Navigation: Where Am I?

When people started traveling, it was imperative to be able to answer the question: where am I? This is not such a problem with land navigation because there are lots of landmarks to guide the traveler. Early, the Portuguese sailors used sets of directions they called rutters. A rutter might say,

“Sail directly west from Sagres until you see a small Island. If you arrive there after October 30, wait until April 1 to proceed north or you will never make it…”.

The Portuguese kept their rutters out of foreign hands. The invention of latitude and longitude to map the earth made the rutters obsolete. But how do you know the latitude and longitude of your present position?

Latitude is One Thing

The idea of latitude had been used by the Polynesian sailors for many centuries. They explored the Pacific using a latitude hook. It consisted of a straight piece of wood with a crosspiece near the bottom and an open hole at the top, like this:

O————|——

The hook was held up so North Star showed in the “O” and the crosspiece was so affixed that it lay over the Pacific Ocean’s horizon. If they kept this configuration of the hook, the Polynesians could sail east or west and always get home.

The illustration below shows how the hook worked. To discover latitude probably took little more than taking an interest in the matter. According to Daniel J. Boorstin¹, “The Greeks’ way of determining latitude—by merely noting the elevation of the circumpolar stars (stars that from a given observer’s latitude does not go below the horizon)—actually required no nautical instrument at all.” This idea is just a generalization of Polynesian sailing, and making the crosspiece adjustable made it even more useful.

Longitude is Another Thing

The knowledge of one’s longitudinal position took many more centuries and many less than satisfactory attempts. The problem was finally solved by John Harrison’s building of a seaworthy clock. Here is how having such a clock aids in finding one’s longitude.

1. Below is a depiction of the imaginary longitude line in degrees wrapped around the equator. Of course, -180 longitude and +180 longitude coincide. The “00” center value was chosen to be at Greenwich, England.

-180_-150_-120_-90_-60_-30_00_+30_+60_+90_+120_+150_+180

The longitudinal distance between the 24 time zones is 15°. Twenty-four zones times 15 degrees per time zone equals the 360 degrees of a circle.
2. You have John Harrison’s clock (set to Greenwich time) on board your ship.
3. Knowing the local time of one’s position can be determined from the position of the sun.

Navigation Problem 1

It is 12:00 pm in Greenwich (longitude 0.0°), and our time² is 6 am. What is our longitude?

Answer: We are 6 hours behind Greenwich, thus -90° (6 x 15°, and the minus symbol is included, since we are behind Greenwich) is our longitude.

Navigation Problem 2

It is 12:00 pm in Greenwich, and our time is 3:00 pm. What is our longitude?

Answer: We are three hours ahead of Greenwich, thus +45° (3 x 15°, positive, because we are ahead of Greenwich in this instance) is our longitude.

¹ In The Discoverers, Random House, Inc.

² Our time refers to wherever we are in the problem.

Note: the reader might be interested in reading the account in Boorstin’s book of John Harrison’s travail in proving that his clock was seaworthy. There was a ₤2,000 reward for finding such, and Harrison was required to accompany his clock on a several year sea voyage. He never received the entire sum.

By E.H. Fenwick

Note: You might also enjoy Mysterious St. Elmo’s Fire

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