, Inc., guiding development of GPS- and software-based products for surveying, mapping, measurement and positioning. He has also held senior technical management positions in The Lietz Co. and Sokkia Co. Ltd. Prior to that was assistant professor of civil engineering at the University of Missouri-Columbia, and a partner in a surveying/civil engineering consulting firm. He has continued his interest in teaching by serving as an adjunct instructor for online course development and teaching at the Missouri University of Science and Technology. His key contributions in the development field are: design of software flow for the SDR2, SDR20 series and SDR33 Electronic Field Books and software interface for the Trimble TTS500 total station. He is a registered Professional Engineer and Professional Land Surveyor, has served as ACSM representative to the Accrediting Board for Engineering and Technology (ABET), serving as a program evaluator, team chair, and commissioner and has more than 30 years experience working in civil engineering, surveying and mapping. He writes for POB, GeoDataPoint and The Empire State Surveyor magazines and has been a past contributor of columns to Civil Engineering News. Joe has also been a consultant to the Geomatics Industry Association of America, later reorganized under the Association of Equipment Manufacturers (AEM) as the Geospatial Industry Group, Joe has organized and presented workshops and authored and edited articles for the technical press in this role. Joe can be contacted at [email protected]
January 2014