Radius of Sharp Bent Cylinder given Bent Diameter Calculator

Formula Used:

\[ r = \sqrt{\left(\frac{D_{Bent}}{2}\right)^2 - \left(\frac{h_{1(Long)} - h_{1(Short)}}{2}\right)^2} \]

Bent Diameter of Sharp Bent Cylinder:

First Long Height of Sharp Bent Cylinder:

First Short Height of Sharp Bent Cylinder:

Radius of Sharp Bent Cylinder:

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1. What is Radius of Sharp Bent Cylinder?

The Radius of Sharp Bent Cylinder is the distance between the center and any point on the circumference of the base circular face of the Sharp Bent Cylinder. It is a fundamental geometric parameter used to characterize the cylindrical shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ r = \sqrt{\left(\frac{D_{Bent}}{2}\right)^2 - \left(\frac{h_{1(Long)} - h_{1(Short)}}{2}\right)^2} \]

Where:

\( r \) — Radius of Sharp Bent Cylinder (m)
\( D_{Bent} \) — Bent Diameter of Sharp Bent Cylinder (m)
\( h_{1(Long)} \) — First Long Height of Sharp Bent Cylinder (m)
\( h_{1(Short)} \) — First Short Height of Sharp Bent Cylinder (m)

Explanation: This formula derives from geometric relationships in a bent cylinder, using the Pythagorean theorem to calculate the radius based on the bent diameter and height differences.

3. Importance of Radius Calculation

Details: Calculating the radius is essential for understanding the geometry of bent cylindrical structures, which is crucial in engineering design, manufacturing processes, and structural analysis applications.

4. Using the Calculator

Tips: Enter bent diameter and both height values in meters. All values must be positive, and the long height must be greater than the short height for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Sharp Bent Cylinder?
A: A Sharp Bent Cylinder is a cylindrical shape that has been bent or deformed, creating an elliptical cross-section while maintaining a circular base.

Q2: Why are two different heights needed?
A: The height difference between the long and short sides is crucial for calculating the radius using geometric relationships in the bent configuration.

Q3: What units should be used?
A: The calculator uses meters for all measurements, but consistent units can be used as long as all inputs are in the same unit system.

Q4: When is this calculation applicable?
A: This calculation is useful in mechanical engineering, piping systems, and any application involving bent cylindrical components.

Q5: What if the calculated radius is negative?
A: The radius should always be positive. A negative result indicates invalid input values where the height difference exceeds the geometric constraints.