Technical note 9

TN-9: The Keel

The chair's information lives in one member. First draft 17 Aug 2026, from KU's ledger board sketch of the same day and the geometry already published in the cut list. Status: DRAFT, a geometry and method note; every number in it is derived from the project's own Keel Chair cut list rather than measured afresh.

The claim

The triangle explains why the chair is stiff. It does not tell you how to build it. The member we have been calling the rear leg, and now call the KEEL, is the only part that touches all four others, it carries every difficult joint in the frame, and all of its stations are measured from one end. Build the keel first and the rest of the chair can be scribed into place without a rule. The triangle is the argument; the keel is the instruction.

The contacts

Every joint on the keel, measured axially from its top end [DERIVED from the K2 cut list, make_k2_miter_cutlist.py]:

Four contacts. No other member in the chair touches more than two. And 405 is 70 + 335, so the third station is the second station struck again from the first mark.

Why they are the hard ones

Count the six joints in a side frame by difficulty rather than by number. The keel owns four: two at 40 degrees and two at 60. In the mitered build those are the two 50 degree bevels, which want a saw that swings past 45, and the two 30 degree bevels. The two joints the keel does NOT own are the seat to back and tie to front apexes, both at 80 degrees, which is 10 degrees off square, a run of 3.2 mm at 18 thick [DERIVED: run = t/tan θ].

So the keel carries every awkward cut in the frame and leaves behind the two that are very nearly square. That is a stronger statement than it first appears, and it is checkable line by line against the cut list.

What it does not encode

Three numbers, and all three are comfort rather than geometry [DERIVED]:

• the back above its seat kiss, 687 less 219, so 468
• the seat forward of its keel kiss, 413 less 295, so 118
• the floor line, which sets both feet at once: the keel 177 below the tie station and the front 156 below its tie station

The tie needs nothing: 295 long, a kiss at each end, no overhang anywhere. It is a pure triangle side, which is why it closes the frame.

So: the keel plus the three angles is the truss, and three further numbers make it a chair. KU's "(almost)" is exactly three numbers wide.

The real argument: one datum

This is the part that matters more than the build order. Three stations measured from one end of one part is single datum dimensioning, and it removes tolerance stack-up by construction rather than by care.

Today an error in a keel station, an error in block thickness, and an error in a member length all add into the same joint. With the keel as the sole datum and the other members scribed in place, only the three stations carry error, they are all struck from the same end, and nothing accumulates. The scribed members cannot be wrong, because a scribed member is by definition the length of the gap it fills.

It also retires the failure mode named in TN-8. The recurring cost in this project has been the unstated datum, which face, which end, which corner. A keel has one end and two faces, and the face assignment is on the drawing.

The trade already has words for this

A STORY POLE is a narrow board carrying every position that matters along one axis, used to transfer them without measuring again; also storey pole, story stick, storey rod, jury stick, scantling, scantillon [VERIFIED against the Wikipedia entry and the Fine Woodworking article, 17 Aug 2026]. A ROD, in British cabinetmaking, is the full size 1:1 setting out from which every component and joint is taken [VERIFIED against Rowden Atelier, 17 Aug 2026].

The keel is both, and then it does something neither of them does: it stays in the chair. A story pole is thrown in the corner when the wall is up. This one takes the load. That is the whole idea in one sentence, and it is why the name comes from boatbuilding instead: a keel is laid first, is the primary structural member, and is the datum the rest is lofted from.

Two dimensions and a thickness

There is no flip, and there is no handedness. The reason is more useful than the conclusion.

The chair is a two dimensional design carried across the room on a thickness. Every member is a profile in the side elevation, extruded in Y, across the chair: the staves 75, the panels 400. The keel's 18 lies IN the side elevation and its 75 runs across the chair, which is why the two triangles sit on the keel's two in plane faces and why the offset between them is 17.5 measured in the side elevation itself [DERIVED: the kiss points A and TEE lie on the line y - x = 98.40, V and S2 on y - x = 123.10, both bearing exactly 45.00 degrees, perpendicular separation 17.47]. Both end miters are inclined in that same plane, across the 18, which is why the cut list computes the run from t = 18 and speaks of a short face and a long face.

A part that is a profile extruded in Y is symmetric about its own mid width plane by construction. Its mirror image is itself. So the second keel is not a mirrored part and it is not a flipped part: it is the same part translated in Y to the seat width. As KU put it, route it from two plies stacked, separate the plies, done.

That holds for every member, which is the larger point: the whole chair is a 2D drawing plus a Y translation, and the left frame is a translated copy of the right frame rather than a mirror of it.

