Concept

Lock-in — where it appears

The range of wind speed in which vortices shed from a slender body abandon their own frequency and follow the structure's, driven by its motion. Inside the band the structure oscillates at its natural frequency with an amplitude set by its Scruton number.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as scruton number — the same set of essays touches all of them, so they are one junction rather than several.

Lock-in: the frequency the wind sheds at, and what it does to the chimney. A 1.2 m cylinder at 0.9 Hz. Vortices leave it at St·U/D, so the critical speed at which they match the structure is 6 m/s — a breeze, met many times a year rather than once in fifty. The upper panel shows the shedding frequency locking on to the structure across a band from 5.1 to 7.8 m/s; the lower shows the amplitude that results. At a Scruton number of 11.2 the peak amplitude is 180.94 mm, which is 15% of the diameter.

The wind that brings its own frequency

Every other load in this subject arrives at whatever rate it happens to arrive at. Vortex shedding arrives at a rate set by the wind speed — so for any chimney, mast or cable there is always a wind speed at which the shedding matches the structure exactly, and it is a breeze rather than a storm.

dynamics · Vortex shedding

The chimney that locks in most is tuned above the commonest wind. Lock-in cycles a year at the full lock-in amplitude that do the same damage as the whole band (millions), for 1.2 m cylinders of every frequency in hourly mean winds at the top Rayleigh-distributed with scale 5.5 m/s, against the critical speed as a multiple of that scale. Solid, the count through the amplitude envelope; dashed, EN 1991-1-4's closed form 2·T·f₀·ε₀·(Ucr/v0)²·exp(−(Ucr/v0)²) at band widths ε₀ of 0.1 and 0.3. All three peak at a critical speed of √(3/2) = 1.22 times the scale, 6.7 m/s — above the commonest wind (0.71) and the mean (0.89). The envelope is EN's formula with ε₀ = 0.22. The chimney drawn, at 6.0 m/s, collects 4.6 million a year.

The breeze that uses up a chimney

A chimney that locks in to vortex shedding at a breeze is usually told to accept the motion and check its fatigue. Counting the cycles a real wind climate delivers turns that into arithmetic, and the arithmetic has two surprises. The chimney that collects the most cycles is not the one tuned to the commonest wind but to one a fifth stronger than the climate's scale, so stiffening a chimney can shorten its life. And damping does not lengthen the life in proportion: it ends the count, all at once, at the damping that puts the largest stress range under the detail's cut-off.

dynamics · Vortex shedding

Named alongside it

The objects these essays reach for when they reach for this one.

Scruton number Vortex shedding Aeroelasticity Cross wind response Cut-off limit Damping Fatigue Miners rule Resonance Stress range Strouhal number Wind climate

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