Transition curves — why are transition (spiral) curves provided at the ends of a circular curve in highway/rail alignment? Choose the most correct objective.

Introduction / Context:
Vehicles cannot safely jump from a straight tangent (zero curvature) to a full circular curve at once. Transition curves (such as clothoids/spirals) smooth this change by gradually introducing curvature and the associated super-elevation, enhancing comfort and safety and reducing lateral jerk.

Given Data / Assumptions:

• Plan (horizontal) curve design is considered.
• Super-elevation is applied progressively along the transition.
• Vertical gradient changes are handled by separate vertical curves.

Concept / Approach:
A proper transition curve ensures curvature varies linearly with length so that lateral acceleration and its rate of change (jerk) are controlled. At the same time, the roadway crossfall is rotated gradually to the required super-elevation. Vertical gradient transitions are unrelated and are designed with parabolic vertical curves, not with horizontal transitions.

Step-by-Step Solution:

Verification / Alternative check:
Design manuals specify transition length based on speed, design radius, comfort jerk limits, and super-elevation runoff, confirming the dual role.

Why Other Options Are Wrong:

• (a) alone omits the essential super-elevation runoff.
• (b) alone omits the curvature ramp.
• (c) confuses horizontal transitions with vertical curves.
• (d) is incorrect because (a)+(b) is the correct purpose.

Common Pitfalls:
Mixing vertical and horizontal design elements; forgetting that comfort depends on controlling jerk as curvature changes.

Final Answer:
Both (a) and (b)