Highway and railway alignment – identifying an S-shaped transition In geometric design and surveying terminology, the curve composed of two circular arcs of different radii whose centers lie on opposite sides of the curve (producing an S-shaped path) is known as:

Introduction / Context:
A designer often needs to connect two tangents that deflect in opposite senses, for example when a road or railway alignment bends first to the left and then to the right. Surveying terminology distinguishes between several multi-arc combinations. This item tests your ability to recognize the specific case where two arcs have different radii and their centers are on opposite sides of the path, producing an S-shaped transition commonly used in constrained corridors.

Given Data / Assumptions:

• Two circular arcs are used in succession.
• The radii are different (R1 ≠ R2).
• The centers of curvature are on opposite sides of the curve, implying opposite senses of curvature.
• Plan view geometry is considered; not a vertical profile issue.

Concept / Approach:

Curve classification in plan is based on the relative position of arc centers and curvature direction. If centers are on the same side, the combination is called a compound curve. If they are on opposite sides, the path reverses curvature, creating an S-shape, and is called a reverse curve (also termed a serpentine curve). Simple curves contain only one constant-radius arc, and vertical curves pertain to profiles rather than planimetric alignment.

Step-by-Step Solution:

Verification / Alternative check:

Highway and railway manuals define compound curves as successive arcs curving the same way (centers on the same side), and reverse curves as arcs curving in opposite directions (centers on opposite sides). The problem statement clearly matches the latter definition.

Why Other Options Are Wrong:

Simple curve: only one arc; does not reverse curvature.

Compound curve: centers on the same side; same curvature sense.

Vertical curve: concerns grade changes in profile, not plan direction changes.

Common Pitfalls:

Confusing compound with reverse because both may use two arcs; forgetting that “opposite sides” of centers is the key distinguishing feature.

Final Answer:

A reverse curve