Short answer
A square to round is laid out by triangulation: four flat triangles on the sides and four corner pieces, each split into thin triangles from the corner of the square to points on the circle. Every line's true length is √(plan length² + height²); the triangles are then drawn one after another on the sheet.
A square to round joins a square duct, hopper or flange to a round pipe or fan. It turns up in ventilation, dust extraction, chutes and tank outlets, and it is one of the first parts a plater learns to lay out, because every other transition is laid out the same way.
What the part is made of
Look at a square to round from above. Each side of the square is the base of a flat triangle whose tip touches the circle at its nearest point. Between two flat triangles, at each corner of the square, is a corner piece: a cone-like surface that fans out from the corner of the square to a quarter of the circle.
The flat triangles stay flat. The corner pieces are formed, either rolled or broken on press lines that run from the corner of the square to the circle. Those press lines are the lines you triangulate.
True lengths, step by step
None of the lines you need is seen at its real length in a plan or an elevation, because each one slopes in two directions at once. You find each length from two things you can measure: its length in plan and the height.
- Draw the plan. Draw the square and the circle on the same centre.
- Divide the circle. Split each quarter of the circle into equal parts: three is enough for a small part marked out by hand.
- Draw the lines. From each corner of the square, draw a line to every division point in its quarter.
- Measure the plan lengths. Measure each line in plan, and the seam line: from the middle of one side to the nearest point of the circle.
- Find the true lengths. For each line, true length = √(plan length² + height²).
- Draw the pattern. Start at the seam: draw it at its true length, then add the triangles one at a time, each from two true lengths and one known edge (a side of the square or a chord of the circle).
A worked example
Take a square of 600 mm, a round of 400 mm diameter and a height of 500 mm, sharp corners, thin sheet. Each quarter of the circle is divided into three, so the points on the circle are 30° apart and the chord between two points is 2 × 200 × sin 15° = 103.53 mm.
From one corner of the square, at (300, 300) with the centre at (0, 0):
| Line | Point on the circle | Plan length | True length |
|---|---|---|---|
| Corner to 0° | (200, 0) | 316.23 mm | 591.61 mm |
| Corner to 30° | (173.21, 100) | 236.81 mm | 553.24 mm |
| Corner to 60° | (100, 173.21) | 236.81 mm | 553.24 mm |
| Corner to 90° | (0, 200) | 316.23 mm | 591.61 mm |
| Seam (side middle to circle) | (200, 0) | 100 mm | 509.90 mm |
Each corner piece is then three triangles: two true lengths from the table and a chord of 103.53 mm. Each flat triangle has the 600 mm side as its base and the two 591.61 mm lines as its other sides. Half a flat triangle, cut on the seam, is a right triangle with sides of 300 mm and 509.90 mm.
The same part, worked out by Unfoldo with the round edge as true arcs. Change the sizes on the part to see the pattern follow:
| Pattern size | 1,921.77 × 813.96 mm |
|---|---|
| Surface area | 946,823.05 mm² |
| Press lines | 28 |
| Parts | 1 |
Where to put the seam
The usual place is the middle of one flat side, square to the base edge. The seam is then a straight line, easy to weld and away from the formed corners, and the pattern comes out as one piece.
Large parts are made in two or four pieces, with seams in the middle of two opposite sides, or at the corners. Pieces are easier to handle and to form, and a four-piece pattern often nests far better on the sheet. Unfoldo offers each of these as a cut type on the shape page.
Thickness and corner radius
On plate, the pattern must be worked out on the mean surface of the sheet, or the part will not fit at one end or the other. A square given as an inside size moves out by half a thickness on each side; the round end gets its own correction, because it may be given inside, outside or on the mean. The article on sheet thickness in flat patterns goes through it with numbers.
A square with rounded corners is laid out the same way, with the corner radius as a small cone of its own between the flat triangle and the corner piece. A rectangle in place of the square gives a rectangle to round, with two pairs of flat triangles of different sizes, and an offset round gives an offset transition with different true lengths at every corner.
Questions
What is a square to round transition?
A sheet metal part that joins a square duct or flange to a round one. It is made of four flat triangles, one on each side of the square, and four curved corner pieces that run from each corner of the square to a quarter of the circle.
How is a square to round laid out?
By triangulation. Divide each quarter of the circle into equal parts, draw lines from the corner of the square to each point, find the true length of every line from its plan length and the height, then draw the triangles one after another on the flat sheet.
How do I find a true length?
True length = √(plan length² + height²). The plan length is the distance between the two points seen from above, the height is the height of the transition.
How many divisions should each corner have?
Three or four per quarter circle are enough for marking out by hand on small parts. The chords are a little shorter than the arc, so the more divisions, the closer the pattern. Unfoldo draws the round edge as true arcs, so the DXF does not depend on the number of divisions.
Where should the seam go?
Usually in the middle of one flat side, square to the base edge: it is a straight line, easy to weld and away from the formed corners. Large parts are often made in two or four pieces with seams on the sides or at the corners.
Does sheet thickness change the pattern?
Yes. The pattern should be worked out on the mean surface of the sheet. A square given as an inside size moves out by half a thickness on each side, and the round end is corrected on its own.