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Which of the following Rankine’s method is also known as
One theodolite method
Tangential angles
Both A and B
None of these
Tangential angles
Rankine’s method is a standard field procedure used in surveying for setting out circular curves. It is known as the 'One Theodolite Method' because it requires only a single theodolite at the point of intersection or the tangent point, and it is known as the 'Tangential Angle Method' because it uses the principle of deflection angles calculated as tangential angles to define chord positions.
Rankine’s method is a standard field procedure used in surveying for setting out circular curves. It is known as the 'One Theodolite Method' because it requires only a single theodolite at the point of intersection or the tangent point, and it is known as the 'Tangential Angle Method' because it uses the principle of deflection angles calculated as tangential angles to define chord positions.
δ=R1719×c — Formula to calculate deflection angle in minutes for a given chord length c and radius R
Δ=2πRL×180 — Relation between total deflection angle Δ and curve length L
The method involves calculating the deflection angle (δ) for each chord length from the tangent. The theodolite is set at the point of curvature, and the telescope is directed along the tangent. The required deflection angle is set on the horizontal plate, and the end of the chord is established by shifting the chain along the radial line at the specified distance.
Rankine's method is highly accurate and commonly used for long curves.
It is a versatile method as it does not require a second instrument for point location.
The method is based on the property that the angle between the tangent and the chord is equal to half the angle subtended by the chord at the center.
Calculations are based on the accumulation of deflection angles.
Highly accurate for setting out curves.
Requires only one theodolite, reducing equipment logistics.
Applicable for curves of any radius.
Cumulative errors can occur if the setup is not precise.
Calculation of angles for each stake requires significant time.
Railway track alignment setting.
Highway and road curve transitions.
Construction surveying for circular paths.
The constant 1719 is derived from (180×60)/(2×π)≈1718.87.
Option B is correct because the angles measured from the tangent are 'tangential angles', synonymous with 'deflection angles' in this context.
C is correct — Rankine’s method utilizes deflection angles measured from a tangent point, leading to its identification as both the One Theodolite method and the Tangential Angle method.
Always remember that in curve surveying, the deflection angle for any chord is always half the central angle subtended by that chord.