In planning routes between well-defined points of departure and arrival, both aircraft and ships can take into account forecast values of certain geophysical parameters so that the route chosen is in some sense optimized. For aircraft flying the North Atlantic, the methods used are described in the papers by Attwooll, Bennett, and Monk (all 1982). There have been a number of papers on ship-routeing; they were reviewed by Motte and Calvert (1988). It should be noted that whereas for aircraft the dominant consideration is the wind (for which the maritime equivalent is the current), ship-routeing on the trans-oceanic scale is dominated by considerations of waves. However, on smaller scales, currents can be the dominant consideration: for example, see the paper by Fales (1991). That paper does not make use of the basic theory that was applied to the aeronautical problem in the 1940s. Although the work reported here is orientated to aeronautical applications, it clearly has ramifications for certain maritime problems.