FabLayout

Conical roof flange flat pattern calculator

A cone with a square-cut top and a bottom cut at the roof pitch, such as a roof collar. Enter both diameters, the axis length and the cut angle; you get the curved pattern.

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342.2 mm313.5 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

122.3mm

Exact geometry

Cut length
In the app
Arc length
In the app
Sheet size
In the app

Every result is in Trueflat

The free web version shows the main result and the drawing. Trueflat gives you every mark and measurement, and exports a cut sheet. It is free to download.

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How to lay it out

  1. Swing the top arc

    From a centre point, swing an arc at the top pattern radius, the slant distance from the apex to the top circle.

  2. Step off the divisions

    Divide the plan circle into equal parts and step the same number of equal spaces along a stretchout arc swung at the slant distance to the axis point. Draw a line from the centre through each mark.

  3. Find each element's length

    In the elevation, run each element from the apex down to the slanted cut line and take its true length from the apex by projecting across to the outside element.

  4. Mark and join the cut curve

    Set off each true length along its matching radial line, then bend a batten through the marks to draw the bottom edge.

  5. Close at the short side

    Put the seam on the shortest element, draw both seam lines between the curve and the top arc and add your allowance.

Good to know

  • FabLayout runs the same code as Trueflat; the result is exact geometry.
  • Source: Kittredge, The New Metal Worker Pattern Book (1917), Problem 135, Fig. 484, p. 265; Daugherty, Sheet-Metal Pattern Drafting (1922), Problem 45, Fig. 82, p. 66; Longfield, Sheet Metal Drafting (1921), Problem 22 "Conical Roof Flange", p. 89

Method and formula

The part is still a right cone, so it unrolls exactly into a sector around the apex. Only the bottom edge changes: each element ends where it meets the slanted plane, so its distance from the apex varies around the pattern.

  • Lower diameter D1 is the cone's diameter where the slanted plane crosses the axis, not at the low or high rim.
  • Cone angle tan β = (D1 − D2) ÷ (2H); the sector angle is 360° × sin β.
  • Bottom edge s = L ÷ (1 + ε cos θ), with L = (D1 ÷ 2) ÷ sin β, ε = tan α × tan β, and θ the angle around the plan from the short side.
  • Top arc radius (D2 ÷ 2) ÷ sin β.

The cut must not run nearly parallel to the cone's side: ε may be at most 0.95. Above that, lower the cut angle or make the cone steeper.

Worked example

D1 = 200 mm, D2 = 100 mm, axis length 100 mm, cut 30°: tan β = 0.5, sin β = 0.4472, ε = 0.2887, L = 223.61 mm. The top arc radius is 111.80 mm. The bottom edge is 173.52 mm from the apex on the short side and 314.35 mm on the long side. The sector angle is 161.00°, and the two seam edges total 123.43 mm (the Seam row).

Questions

Where do I measure the lower diameter?

At the point where the roof plane crosses the cone's axis, square to the axis. The axis length runs from that point to the top. Measuring at the low or high edge of the cut gives a different cone.

How is this different from a pipe cut at an angle?

A pipe roof flashing is a cylinder, so its pattern is a straight band with a sine-shaped edge. A conical flange tapers, so its pattern is a sector with a curved bottom edge, and the angle of the sector depends on the taper.

Why is a steep cut rejected?

When tan α × tan β approaches 1, the roof plane runs almost parallel to the long side of the cone and that element grows without limit. Trueflat stops at 0.95; lower the roof angle or give the cone a steeper side.

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