Highway alignment – lemniscate transition curves: A lemniscate is considered not to remain transitional throughout if the deflection angle of the curve is greater than which value?

Introduction / Context:
Transition curves provide a gradual change of curvature from a tangent (infinite radius) to a circular arc (finite radius), improving comfort and safety. Lemniscate curves are a family of spirals used where large deflection angles are involved. The question checks the commonly cited limit beyond which a lemniscate does not remain transitional throughout its length.

Given Data / Assumptions:

• Transition curve purpose: vary curvature progressively to avoid sudden lateral acceleration.
• Lemniscate properties are used for large deflection angles but are bounded by practical geometry.
• “Transitional throughout” means the entire curve maintains the desired monotonic curvature change.

Concept / Approach:
Standard references note that lemniscates behave as desirable transition spirals up to about a right angle of total deflection. Beyond this, the curvature progression or practical setting out may cease to meet the continuous transition requirement for the entire extent, and composite solutions are adopted. Thus, the threshold value used in classical design problems is 90°.

Step-by-Step Solution:

Verification / Alternative check:
Design literature often contrasts lemniscates with clothoids; while clothoids can be extended, lemniscates are quoted with practical deflection limits to preserve the transitional property throughout.

Why Other Options Are Wrong:

• 45° and 60°: overly conservative; lemniscates remain transitional within these smaller angles.
• 120° and 180°: too high; beyond 90° the entire curve may not satisfy a single transition spiral behavior.

Common Pitfalls:
Assuming all transition curves are interchangeable without limits; ignoring vehicle dynamics and sight distance which also govern feasible deflection management.

Final Answer:
90°