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

Inclination Angle Formula:

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

Length of Curve (L_s):

Sight Distance (S):

Deviation Angle (N):

Driver Sight Height (h₁):

Inclination Angle (radians):

Inclination Angle (degrees):

1. What is Inclination Angle given Length of Valley Curve?

Definition: This calculator determines the inclination angle when the length of a valley curve is less than the stopping sight distance.

Purpose: It helps transportation engineers design safe vertical curves on roads where visibility is limited.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \alpha \) — Inclination angle (radians or degrees)
\( L_s \) — Length of the curve (meters)
\( S \) — Sight distance (meters)
\( N \) — Deviation angle (±5%)
\( h_1 \) — Driver's eye height (meters)

Explanation: The formula calculates the angle based on the geometric relationship between the curve length, sight distance, deviation angle, and driver's eye height.

3. Importance of Inclination Angle Calculation

Details: Proper calculation ensures safe road design with adequate visibility for drivers approaching or on vertical curves.

4. Using the Calculator

Tips: Enter the curve length, sight distance, deviation angle (±5%), and driver's eye height. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a valley curve?
A: A valley curve is a concave vertical curve on a road where the alignment changes from downward to upward slope.

Q2: Why is sight distance important?
A: Sight distance ensures drivers can see far enough to stop or maneuver safely when encountering obstacles.

Q3: What's a typical driver eye height?
A: Standard design uses 1.08 meters (3.5 ft) for passenger cars and 2.33 meters (7.6 ft) for trucks.

Q4: How does deviation angle affect the calculation?
A: The deviation angle (typically ±5%) accounts for the grade change at the curve.

Q5: When is this formula applicable?
A: This formula applies when the curve length is less than the stopping sight distance.