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Level book TBM1 to TBM2 (4th, 7th)

Short answer

Computed RL of TBM2 is 1448.701 m, misclosure –0.009 m. Correct proportionally by distance (equal spacing assumed). Adjusted RLs: TBM1 1449.870, Pt2 1449.557, Pt3 1449.739, CP1 1450.569, Pt6 1451.077, CP2 1450.780, TBM2 1448.710 m.

The following readings were taken during a levelling work from TBM1 to TBM2: 2.191, 2.505, 2.325, 1.496, 3.019, 2.513, 2.811, 1.752 and 3.824 m. The level instrument was changed after the 4th and 7th readings. Enter the above readings in a level field book format and compute RLs of all the points and adjust the RLs if error arises. RLs of TBM1 and TBM2 are 1449.870 and 1448.710 m respectively. (Distance between TBM1 and TBM2 was 200 m.)

Entering the readings. The level was set up three times (it was changed after the 4th and 7th readings), so:

  • Setup 1: 1st reading 2.191 = BS on TBM1; 2nd (2.505) and 3rd (2.325) = IS; 4th (1.496) = FS on change point CP1.
  • Setup 2: 5th (3.019) = BS on CP1; 6th (2.513) = IS; 7th (2.811) = FS on change point CP2.
  • Setup 3: 8th (1.752) = BS on CP2; 9th (3.824) = FS on TBM2.

HI == RL of point ++ BS, and RL of a point == HI −- staff reading.

Level field book (height of instrument method)

StationBSISFSHI (m)RL (m)
TBM12.1911452.0611449.870
22.5051449.556
32.3251449.736
CP1 (4th/5th)3.0191.4961453.5841450.565
62.5131451.071
CP2 (7th/8th)1.7522.8111452.5251450.773
TBM23.8241448.701

Arithmetic check

ΣBS−ΣFS=6.962−(8.131)=−1.169\Sigma BS - \Sigma FS = 6.962 - (8.131) = -1.169 ; last RL −- first RL =1448.701−1449.870=−1.169= 1448.701 - 1449.870 = -1.169. Both are equal, so the reduction is correct.

Adjustment of misclosure

Computed RL of the last point = 1448.701 m; known RL = 1448.710 m.

Closing error=1448.701−1448.710=−0.009 m\text{Closing error} = 1448.701 - 1448.710 = -0.009\ \text{m}

The correction at a point is −(−0.009)×d/200-(-0.009) \times d / 200, where dd is the distance of the point from TBM1. The 7 staff points are taken at equal spacing, so the 200 m is divided into 6 equal parts of 33.33 m.

StationDistance (m)Correction (m)Adjusted RL (m)
TBM10+0.00001449.870
233.3333+0.00151449.557
366.6667+0.00301449.739
CP1 (4th/5th)100+0.00451450.569
6133.333+0.00601451.077
CP2 (7th/8th)166.667+0.00751450.780
TBM2200+0.00901448.710

Answer: the computed RL of TBM2 is 1448.701 m against the known 1448.710 m, a closing error of −0.009 m (9 mm low). Adjusted RLs: TBM1 1449.870, point 2 1449.557, point 3 1449.739, CP1 1450.569, point 6 1451.077, CP2 1450.780, TBM2 1448.710 m.

Assumption: the distances to the intermediate points are not given, so equal spacing between successive staff points is assumed for the proportional adjustment.

✓ Answer checked by Claude Opus 5.5 (high effort)

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