Motion through one minute of latitude around a great circle of latitude represents a movement of 1 Nm across the surface of the Earth. Motion across one minute of longitude at the equator represents an equal distance, 1Nm. The surface motion for a one minute change of longitude is reduced as latitude increases. The longitude scale on a conventional plotting sheet is designed to take account of this change of scale.

I used a conventional plotting sheet to solve Ex6 q1 of the RYA ocean yachtmaster course:

Plot the first position line (Noon latitude in this case)
Plot the second position line
From any point on the first PL draw a vector to show the run of the boat
Run a line parallel with the first PL to the end of the boat vector
The intersection with the second PL shows the new Observed Position

The longitude scale was defined by the grid at the bottom right of the plotting sheet. How to use draw software to solve the problem:

The radius of a circle of longitude varies with the cosine of the latitude. So the longitude scale is proportional to the cosine of the latitude.

We are at latitude 50S;  cos 50 = 0.64. Draw a large square and set the height:width as 1:0.64;  centre on this rectangle and sub divide the scale in one minute steps


Using real graph paper the vertical scale would be easy to define. You might chose 2cm to represent 1 minute of latitude at 50 N. If so the horizontal scale for longitude would become 2*0.64 = 1.28 cm per minute.

Solution for Ex6 Q2

And for Ex6 Q3 on a plotting sheet

Click here for a latitude 50 degrees plotting sheet

These bookish questions are interesting however for a sample of reality follow the link for Sun Run Sun where you will find log extracts and a plot for the afternoon of July 31 1988 when Tony Burris was on passage between Egypt and Crete.