Truncated Cone Pattern Calculator

Truncated Cone Pattern:

\[ \text{Pattern dimensions} = f(\text{radius\_large}, \text{radius\_small}, \text{height}) \]

Pattern Angle:

Pattern Large Radius:

Pattern Small Radius:

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1. What is a Truncated Cone Pattern?

A truncated cone (frustum) pattern is the 2D development of a conical section that has had its top cut off parallel to the base. This calculator helps create the flat pattern needed to construct a truncated cone from sheet material.

2. How Does the Calculator Work?

The calculator uses geometric formulas to determine the pattern dimensions:

\[ \text{Slant height} = \sqrt{(R - r)^2 + h^2} \] \[ \text{Pattern angle} = 360° \times \frac{R}{\text{Slant height}} \]

Where:

\( R \) — Large radius (base) of the truncated cone
\( r \) — Small radius (top) of the truncated cone
\( h \) — Height of the truncated cone

Explanation: The pattern is a sector of an annulus (ring shape) with inner and outer radii corresponding to the slant heights of the cone.

3. Importance of Pattern Calculation

Details: Accurate pattern calculation is crucial for sheet metal work, piping transitions, and any application where a conical section needs to be fabricated from flat material.

4. Using the Calculator

Tips: Enter all dimensions in meters. The large radius must be greater than the small radius. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if my cone is very tall and narrow?
A: The calculator works for all proportions, but very tall/narrow cones may result in patterns that are difficult to fabricate from single sheets.

Q2: How do I account for material thickness?
A: For thick materials, you may need to adjust dimensions based on whether you're measuring to the inside, outside, or middle of the material.

Q3: Can I use different units?
A: The calculator uses meters, but you can use any unit as long as you're consistent (all dimensions in mm, inches, etc.).

Q4: What about cones with non-parallel tops?
A: This calculator is for right circular truncated cones only. For oblique cones, more complex calculations are needed.

Q5: How accurate are the results?
A: The calculations are mathematically precise. Practical accuracy depends on your measurements and fabrication skills.