Before revision: We present a deterministic algorithm that computes\tilde \tilde  the diameter of a directed planar graph with real arc lengths in O(n^{5/3}) time.
After revision: We present a deterministic algorithm that computes\tilde O(nb^2) time so that one can compute any additively weighted Voronoi diagram for these sites in\tilde the diameter of a directed planar graph with real arc lengths in O(n^{5/3}) time.