Setting out simple circular curve by rankines method

Theory

In this method the curve was lagged out by a tangential angles with a theodolite and a chain or tape. This method is also called as chain and theodolite method. The tangential angle is the angle between the tangent and the cord drawn from the same point.

Items required

1.      Theodolite

2.    30 Meter chain

3.    Tape

4.    Arrows

5.     Ranging rods

Diagram

Procedure

1.   The first step was to locate the tangent point T₁, T₂ on the straight AB and CB.

2. The theodolite was setup at the beginning of the curve at T₁ and it was leveled.

3. The plates where clamped at zero and the telescope was directed towards the ranging rod at the point of intersection (B) to bisect it.

4. The upper plate was released and the vernier was set to Δ_1, the telescope being directed along T₁ D.

5.   Measure along the line T₁ D. The length equal to first sub cord length ‘C’. Thus fixing first point ‘D’ on the curve.

6. Unclamp the vernier plate now and set vernier ‘A’ to the second total tangential angle Δ₂. The line of site was now directed along T₁ D

7.     With the zero end of tape at D and with a arrow hence at the distance of DE  ie. Full cord length (C₂) see on the tape above D until the line of site bisects the arrow. Thus the second point E was fixed on the curve.

8.    Procedure was repeated until the last point T₂ was reached.

Calculation

1.      The radious of the curve will be 1718.4

2.    Height of the tangent = R tan Ø/2 = 572.90 tan 90⁰

                                                          = 101.02

3.    Length of the curve R_Ø  3.14/100 = 572.96 X 20 X 314/180 = 200

4.    Height of chord 2R sin Ø/2 = 2 X 572.96 sin 10 = 198.98

5.     Change magnetic bearing 9308.98 M

6.    Change the curve = length of equal cord + length of beam

                              = 5508.98

7.     No. of fuel chord = 183 – 177 = 6

8.    Length of 1^st chord = 30 – 28.8 = 1.2 M

9.    Length of last chord = 19 M

Check

6 X 30 + 1.2 + 19.8 = 200

Tangent angle = It is denoted by δ _n = 1718.9/R X C.H

δ _n1 = 1718.9/572.96 X 1.2 = 3.6 = 0⁰ 3’ 36”

δ _n2 = 1718.9/572.96 X      = 3 X 31.2 = 0⁰ 03⁰ 36”

δ _n8 = 1718.9/572.96 X 18.8 = 56’ 29”

δ ₂ = δ ₃ = δ 4 = δ ₅ = δ ₆ = δ₇ = 1⁰ 30’

Δ₁ = δ₁ = 3⁰ 36”

Δ₂ = Δ₁ + δ₂ = 1⁰ 33’ 36”

Δ₃ = Δ₂ + δ₃ = 3⁰ 33’ 36”

Δ₄ = Δ₃ + δ₄ = 4⁰ 33’ 36”

Δ₅ = Δ₄ + δ ₅ =

Δ₆ = 7⁰ 33’ 36”

Δ₇ = 9⁰ 33’ 36”

Δ₈ = 10⁰ 0’ 00”