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TAPPI T 232 2013 Edition, January 1, 2013
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Fiber length of pulp by projection
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This is a projection method (1) by which the weighted average fiber length of a pulp may be measured relatively quickly and easily.

If 1 is the length of any fiber in a sample of pulp, w its weight, and if N fibers are measured, their total length (Σ1) being L, the numerical or arithmetical average length is Σ1/N or L/N; their weighted average length by length =Σ(l2) Σ l and their weighted average length by weight Σ(lw)/Σw.

The numerical or arithmetical average fiber length of paper pulps is a not a commonly used value, since the pulps consist of whole tracheids and shorter elements down to submicroscopic lengths, which are included in the arithmetic fiber length and there tends to be a larger quantity of them as fiber length decreases. The stated average is especially meaningless if the least length arbitrarily adopted as the lower length limit for a "fiber" or particle is not also given. The shortest fibers contribute very little to the total measured length, but numerically they are just as important and influence the final result of an arithmetical average just as much as the longest fibers. On the other hand, the weighted average fiber length is a fundamental property of pulps and relates directly to paper properties (2). The shortest fibers in an average specimen of pulp contribute very little, either to length or to weight in the calculation of the weighted average length and hence have an almost negligible effect on most test results. This corresponds in many cases to their almost negligible effect on the common properties of a pulp other than groundwood, except for its freeness and the transverse tensile strength, light scattering, or the air permeability of test sheets made from it. Fines and short fiber influence paper properties in a very different way from long fibers, thus, it is generally best to look at fines and longer fiber separately.