  A lattice-based model for continuum percolation is applied to the case of
randomly located, partially aligned sticks with unequal lengths in 2D which are
allowed to cross each other. Results are obtained for the critical number of
sticks per unit area at the percolation threshold in terms of the distributions
over length and orientational angle and are compared with findings from
computer simulations. Consistent with findings from computer simulations, our
model shows that the percolation threshold is (i) elevated by increasing
degrees of alignment for a fixed length distribution, and (ii) lowered by
increasing degrees of length dispersity for a fixed orientational distribution.
The impact of length dispersity is predicted to be governed entirely by the
first and second moments of the stick length distribution, and the threshold is
shown to be quite sensitive to particulars of the orientational distribution
function.
