Two round tubes cannot be joined at an angle by cutting one of them square. A square cut meets a curved surface at a single point and leaves a gap that widens to either side. The end has to be shaped to the surface it lands on, and that shape is a saddle: a curve in one plane and a different curve in the other.
This is why notching is the step in tube fabrication where inexperienced work shows first. A notch that is roughly right will weld, with enough filler, and the joint will look acceptable from outside. A notch that is right welds with a consistent gap, a consistent bead, and a fraction of the heat.
Picture the branch tube standing on the header at an angle. The line where its wall meets the header wall is the intersection curve. On the branch, that line rises and falls around the circumference: deepest on the side where the branch points along the header, shallowest where it crosses over the top.
The notch therefore has two long points, called horns, on the sides, and a shallow saddle between them. Cut too deep and the horns disappear and the joint gaps at the sides. Cut too shallow and the branch stands off the header on a ring of contact with a gap underneath. Both failures look similar once the parts are tacked, which is why the fit is checked before anything is tacked.
The shape of the saddle is not a matter of taste. It is a function of two things: the ratio of branch diameter to header diameter, and the angle between them.
A small branch on a large header produces a shallow saddle, because the header wall curves away slowly relative to the branch. Two tubes of similar size produce a deep saddle with long horns. As the angle closes toward a right angle the horns shorten; as the branch leans along the header, the saddle deepens and the horns lengthen. Two branches that look identical in a photograph can need completely different notches because one is landing on a larger header or meeting it at a different angle.
This is also why a notch template is specific to one combination. A template that works for one branch on one header does not transfer to a different size, and using it anyway produces a joint that is close enough to tack and wrong enough to fail later.
A hole saw of the header's diameter, run into the end of the branch, produces a saddle for a right-angle joint. It is fast and accurate when the sizes match exactly, and it is limited to that geometry. A tube notcher holds the branch at a set angle and cuts with a hole saw or an end mill, which extends the method to angled joints.
Abrasive and hand grinding is the universal method: mark the profile, cut roughly, and shape to the line. It depends entirely on the operator, and it is the method most likely to produce a joint that fits well enough to weld and badly enough to leak at the horns.
Laser and waterjet cutting of the developed profile is the repeatable method. The tube is cut as a flat development or on a rotating axis, and the notch comes out the same every time. It is the only method that scales, and it is the one that makes sense once a part is made in quantity.
A tube-to-tube joint has no backing and no root gap to hide behind. The fit is the weld preparation. If the notch is tight against the header, the arc cannot reach the root, the two walls sit in contact, and the weld sits on top as a fillet that penetrates nothing. If the notch is loose, the welder has to bridge a gap, and on thin wall that means either burning through or adding so much filler that the joint becomes a lump with a shrinkage problem.
The correct fit is a small, even gap all the way round, and the horns are where it is hardest to achieve because the material there is thin and the angle is acute. A horn that is a sliver is worse than a horn that is slightly short: a sliver of wall heats instantly and disappears under the arc.
Inside the header, the branch interrupts the flow. A branch that protrudes into the bore is a wall in the path; a branch that is flush is a hole in the wall. Neither is neutral, but the protruding version is the one that costs flow and generates turbulence, and it is the version you get when the notch is too shallow and the branch is pushed in until it touches.
The opposite error is a notch cut so deep that the branch sits inside the header wall, leaving a lip of header material protruding into the joint. That lip is difficult to weld and impossible to inspect, and it is where a crack will start under vibration.
Several branches landing on one collector is the hardest version of this problem, because each notch interacts with the others. The first branch is cut against an uninterrupted wall. The second lands partly on the wall and partly on the first weld. The third may land on both.
The practical answer is to fit in sequence and to allow the later branches a little more clearance, since their seat is no longer a clean curve. It also helps to keep the weld toes of earlier joints out of the path of later notches, because a notch that cuts across an existing weld produces a joint with hard, mixed material at the root and a fit that changes as the arc crosses it.
Push the branch into place without clamping and look at the gap around the circumference. It should be visible and roughly even, and the horns should meet the header without force. If the branch rocks, the saddle is too shallow. If it sits high on the horns, the saddle is too deep.
A light behind the joint shows the gap better than the eye does, and a marker line around the branch at the seated depth shows whether the branch has gone in evenly. Both checks take less time than the repair.
Notched and coped joints are part of the tube work grouped under exhaust pipe sections, exhaust pipe and exhaust pipe, and the welding that closes them is described under TIG stainless steel welding.
Notch geometry is decided by the two diameters and the angle, so those are the numbers that have to be right before anything is cut.
The titanium version of this joint work is shown under TIG titanium welding parts and among our titanium fabrication components, where the same saddle geometry is cut and welded in a different alloy.
