Night visibility and valley-curve design checks: Select the correct statements used in headlight-sight-distance considerations for valley curves on highways.

Introduction / Context:
At night, the safety on valley curves is checked using the headlight sight distance concept. The geometry must ensure that the illuminated beam can reveal an obstacle in time for a driver to react and stop. This check uses standardized assumptions about headlight mounting height, beam angle, and object height.

Given Data / Assumptions:

• Headlight height above road surface ≈ 0.75 m.
• Beam angle ≈ 1 degree above the grade line.
• Object height for nighttime visibility on valley curves ≈ 0 m (lying object).

Concept / Approach:

In a valley curve, the vehicle dips; the headlight beam may overshoot if the curve is too sharp. Using a standard headlight height and small upward beam angle, the length of curve must be sufficient so the beam hits the road surface far enough ahead to provide the required stopping sight distance. Assuming object height zero is conservative for safety.

Step-by-Step Solution:

Verification / Alternative check:

These assumptions are widely used in highway design manuals to simplify a complex light-geometry problem while maintaining conservative safety margins.

Why Other Options Are Wrong:

• Any single statement alone is incomplete; all three together describe the standard headlight criterion.
• “None of these” contradicts established practice.

Common Pitfalls:

• Using object height 0.15 m (daytime summit-curve check) instead of 0 m for valley curves at night.

Final Answer:

All the above.