April 5, 2003

Not so very long ago, airplanes had no GPS receivers, no Loran, and no VOR and DME to answer, in an instant, that age-old question posed by aviators, sailors, motorists, hikers, and anyone going anywhere: Where am I?

Pioneers of aviation had to answer that question the hard way. When out of range of the few ground-based navigation aids that existed, these aviators had one resource for determining where they were — the same one that sailors had used for centuries before. The aviators of that time will tell you how they had the luxury of choosing from 63 navigation aids! These were the sun, the moon, Jupiter, Mars, Venus, Saturn, and a collection of 57 stars whose visibility in the night sky afforded the navigator a good view. The collection of methods by which observations of the heavenly bodies are used to find one's way around the globe is called celestial navigation.

How accurate is it? Boeing 767 Capt. Dave Austin remembers his days doing celestial navigation in Navy P-2s. The young naval officer would climb up to the airplane's sextant port, take a few star sights, and then come down to the nav table to crunch the numbers. Austin recalls: "The aircraft commander used to tell me that if I could predict the time we'd hit a certain fix within two minutes of accuracy, he'd let me do the landing. And I did."

Aviation attorney and flight instructor Gary LaPook recalls the time, some years later, when he crossed the Atlantic Ocean in a Cessna 172 armed with nothing more than a sextant, the instrument used to make celestial observations. LaPook was headed for the Azores, that small cluster of islands that lies about 800 miles off the coast of Portugal. When asked how confident he felt venturing out to look for a few specks of terra firma in the middle of a 36 million-square-mile ocean, he replied: "No sweat." LaPook relied on his old friends in the sky to guide him to his destination, and he made it without incident.

Talking to these pilots, you quickly get one thing straight in your head: They didn't need a GPS to get where they were going.

Pilots like Austin and LaPook represent a generation of aviators who may be flying a direct course to the endangered species list, the kind of pilot who understands and uses traditional methods of navigation.

Do these pilots still use celestial navigation today? "Absolutely," says LaPook. On a recent trip from Los Angeles to Oakland, California, LaPook flew offshore and used his Fairchild Model A10A sextant to calculate a landfall into the Bay Area.

Why bother with celestial navigation in the age of the computer? With all the whiz-bang technology available that can give us laser-precision guidance to arbitrary points on the globe, who needs to do things the hard way?

If you put this question to experienced aviators like Austin and LaPook, be prepared to get an earful.

They'll tell you that learning to navigate the old-fashioned way helps to develop the basic visualization and problem-solving skills needed to competently use any system of navigation, regardless of how new or old it may be. If you think about it, nothing has really changed. We still have to find our way around the same Earth we did centuries ago. The problem didn't get any easier, and the penalties for getting lost haven't gotten any less.

Veteran flight instructors are quick to point out how easily the fundamental skills that underlie all forms of navigation can go away when not practiced regularly. In his classic book The Student Pilot's Flight Manual, William Kershner points out: "Too many pilots rely on radio navigation and find themselves rusty in pilotage or use of the sectional chart if the radios go out." (See " Advice to Pilots," beginning on page 137.)

As one airline captain summed up in five words: "Use it or lose it."

Jim Wolper, a mathematics professor at Idaho State University and a flight instructor, insists that time spent learning about celestial navigation will pay the student many dividends. Wolper teaches his students simple celestial navigation techniques as "a valid emergency method that novices can do to some extent with very little training." He adds that "the calculations of celestial navigation are identical to those used by GPS and FMS." Wolper devotes considerable time explaining celestial navigation techniques in his new book Understanding Mathematics for Aircraft Navigation.

How can you get started doing celestial navigation? The quickest way to start adding celestial techniques to your navigational repertoire is to learn to identify planets and stars in the sky. Aside from having a lot of backyard fun, you'll quickly learn that the heavenly bodies offer many road signs that can help you find your way around. Like other navigation aids, you just have to invest a little time learning how to read them.

There are many books on the topic of astronomy and stargazing that can help you get started. My personal favorite of the learning tools is a software program called Starry Night Backyard ( www.starrynight.com). Designed for both PC and Mac, Starry Night allows you to enter a date, time, and location on the Earth. The program then generates an out-the-window view of what you see in the sky. You can rotate the view to look in all directions, and can even move the viewpoint around the solar system and watch the sunrise from other planets.

A first heavenly body to acquaint yourself with is Polaris, a friend to navigators for centuries. Polaris is the one that, in modern times, appears to be located almost directly above the Earth's North Pole. Even simpler to use than an ADF, Polaris is that signpost in the sky that says: "North is this way."

Polaris isn't the brightest or the easiest star to find in the sky. When the Big Dipper is visible in the sky, finding Polaris becomes much easier; just follow the cup . When there's no Big Dipper, finding Polaris takes more practice. Every pilot is trained to get weather briefings before every flight. How about getting a celestial briefing?

The position of the heavenly bodies at every minute of the day is well known, documented, and published in an almanac created by the U.S. Naval Observatory and made available to pilots, sailors, and astronomy buffs worldwide. And if you don't feel like making the trip to the store, you can see it all online . Visit the Web site to get started ( http://aa.usno.navy.mil).

Maintained by the U.S. Naval Observatory, this site allows you to type in a date and time, along with any latitude/longitude coordinates. In return, you'll get a schedule of the positions of the sun or the moon, as they will appear from your general location, throughout the day.

