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Lost at Sea: The Search for Longitude

Teacher's Ideas

Navigating Around the World by Observing the Sun
James I. Sammons, Jamestown School Rhode Island

The NOVA adventure, "Lost at Sea: The Search for Longitude," provides an exciting view of navigation at sea and how that skill shaped world exploration. But how does that work? You find your position by pointing a cross staff at the sun and checking a clock? Actually, the process is fairly easy and provides an interesting opportunity for your class to relive the vital skills of the marine navigator.

Your classes can determine their Latitude using school yard stuff. At the same time, they can determine Local Apparent Noon, and find their longitude using the exact same method used by the navigators as described in "The Search...". The method involves observing the length and the time that the shadow of a pole of known height crosses a true north-south line. The method is simple, the math is simple, and middle graders can get the big picture. From the length of the shadow, Latitude is found. Longitude is found from the observed time. Together, the position of your school yard can be determined. Spin-offs from this exercise involve Science, Math, Social Studies, and Literature.

See Navigating Around the World by Observing the Sun below to download instructions for this activity, complete with references to related lessons, and a student packet.

Navigating Around the World by Observing the Sun
To the Teacher | Math and Science | Social Studies | Social Studies II | Literature | Classroom Tips

To the Teacher
This packet is designed to provide extension activities to accompany the NOVA episode Lost at Sea: the Search for Longitude. This section will be more useful if you review the student packet first.

This activity requires a clear view to the south. It can be done indoors behind a south facing window, but most will want to go outside. A vertical pole is needed and enough free space north of its base to be able to measure the length of its shadow. Flagpoles are ready made for this, but a six foot dowel will do. You'll also need a compass, a watch with a second hand, and depending on how you find the observed Sun angle, a tape measure or a protractor. Finally, you'll need three pieces of information: a reasonably accurate time source to set the watch by, the Magnetic Variation for your area, and a copy of the Analemma. This list may seem daunting, especially that last item, but stay with me, it's all part of the undeserved reputation that "it must be hard".

Related Lessons
Math and Science
The determination of Latitude provides an opportunity to apply the Geometry concept of Complimentary Angles. When introducing the process as described in the student packet, it's helpful to sketch these angle relationships for students to see.

To streamline the instructions, the student packet assumes that students are working in the continental United States, that is, north of the Tropic of Cancer. Examples show the observed height of the sun as a positive number no greater than 90. As an extension activity, ask your go getters how they would handle the height of the Sun if they were observing between the Tropic of Cancer and the Equator, but further south than the position of the Sun. In this case, the noon Sun appears to their north. If they make up and sketch out a known example, they'll realize that the Latitude formula still works, but that a northerly observation is like bending over backward and produces observed heights greater than 90 degrees. When this greater-than-90-degree height is subtracted from 90, a negative number is produced. Applying the Declination of the Sun correction in the standard manner works out just fine. How about observations made in the Southern Hemisphere? Again, sketches will show that the geometry is unchanged, but the addition and subtraction of the Declination of the Sun is reversed. If your kids are comfortable with signed numbers, see if they can derive a universal Latitude formula that assigns positive and negative values instead of Latitudes north and south. (That's how it's done using a hand calculator.)

When the TV tells you that the time of sunrise, sunset, moonrise, or moonset is such and such, the time is for the center of your time zone. The zone center is always a multiple of 15°. If you live several degrees east or west of the center, those times will be up to thirty minutes earlier or later respectively. With the results of your determination of longitude, you can correct the TV time to produce your actual times. Then go out and see!

Social Studies
You can make the solar observatory permanent with a little effort. If you chose to use a permanent shadow source such as a flagpole, all that is needed of the true north line is that portion where the top of the shadow falls. The shortest shadow is formed on June 21st. and the longest on December 21st. If you work backwards from your known Latitude and the Declination of the Sun on those dates, you can determine the length of line segment needed for any date of the year. You can place cross tics on the north line segment labeled for degrees of observed Sun height. This makes use of the observatory very simple. These markings can be made permanent by making them on bricks or flagstones set in the ground.

If you really want to do it in style, dig a trench and build a long rectangular form to be filled with concrete. Scribe the concrete before it sets, maybe place symbols at shadow angles corresponding to events of interest. Isn't that how the Egyptians kept track of the flood season in the Nile valley? While you're at it, set a brick in the ground so that on the summer solstice (June 21st. ), the shadow of the pole falls across the brick just as the Sun rises. Because this is more sensitive than the symbols on the north line segment, this is the way early civilizations kept track of annual events. Add other side markers as your imagination dictates. At this point you've recreated the Native American Medicine Wheels. Show your class a picture of these spoked circles made of boulders. Will they be able to figure out that the spokes serve the same purpose as your side markers? Obtain a clear picture of a Medicine Wheel. Can your students work backwards to determine the dates for the spokes? And what about those dates, do any seem unrelated to solar events? Hmmm, maybe that spoke that matches a fall date has something to do with animal migrations - Buffalo? Your class will have fun with this one.

A note of caution here. The Medicine Wheels were observed by sighting along the boulders toward the rising or setting Sun. That's probably more accurate than watching for the pole shadow to fall on a side marker, but the shadow technique is a whole lot safer than having school kids eyeballing the rising Sun.

