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Clackson scroll formula
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The Clackson scroll formula, :<math>l = \pi \cdot s \cdot n^2</math> is used in blacksmithing for estimating the length <math>l</math> of stock required to produce a scroll of <math>n</math> turns with a (on-center) spacing <math>s</math> between the turns. Derivation We can think of the scroll as having a thickness of s and being wound tightly so that there is no space between the layers. When wound up the scroll is roughly a cylinder with a radius of s·n, so its cross-sectional area is roughly πr πs n . On the other hand, the scroll's cross-sectional area whether wound up or not is l·s. Thus we have ls πs n , or l = πsn . |
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