California Coordinate System. Capital Project Skill Development Class (CPSD) G100497. California Coordinate System. Thomas Taylor, PLS Right of Way Engineering District 04 (510) 286-5294 [email protected] Course Outline. History Legal Basis The Conversion Triangle
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
California Coordinate System
Capital Project Skill Development Class (CPSD)
G100497
California Coordinate System
Thomas Taylor, PLS
Right of Way Engineering
District 04
(510) 286-5294
Point of Origin
Plane
Apex of Cone
Ellipsoid
Axis of Cone & Ellipsoid
Axis of Ellipsoid
Tangent Plane
Local Plane
Line of intersection
Axis of Cylinder
Ellipsoid
Ellipsoid
Intersecting Cylinder
Transverse Mercator
Intersecting Cone
2 Parallel Lambert
What Map Projection to Use?
What will be given?
g , q , mapping angle, convergence angle.
(N,E), (X,Y), Latitude(F), Longitude(l)
R0
What are constants or given information within the Tables?
Nbis the northing of projection origin 500,000.000 meters
u
R
E0 is the easting of the central meridian 2,000,000.000 meters
R b
B0
Rbis mapping radius through grid base
B0 is the central parallel of the zone
northing/easting
Latitude(F),Longitude(l)
R0is the mapping radius through the projection origin
What must be calculated using the constants?
Nb
R is the radius of a circle, a function of latitude, and interpolated from the tables
E0
u is the radial distance from the central parallel to the station, (R0 – R)
g , q is the convergence angle, mapping angle
B = north latitude of the station
B0 = latitude of the projection origin (tabled constant)
u = radial distance from the station to the central parallel
L1, L2, L3, L4 = polynomial coefficients (tabled constants)
R = mapping radius of the station
R0 = mapping radius of the projection origin (tabled constant)
u = radial distance from the station to the central parallel
g = convergence angle
L = west longitude of the station
L0 = longitude of the projection and grid origin
(tabled constant)
Sin(B0) = sine of the latitude of the projection origin
(tabled constant)
n = N0 + u + [R(sin(g))(tan(g/2))]
or
n = Rb + Nb – R(cos(g))
n = the northing of the station
N0 = northing of the projection origin (tabled constant)
Rb, Nb = tabled constants
e = E0 + R(sin(g))
e = easting of the station
E0 = easting of the projection and grid origin
Compute the CCS83 Zone 6 metric coordinates of station “Class-1” from its geodetic coordinates of:
Latitude = 32° 54’ 16.987”
Longitude = 117° 00’ 01.001”
n = Rb + Nb – R(cos(g))
n = 9836091.7896 + 500000.000
– 9754239.92234(cos(-0.4122909785))
n = 582104.404
e = E0 + R(sin(g))
e = 2000000.000 + 9754239.92234(sin(-0.4122909785))
e = 1929810.704
Compute the CCS83 Zone 3 metric coordinates of station “SOL1” from its geodetic coordinates of:
Latitude = 38° 03’ 59.234”
Longitude = 122° 13’ 28.397”
EB = 0.315384453°
u = 35003.7159064
R = 8211926.65249
g = -1° 03’ 20.97955” (HMS) 0r -1.05582765°
n = 675242.779
e = 1848681.899
g = arctan[(e - E0)/(Rb – n + Nb)]
g = convergence angle at the station
e = easting of station
E0 = easting of the projection origin (tabled constant)
Rb = mapping radius of the grid base (tabled constant)
n = northing of the station
Nb = northing of the grid base (tabled constant)
L = L0 – (g/sin(B0))
L = west longitude of the station
L0 = longitude of the projection origin (tabled constant)
sin(B0) = sine of the latitude of the projection origin
(tabled constant)
u = n – N0 – [(e – E0)tan(g/2)]
g = convergence angle at the station
e = easting of the station
E0 = easting of the projection origin (tabled constant)
n = northing of the station
N0 = northing of the projection origin
u = radial distance from the station to the central parallel
B = B0 + G1u + G2u2 + G3u3 + G4u4
B = north latitude of the station
B0 = latitude of the projection origin (tabled constant)
u = radial distance from the station to the central parallel
G1, G2, G3, G4 = polynomial coefficients (tabled constants)
Compute the Geodetic Coordinate of station “Class-2” from its CCS83 Zone 4 Metric Coordinates of:
n = 654048.453
e = 2000000.000
g = arctan[(e - E0)/(Rb – n + Nb)]
g = arctan[(2000000.000 – 2000000.000)/
(8733227.3793 – 654048.453 + 500000.000)]
g = arctan(0)
g = 0
L = L0 – (g/sin(B0))
L = 119° 00’ 00’’ – (0/sin(36.6258593071°))
L = 119° 00’ 00’’
u = n – N0 – [(e – E0)tan(g/2)]
u = 654048.453 – 643420.4858
- [(2000000.000 – 2000000.000)(tan(0/2)]
u = 10627.967
B = B0 + G1u + G2u2 + G3u3 + G4u4
B = 36.6258593071° + 9.011926076E-06(10627.967)
+ -6.83121E-15(10627.967)2
+ -3.72043E-20(10627.967)3
+ -9.4223E-28(10627.967)4
B = 36° 43’ 17.893’’
Compute the Geodetic Coordinate of station “CC7” from its CCS83 Zone 3 Metric Coordinates of:
n = 674010.835
e = 1848139.628
g = -1° 03’ 34.026” or -1.0594517°
L = 122° 13’ 49.706”
u = 33761.9722245
B = 38° 03’ 18.958”
g = arctan[(e – E0)/(Rb – n + Nb)]
or
g = (L0 – L)sin(B0)
t = a – g + d
t = grid azimuth
a = geodetic azimuth
g = convergence angle (mapping angle)
d = arc to chord correction, known as the second order term (ignore this term for lines less than 5 miles long)
Station “Class-3” has CCS83 Zone 1 Coordinates of n = 593305.300 and e = 2082990.092, and a grid azimuth to a natural sight of 320° 37’ 22.890”. Compute the geodetic azimuth from Class-3 to the same natural sight.
