This page bends a sword with WebGL2, and your browser did not offer it. The essay below still reads; the blade will not move.
A blade is a tuned bar
Every sword has two points that do not shake, one point where it balances, and one point where a blow costs the hand nothing. None of them is where you would guess. This is a fifteenth-century longsword, solved live. Strike it.
Tap the blade to strikeDrag the grip to move your handDrag elsewhere to turn
I
Pick up any sword and the first thing your hand reports is the point of balance, the place it would rest on one finger. Catalogues print it. Buyers argue over it. It is the least useful number on the page. Balance tells you how the sword sits still, and nothing about a sword is still.
Hold the number anyway. Every point that matters is measured from it.
Positions are measured from the cross. Positive is toward the point.
II
Strike the blade and it rings in a shape. The whole sword bends like a plucked ruler, point and pommel swinging one way while the middle swings the other. Two places stay still. Smiths have known them for centuries as the nodes. A blow that lands on the blade node does not shake the sword. A hilt node inside your hand means the sword does not shake you.
Strike anywhere along the blade. The rings never move. Land on the far ring and the blade goes quiet in the hand. Land near the point and it stings to the pommel.
The first mode is the shudder you feel, not the note you hear. The ring is the fourth mode and up.
III
Now the rigid fact under the ringing one. Hit a bar anywhere but its balance and it both flies and spins. Somewhere along it those two motions cancel, and for an instant one point stays put. Choose where you hold, and the sword chooses that point for you. It is the center of percussion, and it obeys one rule: the distance from balance to hand, times the distance from balance to strike, equals the square of the radius of gyration.
Move your hand. The blue ring slides. Strike inside it and the meter reads zero: the hand feels the cut and nothing else. Choke up and strike the point, and the hand takes more than the blow.
Reaction is the grip's recoil per unit blow. 100% is a blow straight through the balance point.
IV
Why steel. Not for the edge; bronze holds an edge. The pitch of a bar depends on its shape and on one property of the metal, the speed of sound in it, which is the square root of stiffness over density. Steel, 5,050 metres a second. Titanium, 5,030. Aluminium, 5,060. Three metals, one note, at half the weight. Bronze, 3,450: nearly a fifth lower, and heavier.
Change the metal. The nodes barely move, because they belong to the shape. The pitch and the weight are the metal's.
V
The sword is an Oakeshott Type XVIIIb: a 95 cm diamond-section blade with strong profile and distal taper, a 20 cm grip, a straight cross, and a scent-stopper pommel, in the proportions of fifteenth-century originals. It is modelled as a free-free Euler-Bernoulli beam in sixty-two finite elements, the cross and pommel as lumped masses, and solved by Jacobi rotation for its first eight bending modes whenever the metal changes.
The blade on screen is bent on the GPU by summing those eight shapes every frame. The sound is the same eight frequencies as decaying sines, each damped by how much it moves under your hand. The pivots come from the same mass distribution. Tests assert that a uniform beam recovers Rayleigh's node positions, that a rod pivoted at one end percusses at two thirds, and that this sword weighs what a longsword weighs.
Built by Tommy Caruso with Claude, 2026. Set in Instrument Serif and JetBrains Mono.