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CHAPTER  13 HORIZONTAL CONTROL
Converting Azimuths to Bearings or Vice Versa

Engineering Aid 3 - Beginning Structural engineering guide book
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This  figure  shows  two  meridians  or  parallel lines that are intersected by another line called a traverse. It can be proved geometrically that the angles  A and  Al, B and  B1, Az and  A3, and  Bz and  B3  are  equal  (vertically  opposite  angles). It  can  also  be  shown  that  angles  A = A2,  and B = B2   (corresponding   angles).   Therefore, It can also be shown that the sum of the angles that form a straight line is 180°; the sum of all the  angles  around  the  point  is  360°. Figure  13-2  shows  a  traverse  containing traverse  lines  AB,  BC,  and  CD.  The  meridians through  the  traverse  stations  are  indicated  by  the lines NS, N´S´, and N´´S´´. Although meridians are not, in fact, exactly parallel, they are assumed to be,  for  conversion  purposes.  Consequently,  we have   here   three   parallel   lines   intersected   by traverses,  and  the  angles  created  will  therefore  be equal,  as  shown  in  figure  13-1. The bearing of AB is given as N20°E, which means  that  angle  NAB  measures  20°.  To  deter- mine  the  deflection  angle  between  AB  and  BC, you  proceed  as  follows:  If  angle  NAB  measures 20°,  then  angle  N’BB’  must  also  measure  20° because the two corresponding angles are equal. The bearing of BC is given as S50°E, which means angle  S´BC  measures  50°E.  The  sum  of  angle Figure  13-2.-Converting  bearings  to  deflection  angles  from given traverse data. N´BB´   plus   S´BC   plus   the   deflection   angle between  AB  and  BC  (angle  B´BC)  is  180°. Therefore,  the  size  of  the  deflection  angle  is The  figure  indicates  that  the  angle  should  be turned  to  the  right;  therefore,  the  complete deflection  angle  description  is  11°R. The  bearing  of  CD  is  given  as  N70°E; therefore,  angle  N´´CD  measures70°.  Angle  S´´CC´ is equal to angle S´BC and therefore measures 50°. The deflection angle between BC and CD equals The  figure  indicates  that  the  angle  should  be turned to the left. Converting Deflection Angles to Bearings Converting  deflection  angles  to  bearings  is simply the same process used for a different end result. Suppose that in figure 13-2, you know the deflection   angles   and   want   to   determine   the corresponding  bearings.  To  do  this,  you  must know the bearing of at least one of the traverse lines. Let’s assume that you know the bearing of AB and want to determine the bearing of BC. You know the size of the deflection angle B´BC is 110°. The size of angle N´BB´ is the same as the size of  NAB,  which  is  20°.  The  size  of  the  angle  of bearing  of  BC  is The figure shows you that BC lies in the second or SE quadrant; therefore, the full description of the  bearing  is  S50°E. Converting Bearings to Interior and Exterior Angles Converting  a  bearing  to  an  interior  or  exterior angle is, once again, the same procedure applied for a different end result. Suppose that in figure 13-2, angle ABC is an interior angle and you want to determine the size. You know that angle ABS´ equals angle NAB, and therefore measures 20°. 13-2







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