What does the larger diameter measure, if the big mouth is a saddle?

It measures the cone's FICTITIOUS base at the pipe's axis — the diameter it would have if it ran down that far. The big mouth is a saddle and has no circle in any plane, so there is nothing to measure on it; the fictitious base is the catalogue convention, and it is the only measurement that closes the part alongside the collar and the length.

Is the mouth an arc struck with a compass?

No. The collar is, and it is the sector's constant-radius arc — struck with the compass at the apex. The mouth has a different radius at every station and is marked point by point, like the angle-cut cone's. The difference is that there the polyline was on the inside and here it is on the outside.

Why does the length have a minimum that depends on the angle?

Because on a tilted nozzle the mouth is shallower on one side, and if the collar falls short of it the part would have negative length there. The condition falls out of the arithmetic: 2·c·sin(ang) has to exceed d2 + d·cos(ang). At 90 degrees that becomes c greater than half of d2, which is the ordinary branch's guard.

And if the taper is very small?

The part is a cylindrical branch, and there is a part for that. Below a millimetre of difference between the two diameters the cone's apex runs too far away and the sector degenerates — the calculation refuses, for the same reason and with the same guard the cone has.

Conical Tap (Conical Tee) development

What it is

The nozzle that leaves the pipe flared at the base and tapers to the collar. The ordinary branch handles a cylindrical branch on a pipe and the cone branch handles a cylindrical branch on a cone; what was missing is the CONICAL branch on a pipe — the real nozzle on most vessels, because flaring the base spreads the weld's stress instead of concentrating it in a narrow mouth.

Where it is used

Pressure vessel and tank nozzles, reinforced take-offs on headers, cyclone inlets with a flared base, conical manway necks.

Measurements the calculation needs

D Diameter of the collar (smaller mouth)
D1 Diameter of the notional base, on the pipe axis
D2 Diameter of the pipe
C Length, from the pipe axis to the collar
ANG Angle of the nozzle to the pipe axis (90° = upright)
DV Divisions
THK Plate thickness

Worked example

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

Diameter of the collar (smaller mouth)	200 mm
Diameter of the notional base, on the pipe axis	400 mm
Diameter of the pipe	600 mm
Length, from the pipe axis to the collar	500 mm
Angle of the nozzle to the pipe axis (90° = upright)	90°
Divisions	32
Plate thickness	6 mm
The flat pattern fits a plate of	808 × 307 mm

Result of the example

Plate	808 × 307 mm
Arc radii	494.9 mm
Sector angle	70.6°

Conical Tap (Conical Tee) flat pattern: drawing of the template with the worked example dimensions — Cut lines in purple, welds in green and reference lines in orange. Plate 808 × 307 mm.

Frequently asked questions

What does the larger diameter measure, if the big mouth is a saddle?: It measures the cone's FICTITIOUS base at the pipe's axis — the diameter it would have if it ran down that far. The big mouth is a saddle and has no circle in any plane, so there is nothing to measure on it; the fictitious base is the catalogue convention, and it is the only measurement that closes the part alongside the collar and the length.
Is the mouth an arc struck with a compass?: No. The collar is, and it is the sector's constant-radius arc — struck with the compass at the apex. The mouth has a different radius at every station and is marked point by point, like the angle-cut cone's. The difference is that there the polyline was on the inside and here it is on the outside.
Why does the length have a minimum that depends on the angle?: Because on a tilted nozzle the mouth is shallower on one side, and if the collar falls short of it the part would have negative length there. The condition falls out of the arithmetic: 2·c·sin(ang) has to exceed d2 + d·cos(ang). At 90 degrees that becomes c greater than half of d2, which is the ordinary branch's guard.
And if the taper is very small?: The part is a cylindrical branch, and there is a part for that. Below a millimetre of difference between the two diameters the cone's apex runs too far away and the sector degenerates — the calculation refuses, for the same reason and with the same guard the cone has.

Conical Tap (Conical Tee) dimension drawing: D (Diameter of the collar (smaller mouth)), D1 (Diameter of the notional base, on the pipe axis), D2 (Diameter of the pipe), C (Length, from the pipe axis to the collar), ANG (Angle of the nozzle to the pipe axis (90° = upright)), DV (Divisions), THK (Plate thickness), marked on the part

Calculate a Conical Tap (Conical Tee)

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