Where on Earth am I?

It is a ritual every summer. Families all over the US are gathering up the kids and dogs, loading up the car or van and heading out for cross country vacation drives over the fruited plains. As they hurtle down wide 6-lane freeways, after a few hours, every driver wonders, “Where am I?” The feeling of emptiness and disorientation about the location is compounded by the whining and droning coming from the rear seat, every 2-3 minutes, “Are we there yet?”

A few days back, I was flying at a meager 3,000 feet in a single engine, two-seater aircraft, practicing my piloting skills. My instructor put me through some very sharp turns in many directions and then into a sharp climb and then decided to finish the lesson. “Take us home”, she said. I leveled off and looked around, and gazed at the rugged beauty of the Arizona desert, dry scrub, mountains and clusters of houses. I had no idea where I was, or worse, where the airport was.

Commercial transport crisscrosses the earth all the time, over sea, land and air. People, cargo, letters, packages, animal and other esoteric junk are transported over large distances safely and accurately. At any point in time, it is the responsibility of the operator of the vehicle to know where he is located and where the vehicle should be headed. The art of location tracking is called “navigation”.

Navigation has it roots in the in the 15^th century. While many things have evolved since the seafaring days of Christopher Columbus and the caravans of Marco Polo, even today there are three forms of navigation: 1) pilotage, 2) dead reckoning and 3) instrumental navigation.

Pilotage is defined as navigation by visual reference to landmarks. Car drivers use buildings, road signs, shopping centers and such. Pilots of small aircraft use major highways, cities, mountains, and lakes. Ships use islands, shorelines. Men believe they are uncanny pilotage experts and keep driving till they are hopelessly lost. Women stop and ask directions every three minutes.

Dead reckoning is a method of pre-calculating the course on paper. The calculations include direction, time, fuel needs, distance traveled, when to turn and so on. There is some debate as to the origin of the term dead reckoning. Some say it comes from maritime navigation (“you reckon right, or you are dead”). Others say it is a short form of “deductive reckoning”.

Instruments for navigation are nothing new. Historic gadgets include the compass, the sextant and various thingamajigs that help in using the sun and the stars to estimate time and position. Today, the instruments are highly sophisticated and uncannily accurate. These include digital compasses, gyroscopes, radio navigation aids (LORAN, VOR) and satellite navigation (GPS).

Suppose you are seated in the comfortable seats of a wide body Boeing 747 as the engines hum reassuringly and the plane is gracefully flying out of Tokyo’s Narita Airport. As you congratulate yourself of having escaped the dreary grunginess of one of the world’s worst major International airports, a soothing voice comes over the PA system.

“Welcome ladies and gentlemen. This is your first officer, Smith, from the flight deck. We are climbing through 10,000 feet towards our initial altitude of 25,000 feet. Later we will be cruising at 35,000 feet. Our flight path to San Francisco, today will take us North, close to the Bering Sea and the Aleutian islands, over the Gulf of Alaska and then South to San Francisco. Landfall will be at Sonoma county, about 100 miles short of touchdown. We have a helpful 50 knots of tailwind, and our flight time will be nine hours and ten minutes, putting us at an early touchdown in San Francisco at 8:45am. Have a good flight.”

The above seemingly innocuous paragraph is loaded with navigation hints. The reference to the Bering Sea, Aleutian Islands and Sonoma county are just a part of the pilotage that will be used. Regardless of all the sophisticated instruments telling the pilot all about location and direction, there is nothing more reassuring to a human being to see the green coastline with the familiar beaches joining up with the blue sea, about a 100 miles short of the destination. The sight cues still are and always will be an integral part of navigation.

The statement (above) about paths and timings are derived from an elaborate pre-flight planning of the trip, using dead reckoning. The pilot has calculated the route, taking into account the wind speeds (varies all over the route, and at different altitudes) and turns the plane has to make along the way (and at what time). Note that aircraft fly “great circles” which means, they take the shortest path, thus they have to keep making changes in direction. The great circle from Tokyo to San Francisco goes North and then curves over to the East and finally ends up going south.

Pilotage is the most common form of navigation used in daily life. We walk around using pilotage. Even when we walk the same route everyday, we unconsciously use landmarks. Even when driving around in familiar neighborhoods we use pilotage, but driving in unfamiliar territory requires dead reckoning. Trains of course need no navigation.

Lets suppose we are going to drive a car from point A to point B. We first look at a road map and find a set of roads that connect A to B. Then we write down each turn (e.g., from road X to road Y, turn left) that we have to make on the way. Next we estimate the distance between each turn and the average speed of travel over this distance. In so doing, we can estimate time between turns. Now we can deduce, often quite accurately the total distance, the total time, the fuel needs, the need for overnight stays (if A and B are very far apart). With good maps we can make plans of stopping on the way, finding places to eat, to stay or even finding interesting detours. All this activity of route planning is of course dead reckoning.

When dead reckoning is used to fly aircraft, the procedure is different. While there are no roads in the air, there are rules defining permissible tracks. There are VOR highways, and height restrictions. To make a long story short, to go from point A to B, we first pick a straight line connecting A and B. Then we make detours to avoid restricted airspace (like large airports), high mountains and turbulent zones. We also obtain elaborate weather reports from monitoring stations all along the routes. This lets us plan the elevation to fly (it will vary along the route).

Next we calculate the direction of travel. Suppose we want to travel North at about 100mph, but there is a wind blowing from the East at 20mph. We use a calculator to realize that if we flew 11.5 degrees towards the East, at 100mph, we would be really going north at 98mph. Now we use 98mph as the speed for calculating elapsed time. Then we use the time to calculate fuel consumption. We use fuel consumption rate to calculate the decreasing weight of the aircraft. The decrease in weight may lead to the ability to fly higher or faster, which then has to be plugged back into the formulae to get a more accurate time prediction. Of course, the wind speed varies with location and altitude and hence the whole exercise is much harder than this example.

Augmenting pilotage and dead reckoning is instrumental navigation. Instruments range from simple radio direction finding to complex satellite based systems. Onboard gyroscopic instruments can provide a cumulative view of direction traveled. Radio beacons provide references to ground stations and help in determining answers to the ubiquitous question of “Where am I”. Satellite based navigation can accurately pinpoint locations at any point on earth. Radar can provide pilotage when sight is blocked by weather. Radar can also show nearby obstacles.

With instruments it is possible to fly over unknown territory, in blinding fog (or clouds) and be aware of position, height and speed all the time. Even in the oceans instruments, provide location information, and allow corrections for winds, ocean currents to be made accurately and dependably. Instruments can automatically download weather information from a multitude of ground stations. The current set of instrumental aids in navigation provides uncanny accuracy and dependability. Next week we will look at some of the established and newer forms of instrumental navigation.

Partha Dasgupta is on the faculty of the Computer Science and Engineering Department at Arizona State University in Tempe. His specializations are in the areas of Operating Systems, Cryptography and Networking. His homepage is at http://cactus.eas.asu.edu/partha.