The spreadsheet composite.xls takes the initial great-circle course from sailings.xls (cell C6) and modifies this calculated great-circle route from the point of Departure (cells B2, C2) to Destination (cells E2, F2) so as not to go beyond the chosen limiting parallel of latitude (cell B9). The resulting two waypoints along this limiting parallel (plus the third waypoint, which is the Destination) are displayed in rows 12, 13, and 14. The courses shown in cells F12 and F14 are the initial great-circle (spherical Earth) courses to the first waypoint and to the Destination, respectively. The constant course in cell F13 reflects the east or west direction of the latitude sailing along the limiting parallel from the first to the second waypoint. If needed, waypoints along the two great-circle legs of this trip can be calculated with waypoints.xls.

Yellow cells in rows 5 and 9 display text messages about the result and status of the composite sailing calculation. These messages are:

• cell D9: INVALID: the limiting parallel was chosen between the equator and either the Departure or the Destination point. Composite sailing path cannot be computed in this case. Rows 12, 13, and 14 are zeroed out.

• cell F9: Composite OK: Non-trivial composite sailing path is successfully calculated.

• cell E9: Unconstrained gc (great circle): The limiting parallel is between the vertex and its Pole and therefore does not affect the originally computed great-circle sailing path. The first and second waypoints are identical as they coincide with the vertex.

• cell C5: Vertex beyond destination: This happens for relatively close Departure and Destination points, which are not separated by the vertex. The choice of limiting parallel is voided in this case and rows 13 and 14 are zeroed out. A great-circle sailing calculation is displayed in row 12. The Unconstrained gc message is also displayed in cell E9 in this case.

Summary for spreadsheet composite.xls:

Input cells: B2, C2, E2, F2, B9

Output cells: row 7, block B12 through F14, E15