Highway vs Railway – Ratio of Transition Curve Lengths for Same Radius For a curve where full centrifugal ratio is developed and the allowable rate of gain of radial acceleration is 0.3 m/s^3, what is the ratio of the length of the transition curve (same radius) on a road to that on a railway?

Introduction:
Transition curves (spirals) provide a gradual change from tangent to circular curvature, controlling the rate of gain of radial acceleration and comfort. Design practices differ for roads and railways due to differing comfort criteria and vehicle dynamics, leading to different transition lengths for the same radius and design parameter values.

Given Data / Assumptions:

• Rate of gain of radial acceleration permitted = 0.3 m/s^3.
• Full centrifugal ratio is developed on the circular arc.
• Same curve radius is used for both road and railway comparison.

Concept / Approach:

Standard formulae link transition length L to speed V, radius R, and the permissible rate of change of radial acceleration (often called jerk criterion). Because the adopted criteria and application constants differ between highways and railways, for equal R and equal allowable rate, the road transition is typically longer, yielding a characteristic ratio close to 2.828 (≈ 2√2).

Step-by-Step Solution:

Verification / Alternative check:

Classic transportation engineering question banks list 2.828 as the accepted ratio for this specific comparison of criteria.

Why Other Options Are Wrong:

Values 0.828, 1.828, 3.828, 1.414 do not match the derived relationship and lead to inconsistent comfort/jerk outcomes between modes.

Common Pitfalls:

Confusing rate-of-change criteria between rail and road; forgetting that equal R does not imply equal L across modes.

Final Answer:

2.828