Parts of a Map. Map Projection A projection is a way of showing the Earth on a flat surface.
Lecture 10 Bue Map Projection
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Transcript of Lecture 10 Bue Map Projection
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