Deviation Angle given Total Length of Valley Curve Calculator

Deviation Angle Formula:

\[ N = \left(\frac{L_s}{2}\right)^2 \times \frac{C_a}{v^3} \]

Length of Curve (Ls):

Rate of Change of Acceleration (Ca):

m/s²

Design Speed (v):

m/s

Tolerance:

Deviation Angle (N):

1. What is Deviation Angle in Valley Curves?

Definition: The deviation angle (N) is the angle between the reference direction and the observed direction in a valley curve.

Purpose: It helps in designing smooth vertical transitions on roads where the alignment changes from upward to downward slope.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N = \left(\frac{L_s}{2}\right)^2 \times \frac{C_a}{v^3} \]

Where:

\( N \) — Deviation Angle (radians)
\( L_s \) — Length of Curve (meters)
\( C_a \) — Rate of Change of Acceleration (m/s²)
\( v \) — Design Speed (m/s)

Explanation: The formula calculates how much the vertical alignment deviates based on curve length, acceleration changes, and design speed.

3. Importance of Deviation Angle Calculation

Details: Proper calculation ensures comfortable transitions for vehicles, prevents sudden changes in vertical acceleration, and maintains safety standards.

4. Using the Calculator

Tips:

Enter the length of the valley curve in meters
Input the rate of change of acceleration (typically 0.3-0.6 m/s³ for comfort)
Specify the design speed in m/s
Set tolerance percentage (default ±5%)

5. Frequently Asked Questions (FAQ)

Q1: What is a typical rate of change of acceleration?
A: For comfortable rides, Ca is typically between 0.3 to 0.6 m/s³, with 0.6 being the maximum for highways.

Q2: How does design speed affect the deviation angle?
A: Higher design speeds generally require smaller deviation angles to maintain comfort and safety.

Q3: What's the purpose of the tolerance value?
A: The tolerance accounts for construction variations and material properties, ensuring the design remains effective within specified limits.

Q4: How do I convert the result to degrees?
A: Multiply the radians result by (180/π) to convert to degrees.

Q5: When would I need to adjust the tolerance?
A: Adjust tolerance based on project specifications, material variability, or when higher precision is required.