1. What is a Length of Vertical Curve Calculator?

Definition: This calculator determines the required length of a vertical curve based on the change in grade and the permissible rate of grade change.

Purpose: It helps transportation engineers design smooth vertical transitions between different grades in roads and railways.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( L \) — Length of Vertical Curve
• \( N \) — Change in Grade (algebraic difference between two grades)
• \( P \) — Permissible Rate (maximum allowable rate of change in grade)

Explanation: The absolute value of the grade change is divided by the permissible rate to determine the minimum curve length needed for a smooth transition.

3. Importance of Vertical Curve Calculation

Details: Proper vertical curve design ensures driver comfort, adequate stopping sight distance, and safe vehicle operation by preventing abrupt changes in slope.

4. Using the Calculator

Tips: Enter the change in grade (as a percentage, can be positive or negative) and the permissible rate (default 0.1% for summits). Permissible rate must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical permissible rate for highways?
A: For highways, 0.5% to 1.0% per station (100 feet) is common, but exact values depend on design speed.

Q2: How do I determine the change in grade?
A: Subtract the incoming grade from the outgoing grade (e.g., +3% to -2% is a change of 5%).

Q3: Are different rates used for crest vs. sag curves?
A: Yes, sag curves typically use lower permissible rates (e.g., 0.05%) than crest curves (e.g., 0.1%).

Q4: What units are used in this calculation?
A: The calculation uses consistent units - typically percentages for grades and stations or meters for length.

Q5: Does this account for stopping sight distance?
A: No, this is a basic calculation. Final design should verify adequate sight distance for the design speed.

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