Knitting Elements
Needles are not broken by one heavy pull. They are broken by a hundred million light ones, which is why the breaking load is the wrong number to design against.
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Allowable fatigue load over the peak hook load
The fatigue fraction is a material and geometry property of the needle — take it from the element supplier rather than assuming a generic value. Latch and butt loads are separate failure paths not covered here.
Knitting Needle Hook Load & Fatigue Limit Calculator — free, with the formula and a worked example, at Textile School.