Duct sizing and geometry
Enter opposing elbow geometry and offset or straight gap to calculate connector cuts and developed length.
Calculate a two-elbow offset from a required total movement, signed rise and over, or an installed middle gap using actual fitting dimensions.
A two-elbow offset combines circular bend projections with a straight distance between inward fitting ends. The elbows have equal opposing deflections so the inlet and outlet return parallel, although their centerline radii may differ. Inward tangent tails contribute to the offset and axial run along with the middle gap; outer parallel tails add axial run without increasing the transverse offset.
Installed gap and straight-piece cut length have different reference planes. Insertion allowance is extra material overlapping the connections and therefore does not increase installed travel. For signed rise and over, the resultant magnitude locates the offset plane and the coordinate angle describes its direction in the chosen drawing viewpoint. It does not supply connector clocking, seam orientation or clearance around the duct’s outer envelope.
Let R=R1+R2, θ=equal elbow deflection, B=sum of diagonal tangent tails, E=sum of outer parallel tails and G=installed gap between fitting ends. Offset O=R(1−cosθ)+(G+B)sinθ; axial run L=Rsinθ+(G+B)cosθ+E; G=[O−R(1−cosθ)]/sinθ−B; cut length=G+entered total insertion allowance; developed centerline length=Rθ+G+B+E, θ in radians. For rise/over mode, O=√(rise²+over²) and transverse direction φ=atan2(rise,over) in [−180,180) degrees.
R1/R2 = elbow centerline radii; G = installed connector gap; B/E = inward/outward tangent-tail sums; O = total transverse offset; L = axial run, all inches. θ is the common elbow deflection, evaluated in radians in trigonometric expressions.
Use installed gap for the face-to-face layout, cut length for the stated insertion convention, and axial run for end-to-end centerline projection. Check actual shop drawings and clearance independently; developed centerline length is not a sheet-metal takeoff.
Inputs: Constructed 90° bends with 6 in centerline radii each, inward tails totaling 2 in, outer tails totaling 3 in, insertion allowance 1 in and required offset 20 in.
Calculation: Circular bends contribute 12 in offset. Remaining diagonal length is 8 in; subtract 2 in fitting tails to obtain 6 in gap. Cut=6+1=7 in; axial run=12+3=15 in.
Result: 7 in straight-piece cut, 20 in centerline offset and 15 in installed axial run.
Inputs: Constructed installed gap 6 in; opposite 90° bends with 6 in centerline radii each, inward tails totaling 2 in, outer tails totaling 3 in and insertion allowance 1 in.
Calculation: Straight tangent-to-tangent length=6+2=8 in. Offset=12+8=20 in; axial run=12+3=15 in; cut=6+1=7 in.
Result: 7 in straight-piece cut, 20 in centerline offset and 15 in installed axial run.
Inputs: Constructed signed rise +12 in and over +16 in in one transverse coordinate drawing. Two opposite 90° bends with 6 in centerline radii each; inward tails 2 in total; outer tails 3 in total; insertion allowance 1 in.
Calculation: True offset=√(12²+16²)=20 in. Direction=atan2(12,16)=36.869898° counterclockwise from +over. Existing arc/tail geometry gives gap=20−12−2=6 in; cut=6+1=7 in; axial run=12+3=15 in.
Result: 7 in straight-piece cut, 20 in resultant offset and 15 in axial run; coordinate direction +36.870°, not an installation rotation instruction.
The two bends and their inward tangent tails already create a minimum transverse displacement. A smaller target would require a negative installed gap in this geometry; revise the actual fitting arrangement rather than interpreting that as a cut length.
No. Radii already generate the arc projections. Tangent tails start at the arc tangent planes and include only the actual straight portions to the fitting ends. Adding radius takeout again double-counts geometry.