1.15.5. Reduction of levels

The reduction of level is the operation where the observed staff readings are used to find out the elevation (RLs) of points. There are two methods for reduction of levels:

The reduction of levels is a fundamental process in surveying where the readings obtained from the levelling staff are utilized to calculate the elevations of various points. This is critical for establishing a clear understanding of the terrain and ensuring accurate construction and design work.

Imagine a zookeeper who wants to build a fence around an enclosures. To ensure the fence is level around the entire area, they must measure the height at several points. The zookeeper writes down the height measurements from various spots. The process of reduction of levels is similar to how they would use those measurements to ensure that the fence doesn't end up lower in one area than another.

(a) Rise and Fall Method Since the ground is undulating, the Staff reading will be more if kept at a lower point, and less if kept at a higher point. Thus, the staff readings provide information regarding relative rise and fall of ground points. The difference in the staff readings indicates a rise or fall according to if the staff reading is smaller or greater than that at the preceding point, respectively. The difference between consecutive points is calculated by comparing each point after the first with that immediately preceding it. The RL of each point is then determined by adding rise or subtracting fall to/from the RL of the preceding point. This is the basic concept behind rise and fall method for finding out the elevations of unknown points. If BS - FS is positive. then it is the rise, and if BS - FS is negative, it is fall.

RL of the point = RL of previous point ± (rise or fall)

At the end of all computations, check is applied as:

Σ BS – Σ FS = Σ Rise – Σ fall = First RL – Last RL (1.6)

The Rise and Fall Method is a technique to determine the changes in elevation across uneven terrain. The method involves looking at staff readings of points on the ground. If the staff reading is higher at the next point, it indicates a 'fall', while a lower reading indicates a 'rise'. The current point's RL (reduced level) is then calculated based on the previous point's RL, adding or subtracting the respective rise or fall. Overall, it ensures that accurate elevations are recorded that reflect the terrain's undulations.

Picture hiking up a hill. At each step, you either go up or down depending on the terrain. If you record your height every few steps, you can identify how steep your hike is overall—whether you're climbing or descending by comparing your height at each step to your last.

(b) Height of Instrument method Height of Instrument (HI) method deals with obtaining the RL of the line of collimation by adding BS reading of a point whose RL is known, as shown in Figure 1.28. The RL of line of collimation is called the Height of Instrument. From this, the staff readings of all intermediate stations are subtracted to get the RL at those points. It is always measured from the benchmark. The HI method involves less computation in reducing the levels, so when there are large numbers of intermediate sights, it is used. It is a faster than the rise and fall method, but it has a disadvantage of not having check on intermediate sights.

HI = RL of BM + BS RL of point = HI - FS of that point

At the end of all computations, check is applied as:

Σ BS – Σ FS = First RL – Last RL (1.7)

The Height of Instrument Method simplifies the process of determining the elevation levels of points in surveying. In this method, you find the RL of the line of sight (known as the Height of Instrument) by adding the back sight (BS) reading from a known reference point (the benchmark). Once you have this height, you simply subtract the fore sight (FS) reading for each point to derive their specific elevations. This method is beneficial when you have many points to read quickly, though it does not offer checks on the intermediate readings, making it slightly less precise.

Consider standing atop a diving board with a known height. If you know the height of the board (RF) and can measure the distance from that height to the water's surface, you can quickly determine how deep the water is below the board without having to measure from the ground up every time. This is akin to how the Height of Instrument method helps surveyors quickly deduce elevations from a benchmark.

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