How do you calculate reduced levels in leveling?

Short Answer:

Reduced levels (RL) in leveling are calculated by using either the Height of Instrument (HI) method or the Rise and Fall method. The RL tells us the vertical height of a point compared to a known reference point, usually called a benchmark. It helps surveyors understand the height difference between various points on the ground.

To calculate RL using the HI method, we first find the height of the instrument (HI) by adding the back sight (BS) reading to the RL of a known point. Then we subtract fore sight (FS) or intermediate sight (IS) readings from the HI to get the RLs of other points.

Detailed Explanation:

Reduced levels in leveling

Reduced level (RL) is the vertical height or elevation of a point in relation to a known reference point, commonly called a benchmark (BM). In leveling, calculating RLs is a basic task that helps in understanding the ground profile. It is mainly used in construction, road work, drainage planning, and land development to determine whether a point is higher or lower than another point.

To calculate RLs, surveyors use leveling instruments like dumpy level or auto level along with a leveling staff. Two main methods are used to calculate RLs: Height of Instrument method and Rise and Fall method.

  1. Height of Instrument (HI) method

This is the most commonly used method in fieldwork. It involves the following steps:

  • Start with a benchmark that has a known RL.
  • Take a back sight (BS) reading on this benchmark.
  • HI = RL of benchmark + BS
  • Now, for any other point, take an intermediate sight (IS) or fore sight (FS).
  • RL = HI – IS or RL = HI – FS

Example:
If BM has RL = 100.000 m and BS = 1.200 m, then HI = 101.200 m.
If FS on a new point = 1.600 m, then RL = 101.200 – 1.600 = 99.600 m.

This method is quick and simple when you need to find RLs of many points from one instrument position.

  1. Rise and Fall method

This method involves comparing the difference in staff readings between two points:

  • If the next reading is smaller, there is a rise.
  • If the next reading is larger, there is a fall.

Steps:

  • First, take BS on benchmark.
  • Then take IS and FS on other points.
  • Calculate rise or fall between each pair of readings.
  • RL of new point = RL of previous point + rise
    or
    RL of new point = RL of previous point – fall

This method is more time-consuming but provides a check for accuracy because all rises and falls are summed and compared to the total difference in RL.

Why RL calculation is important

  • It helps in designing drainage and sewer lines where slope is needed.
  • Used in foundation leveling to ensure flat base levels.
  • Essential in road and highway design for slope and alignment.
  • Required in cutting and filling earthwork operations.
  • Useful in topographic mapping to show terrain profile.

Accurate RL calculations ensure safety, proper water flow, and correct construction levels. Errors in RL can lead to waterlogging, wrong building height, or slope problems.

Conclusion:

Reduced levels in leveling are calculated to find the height of ground points in relation to a known benchmark. They are calculated using either the height of instrument method or the rise and fall method. These methods are simple and reliable and are used in almost every construction and survey project for accurate height measurement.