Computation on the ellpsoid

 Before proceding with the computation of ellipsoidal coordinates , it is necessary to consider certain aspects of direction . In plane surveying , for instance , the direction of BA differs from that of AB by exactly 180 . However , as shown in figure 8.13 

Azimuth BA = AB + 180 + BA 

where a is the addittonal correction due to convergence of the meridians AP and BP . 

Useing the corrected ellipsodal azimuths and distances , the coordinates are now calculated relative to a selected point of origin 

The basic problems are know as the direct and reverse problems and are analogous to com-putting the polar and join in the plane surveing . The simplest computing routine is one that involves mid-latitude formulae 

The mid-latitude formulae are generally expressed as : 


298 Enginneering Surveing 


The above formulae are accurate to 1 ppm for lines up to 100 km in length 

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