FabLayout

Lobster back elbow calculator

Enter the pipe diameter, bend radius, elbow angle and number of pieces of a segmented (lobster back) elbow. You get the end and middle piece patterns, their axis lengths and a scale drawing of each.

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Lobster back elbow

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1,345.8 mm107.7 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

2,274.8mm

Exact geometry

Cut length
640.9 mm
Axis length
241.2 mm
Sheet size
1,345.8 × 107.7 mm

How to lay it out

  1. Work out the miter angle

    Count the miters (pieces minus one) and divide the elbow angle by twice that number. This is the tilt of each cut.

  2. Draw the middle piece stretchout

    Draw a base line as long as the pipe circumference on the sheet middle, divide it into equal parts and square a line through each point.

  3. Mark both miter curves

    On each line, mark the bottom and top curves, each r × tan β × cos θ from the miter points on the axis. The lines are shortest at the throat, where the seam goes, and longest at the back.

  4. Draw the end piece

    Lay out the end piece the same way with half the axis length: one end is square, the other is mitered.

  5. Cut the set

    Cut the end piece twice and the middle piece once for every middle piece in the elbow, with seam allowance added at the throat lines.

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 38, p. 130, Problem 40, Fig. 320, p. 132, and Problem 41, pp. 132–133; Daugherty, Sheet-Metal Pattern Drafting (1922), Problem 16, pp. 38–39

Method and formula

A segmented elbow builds a bend from straight pipe pieces joined at miters. With m pieces there are N = m − 1 miters. The two end pieces are half pieces; the pieces between them are full pieces.

  • Miter angle β = α ÷ (2N), where α is the elbow angle.
  • Axis length: end piece R × tan β, middle piece 2 × R × tan β, where R is the bend radius of the pipe centre line.
  • Miter curves: at angle θ around the pipe, a mitered end moves rn × tan β × cos θ from its point on the axis. θ = 0 is the throat.

The top curve of one piece and the bottom curve of the next are the same curve, so the pieces meet without gaps. With sheet thickness each piece is developed on the middle of the sheet; the bend radius and the miter planes do not move. Each piece is an exact cylinder, so the patterns are exact.

Worked example

D = 100 mm, R = 150 mm, 90°, 4 pieces, thin sheet: N = 3, β = 15°, r × tan β = 13.40 mm. End pieces are 40.19 mm long on the axis, middle pieces 80.38 mm. On a middle piece the bottom curve sits at 13.40, 0 and −13.40 mm at 0°, 90° and 180°, and the top curve at 66.99, 80.38 and 93.78 mm. The throat line is 53.59 mm long.

Questions

Is the bend radius measured to the throat or to the centre line?

To the centre line of the pipe. It does not change with sheet thickness. It must be at least one pipe diameter and at most 100 diameters.

Why are the end pieces half as long?

An end piece has one square end and one miter, so it turns the pipe by only β. A middle piece has a miter at each end and turns it by 2β. A 4-piece elbow has 3 miters, 2 end pieces and 2 middle pieces.

Is the pattern exact?

Yes. Each piece is a true cylinder cut by flat planes. The elbow itself is a stepped version of a smooth bend; more pieces bring it closer to the smooth bend.

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