Unequal trouser piece calculator
For a breeches pipe whose two legs have different diameters. Enter the main diameter, both leg diameters, height and mouth spacing to get a separate pattern for each leg.
Enter your measurements
Seam
3,036.4mm
Approximate, within ±2.5 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.
How to lay it out
Divide each leg on its own
Each leg has its own seat on the main pipe, wider for the larger leg. Divide that seat and the rest of the circle into equal parts, and the leg mouth at the same angles.
Mark the crotch points
Join matching points with generators and mark where each crotch-side generator crosses the leaning crotch plane.
Take the true lengths
Find the true length of every generator and of each diagonal between neighbours, leg by leg.
Lay out both legs
Triangulate each leg from its outer seam line. The two patterns are different shapes; label them by diameter.
Seam the crotch
Join the edges with smooth curves. The crotch edges of the two legs have the same length and are seamed together.
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
Here the two legs have different diameters, d1 and d2. Each is a slanting cone from the main pipe circle to its own mouth. It is not obvious that two different cones meet on a flat crotch, but they do. Subtract the two cone equations and the squared terms cancel, leaving the equation of a plane:
- 2x Δp + 2y Δq − κz + 2R0 Δr = 0, with Δp, Δq the difference of the mouth centres, Δr the difference of the radii, R0 = Dg ÷ 2 and κ a constant from the sizes and height.
Since the crotch is planar, every facet is flat and each leg is triangulated without twist. The plane sits closer to the smaller leg, so the larger leg takes a wider seat on the main pipe. The half-angle of that seat is w = atan2(√(Δp² + Δq² − Δr²), −Δr), and each leg gets its own w.
The only error is the chord used for each curve segment: the mouth is short by at most r(w³ + (π − w)³) ÷ (12n²) per leg. Inside or outside sizes are converted approximately and rejected above 1 mm of mouth deviation. Both leg diameters must lie between Dg ÷ 10 and Dg.
Worked example
Dg = 400 mm, d1 = 250 mm, d2 = 150 mm, H = 400 mm, c = 450 mm, n = 4. The larger leg's seat half-angle is 96.38° and the smaller leg's is 83.62°. The middle crotch point sits 246.15 mm up, the mouths clear the crotch plane by 111.07 mm, and the shortest generator is 192.31 mm. The larger leg has an area of 338 876.98 mm² and the smaller 263 891.60 mm². The chord error bound is 5.12 mm at n = 4.
Questions
Is the crotch still flat with unequal legs?
Yes. Two slanting cones that start on the same main pipe circle always meet on a plane, whatever their mouth sizes. The plane just sits closer to the smaller leg, so the crotch seam is still a single flat curve.
How is this different from the equal-leg trouser piece?
With equal legs the crotch is the centre plane and the legs are mirror images. With unequal legs the crotch leans, each leg takes a different share of the main pipe and the two patterns are different shapes.
Is the pattern exact?
Apart from chords. Each leg has its own seat angle w, so each has its own bound r(w³ + (π − w)³) ÷ (12n²); the larger of the two is 5.12 mm in the example at n = 4. Doubling n cuts it to a quarter.
Similar calculators
More in TrueflatConeTruncated coneCone by triangulationSee what the app does