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If the value of length of the chord is given as 5.236 m and the radius of the curve as 100m, find the tangential angle using Rankine’s method.
A) 120°
B) 1°30′
C) 130′
D) 1°20′
1°30′
Rankine's method (method of tangential angles) is used to set out circular curves using a transit theodolite and a tape. The tangential angle for any chord is given by the formula δ=1718.9×RC minutes, where C is the length of the chord and R is the radius of the curve. Substituting C=5.236 m and R=100 m gives δ=90′=1°30′, making Option B the correct answer.
Rankine's method (method of tangential angles) is used to set out circular curves using a transit theodolite and a tape. The tangential angle for any chord is given by the formula δ=1718.9×RC minutes, where C is the length of the chord and R is the radius of the curve. Substituting C=5.236 m and R=100 m gives δ=90′=1°30′, making Option B the correct answer.
δ=1718.9×RC minutes — Tangential angle for a chord of length C and radius R
Δn=∑i=1nδi — Total deflection angle for point n
In Rankine's deflection angle method, the deflection angle to any point on the curve is equal to half the angle subtended by the arc at the center. For small chord lengths, the arc length is approximated by the chord length C. The tangential angle δ in minutes is derived from the relation \delta = \frac{C}{2R} \times \frac{180°{\pi} \times 60' \approx 1718.873 \times \frac{C}{R} minutes.
Rankine's method is suitable for setting out simple circular curves when the curve is long and high precision is required.
The total deflection angle to any point on the curve is equal to the sum of the tangential angles of all preceding sub-chords.
The chord length C and radius R must be measured in the same units (meters).
Highly accurate and suitable for long circular curves in field surveying.
Linear measurements are made with a tape while angular measurements are taken with a theodolite.
Slower compared to offset methods due to continuous sight setting and transit usage.
Accumulation of errors can occur if individual chord measurements or tangential angle settings are inaccurate.
Setting out circular curves for highways and railway track alignments.
Precision alignment where offset methods are impractical due to terrain obstacles.
Calculation: δ=1718.9×1005.236=89.999... minutes≈90′=1°30′.
Option A (120°) represents an incorrect large degree conversion.
Option C (130ˈ) uses an incorrect arithmetic evaluation of 1718.9×0.05236.
Option D (1° 20ˈ) corresponds to 80′ which is a computational error.
B is correct — Using Rankine's formula δ=1718.9×1005.236=90′, which equals 1°30′.
Remember that 1°=60′. In competitive exams, questions on Rankine's method frequently expect the result in degrees and minutes, so always divide the calculated minutes by 60 to convert to degrees.