rise and fall method

Rise and Fall Method | Numericals of Rise and Fall Method

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Rise and Fall Method is the method of calculating the difference in elevation between consecutive points in levelling work. Some of the points you have to know before starting numerical are:

Back sights:

The first reading after seeing the instrument is called back sights. This is taken at a known point like B.M or F.S. It is denoted as B.S.

Inter sights:

All readings taken between B.S and F.S are known as inter sights. It is denoted as I.S.

Fore sights:

The last reading after setting the instrument is known by foresight. It is denoted as F.S.

Benchmark:

Benchmark is a point with known elevation. It is denoted as B.M.

 

 

Steps in Numerical Calculation

a. Determine  rise or fall using:

B.S – I.S  or I.S – F.S

b. If:

B.S – F.S= +ve →Rise

B.S – F.S= -ve →Fall

c. Determine new RL:

New R.L = Old R.L – Fall = Old R.L + Rise

d. Arithmetic checking:

∑B.S – ∑F.S = ∑Rise – ∑Fall = Last R.L – First R.L

 

 

Numerical Examples of Rise and Fall Method

Note: Tilt your mobile phone to view full table

 

Question no. 1:

The following readings were observed successively with a levelling instrument. The instrument was shifted after fifth and eleventh readings.
0.485, 1.210, 1.635, 3.395, 3.775, 0.650, 1.400, 1.795, 2.575, 3.375, 3.895, 1.735, 0.635, 1.605 m
Determine the R.L of various points and show the entries in a level book, if the R.L of the first point is 100m, using rise and fall method.

Solution,

 

StationB.SI.SF.SRiseFallRLRemarks
10.485100B.M
21.2100.72599.275
31.6350.42598.850
43.3951.7697.09
50.6503.7750.3896.71C.P.1
61.4000.7595.96
71.7950.39595.565
82.5750.7894.785
93.3750.8093.985
101.7353.8950.5293.465C.P.2
110.6351.1094.565
121.6050.9793.595
Total2.879.2751.107.505

( Note: C.P. denotes Changing Point)

Arithmetic Check

∑B.S – ∑F.S = ∑Rise – ∑Fall = Last R.L – First R.L

2.870 – 9.275 = 1.1 – 7.505 = 93.595 – 100.00

– 6.405 = -6.404 = – 6.405

Hence checked.

 

 

Question no. 2:

The data from a survey are shown below. Use Rise and Fall method to reduce the data. Use arithmetic checks to support your answer.

StationPointB.SI.SF.SRiseFallR.LRemarks
1TBM0.771
1,2A0.8021.552
2B2.311
2,3C3.5801.990
3D1.220
3E3.675
3,4F2.4084.02
4G0.339
4H0.157

 

Solution;

StationPointB.SI.SF.SRiseFallR.LRemarks
1TBM0.77143.000B.M
1,2A0.8021.552(0.771-1.552)
0.781
(43.00-0.781)
42.219
C.P.1
2B2.311(0.802-2.311)
1.509
(42.219-1.509)
40.710
2,3C3.5801.990(2.311-1.990)
0.321
(40.710 +0.321)
41.031
C.P.2
3D1.220(3.580-1.220)
2.360
(41.031 +2.360)
43.391
3E3.675(1.220-3.675)
2.455
(43.391-2.455)
40.936
3,4F2.4084.02(3.675-4.020)
0.345
(40.936-0.345)
40.591
C.P.3
4G0.339(2.408-0.339)
2.069
(40.591 +2.069)
42.660
4H0.157(0.339-0.157)
0.182
(42.660 +0.182)
42.842
Total7.5617.7194.9325.090

 

Arithmetic check:

1. Last R.L – First R.L = 42.842 – 43.000 = -0.158 m

2. ∑B.S – ∑F.S = 7.561 – 7.719 = -0.158 m

3. ∑Rise – ∑Fall = 4.932 – 5.090 = -0.158 m

Hence checked.

 

 

Question no. 3:

The following readings were taken with a level and 4m staff having initial B.M=100 m.

0.578, 0.933, 1.768, 2.450, 0.567, 1.888, 1.181, 3.679, 0.612, 0.705, 1.810

The instrument is shifted after 5th and 9th reading. Determine the R.L of various points.

Solution,

 

StationB.SI.SF.SRiseFallR.LRemarks
10.578100B.M
20.9330.35599.645
31.7680.83598.81
42.4500.68298.128
50.5672.0050.44598.573C.P.1
61.8881.32197.252
71.1810.70797.959
80.6123.6792.49895.461C.P.2
90.7050.09395.368
101.8101.10594.263
Total1.75787.4941.1526.889

 

Arithmetic check:

∑B.S – ∑F.S = ∑Rise – ∑Fall = Last R.L – First R.L

1.7578 – 7.494 = 1.152 – 6.889 = 94.263 – 100

-5.737 = -5.737 = -5.737

Hence checked.

 

 

Question no. 4:

The following readings (in meter) were taken with a levelling instrument using the staff of 4m long.

2.0, 2.5, 3.1, 3.9, 0.6, 1.3, 2.0, 2.8, 2.1, 3.1, 0.9, 3.0, 1.2, 2.3, 0.8

The instrument was shifted after 4th, 9th, 11th and 13th reading. The first reading was taken on BM of RL 100m. Calculate RL of all points.

Solution,

StationB.SI.SF.SRiseFallR.LRemarks
A2.0100B.M
B2.50.599.5
C3.10.698.9
D0.63.90.898.1C.P.1
E1.30.797.4
F2.00.796.7
G2.80.895.9
H3.12.10.796.6C.P.2
I3.00.92.298.8C.P.3
J2.31.21.8100.6C.P.4
K0.81.5102.1
Total8.96.24.1

 

Arithmetic check:

∑B.S – ∑F.S = ∑Rise – ∑Fall = Last R.L – First R.L

11 – 8.9 = 6.2 – 4.1 = 102.1 – 100

2.1 = 2.1 = 2.1

Hence checked.

 

Read More: Preliminary Estimate

Read More: Materials calculation in concrete

 

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