Handedness can only enter by adding a feature that is not prismatic in Y: a pocket on one side, a chamfer on one edge, a boss, a single sided scoop. So the design rule for a net shape keel is one line: KEEP THE PROFILE PRISMATIC IN Y. Note that this is a rule about the woodwork only. The printed barrel nut holder of the previous week has a single sided swing slot and is therefore handed; hardware can acquire a hand even where the frame cannot.

Why this is the manufacturing argument, not a footnote

A prismatic profile is the cheapest class of part to make accurately, and nearly every process that is good at it is a two and a half axis process: CNC routing, waterjet, laser, die cutting, bandsaw against a template, and extrusion or roll forming in metal. An organic keel is therefore free: the silhouette can be any curve at all, deep where the moment is and slim where it is not, at no cost in tooling, because the third dimension never varies.

And cutting the pair from one stack is worth more than it looks. Two keels routed together are identical to each other by construction, not by care, and identical to each other is the property that actually squares the chair. It is the same single datum argument one level up: the pair is its own comparator.

How wide does the rafter have to be?

KU, on seeing the keel drawn as a little rafter with fish mouths: it does not need to do much work in bending, so the width is really set by lateral stability and by the size of the mating shelf. That is right, and the numbers say it more sharply than the intuition does.

All of the following is DERIVED, from keel_width_check.py, and every input is an assumption printed with the result. Seat load 1500 N on the chair, so 1061 N of axial in one keel at the 45 degree rake. Lateral shove 300 N at the foot. Plywood E 7000 MPa and MOR 33.7 MPa [STANDARD: FPL GTR-282 Table 12-1 gives MOE 6.96 to 8.55 GPa and MOR 33.7 to 42.6 MPa], allowable taken as MOR/3.5, so 9.6 MPa. Kiss bearing allowable 1.5 MPa. The duty loads are the weak link here and are on the verification queue.

The keel is loaded at its four stations and nowhere between them, so it has no transverse span to speak of. Its in plane bending comes only from eccentricity: the truss line is the keel's FACE, not its centroid, so the axial force acts 9 mm off axis and the moment is 9.5 N.m. That is the whole bending demand.

So as a rafter it wants to be SQUARE: 18 wide in 18 ply. Bending is not a design consideration at this scale, it is a rounding error. The width is set by the joint, exactly as KU guessed, and the fish mouth governs: a seat cut one member thickness deep, held to the carpenter's one third rule, needs 54. The published 75 gives a 25 deep shelf inside the same rule, which is comfortable rather than extravagant.

The one case that is not solved by width

Out of plane is a different story, and it is the one that matters.

The keel cantilevers 177 from the tie station at 405 to the foot at 582, and that cantilever is unbraced. Under the assumed 300 N shove at the foot:

Against 9.6 allowable, 18 mm ply fails this case at any sensible width and 25 mm passes. The reason is in the section modulus: out of plane capacity goes as w.t squared, so going from 18 to 25 thick buys 1.93 times while widening from 40 to 80 buys only 2.00 times for twice the material. WIDENING THE RAFTER IS ALMOST USELESS HERE. KU's instinct that lateral stability drives the design is right; his instinct that width is the variable that answers it is not.

Three things do answer it, in order of how much they buy:

1. KILL THE CANTILEVER. The stress is linear in its length, so a rear stretcher between the two keels near the floor, or dropping the tie station, halves the stress for the price of one stick. This is the cheapest fix by a wide margin and it costs no material in the keel at all.
2. THICKNESS. 25 mm ply, which is what KU's two ply illustration assumed anyway, nearly doubles the capacity.
3. WIDTH, last and least, and only because the fish mouth wanted it anyway.

How deep is the fish mouth, and how wide the board

A member of thickness t meeting the keel at joint angle theta has a square end face perpendicular to its own axis, so seating that whole end face removes, measured across the keel's width,

d = t cos(theta)

and the notch's footprint along the keel axis, kiss arris to far arris, is t / sin(theta). At t = 18 [DERIVED, keel_notch_check.py]:

KU's construction, an 18 core with one notch coming in from each edge, gives 18 + 13.79 + 9.00 = 40.79. The carpenter's one third rule applied to the deepest notch alone gives 3 x 13.79 = 41.37. Two different arguments, six tenths of a millimeter apart, which is the pleasant kind of agreement.

One correction to the construction, in the direction of less material. The back and the tie sit on OPPOSITE faces and 70 apart, and their notches never meet: worst case, both wedges pointed at each other, the back notch reaches 355.8 and the tie notch starts at 377.0, clear by 21.2 mm. So the two depths do not have to be stacked. The deepest single notch governs, and it is the tie's 13.79 at 40 degrees.

Either road lands on about 41. Call it 45 in hardwood and the tie notch leaves 69 percent of the section, just inside the rule, with a round number on the tape.

The hardwood keel as drawn, 17 Aug

KU's build spec, and the drawing that goes with it (k2-keel-layout.pdf). A board 50 deep and 25 to 32 across, the canonical Keel geometry untouched.

