## Grid Systems

One of the oldest systematic methods of location is based upon the geographic coordinate system. While this information is basic, a short review is included for reference. By drawing a set of east-west rings around the globe (parallel to the equator), and a set of north- south rings crossing the equator at right angles and converging at the poles, a network of reference lines is formed from which any point on the earth's surface can be located.

The distance of a point north or south of the equator is known as latitude. The rings around the earth parallel to the equator are called parallels of latitude or simply parallels. Lines of latitude run east-west, with north-south distances measured between them. A second set of rings around the globe at

### LATITUDE AND LONGITUDE

right angles to lines of latitude and passing through the poles are known as meridians of longitude or simply meridians. One meridian is designated as the prime meridian. The prime meridian accepted by the majority of the world runs through Greenwich, England, and is known as the Greenwich meridian.

The distance east or west of a prime meridian to a point is known as longitude. Lines of longitude (meridians) run north-south, with east-west distances measured between them. Geographic coordinates are expressed angular measurement. Each circle is divided into 360°, each degree into 60 minutes, and each minute into 60 seconds.

The degree is symbolized by (0), the minute by ('), and the second by (''). Starting with 0° at the equator, the parallels of latitude are numbered to 90° both north and south. The extremities are the North Pole at 90° north latitude and the South Pole at 90° south latitude. Latitude can have the same numerical value north or south of the equator, so the direction N or S must always be given. It can also be further defined as Geographic/Geodetic or Geocentric Latitude.

Geodetic is the angle that a line perpendicular to the surface of the earth makes with the plane of the equator. It is slightly greater in magnitude than the Geocentric latitude, except at the equator and poles where it is the same due to the earth's ellipsoidal shape. The Geocentric latitude is the angle made by a line to the center of the earth at the equatorial plane.

Starting with 0° at the prime meridian, longitude is measured both east and west around the world. Lines east of the prime meridian are numbered to 0° to +180° and identified as east longitude: lines west of the prime meridian are numbered to 0° to -180° and identified as west longitude. The direction E (+) or W (-) must always be given. The line directly opposite the prime meridian, 180°, may be referred to as either east or west longitude.

### Geographic Datum

For most atlas maps and any directional drilling map, the earth may be considered a sphere. Actually it more nearly resembles an oblate ellipsoid flattened by approximately one part in three hundred at the poles due to rotation. On small-scale maps this oblateness is negligible. However, different ellipsoids will produce slightly different coordinates for the same point on the earth and therefore warrant a brief summary.

More than a dozen principal ellipsoids have been measured in the past two hundred years, which are still in use by one or more countries. An official shape was designated in 1924 by the International Union of Geodesy and Geophysics (IUGG) and adopted a flattening ratio of exactly one part in 297. This was called the International Ellipsoid and was based on Hayford's calculations in 1909 giving an equatorial radius of 6,378,388 meters and a polar radius of 6,356,911,9 meters. Many countries did not adopt this ellipsoid however, including those in North America. The different dimensions of the other established ellipsoids are not only the result of varying uncertainties in the Geodetic measurements that were made, but also are due to a non-uniform curvature of the earth's surface due to irregularities in the gravity field. It is for this reason that a particular ellipsoid will be slightly more accurate in the areas it was measured, rather than using a generalized ellipsoid for the whole earth. This also includes satellite-derived ellipsoids such as WGS72. The following table illustrates some of the official ellipsoids in use today.

 Equatorial Radius, a, PolarRadius Flattening Name Date Meters b, metere f Use GRS 19802 1980 6,378,137 6,356,752.3 1/298.257 Newly adopted WGS 723 1972 6,378,135 6,356,750.5 1/298.26 NASA Australian 1965 6,378,160 6,356,774.7 1/298.25 Australia Krasovaky 1940 6,378,245 6,356,863.0 1/298.25 Soviet Union Internat'1 1924 6,378,388 6,356,911.9 l/297 Remainder of the world Hayford 1909 6,378,388 6,356,911.9 1/297 Remainder of the world Clarke 1880 6,378,249.1 6,356,514.9 1/293.46 Most of Africa; France Clarke 1866 6,378,206.4 6,356,583.8 1/294.98 NA; Philippines

Map Projections. A map projection is a method of transferring part or all of a round body on to a flat sheet. Since the surface of a sphere cannot be represented accurately on a flat sheet without distortion the cartographer must choose characteristics he wishes to display precisely at the expense of others. There is consequently no best method of projection for map making in general. Different applications require different projections.

Some characteristics normally considered in choosing a particular projection are: true shape of physical features, equal area, true scale and size, great circles as straight lines, rhomb (compass point)

lines as straight lines, and correct angular relationships. A map of relatively small size, such as a directional well path, will closely achieve most or all of these characteristics with any method of projection.

Map projections are generally classified with respect to their method of construction in accordance with the developable surface from which they were devised, the most common being cylindrical, conical, and planer.

TRANSVERSE CYLINDRICAL MAP PROJECTION

An examination of these projections shows that most lines of latitude and longitude are curved. The quadrangles formed by the intersection of these curved parallels and meridians are of different sizes and shapes, complicating the location of points and the measurement of directions. To facilitate these essential operations, a rectangular grid maybe superimposed upon the projection.

Universal Transverse Mercator Grid (UTM). The most common worldwide grid system used in directional drilling is the UTM. The U.S. Army adopted this system in 1947 for designating rectangular coordinates on large

scale military maps of the entire world. The UTM is based on the Cylindrical Transverse Mercator Conformal Projection, developed by Johann Lambert in 1772, to which specific parameters have been applied, such as central meridians.