Suppose you are flying near the San Francisco Bay area at 1 p.m. If you aim your airplane in the direction of the sun, you know that true course is roughly 191 degrees. What if you want to fly at night? No problem. Just look up the position of the moon, Jupiter, Venus, Mars, Saturn, Mercury, or any of the stars used for navigation.

When a celestial body is high in the sky like the sun during midday, it's difficult to determine its direction with high degrees of accuracy. For your purposes, the lower your celestial body is in the sky, the more accurate your direction estimates will be. If you want the best accuracy, make your observations as your celestial body reaches the horizon (e.g., sunrise, sunset, or moonrise).

If you own a Palm OS personal digital assistant, there's a handy program called CelestNav ( www.mobilegraphics.com) that puts almanac data in your pocket.

If playing around with the basics of celestial navigation gets you hooked like it has me and many other pilots, your next step might be to dig into the real thing. Contrary to what some may think, doing celestial navigation doesn't require math skills beyond simple addition and subtraction. However, there are a lot of numbers to juggle so the process does take some practice. If you want to skip the math altogether, there are a number of software programs like CelestNav that do the math for you.

Here's a quick primer to help you get the basic idea of how celestial position-finding is done.

If you think about the way you describe locations, such as "I am six miles east of San Jose," you'll notice that they all contain three essential pieces of information: (1) a well-known point of reference; (2) a distance from the point of reference; and (3) a direction from the point of reference.

Describing your position using celestial navigation is the same except that you use celestial bodies as points of reference. The almanac mentioned earlier spells out, in no uncertain terms, the location of every important celestial body at every minute of every day. Rather than describing the position of each celestial body in the sky, the almanac tells us the ground position (GP) of the celestial bodies. Imagine drawing a line from a celestial body to the center of the Earth. The point where the line intersects the surface of the Earth is the ground position of that celestial body.

If you determine a distance from the ground position of a celestial body, you know that you are located somewhere on a circle of position that surrounds the celestial GP . Since you haven't determined a direction you still don't know where on the circle you are located.

If you find that your position lies in some direction of travel from the celestial ground point, your knowledge of your position suddenly becomes more precise. Drawing a line from the point of reference in the direction you have determined tells you where on the circle of position you are located .

Finding the distance between your position and the ground position of your chosen celestial body is quite simple if you have a device known as a sextant. Simply stated, a sextant measures angles. Using a configuration of mirrors, a sextant allows you to look at your celestial body and the horizon at the same time. Adjust your sextant until the two are lined up — and then read the angle between them on the side of your sextant.

Let's suppose you just used your sextant to determine that the angle between your celestial body and the horizon is 30 degrees. From the rule of right triangles, we know that the angle between a line extending up from your position and the celestial body is 60 degrees (90 minus 30 equals 60). You can see an interesting relationship between this "angle in the air" you just measured and the angle between your ground position and the celestial GP. In essence, you just measured how many degrees of arc lie between you and the celestial GP traveling on the surface of the Earth .

What does 60 degrees of arc between you and the celestial GP mean? If you remember the old rule that one minute of arc equals one nautical mile, you have your answer. Your distance from the celestial GP is 3,600 nm. You are now entitled to draw a circle of position of radius 3,600 nm around your celestial body, and be reasonably sure that you are somewhere on it.

All you have left to do now is to find your direction from the celestial GP and you are done. As it turns out, scientists and engineers have never been able to design an instrument such as a sextant that can measure the direction (or azimuth) of a celestial body. This means that for now, you'll simply have to make a good guess at your direction from the celestial body. One accepted technique is to estimate the direction from the celestial GP based on your most recent position obtained using other methods such as dead reckoning.

The astute reader will notice that we've cheated a bit here. The maps we've worked with so far show the whole Earth on them. While this large scale nicely allows you to draw circles of position around any point on the globe, it doesn't permit you to see much detail and generally won't be of much use to you when navigating. But what happens when you switch to a more typical map scale? The ground points of your celestial bodies won't lie on your chart (too far away) and there will be no way to draw your circles using simple drawing tools.

The solution to this problem is to use a little math trick that scales the problem down so that all the relevant stuff fits on your chart. This trick is called sight reduction. To use sight reduction, start by picking a location on the chart that you think you are somewhere near. It doesn't really matter if you're that close to the point you pick; you just want a point that you think is on the same chart that you are. This point is called an assumed position . Since you know the location of the assumed position and the celestial GP, it's easy to figure the distance and direction between them. You can then draw a circle of position around your celestial body that passes through the assumed position. The good news is: You have a circle of position drawn on your chart. The bad news is: You're probably not on it. But if you take the math that you used to determine your distance from the celestial GP given a sextant angle, and work it in reverse, you can find what your sextant angle would be if you were located at the assumed position. Let's suppose you work the math and determine that your sextant would read 30 degrees and 2 minutes if you were located at the assumed position. You remember the reading you got from your real position: 30 degrees, zero minutes.

What do you now know? You know that your real circle of position is two minutes, or 2 nm from the one you just drew. You can now measure off 2 nm and draw your real circle of position. Done!

Celestial navigation offers a fun learning experience for aviators and non-aviators alike. And aside from fortifying your understanding of navigation methods old and new, there may come a time when your batteries run out and you'll thank your lucky stars for having invested a few hours learning this fascinating and timeless skill.

*Stephen M. Casner, Ph.D., is a researcher for NASA and the author of two books,* The Pilot's Guide to the Modern Airline Cockpit *and* Cockpit Automation for General Aviators and Future Airline Pilots.