THE WING IS THE NOTCH. Because the two triangle lines stay 17.5 apart and the board grows outward from them, the depth removed at every joint is exactly the wing, 16.25, at all three. That is 32.5 percent of a 50 board, inside the one third rule, and three times 16.25 is 48.75, which is why 50 is the first round board that clears it. Note this is a different quantity from the t cos(theta) figure above: that one is how deep a notch must be to seat a member's end in a keel only as thick as the joint, this one is how far the board was grown.

THE FISH MOUTH IS A TRIANGLE WITH A RIGHT ANGLE AT ITS VERTEX. Its two walls are the member's own faces, its near face and its square end, which are perpendicular to each other, so the two saw cuts are square to each other and meet at a point. Where they cross the edge they make theta and 90 minus theta: 60 and 30 at the front and the back, 40 and 50 at the tie. The openings are 37.5, 37.5 and 33.0.

THE VERTEX IS THE ONLY THING TO LAY OUT. It is the old kiss point, so it does not move, and it is 16.25 in from its own edge at all three. Strike it, drill 1.5 through it, saw both faces down to the hole. Three points and two angles each is the whole layout.

THE DATUM IS THE TIP, not the kiss: the point where the seat bevel runs out on the long edge, which is a physical corner a tape can hook. From it the vertices are 110.2 (front, long edge), 375.3 (back, short edge) and 445.3 (tie, long edge).

THE FOOT is mitered flat to the floor at 45, then the sharp heel is trimmed at 60, parallel to the back, leaving 50 of floor contact. The floor cut begins at 605.7 and the heel finishes at 641.0.

What the frame actually carries, 18 Aug

The built chair made the question concrete, so the frame was solved rather than argued: a plane frame with rigid joints, both keels as one member of 2 x 35 x 50 salvaged hardwood [assumed E 14000 MPa, a dense eucalypt; UNVERIFIED against the actual species], panels 400 x 18 at E 7000 MPa, all loads and results DERIVED from k2_frame_solve.py with every assumption printed beside its result.

Seated, 1500 N on the seat, feet on a frictionless floor:

Reactions 470 N at the rear foot and 1030 N at the front; the horizontal reaction solves to 0.00, which is the frictionless check passing. Three readings follow. THE TIE IS THE ONLY TENSION MEMBER, which is the structural justification for the fish mouth architecture: every other joint is a bearing joint that load keeps closed, so its screws are keepers rather than structure. THE FRONT IS THE WORKHORSE, at three quarters of the total seat load in compression, which bears directly on the timber front leg variant below. And the perch case, 1200 N on the seat nose, lifts the rear foot, because the nose overhangs the front foot by 58 mm; that is a stability watchpoint, not a strength one. Leaning back is carried by friction at the feet, with tipping at about 570 N of rearward push [DERIVED, same solve].

Where the screws matter, and where they only keep

The tie's 501 N arrives at each of its ends whole, so with two screws per end each screw carries about 250 N of shear, far inside the single screw capacity of any 4 mm screw in this ply, so TWO SCREWS PER TIE END, FOUR ON THE TIE, is the count, exactly as KU guessed before the solve. Every other screw in the frame is a keeper: it holds a compression joint closed against handling, transport, and the day someone drags the chair by its back. Keep every screw at least 30 mm from a ply end, and the count stays a judgment call rather than a calculation, because the load path does not pass through them.

One geometric rider from the same model: the keel's top tip lands 65.8 mm short of the seat nose, so nothing interferes and blunting the tip is a robustness choice, not a clearance requirement, exactly as the layout drawing assumes.

The four panel variant, and the Vilbert coming back around

The lateral problem has a name now: the front has nothing to give it lateral stability. KU's answer is to make the front and the tie full width panels, so that all four non keel members are 400 wide.

It is a one line change to the cut list. Every length, every station, every joint angle and every block stays exactly as published; only the quantity and width of two parts move, from two at 75 to one at 400 [DERIVED]:

• part count falls from EIGHT to SIX: four panels and two keels
• material rises 27 percent, from 0.628 to 0.795 square meters of 18 sheet, which is 28 percent of a 2400 x 1200 sheet for a whole chair
• the blocks do not change at all, because a panel still lands on a keel only 75 wide, so the contact and the cleat are the same as before

Structurally it is the answer rather than a patch. The two keels are now joined by a plate at every station instead of by a plate at two stations and a pair of sticks at the others, so the frame becomes four diaphragms carried on two keels, and racking is resisted by panel shear rather than by joint stiffness. The foot cantilevers below the tie remain, but their roots are now plate fixed rather than stick fixed.

