Coil Spring Rate
Rate of a round-wire helical compression/extension spring, plus spring index and Wahl factor.
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The engineering
The fourth power on wire diameter is the number that bites: 10% thicker wire is a 46% stiffer spring, so rate tolerance lives and dies on wire gauge. Mean diameter cubed works the other way — winding the same wire on a bigger mandrel softens the spring fast. Only *active* coils count; the squared-and-ground end coils sit out.
The spring index C = D/d is your manufacturability check — below 4 the spring is brutal to coil and stress-concentrated, above ~12 it tangles and buckles. The Wahl factor is how much the inside of the coil is over-stressed versus the naive torsion formula; multiply it in before you compare against allowable shear stress, not after the spring breaks.
Where this math comes from
Robert Hooke published the spring law in 1678 — first as the anagram 'ceiiinosssttuv', then decoded as 'ut tensio, sic vis': as the extension, so the force. He was protecting priority on watch balance springs, which is fitting, because springs have been precision products with trade-secret economics ever since.
The helical spring formula is really a torsion problem — the wire twists as the coil deflects — and its modern form was settled by A. M. Wahl at Westinghouse, whose 1929 correction factor accounted for coil curvature and direct shear. His book 'Mechanical Springs' remains the field's bible; the factor on this card carries his name.
- 1678Robert Hooke'Ut tensio, sic vis' — the linear spring law published.
- 1929A. M. WahlCurvature correction factor for helical spring stress.
- 1944A. M. Wahl'Mechanical Springs' — the standard design text.
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