I do not claim to be an especial authority on the theory of navigation—indeed, it was as a prisoner of war that I first took up seriously the study of that science. But I believe that sustained and sufficient concentration can give a man what he wants; and on this assumption I decided to learn whatever might be learned about navigation as applied to aircraft. As yet, like most aspects of aËronautics, this is rather indefinite, although research and specially adapted instruments will probably make it as exact as marine navigation.

Navigation is the means whereby the mariner or aviator ascertains his position on the surface of the earth, and determines the exact direction in which he must head his craft in order to reach its destination.

The methods of navigation employed by mariners are the result of centuries of research and invention, but have not yet reached finality—witness the introduction within the last few years of the Gyroscopic Compass and the Directional Wireless Telegraph Apparatus, as well as of improved methods of calculation.

In short journeys over land by aËroplane or airship the duties of a navigator are light, so long as he can see the ground and check his progress towards the objective by observation and a suitable map.

But for long distance flights, especially over the ocean and under circumstances whereby the ground cannot be seen, the navigator of the air borrows much from the navigator of the sea. He makes modifications and additions, necessitated by the different conditions of keeping to a set course through the atmosphere and of keeping to a set course through the ocean but the principles underlying the two forms of navigation are identical.

It is impossible to explain aËrial navigation without seeming to paraphrase other writers on the subject. One of the simplest explanations of the science is that of Lieutenant Commander K. Mackenzie Grieve in "Our Atlantic Attempt," which he wrote in collaboration with Mr. Harry Hawker, his pilot, after their glorious attempt to win the London Daily Mail's transatlantic competition.

The chief differences between the navigation of aircraft and the navigation of seacraft are occasioned by:

(a) The vastly greater speed of aircraft, necessitating more frequent observations and quicker methods of calculation.

(b) The serious drift caused by the wind. This may take aircraft anything up to forty or more miles off the course in each hour's flying, according to the direction and strength of the wind. In cloudy weather, or at night, a change in the wind can alter the drift without the knowledge of the navigator. Hence, special precautions must be taken to observe the drift at all possible times.

(c) The absence of need for extreme accuracy of navigation in the air, since a ten or even twenty mile error from the destination in a long journey is permissible. Another favorable point is that rocks, reefs and shoals need not be avoided. This permits the aËrial navigator to use short cuts and approximations in calculation, which would be criminal in marine navigation.

There are three methods of aËrial navigation—"Dead Reckoning," Astronomical Observation, and Directional Wireless Telegraphy. None should be used alone; for although accuracy may be obtained with any single method, it is highly advisable to check each by means of the others.

As in the case of marine navigation, a reliable compass, either of the magnetic or gyroscopic type, is essential for aËrial navigation, as well as an accurate and reliable chronometer. Suitable charts must be provided, showing all parts of the route to be covered. When the magnetic compass is used, such charts should show the variation between True and Magnetic North at different points on the route.

NAVIGATION BY "DEAD RECKONING"

"Dead Reckoning" is the simplest method of navigation; and, under favorable conditions, it gives a high degree of accuracy. A minimum of observation is required, but careful calculation is essential.

The "Dead Reckoning" position of an aËroplane or airship at any time is calculated from its known speed and direction over the surface of the earth or ocean, and its known course as indicated by the magnetic or gyroscopic compass.

To determine the direction of movement of an aËroplane or airship, as apart from the direction in which it is headed, an instrument known as a Drift Indicator, or Drift Bearing Plate, is used.

One form of Drift Indicator consists of a simple dial, with the center cut away and a wire stretched diametrically across it. The outer edge of the dial is divided into degrees, in a similar manner to that of the compass. It is mounted in such a way that an observer can, by looking through the center of the disc, see the ground or ocean below him. The disc is then turned until objects on the ground—or white-caps, icebergs, ships, or other objects visible on the surface of the ocean—are seen to move parallel with the wire, without in any way deviating from it. The angle which the wire then makes with the direction in which the nose of the aËroplane or airship is pointing gives the angle of drift.

