Surveying For Petroleum Engineers

PTRL05C02

Lecture 10

Map Projections

Prof. Dr. Mohamed Elwageeh

Map Projections

Earth to Globe to Map

Representative Fraction

Globe distance

Earth distance =

Map Scale: Map Projection:

Scale Factor

Map distance

Globe distance =

(e.g. 1:24,000) (e.g. 0.9996)

Coordinate System

(fo,lo)

(xo,yo)

X

Y

Origin

A planar coordinate system is defined by a pair

of orthogonal (x,y) axes drawn through an

origin

Projected Coordinate Systems

• A map projection is the systematic transformation of locations on the earth (latitude/longitude) to planar coordinates

• The basis for this transformation is the

geographic coordinate system (which references a datum)

• Map projections are designed for specific purposes

Map Projection

This process of flattening the earth will cause distortions in one or

more of the following spatial properties:

• Shape

– Conformal map projections preserve shape

• Area

– Equal area map projections preserve area

• Distance/Scale

– Equidistant map projections preserve distance

• Direction/Angle

– Azimuthal map projections preserve true direction

The Globe

• Advantages

– most accurate map

• Distances, Directions, Areas (sizes), and Angles

– Latitude & Longitude Lines

• Latitude are Parallel

• Longitude Meridians Converge at the Poles

• Parallels & Meridians meet at Right Angles

• Parallels become shorter toward the poles

• Disadvantages

– expensive to make

– cumbersome to handle & store

– difficult to measure

– not fully visible at once

Flat Paper or Screen Map

• Advantage

– has none of the Globe’s disadvantages

• Disadvantage

– must transform the spherical surface into a flat surface

– not able to maintain all forms of accuracy

• Area/Size OR Angles OR Distance OR Direction

• Projection

– How the Earth’s Spherical Surface is Transformed into a Flat

Plane Surface

– only able to maintain one or two forms of accuracy only

• Correct Projection = more useful than a globe

• Wrong Projection = major problems & deceptions

Types of Projections • Conic: Screen is a conic surface. Lamp at the center of the

earth. Examples: Albers Equal Area, Lambert Conformal

Conic. Good for East-West land areas.

• Cylindrical: Screen is a cylindrical surface. Lamp at the

center of the earth. Examples: (Transverse Mercator). Good

for North-South land areas.

• Azimuthal: Screen is a flat surface tangent to the earth.

Lamp at the center of the earth (gnomonic), at the other

side of the earth (stereographic), or far from the earth

(orthographic). Examples: Lambert Azimuthal Equal Area.

Good for global views.

Types of Projections

Types of Projections

Equal Area: maintains accurate relative sizes. Used for maps that show

distributions or other phenomena where showing area accurately is

important. Examples: Lambert Azimuthal Equal-Area, the Albers Equal-

Area Conic.

Conformal: maintains angular relationships and accurate shapes over

small areas. Used where angular relationships are important, such as for

navigational or meteorological charts. Examples: Mercator, Lambert

Conformal Conic.

Equidistant: maintains accurate distances from the center of the

projection or along given lines. Used for radio and seismic mapping, and

for navigation. Examples: Equidistant Conic, Equirectangular.

Azimuthal or Zenithal: maintains accurate directions (and therefore

angular relationships) from a given central point. Used for aeronautical

charts and other maps where directional relationships are important.

Examples: Gnomonic projection, Lambert Azimuthal Equal-Area.

Projections Preserve Some Earth Properties • Area - correct earth surface area (Albers Equal Area) important

for mass balances

• Shape - local angles are shown correctly (Lambert Conformal

Conic)

• Direction - all directions are shown correctly relative to the

center (Lambert Azimuthal Equal Area)

• Distance - preserved along particular lines

• Some projections preserve two properties

• Some projections preserve none of the above but attempt to

minimize distortions in all four

• The degree and kinds of distortion vary with the projection

used. Some projections are suited for mapping large areas that

are mainly north-south in extent, others for large areas that are

mainly east-west in extent.

