Transition Curve Length from Rate of Gain of Radial Acceleration A horizontal circular curve has deflection angle 55° and radius R = 250 m. Provide a transition curve at each end such that the rate of gain of radial acceleration C is 0.3 m/s^3 at design speed v = 50 km/h. What is the required transition length L (per end)?

Introduction / Context:Transition (spiral) curves are designed so that curvature increases linearly with length, which makes the lateral acceleration build-up smooth. A key comfort/safety criterion is limiting the rate of gain of radial acceleration, C, at the design speed. This directly determines the required transition length for a given radius and speed.

Given Data / Assumptions:

• Curve radius R = 250 m.
• Design speed v = 50 km/h.
• Allowable rate of gain of radial acceleration C = 0.3 m/s^3.
• Standard spiral where curvature varies linearly with chainage.

Concept / Approach:

For a spiral, the relation between C, v, R, and L is C = v^3 / (R * L), with v in m/s. Rearranging gives L = v^3 / (C * R). Convert v from km/h to m/s before computation.

Step-by-Step Solution:

Verification / Alternative check:

Using standard design charts for similar R, v, and C yields nearly the same value, confirming the computation. Note that the deflection angle affects the central circular arc length but not the transition length from the C-based criterion.

Why Other Options Are Wrong:

• 2.57 m and 33.33 m: Too short to limit C at the given speed.
• 1666.67 m: Unrealistically long and inconsistent with the formula.

Common Pitfalls:

Forgetting to convert km/h to m/s; using e + f formulas instead of the C-based comfort criterion; applying the total two-ended length instead of per-end length.

Final Answer:

35.73 m