 # Rise and Fall Method | Numericals of Rise and Fall Method

### 1. Introduction

The 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.

### 2. 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

### 3. Numerical Examples of Rise and Fall Method

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#### Question no. 1:

The following readings were observed successively with a leveling instrument. The instrument was shifted after the 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 the rise and fall method.

Solution,

 Station B.S I.S F.S Rise Fall RL Remarks 1 0.485 100 B.M 2 1.210 0.725 99.275 3 1.635 0.425 98.850 4 3.395 1.76 97.09 5 0.650 3.775 0.38 96.71 C.P.1 6 1.400 0.75 95.96 7 1.795 0.395 95.565 8 2.575 0.78 94.785 9 3.375 0.80 93.985 10 1.735 3.895 0.52 93.465 C.P.2 11 0.635 1.10 94.565 12 1.605 0.97 93.595 Total 2.87 9.275 1.10 7.505

( 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.

 Station Point B.S I.S F.S Rise Fall R.L Remarks 1 TBM 0.771 1,2 A 0.802 1.552 2 B 2.311 2,3 C 3.580 1.990 3 D 1.220 3 E 3.675 3,4 F 2.408 4.02 4 G 0.339 4 H 0.157

Solution;

 Station Point B.S I.S F.S Rise Fall R.L Remarks 1 TBM 0.771 43.000 B.M 1,2 A 0.802 1.552 (0.771-1.552) 0.781 (43.00-0.781) 42.219 C.P.1 2 B 2.311 (0.802-2.311) 1.509 (42.219-1.509) 40.710 2,3 C 3.580 1.990 (2.311-1.990) 0.321 (40.710 +0.321) 41.031 C.P.2 3 D 1.220 (3.580-1.220) 2.360 (41.031 +2.360) 43.391 3 E 3.675 (1.220-3.675) 2.455 (43.391-2.455) 40.936 3,4 F 2.408 4.02 (3.675-4.020) 0.345 (40.936-0.345) 40.591 C.P.3 4 G 0.339 (2.408-0.339) 2.069 (40.591 +2.069) 42.660 4 H 0.157 (0.339-0.157) 0.182 (42.660 +0.182) 42.842 Total 7.561 7.719 4.932 5.090

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, 2.005, 0.567, 1.888, 1.181, 3.679, 0.612, 0.705, 1.810

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

Solution,

 Station B.S I.S F.S Rise Fall R.L Remarks 1 0.578 100 B.M 2 0.933 0.355 99.645 3 1.768 0.835 98.81 4 2.450 0.682 98.128 5 0.567 2.005 0.445 98.573 C.P.1 6 1.888 1.321 97.252 7 1.181 0.707 97.959 8 0.612 3.679 2.498 95.461 C.P.2 9 0.705 0.093 95.368 10 1.810 1.105 94.263 Total 1.7578 7.494 1.152 6.889

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 leveling instrument using a 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,

 Station B.S I.S F.S Rise Fall R.L Remarks A 2.0 100 B.M B 2.5 0.5 99.5 C 3.1 0.6 98.9 D 0.6 3.9 0.8 98.1 C.P.1 E 1.3 0.7 97.4 F 2.0 0.7 96.7 G 2.8 0.8 95.9 H 3.1 2.1 0.7 96.6 C.P.2 I 3.0 0.9 2.2 98.8 C.P.3 J 2.3 1.2 1.8 100.6 C.P.4 K 0.8 1.5 102.1 Total 8.9 6.2 4.1

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.