Compound vs. reverse curves: If two curves have the same radius, how does the length of the common tangent compare between a compound curve and a reverse curve?

Introduction / Context:
Understanding curve combinations is essential for geometric design, vehicle maneuvering, and safety. Compound and reverse curves behave differently in terms of tangency and steering demand.

Given Data / Assumptions:

• Two curves considered have equal radii.
• Definitions: compound curve = same turning direction, arcs meeting at a common tangent point; reverse curve = opposite turning directions separated by a tangent between arcs.

Concept / Approach:
In a compound curve, the arcs meet at a common point without any finite tangent length between them; effectively, the intervening tangent length is zero. In a reverse curve, a nonzero tangent is required between the oppositely curving arcs to allow a change in curvature sign and feasible vehicle path.

Step-by-Step Solution:
Identify that a compound curve has zero intervening tangent by definition.Recognize that a reverse curve requires a finite common tangent between opposing curves.Therefore, for equal radii, the reverse curve has the longer common tangent.

Verification / Alternative check:
Typical geometric diagrams show back-to-back arcs for compound curves, versus arcs separated by tangent for reverse curves, confirming the conclusion.

Why Other Options Are Wrong:

• Compound curve more/equal: contradicts definitions.
• None: terminology provides clear comparison.

Common Pitfalls:

• Confusing broken-back layouts with compound curves.
• Ignoring the operational disadvantage of short tangents in reverse curves at high speed.

Final Answer:
Common tangent of the reverse curve will be more