Abstract
Propositions are set with mathematical definitions for fiber orientation and its distribution in a fiber assembly whose constituent fibers are arbitrarily crimped.
It is found that the density function of orientation can be estimated by solving an integral equation which relates it to the average numbers of fiber cut-ends formed by unit areas of randomly positioned and variously oriented secant planes.
The formula obtained is as follows: where L is the total length of the fibers in unit volume, Ω (θ, _??_) sin θ the density function of fiber orientation, ν (Θ, Φ) the areal density of the number of intersections formed by a secant plane with an orientation of (Θ, Φ), and A (θ, _??_; Θ, Φ) defined as |sin θ sin Θ cos (_??_-Φ)+cosθ cosΘ|.
