Basic Concepts of Levelling
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Basic concept of levelling
Imagine we have two points on the ground; point A is where we are standing and point B which is a few paces away down a slope. We want to know how much lower point B is compared to point A i.e. what is the difference in height (or level) between points A and B?
In the figure opposite, the difference in level between point A on the ground and point B on the ground is found by projecting a horizontal line out from point A and then measuring the distance vertically from point B up to this line.
In practice we can discover this by defining a horizontal plane above both points and then measuring vertically from each point up to this horizontal plane. The difference between the two measurements will be the difference in height (level) between the two points.
For instance, we measure a distance of 1.0m from point A vertically up to our horizontal plane. In the figure above this is labelled as htA. We now move down the slope to point B and measure a distance of 1.5m vertically up to our horizontal plane. In the figure above this is labelled as htB. The difference between the two values is 1.5m – 1.0m = 0.5m. In the figure above this is labelled as h (delta h). This is the difference in height, or the difference in level, between the two points. Because point B is lower than point A then this difference is referred to as a fall. If it had been higher then it would be called a rise.
HPC in the figure above stands for Height of Plane of Collimation and is the arbitrary horizontal plane from which to measure. This will be explained in more detail later.
Assume we know that point A in the figure above is 100 metres above mean sea level. This is called its Reduced Level and is labelled in the figure above as RLA. To calculate the Reduced Level of point B (RLB) we can see that:
dh = htA – htB = 1.0 -1.5 = -0.5
RLB = RLA + dh
RLB = 100 + -0.5 = 99.5 metres above mean sea level.
To find the Reduced Level of a point C further down the slope we can repeat the process, but this time start from point B and so on, finding the Reduced Level of points as we progress. If we know the Reduced Level of the point that we finish on, either because it has been previously calculated, or we have returned to the point at which we started then we can compare the known Reduced Level with our calculated Reduced Level. The difference in values is known as the misclosure and is a measure of the accuracy of our work. There will be a fuller explanation of misclosures later.