Length of Valley Curve for Head Light Sight Distance when Length is less than SSD Calculator

Valley Curve Length Formula:

\[ LV_c = 2 \times SSD - \left( \frac{2 \times h_1 + 2 \times SSD \times \tan(\alpha)}{N} \right) \]

Stopping Sight Distance (SSD):

Average Head Light Height:

Beam Angle:

rad

Deviation Angle:

Length of Valley Curve (LV_c): m

1. What is Length of Valley Curve for Head Light Sight Distance?

Definition: This calculator determines the minimum length of a valley curve when the length is less than the stopping sight distance, considering headlight illumination.

Purpose: It helps highway engineers design safe vertical curves that provide adequate nighttime visibility for drivers.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ LV_c = 2 \times SSD - \left( \frac{2 \times h_1 + 2 \times SSD \times \tan(\alpha)}{N} \right) \]

Where:

\( LV_c \) — Length of valley curve (meters)
\( SSD \) — Stopping sight distance (meters)
\( h_1 \) — Average head light height (meters, typically 0.75m)
\( \alpha \) — Beam angle (radians)
\( N \) — Deviation angle (with ±5% variation)

Explanation: The formula accounts for headlight illumination distance and the driver's ability to see obstacles at night.

3. Importance of Valley Curve Calculation

Details: Proper valley curve design ensures safe nighttime driving conditions by providing adequate visibility of the road ahead.

4. Using the Calculator

Tips: Enter the stopping sight distance, average headlight height (default 0.75m), beam angle (default 0.0367 rad), and deviation angle (default 0.08 ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical headlight height used in calculations?
A: Most calculations use 0.75 meters as the average headlight height for passenger vehicles.

Q2: How is the beam angle determined?
A: The beam angle is typically about 1 degree (0.0175 rad) for low beams and 2.1 degrees (0.0367 rad) for high beams.

Q3: What does the deviation angle represent?
A: The deviation angle is the algebraic difference in grades, with a typical ±5% variation in vertical curve design.

Q4: When is this formula applicable?
A: This formula is used when the length of the valley curve is less than the stopping sight distance (L < SSD).

Q5: How does this differ from crest vertical curve calculations?
A: Valley curves consider headlight illumination, while crest curves consider daylight visibility over the curve.