The UTM divides the world into 60 equal zones (6° wide) between latitude 84°N and latitude 80°S. Polar regions are normally covered by a separate planer projection system known as Universal Polar Stereo-graphic. Each of the 60 zones has its own origin at the intersection of its central meridian and the equator. The grid is identified in all 60 zones. Each grid is numbered, beginning with zone 1 at the 180th Meridian, International Date Line, with zone numbers increasing to the east. Most of the North America is included in Zones 10-19. Each zone is flattened and a square grid superimposed upon it.

Any point in the zone may be referenced by citing its zone number, its distance in meters from the equator ("northing") and its distance in meters from a north-south reference line ('easting"). These three components: the zone number, easting and northing make up the complete UTM Grid Reference for any point, and distinguish it from any other point on earth. The Figure below shows a zone, its shape somewhat exaggerated, with its most important features. Note that when drawn on a flat map, its outer edges are curves, (since they follow meridian lines on the globe), which are farther apart at the equator than at the poles.

UTM zones are sometimes further divided into grid sectors although this is not essential for point identification. These sectors are bounded by quadrangles formed every 8° in latitude both north and south and are designated by letters starting with C at 80° South to X at 72° North, excluding I and O. Dallas for example is in grid zone 14s covering a quadrangle from 96° to 102°W and from 32° to 40°N. Sectors may be further divided into grid Squares of 100,000 meters on a side with double letter designations including partial squares of 10,000 meters, 1,000 meters and 100 meters designated by numbers and letters.

The two most important features of the zones are the equator, which run east and west through its center, and the central meridian. Easting and northing measurements are based on these two lines. The easting of a point represents its distance in meters from the central meridian of the zone in which it lies. The northing of a point represents its distance in meters from the equator.

By common agreement, there are no negative numbers for the castings of

points west of the central meridian. Instead of assigning a value of 0 meters to the central meridian of each zone, each is assigned an arbitrary value of 500,000 meters, increasing to the east.

Since along the equator at their widest points, the zones somewhat exceed 600,000 meters from west to east, easting values range from approximately 200,000 meters to approximately 800,000 meters at the equator, with no negative values. The range of possible casting values narrows as the zones narrow toward the poles. Northings for points north of the equator are measured directly in meters, beginning with a value of zero at the equator and increasing to the north. To avoid negative northing values for points south of the equator, the equator is arbitrarily assigned a value of 10 million meters, and points are measured with decreasing, but positive, northing values heading southward. Some maps, particularly in the U.S., have converted UTM coordinates from meters to feet.

In utilizing the Transverse Mercator Projection, the central UTM meridian has been reduced in scale by 0.9996 of True to minimize variation in a given zone. This scale factor (grid distance/true distance) changes slightly as you move away from the central meridian and should be considered if very accurate measurements are desired. However, this error is very small in directional drilling maps and is usually ignored.

Approximately 60 countries use the UTM as the most authoritative and general use projection within the world, although some also use secondary local projections and grid references. The Russia, China and other European countries use the Transverse Mercator (Gauss-Kriiger) with 6° zones. Approximately 50 countries use other projections. Lambert Conformal Conic Projection. The Lambert System is based on a conformal conic projection and is particularly useful in mapping regions that have a predominately east-west expanse. This system has heavy use in North America and is the official U.S.

state plane coordinate system for more than half of the 48 contiguous states, including the majority of those where oil is drilled and produced (i.e. Texas, Louisiana, Oklahoma, California, Colorado, Kansas, Utah, and Michigan). The remainder of the states, including Wyoming, uses the Transverse Mercator with Alaska using a combination.

This projection was first described by Lambert in 1772, but received little use until the First World War where France revived it for battle maps. The features of this conic projection include:

• Parallels of latitude are unequally spaced arcs of concentric circles
• Meridians of longitude are equally spaced radii cutting the parallels at right angles
• Scale is normally true along two defined parallels, but can be true along one
• Pole in same hemisphere is a point, other pole is at infinity

Since there is no distortion at the parallels, it is possible to change the "standard parallels" to another pair by changing the scale applied to the existing map and recalculating standards to fit the new scale. Each state or area has it's own standard parallels, or sets of the same depending on its size, to reduce distortion at the center. For example, Louisiana is divided into three zones as shown in the Table below.

The grid origins for most states are measured in feet, with the east-west axis starting at 2,000,000 feet and the north-south axis set at 0 feet.

Local Grid systems. There are numerous local grid systems in use around the world today. These systems all have different base line coordinates and projections, covering different sizes of surface areas, but all serve the same basic purpose as outlined for UTM and Lambert. In the U.S. lease lines often are used as a convenient grid reference, as well as other privately surveyed grids. Outside the U.S., local grids are used in Holland, the U.K., Brunei, Australia, and other countries. Several countries have also shifted the starting of the UTM grid zones to fall inside their own territory.

In some situations when using standard grid coordinates, the well's target location may lie in a different zone from the surface location. In these cases creating a nonstandard zone normally produces a special local grid. This is done by either extending the surface location zone by a few miles to include the target, or shifting the zone center, as sometimes is done with UTM, 3° to the zone boundary.

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### Responses

• jens
How to latitude and longitude?
8 years ago
• Enrica
Where are the longitude and latitude located on the globe?
7 years ago
• jennifer krueger
WHICH GRID COORDINATE RUNS EASTWEST ALONG THE SURFACE OF THE EARTH?
7 years ago