FabLayout

Trouser piece calculator (breeches pipe)

Enter the main pipe diameter, leg diameter, height and the spacing between leg mouths. You get the leg pattern of a symmetric trouser piece; both legs are mirror images.

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Enter your measurements

Your dimensions are measured to the

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1:1 PDF and DXF files of this flat pattern are made in Trueflat, ready for print, plasma, laser or waterjet. It works offline on site.

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1,537.3 mm801.0 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

3,073.9mm

Approximate, within ±1.9 mm

Cut 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. Divide the circles

    In plan, divide the half of the main pipe circle on the leg's outer side into 2n equal parts and the crotch half into 2n equal parts. Divide the leg mouth at the same angles.

  2. Find the crotch points

    Join matching points with generators. Where a crotch-side generator crosses the centre plane between the legs, mark its crotch point.

  3. Take the true lengths

    Find the true length of each generator, from main pipe or crotch point up to the mouth, and of each diagonal between neighbouring generators.

  4. Lay out the triangles

    Start at the outer seam line and lay out the triangles one by one from their true lengths, working round the leg.

  5. Draw the edges

    Join the mouth points, the main pipe points and the crotch points with smooth curves. The crotch edge is seamed to the other leg.

Good to know

  • This pattern is approximate; the result card shows how close it is.
  • Source: Derived from first principles: each leg is the oblique cone between the main-pipe circle and the leg mouth, the crotch lies in a plane, so every facet is flat and the leg is laid out by triangulation on the middle of the sheet. Checked against an independent reference implementation in Trueflat.

Method and formula

A trouser piece (breeches pipe) divides one round pipe into two legs. Each leg is a slanting cone that joins the main pipe circle, diameter Dg at the bottom, to its leg mouth, diameter d at height H. Points at the same angle on the two circles are joined by straight generators. When d = Dg the leg becomes a slanting cylinder.

The two cone surfaces meet on a plane. With equal legs placed at ±c ÷ 2 that plane is simply the centre plane between them, x = 0. Half of the main pipe circle, on the outer side, is the leg's seat on the main pipe; the other half crosses the crotch.

Because the crotch is planar, every four-sided facet between two generators is flat. The leg is laid out from true lengths with no twist, and the only error is the chord used for each curve segment. The mouth length is short by at most

  • π³r ÷ (48n²), with r = d ÷ 2 and n the curve samples per quarter.

The crotch curve has no proven bound but shrinks at the same 1 ÷ n² rate. Inside or outside sizes are converted approximately and rejected above 1 mm of mouth deviation.

Limits: d between Dg ÷ 10 and Dg; leg axis no more than 60° from the main pipe; leg mouths at least 5 mm clear of the crotch plane.

Worked example

Dg = 400 mm, d = 200 mm, H = 400 mm, c = 400 mm, n = 4. The crotch plane is x = 0. The middle crotch point sits 266.67 mm up, and the shortest generator is 500 ÷ 3 = 166.67 mm. The leg mouth clears the crotch plane by 100 mm. The mouth chord error bound is 100 × 2(π ÷ 2)³ ÷ 192 = 4.04 mm; raising n reduces it by the square. Each leg axis leans 26.57°.

Questions

Is the pattern exact?

The facets are exactly flat, so the layout from true lengths has no twist. The only error is drawing each curve with straight chords: the mouth length is short by at most π³r ÷ (48n²) per leg, 4.04 mm with d = 200 and n = 4. Raise the curve samples to shrink it.

How is this different from a Y branch?

A Y branch keeps all three pipes at one diameter and uses mitered cylinders. A trouser piece splits the main pipe into two smaller legs, each a slanting cone. For legs set by an angle instead of a mouth spacing, use the tapered Y page.

What is the leg mouth spacing?

The centre-to-centre distance c between the two leg mouths at the top. It must be at least the leg diameter, and the legs must not lean more than 60° from the main pipe axis.

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