Total Length of Valley Curve Calculator

Length of Curve Formula:

\[ L_s = 2 \times \sqrt{\frac{N \times v^3}{C_a}} \]

Deviation Angle:

radians

Design Speed:

m/s

Rate of Change of Acceleration:

m/s³

Tolerance:

Length of Curve (m):

1. What is a Total Length of Valley Curve Calculator?

Definition: This calculator determines the required length of a valley curve in road design based on deviation angle, design speed, and rate of change of acceleration.

Purpose: It helps civil engineers design safe and comfortable vertical curves in roadways where the alignment changes from upward to downward slope.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_s = 2 \times \sqrt{\frac{N \times v^3}{C_a}} \]

Where:

\( L_s \) — Length of valley curve (meters)
\( N \) — Deviation angle (radians)
\( v \) — Design speed (meters/second)
\( C_a \) — Rate of change of acceleration (m/s³)

Explanation: The formula calculates the minimum curve length needed to provide adequate driver comfort and safety when transitioning between grades.

3. Importance of Valley Curve Calculation

Details: Proper valley curve design prevents sudden changes in vertical acceleration that could cause discomfort or loss of vehicle control.

4. Using the Calculator

Tips: Enter the deviation angle in radians, design speed in m/s, rate of change of acceleration in m/s³, and tolerance percentage. All values must be > 0 (except tolerance which can be 0).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical rate of change of acceleration?
A: Common values range from 0.3 to 0.9 m/s³, with 0.6 m/s³ often used for comfortable design.

Q2: How does design speed affect curve length?
A: Curve length increases with the cube of design speed - higher speeds require significantly longer curves.

Q3: What's the purpose of the tolerance field?
A: It calculates a ± range around the calculated length to account for design flexibility (default ±5%).

Q4: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.01745). 1° ≈ 0.01745 radians.

Q5: When would I use a shorter curve than calculated?
A: Only in constrained situations, as shorter curves may cause discomfort or safety issues at design speed.