Deviation Angle Given Length of Valley Curve Less than Stopping Sight Distance Calculator

Deviation Angle Formula:

\[ N = \frac{2S - (2h1 + 2S \cdot \tan(\alpha))}{L_s} \]

Sight Distance (S):

Driver Sight Height (h1):

Inclination (α):

Length of Curve (L_s):

Tolerance:

Deviation Angle (N):

1. What is Deviation Angle in Valley Curves?

Definition: The deviation angle (N) is the angle that accounts for the difference between the line of sight and the road alignment on valley curves with limited stopping sight distance.

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N = \frac{2S - (2h1 + 2S \cdot \tan(\alpha))}{L_s} \]

Where:

\( N \) — Deviation angle (dimensionless)
\( S \) — Sight distance (meters)
\( h1 \) — Driver's eye height (meters)
\( \alpha \) — Inclination angle (degrees)
\( L_s \) — Length of curve (meters)

Explanation: The formula calculates how much the line of sight deviates from the road alignment based on sight distance, driver height, road inclination, and curve length.

3. Importance of Deviation Angle Calculation

Details: Proper calculation ensures that valley curves are designed with sufficient visibility to allow drivers to see upcoming road conditions and stop safely if needed.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a typical driver eye height?
A: Standard driver eye height is 0.75m for passenger cars, but may be higher for trucks (1.05-1.20m).

Q2: Why include a tolerance percentage?
A: The tolerance accounts for variations in vehicle types, driver characteristics, and measurement inaccuracies.

Q3: What's a reasonable inclination angle for roads?
A: Most roads have grades between -6% (downhill) to +6% (uphill), with steeper grades in mountainous areas.

Q4: How does curve length affect the deviation angle?
A: Longer curves generally result in smaller deviation angles, improving visibility and safety.

Q5: When is this calculation most critical?
A: This is especially important for sag vertical curves at night, where headlight illumination distance may be limited.