Rectangular duct elbow calculator
Enter the duct width and depth, throat radius, angle and pieces (0 for a radius elbow). You get both cheeks and the throat and heel wrappers of a rectangular duct elbow.
Enter your measurements
Seam
3,769.6mm
Exact geometry
- 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
Draw the cheek
From one centre, swing the throat arc at the throat radius and the heel arc at throat radius plus duct width, through the elbow angle. For a mitered elbow, draw the straight chords between the miter corners instead.
Close the cheek
Join the arc ends with two straight lines; these are the duct mouths. Cut two cheeks the same.
Lay out the heel wrapper
Draw a strip as wide as the duct depth and as long as the heel edge of the cheek, measured along the arc. For a mitered elbow, mark a bend line at each miter corner.
Lay out the throat wrapper
Draw a second strip, duct depth wide and as long as the throat edge, measured the same way.
Form and assemble
Roll the wrappers to the cheek curves (or fold them on the bend lines) and seam them to the cheeks, heel to the outer edge and throat to the inner edge.
Good to know
- FabLayout runs the same code as Trueflat; the result is exact geometry.
- Source: No published source. Flat cheeks are drawn to true shape and the throat and heel wrappers are unrolled to their true arc or polyline length, in closed form on the middle of the sheet; checked against an independent reference implementation in Trueflat.
Method and formula
A rectangular duct elbow is four parts: two flat cheeks in the plane of the bend and two wrappers that run round the throat and the heel. The duct width A lies in the plane of the bend; the depth B is the distance between the cheeks.
The centre-line radius is R = Ri + A ÷ 2. The throat radius is Ri and the heel radius is Ri + A.
- Radius elbow (pieces = 0): the cheek is a ring segment between the two arcs. The wrappers are ρ × α long, using the true arc and not a chord sum. The cheek outline is drawn with n chords; the bend lines on the wrapper are only marks for rolling.
- Mitered elbow (pieces 2 to 12): N = pieces − 1 and β = α ÷ (2N), the same axis as a round segmented elbow. The cheek edges become straight lines between the miter corners, and each wrapper is 2Nρ tan β long with a bend at every corner.
Both are exact. With sheet thickness, inside or outside sizes are converted to the sheet middle: width and depth change by the thickness and the throat radius by half of it, so the centre line stays put.
Worked example
A = 100 mm, B = 100 mm, Ri = 100 mm, α = 90°, so R = 150 mm.
As a radius elbow, the cheek area is (π ÷ 2) × 150 × 100 = 23 561.94 mm², the heel wrapper is 200 × π ÷ 2 = 314.16 mm and the throat wrapper 157.08 mm long.
With 2 pieces, β = 45°: the heel wrapper is 400 mm, the throat wrapper 200 mm, and the cheek area is 200² − 100² = 30 000 mm².
Questions
What does pieces = 0 mean?
It means a radius elbow: smooth arcs on the cheeks and rolled wrappers. Enter 2 to 12 for a mitered (gored) elbow made of straight sections, with the wrappers folded at each corner. 1 is not allowed.
Which side is the width?
The width A is the side that lies in the plane of the bend, so it runs from throat to heel. The depth B is the cheek-to-cheek size, which is also the width of both wrapper strips.
Can the throat be square?
Not in this version. The throat radius must be at least 10 mm. A square-throat elbow with a zero radius is a different part.
Similar calculators
More in TrueflatConeTruncated coneCone by triangulationSee what the app does