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TRAVERSE COMPUTATIONS - 14071_129
Figure 7-8.Latitude and departure. - 14071_131

Engineering Aid 2 - Intermediate Structural engineering guide book
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air base; for road railroad, and pipeline alignment; for the control of hydrographic surveys; and for many other projects. A traverse is always classified as either a closed traverse or an open traverse. A closed traverse starts and ends  at  the  same  point  or  at  points  whose  relative horizontal positions are known. An open traverse ends at the station whose relative position is not previously known and, unlike a closed traverse, provides no check against  mistakes  and  large  errors.  In  the  EA3 TRAMAN,  you  studied  field  procedures  for  laying  out traverses. In this chapter you will study computations that are necessary for adjusting and determining the areas of traverses. Checking and Reducing Angles Begin  traverse  computations  by  checking  to  make sure  that  all  the  required  angles  (including  closing angles) were turned and that the notes correctly indicate their sizes. For deflection angles, check to make sure that angles marked L or R were actually turned and have been turned in those directions. Check your sketches and be sure they agree with your field notes. Next, you reduce  repeated  angles  to  mean  angles  using  the procedures that you learned in the EA3 TRAMAN. Checking and Reducing Distances Check to make sure that all required linear distances have  been  chained.  Reduce  slope  distances  when needed. If you broke chain on the slopes, you check to make  sure  that  the  sums  of  break  distances  were correctly  added. Finally,  you  should  apply  standard  error,  tension, and  temperature  corrections  if  needed. Adjusting  Angles From your study of the EA3 TRAMAN, you should recall  the  following  three  conditions  for  a  closed traverse:  (1)  the  theoretical  or  geometrical  sum  of  the interior angles is 180° x (n  – 2), n being the number of angles measured; (2) the sum of the exterior angles is 180° x (n + 2), where n = number of angles measured; and (3) the difference between the sum of the right deflection angles and the sum of the left deflection angles  is  360°.  Any  discrepancy  between  one  of  these sums and the actual sum of the angles as turned or measured constitutes the angular error of closure. You  adjust  the  angles  in  a  closed  traverse  by distributing an angular error of closure that is within the allowable  maximum  equally  among  the  angles. Figure  7-7.—Closed  traverse  by  deflection-angle  method. Figure  7-7  shows  a  traverse  in  which  one  of  the deflection angles was turned to the lefft, all others to the right. The sum of the right deflection angles is 444°59'. Then, by subtracting the left deflection angle (85°01'), you find that the angular error of closure is 02', which is an average of 20" per deflection angle. This average angular error of closure is then added to each right deflection  angle  and   subtracted   from  each  left deflection  angle.  After  applying  this  adjustment  to  each deflection angle in this example, you find, then, that the sum of the adjusted angles to the right equals 445°00'40" and that the sum of the left angles (of which there is only one) is 85°00'40". The difference between these values is 360°00'00", as it should be. Remember  that  in  adjusting  the  angles  in  a deflection-angle  traverse,  you  apply  the  adjustments  to right  and  left  angles  in  opposite  direction. Adjusting for Linear Error of Closure The procedure for distributing a linear error of closure (one within the allowable maximum, of course) over the directions and distances in a closed traverse is called balancing or closing the traverse. Before you can understand how to do this, you must have a knowledge of latitude and departure. LATITUDE AND DEPARTURE.— Latitude  and departure are values that are employed in the method of locating a point horizontally by its plane coordinates. In the plane coordinate system, a point of origin is arbitrarily y selected for convenience. The location of a point is given in terms of its distance north or south and its distance east or west of the point of origin. The plane coordinate system will be explained later in this chapter. 7-8







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