Rankine’s Method – Deflection Angle for Normal Chord on a 100 m Radius Curve For a simple circular curve of radius R = 100 m and a normal chord length c = 10 m, what is the Rankine’s deflection angle (to the chord) from the tangent point?

Introduction:
In the theodolite method of setting out curves, Rankine’s formula gives the deflection angle corresponding to a given chord length on a curve of known radius. Accurate computation of these angles is essential for pegging points precisely along the alignment.

Given Data / Assumptions:

• Radius R = 100 m.
• Normal chord c = 10 m.
• Deflection angle δ (in minutes) is given approximately by δ = 1718.9 * c / R.

Concept / Approach:

Apply Rankine’s formula to obtain the deflection to the end of the first chord from the tangent. Convert minutes to degrees and minutes for comparison with options. Ensure rounding matches practical field tabulations.

Step-by-Step Solution:

Verification / Alternative check:

Using a rounded constant 1720 yields 172.0 minutes → 2°52', which is consistent with the selected option to typical field precision.

Why Other Options Are Wrong:

Smaller angles (e.g., about 0.3° or 1.4°) correspond to much longer radii or shorter chords and do not fit R = 100 m with c = 10 m.

Common Pitfalls:

Mixing radians and degrees; forgetting that the formula gives minutes, requiring conversion to degrees and minutes.

Final Answer:

2°51'.53