CivilForge

Differential Leveling Closure

\sum BS - \sum FS = Δ Elev e = Elev_{comp} - Elev_{known}

For a line of levels the algebraic difference of all backsights and foresights equals the net elevation change. Closing on a known BM gives a misclosure e that is distributed with distance (or per setup). Allowable closure is often 0.05√M ft (M in miles) or 8√K mm (K in km) class rules.

\sum BS

Sum of backsights

\sum FS

Sum of foresights

Δ Elev

Net elevation change

e

Misclosure on a known BM

Step-by-step solved example

BS: 4.32, 5.10, 3.88 ft. FS: 6.18, 4.55, 2.21 ft. Start BM = 100.000 ft. Find ending elevation.

ΣBS − ΣFS = net elevation change between BM and TP.

1. Sums
ΣBS = 4.32+5.10+3.88 = 13.30 ft; ΣFS = 6.18+4.55+2.21 = 12.94 ft.
2. Check
ΔElev = 13.30 − 12.94 = +0.36 ft.
$Δ Elev = + 0.36 ft$
3. End
Elev_end = 100.000 + 0.36 = 100.360 ft.
$Elev = 100.360 ft$

Answer: Elev_end = 100.360 ft

10 practice questions

0/10 correct

1.ΣBS = 12.446 m, ΣFS = 11.902 m. Net ΔElev is

2.A loop starts and ends on the same BM. Perfectly closed means

3.Computed close = 412.018, true BM = 412.050. Misclosure e is

4.Allowable 3rd-order closure 0.05√M ft for a 4-mile circuit is nearest

5.Balancing a loop distributes e in proportion to

6.Three-wire leveling reduces error by

7.ΣBS − ΣFS on a closed loop equals the misclosure and should be compared with

8.Starting elev 50.000 m, ΣBS = 8.20, ΣFS = 9.45. Ending elev is

9.Curvature and refraction become important when

10.IFS readings are omitted from ΣBS − ΣFS because they