Where does torsion collide?

The twisting of a structural member about its longitudinal axis when an applied torque acts on it, producing a shear stress that grows from zero at the centre to a maximum at the surface. In Timoshenko and Goodier's Theory of Elasticity, the elastic torsion problem, following Saint-Venant, relates the torque to the angle of twist per unit length through the shear modulus and a torsion constant, and for a circular shaft this yields the familiar torsion equation. The referent is a mechanical response of a solid bar to a turning load, measured as stress in pascals and twist in radians, not an algebraic invariant, a strangled organ, or a coiling flower.[1]

Unit

Shear stress and angle of twist in a loaded bar, in pascals and radians

Recovery means

Within the elastic limit the bar untwists fully when the torque is removed, storing and returning strain energy

Measured by

Found from the applied torque, the polar second moment of area, and the shear modulus, or measured directly as the angle of twist over a gauge length

For a curve in space, the torsion measures how sharply the curve twists out of its osculating plane, that is the rate at which the binormal turns as one moves along the curve at unit speed. In do Carmo's Differential Geometry of Curves and Surfaces, the Frenet-Serret formulas define torsion as the coefficient tying the derivative of the binormal to the principal normal, so a plane curve has zero torsion while a helix has constant nonzero torsion. The referent is a scalar geometric invariant of a smooth curve, carrying units of inverse length, and it has nothing to do with a stressed shaft, a twisted testicle, or an inverted petal.[2]

Unit

A curve's rate of departure from its osculating plane, in inverse length

Recovery means

Not applicable

Measured by

Computed from the first three derivatives of a parametrised curve, through the scalar triple product divided by the squared magnitude of the cross product of the first two

In clinical medicine, torsion is the twisting of an organ upon the vascular pedicle that supplies it, which strangles its own blood flow and threatens the tissue with ischaemic death unless it is untwisted urgently. Laher, Ragavan, Mehta, and Adam's review of testicular torsion describes how the spermatic cord twists and cuts off perfusion to the testis, so that salvage depends on rapid diagnosis and surgical detorsion within a few hours. The referent is a surgical emergency defined by loss of perfusion through a rotated pedicle, timed against tissue viability, unlike a bar under torque, a curve's invariant, or a twisting flower stalk.[3]

Unit

An organ rotated on its blood supply, timed against ischaemic tissue loss

Recovery means

Perfusion can return if the organ is untwisted before infarction, but prolonged torsion causes irreversible necrosis

Measured by

Assessed clinically and by Doppler ultrasound for absent blood flow, and confirmed at surgical exploration

In botany, resupination is the twisting of a flower or its stalk through about half a turn during development, so that the flower comes to rest inverted relative to its bud, a movement conspicuous in most orchids where the lip ends up lowermost. Cardoso, Johnson, and Oliveira's study tests whether gravity guides this reorientation, measuring the twist of orchid flowers held at different angles. The referent is a directed growth movement that reorients a plant organ by twisting, described by its angle and direction, and it is distinct from a shaft under torque, a curve's torsion, or an organ strangled on its pedicle.[4]

Unit

The developmental twist of a flower or its stalk, in degrees of rotation

Recovery means

Not applicable

Measured by

Recorded as the angle through which the flower or pedicel rotates during development, often close to one hundred and eighty degrees