Width of Circular Ring Given Longest Interval and Outer Radius Calculator

Formula Used:

\[ w = r_{Outer} - \sqrt{r_{Outer}^2 - \left(\frac{I_{Longest}}{2}\right)^2} \]

Width of Circular Ring:

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1. What is the Width of Circular Ring Formula?

The formula calculates the width of a circular ring given its outer radius and the longest interval (chord tangent to the inner circle). It provides a geometric relationship between these measurements in concentric circles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ w = r_{Outer} - \sqrt{r_{Outer}^2 - \left(\frac{I_{Longest}}{2}\right)^2} \]

Where:

\( w \) — Width of Circular Ring (m)
\( r_{Outer} \) — Outer Radius of Circular Ring (m)
\( I_{Longest} \) — Longest Interval of Circular Ring (m)

Explanation: The formula derives from the Pythagorean theorem applied to the right triangle formed by the outer radius, half the longest interval, and the inner radius.

3. Importance of Width Calculation

Details: Calculating the width of a circular ring is essential in various engineering and design applications, including mechanical components, architectural elements, and manufacturing processes where precise annular measurements are required.

4. Using the Calculator

Tips: Enter outer radius and longest interval in meters. Both values must be positive numbers. The longest interval should be less than or equal to twice the outer radius for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is a circular ring?
A: A circular ring is the area between two concentric circles, forming an annular shape with inner and outer boundaries.

Q2: What does the longest interval represent?
A: The longest interval is the chord of the outer circle that is tangent to the inner circle, representing the maximum distance between two points on the outer circle that doesn't intersect the inner circle.

Q3: Can this formula be used for elliptical rings?
A: No, this formula is specifically designed for circular rings with concentric circles. Elliptical rings require different geometric calculations.

Q4: What are practical applications of this calculation?
A: This calculation is used in pipe design, bearing manufacturing, optical systems, and any application involving annular spaces with specific dimensional requirements.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect concentric circles. Real-world applications may require considering manufacturing tolerances and material properties.