Let us consider an example as given below.
The following readings were observed with a leveling instrument.
0.450, 1.860, 2.755, 3.250, 3.675, 3.930, 0.885, 1.150, 1.945, 2.850, 3.635, 0.975, 1.950, & 2.585. The instrument was shifted after the 6th & 11th readings. The elevation of 1st reading was 480.65m. Calculate the RL of all the points by using the Height of instrument method.
Calculation:
As you can observe in the above drawing, the instrument is shifted after the 6th & 11th reading.
So, 1st, 7th, & 12th readings 👉 BS
6th, 11th, & 14th 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.
CP 👉 change point.
HI 👉 height of instrument.
RL 👉 reduced level.
Now, let us prepare the Height of instrument table from the above-mentioned data.
Following are the rules or formulas you should remember while calculating the RL in the height of instrument method.
1. HI = [RL + BS]
Whenever you get the BS reading, you have to calculate the height of instrument in that particular change point. By adding the RL to the BS you will get the HI when you establish the instrument in the new change point.
2. RL = [HI - IS or FS]
Once the height of instrument is calculated, you have to deduct the IS and FS from the HI to calculate the RL of that particular station. This procedure should be continued until you get a new HI at the change point.
Keeping in mind, the above-given formulas, let us start the calculation procedure.
1. 1st HI = [1st given RL + 1st BS] = [480.65 + 0.45] = 481.10
2. 2nd RL = [1st HI - 1st IS] = [481.10 - 1.860] = 479.240
3. 3rd RL = [1st HI - 2nd IS] = [481.10 - 2.755] = 478.345
4. 4th RL = [1st HI - 3rd IS] = [481.10 - 3.250] = 477.850
5. 5th RL = [1st HI - 4th IS] = [481.10 - 3.675] = 477.425
6. 6th RL = [1st HI - 1st FS] = [481.10 - 3.930] = 477.170
As you can observe in the below-given table, the IS & FS is deducted from the same HI until you shift the instrument and note down the new BS reading.
Once you note down the BS reading for change point, again you have to calculate the HI & by adding RL to the BS.
7. 2nd HI = [ 6th RL + 2nd BS] = [477.170 + 0.885] = 478.055
8. 7th RL = [2nd HI - 5th IS] = [478.055 - 1.150] = 476.905
9. 8th RL = [2nd HI - 6th IS] = [478.055 - 1.945] = 476.110
10. 9th RL = [2nd HI - 7th IS] = [478.055 - 2.850] = 475.205
11. 10th RL = [2nd HI - 2nd FS] = [478.055 - 3.635] = 474.420
Again calculate HI for the 3rd BS
12. 3rd HI = [ 10th RL + 3rd BS] = [474.420 + 0.975] = 475.395
13. 11th RL = [3rd HI - 8th IS] = [475.395 - 1.950] = 473.445
14. 12th RL = [3rd HI - 3rd FS] = [475.395 - 2.585] = 472.810
All the calculated values should be entered as shown in the below-given table.
|
Station |
BS |
IS |
FS |
HI |
RL |
Remark |
|
1 |
0.450 |
|
|
481.10 |
480.650 |
BM |
|
2 |
|
1.860 |
|
|
479.240 |
|
|
3 |
|
2.755 |
|
|
478.345 |
|
|
4 |
3.250 |
|
477.850 |
|||
|
5 |
|
3.675 |
|
477.425 |
|
|
|
6 |
0.885 |
3.930 |
478.055 |
477.170 |
CP1 |
|
|
7 |
1.150 |
476.905 |
||||
|
8 |
|
1.945 |
|
476.110 |
|
|
|
9 |
|
2.850 |
|
475.205 |
|
|
|
10 |
0.975 |
3.635 |
475.395 |
474.420 |
CP2 |
|
|
11 |
1.950 |
473.445 |
||||
|
12 |
2.585 |
472.810 |
||||
|
Total Ʃ |
2.310 |
|
10.150 |
|
|
Arithmetic check:
[∑FS - ∑BS] = [1st RL - last RL]
[∑FS - ∑BS] = [ 10.150 - 2.310] = 7.840 ✔
[1st RL - last RL] = [ 480.650 - 472.810] = 7.840 ✔
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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