1. What is Length of Summit Curve Given Angle Grades?

Definition: This calculator determines the required length of a summit vertical curve based on sight distance, driver eye height, obstruction height, and grade angles.

Purpose: It helps highway engineers design safe vertical curves that provide adequate stopping sight distance.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Ls \) — Length of summit curve (meters)
• \( S \) — Sight distance (meters)
• \( h1 \) — Driver's eye height (meters, typically 0.75m)
• \( n1 \) — Positive grade angle (radians)
• \( h2 \) — Obstruction height (meters, typically 0.36m)
• \( n2 \) — Negative grade angle (percentage)

Explanation: The formula combines the sight distance requirements with the geometric constraints of the vertical curve.

3. Importance of Summit Curve Calculation

Details: Proper summit curve design ensures drivers have adequate visibility to stop for obstacles, preventing accidents on crest vertical curves.

4. Using the Calculator

Tips: Enter sight distance, driver height (default 0.75m), positive grade angle (default 0.785 rad ≈ 45°), obstruction height (default 0.36m), and negative grade angle (default -45%).

5. Frequently Asked Questions (FAQ)

Q1: What's a typical driver eye height?
A: Standard passenger vehicles use 0.75m (750mm), while trucks might use 1.05m or more.

Q2: What obstruction height should I use?
A: 0.36m is common for passenger vehicles, but use 1.05m for truck visibility calculations.

Q3: How do I convert grade percentage to radians?
A: Use arctan(grade%/100). For example, 5% grade = arctan(0.05) ≈ 0.0499 radians.

Q4: Why is negative grade shown as percentage?
A: Road grades are traditionally expressed as percentages (rise/run × 100).

Q5: What if my curve is sag rather than summit?
A: This calculator is specifically for summit curves. Different formulas apply to sag curves.

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