Length of Valley Curve Less than Stopping Sight Distance Calculator

Length of Curve Formula:

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

Sight Distance (S):

Driver Sight Height (h₁):

Inclination (α):

Deviation Angle (N):

Length of Curve (Lₛ): m

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

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

Purpose: It helps highway engineers design safe vertical curves that allow drivers to see far enough to stop safely.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( L_s \) — Length of curve (meters)
\( S \) — Sight distance (meters)
\( h_1 \) — Driver's eye height (meters, default 0.75m)
\( \alpha \) — Inclination angle (degrees)
\( N \) — Deviation angle (±5%)

Explanation: The formula accounts for driver eye height, road inclination, and the deviation angle to calculate the safe curve length.

3. Importance of Valley Curve Calculation

Details: Proper valley curve design prevents accidents by ensuring drivers have sufficient visibility to stop for obstacles.

4. Using the Calculator

Tips: Enter sight distance (S), driver eye height (default 0.75m), inclination angle (degrees), and deviation angle (default 0.88 for ±5% grade).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical driver eye height?
A: The standard is 0.75m (2.5ft) for passenger vehicles, but may be higher for trucks.

Q2: How is inclination angle measured?
A: It's the angle between the road surface and horizontal plane, entered in degrees.

Q3: What does the deviation angle represent?
A: It accounts for the algebraic difference in grades (±5% in this case).

Q4: When is this formula applicable?
A: For valley curves where the length is less than the stopping sight distance.

Q5: How does this differ from crest curve calculation?
A: Crest curves have different sight distance considerations as they deal with visibility over a hill rather than into a valley.