Let us consider an example given below.
The following readings were taken with a dumpy level
0.745, 1.523, 2.864, 2.957, 0.847, 0.595, 0.487, 0.212, 1.257, 0.884,& 2.015. The instrument was shifted after the 4th & 8th readings. The 1st reading was taken on the benchmark of RL 450.527m. Calculate the RL of all the points.
Calculation:
As you can observe in the above drawing, the instrument is shifted after the 4th & 8th reading.
So, 1st, 5th, & 9th readings 👉 BS
4th, 8th, & 11th readings 👉 FS &
all other remaining readings 👉 IS
Please remember: 👉 While surveying, the 1st reading becomes BS & the last reading becomes FS.
Note:
BS 👉 backsight
FS 👉 foresight
IS 👉 intermediate sight.
Now, let us prepare the rise & fall table from the above-mentioned data.
Following are the rules you should remember while calculating the RL in the rise & fall method.
1. Deduction of values should be done from left to right, as shown with the arrow mark in the above-given table.
For eg:
1st BS reading - 2nd IS reading ✔
2nd IS reading - 3rd IS reading ✔
3rd IS reading - 4th FS reading ✔
You cannot calculate by deducting in the reverse direction.
i.e. 4th FS reading - 5th BS reading ❌
6th IS reading - 5th BS reading ❌
2. After deduction, if the answer is +ve, it should be entered in the rise column, & if the answer is -ve, it should be entered in the fall column.
3. To calculate the RL of the 2nd station, you have to add or subtract the rise or fall from the given benchmark RL. Again to calculate the 3rd RL, you have to add or subtract the consecutive rise or fall.
Keeping in mind, the above-given rules, let us start the calculation procedure.
Rise & fall calculation:
1. [1st BS - 2nd IS] = [0.745 - 1.523] = -0.778
The value is -ve, so it should be entered in the fall column.
2. [2nd IS - 3rd IS] = [1.523 - 2.864] = -1.341
The value is -ve, so it should be entered in the fall column.
3. [3rd IS - 4th FS] = [2.864 - 2.957] = - 0.093
The value is -ve, so it should be entered in the fall column.
4. [5th BS - 6th IS] = [0.847-0.595] = + 0.252
The value is +ve, so it should be entered in the rise column.
5. [6th IS - 7th IS] = [0.595 - 0.487] = + 0.108
The value is +ve, so it should be entered in the rise column.
6. [7th IS - 8th FS] = [0.487 - 0.212] = + 0.275
The value is +ve, so it should be entered in the rise column.
7. [9th BS - 10th IS] = [1.257- 0.884] = 0.373
The value is +ve, so it should be entered in the rise column.
8. [10th IS - 11th FS] = [ 0.884 - 2.015] = - 1.131
The value is -ve, so it should be entered in the fall column.
All these calculated values of the rise & fall should be entered as shown in the below-given table.
|
Station |
BS |
IS |
FS |
Rise(+) |
Fall(-) |
RL |
Remark |
|
1 |
0.745 |
|
|
|
|
450.527 |
BM |
|
2 |
|
1.523 |
|
|
0.778 |
|
|
|
3 |
|
2.864 |
|
|
1.341 |
|
|
|
4 |
0.847 |
|
2.957 |
|
0.093 |
CP1 |
|
|
5 |
|
0.595 |
|
0.252 |
|
|
|
|
6 |
|
0.487 |
|
0.108 |
|
|
|
|
7 |
1.257 |
|
0.212 |
0.275 |
|
CP2 |
|
|
8 |
|
0.884 |
|
0.373 |
|
|
|
|
9 |
|
|
2.015 |
|
1.131 |
|
|
|
|
|
|
RL calculation:
1. Given benchmark RL = 450.527
2. 2nd RL = [benchmark RL - fall] = [450.527 - 0.778] = 449.749
3. 3rd RL = [ 2nd RL - fall] = [449.749 - 1.341] = 448.408
4. 4th RL = [ 3rd RL - fall] = [448.408 - 0.093] = 448.315
5. 5th RL = [ 4th RL + rise] = [ 448.315 + 0.252] = 448.567
6. 6th RL = [ 5th RL + rise] = [ 448.567 + 0.108] = 448.675
7. 7th RL = [ 6th RL + rise] = [ 448.675 + 0.275] = 448.95
8. 8th RL = [ 7th RL + rise] = [ 448.95 + 0.373] = 449.323
9. 9th RL = [ 8th RL - fall] = [ 449.323 - 1.131] = 448.192
All these calculated values of RL should be entered as shown in the below-given table.
|
Station |
BS |
IS |
FS |
Rise(+) |
Fall(-) |
RL |
Remark |
|
1 |
0.745 |
|
|
|
|
450.527 |
BM |
|
2 |
|
1.523 |
|
|
0.778 |
449.749 |
|
|
3 |
|
2.864 |
|
|
1.341 |
448.408 |
|
|
4 |
0.847 |
|
2.957 |
|
0.093 |
448.315 |
CP1 |
|
5 |
|
0.595 |
|
0.252 |
|
448.567 |
|
|
6 |
|
0.487 |
|
0.108 |
|
448.675 |
|
|
7 |
1.257 |
|
0.212 |
0.275 |
|
448.95 |
CP2 |
|
8 |
|
0.884 |
|
0.373 |
|
449.323 |
|
|
9 |
|
|
2.015 |
|
1.131 |
448.192 |
|
|
Total Ʃ |
2.849 |
|
5.184 |
1.008 |
3.343 |
|
|
Arithmetic check:
[∑FS - ∑BS] = [∑fall - ∑ rise] = [1st RL - last RL]
[∑FS - ∑BS] = [ 5.184 - 2.849] = 2.335 ✔
[∑fall - ∑ rise] = [ 3.343 -1.008] = 2.335 ✔
[1st RL - last RL] = [ 450.527 - 448.192] = 2.335 ✔
Hence, the calculation is correct.
To understand A to Z of surveying, click here.
Thank you for going through these calculation steps❤. Have a good day 😄.
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