Rankine’s method – deflection angle per chord: According to Rankine’s method of tangential (deflection) angles, the deflection angle in minutes for a sub-chord is obtained by multiplying the chord length by which quantity?

Introduction / Context:
Setting out circular curves by Rankine’s method uses tangential (deflection) angles from the tangent. The convenient field rule links the size of each deflection to the chord length and the degree of curve, enabling quick computation without repeatedly using radius values.

Given Data / Assumptions:

• D = degree of curve (as per the adopted definition for the project).
• c = chosen chord length (sub-chord or full chord).
• Angles are handled in minutes for easy mental multiplication.

Concept / Approach:
For Rankine’s method, the tangential (deflection) angle to any chord is proportional to its length. Using the standard unit system, the deflection in minutes is obtained by multiplying the chord length by the degree of curve (with appropriate scaling if the degree is defined per a standard chord rather than an arc). This linear rule streamlines field computation and accommodates variable sub-chords near the curve ends.

Step-by-Step Solution:

Verification / Alternative check:
Derivations from R = K / D with K constant (based on the chosen definition) lead to linear chord–deflection relations, validating the field rule used in Rankine’s setting-out tables.

Why Other Options Are Wrong:

• Square or inverse relationships do not match the linear geometry of deflection with chord length for small angles in Rankine’s method.
• “None of these” ignores the accepted field rule.

Common Pitfalls:
Mixing definitions of D (per arc vs per chord); forgetting scaling when sub-chords differ from standard length; accumulating rounding errors without periodic checks.

Final Answer:
The degree of the curve