CALCULATION OF PLANE COORDINATES ON A LAMBERT GRID
the geographic coordinates of a point can be In this section, we consider how the geographic coordinates of transformed into plane coordinates. For a particular Lambert projection 2012 meridian is established near the center of the zone, and is given an 2.000.000 ft. The x axis is placed well below the southern edge of the Zone and given a v value of zero. Thus all x and v position in the projection area will be positive. This information is shown in Fig. 10-13 together with the other information needed to transform the geographic coordinates of point P into Lambert grid coordinates.
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X-Rsino + c
y = R6-Reoso
R cos 0
ex: ON PAGE
width We also discuss several other topics like What is the importance of the unconscious and childhood relationships in shaping personality?
R - R cose
C = 2,000,000 ft
R sin 0
X = 0
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cone from which the area is projected, line
is the x-coordinate of that meridian, equal to care straight lines that converge at point 0. The parallels
ic circles that have their centers at point O (see Figs. 10 If you want to learn more check out Which enzymes regulate the phosphorylation status of a protein?
In the figure point O is the apex of the cone from which the one OE is the central meridian and C is the x-coordi 2.000.000 ft. The meridians are straight lines t1 of latitude are arcs of concentric circles that have 8 and 10-13).
Line OP represents part of a meridian through point on R. The y-coordinate of point O is a constant equal i OE and OP is called the mapping angle or convergence We also discuss several other topics like What's the difference between a trait and a "type"?
The National Geodetic Survey has available for projection the necessary information needed to use information are values of R for each whole minute whole minute of longitude as well as the latitude control stations. Tables E and F in Appendix A she calculations necessary to compute the state plane
ugh point O and has a length equal to nstant equal to Ry. The angle between lines
mailable for each state using the Lambert d to use plane coordinates. Included in this minute of latitude and values of O for each
Latitude and longitudes for each of their ndix A show this type of information. The ate plane coordinates for these stations are
illustrated in this section even though the National Geodetic Survey provides these coordinates for many of their stations. From Fig. 10-13 the x- and y-plane coordinates of point P can be seen to equal the following:
x= R sin 0 + C
y= Rp - R cos
If the angle o is to the left of the central meridian, it will have a negative value and thus the value of R sin will be negative for computing the x coordinate. In computing the y-coordinate for point R, cos 0 will always be subtracted. Example 10 1 that follows illustrates the determination of the Lambert plane coordinates for a particular station in South Carolina.
South Carolina is divided into two Lambert zones, north and south, both having a central meridian of 81°00'00”W. The north zone has standard parallels at 33°46' and 34°58'N latitudes, and the south zone has standard parallels at latitudes 32°20' and 33°40'N, as shown in Fig. 10-14, where they are labeled Scale Exact. It should be noted in this figure that the exact division between the north and south zones is not a line of constant latitude. Rather, the dividing line follows the somewhat irregular county lines. This means that all counties fall completely in one zone or the other.
U $ DEPARTMENT OF COMMERCE
COAST AND GEODETIC SURVEY
STATE PLANE COORDINATE ZONES
Figure 10-14 State Plane Coordinate Zones for South Carolina
It is considered necessary to make calculations for lane coordinates to at least 10 place accuracy, and this practice is followed in this chapter. Trigonometric functions can be determined to 10 places with some pocket and desk calculators. Special Publication No. 246 of the U.S. Coast and Geodetic Survey, entitled "Sines, Cosines, and Tangents Ten Decimal Places with Ten Second Interval 0o-6°," can be helpful in this regard. This publication can be obtained from the U. S. Department of Commerce, National Oceanic and Atmospheric Administration, National Geodetic Survey, Rockville, MD 20852.
dix A are taken from Special Publication No. 273 of th Tables E and F of Appendix A are taken from Special Publicati
Coast and Geodetic Survey entitled “Plane Coordinat U. S. Department of Commerce Coast and Geodetic Survey entitled Project Tables South Carolina (Lambert).” The reader can obtam we
his or her state by writing the address given in the preceding paragraph Table E provides information as to R values for different latitudes, and provides values of 0 for different longitudes. These values are needed to be of Example 10-1.
