Transition curve basics – how radius varies along the length For a highway transition curve connecting a tangent to a circular curve, how does the radius of curvature vary along the transition portion?

Introduction / Context:
Transition curves provide a gradual change in curvature, allowing a comfortable shift of centrifugal acceleration and superelevation from tangent to circular curve. Understanding the curvature progression is essential for setting out spirals and computing run-off lengths.

Given Data / Assumptions:

• A standard highway transition (e.g., spiral or cubic parabola) connects tangent and circular arc.
• Vehicle speed and lateral acceleration change smoothly along the transition.

Concept / Approach:
Curvature k is the reciprocal of radius R. On a tangent, k = 0 (R = infinity). At the entry to the main circular arc, k = 1/Rc (Rc = circular-curve radius). A proper transition increases curvature progressively from 0 to 1/Rc over the transition length.

Step-by-Step Solution:
At the start of transition: R → infinity (k = 0).Along the length: curvature increases smoothly (R decreases).At the end (junction with circular curve): R = Rc.Therefore, radius varies from infinity to the circular-curve radius.

Verification / Alternative check:
Standard formulas for spiral length include rate of change of centrifugal acceleration proportional to distance, consistent with curvature rising linearly from 0 to 1/Rc.

Why Other Options Are Wrong:
Constant radius describes only the circular portion; “minimum at the beginning” reverses the physical reality; equality to Rc throughout contradicts the definition of a transition.

Common Pitfalls:
Confusing transition with the main circular curve; neglecting to coordinate superelevation runoff with curvature change.

Final Answer:
varying from infinity to the radius of the circular curve