Compound horizontal curve design: the minimum desirable ratio of the radii of the two constituent circular arcs (R1/R2) is generally kept at or above which value to ensure a smooth transition?

Introduction / Context:
Compound curves—two or more circular arcs of different radii joined tangentially—are used when geometric constraints prevent a single-radius curve. To preserve driver comfort and avoid abrupt changes in curvature, the radii should not differ too much; a commonly adopted minimum ratio helps maintain a gentle curvature progression.

Given Data / Assumptions:

• Two adjacent circular arcs with radii R1 and R2.
• Requirement: minimum ratio R1/R2 for desirable operation and aesthetics.

Concept / Approach:
A very small inner radius paired with a much larger outer radius causes sudden curvature change at the junction, which impairs comfort and may challenge superelevation transitions. A rule of thumb is to maintain R1/R2 ≥ 1.5 so that curvature increases or decreases moderately across the junction, allowing consistent steering and superelevation/runoff within limited lengths.

Step-by-Step Solution:
Define curvature change between adjacent arcs. Apply the recommended practice: R1/R2 not less than about 1.5. Choose 1.5 as the minimum ratio from the options provided.

Verification / Alternative check:
Design guides often permit a range but discourage ratios below 1.5 because they create a near “kink” in curvature even if tangency is satisfied, undermining comfort and drainage transitions.

Why Other Options Are Wrong:

• 1.25: Too small; curvature change remains abrupt.
• 1.75 or 2.0+: Acceptable but more restrictive than the common minimum; not “minimum”.

Common Pitfalls:

• Using compound arcs without adequate transition lengths or superelevation runoff, especially on high-speed facilities.

Final Answer:
1.5.