  Many natural fibrous networks with fiber diameters much smaller than the
average poresize can be described as three-dimensional (3D) random line
networks. We consider here a `Mikado' model for such systems, consisting of
straight line segments of equal length, distributed homogeneously and
isotropically in space. First, we derive analytically the probability density
distribution $p(r_{no})$ for the `nearest obstacle distance' $r_{no}$ between a
randomly chosen test point within the network pores and its closest neighboring
point on a line segment. Second, we show that in the limit where the line
segments are much longer than the typical pore size, $p(r_{no})$ becomes a
Rayleigh distribution. The single parameter $\sigma$ of this Rayleigh
distribution represents the most probable nearest obstacle distance and can be
expressed in terms of the total line length per unit volume. Finally, we show
by numerical simulations that $\sigma$ differs only by a constant factor from
the intuitive notion of average `pore size', defined by finding the maximum
sphere that fits into each pore and then averaging over the radii of these
spheres.
