As you learned in the EA3 TRAMAN, to reduce the slope distance of a line to horizontal distance, you need to know either the vertical angle of the line measured from the instrument or the difference in elevation between the ends of the line. With that information you can use the equations that you studied in chapter 12 of the EA3 TRAMAN to reduce the slope distance. As applied to chaining or transit-tape operations, the calculations are simple; however, as applied to EDM operations, the procedures are frequently a little more complicated, as you will see below. The methods of slope reduction that we will discuss in this chapter should be used only for slope distances that are less than 2 miles in length or for observed vertical angles that are less than 5 degrees. For a discussion of slope reduction when distances of over 2 miles or vertical angles greater than 5 degrees are encountered, you should study commercial publications, such as Surveying Theory and Practice, by Davis, Foote, Anderson, and Mikhail.

When the slope distance and the vertical angle are obtained from separate setups of an EDM and a theodolite, additional information is required for reducing the slope distance. This information includes the heights above the ground (h.i.) of the EDM transmitter and the reflector or remote unit, the h.i. of

Figure 12-3.An electro-optical distance-measuring instrument (Geodimeter).

Figure 12-4.Slope reduction using vertical angle and slope distance.

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 D. is the correction that must be calculated to determine the corrected vertical angle, , 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 (Dh.i. ) can be calculated as follows:

With Dh.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, , by using the formula:

NOTE: The sign of D_a is a function of the sign of the difference in h.i., which can be positive or negative. You should exercise care in calculating so as to reflect the proper sign of _a, D and D_a.

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, lets consider an example. Lets 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 is43000". 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

electro-optical systems, however, have the EDM transmitter built into the theodolite. In this way, the vertical angle and the slope distance can be observed simultaneously. In some of these models, there is a vertical offset between the electrical center of the transmitter and the optical center of the theodolite. Also, the height of the EDM reflector may not be at the same height as the target used to observe the vertical angle. For these conditions, you still need to consider these vertical offsets in the reamer described above.