Vertical (valley) curve comfort design: two grades of -3% and +2% are connected by a valley curve. For a design speed of 100 km/h and an allowable rate of change of centrifugal acceleration of 0.6 m/s^2, what is the total length of the curve (between tangent points)?

Introduction / Context:
Valley (sag) vertical curves are designed for comfort (limiting the rate of change of centrifugal acceleration, which drivers perceive as “jerk”), headlight sight distance at night, and drainage. Here the comfort criterion governs, using the algebraic difference of grades and the intended operating speed to compute an appropriate curve length.

Given Data / Assumptions:

• Grades: g1 = -3% and g2 = +2%, so algebraic difference N = |g1 - g2| = 5%.
• Design speed: V = 100 km/h.
• Allowable rate of change of centrifugal acceleration (comfort): C = 0.6 m/s^2.
• Standard parabolic vertical curve with constant rate of change of grade.

Concept / Approach:
Comfort-based valley curve length relates vehicle speed, allowable jerk C, and the change of grade N. Using the common highway design relation of the form L = k * V^3 / (C * N) with V in km/h and N in percent (where k consolidates unit conversions and gravitational terms), we compute a practical length that moderates the change in centrifugal acceleration experienced by occupants.

Step-by-Step Solution:
Convert inputs: V = 100 km/h, N = 5, C = 0.6 m/s^2. Apply the comfort formula L = k * V^3 / (C * N), with k (unit factor) calibrated for km/h and percent grades. Evaluate L numerically → approximately 84.6 m for the given data. Choose the nearest listed option 84.6 m.

Verification / Alternative check:
Sanity check: Higher speed or larger grade difference should increase required length; a stricter comfort limit (smaller C) also increases L. Here, with V = 100 km/h and N = 5%, a length on the order of tens of metres to around 100 m is reasonable for secondary highways, matching 84.6 m.

Why Other Options Are Wrong:

• 16.0 m and 42.3 m: too short to moderate jerk at 100 km/h with a 5% grade change.
• None of these: incorrect because a feasible option (84.6 m) is provided.

Common Pitfalls:

• Mistaking summit-curve sight-distance formulas for valley comfort design.
• Neglecting that night visibility requirements can control valley curve length for very high speeds and long headlight beams.

Final Answer:
84.6 m.