Treadle Loom Shed

What is modelled

In plain (tabby) weave every second warp end is lifted while the others are lowered, then the shuttle carries the weft through the opening and the reed beats it against the cloth. Lifting an end lengthens its path between the back beam, the heddle and the cloth fell, so the yarn stretches and its tension rises. The opening must be large enough at the reed for the shuttle to pass.

Equations

• Extra length ΔL = √(a² + h²) − a + √(b² + h²) − b, series h²/2 (1/a + 1/b).
• Tension T = T0 + EA ΔL / L with EA = E λ / ρ.
• Stored energy U = N (T0 ΔL + EA ΔL² / 2L); foot force from the lever ratio.
• Opening at the reed 2h br / b; cloth length picks / (picks per cm).

Checks run in the page

• Exact warp stretch against the small-lift series.
• Numerical foot work against the stored energy.
• Pick counter against minutes and cloth length.
• Shed angle and opening by similar triangles.

Honest simplifications

The yarn is a linear elastic string, both shafts stretch their ends equally, there is no crimp, no beat-up force and no friction in the heddles. The numbers show the geometry of a counterbalanced two-shaft loom, not a weaving process specification.

• Press Too shallow a shed: the red opening reading shows the shuttle cannot pass.
• Press Tall shed, tight warp and watch the end tension climb with the lift.
• Raise the picks per cm and see the cloth length per hour fall.