Tube coping and mitre templates

Tell it the main tube and the branch, and it works out the line where the branch meets the main tube, unrolls it round the branch (π × OD long) and prints it at real size. Wrap the paper round the branch, tape it, scribe or grind to the red line, and the tube sits down on the main tube.

How to use it

Main tube: round (outside diameter), or square/rectangular with its corner radius.
Branches: outside diameter and wall, the angle to the main tube (90° is a T; down to 15°), an offset if the branch’s axis misses the main tube’s axis (a side entry), and for several branches into one node their position round and along the main tube. A later branch is also fitted against the branches before it — a bike’s down tube against the seat tube at the bottom bracket, or the two braces of a truss K-joint. The examples menu has these.
Cope to:
- inside diameter — the inside edge of the wall sits on the main tube all round and the outside edge stands off a little, leaving a V for the weld. The usual choice when welding.
- outside diameter — the outside edge fits, but on thick wall the inside edge digs in at the ears; fine for thin wall, or if you will bevel the inside.
- mean — between the two; good for thin-wall bike tubing and for brazing. The dotted lines on the template are the other two, so you can see how much they differ.
The template has a square line (line it up with a line squared round the tube), the 0°, 90°, 180° and 270° marks (0° is the acute side, in the plane of the two tubes; 0° and 180° are the tube’s centrelines), 15° ticks, the red cut line, the waste shaded, and a glue tab.
Print at real size: pick the paper (A4, Letter or A3) and download the PDF or print. Templates wider than the paper are tiled across pages with an overlap, trim lines, ⊕ registration marks and a page map; page 1 (or the corner of a one-page template) has a 100 mm square. Print at 100 % — “Actual size”, no “fit to page” — and measure the square before you cut. SVG is true size in millimetres; DXF (R12, mm) has the cut line on its own layer for a plasma or laser tube cutter.

The Mitre tab does plane cuts: two tubes meeting at a corner (each cut at half the angle), or a tube onto a flat face. The Hole-saw method tab gives, for each pass, the saw (the exact size if a common hole saw matches, otherwise the nearest bigger and smaller), the joint angle, the setting on a notcher that reads 0° for a square joint, the offset to set between the tube and the saw, and how far to turn the tube for a second pass against an earlier branch.

For welding settings see the welding reference; for the weight of the tube, the metal weight calculator; and for flat parts, the sheet-metal bending tool.

How it works

The cut is where lines along the branch’s surface, coming in from the far end, first touch the main tube (or an earlier branch). Each body is a set of points within a radius of a core — a rectangle swept along the main tube (a round tube is a rectangle of size zero), or the axis of a branch — so along a line the distance is convex, and the touching point is found by a ternary search and then bisection. For a round main tube that gives back the textbook result, t(α) = (√(R² − (e + r sin α)²) + r cos α cos θ) / sin θ; equal tubes at 90° give a saddle as deep as the radius. The 3-D view (three.js) shows the joint with the cut edge in red.

Browser support

Any current browser. The 3-D preview needs WebGL; printing uses the browser’s print dialog.

Privacy

Everything is worked out in your browser and your settings stay in its local storage. The page loads three.js (the 3-D view) and, when you download a PDF, jsPDF, both from cdn.jsdelivr.net; nothing you type is sent anywhere.