Distribution of Fiber Intersections in Two-Dimensional Random Fiber Webs — A Basic Geometrical Probability Model

Fundamental theories governing the number of fiber intersections in random nonwoven fiber webs were developed based on the planar geometry of fiber midpoints distributed in a two-dimensional Poisson field. First, the statistical expectation and variance for the number of fiber intersections in unit web area were obtained as functions of a fixed number of fibers with equal lengths. The theories were extended to the case of a two-dimensional Poisson field by assuming that the number and locations of the fibers are random. The theories are validated by a newly developed computer simulation method employing the concept of “seeding region” and “counting region.” Unlike all previously published papers, it was shown for the first time that the expectations and variances obtained theoretically matched that from computer simulations almost perfectly, validating both the theories and simulation algorithms developed.