surveying ii ajith sir class 2,3,4

Graticule

A graticule is a network of lines which can be used for geographic plotting, scale, and focusing, depending on the application.

sometimes described as a grid

A common example of a graticule is a grid of lines on a map

which corresponds to longitude and latitude.

Graticule

Important properties of a projection

Shape

Area

Distance

Direction

Important properties of a projection

DistortionDistortion, great or small, is always present in at least one region of planar maps of a sphere.

Distortion is a false presentation of angles, shapes, distances and areas, in any degree or combination.

ShapeShape• Map projections that represents the true or correct

shape of the earth’s features are called conformal conformal projections .projections .

• To preserve the shape, angles between the lines on the reference globe should be maintained in the map.

• Usually these projections can show only small areas of the earth’s surface at one time.

Area

• ‘‘Equal area projections’ Equal area projections’ are drawn so that they illustrate the same representation of the area of the feature.

• All mapped areas have same proportional relationship to the areas on earth.

• sx*sy = 1, an increase in scale factor in one direction must be compensated by decrease in the other direction.

• Shape distortion

Distance

• Projections that attempt to minimize distortions in measures of distance.

• No projection can measure distances correct on the entire map.

• Maintain more standard lines.

• Important for travellers

Direction

• Lines of constant direction are called rhumb lines or loxodromes.

• They are all curved except on Mercator projection.

• Important for navigators.

Standard parallel and standard meridian

• A parallel or a meridian on a map or chart along which the scale is as stated for that map or chart.

• The standard line refers to the line of tangency between the projection and the reference globe.

• There is no distortion along this line

Different map projection criteria

Map projection

• according to the developable surface.

• according to the method of deviation (source of light).

• according to the global properties

Developable surface

• Cones and cylinders are developable surfaces with zero Gaussian curvature

• Distortion always occur when mapping a sphere onto a cone or cylinder, but their reprojection onto a plane incurs in no further errors.

Map projection according to the developable surface

Conic ProjectionsConic Projections Conic ProjectionsConic Projections

Cylindrical ProjectionsCylindrical ProjectionsCylindrical ProjectionsCylindrical Projections

Polar or Azimuthal ProjectionPolar or Azimuthal ProjectionPolar or Azimuthal ProjectionPolar or Azimuthal Projection

Conic Projections

Map wrapped on a cone

Conic Projections(Albers, Lambert)

Conic Projections

The simplest conic projection is tangent to the globe along a line of latitude called the standard parallel.

Conic Projections

The meridians are projected on to the conical surface meeting at the apex or point of the cone

Conic Projectionsproperties

• Meridians are straight lines, converging at a point. Compared with the sphere, angular distance between meridians is always reduced by a fixed factor, the cone constant

• Parallels are arcs of circle, concentric in the point of convergence of meridians. As a consequence, parallels cross all meridians at right angles. Distortion is constant along each parallel

Conic Projectionsproperties

• The distance between the meridians decreases towards pole.

• Conic projections can represent only one hemisphere at a time, either northern or southern

Equidistant Conic Projections

Equidistant Equidistant (also called simple) conic projections are obtained by adjusting the spacing of the parallels, so that they are equally spaced along meridians and the distance between the parallels on the map is equal to the arc length between the parallels on the generating globe

Equidistant Conic projection

• They are suitable for points in the vicinity of a parallel on one side of Equator.

• Scale is the same along all meridians. Commonly one or two parallels are chosen to have the same scale, suffering from no distortion.

• It is neither equal-area nor conformal

Equidistant Conic Projections at 30

Properties of simple conic projection

1. Parallels are concentric arcs of the circles.

2. The pole is represented by an arc.

3. The meridians are straight lines and they intersect the parallels at right angles.

4. The distance between the meridians decrease towards the pole.

Uses of simple conic projection

1.Railways, roads, narrow river valleys and international boundaries running for a long distance in the east- west direction can be shown on this projection.

2.Since the scale along the meridian is correct a narrow strip along a meridian is represented satisfactorily

• Axis of the cone does not line up with polar axis of globe is called obliqueoblique


2. Cylindrical Projections

The globe is projected on to a cylinder that has its entire circumference tangent to the Earth’s surface along a great circle (e.g. equator).

The cylinder is then cut along the meridian and stretched on to a flat surface

Cylindrical Projections

Cylindrical Projections(Mercator)

Transverse

Oblique

Properties of cylindrical projections

In the equatorial aspect (the most common, and In the equatorial aspect (the most common, and frequently the only useful) of all cylindrical projections: frequently the only useful) of all cylindrical projections:

• All coordinate lines are straight

• Parallels (by convention horizontal) cross meridians always at right angles

• Scale is constant along each parallel, so meridians are equally spaced

• All parallels have the same length; the same happens to meridians

Therefore…..

Properties of cylindrical projections

• Whole-world maps are always rectangular • Scale is identical in any pair of parallels equidistant from

Equator

• Scale differs considerably among parallels, reaching infinity at poles, which have zero length on the Earth but are as long as the Equator on a cylindrical map

cylindrical projectionscylindrical projections

• As a group, cylindrical projections are more appropriate for mapping narrow strips centered on a standard parallel.

