How is the height of an instrument calculated?

Short Answer:

The height of an instrument (HI) in surveying is calculated by adding the back sight (BS) reading to the known elevation of a benchmark (BM). This gives the height of the instrument above the mean sea level or reference point. HI is then used to find the elevation of other points in the area.

This method helps surveyors easily calculate the reduced levels (RL) of unknown points by subtracting the staff readings (intermediate sight or fore sight) from the HI. It is a basic and very useful step in leveling operations to ensure accurate elevation data.

Detailed Explanation:

Height of an instrument calculation

In leveling work, determining the height of the instrument (HI) is a key step. It is the vertical height of the leveling instrument’s line of sight above a known reference point, usually a benchmark (BM). A benchmark is a point whose elevation is already known. The height of the instrument helps in calculating the elevation (also called reduced level or RL) of all other points in the area.

The calculation of HI is done using a simple formula:

HI = RL of benchmark + Back Sight (BS)

Here, the Back Sight (BS) is the first staff reading taken from the instrument to the benchmark. Once the HI is known, the elevations of other points are calculated by subtracting the staff readings from the HI.

For example, if the RL of the benchmark is 100.000 m and the BS reading is 1.200 m, then:

HI = 100.000 + 1.200 = 101.200 m

Now, if the Fore Sight (FS) reading on a new point is 1.800 m, then the RL of that point is:

RL = HI – FS = 101.200 – 1.800 = 99.400 m

Steps followed during fieldwork

  1. Set up the instrument: The leveling instrument is set up and leveled properly at a suitable location.
  2. Take BS on a benchmark: A staff reading is taken on a benchmark whose RL is already known. This gives the BS value.
  3. Calculate HI: Add the BS value to the RL of the benchmark to get the HI.
  4. Take IS or FS readings: Intermediate sights (IS) and fore sights (FS) are then taken on unknown points.
  5. Calculate RLs: Subtract the IS or FS from the HI to get the reduced levels of those points.

This method is known as the height of instrument method, and it is commonly used because of its simplicity and accuracy. It is especially useful when many points need to be leveled from one instrument setup.

Importance of calculating HI

  • Quick and accurate results: Once the HI is known, finding the RL of other points becomes quick and easy.
  • Avoids repeated calculations: Instead of using complex leveling loops, HI method allows calculation of multiple point elevations from a single setup.
  • Used in construction and drainage design: Knowing the exact height of land points helps in planning the slope of drains, placement of foundations, and road levels.
  • Error detection: Re-checking the calculated RLs can help in spotting any reading mistakes or equipment errors early.
  • Foundation for mapping: The height data collected using HI is used to create contour maps, slope analysis, and earthwork planning in civil engineering.

The method is simple enough to be used by students and accurate enough for professional engineers. It is one of the first things taught in field surveying and is used in almost every type of leveling project.

Conclusion:

The height of an instrument is calculated by adding the back sight reading to the known elevation of a benchmark. This value is essential in leveling, as it helps to find the reduced levels of other points by subtracting staff readings. The method is simple, accurate, and widely used in all types of civil engineering field surveys.