The ground speed (or speed over the surface of the earth) of aircraft can be measured by observing the time taken in passing over any fixed or very slowly moving object, while a certain angular distance is described—this being found by suitable sights, attached to the Drift Bearing Plate. From the result, considered in conjunction with the height of the aËroplane or airship, the actual speed over the surface is calculated. This speed will be in the direction shown by the wire of the Drift Bearing Plate.

The ground speed so found will differ nearly always from the air speed, as shown by the air speed meter, because of the effect of the wind. The difference is greater or less according to the wind's relation to the direction in which the aËroplane or airship is headed.

Having found by observation the drift, the ground speed and the air speed, a simple instrument such as the Appleyard Course and Distance Calculator then permits the aËrial navigator to discover without difficulty, as on a slide rule, the strength and direction of the wind. Should the actual track of aircraft over the earth's surface not coincide with the desired course, the Course and Distance Calculator, or a similar instrument, can thus be used to calculate, in connection with the wind velocity and direction already found, the direction in which the nose of the craft must be pointed in order to correct the deviation due to drift.

Knowing the latitude and longitude of the point of departure, and noting carefully the time that elapses between each separate observation of the ground speed and of the course, the air navigator, with the aid of a specially prepared set of "traverse tables" (as used by mariners), can easily plot on his chart the distance covered and the direction in which it has been covered. Hence the position of the aircraft at any time is either known definitely, or can be forecast with a fair degree of accuracy.

For aËrial navigation by means of "Dead Reckoning," frequent observations of ground speed and drift are necessary. If aircraft are cut off by clouds or fog from all possibility of sighting the surface of the earth, grave errors may occur, since in long distance flights the wind's velocity and direction often change without the pilot's knowledge.

NAVIGATION BY ASTRONOMICAL OBSERVATION

In navigation by astronomical observation, the position of the aËroplane or airship is found by observing the height above the horizon of either the sun or another heavenly body, such as a star that is easy of recognition. The method depends upon the known fact that at any given instant the sun is vertically above some definite point on the earth's surface. This point can be calculated from the time of the observation and the declination and equation of time, as tabulated in the nautical almanac.

In the case of stars, the right ascension of the sun and of the star also enter into the calculation. The method of carrying out such calculations is too involved for the scope of this volume, and the reader is referred to many of the excellent text books published on the subject of navigation.

Since the navigator knows, from the time of his observation, the point on the earth's surface over which is the heavenly body in question, it is clear that around this point circles on the surface of the earth may be described. From any point in any one circle the heavenly body will appear to have the same altitude or elevation above the horizon. A single observation of the altitude of any one heavenly body shows, therefore, only that the observer may be at any point on such a circle of equal altitude—otherwise known as a Sumner circle. But it does not fix that point.

A second simultaneous observation, of a different heavenly body, will give a different circle, corresponding to the position of the second body. The intersection of these two circles determines the point of observation.

This fact constitutes a reliable basis for fixing one's position during a clear night, when many stars are visible and choice of suitable heavenly bodies may be made. During the day, however, the light of the sun prevents other heavenly bodies from being seen, so that only a single observation is possible.

If the aËroplane or airship were not moving, then two successive observations of the sun, with an interval of an hour or more between them, would give the intersecting circles and fix the position. But the aircraft being in motion, it is necessary to combine the method of "Dead Reckoning" with the use of the Sumner circles, as found by observation of the sun's altitude.

In order to avoid drawing the entire circle, a small portion only of it is shown on the chart—so small that it may be regarded as a straight line. Such a small section of the Sumner circle is known as a "position line."

The desired track is laid out on the chart, and the "Dead Reckoning" position for the time of the solar observation is indicated on it. The track should be intersected at this point by the position line, the observation thus forming a check upon the "Dead Reckoning."

The altitude of the sun or of a star is measured by the sextant. For such an observation to be exact, it is necessary that not only should the sun or stars be viewed clearly, but that a clear horizon, formed either by the ocean or by suitable clouds, should be visible.

Corrections must be applied to the observed altitude for the aircraft's height above the horizon, for refraction, and for the diameter of the body under observation—the latter two corrections being given in the nautical almanac. There may be, also, an error inherent in the sextant itself. For extremely refined navigation, corrections are applied in accordance with the direction and velocity of the aËroplane or airship; but these are not really necessary, since navigation of aircraft does not require such close calculation.

