http://www.amazon.com/Weems-Plath-Navigation-Universal-Plotting/dp/B000IMWXRIHINT: Meridians go up and down, Parallels go left and right.

I hesitated adding this chapter to the CelNav course because it is additional material, and you don't really need it to get started in celestial navigation. But it occurred to me that most of you will be plotting your fixes on your own charts, and that will quickly cover expensive charts with scribbles and erasures, so you really need a plotting sheet. Also, at sea, you will probably not have large scale charts of mid-ocean areas, so you will have to plot your fixes on a plotting sheet anyway.

A plotting sheet is merely a pre-printed form which can be used in place of a chart for plotting fixes. They can be purchased from marine suppliers and many chandleries carry them, or you can buy them off the internet. The link above will show you one place where you can order them in bulk, as well as show you a picture of one. A plotting sheet is a generalized chart showing just grid lines and a compass rose, and it can be used to create a mini-chart of any part of the world you like so you can plot your fixes and erase mistakes, scribble down notes, and put the final result in your notebook in case you need to review it later (or use it for evidence in a court trial!).

A plotting sheet consists of grid lines representing parallels of latitude and meridians of longitude, as well as a linear interpolator graphic printed in the lower right-hand corner. Centered in the middle of the sheet is a compass rose, with the 360 azimuth degrees printed on the inside, and a set of degree numbers in reverse order printed on the outside, eastern edge of the rose. These "outside" markings are used to customize the plotting sheet for your latitude. The central meridian of the chart is marked off in minutes of latitude, which you will recall are the same as nautical miles.

If you study your charts, you will see that a degree of latitude is LARGER than a degree of longitude (except at the equator, where they are identical). The further away from the equator you are, the smaller the longitude degrees become as the longitude lines converge at the poles. This won't be very noticeable in Florida, unless you carefully measure and compare the distance between latitude and longitude lines. But at higher latitudes, the difference is really obvious on a Mercator projection chart. This distortion is deliberately introduced by the nautical chart map projection so that a straight line drawn on the chart corresponds to a course line on the compass. This is why Greenland looks bigger than Brazil on a Mercator map.

To use the plotting sheet, mark the very center as your Assumed Position. This is why I like to use an AP that's a round-numbered lat/long combination, such as 26N 80W. The Pepperday table, unlike some of its competitors, lets you use any AP you like. Other sight reduction methods force you to use AP's which do not lie at exact lat-lon intersections, making it very easy to get confused and misplot fixes.

Now work yourself along the right hand, outside edge of the compass rose and find a degree marking equal to your latitude, (in my case, that would be 26, in the upper right quadrant of the compass rose because I live N of the equator. Place a dot there with your pencil, and using your parallel rulers, drop a vertical line from the dot so it crosses all the latitude lines at right angles. With your dividers, measure off the distance from the vertical you've just drawn to the central meridian and use it to construct another vertical on the other side of the meridian. These are the custom longitude lines for your AP latitude. You can see that the further north you are, the skinnier and taller the one-square-degree boxes formed by the lat/lon line crossings. With your ruler and dividers you can construct additional verticals (new longitude lines) if you need them. Label the parallels and meridians of your customized Mercator plotting sheet.

After you have reduced all your sights, you will have a list of Azimuths and Intercepts for each sight. Plot each azimuth from the central AP, using the compass rose inner degree scale to aim the azimuth at the body's GP. They will look like spokes of a wheel with a hub at the AP . Using your dividers, scale off each intercept using the central meridian nautical mile scale and place it (Toward or Away from the GP, as the CGA Rule dictates). At each intercept, draw your LOP at right angles to the azimuth (I usually use a different color pencil or ink for the LOPs to keep them from getting confused with the azimuths). If the observations were not taken within a few minutes of each other, or if you ship is fast, you may need to use your parallel ruler and dividers to DR your LOPs to the same time (a running fix). Where the LOP's now cross is your fix.

So what's the funny-looking graphic in the lower right of the plotting sheet for? That's the fun part!

The Mercator projection plotting sheet you've just created is a real nautical chart. It accurately preserves distances and directions on the Earth's curved surface, but it does so at a price, it must distort the longitude meridians so they are parallel, when in reality they are not. So once you carefully mark your fix on the chart, use your dividers to scale off the latitude directly on the sheet. Write it down before you forget it. Locate that latitude on the vertical scale of the graphic. Now measure off with the dividers the distance from the meridian of the AP. Place one point of the dividers on the appropriate latitude of the graphic, and from the other point read off the curved longitude lines the correct longitude for that latitude from the horizontal scale. Write it down and you now have the latitude and longitude of your position, which can be logged and plotted on your small-scale ocean chart. You will note the graphic interpolator is only needed to convert your plotted position to a numerical lat-lon, because there is no printed longitude scale on the plotting sheet as there is on a proper chart.