Length of Valley Curve Greater than Stopping Sight Distance Calculator

Length of Curve Formula:

\[ L_s = \frac{N \times S^2}{2h_1 + 2S \times \tan(\alpha)} \]

Deviation Angle (N):

rad

Sight Distance (S):

Driver Sight Height (h₁):

Inclination (α):

rad

Tolerance:

Length of Curve (Lₛ): m

1. What is Length of Valley Curve Greater than Stopping Sight Distance?

Definition: This calculator determines the minimum length of a valley curve required to ensure adequate stopping sight distance for drivers.

Purpose: It helps highway engineers design safe vertical curves that provide sufficient visibility for drivers to stop safely.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_s = \frac{N \times S^2}{2h_1 + 2S \times \tan(\alpha)} \]

Where:

\( L_s \) — Length of curve (meters)
\( N \) — Deviation angle (radians)
\( S \) — Sight distance (meters)
\( h_1 \) — Driver's eye height (meters, typically 0.75m)
\( \alpha \) — Inclination angle (radians)

Explanation: The formula calculates the minimum curve length needed to ensure the sight distance S is available throughout the curve.

3. Importance of Valley Curve Length Calculation

Details: Proper valley curve design prevents "headlight sight distance" issues at night and ensures safe stopping distances are maintained.

4. Using the Calculator

Tips: Enter the deviation angle (N), sight distance (S), driver eye height (h₁, default 0.75m), and inclination angle (α, default 0.03 rad). The optional tolerance field allows for design margin (±5% typical).

5. Frequently Asked Questions (FAQ)

Q1: What's a typical driver eye height?
A: For passenger cars, 0.75m is standard. For trucks, use 1.05-1.20m depending on vehicle type.

Q2: How is deviation angle determined?
A: It's the algebraic difference between the incoming and outgoing grades (in radians).

Q3: Why include a tolerance factor?
A: The ±5% tolerance accounts for construction variations and provides a safety margin.

Q4: What's a typical inclination angle?
A: For most highways, 0.03 radians (≈1.72°) is common, but this varies by design speed.

Q5: How does sight distance affect the calculation?
A: Longer sight distances require proportionally longer curves to maintain visibility.