Analemma Earth
Analemma Earth

Analemma Earth

The emergency here is twofold. First you have lost all electronic navigation, and secondly you don’t know how to plot a celestial fix! Here then is how to do it (excerpted from a fifth grade course).

There are two things required to plot a fix: knowing where the sun is at a particular time (you do need a watch!), and knowing how far away from your overhead the sun is. You will also need to plot on a globe which takes all of the math out of it. Sure it is not very accurate, maybe 30 to 60 miles but hey, you’re not lost! It’s also a good way to learn the basics of celestial.

Where is the sun?  Using the analemma shown here, estimate the current date and read off the latitude of the point directly beneath the sun (it’s subpoint) on the vertical scale. Then reading the horizontal scale you will see how early or late the sun passes Greenwich in England. The positive numbers on the right are the minutes the sun arrives early. The negative numbers are the minutes late. Starting with the fact that the sun passes Greenwich around noon each day and travels 15 degrees of longitude per hour, you can use this correction to fine tune it’s longitude for your date. Plot this position on the globe.

How far away is the sun from your overhead?  The traditional way is to use a sextant which measures angles accurately. But in an emergency a simple yardstick may be used to measure the length of the sun’s shadow.

To plot a line of position (LOP), take these steps:

1. Using the analemma shown here, mark the sun’s position for the desired time of the LOP.

2. Holding the yardstick vertically, mark the end of the sun’s shadow then lay the yardstick down to measure it’s length.

3. Draw the triangle to scale formed by the 36 inch yardstick, the sun’s shadow length and the connecting hypotenuse. Measure the vertex angle with a protractor. This is the anglular distance the sun is away from your overhead.

4. Go back to the globe. Using a string, measure this angle upwards from the equator. Say the angle was 25°.You would measure from the equator up to 25° north latitude. Holding one end of the string on the sun’s position mark, draw a circle using the string as it’s radius. This is a circular LOP on which you are somewhere located. Doing this process at a different time and a different sun position yields another circle which intersects the first one yielding your position.

1 Comment
  1. Steve Carleton 6 months ago

    Ken:
    I love these boil-it-down-to-the-minimal-requirements solutions. So, empirically create a sundial on a level surface with a gnomon formed by a suspended plumb bob two meters in length, then measure the distance in millimeters from the base of the gnomon to its shadow tip to an accuracy of several millimeters, and note the time of each measurement with an accuracy of a second or so, then average many results over an period of hours. Apply a little trigonometry to get the average altitude of the sun for the averaged time of the observation, then calculate a LOP. What degree of accuracy do you suppose you could achieve? And, if coupled with determining the time when the shortest shadow was noted, again by averaging observations before and after LAN, how accurate might be the resulting fix? If a paper copy of the analemma was carried with a pocket calendar and an awareness of the date, the approximate declination would be known to assist in the calculations. Everything needed might fit into a pocket and yield the potential for a minimalist time sight and minimalist noon sight to fix position…kinda.

    Thoughts? This is another thing I plan to try out when I have a day off and sunshine, along with the “cell phone as sextant” fix I mentioned in an earlier post.

    Finally, I occasionally see Soviet-era Star Globes on eBay, and I believe Celestaire also had them once upon a time. We’re these used in a similar manner to that outlined in your article to obtain quick-and-dirty navigational solutions mechanically to produce a general idea of location while cruising around in the trackless sea in a warship, or were they just 3D versions of the Rude Star Finder?

    Curiously,

    Steve

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