# Answer_Exercise3 - LSGI 3342 Geodetic Control Exercise...

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LSGI 3342 Geodetic Control Exercise Three November 26, 2007 Name: Chong Wai Ming SID: 06701301D

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1) Compare four different height systems (ellipsoidal, orthometric, normal, and dynamic heights) and establish relationships among the four systems. Only using conventional distance leveling measurement between any two equipotential surfaces may have distinct measurements at different location. It is far more accurate to measure the potential different along the plumb line instead, since the potential different is always the same between any two equipotential surfaces at any point. Heights are measurements based on the Geo-potential difference C, which is the potential difference ) ( 0 W W i - - between two equipotential surfaces. The reference point is infinite (W = 0) and Geoid 0 W can be used as a reference. Dynamic Height The dynamic height D i H is using Geopotential number i C is divided by a constant gravity R g , where R i D i g C H = On one equipotential surface, Dynamic heights are the same. However, the geometrical distances between equipotential surface and geoid are difference. Its’ unit is meter, but it is not the same as the meter in geometrical distance, since the potential is divided by R g , which is a scale factor. Dynamic height is unique and can be measured, and it is useful for water direction measurement. Orthomatric Height The Orthomatric height O i H is measured by the geometric distance between geoid and D P H P Equipotential surface at P Geoid
along the plumb line of a point P, where _ g C H i O P = and _ g is the mean value of gravity from P0 to P along the plumb line. Orthomatric height also use meter as unit. The same orthometric heights have different potential value, since the mean gravity along different plumb lines are different. It is unique and can close loop from leveling. Normal Height Normal Height N i H measure the distance between the earth’s surface to the quasigeoid, along the plumb line of point P, and divided by the mean normal gravity _ i γ , where _ i i N i C H γ = ` Normal height is unique, and it also uses meter as unit. Since the mean normal gravity

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