Hole Radius Of Torus Given Radius Of Circular Section And Breadth Calculator

Formula Used:

\[ r_{Hole} = \frac{b}{2} - (2 \times r_{Circular\ Section}) \]

Hole Radius of Torus (r_Hole):

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1. What is the Hole Radius of Torus?

The Hole Radius of Torus is the shortest line connecting the center of the Torus to the nearest point on the circumference of the circular cross-section of the Torus. It represents the distance from the center of the torus to the inner edge of its ring structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Hole} = \frac{b}{2} - (2 \times r_{Circular\ Section}) \]

Where:

\( r_{Hole} \) — Hole Radius of Torus (m)
\( b \) — Breadth of Torus (m)
\( r_{Circular\ Section} \) — Radius of Circular Section of Torus (m)

Explanation: The formula calculates the hole radius by taking half of the torus breadth and subtracting twice the radius of the circular cross-section.

3. Importance of Hole Radius Calculation

Details: Calculating the hole radius is essential in geometry and engineering applications involving toroidal shapes. It helps in determining the inner dimensions of torus-shaped objects, which is crucial for manufacturing, structural design, and mathematical modeling of toroidal surfaces.

4. Using the Calculator

Tips: Enter the breadth of the torus and the radius of its circular section in meters. Both values must be positive numbers. The calculator will compute the hole radius based on the provided dimensions.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a three-dimensional geometric shape that resembles a doughnut or an inner tube. It's a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: How is the hole radius different from the major radius?
A: The hole radius is the distance from the center of the torus to the inner edge, while the major radius is the distance from the center of the torus to the center of the circular cross-section.

Q3: Can the hole radius be negative?
A: In practical terms, the hole radius should be positive. A negative result would indicate that the circular cross-section radius is too large relative to the breadth, which would not form a valid torus shape.

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

Q5: What are some real-world applications of torus geometry?
A: Torus shapes are used in various applications including architecture (domed structures), engineering (pipes, tires), physics (magnetic confinement in fusion reactors), and mathematics (topology studies).