Global Positioning System Reference
In-Depth Information
shoot the noonday sun, also obtained his heading without calculations
because, of course, the noon sun is directly south for an observer in the
northern hemisphere.
Much closer to home, a pilot often needed to estimate his distance from
a nearby shore. If he knew that rocks, a reef, or a sandbar lurked just
beneath the surface, then learning how far he stood o√shore became a
matter of some importance and urgency to an anxious mariner. As sea
tra≈c increased, especially o√ the shores of newly found lands with coast-
lines that had not been completely surveyed, such as the Spanish Main (the
Caribbean Sea and the Gulf of Mexico), this problem was exacerbated.
There are a couple of very old rough-and-ready techniques that have been
employed for centuries by men of the sea to gauge how far a ship stands o√
from shore. Both methods require the mariner to extend his thumb at arm's
length. The width of a thumb at the end of an arm subtends an angle of
about 1.6\. Suppose a pilot sees a church steeple, a tree, or some other
object of known height on the shore. He can hold out his thumb horizon-
tally and estimate the size of the steeple or tree compared with his thumb.
To provide a specific example germane to this period, let us say that a
Spanish galleon is returning home from Cartagena and is passing along the
northern coast of South America, perhaps laden with silver, in the year
1550. From his charts, the pilot knows that a coastal cli√ he is passing is
50 m high. He also knows that just beyond this promontory, a hidden reef
extends 2 km into the sea. He judges that the cli√ height is half the width of
his extended thumb, held horizontally. Does he need to steer a course
further out to sea? No, in this case, assuming that he does not have a
particularly fat thumb: from the trigonometry we can see that the cli√ is
more than 3
1
⁄
2
km distant.
The second thumb method is equally venerable: it is still used today by
weekend navigators as a handy (pardon the pun!) technique. The
eye-blink
method makes use of the idea of
parallax
—that separated observers looking
at the same object see a di√erent background. In this case, the pilot knows
that two coastal features—say, a lighthouse and a small islet—are 1 km
apart, and he wants to estimate his distance from the coast. This time he
extends his arm with the thumb up. He closes his left eye and, with his
right eye, lines up his thumb with the lighthouse. He then closes his right
eye and sees how far toward the islet his thumb appears with his left eye.
Let us say that his thumb as viewed through his left eye is exactly lined up
with the islet. An arm length is about ten times the distance between a pair
of eyes; then, from elementary trigonometry we know that the angle be-
