Radius of Road given Grade Compensation formula 1 Calculator

Radius of Circular Curve Formula:

\[ Rc = \frac{30}{(s - 1)} \]

Radius of Circular Curve (m):

1. What is Radius of Road given Grade Compensation?

Definition: This calculator determines the radius of a circular curve based on the percent grade compensation formula.

Purpose: It helps road engineers and designers calculate the appropriate curve radius for road grading projects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Rc = \frac{30}{(s - 1)} \]

Where:

\( Rc \) — Radius of circular curve (meters)
\( s \) — Percent grade (%)

Explanation: The formula calculates the radius needed for a road curve based on the grade percentage, where the grade cannot be exactly 1% (to avoid division by zero).

3. Importance of Radius Calculation

Details: Proper radius calculation ensures safe vehicle operation, proper drainage, and comfortable driving experience on graded roads.

4. Using the Calculator

Tips: Enter the percent grade (%). The value must not be exactly 1% (to prevent division by zero). Typical values range from ±5%.

5. Frequently Asked Questions (FAQ)

Q1: Why can't the grade be exactly 1%?
A: The formula would require division by zero when grade is 1%, which is mathematically undefined.

Q2: What's a typical grade percentage range?
A: For most roads, grade percentages typically range between -5% to +5% for safety and comfort.

Q3: How does radius affect road design?
A: Larger radii provide gentler curves that are safer at higher speeds, while smaller radii are used for tighter curves at lower speeds.

Q4: When would I need to calculate this?
A: When designing road vertical curves, highway interchanges, or any situation where grade changes occur on curved sections.

Q5: Does this include safety factors?
A: No, engineers should apply appropriate safety factors based on road type, speed limits, and other design considerations.