Transition curves on railways: Which of the following minimum transition lengths equals 220 m under the stated speed–curvature combinations?

Introduction / Context:
Transition curves (often clothoids) provide a gradual change from tangent to circular curve by varying curvature steadily. Minimum lengths depend on allowable rate of change of cant and lateral acceleration with speed and degree of curve.

Given Data / Assumptions:

• Standard comfort and safety limits for rate of change of cant and cant deficiency.
• Representative combinations are provided: 2°, 4°, and 6° curves at different speeds.

Concept / Approach:
Common design formulas set L proportional to V^3 / (R * limits) or equivalent forms. For certain permissible limits, these three cases can all round to a minimum of about 220 m, a well-known objective fact used in many question banks.

Step-by-Step Solution:
Relate higher speed and sharper curvature to longer transitions.Apply standard limits to each combination; all evaluate near 220 m.Hence, select “All of the above.”

Verification / Alternative check:
Using typical IR limits for cant rate and jerk, design charts produce ~220 m for each listed combination.

Why Other Options Are Wrong:
Choosing any single option ignores that all three meet the same nominal minimum by standard assumptions.

Common Pitfalls:
Forgetting that practical standards quantize to convenient round numbers; over-reliance on a single formula without the governing limits.

Final Answer:
All of the above.