Deviation Angle given Length of Valley Curve Greater than Stopping Sight Distance Calculator

Deviation Angle Formula:

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

Length of Curve (L_s):

Driver Sight Height (h₁):

Sight Distance (S):

Inclination (α):

Tolerance:

Deviation Angle (N):

1. What is Deviation Angle in Valley Curves?

Definition: The deviation angle (N) is the angle that accounts for the vertical alignment change in valley curves to ensure proper stopping sight distance.

Purpose: It helps highway engineers design safe vertical curves where the length is greater than the stopping sight distance requirement.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the required deviation angle to maintain visibility along a valley curve.

3. Importance of Deviation Angle Calculation

Details: Proper calculation ensures drivers have adequate stopping sight distance when approaching a valley curve, preventing accidents.

4. Using the Calculator

Tips: Enter the curve length, driver eye height (default 0.75m), sight distance, inclination angle (default 2°), and tolerance (default ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the typical driver eye height?
A: Standard is 0.75m (750mm) for passenger vehicles, but may vary for trucks (up to 2.4m).

Q2: Why include a tolerance value?
A: The ±5% tolerance accounts for variations in vehicle types, road conditions, and driver behavior.

Q3: When is this formula applicable?
A: Only when the curve length (L_s) is greater than the stopping sight distance (S).

Q4: What's a typical inclination angle?
A: Usually between 1-3 degrees for highway design, with 2° being a common default.

Q5: How does this differ from crest curves?
A: Valley curves consider headlight illumination at night, while crest curves consider daytime visibility.