Calculating Elevation Using a Level Line
The diagram above illustrates how the elevation of a new benchmark is determined from a benchmark of known elevation along a standard level line. In the illustration, “BM” stands for benchmark, “INST” for the instrument (or level), and “HI” represents the height of the instrument. The benchmark of known elevation (100 feet) is on the far left. The objective is to determine the elevation of a new point, so that a new vertical benchmark (on the far right) can be established.
All of the necessary measurements for making the calculation are shown in the diagram. In this example, the height of the new benchmark (on far right) is at an elevation of 96 feet. How was this elevation calculated? Here are the steps:
Starting with the benchmark of known height (far left), the height of the level or instrument must be calculated. First, Rod 1 is placed over the benchmark of known elevation, as shown on the far left of the diagram, and the level is placed some distance from it. The height of the level is simply the height of the benchmark of known elevation added to the backsight reading of Rod 1.
HI (Height of the Instrument) = 100 ft + 5 ft = 105 ft
This simply tells us that the instrument is located at an elevation of 105 feet. Now, to determine the elevation of the middle location (the location of Rod 2 in the diagram), we simply turn the level around to take a foresight reading of Rod 2, which, in this case, is six feet.
Now, to calculate the elevation of the middle point, the height of the instrument (HI) is subtracted from the foresight reading of Rod 2.
Elevation of middle point = 105 ft – 6 ft = 99 ft
The next step in extending the level line is to move the level to a new location between Rod 2 and the new point or benchmark. Pointing the level back at Rod 2 gives a backsight reading of 4.5 feet. Then, Rod 1 is moved from its first location over the old benchmark to the new benchmark. Turning the level around and taking a foresight reading gives us 7.5 feet. Now all we have to do to determine the elevation of the new benchmark is subtract the first reading from the second reading and then add that result to the elevation of the middle point. Here is the calculation:
Elevation of new benchmark = backsight reading of Rod 1 – foresight reading of Rod 2 + elevation of middle point
Elevation of new benchmark = 4.5 ft – 7.5 ft + 99 ft = 96 ft
In other words, the new benchmark is three feet lower than the middle location, or 96 feet in elevation. Easy, right?