Transition Curve (Cubic Parabola) – Maximum Perpendicular Offset from the Tangent A transition curve of length L = 90 m is inserted between a straight and a circular curve of radius R = 500 m. For a standard cubic parabola transition, what is the maximum perpendicular offset (shift) from the tangent due to the transition curve?

Introduction / Context:
Transition curves provide gradual change from zero curvature on the tangent to the full curvature of a circular arc, improving riding comfort and safety for highways and railways. Designers commonly use the cubic parabola, for which several handy formulas exist. One such quantity is the maximum perpendicular offset (also called shift) produced by the transition relative to the original tangent alignment.

Given Data / Assumptions:

• Transition type: cubic parabola connecting tangent to a circular arc.
• Length of transition L = 90 m.
• Circular radius R = 500 m.
• Standard formula for shift (maximum perpendicular offset) applies.

Concept / Approach:

For a cubic parabola transition, the shift S (maximum perpendicular offset from the tangent to accommodate the transition) is given by the widely used relation S = L^2 / (24 * R). This small lateral movement of the circular curve ensures a smooth curvature ramp while preserving the external geometry. It is independent of speed but depends on L and R.

Step-by-Step Solution:

Verification / Alternative check:

Cross-check order of magnitude: for L/R ≈ 0.18, a sub-metre shift is expected. If L doubled, shift grows with L^2, highlighting sensitivity to transition length selection.

Why Other Options Are Wrong:

1.70 m, 2.70 m, 3.70 m, and 4.70 m exceed the computed shift by large margins and would correspond to much longer transitions or much smaller radii, inconsistent with the data.

Common Pitfalls:

Confusing shift with mid-ordinate of the circular curve or with the offset y at a partial length; applying a wrong constant (e.g., 6 or 12 instead of 24) in the denominator leads to significant overestimation.

Final Answer:

0.70 m