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STEM Program Prep Materials Navigation___________________________________________________________________

During this STEM-focused program, we use the navigation component of our TopSail Program to enhance students’ interests in mathematics and puts math into a real world setting.

BIG IDEA:

Sailors have been responsible for charting a safe course and determining location using simple tools for centuries. The practice of navigation has continued to be relevant and useful in present day sailing.

Performance Objectives

During our activity students will be able to:

• Chart a course from San Pedro to Catalina (Two Harbors) • Understand the concepts of longitude, latitude and cardinal directions • Understand how to use a compass • Determine a current position • Use mathematics to extrapolate future position

Background Terms to Know and Review:

• Latitude • Longitude • Prime Meridian • Degree • Nautical mile • Compass rose • True North

Resources: Background Information

Lines of latitude and longitude have been around for at least three centuries. The Greek astronomer Ptolemy plotted them on the world’s first atlas, and is credited for being the first to mark the Equator on a map as the zero-degree parallel of latitude. This was based on the observance of the natural movement of the Sun, Moon and planets that pass almost directly overhead at the Equator. The Prime Meridian was not so easy. Although the zero-degree parallel of latitude is fixed by the natural world, the zero-degree meridian of longitude is man-made.

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Latitude The determination of latitude at sea was accomplished easily using celestial navigation. When sailing in the Northern Hemisphere, latitude was determined by measuring the altitude of the North Star (Polaris) above the horizon. The degree of the angle established the latitude position of the ship.

Nautical charts, first created in the mid-thirteenth century, were not very accurate but were considered quite valuable and were usually kept secret from other sailors. Early charts did not include demarcation lines of latitude or longitude, but instead displayed a compass rose, which specified the direction to travel (the term “compass rose” comes from the diagram’s compass points, which resemble rose petals).

Some of the early instruments used to assist sailors in determining latitude were the cross-staff, astrolabe, and quadrant. The astrolabe dates back to ancient Greece, and was used to measure the altitude of the Sun and stars to determine latitude. The English mathematician John Hadley, and American inventor Thomas Godfrey, independently invented the sextant. This instrument afforded a more accurate method of ascertaining the angle between the horizon and the Sun, Moon, or stars when calculating latitude because the sextant allows objects to be measured relative to the horizon, rather than to the instrument itself.

Before the invention of the marine chronometer, latitude sailing was the method used in deep-water voyages. A vessel sailed along a coast until it achieved the latitude of its destination. It then sailed due east or west using the sextant to keep the vessel at the same latitude until the destination came into sight. If the heavens could not be seen, the vessel had to fall back on dead reckoning. Miscalculations with the lead line, the chip log and the lookout caused many a vessel to run aground, and sent many a sailor early to the fiddler’s green

Longitude Dead Reckoning

Subsequent to the invention of the marine chronometer, dead reckoning was the standard method of determining longitude by early mariners The term dead reckoning is short for deductive reckoning. It was accomplished using a compass and factoring in the direction and speed of the vessel. Theoretically, if a navigator knew the direction and speed a vessel was traveling from a fixed point, he could deduce the location of that vessel at any time. Chip logs were used to measure speed, and consisted of a small wooden float attached to a long spool of line. The chip, when thrown off the stern of a boat, floats vertically in the water—resistant to moving. The vessel moves away from it, spooling line off a freely turning drum. The navigator simply counts how

many of the recalibrated knots tied on this line spool off and out to sea in a set time (usually thirty seconds, measured by a sandglass). The chip log gives the speed in nautical miles per hour. The navigator then need only find out how long the vessel has been sailing along a course to calculate the distance traveled. A vessel’s longitudinal location found through dead reckoning was at best, an educated guess. Errors in dead reckoning added up, day after day, mile after mile. Small errors could end a vessel on a rock or shoal after a long ocean crossing.

