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

Inclination Angle Formula:

\[ \alpha = \arctan\left(\frac{N \cdot S^2 - 2 \cdot h_1}{2 \cdot S \cdot L_s}\right) \]

Deviation Angle (N):

Sight Distance (S):

Driver Sight Height (h₁):

Length of Curve (Lₛ):

Inclination Angle (α):

1. What is Inclination Angle for Valley Curve?

Definition: This calculator determines the inclination angle (α) for valley curves where the length is greater than the 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:

\[ \alpha = \arctan\left(\frac{N \cdot S^2 - 2 \cdot h_1}{2 \cdot S \cdot L_s}\right) \]

Where:

\( \alpha \) — Inclination angle (degrees)
\( N \) — Deviation angle (percentage)
\( S \) — Sight distance (meters)
\( h_1 \) — Driver sight height (meters)
\( L_s \) — Length of curve (meters)

Explanation: The formula calculates the angle needed to ensure proper visibility along a valley curve.

3. Importance of Inclination Angle Calculation

Details: Proper inclination angle ensures safe stopping sight distance, preventing accidents on vertical curves.

4. Using the Calculator

Tips: Enter the deviation angle (%), sight distance (m), driver sight height (m), and length of curve (m). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical deviation angle?
A: Deviation angles typically range from ±1% to ±10% depending on road design standards.

Q2: What's the standard driver sight height?
A: Most designs use 1.05-1.15 meters for passenger vehicles (eye height of average driver).

Q3: Why is this specific to valley curves?
A: Valley curves have different visibility requirements than crest curves due to their concave shape.

Q4: How does sight distance affect the result?
A: Longer sight distances typically require gentler inclination angles for safety.

Q5: What if my curve length is less than stopping sight distance?
A: A different formula applies - use our "Short Valley Curve" calculator instead.