cassini and UTM PDF

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THE TECHNICAL UNIVERSITY OF KENYA REG. NO.: 111/05383 BACHELOR OF ENGINEERING IN GEOSPATIAL ENGINEERING YEAR FOUR SECOND SEMESTER CADASTRAL SURVEYING DIFFERENCES AND SIMILARITIES BETWEEN UNIVERSAL TRANSVERSE MERCATOR AND CASSINI-SOLDNER PROJECTIONS. DIFFERENCES AND SIMILARITIES BETWEEN UNIVERSAL TRA...

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THE TECHNICAL UNIVERSITY OF KENYA

REG. NO.: 111/05383

BACHELOR OF ENGINEERING IN GEOSPATIAL ENGINEERING

YEAR FOUR SECOND SEMESTER

CADASTRAL SURVEYING

DIFFERENCES AND SIMILARITIES BETWEEN UNIVERSAL TRANSVERSE MERCATOR AND CASSINI-SOLDNER PROJECTIONS.

DIFFERENCES AND SIMILARITIES BETWEEN UNIVERSAL TRANSVERSE MERCATOR AND CASSINI-SOLDNER PROJECTIONS. SIMILARITIES  Both universal transverse Mercator and Cassini projections are cylindrical projections  They are both divided into zones so as to reduce distortions of areas far from the central meridian.  In both cases the equator and the central meridians appear perpendicular straight lines and at all times are used as the reference point.  Both conserve scale only along the central meridian and parallel meridians i.e. the scale factor is 1.  Both are based on Clarke ellipsoid as there reference ellipsoid as it is the best fitting ellipsoid in eastern Africa.  In both cases the zones has a limit of 84 0 N and 800 S beyond which the distortion are thought maximum as the parallel nature is lost as they meet at the poles. DIFFERENCES a. Universal Transverse Mercator projection It’s based on Clarke 1880 reference ellipsoid and is based on arc 1960 as the datum. Is a cylindrical conformal projection. It’s based on a modified Mercator projection in that the cylinder is rotated (transverse) 900 so that the rotational axis of the ellipsoid is perpendicular to the axis of the cylinder. It’s divided into 60 zones of 60 apart with a central meridian that is at 3 0 from either meridian. The limit of the zones is 84 0 N and 800 S.

The scale factor of the lines of secancy is 1. The scale factor decreases towards central meridian to 0.9996. The scale factor increases towards limits to approximately 1.001 at the equator. Lines lying 180km east and west of and parallel to the central meridian have a scale factor of 1.

Fig. Line Distortion and Scale Factor in the TM Projection The origin of each zone is its central meridian and the equator. To eliminate negative coordinates, the coordinate system alters the coordinate values at the origin. The values given to the central meridian is the false easting and the false easting value of 500,000 meters is assigned. A north zone has a false northing of 10,000,000 meters. It has an accurate representation of small shapes. Minimal distortion of larger shapes within the zone. Errors and distortion increase for regions that span more than one UTM zone. This is because UTM is not designed to areas that span more than two zones.

Data on spheroid or ellipsoid cannot be projected beyond 900 from the central meridian. In fact, the extent on a spheroid or ellipsoid should be limited to 150 – 200 on both sides of the central meridian. It is used for United States topographic quadrangle at a scale of 1:100,000. Many countries use UTM zones based on the official geographic coordinate system in use.

b. Cassini – Soldner projection It’s made by treating all meridians as planes that extend from the ellipsoid out of the cylinder. It uses Clarke 1858 reference ellipsoid with arc 1950 as the datum. The projection causes equator and central meridian appear to be perpendicular straight lines. All other meridians appear as lines that intersect the equator at right angles and curve towards the central meridian except for those meridians that are located 900 from the central meridian. It is divided into zones 20 apart with an odd central meridian at 1 0 from either of the meridian. It maintains scale along the central meridian and all lines parallel to it. It is most suitably used for large scale mapping of areas predominantly north-south in extent. It’s achieved by projecting conceptually a cylinder onto the globe and is tangent along the central meridian. Distortion increases with distance from the central meridian. Scale distortion increases with distance from the central meridian. The extent on a spheroid is limited to 50 to either side of the central meridian; beyond this limit distortion is observed. It was used for the ordinance survey of Great Britain and some German states in the late 19th century.

References Snyder, J. P. (1993). Map Projections: A Working Manual. washington: USGS Professional Paper 1395. Soler, T. a. (1989). Important Parameters Used in Geodetic Transformations. Journal of Surveying Engineering 112(4):414–417. Torge, W. (1991). Geodesy. New York: de Gruyte....