The Airbus A330 that I fly across the Atlantic to any of several European cities is equipped with onboard navigation computers that tell us in the cockpit exactly where we are at any time.

But when the routes I fly were pioneered some 60 years ago, computers and Global Positioning System satellites weren’t on hand to help pilots find their way across oceans at night. In my flight bag is a World War II-vintage Pioneer-Bendix bubble sextant, which I use—just for fun—to see how close those earlier navigators could come to the position fixes now provided by our sophisticated navigation equipment. I try to imagine what it was like to stand in the bubble window protruding into the slipstream from the top of those old transports and figure a position from the stars.

A sextant is used to measure the altitude of a celestial body above a horizontal line of reference. (“Altitude” in this case is a special use of the word describing an angular measure, not a distance in feet above sea level.) A mariner can use the horizon as this line of reference, but when an airplane is above the clouds or flying at night, its navigator can’t see the horizon. The bubble sextant solves this problem by providing an artificial horizon. It takes its name from an air bubble in a liquid-filled chamber that functions like a carpenter’s level, indicating when the sextant is aligned horizontally. When I look through the eyepiece of my sextant, I locate a star and, with a drum on the side of the instrument (like a camera’s focus ring), adjust the angle of a rotatable prism until the star showing in the eyepiece is aligned beside the bubble. The prism and drum are geared to circular scales, marked off in degrees. From these scales I read the star’s altitude.

But acceleration of the aircraft and turbulence frequently deflect the true vertical; therefore, a single reading may not be accurate. For that reason, the bubble sextant also has a mechanical averager with a wind-up clock. It takes 60 altitude readings over a two-minute period, using a little counter that looks like a car’s speedometer to average and display the measurements.

Once I know the the star’s altitude, I can find where I am on an imaginary line extending from me toward the star’s geographic position. But finding the altitude of the star is the second step in plotting my position.

The first step is to assume a position, a set of coordinates I determine by deduced, or dead, reckoning. Based on three pieces of data—this assumed position, the altitude of the star, and its azimuth (its angular distance from true north), I calculate where I am by proving that I’m not where I assumed! Here’s an example:

Last January 9, at 02:30 Universal Time, I assumed that I was at latitude N50° and longitude 30°53.9’W. With my sextant, I measured the altitude of the star Sirius to be 22°11’. I then went to The Nautical Almanac, where a number of tables helped me compute the declination (similar to latitude) and Greenwich Hour Angle (similar to longitude) of Sirius on the celestial sphere for that time at that date. With more formulas and tables (there are about eight steps in all), I calculated the altitude of Sirius to be 22°05’. Since my observed altitude of Sirius was 6’ greater than the altitude calculated for the assumed position, my true position must be 6’ closer to Sirius’ geographic position. Next I drew what is known as a “line of position” perpendicular to the azimuth of Sirius, and then I started the whole process over again with the star Regulus, and again with Polaris, which, as the North star, is a special case. The intersection of three lines of position gives a fix.

After all this, how close to the actual position do I get?

You can see from the chart that my calculated position—in the triangle formed by the intersection of three lines of position—is only about five nautical miles away from the actual position, given to me by the aircraft’s navigation system. On our North Atlantic plotting charts, 10 nautical miles is about a sixteenth of an inch. At our ground speeds, that size circle of error puts us within one to one and a half minutes of the exact position.

The process of navigation may be complicated, but its concept is simple. As my mom, now 82, puts it, “It’s when you leave home, you know how to get back.”

## The Navigational Triangle

To describe the locations of celestial objects, astronomers imagined a celestial sphere, whose surface is of infinite distance from the Earth. Early navigators used the sphere to plot a navigational triangle, the points of which coincide with the celestial body, the elevated pole, and the zenith, a point directly above the observer. Using spherical trigonometry, the navigator solved the angle at the pole, and from that could calculate his longitude. By referring to charts that gave the star’s angular distance from the celestial equator, or declination, and determining the angle at the star, he could pinpoint his latitude.

Modern navigators have it easier. They find the altitude of a star and know they are somewhere on a circle, where from every point the star is the same angle above the horizontal.

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