1. What is a Truncated Cone Flat Pattern?

A truncated cone flat pattern is the 2D development of a conical frustum that can be rolled into a 3D truncated cone shape. The sector angle determines how much of a full circle is needed to create the pattern.

2. How Does the Calculator Work?

The calculator uses the sector angle formula:

Where:

• \( R \) — Large radius (m)
• \( r \) — Small radius (m)
• \( \text{slant} \) — Slant height of the cone (m)

Explanation: The formula calculates the angle needed to create the flat pattern that will form the truncated cone when rolled.

3. Importance of Sector Angle Calculation

Details: Accurate sector angle calculation is crucial for sheet metal work, piping, and any application where a conical transition piece needs to be fabricated from flat material.

4. Using the Calculator

Tips: Enter all dimensions in consistent units (meters shown). The large radius must be greater than the small radius, and slant height must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What if my cone doesn't have a top (r=0)?
A: For a complete cone (no truncation), simply enter 0 for the small radius (r).

Q2: How do I measure slant height?
A: Slant height is the straight-line distance from the base to the top along the cone's side.

Q3: What units should I use?
A: The calculator works with any consistent units, but outputs will be in the same units you input.

Q4: Can I use this for very shallow cones?
A: Yes, but for very shallow cones (where R ≈ r), the pattern will be nearly flat.

Q5: How do I use the sector angle to make the pattern?
A: Draw two concentric circles with radii equal to your cone dimensions, then mark out the sector angle and cut.