Why is the hole a rectangle at all?

Because the collar's walls meet the cylinder along curves that unroll straight. The two perpendicular to the axis meet it along circles, which become lines of constant position along the pipe; the two parallel to the axis meet it along straight lines, which become lines of constant position around it. Straight on all four sides.

Then why isn't it x by y?

Because the sheet stretches when it unrolls. The side across measures the arc that y occupies: 2·Rn·asin(y/d2). On a 500 shell with a 250 tap it comes out 260.2. The wider the tap relative to the pipe, the worse — at a tap half the pipe's diameter the stretch passes 5%, and near the limit it passes 50%.

What is the limit on the width?

Half a turn. At y equal to the shell's mid-line diameter the hole opens exactly half the circumference and there is no shell left either side of it. The calculation refuses past that.

Does it match the rectangular tap?

It does, and it is its mate. Enter the same pipe and the same collar section in both parts and you have both patterns for the job.

Cylinder with Rectangular Hole development

What it is

The shell with the rectangular tap's hole already marked — the mate of the rectangular tap, and the half that carries the number people get wrong. The hole IS a rectangle, which is what fools everyone; but the side that runs across the shell does not measure y.

Where it is used

Headers receiving rectangular ducts, shells for intake mouths, cyclone bodies with a rectangular inlet, any pipe that has to take a rectangular collar.

Measurements the calculation needs

D2 Outside diameter of the shell
H Length of the shell
X Side of the collar along the axis
Y Width of the collar, across the axis
THK Plate thickness

Worked example

The values the form comes pre-filled with, run through the tool itself:

Outside diameter of the shell	500 mm
Length of the shell	700 mm
Side of the collar along the axis	300 mm
Width of the collar, across the axis	250 mm
Plate thickness	3 mm
The flat pattern fits a plate of	1561 × 700 mm

Result of the example

Plate	1561 × 700 mm

Cylinder with Rectangular Hole flat pattern: drawing of the template with the worked example dimensions — Cut lines in purple, welds in green and reference lines in orange. Plate 1561 × 700 mm.

Frequently asked questions

Why is the hole a rectangle at all?: Because the collar's walls meet the cylinder along curves that unroll straight. The two perpendicular to the axis meet it along circles, which become lines of constant position along the pipe; the two parallel to the axis meet it along straight lines, which become lines of constant position around it. Straight on all four sides.
Then why isn't it x by y?: Because the sheet stretches when it unrolls. The side across measures the arc that y occupies: 2·Rn·asin(y/d2). On a 500 shell with a 250 tap it comes out 260.2. The wider the tap relative to the pipe, the worse — at a tap half the pipe's diameter the stretch passes 5%, and near the limit it passes 50%.
What is the limit on the width?: Half a turn. At y equal to the shell's mid-line diameter the hole opens exactly half the circumference and there is no shell left either side of it. The calculation refuses past that.
Does it match the rectangular tap?: It does, and it is its mate. Enter the same pipe and the same collar section in both parts and you have both patterns for the job.

Cylinder with Rectangular Hole dimension drawing: D2 (Outside diameter of the shell), H (Length of the shell), X (Side of the collar along the axis), Y (Width of the collar, across the axis), THK (Plate thickness), marked on the part

Calculate a Cylinder with Rectangular Hole

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