If the computed great-circle route were to reach into higher than desired latitudes, it is possible to eliminate that problematic section of the voyage with a composite sailing calculation.  Such a path consists of three sections:

1) great-circle route from Departure to the chosen Limiting parallel,
2) parallel sailing along the Limiting parallel,
3) great-circle route from the Limiting parallel to Destination.

The two great circles from parts 1) and 3) are chosen in a way that places both of their vertices on the Limiting parallel.

The example below uses the same San Francisco-Yokohama trip from our earlier SAILINGS blog entry.  Here the Limiting parallel is set at N 40d, below the original great-circle vertex latitude of N 48d 03.7'.  The spreadsheet is composite.xls.