When the sun or star observed is directly south of the aËrial navigator in the northern hemisphere, or north of him in the southern hemisphere, the altitude, corrected for declination of the body under observation, gives the aircraft's latitude. When the navigator is directly east or west, the altitude, corrected for the time of observation, gives its longitude.

If the horizon is invisible, owing to fogs or unsuitable clouds, it may be replaced by means of a spirit level; but great care should be taken in making such observations, since a spirit level on an aËroplane or airship is not wholly reliable, unless the craft is proceeding in an absolutely straight direction, and without sway of any kind.

All methods of navigation by Astronomical Observation fail when the sky is obscured by clouds and the heavenly bodies cannot be seen. As a general rule this drawback does not hamper air navigation to any great extent, since aircraft should be able to climb above most of the obscuring clouds. Yet it may happen, as it did in the case of our transatlantic flight, that the clouds are too high for such a maneuver.

If it were possible to measure accurately the true bearing of the sun or star at the moment of observation, then a single observation of a single heavenly body would fix the position of the craft at the intersection of the line of bearing with the position line. At the time of writing, however, there are no satisfactory means of making such a measurement with the required degree of accuracy. Apparatus which will enable this to be done is now in course of development. Navigation by means of astronomical observation will thereby be simplified greatly.

NAVIGATION BY WIRELESS DIRECTION FINDER

With the great improvements that have been made in the year 1919, the guiding of aircraft by directional wireless telegraphy is rapidly becoming a reliable and accurate means of aËrial navigation. Although complicated in design and construction, the complete receiving equipment for aircraft is now light, compact, and simple of operation.

The receiving equipment on aËroplanes and airships is arranged so as to indicate, with a comparatively high degree of accuracy, the direction from which wireless signals are received. The position of the sending, or beacon, station being known, the bearing of the aircraft from that station may be plotted on a suitable chart, in which small segments of great circles are represented by straight lines. Simultaneous bearings on two known beacon stations are sufficient to fix the observer's position with tolerable accuracy at the intersection of the lines of bearing, provided that they intersect at a reasonable angle—45 degrees or more, where possible.

With the very close tuning rendered possible by the use of continuous waves, beacon stations of the future will probably be provided with automatic means whereby directional signals can be sent out at intervals of one hour or less. Such signals will be coded, so that the crews of aircraft can identify the wireless station. The wave lengths must be chosen so as not to interfere with messages sent from commercial stations.

If there be a beacon station at the air navigator's destination, it is possible for him to direct his course so that the craft is always headed for the beacon; and in due time he will reach his objective.

This simple but lazy method, however, is not to be recommended; for, owing to the action of the wind, the route covered is longer than the straight course. To counteract drift and proceed in a direct line towards his destination, the air navigator frequently has to direct his course so that the craft is not headed straight for the objective. Hence, with a single beacon station, frequent observations of drift are necessary, if the shortest route is to be followed. Thus:

When two or more beacon stations are available, and positions can be ascertained at least once an hour, observation on the surface of the ocean for drift, although desirable, is not absolutely necessary. The drift may be calculated with accuracy enough from the craft's position as found by the lines of bearing indicated in messages from the various beacon stations.

Another method of employing the Wireless Direction Finder is for aircraft to send out signals to two or more beacon stations, which reply by advising the air navigator of his bearing in relation to themselves. This is, perhaps, the most accurate method. Its disadvantage lies in the fact that whereas the heavier and more robust apparatus needed for it can easily be employed in the stationary beacon stations, few aircraft will be able to support wireless sending apparatus of sufficient weight to carry over the long distances they must cover in trans-oceanic aËrial travel.

The greatest advantage of air navigation by means of wireless telegraphy is that it can be employed in any weather. Fogs and clouds do not make it inoperative, nor even less accurate. Another recommendation is that its use does not entail a knowledge of advanced mathematics, as required for navigation by astronomical observation.

I believe firmly that the air navigator of the future will rely upon the Wireless Direction Finder as his mainstay, while using astronomical observation and the system of "Dead Reckoning" as checks upon the wireless bearings given him, and as second and third strings to his bow, in case the wireless receiving apparatus breaks down.