1.15.5.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 Height of Instrument (HI) method is a technique used in levelling to determine the Reduced Level (RL) of different points. To use this method, we first need to establish a known point with a known elevation, often referred to as a Benchmark (BM). We take a reading from the instrument to this benchmark, known as the Back Sight (BS). By adding this BS reading to the elevation of the benchmark, we can calculate the height of the instrument (the line of sight). This HI value becomes the reference for calculating the RL of any other points by subtracting the Forward Sight (FS) readings taken from those points.

Imagine you're measuring the height of a shelf in your room where the height of the room floor is known (the benchmark). You can use a measuring tape from this floor to the shelf in order to find the height of the shelf. If you measure how high your tape goes to the shelf and add that to the floor height, you'd have the total height of the shelf, similar to how we calculate the RL of points using the HI method.

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.

Once we have calculated the height of the instrument, we can proceed to determine the elevations of all intermediate points. This is done by taking sight readings (FS) at these points. The elevation of each point is determined by subtracting the FS reading from the HI. Therefore, if we know our HI and our FS for a specific point, we can easily calculate the RL for that point by the formula: RL of point = HI - FS.

Let's say you have established that the height of your shelf is 200 cm above the floor (HI), and you want to measure how high a book is sitting on that shelf. If the book is 50 cm below the bottom edge of the shelf (FS), then you'd calculate the height of the book as 200 cm - 50 cm which gives you 150 cm from the floor level.

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.

One of the major advantages of the HI method is its efficiency, especially when dealing with multiple intermediate points. Since it allows for quicker calculations, surveyors often prefer it for large-scale projects. However, one of the drawbacks is that it does not offer a built-in system to check the accuracy of intermediate sight readings. This means that if an error occurs, it may not be readily apparent until later in the measurements.

Consider a baker who needs to prepare dozens of batches of cupcakes. If the baker has a simple recipe that allows quick mixing without measuring each ingredient, they can work faster, but if they don’t double-check proportions, they may miscalculate and waste ingredients. Similarly, while the HI method speeds up the process, it requires careful attention to detail to catch any potential mistakes.

At the end of all computations, check is applied as: Σ BS – Σ FS = First RL – Last RL (1.7)

To ensure the accuracy of the readings taken using the HI method, a verification check is performed at the end of all computations. This check involves taking the sum of all Back Sight readings (BS) and subtracting the sum of all Forward Sight readings (FS). The result should equal the difference between the first and last elevations calculated. This method ensures that there are no major discrepancies in the measurements taken.

Let’s compare this to balancing a checkbook. At the end of the month, you assess all your deposits (similar to BS) and withdrawals (similar to FS). You expect that your balance should reflect the difference between the starting and ending amount. If the numbers don’t match up, you know there’s an error somewhere that needs to be fixed.

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