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ADJUSTING A CHAIN OF QUADRILATERALS - CONTINUED
Average Triangle Closure - CONTINUED

Engineering Aid 1 - Advanced Structural engineering guide book
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You know that in logarithms, instead of multiplying you just add logarithms; also, instead of dividing one number by another, you just subtract the logarithm of the second from the logarithm of the first. Note that the logarithm  of  1  is  0.000000.  Therefore,  the  above equation can be expressed as follows: (log sin 1 + log sin 3 + log sin 5 + log sin7) - (log sin 2 + log sin 4 + log sin 6 + log sin 8) = 0 Suppose, now, that after the second figure adjust- ment, the values of the angles shown in figure 15-28 are as  follows: A  table  of  logarithmic  functions  shows  the  log  sines of these angles to be as follows: By subtracting the two sums, you get the following: 9.243442–10 -9.243395–10 0.000047 Therefore, the difference in the sums of the log sines is 0.000047. Since there are eight angles, this means the average difference for each angle is 0.0000059. The next question is how to convert this log sine difference per angle into terms of angular measurement To do this, you first determine, by reference to the table of log functions, the average difference in log sine, per second of arc, for the eight angles involved. This is determined from the D values given in the table. For each of the angles shown in figure 15-28, the D value is as  follows: The average difference in log sine per 1 second of arc, then, is 20.01/8, or 2.5. The average difference in log sine is 5.9; therefore, the average adjustment for each angle is 5.9 +2.5, or about 2 seconds. The sum of the log sines of angles 2, 4, 6, and 8 isS greater than that of angles 1, 3, 5, and 7. There for, you add 2 seconds each to angles 1, 3, 5, and 7 and subtract 2 seconds each from angles 2, 4, 6, and 8. CHECKING  FOR  PRECISION Early in this chapter the fact was stated that the precision of a triangulation survey may be classified according to (1) the average triangle closure and (2) the discrepancy between the measured length of a base line and its length as computed through the system from an adjacent base line. Average Triangle Closure The check for average triangle closure is made after the   station   adjustment.   Suppose   that,   for   the quadrilateral  shown  in  figure  15-28,  the  values  of  the as  follows: 15-37







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