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REDUCTION OF SLOPE DISTANCE - 14071_263
ELECTRONIC  POSITIONING SYSTEMS - 14071_265

Engineering Aid 2 - Intermediate Structural engineering guide book
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Figure 12-4.—Slope reduction using vertical angle and slope distance. the theodolite, and the h.i. of the target. These differing heights of the equipment must be considered in the computations since they result in a correction that must be applied to the observed vertical angle before the slope distance can be reduced. Figure  12-4  illustrates  the  situation  in  which  the slope distance and vertical angle are obtained from separate setups of an EDM and a theodolite. In the figure, the EDM transmitter, reflector, theodolite, and target are each shown at their respective h.i. above the ground. Angle  a is the observed vertical angle and  A. is the  correction  that  must  be  calculated  to  determine  the corrected vertical angle, ß, of the measured line. To reduce  the  slope  distance,  s, we  must  first  make adjustment for the differing heights of the equipment. This  adjusted  difference  in  instrument  heights  (Ah.i.) can be calculated as follows: &h.i. =  (h.i.  reflector  –  h.i.  target) -  (h.i.  EDM  -  h.i.  theodolite). With  Ah.i. known,  you  can  now  solve  for         that is needed to  determine  the  corrected  vertical  angle.  You  can determine    as follows: Now, solve for corrected vertical angle, ß, by using the formula: NOTE: The sign of     is a function of the sign of the difference in h.i., which can be positive or negative. You should exercise care in calculating ß so as to reflect the  proper  sign  of  a, Ah.i.  and    . Finally, you can reduce the slope distance,  s, to the horizontal  distance,  H, by  using  the  following  equation: To understand how the above equations are used in practice, let’s consider an example. Let’s assume that the slope distance, s, from stations A to B (corrected for meteorological conditions and EDM system constants) is 2,762.55 feet. The EDM transmitter is 5.52 feet above the ground, and the reflector is 6.00 feet above the ground.  The  observed  vertical  angle  is–4°30´00".  The theodolite and target are 5.22 feet and 5.40 feet above the ground, respectively. Our job is to calculate the horizontal distance. To solve this problem, we proceed as  follows: The above example is typical of situations in which the slope distance and the vertical angle are observed using  separate  setups  of  an  EDM  and  a  theodolite  over the  same  station.  Several  models  of  the  modern 12-4







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