Length of Valley Curve Calculator

Length of Valley Curve Formula:

\[ L_s = \frac{v^3}{R \times C_a} \]

Design Speed:

m/s

Radius of Curve:

Rate of Change of Acceleration:

m/s²

Tolerance:

Length of Curve (m):

1. What is Length of Valley Curve?

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

Purpose: Proper calculation ensures smooth transitions between grades, preventing discomfort to passengers and maintaining vehicle safety.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_s = \frac{v^3}{R \times C_a} \]

Where:

\( L_s \) — Length of valley curve (meters)
\( v \) — Design speed (meters/second)
\( R \) — Radius of curve (meters)
\( C_a \) — Rate of change of acceleration (m/s²)

Explanation: The formula calculates the minimum length required for a comfortable transition between grades based on vehicle dynamics.

3. Importance of Valley Curve Calculation

Details: Proper valley curve length prevents sudden changes in vertical acceleration that could cause discomfort or safety issues.

4. Using the Calculator

Tips: Enter the design speed, radius of curve, rate of change of acceleration, and optional tolerance percentage. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical rate of change of acceleration?
A: Common values range between 0.3 to 0.6 m/s³ for comfortable transitions.

Q2: How does design speed affect the curve length?
A: Higher speeds require longer curves as the length is proportional to the cube of the speed.

Q3: What's the purpose of the tolerance field?
A: The ±% tolerance provides a range to account for design variations or safety factors.

Q4: How is radius of curve determined?
A: It's typically based on design standards for the road classification and expected vehicle types.

Q5: Can this calculator be used for railway curves?
A: The principles are similar, but railways often use different standards and factors.