And the side elevation does not change at all. The panels are 18 in plane like the staves they replace, so the truss reads exactly as before in profile; the chair only closes up when seen from the front. Which is to say it becomes a Vilbert again. The search began at Panton's four panel chair, went through the fruitful error into a truss of two triangles, and now arrives at four panels plus a keel: the same four surfaces, but with the geometry underneath them that the Vilbert never had.

Two honest cautions. A full width front panel and a full width tie panel close the space under the seat, which is a real ergonomic difference and not only a visual one: feet cannot tuck back. And 27 percent more material in a chair whose argument has been economy is worth spending deliberately rather than by default.

The fish mouth deletes the blocks

Worth stating plainly, because it is the largest practical consequence of the net shape keel. A block exists because a square end cannot locate itself: it fills the acute corner behind the end and gives the screw something to bite. A routed fish mouth is the same block, SUBTRACTED instead of added. Each keel carries four contacts, so four notches replace four blocks a side, which is eight of the chair's twelve.

Two riders. The inside corner of a notch is a stress raiser, and a router physically cannot cut a sharp internal corner, so the fillet arrives free and in the right place. And the block path stays: routed fish mouths belong to the level 3 keel, while the pre blocked board stays level 1, because a notch needs a machine and a block needs a saw.

Implications for making

TEMPLATES. The keel is its own template. A drilling jig or a router template taken from one keel reproduces every station in the chair, and the jig can be the keel. That is the cheapest possible route from one accurate part to many.

THE PRECISION BUDGET GOES IN ONE PLACE. If the keel is right, the chair is right, because everything else is scribed. This is the argument for spending digital manufacture on the keel and nothing else: one CNC part, one casting, one printed jig, four sticks cut with a hand saw.

NET SHAPE WANTS PANEL STOCK, A LAMINATE, OR METAL. The keel is the only member carrying bending from two directions, so an organic keel should be deep where the moment is and slim where it is not. Cut that silhouette from solid sawn timber and the waist has short grain exactly where the moment is highest: taper a plain board and you have designed the failure. Cut it from panel stock, from a laminate whose plies follow the curve, or from metal, and the objection disappears. KU's illustration, routed from plies and separated in Y, is the right instinct twice over: the material that makes the prismatic profile cheap is also the material that makes the taper safe.

LEVELS. The pre blocked keel, a plain board with its four blocks already glued and screwed at the stations, is the maker path and should sit at level 1: it needs no proprietary anything. The net shape keel is a level 3 option. Replacing the maker path with a manufactured part would be the same move we refuse Lamello for.

Open questions

1. The build test. Assemble one side frame from a keel plus scribed members, and one from the published cut list, and record elapsed time, number of measurements taken, and squareness of the result. Until that is measured, the speed claim here is an argument, not a finding.
2. The moment diagram needs a load case before any taper is drawn. Use the standard's duty loads when they publish.
3. Whether a scribed frame is compatible with the standard's conformance idea. Scribed members are not interchangeable between chairs, which is fine for repair by fitting and traditional, but the standard should say so rather than imply parts are swappable.
4. Whether the keel should carry the entire precision budget or share it with the tie, which is the other member with a kiss at both ends.
5. The duty loads. Every number in the width sizing rests on an assumed 1500 N seat load and an assumed 300 N lateral shove at the foot. Pin them against a furniture test standard before any of it is quoted as a result.
6. Plywood design values in the direction that matters. Table 12-1 is for the panel's strong direction; a keel nested at an angle to the face grain is weaker, by how much is unpinned. Nest the keel with its length along the face grain and say so on the drawing.
7. The lateral case wants a physical test, not an assumed load: push the foot sideways on a built chair and measure. The four panel variant should be in that test as the comparison, since it is the proposed answer.
8. Whether the closed space under the seat in the four panel variant is acceptable to sit in. This is a build and sit question, not an analysis one.

Revisions

17 Aug 2026: first draft, from KU's ledger board sketch. Names standardized in the same pass: back, seat, keel, front, tie.

17 Aug 2026, third pass: KU confirmed the wing reading is compatible with the canonical K2 and specified the build, so the hardwood keel section and the layout drawing were added.

17 Aug 2026, same day, corrected: the first draft claimed the second keel was the first one flipped 180 degrees about its long axis, on the mistaken reading that the two triangles were separated ACROSS the chair rather than within the side elevation. KU: "There is no flip... just a translation in Y." He is right, and the corrected section is stronger than the one it replaces, because the reason there is no flip is that the whole chair is a 2D profile extruded in Y. The first draft's caution about a foot bevelled flat to the floor was wrong for the same reason and has been removed: that cut is in plane, so it is prismatic like everything else.

Technical Notes of the Hundred-Year Chair: public from first draft, refined iteratively, forever. A claim is VERIFIED, STANDARD, DERIVED, or UNVERIFIED, and says which. The register · the verification ledger · hundredyearchair.com