FabLayout

Sphere gore pattern calculator

Make a ball or dome from pointed segments running pole to pole. Enter the sphere diameter and the number of gores; you get the gore length, its width at the equator and the curved outline.

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Enter your measurements

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631.5 mm105.2 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

1,284.3mm

Approximate, within ±10.8 mm

Gore length
In the app
Gore width (equator)
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. Draw the centre line

    Draw a straight line half the sphere's circumference long: this is the meridian from pole to pole.

  2. Divide the centre line

    Divide the line into equal parts and draw a cross line at each division.

  3. Mark the widths

    On each cross line, mark half the gore width either side of the centre: the equator width times the cosine of that point's latitude.

  4. Draw the outline

    Bend a batten through the marks on each side so both edges meet in a point at each pole.

  5. Cut and form

    Cut one gore for every segment, add seam allowance, and form each gore to the sphere's curve before joining.

Good to know

  • This pattern is approximate; the result card shows how close it is.
  • Source: Kittredge, The New Metal Worker Pattern Book (1917), Problem 30, Fig. 309, p. 124. The book measures widths from a polygon section; Trueflat uses the true arc of each parallel circle

Method and formula

A sphere cannot be unrolled, so any flat gore is approximate. Trueflat keeps two things true: the length along the centre line, and the width at every latitude, which is the real arc of that parallel circle. That makes the gore's area exactly 1/N of the sphere.

  • Gore length π × R, half the circumference.
  • Equator width 2π R ÷ N.
  • Width at latitude φ 2π R cos φ ÷ N.

The cost is at the edges: the curved edge is longer than the true meridian by at most π³R ÷ (4N²), a stretch of at most π² ÷ (4N²). That difference is taken up by pressing or stretching the gore to shape. More gores mean less forming.

Worked example

D = 100 mm, 12 gores: gore length 157.08 mm, equator width 26.18 mm. Each edge is 159.74 mm, 2.66 mm longer than the meridian, inside the bound of 2.69 mm (1.69 % stretch). The area of one gore is 2617.99 mm², one twelfth of the sphere.

Questions

How accurate is a gore pattern?

It is approximate, because a sphere cannot be flattened. The area is exact, but each curved edge is longer than the meridian by at most π³R ÷ (4N²). With 12 gores on a 100 mm sphere the edge is 2.66 mm longer than the meridian; pressing the gore to shape takes this up.

Gores or zones: which should I use?

Gores run pole to pole and need forming, but give a full sphere with seams only along meridians. Zones are bands of shallow cones that roll without forming but leave small ridges. Use zones for a band or dome section, gores for a full ball or a smooth dome.

How many gores should I use?

From 4 to 72. More gores mean narrower pieces and less stretching: the stretch falls with the square of the count. Fewer than 4 stretches the edges more than 15 %.

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