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Which of the following method is useful for setting out curves for railway, highway with more accuracy?
Tacheometric method
Rankine’s method
Two theodolite method
All of the above
Rankine’s method
Rankine's method of tangential angles (or deflection angles) is widely considered the most accurate and practical method for setting out simple circular curves in railway and highway engineering · It uses a theodolite set up at the Point of Curve (PC) along with a chain or steel tape to locate points on the curve by measuring deflection angles and chord lengths.
Rankine's method of tangential angles (or deflection angles) is widely considered the most accurate and practical method for setting out simple circular curves in railway and highway engineering · It uses a theodolite set up at the Point of Curve (PC) along with a chain or steel tape to locate points on the curve by measuring deflection angles and chord lengths.
δn=R1718.9×Cn minutes — Tangential angle for an individual chord
Δn=Δn−1+δn — Total deflection angle for point n
Cn — Length of the nth chord, R — Radius of the curve
The method is based on the geometric principle that the deflection angle to any point on a circular curve is equal to half the angle subtended by the arc (or long chord) at the center of the curve · By turning calculated tangential angles from the initial tangent line using a theodolite and measuring cumulative chord lengths along that direction, individual points on the curve are precisely established.
Requires one theodolite at the Point of Curve (PC) and one chain/tape for linear measurement.
Highly accurate for long-radius curves commonly used in railway and highway alignments.
Cumulative deflection angle to the end point (Point of Tangency) equals half of the total deflection angle (Δ/2).
Provides higher accuracy compared to offset methods.
Only requires one instrumental setup at the Point of Curve (PC).
Easy field calculations and systematic checking at the final point.
Requires clear line of sight along all chord directions.
Cumulative errors in chord chaining can carry forward if chaining is not executed precisely.
Setting out simple circular curves for high-speed railway lines.
Aligning national highways, expressways, and urban roadways requiring high precision.
Option A (Tacheometric method) is useful when linear measurements with tape/chain are difficult due to rough or broken ground, but it offers relatively lower precision compared to direct tape measurement.
Option C (Two theodolite method) is used when chaining is impossible (e.g., across a river or swamp), but it requires two instrumental setups and two observers.
Option D is incorrect because Rankine's method is specifically preferred for standard railway and highway curve setting due to its superior combination of speed, accuracy, and operational efficiency.
B is correct — Rankine’s method of tangential angles uses a theodolite and steel tape to provide high precision and convenience required for railway and highway curve alignment.
Remember that for simple circular curves, the total deflection angle to the Point of Tangency (PT) is always equal to 2Δ, where Δ is the angle of intersection of the main tangents.