Square-to-Round Transition Development

Any line on a square-to-round that is neither vertical nor horizontal appears shorter in every orthogonal view than it really is, so laying out from plan dimensions produces a pattern too small and a fitting that will not close. The true length is the hypotenuse of the plan distance and the height, and on an ordinary transition it is far longer than the plan view suggests: a corner element measuring nine inches on the plan can be well over eighteen once the height is in it, which is the error the whole method exists to prevent. The pattern is then built by laying those triangles down in sequence, and the corner elements and the elements to the middle of each side are the two extremes that set everything between them. THE CIRCLE IS DIVIDED INTO ELEMENTS BECAUSE A CURVE CANNOT BE TRIANGULATED DIRECTLY, and the division is where accuracy is won or lost. Each element is developed as a straight chord, so the developed curved edge is a polygon inscribed in the circle and it is always SHORT of the true circumference. More elements close that gap and cost layout time; eight to sixteen per quadrant is common practice, and the shortfall at the entered count is reported here so the choice is made with a number rather than a habit. THE CHECK AT THE END IS WORTH DOING EVERY TIME. The developed pattern's curved edge, measured along its length, should come back to the circumference of the round end. If it does not, an element true length is wrong or the division was uneven -- and finding that on the bench costs a sheet, where finding it at the fitting costs the fitting and the crew. Everything after the development is allowances: seams, laps, and the metal thickness itself on a formed edge, which are added to the developed shape rather than being part of it. This gives the governing true lengths, the element chord, the circumference check, and the sheet the pattern needs. It does not draw the pattern or emit its coordinates, and it does not lay out an eccentric transition's unequal elements individually -- an offset makes every element different and the full development needs all of them. It does not compute bend allowance for the metal thickness and forming method, address stiffening, reinforcing, or the gauge required for the duct pressure class, or select a seam type. SMACNA's duct construction standards, the shop's own layout practice, and a test piece govern.

true length of an element line = sqrt(plan distance squared + height squared); the developed curved edge is the sum of the chords across the elements, each chord being 2 R sin(pi / N) for N elements, which must come back to pi x diameter.

Triangulation development of a square-to-round transition by name. Seam and lap allowances are added to the developed shape, not part of it. It gives the governing true lengths, the element chord, the circumference check and the sheet size; it does not emit pattern coordinates or develop an eccentric transition's unequal elements individually. SMACNA's duct construction standards, the shop's layout practice, and a test piece govern.

One hypotenuse and one sine on dimensions the reader has; no pattern or standard text is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: square_side_in, round_diameter_in, height_in, offset_in, elements_per_quadrant, seam_allowance_in, plan_corner_distance_in, corner_true_length_in, midpoint_true_length_in, circumference_in, developed_arc_in, arc_shortfall_in, sheet_length_in

• A concentric transition's governing elements an offset makes every element different and needs all of themthe shop's layout practice
• No bend allowance the metal thickness and forming method are not in itSMACNA duct construction standards
• Gauge, stiffening and seam type are not selected those follow the duct pressure classSMACNA duct construction standards