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The Marine Chronometer

The accurate measurement of longitude meridians requires the element of time. To establish a longitudinal position on board ship, one must know the ship’s time, and the time at the homeport, at the very same moment. The two separate times allow the navigator to convert the hour difference into a geographical location. Since the earth takes 24 hours to complete one full rotation (three hundred sixty degrees), one hour marks one twenty-fourth of a rotation, or 15 degrees. Each hour’s time difference between the ship’s time and the starting point’s time marks a progress of fifteen degrees of longitude to the east or west.

Every day at sea, the navigator would reset his ship’s clock to local noon when the sun reached its zenith, and then consult the homeport clock. Every hour discrepancy between the two represented fifteen degrees of longitude. Those same fifteen degrees of longitude also correspond to distance traveled. At the equator, fifteen degrees reaches one thousand miles. However, by sailing north or south of that line, the mileage value of each degree decreases.

Absolute knowledge of the hour in two different places was unachievable in the era of pendulum clocks. These clocks would slow down, speed up, or stop running altogether, on ships buffeted by wind and waves. Even routine changes in temperature encountered on typical voyages thinned or thickened the clock’s lubrication oil making its metal parts expand or contract. Barometric pressure or gravity could also cause a clock to gain or lose time.

In 1761, the English clockmaker John Harrison created a friction-free chronometer requiring no lubrication and constructed of materials impervious to rust. It did not have a pendulum, but was composed of different metals in such a way that when one component expanded the other contracted. The specialized construction made it too expensive for the average navigator or captain and it was not until 1825 that the British Navy began to supply their ships routinely with marine chronometers.

Celestial Navigation

Celestial navigation refers simply to observations made of the position of celestial bodies, usually the Sun, and the North Star (Polaris). A device such as a sextant is used to measure the angular distance between the celestial body and the horizon. Location could then be determined by referring to tables and charts in nautical almanacs. Without a marine chronometer, only latitude can be determined in this manner.

Lunar Distance is the angle between the Moon and another celestial body. A skilled navigator can use this reading (also called a lunar) and a nautical almanac to calculate Greenwich time. By comparing the current time on the ship to Greenwich time, longitude can be determined.

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The Sextant The sextant, as it would have been used in 1796, was an incredibly accurate device and would have been found on any deep-water merchant vessel. While appearing complex, it is fairly simple to use. The optical sight is aimed at an object through the clear side of half-mirrored window (for latitude, the horizon). While keeping the horizon in sight, the swinging arm is moved until it reflects the North Star onto the mirror. When the star sits next to the line of the horizon, the angle read at the lower end of the arm is the observer’s latitude.

A sextant can be used to read angles between any two visible objects. This is useful for determining angular heights of objects or (used sideways) horizontal angles between landmarks for lines of position. In the northern hemisphere, sightings were taken between Polaris and the horizon at night. In the southern hemisphere, sightings were taken between the Sun and the horizon during the day. This required colored filters, or shade glasses, that could be adjusted over the line of vision.

VOCABULARY

Dividers - A pair of compasses, as used for dividing lines, measuring, etc.

Compass Rose - A circle divided into 32 points or 360° numbered clockwise from true or magnetic north, printed on a chart or the like as a means of determining the course of a vessel.

Magnetic North - North as indicated by a magnetic compass, differing in most places from True North.

Parallel Rulers - A pair of straightedges connected by two pivoted crosspieces of equal length so as to be parallel at all times, used for various navigational purposes, esp. for transferring the bearing of a plotted course to a compass rose.

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For some great background information and classroom activities, please visit the Institute of Navigation website at www.ion.org

For a great maritime connection – Have your students research Nathaniel Bowditch, a mathematician who is often credited as the founder of modern maritime navigation. His book, The New American Practical Navigator, first published in 1802, is still carried onboard every commissioned U.S. Naval vessel.

Use these activities and turn your classroom into a nautical chart! Objects in the room can become symbols and the compass can be used to direct students around the classroom. You can have a lot of fun utilizing these activities to engage their interests before coming onboard and putting their knowledge to the test.

For more information or if you need pre-trip activities printed or emailed to you, contact tracy.kirby@lamitopsail.org