# Surveying Questions and Answers – Curve Surveying – Rankine’s Method of Tangential Angles

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This set of Tough Surveying Interview Questions & Answers focuses on “Curve Surveying – Rankine’s Method of Tangential Angles”.

1. Rankine’s method will come under which of the following classification?
a) Linear method
b) Instrumental method
c) Angular method
d) Offset method

Explanation: The instrumental methods which are commonly used are rankine’s method, two theodolite method and tacheometric method which are used for setting a circular curve.

2. In Rankine’s method it is assumed that length of arc is equal to its chord.
a) True
b) False

Explanation: Rankine’s method is based o the principle that deflection angle to any point on a circular curve is measured one-half the angle subtended by arc. For that purpose length of arc is assumed to be equal to its chord.

3. According to Rankine’s method, the formula for finding deflection angle can be given as ____________
a) δ = 1718.9 * C + R
b) δ = 1719.8 * C * R
c) δ = 1781.9 * C / R
d) δ = 1718.9 * C / R

Explanation: Rankine’s method defines the formula for deflection angle as δ = 1718.9 * C / R, where c is the chord length, r is the radius of the curve. This deflection angle is useful for determining the curve setting requirements and also determines that deflection angle for any chord is equal to the deflection angle for previous chord.

4. Rankine’s method can be applied for setting curves of large radius.
a) False
b) True

Explanation: The Rankine’s method, when compared to linear and angular methods, is having more accuracy and it is easy to solve which gives systematic solution for the problem raised.

5. Determine the value of radius of the curve if the length of the chord is given as 2m and the tangential angle as 100˚23ꞌ.
a) 34.42m
b) 43.24m
c) 34.24m
d) 43.42m

Explanation: The formula for finding the radius using tangential angle can be given by Rankine’s formula, δ = 1718.9*C / R
On substitution, we get
100˚23ꞌ = 1718.9*2 / R
R = 34.24 m.

6. Which of the following method is capable of delivering more accurate output?
a) Linear methods
b) Angular methods
c) Rankine’s method
d) Two-theodolite method

Explanation: Since two theodolites are used and manual involvement is more in case of two theodolite method, it is capable of producing more accurate output when compared to remaining methods.

7. Which among the following is more expensive process for setting a curve?
a) Linear method
b) Rankine’s method
c) Two theodolite method
d) Angular method

Explanation: The usage of two theodolites makes it more expensive when compared to the remaining methods of setting curves. It also involves three men, one for handling instrument and remaining two for handling chain.

8. Which among the following is a frequently used process?
a) Rankine’s method
b) Tacheometric method
c) Two-theodolite method
d) Bisection of arcs

Explanation: Though two theodolite method is an accurate procedure for obtaining the values, it is a bit expensive when compared to Rankine’s method. Rankine’s method is also capable of producing accurate values. So that it is adopted.

9. If the value of length of the chord is given as 4m and the radius of the curve as 3.65m, find the tangential angle using Rankine’s method.
a) 179˚24ꞌ
b) 173˚4ꞌ
c) 73˚24ꞌ
d) 173˚24ꞌ

Explanation: The Rankine’s angle can be found out by using the formula,
δ = 1718.9*C / R. On substitution, we get
δ = 1718.9*4/ 39.65
δ = 173˚24ꞌ.

10. Rankine’s method is also known as____________
a) Deflection distances method
b) Deflection angles method
c) Tacheometric method
d) Arc bisection method

Explanation: Rankine’s method is also known as deflection angle method because this method involves finding the deflection angle on the curve using point of curvature from tangent to point of curvature of chord.

11. If the degree of the curve is equal to D at 20m chord, find the tangential angle with length of the chord being 5.6m.
a) 2˚28ꞌ
b) 12˚28ꞌ
c) 2˚12ꞌ
d) 22˚28ꞌ

Explanation: The value of tangential angle can be found out by using the formula,
δ = c*D/40. On substitution, we get
δ = 5.6*20/40
δ = 2˚28ꞌ.

12. Which of the following describes the advantage of Rankine’s method?
a) Curve can be set only at P.T
b) Curve can be set only at P.C
c) Curve can be set in multiple operations
d) Curve can be set in one operation

Explanation: The major advantage of this method is that the curve can be set out in one operation when the theodolite is placed at P.I, which finds its purpose of finding angle of intersection.

13. Find the deflection angle for various points if the value of θ is given as 24˚ and Δ = 48˚.
a) 54˚40ꞌ
b) 45˚48ꞌ
c) 45˚40ꞌ
d) 50˚40ꞌ

Explanation: The value of deflection of various points can be determined by using the formula,
Tan α = (1-cos θ) / (tan Δ/2-sin θ). On substitution, we get
Tan α = (1-cos 52˚) / (tan (48˚/2)-sin 4˚)
α = 45˚40ꞌ.

14. Find the tangential angle of the curve, if the length of the chord is given as 65m and the degree of the curve is equal to D at 100ft length.
a) 32˚38ꞌ
b) 32˚30ꞌ
c) 23˚30ꞌ
d) 2˚30ꞌ

Explanation: The value of tangential angle if the degree of the curve is equal to D at 100ft length can be determined by,
δ = c*D/200. On substitution, we get
δ = 65*100/200
δ = 32˚30ꞌ.

15. Find the chord length using Rankine’s method with radius of the curve being 43.76m and the tangential angle is 87˚45ꞌ.
a) 2.23m
b) 3.22m
c) 3.98m
d) 5.43m

Explanation: From Rankine’s method, the chord length can be given as
δ = 1718.9*C / R. On substitution, we get
87˚45ꞌ = 1718.9*C / 43.76
C = 2.23 m.

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