Determine the x and y Lambert coordinates for the following NGS monument in the
South Carolina North Zone:
Name and location of Station: “Blaney,” 12 miles southeast of Camden, SC
Geodetic latitude = 34°10'18.883°N
Geodetic longitude = 80°47'30.989”W
C = 2,000,000.00 ft Ry for North Zone of SC = 31,127,724.75 ft
R= 30,703.171.70 at 34°10'N (Table E-1)
To find & you need to use the table and then
correct the giun
R, as the table - does not have
minus correction for 18.873” farther north (Table E-1)
= 30,703,171.70 - (18.73)(101.08333)
= 30,701,263.95 ft
0= +0°07'20.3080” for longitude 80°47'W (Table E-2)
minus (30.989/60)(change from 0 from 80°47' to 8004999
from 80°47' to 80°48"W longitude)
+0°07'20.3080” minus (30.989/60)(33.8699)
x= R sin
= (30,701, (30.701,263.95)(0.0020498626) + 2,000,000.00
y= Ro-R cos e
31,127,724.75 - (30,701,263.95)(0.9999978900
CALCULATION OF PLANE COORDINATES ON A MERCATOR GRID
For the Mercator projection, the central meridian is set at an x distance usually equal to 500,000 ft, while the x axis, as in the Lambert projection, is placed well below the southern edge of the zone. Again the x- and y-coordinates of all points in the projected area will be positive.
The x and y Mercator grid coordinates of some point P can be determined with the equation given at the end of this paragraph, in which A2” is the difference in seconds between the longitude of the central meridian and point P. The value of A2" will be positive if P is to the east of the central meridian and negative if it is to the west. In the expressions that follow, x' is the distance to point P either east or west of the central meridian. In the expression for x and y the terms yo, H, V, and a are values based on the geographic latitude, while b and c are based on A2”. The magnitudes of these values are given in the tables available from the NGS for individual states. If the sign of ab is positive, it increases the value of x'; a negative value decreases it.
x' = H • A2” ab
x = x' + 500,000
y=yo + V(AV/100)2 + c
Space is not taken here to present a transverse Mercator projection example because of its similarity with the Lambert case.
Engineering site maps are typically at a 1:1000 scale. How long a role of paper would be needed to map the equator at this scale. The Clemson Civil Engineering Building is located at Latitude 34 degreed 40' 18.68471" N and Longitude 82 degrees 49' 40.96840"W. If the x coordinate of the meridian is 2,000,000 ft., determine the location's State Plane Coordinates. The UTM coordinates for Anderson is Northing:3800333.333 meters and Easting: 377,550.3956 meters. What would be the approximate Latitude and Longitude. Take average radius of earth to be 6,367,444.65 meters. Determine both the State Plane coordinates and UTM coordinates for GSP in South Carolina North zone. Latitude: 34degrees 18'N Longitude: 82degrees 19' 18" W C= 2,000,000.00 Rb = 31,127,724.75 San Francisco is on the central meridian of UTM zone 10. Its latitude is 37degrees 37'12"North of the equator. Estimate its UTM coordinates.
10-6 Assume that the state plane coordinates for the Seneca Walmart is Northing
20.0, Casting: 2,062,933.0'. What would the corresponding Latitude and Longitude be to the nearest second? Assume that the distance from the
pex (O) to the x-axis (y=0) is 31,127,724.75 for the north zone of SC. (the following might be helpful though there are different ways to solve this: sin
a/cos a =tan a). 10-/ Estimate your latitude if you have traveled 2423 kilometers due North of the
equator. What is your UTM Northing? What is your Longitude if your UTM Easting coordinate is 500,000 meters and the longitude of your central
meridian is 81 degrees West. 10-8 What would your answers be in #7 if you traveled 2423 kilometers due
South of the Equator.