A Method of Fibre-Length Analysis Using the Fibrograph

Abstract

The fibrograph is an optical instrument employing photovoltaic cells for scanning samples of parallel fibres and tracing a type of length- frequency curve. The theory is developed for a sample of parallel fibres in which the fibres are positioned at random. The geometrical interpreta tion of the resulting curve, or fibrogram, indicates simple length and area measurements that give various average lengths and statistical quantities, such as standard deviation and coefficient of variation. Experimental fibrograms are compared with the equivalent data derived from absolute length measurements, using a projection method. The waviness and taper of the fibres, along with other minor factors, cause the fibrogram to be too short. When the length coördinates are increased 19%, the fibrogram is equivalent to the curve obtained from absolute measurements. The instrument makes possible the rapid measurement of fibre length and fibre-length uniformity of raw fibre samples.

Macro and Micro Characterization of Biopolymers: Case of Cotton Fibre

“…The original idea of the photoelectric scanning or Fibrograph method (ASTM D1447-83) has been developed by Hertel in 1940 for testing cotton lint (Hertel, 1940). This test method covers the measurement of the length and length uniformity of cotton fibres.…”

The Mathematical Basis of Fiber-Length Analysis from Fibrogram Data

“…Therefore, the fibrogram model is t Performing the integration with respect to X gives The probability density function of fiber length con-. tained in the clamp, given a specific total fiber length of L, was designated g(X ~ L) in Equation 1, where it first appeared. In building the model, it was assumed that the length of fiber contained in the clamp is equally likely to be any length between m and I,.…”

An investigation of the sampling bias of the beard method as used in HVI™

“…At the very beginning, when Hertel developed the fibrogram theory, he assumed that the probability of a fiber being sampled for fibrogram was proportional to its length; this is the length-biased sampling assumption (Hertel, 1940;Hertel & Zervigon, 1936). Zeidman, Batra, and Sasser (1991a) provided a derivation that used the unit step function to prove that sampling for fibrograph is length biased.…”