Figure 12-4.—Slope reduction using vertical angle and slope distance.the theodolite, and the h.i. of the target. These differingheights of the equipment must be considered in thecomputations since they result in a correction that mustbe applied to the observed vertical angle before the slopedistance can be reduced.Figure 12-4 illustrates the situation in which theslope distance and vertical angle are obtained fromseparate setups of an EDM and a theodolite. In thefigure, the EDM transmitter, reflector, theodolite, andtarget are each shown at their respective h.i. above theground. Angle a is the observed vertical angle and A. isthe correction that must be calculated to determine thecorrected vertical angle, ß, of the measured line. Toreduce the slope distance, s, we must first makeadjustment for the differing heights of the equipment.This adjusted difference in instrument heights (Ah.i.) canbe 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 forthat is neededto determine the corrected vertical angle. You candetermineas follows:Now, solve for corrected vertical angle, ß, by using theformula:NOTE: The sign ofis a function of the sign ofthe difference in h.i., which can be positive or negative.You should exercise care in calculating ß so as to reflectthe proper sign of a,Ah.i. and.Finally, you can reduce the slope distance, s, to thehorizontal distance, H, by using the following equation:To understand how the above equations are used inpractice, let’s consider an example. Let’s assume that theslope distance, s, from stations A to B (corrected formeteorological conditions and EDM system constants)is 2,762.55 feet. The EDM transmitter is 5.52 feet abovethe ground, and the reflector is 6.00 feet above theground. The observed vertical angle is–4°30´00". Thetheodolite and target are 5.22 feet and 5.40 feet abovethe ground, respectively. Our job is to calculate thehorizontal distance. To solve this problem, we proceedas follows:The above example is typical of situations in whichthe slope distance and the vertical angle are observedusing separate setups of an EDM and a theodolite overthe same station. Several models of the modern12-4
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