Conic Projections

Albers and Lambert

Lambert Projection

The Lambert projection is a conical conformal projection. The imaginary cone is placed around

the earth so that the apex of the cone is on the earth’s axis of rotation above the north pole, for

northern hemisphere projections. The location of the apex depends on the area of the ellipsoid

that is being projected. Figure 3 shows that, although the east- west direction is relatively free

from distortion, the north- south coverage must be restrained (to 158 miles) to maintain the

integrity of the projection

Lambert conformal conic projection is preferred for east- west extended land areas.

Cylindrical Projections

Transverse

Oblique

Tangent Secant

Mercator

Transverse Mercator Projection

Transverse Mercator projection is created by placing an imaginary cylinder around the earth, with its

circumference tangent to the earth along a meridian (central meridian). When the cylinder is flattened, a

plane is developed that can be used for grid purposes. At the central meridian the scale becomes

progressively more distorted as the distance east and west of the central meridian increases

The distortion, which is always present when a spherical surface is projected onto a plane, can be minimized

in two ways. First, the distortion can be minimized by keeping the zone width relatively narrow ( about 158

miles in an east- west direction). Second, the distortion can be lessened by reducing the radius of the

projection cylinder (secant projection) so that, instead of being tangent to the earth's surface, the cylinder cuts

through the earth's surface at an optimal distance on either side of the central meridian. The scale factor at the

central meridian is less than unity (0.9999), it is unity at the line of intersection at the earth's surface and

more than unity between the lines of intersection and the zone limit meridians

Transverse Mercator projection is preferred for north- south extended land areas.

Azimuthal

Lambert

Universal Transverse

Mercator Coordinate

System

• Uses the Transverse Mercator projection

• Each zone has a Central Meridian (lo), zones are 6°

wide, and go from pole to pole

• 60 zones cover the earth from East to West

• Reference Latitude (fo), is the equator

• (Xshift, Yshift) = false easting and northing so you

never have a negative coordinate

– This time in METERS!!!!!

• Commonly used by federal governmental

agencies such as USGS (also a few states)

Universal Transverse Mercator (UTM)

Characteristics of UTM Grid system

• A zone is 6o wide. There is a zone overlap of 0O 30 ’.

• The latitude of the origin is the equator, 0O.

• The easting value of each central meridian = 500,000.000 m.

• The northern value of the equator = 0.0000 m (10,000,000.000 m in the southern hemisphere)

• Zone numbering commences with 1 in the zone 180O W to 174OW and increases eastward to zone 60 at the zone 174OE to 180O E.

• Projection limits of latitude 80O S to 80O N.

Zone 1

International Date

Line - 180

Equator

Zone 18 o

Universal Transverse Mercator-

Grid

Universal Transverse Mercator

Universal Transverse Mercator Projection

UTM Zone 15

Local Survey Datums of Egypt (1) Egyptian Transverse Mercator (ETM)

Egypt was divided to three zones, considering Helmert ellipsoid representing the earth surface and latitude 30 north as the central latitude

First zone (purple belt), projected on a transverse cylinder tangential to the Helmert ellipsoid at longitude 27 and covering the zone between longitudes 25 to 29 N. The origin of the coordinates was taken Eo= 700,000 m, No= 700,000 m.

Second zone (red belt), projected on a transverse cylinder tangential to the Helmert ellipsoid at longitude 31 and covering the zone between longitudes 29 to 33 N. The origin of the coordinates was taken Eo= 615,000 m, No= 810,000 m.

Third zone (blue belt), projected on a transverse cylinder tangential to the Helmert ellipsoid at longitude 34 and covering the zone between longitudes 33 to 36 N. The origin of the coordinates was taken Eo= 300,000 m, No= 1,000,000 m.

Egyptian Transverse Mercator (ETM)

Local Survey Datums of Egypt (2) Unified Egyptian Transverse Mercator

Based on the Transverse Mercator System with the following modifications:

1) Using the WGS84 ellipsoid as the reference system.

2) The base latitude angle (origin point) is zero.

3) Scale factor at the origin 0.9999.

4) False Easting= 300,000 m and False Northing is zero.

5) Egypt was divided to five zones: from longitude 24 to 27 N, from longitude 27 to 30 N, from longitude 30 to 33 N, from longitude 33 to 36 N, and from longitude 36 to 39 N.

Thank You For Attention