NavList:

Mike Freeman you wrote: I attempted some calculations to try to determine for myself the errors introduced by the half a degree but am unable to analyze my own results.

Mike
Well done on attempting to analyse plotting sheet accuracy, but I think you’re worrying about it unnecessarily when any likely inaccuracy is compared to the standard plotting errors which are there all the time.  Also, any inaccuracy is going to be hard to define, because the first casualty of attempting to make your own mini chart is that angles might not be preserved, so there could be inaccuracies in plotted azimuth as well as in distances measured.  Inaccuracies will also depend upon the observer’s latitude.  They would get larger the closer you were to the Pole.  It’s altogether not worth bothering about unless you’re a Maths post-grad feeling really bored one afternoon.  If you think of all the plotting errors you’ll build in marking and drawing angles, marking tiny intercepts from your ruler, or with your dividers squeezed up as tight as they’ll go to mark 2’ away for example,  adjusting for P&N, MOO & MOB, and Coriolis when required, and allowing your pencil point to deteriorate to the width of a sharpened bar of chocolate, then in temperate latitudes, it’s generally accepted that you need not worry about plotting sheet inaccuracies so long as you don’t stray more than a degree or two either side of the chosen latitude.  

However, it would be wrong to leave this subject without mentioning that it’s often possible not need to worry at all about the effect of changes in latitude upon the length of a minute of longitude, especially in this day and age.  If using AP3270/HO249 to plot a single position line, you could draw your horizontal and vertical axes crossing at the chosen latitude and your assumed longitude.  Your PL would then be perpendicular to a radius vector whose direction is azimuth and whose length is the intercept.  If required you could transfer this PL to your working chart.

If you were reducing your sights using a scientific or programmable scientific calculator, you could simply use graph paper or even the back of an envelope.  You would draw your horizontal and vertical axes crossing at your EP or DR position (whichever you prefer to call it).  You could plot any number of PLs this way on the same sheet to form a fix.  Then all you need do is transfer your fix position to your work chart as a range and bearing from your EP.  DaveP