Social Studies II
Everyone knows that the trade routes to the Far East ran down the west coast of Africa, but why? Once you lost sight of the land to the east, you could be anywhere. This becomes critical in storms because the old square rigged ships could only make good about seventy degrees off the wind. (Imagine the wind coming from top of page to bottom. The ship could sail no closer than a seventy degree line from the wind line.) In heavy weather, a square rigger usually quarters the sea (heads off at a wind angle of 120-140 degrees.) So - when close to shore the trader is a sitting duck for the closer winded lateen rigged pirates; farther off and he's in real danger of becoming truly lost if a storm forces him further out.

Many accounts suggest that Columbus' crew was afraid of sailing off the edge of the world. Not so. The key issue was the ability of his ships to carry enough water for an unknown distance and unknown wind systems. Remember the seventy degree feature of square rigged ships? You can literally spend a lifetime tacking under those condition. Just as aircraft figure their safe operating radius based on fuel capacity, so too did the old timers figure safe sailing range based on water capacity. Examine any coastal chart and note the number of places named "___ Watering Place" or "Bad/Sweet Water" and how `bout Dry Tortugas? Now reexamine the old exploration routes. Do they make more sense with this information? By the way, Columbus ran out of water at just about where he feared he would. His error was in under estimating the circumference of the world. Fortunately, he made landfall (and water) soon after.

All of which brings us to Cooleridge's Rhyme of the Ancient Mariner. Here's a fabulous read if you have any salt in your veins. Cooleridge doesn't place the ballad in any particular time, but the images strongly suggest a connection to the time of early exploration. Let's see what we can do with it. Here's verses 7 and 8:
The Sun came up upon the left,
Out of the sea came he!
And he shone bright, and on the right
Went down into the sea.

Higher and higher every day,
Till over the mast at noon-
The Wedding-Guest here beat his breast
For he heard the loud bassoon.
Verse 7 tells us that the sun was rising (east) on the left and setting (west) on the right. What is the ship's course? Where might they have been going? Why? (Clearly their course was south.)

Verse 8 refers to the sun being "over the mast at noon". If we knew the season we could be fairly precise about the vessel's Latitude, but we don't. So we'll have to settle for somewhere near the Equator. Can your students figure out how far above or below the Equator the vessel could have been? (Between the Tropic of Cancer, L 23.5°N, and the Tropic of Capricorn, L 23.5°S.)

Putting both together, the vessel was probably a spice trader outbound for India. As such, her hold would be filled with fabric and other manufactured goods. Owners would rather load on more trade stuffs than extra water, so the stage is set. Go find that social studies teacher - you can do some neat stuff here.

Verse 12:
With sloping masts and dipping prow,
As who pursued with yell and blow
Still treads the shadow of his foe,
And forward bends his head,
The ship drove fast, loud roared the blast,
And southward aye we fled.
Uh-oh, we're gonna get lost... Can your students guestimate the vessel's route? Have them look up the Doldrums (Southwestern corner of the North Atlantic) as an important clue. Verse 29, the well-known "Water, water, every where," is a good place to stop if you want to shorten down.

Classroom Tips
Lost at Sea: the Search for Longitude and this packet in particular presumes a working knowledge of Latitude and longitude. Some students have a rote understanding of position, limited to "lines of Latitude run sideways, but lines of longitude run up and down". A useful analogy to help students toward a working knowledge is to compare lines of position to a ladder. Yes, lines of Latitude do run sideways, just like the rungs of a ladder. But they are used to measure movement north and south, just as the rungs of the ladder allow movement up and down. Some practice with position is highly recommended before students attempt to find the position of their school. The venerable game Battleship in all of its many forms is good for this. Probably the best version is the simple full graph (four quadrants) on a piece of graph paper where the x axis becomes the Equator and the y axis becomes the Prime Meridian. Positive and negative values for y become north and south Latitude respectively, and positive and negative values for x become east and west longitude respectively.

The calculation of longitude often involves minutes of arc or time. Students may need to be introduced to the concept of "borrowing" in place values of 60 rather than the more familiar 100.

               18h:06'  GMT
             - 00h:09'  Equation of Time
17h:57' Greenwich Apparent Time

In precise marine navigation, this type of calculation is very common and as you would expect, a primary source of error. Fortunately, the level of precision required here is very low. Accuracy to the nearest few tenths of a degree is probably the best that can be expected. Therefore, the main skill need by students is to be able to round off to the nearest degree, knowing that the maximum number of minutes per degree is 60. For example, 13 degrees 47 minutes becomes 13.8 degrees.

        47 minutes  ÷  60 minutes / degree  ~  0.8 degrees
The calculation of Latitude and longitude is an ideal activity for multiple small groups. If students are working from the packet that follows, eclectic groups whose members include careful readers, logical thinkers, connection makers, and left fielders will excel. It will prove helpful for all to post some of the formulae and interpretive guidelines such as: "Local time earlier, position is westward ..." in a conspicuous location for all to see.

One idea that invariably occurs to someone is the possibility of stopping time by travelling westward. If, for example, at the very instant that the Sun were right over your head, noon, you jumped into your wonder car and drove west, you could get ahead of the Sun and have noon all over again. If your wonder car could go at just the right speed toward the west, you could have time appear to stand still and give you continuous noontime. In fact, this is precisely why flights that leave Paris at 1:00 PM arrive in Boston at a little after 2:00 PM. Although the flight takes six hours, the plane is travelling westward nearly as fast as the Earth is spinning eastward. Not only is this possible, but at very high Latitudes where the Earth's circumference is quite small, you could walk fast enough to achieve continuous noon!

James I. Sammons, Jamestown School Rhode Island


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