The spiral bore

The swept-curve trumpet that exists in wood. A rectangle swept along a flat coil: 1000mm of centreline in 19 facets of 45° — 17 of them the coil, with a straight lead in and out — winding out from R34.7 to R112.9. Two faces of the tube are flat and two are faceted, which is what a swept curve buys — the section grows +8.2% at a mitre where a 90° lattice corner grows 41.4%.

Its viewer is a page of its own, drawn as built: the bell in the port and the mouthpiece on the straight tail, with a box to take them off. Drag to rotate, and the slider reveals the spiral a facet at a time. Turn it →

The cheek is the whole drawing

The cheek sheet has been cut, and cut twice, because the two cheeks are the same part and both go on the same way up.

The two cheek plates as cut, one lying on the other on a scratched workbench: a faceted band of pale masked ply winding a little over two turns out from a small centre to a straight tail, both rims crenellated with open notches, a number engraved beside each notch, and a small square hole at the inner end

The band is a single closed outline of 40 vertices, 216.50 × 218.51mm on a 236.50 × 238.51mm sheet, and it carries 149 mortices for 36 wall panels. Every one of those mortices is open at the rim, which is what --narrow buys: the cheek is no wider than the duct, so each tab is held across its thickness on one side only. The square hole near the inner end is the port — a 10mm square, drawn 9.85mm because the 0.15mm kerf opens it the rest of the way, and square rather than round because --port-square asks for the bore's own section. The wall panels that stand in the mortices are a second sheet, 574.95 × 96.60mm, and are not in the photograph.

36 panels and not 38, because the square port is what makes the lead panel go away. Each wall's lead is 20mm and carries a single tooth, dead centre, right where the port wants to be; --port-square folds that panel into the facet it already lies on — they are collinear, so nothing about the airway moves — and two panels with one tooth each leave the drawing. The plain sheet beside it, with no port at all, is 38 panels and 151 mortices.

Press-fit, and not airtight

Both sheets are cut now, and the bore is press-fit — the wall panels standing in the mortices between the two cheeks, a mouthpiece on the straight tail and a bell on the port at the inner end.

The spiral press-fit on a dark wood floor: a pale ply band winding a little over two turns, cornered at every facet, both rims crenellated with tabs and a number engraved beside each one; a straight tail leaves the outer end and carries a dark, glossy mouthpiece, and a bell engraved 10. stands on a dark ribbed throat at the inner end

It is not airtight. A press-fit with this many joints — a mitre at every facet and a tab at every mortice — leaves air gaps all along both rims, and they are closed the same way they are closed on the built instrument: several coats of shellac, which seal the ply and fill the gaps in the same pass. The three-turn trumpet, the grid-block trumpet, is the colour it is because it has had them.

Finished

The spiral has had them too, and it is finished: shellacked the same amber-brown as the three-turn, the tabs along both rims standing out darker than the faces around them. It has been blown; its note is not yet reported.

The finished spiral standing upright on its bell on grey card: the bell's round rim flat on the card and its ribbed throat rising into the port at the inner end of the coil, the faceted band winding a little over two turns above it in glossy amber-brown with darker tabs along both rims, and the straight tail leaving the outer end to carry a dark ring-stacked mouthpiece up to the top left

The numbers

curve a compass spiral, stepping its arc radius facet by facet
centreline 1000.0mm
facets 17 at 45°, plus a straight lead in and out
bend radius R34.662 at the centre out to R112.903 at the rim
R / bore 3.5 at the tightest
airway 10 × 10mm square, 100mm²
section at a mitre +8.2%
play 0.025mm per side
parts 36 wall panels + 2 cheeks + 1 end cap = 39, over 2 sheets
the cheek 237 × 239mm — cut this sheet twice
the wall panels 575 × 97mm

Three sheets, and which one was cut

The design ships three variants, each as a cheek sheet and a panel sheet, in ../built/ribbon-spiral-bore10-45deg-R35to113/cut-files/:

port panels mortices panel sheet
-narrow none 38 151 579 × 97mm
-ported-narrow round, 7 × 14mm 38 + a cap 151 579 × 97mm
-ported-square-narrow square, 10 × 10mm 36 + a cap 149 575 × 97mm

The square-ported one is what the photographs show. A round port needs no lead panel moved and so keeps all 38; the square one asks for the bore's own section and pays two panels for it.

Rebuild it

The generator is ribbon_bore.py, at the root of this repository, and both commands run from there. Report only, writing nothing:

python3 ribbon_bore.py \
    --shape=spiral --port --port-square --cap --narrow --no-write

Every number on this page comes off that report. Writing needs an --out whose name says narrow, which the generator insists on so a sheet cannot overwrite its full-width twin:

python3 ribbon_bore.py \
    --shape=spiral --port --port-square --cap --narrow \
    --out=built/ribbon-spiral-bore10-45deg-R35to113/cut-files/ribbon-spiral-bore10-45deg-R35to113-1000mm-ported-square-narrow.svg

These sheets were cut. Both of them reproduce byte-identically from the line above, which is what makes the numbers here measurements rather than notes.

The rest

every swept-curve design · the bell and the mouthpiece, from trumpet-elbows-allowed · the grid-block trumpets