Design Speed given Total Length of Valley Curve Calculator

Design Speed Formula:

\[ v = \left(\frac{(L_s/2)^2 \times C_a}{N}\right)^{1/3} \]

Design Speed (v):

m/s

Tolerance:

1. What is Design Speed given Total Length of Valley Curve?

Definition: This calculator determines the appropriate design speed for a valley curve based on its length, rate of change of acceleration, and deviation angle.

Purpose: It helps transportation engineers ensure safe and comfortable transitions between different grades on roads or railways.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ v = \left(\frac{(L_s/2)^2 \times C_a}{N}\right)^{1/3} \]

Where:

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

Explanation: The formula calculates the maximum safe speed that can be maintained through a valley curve while maintaining passenger comfort and safety.

3. Importance of Design Speed Calculation

Details: Proper design speed ensures smooth vertical transitions, prevents discomfort from rapid acceleration changes, and maintains vehicle control.

4. Using the Calculator

Tips: Enter the curve length in meters, rate of change of acceleration (default 4.2 m/s³), and deviation angle (default 0.88 rad). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical rate of change of acceleration?
A: For comfortable riding, C_a is typically between 0.3-0.6 m/s³ for highways and 0.4-0.7 m/s³ for railways.

Q2: How do I determine the deviation angle?
A: The deviation angle is the algebraic difference between the two intersecting grades.

Q3: Why is the length divided by 2 in the formula?
A: The formula considers the symmetrical nature of valley curves, where the maximum vertical acceleration occurs at the midpoint.

Q4: What is the tolerance (±5%) for?
A: The tolerance accounts for variations in vehicle performance, driver behavior, and environmental conditions.

Q5: How do I convert the result to km/h?
A: Multiply the m/s result by 3.6 to convert to km/h.