A Critical Evaluation of the Relationships Between Arealometer Instrument Values and Cotton Fiber Perimeter: Part I: Fundamentals and Computer Simulation

Arealometer instrument values are computer simulated to study the error in the calculated fiber perimeter P due to instrumental errors. (This airflow device senses the fiber's specific surface at two different specimen compressions; P and wall thickness t are computed from the readings.) Systematic changes over time in instrument values from designated true values are classified into thirteen nontrivial combinations. Each combination results in different P values and, consequently, a unique drift or error in P. Simulations of 50,000 Arealometer observations using actual standard deviation data from a control cotton are also run. These simulations show that random variations in instrument values over time are, in effect, an unordered sequence of the nontrivial combinations. Also, a mean taken from only two to six Arealometer observations— the accepted practice—does not adequately characterize a cotton sample. Fundamental relationships are probed with partial and total derivatives of Arealometer functions. There is more variability in the calculated P than in the t value. The total differential dP accurately measures the error in P, given the error in the instrument values.