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Which of the following indicate the angular method of setting out the curve?
Tacheometric method
RankineтАЩs method
Two theodolite method
All of the above
All of the above
Methods of setting out simple circular curves in surveying are broadly classified into linear methods (using chains/tapes only) and angular methods (using angle-measuring instruments like theodolites or tacheometers) ┬╖ The tacheometric method, Rankine's method of deflection angles, and the two-theodolite method all employ angular measurements to locate curve points.
Methods of setting out simple circular curves in surveying are broadly classified into linear methods (using chains/tapes only) and angular methods (using angle-measuring instruments like theodolites or tacheometers) ┬╖ The tacheometric method, Rankine's method of deflection angles, and the two-theodolite method all employ angular measurements to locate curve points.
╬┤nтАЛ=1718.9├ЧRCnтАЛтАЛ┬аminutes тАФ Deflection angle formula in Rankine's method (where CnтАЛ is chord length and R is radius of curve)
╬ФnтАЛ=тИС╬┤nтАЛ тАФ Total deflection angle to point n from the tangent line
Angular methods rely on measuring deflection angles, transit angles, or stadia intervals to fix the position of points on a curve ┬╖ In Rankine's method, points are located using tangential angles and chord lengths from a single theodolite station ┬╖ The two-theodolite method intersects line of sights from two instruments placed at the tangent points, eliminating the need for distance measuring tapes, while the tacheometric method determines both angular direction and distance optically using stadia hair readings.
Rankine's method uses a theodolite set at point of curve (T1тАЛ) and a steel tape to measure chords.
Two-theodolite method is completely optical and requires no chain or tape, making it ideal for rough or marshy terrain.
Tacheometric method relies on a tacheometer to determine both horizontal angles and staff distances simultaneously.
Higher precision compared to purely linear offset methods.
Suitable for setting out long curves with large radii.
Two-theodolite method allows curve setting across obstacles like rivers or ravines.
Requires specialized optical instruments (theodolites/tacheometers) and skilled labor.
Two-theodolite method requires clear intervisibility between both tangent points.
Setting out alignment curves for highways, railways, and canals.
Precision surveying where chaining errors need to be minimized.
Linear methods include: Offsets from Long Chord, Successive Bisection of Arcs, Offsets from Tangents, and Offsets from Chords Produced.
Since Tacheometric, Rankine's, and Two-Theodolite methods all involve horizontal angle measurements with optical instruments, Option D (All of the above) is the correct choice.
D is correct тАФ All three listed methods (Tacheometric, Rankine's, and Two-theodolite) utilize angular measurements to set out points on a curve.
For competitive exams like GATE and SSC JE, remember that the Two-Theodolite method requires NO linear measurement at all, whereas Rankine's method combines one angular measurement with linear chord chaining.