Simple and Differential Levelling

As mentioned earlier, simple levelling is the simplest levelling operation (Figure 2(a)). Now let the staff readings at A and B stations be HA and HB. If RL of A is 100.00, RL of station B can be obtained as follows

HI at O = 100.00 + H_A

RL of B = 100.00 + H_A - H_B

And the level difference between A and B = [H_A - H_B].

The case of differential levelling is explained earlier and shown in Figure 2(b). The instrument is set and levelled at O₁ and staff reading of station A (Back sight) of known level (say a bench mark) is taken. Station C in a firm ground (change point) is chosen and staff reading at C recorded from O₁ (foresight). Stations A and C are visible from instrument station O₁. O₁C is approximately taken as O₁A to minimize error because of line of collimation not being exactly horizontal. Instrument could then be shifted to another station O₂ from that change point C and another selected change point D (such that O₂C = O₂D) are visible. Staff reading, through instrument at O₂, of station C (backsight) and of station D (foresight) is recorded. Various change points, i.e. E, F, G etc. could be chosen along with instrument stations O₃, O₄, O₅ etc. till last change point and station B are visible from last instrument station. The staff reading of last modify point from last instrument station will be a backsight, although that at station B will be foresight. The reduced level (RL) of station B can be acquired from a series of calculations if RL of A is known. Thus level difference between A and B can be acquired. Let the RL of A is RL_A, then

(HI)_A = RL_A + h_A (BS at A)

RL of C = RLA + h_A - h_C (FS at C) = RL + BS_A - FS_C

RL of D = RL_A + BS_A - FS_C + BS_C - FS_D

= RL_A + (BS_A + BS_C) - (FS_C + FS_D)

RL of B = RL_A + ∑ BS - ∑ FS

Therefore, RL of B = RL_A + Difference between sum of all backsights and sum of all foresights.

And level difference between A and B = Difference among sum of backsights and sum of foresights.