From: Frank Reed
Date: 2016 Dec 24, 10:17 -0800
John Howard, you wrote:
"Many people think the plotting sheets are Mecator but they are not."
Exactly. They think they're Mercator, because they are quite frequently printed with that label at the top. This is wrong. Standard plotting sheets are, however, conformal --like the Mercator projection as well as a number of other map projections. This means that angles are correct, and therefore azimuths can be plotted from a simple compass rose. This is an important feature of standard plotting sheets. It requires a specific scaling, cos(latitude), of latitude divisions to longitude divisions. Conformal plotting sheets are generally required by the intercept method since the method depends on drawing the intercept line at a true azimuth. By contrast two-point lines of position (often called Sumner lines) can be plotted on any graph paper (or two sheets of lined notebook paper crossed at 90 degrees as makeshift graph paper). That's what David meant when he referred to a "plane" plot. It would be safer to say a "rectangular" plot since the key feature here is that the scaling of latitude to longitude doesn't matter, and it's usually convenient to select one-to-one: the latitude divisions equal to the longitude divisions.
One important note here: if we give up conformal plotting sheets, which I do recommend, then we need some alternative method for advancing lines of position in a running fix. The procedure for this is not complicated, but it's a little extra work. We pick either of the points used to plot the original LOP and adjust its latitude by ±speed·time·cos(course) and its longitude by ±speed·time·sin(course) with + or - chosen as usual, or if you keep north latitudes and east longitudes positive, the signs take care of themselves. This is not difficult at all, but it's an important distinction.
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA