Cone Flat-Pattern Development (Radial Line)
The flat blank a cone rolls up from, and the sweep to cut it.
Example
You enter
- Base radius (in) 6
- Vertical height (in) 8
You get
- Slant height / pattern radius 10 in
- Sector sweep angle 216 deg
Details, formula, and sources
Flat pattern of a right cone: slant L = sqrt(r^2 + h^2), sector radius = L, sweep = 360 r / L. R 6 in, h 8 in -> L 10 in, 216-degree sector; a taller R 6/h 16 cone -> 17.09 in slant, a narrower 126-degree sector. Add seam and bend allowance. A layout aid; verify against a test piece.
L = sqrt(base_radius^2 + height^2); pattern radius = L; sweep = 360 x base_radius / L.
Radial-line development of a right cone, standard sheet-metal layout, by name.
The slant-height and sector-sweep relations are public sheet-metal layout geometry.
Estimate. AHJ and licensed professional govern.
Field names used by the API: base_radius_in, height_in, slant_L_in, sweep_deg
- Slant height L = sqrt(base_radius^2 + height^2)right-cone geometry
- Sector sweep angle = 360 x base_radius / Lsheet-metal layout
- Neutral line add seam/lap and bend allowance; verify on a test piecescope of this tile