• Although useful for comparison of regions at similar latitudes, they are badly suited for world maps because of extreme polar distortion.

Cylindrical equidistant projections

• The graticules are perfect squares, the equator becomes a straight line of length 2 r and meridians are r long. Graticules are standard in the North South directions and along equator in the East West direction.

Cylindrical equidistant projection

Special case of equidistant cylindrical projection with standard latitude 0°

Cylindrical equidistant projection

Special case of equidistant cylindrical projection with standard latitudes 45°N and S

Types of cylindrical projection

• Mercator projection

• Transverse Mercator

• Universal Transverse Mercator

Mercator projection

• Flemish geographer Gerardus Mercator, in 1569.

• cylinder tangent to the equator and parallel to the polar axis.

• lines of constant bearing, known as rhumb lines or loxodromes, are represented as straight segments.

• It is a conformal projection

Mercator projection

conformality and straight rhumb lines, make this projection uniquely suited to marine navigation:

Properties of Mercator projection 1.Parallels and meridians are straight lines, and intersect at

right angles.

2. The distance between the parallels go on increasing towards the pole, but the distance between the meridians remains the same.

3. All parallels are of the same length equal to that of equator.

4. The meridians are longer than the corresponding meridians on the globe.

Limitations of Mercator projection

1. Since the scale in zones of high latitudes are greater, the sizes of countries there are very large.

2. Poles cannot be shown because the exaggeration in scales along the 90 degrees where the parallel and the meridian touch them will become infinite.

Uses of Mercator projection

1. Used for navigational purposes both on the sea and in air.

2. Ocean currents, wind directions and pressure systems are shown, as the directions are maintained truly.

3. Since exaggeration in size and shape in tropical regions is minimum, maps of tropical countries are shown on this projection for general purposes.

Transverse Mercator ProjectionTransverse Mercator Projection

The cylinder is rotated 90° (transverse) relative to the equator

projected surface is aligned to a central meridian rather than to the equator

Characteristics of

Transverse Mercator ProjectionTransverse Mercator Projection • The map is conformal,

• The central meridian is straight,

• Distances along it are proportionally correct, that is, the scale is constant along the central meridian.

• since meridians are not straight lines, it is better suited for large-scale topographic maps than navigation

• Indian National grid system

Universal Transverse Mercator Universal Transverse Mercator

(UTM)(UTM)

The UTM defines a grid covering the world between parallels 84°N and 80°S.

The grid is divided in sixty narrow zones, each centered on a meridian.

Zones are identified by consecutive numbers, increasing from west to east

Universal Transverse Mercator (UTM)


3.Azimuthal Projections

Azimuthal Azimuthal (or zenithal) Projections are projections on to a plane that is tangent to some reference point on the globe.

Azimuthal ProjectionsAzimuthal Projections

• If the reference point is on the poles, the projections are polar azimuthal polar azimuthal (zenithal)


• If the reference point lies on the equator the projections are termed transversetransverse.


…for all other reference points, the projections are obliqueoblique

Azimuthal Projections

• All azimuthal projections preserve the azimuth from a reference point (the conceptual center of the map), thus presenting true direction (but not necessarily distance) to any other points.

• They are also called planar since several of them are obtained straightforwardly by direct perspective projection to a plane surface.


if one of the poles is the central point;

• meridians are straight lines, radiating regularly spaced from the central point

• parallels are complete circles centered on the central point

• projections are only distinguished by parallel spacing .

• The outlines of maps are circular.


Transverse equatorial aspect of the azimuthal equidistant projection

Normal North polar aspect of the azimuthal equidistant projection

Azimuthal Orthographic Projection

• In this projection it is assumed that the light source is at infinite distance from the point of tangency, resulting in the ray of light being parallel to each other and perpendicular to the projection surface

Properties of Orthographic Projection

1. Since the scale along the meridian decreases rapidly away from the center, the shapes are much distorted, the distortion increasing away from the center of projection.

2. The parallels are concentric circles.

3. The meridians intersect the parallels at right angles

Limitations of Orthographic Projection

• The shapes are much distorted near the margin of the projection.

• The sizes of the areas are diminished away from the center of projection.

• It is only a small area in the central part of the projection that can be represented in a satisfactory way

Azimuthal Stereographic Projection

An azimuthal stereographic map has a simple geometric interpretation:

rays emanating from one point pierce the Earth's surface hitting a plane tangent at the point's antipode

Properties of Stereographic Projection

1. The parallels are not spaced at equal distances.

2. The scale along the parallels also increases away from the center of projection.

3. Areas are exaggerated, the exaggeration increase away from the center of projection.

Limitations of Stereographic Projection

• Since the areas are enlarged away from the centre of projection only small area in the central part of the projection can be represented satisfactorily

Gnomonic Projection

The gnomonic (also called central, or azimuthal centrographic

the ray source is located exactly on the sphere's center

Properties of Gnomonic Projection

1. The parallels are concentric circles.

2. The meridians intersect the parallels at right angles.

3. The scale along the parallels increases from the center of projection.

4. The spacing of parallels are not equal

surveying ii ajith sir class 2,3,4

Engineering