Length of Valley Curve given Time and Design Speed Calculator

Length of Curve Formula:

\[ Ls = v \times t \]

Length of Curve (m):

1. What is Length of Valley Curve?

Definition: Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave.

Purpose: It helps transportation engineers design safe and comfortable vertical curves in roadways.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Ls = v \times t \]

Where:

\( Ls \) — Length of Curve (meters)
\( v \) — Design Speed (meters/second)
\( t \) — Time (seconds)

Explanation: The length of the valley curve is calculated by multiplying the design speed by the time it takes for a vehicle to traverse the curve.

3. Importance of Valley Curve Calculation

Details: Proper calculation ensures safe transitions between grades, adequate sight distance, and comfortable ride quality for vehicles.

4. Using the Calculator

Tips: Enter the design speed in m/s (±5%) and time in seconds (±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is design speed important for valley curves?
A: Design speed determines the required length to ensure driver comfort and safety during the vertical transition.

Q2: What factors affect the time component?
A: Time depends on the rate of change of acceleration that's comfortable for passengers and safe for vehicles.

Q3: How does this differ from crest vertical curves?
A: Valley curves consider headlight sight distance at night, while crest curves consider daylight sight distance.

Q4: What's a typical design speed for highways?
A: Design speeds typically range from 50-130 km/h (14-36 m/s) depending on road type and location.

Q5: Should I include a safety factor?
A: Yes, it's recommended to add a safety margin beyond the calculated minimum length.