g = arctan[(e – E0)/(Rb – n + Nb)]
g = arctan[(2082990.092 – 2000000.000)/
(7556554.6408 – 593305.300 + 500000.000)]
g = arctan[0.0111198338]
g = 0° 38’ 13.536’’
t = a – g
a = t + g
a = 320° 37’ 22.890’’ + 0° 38’ 13.536’’
a = 321° 15’ 36.426’’
Station “D7” has CCS83 Zone 6 Coordinates of n = 489321.123 and e = 2160002.987, and a grid azimuth to a natural sight of 45° 25’ 00.000”. Compute the geodetic azimuth from D7 to the same natural sight.
g = 0° 55” 51.361’ (0.9309335°)
Geodetic Azimuth = 46 20’ 51.361”
Ground
h
H
Ellipsoid
N
Radius of the Ellipsoid
Combined Grid Factor (Combined Scale Factor)
R
EF =
R + N + H
R
=
Radius of Curvature.
N
=
Geoidal Separation.
H
=
Mean Height above
Geoid.
h
=
Ellipsoidal Height
Combined Grid Factor (Combined Scale Factor)
B’
A’
C
A
B
D
C’
Zone Limit
Zone Limit
D’
Scale
Decreases
Scale
Increases
Scale
Increases
- Grid Distance A-B
is smaller than Geodetic
Distance A’-B’.
- Grid Distance C-D is
larger than Geodetic
Distance C’-D’.
Scale
Decreases
Ra = r0/k0
Ra = geometric mean radius of curvature of the ellipsoid at the projection origin
r0 = geometric mean radius of the ellipsoid at the projection origin, scaled to grid (tabled constant)
k0 = grid scale factor of the central parallel (tabled constant)
re = Ra/(Ra + N + H)
re = elevation factor
Ra = radius of curvature of the ellipsoid
N = geoid separation
H = elevation
k = F1 + F2u2 + F3u3
k = point scale factor
u = radial difference
F1, F2, F3 = polynomial coefficients (tabled constants)
cgf = re k
cgf = combined grid factor
re = elevation factor
k = point scale factor
Ggrid = cgf(Gground)
Note: Gground is a horizontal ground distance
Gground = Ggrid/cgf
In CCS83 Zone 1 from station “Me” to station “You” you have a measured horizontal ground distance of 909.909m. Stations Me and You have elevations of 3333.333m and a geoid separation 0f -30.5m. Compute the horizontal grid distance from Me to You. (To calculate the point scale factor assume u = 15555.000)
Ra = r0/k0
Ra = 6374328/0.999894636561
Ra = 6374999.69189
re = Ra/(Ra + N + H)
re = 6374999.69189/(6374999.69189 – 30.5 + 3333.333)
re = 0.9994821768
k = F1 + F2u2 + F3u3
k = 0.999894636561 + 1.23062E-14(15555)2
+ 5.47E-22(15555)3
k = 0.9998976162
cgf = re k
cgf = 0.9994821768(0.9998976162)
cgf = 0.999379846
Ggrid = cgf(Gground)
Ggrid = 0.999379846(909.909)
Ggrid = 909.3447
In CCS83 Zone 4 from station “here” to station “there” you have a measured horizontal ground distance of 1234.567m. Station here and there have elevations of 2222.222m and a geoid separation 0f -30.5m. Compute the horizontal grid distance from here to there. (To calculate the point scale factor assume u = 35000)
Ra = 6371934.463
re = 0.999656153
k = 0.999955870
cgf = 0.999612038
Ggrid = 1234.088m
CC7 has a metric CCS Zone 3 coordinate of n = 674010.835 and e = 1848139.628. Compute a CCS Zone 2 coordinate for CC7.
n = 543163.942
e = 1979770.624