Longest Interval Of Circular Ring Calculator

Formula Used:

\[ Longest\ Interval = 2 \times \sqrt{Outer\ Radius^2 - Inner\ Radius^2} \]

Longest Interval:

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1. What is the Longest Interval of Circular Ring?

The Longest Interval of Circular Ring is the length of the longest line segment within the Circular Ring, which is the chord tangent to the inner circle. It represents the maximum distance between any two points on the outer circumference that can be connected through the ring.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ Longest\ Interval = 2 \times \sqrt{Outer\ Radius^2 - Inner\ Radius^2} \]

Where:

\( Outer\ Radius \) — The radius of the larger outer circle (m)
\( Inner\ Radius \) — The radius of the smaller inner circle (m)

Explanation: This formula is derived from the Pythagorean theorem, where the longest chord of the circular ring is twice the length of the tangent from the outer circle to the inner circle.

3. Importance of Longest Interval Calculation

Details: Calculating the longest interval is crucial in various engineering and geometric applications, particularly in mechanical design, architecture, and manufacturing where circular ring shapes are used. It helps determine maximum clearances, material requirements, and structural integrity.

4. Using the Calculator

Tips: Enter both outer and inner radius values in meters. The outer radius must be larger than the inner radius. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a circular ring?
A: A circular ring is the region between two concentric circles - a larger outer circle and a smaller inner circle.

Q2: Why is this called the "longest interval"?
A: It's the longest possible straight line segment that can be drawn entirely within the ring area, connecting two points on the outer circumference.

Q3: What are practical applications of this calculation?
A: Used in pipe design, bearing calculations, architectural elements, and any application involving annular shapes where maximum dimensions need to be determined.

Q4: What units should I use?
A: The calculator uses meters, but you can use any consistent unit of length as long as both radii are in the same units.

Q5: What if the inner radius is larger than the outer radius?
A: The calculation requires that the outer radius be larger than the inner radius. If this condition is not met, the result will be mathematically invalid.