A curve whose radius varies from infinity to a certain value is called...
Try it first: pick an option, then read the explanation.
Detailed Explanation: Defining Curve Types by Radius Behaviour
Different curve types used in highway and railway alignment are most fundamentally distinguished by how their radius behaves along the curve's length. This question tests the defining characteristic of the transition curve specifically.
Fig: A transition curve's radius decreases smoothly from infinity (matching the straight) down to the circular curve's fixed radius R.
Why this defines a transition curve:A straight line can be thought of as having an infinite radius of curvature. A transition curve is specifically designed so its radius starts at infinity (matching the preceding straight tangent seamlessly) and gradually decreases, reaching the fixed radius R of the circular curve exactly at the point where the two curves meet. This gradually varying radius is precisely what allows a smooth, comfortable transition of centrifugal force (Q16) and super-elevation, avoiding any sudden change in curvature.
Curve Type Comparison
| Curve type | Radius behaviour |
|---|---|
| Transition curve | Varies continuously from infinity to a fixed value R |
| Circular curve | Constant radius throughout |
| Compound curve | Two or more circular arcs of different (but each individually constant) radii, joined consecutively in the same direction |
| Reverse curve | Two circular arcs of constant radii curving in opposite directions, joined at a common tangent point |
Why the Other Options Are Wrong
A — Compound curve: Each component arc of a compound curve has its own constant radius — the radius does not continuously vary within any single arc, unlike the transition curve.
B — Circular curve: By definition, a circular curve has a single, constant radius along its entire length — the opposite of the continuously varying radius described in the question.
C — Reverse curve: Composed of two constant-radius circular arcs curving in opposite directions — again, no continuously varying radius within either arc.
Key Concepts for Students
- "Radius varies from infinity to R" is the defining signature of a transition curve: Whenever a question describes a continuously changing radius (rather than one or more constant-radius arcs), the answer is always transition curve.
- Mathematical forms of transition curves: Common geometric forms include the cubic parabola, the clothoid (Euler/Cornu spiral), and the lemniscate — all share this same infinity-to-R radius variation property, differing only in their precise mathematical curve equation.
- Compound and reverse curves are both built from constant-radius arcs: Don't confuse these "combination of circular arcs" curve types with the transition curve's smoothly varying radius — the key distinguishing question is always "does the radius change continuously within a single curve segment, or only between separate constant-radius segments?"