The Cant Frame

In the midsection of a wooden ship, the frames stand perpendicular to the keel — square frames, evenly spaced, defining the hull's cross-section. But near the bow and stern, the hull narrows so sharply that a frame set perpendicular to the keel would barely contact the planking. The wood would be almost parallel to the surface it is supposed to support. So the builder cants the frame — angles it relative to the keel so that it meets the planking at a useful angle. These cant frames fan out from the bow like ribs from a spine, each one oriented not to the keel's axis but to the hull surface at its location.

Fan vaulting in Gothic architecture follows the same geometric logic. Along the nave, ribs spring from columns at regular angles to support the vault. But at the apse — where the building curves — ribs set perpendicular to the main axis would converge awkwardly or miss the vault surface entirely. The masons fanned the ribs outward, each one angled to meet the curved ceiling at a structurally useful orientation. The fan vault at King's College Chapel in Cambridge is often admired as decoration, but the fanning is structural: it is the solution to the problem of supporting a curved surface from a narrowing plan.

Bicycle wheel spoking uses the same principle in miniature. At the hub, spokes cannot all emerge perpendicular to the rim — they would interfere with each other and provide no lateral stability. Instead, they are laced in crossing patterns, each spoke angled tangentially to the hub flange. The cant gives each spoke a component of force in the lateral direction, preventing the wheel from collapsing sideways under load. A wheel with all spokes radial (perpendicular to the hub) resists vertical loads but buckles when the rider leans into a turn. The canted spoke handles the force that the perpendicular one cannot.

The cant frame is the admission that a single orientation cannot serve a changing geometry. Perpendicular works where the shape is regular. Where the shape curves, narrows, or transitions, the structural member must reorient to maintain contact with the surface it supports. The principle that works amidships does not work at the bow. The solution is not to abandon the principle but to rotate it until it meets the new conditions at a useful angle.