Topic 2 : Levelling
How levelling is conducted In the figure below the height (or reduced level) of A is known and the heights of B and C need to be estimated.
To determine the height of point B a level is set up at position I1 is between A and B. staff readings R1 and R2 are taken. Since the reduced level of A is known (RLA) the height of the line of sight or height of the plane collimation (HPC) at I1 is:
HPC at I1 = RL A + R1
To obtain the reduced level at B (or RLB):
RLB = HPC - R 2 = (RL A + R1 ) - R 2 = RL A + (R1 − R 2 )
The direction of the levelling is from A to B. Reading R1 is taken with the level facing in the opposite direction, for this reason it is called a back sight (BS). Reading R2 is taken with the level facing in the direction from A to B, for this reason it is called a fore sight (FS). The change in height from A to B, in magnitude and sign, is given by the difference of the two staff readings. Because R1 is bigger than R2, (R1 – R2) is positive and is know as a rise. To obtain the height of C the level is moved to a new position I2. A back sight is taken at B (R3) and a foresight at C (R4) the reduced level of C is:
RLc = RL B + (R 3 − R 4 )
In this case R4 is bigger than R3 , (R3 - R4) is negative and is known as a fall. At point B, both a FS (R2) and a BS (R3) have been taken from different instrument positions this is called a change point. When calculating a rise or fall this is always given by (back sight – foresight). If this is positive a rise is obtained and if negative a fall is obtained. A back sight is the first reading taken after the level has been set up, a foresight is the last reading taken at an instrument position. Any readings taken between a back sight and a foresight are known as intermediate sights.
1. The level is set up at some convenient position I1 and BS of 2.191m is taken to TBM 1. 2. The staff is then moved to points A and B in turn and intermediate sights of 2.505m and 2.325m are taken 3. A change point must be used in order to reach point D. 4. The position of the change point is at C, the staff is moved to this and a FS of 1.496m is taken 5. While the staff remains at C, the instrument is moved to another position, I2 6. A BS of 3.019m is taken from the new level position to the staff at change point C 7. The staff is moved to D and E in turn and readings of 2.513m (IS) and 2.811m (FS) are taken where E is another change point (CP) 8. The last step is to move the level to I3 , a BS of 1.752m taken to E and a FS of 3.824m is taken to TBM 2.
The final staff position is at a TBM, this is most important as all levelling field work must start at and end at a bench mark – otherwise it would be difficult to detect errors when levelling. When levelling, all readings must be identified as back sight, fore sight or intermediate sight. Calculating reduced levels Two methods of calculating reduced levels: 1. Rise and fall method 2. The height of collimation method
Rise and fall method Example: calculate the reduced level of points A to E in the previous example using the rise and fall method. Solution: all the readings for the survey from A to E are shown in the table below. These measurements would be taken from the field book used on site. Each row of the field book corresponds to a staff position and which is shown in the remarks column. The calculations for this method follow a point by point basis starting at TBM1.
From TBM1 to A there is a small fall. A BS of 2.191m was recorded at TBM1 and an IS of 2.505. The fall from TBM1 to A is given by (2.191-2.505) = -0.314m. The negative sign indicates that there is a fall and this is entered in the fall column. This fall values is subtracted from the RL of TBM1 as (49.873-0.314) = 49.559m The procedure is repeated for point B with the height difference given by 2.505-2.325 = +0.180m. This positive sign demonstrates a rise from point A and the RL at B is given by (RLA +...
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