  Two-stage methods addressing continuous shortest path problems start local
minimization from discrete shortest paths in a spatial graph. The convergence
of such hybrid methods to global minimizers hinges on the discretization error
induced by restricting the discrete global optimization to the graph, with
corresponding implications on choosing an appropriate graph density. A prime
example is flight planning, i.e., the computation of optimal routes in view of
flight time and fuel consumption under given weather conditions. Highly
efficient discrete shortest path algorithms exist and can be used directly for
computing starting points for locally convergent optimal control methods. We
derive a priori and localized error bounds for the flight time of discrete
paths relative to the optimal continuous trajectory, in terms of the graph
density and the given wind field. These bounds allow designing graphs with an
optimal local connectivity structure. The properties of the bounds are
illustrated on a set of benchmark problems. It turns out that localization
improves the error bound by four orders of magnitude, but still leaves ample
opportunities for tighter error bounds by a posteriori estimators.
