I must forewarn you that this lecture will deal only with very elementary mathematics. Its subject is what may be termed the preparatory school stage in the education of the navigator. Nevertheless, it is a subject of particular interest and importance because it is in the field of navigation that we first meet with mathematics quite outside learned academic circles. It was among sailors that the process was begun (and it is not yet complete) of transforming the craftsman—whose skill rests on tradition and experience—into the technician—who works on established scientific principles. For the scholar, mathematics is like poetry—an end in itself.

The basic values for dead reckoning, course and speed, are ascertained by inadequate references. The log does not measure the ground-speed but the speed relative to the water. The accuracy of magnetic compasses is limited by the instability of variation and deviation; gyro-compasses are better, but neither does away with steering errors. All classes of position-fixing permit the derivation of course and speed from two fixes but are influenced by the errors inherent in the methods. An astro fix is subject to irregularities of dip and the inefficiency of artificial horizons. The uncertainty of course and speed errors in running fixes is estimated and does not give very satisfactory results for astronomical and radio fixes, with the exception of methods giving an accuracy of 1 n.m. (e.g. Decca). Standard errors are referred to throughout.

Development of Dead Reckoning in the Air. Air navigation is the child of sea navigation. Hence navigation across the skies tended to follow the pattern of navigation across the oceans. It was built around the dead-reckoning plot, into which was fed all varieties of information. At take-off and landing, there was also a little pilotage, but this was hardly mentioned in polite air navigation circles.

The paper outlines some of the factors to be considered in the design of any complete airborne automatic navigation and control system. It is pointed out that such a system should lower the work-load on the pilot or navigator as well as contributing to flight safety. Modern engineering techniques have produced a wide range of navigation devices, and their safe and economical use in a complete system involves the consideration of a control loop including the displays and the human navigator. The paper examines this navigation loop in some detail. Some simple and some more complex methods of securing safe operation are suggested.

The view is taken in this paper that an automatic navigation system should be capable of weighing up data and issuing instructions, in the same manner as a human navigator. Conventional information tends to offer static rather than dynamic data.

It is suggested that there are several stages of development towards completely automatic navigation: (i) a dynamic interpretation of the existing navigational situation, (ii) the automatic prediction of future situations, (iii) automatic navigational advice, (iv) automatic control of a ship under the supervision of a navigator. Such control would not take care of all situations but would be particularly suited to some; a list of the information likely to be required for presentation is given.

For entirely automatic navigation to be feasible, the whole of the process of transport at sea may have to be reviewed. It is suggested that the trend should be towards presenting error, rate of change and forecast data.

It is pointed out that the demand by navigators for more information in a given time or for the same information in a shorter time can only be met at the price of increased complexity (and, therefore, cost) and unreliability. To provide examples supporting this statement, a number of well-known systems are described briefly; for example, in the family of hyperbolic systems there is a clear indication that those providing immediate access to an unambiguous fix are more complex, in the wide sense, than those achieving similar accuracy but at the expense of ambiguities. This is even more true when various degrees of automatic operation and display are considered, and the paper includes a description of some of the techniques involved in the provision of these facilities. Finally, brief reference is made to the suitability for automatic computing of the geometry of the various systems and it is pointed out that those working in polar coordinates or Earth axes (such as VOR/DME and doppler/compass respectively) have advantages over the hyperbolic systems.

The requirements of navigation entering or leaving harbour or in narrow waters are exacting, and a very accurate position is usually essential. For this reason it is believed that inertial techniques should be applied in the first instance only to ocean navigation as, although the system will give the ship's position continually, the accuracy will be of the order of one mile.

The latitude and vertical references are absolute, but the longitude reference is relative to a known starting point. Besides position, an inertial system can also provide course, sidereal time and roll and pitch and, by comparison of successive positions, course and speed made good, and leeway. Furthermore the system could be used to feed position into an automatic plotting table, with a chart of suitable scale superimposed, so that the vessel's geographical location would be visible at a glance.

Some general features of inertial and hybrid inertial systems are examined in relation to the navigational problem in its two essential aspects:

(i) The present situation.

(ii) The action required.

As the fundamental D.R. system, inertial navigation has the virtue of independence but suffers from time-dependent errors. The engineering complexity and delicacy of adjustment of purely inertial navigation systems of long-period accuracy detract from its general application where other aids are available. On the other hand, increasingly stringent demands on flight-path computation and control justify an examination of the benefits to be derived from exploitation of the particular short-period merits of an inertial element used in conjunction with other aids.

Principles of mixing are discussed in relation to quantity and quality of information inputs. Examples are then given of fallacies which may arise from the omission of essential information or from ignoring cross-coupling, and of the impracticability of mixed systems which assume too much of the quality of the input information.

After summarizing the main features of inertial, radio/radar and astro aids, examples are given of practical and useful mixed systems which do not require the highest precision of inertial components. For example, auto-astro and inertia/doppler/ground fix contain the necessary and sufficient ingredients for combining long-period accuracy with short-term memory, speed of response in manoeuvre and instantaneous outputs such as are required for precise control and for flight path monitoring.

Summarizing, it may be said that the value of true and hybrid inertial systems in the military context is evident. For more general application we may hope to see a gradual evolution of small, accurate and reliable central reference systems which will permit the employment of inertial methods suitable for mixing, especially with doppler in an accurate D.R. system. The outputs will be suitable not only for flight-path monitoring, but as providing information of a quality very well suited for integration into the control system and so into any overall system of flight automation.

The basic principles of radio sextants are reviewed and their application is compared and contrasted with that of infra-red and visual wavelength sextants. For maximum versatility an automatic sextant should be able to operate both on radio wavelength and at one of the others. A complete automatic system requires not only a means of making automatic celestial observations but also a means of carrying the data forward—that is to say, as inertial reference. In the paper presented in Paris the development of inertial systems was briefly reviewed with particular reference to linear vibration gyrostats which lend themselves readily to light and compact systems where the highest accuracy is not required.

It is suggested that future developments in automatic navigation may well see novel forms of inertial reference coupled to radio sextants of millimetre wavelengths.

Three types of self-contained navigation systems may perhaps be found, operating independently on airliners flying polar routes; doppler, astro and inertial. We may also find hybrid systems with doppler, astro and inertial components. The combination of doppler and astro systems should be the first step towards self-contained automatic navigation and this combination could be used with great advantage by the airlines for global operations. The more sophisticated doppler and inertial combination may be found too expensive for airline operators and may therefore be restricted to military uses.

In polar regions great reliance has to be placed on the directional information provided by a free azimuth gyro. For sufficient reliability the use of three such gyros is advocated. An analysis is made of ‘the best two out of three’ principle—taking into account the fact that in practice no two gyro readings will be identical.

It is demonstrated that for a given reliability attaching to an individual gyro, the reliability of a three-gyro system represents a vast improvement over a single instrument and that there is an optimum way of using the information presented. The advantages of middle signal selection are pointed out and the dangers associated with mean signal selection are explained. Attention is drawn to the extension of this principle to the problems of triple-signal selection in the automatic navigation system of the future.

This paper discusses the operation of a simple computer which, when used in conjunction with a doppler sensor, will enable automatic navigation to be performed. It is primarily designed for the civil air operator. A series of rhumb lines may be flown and position relative to the desired track and destination will then be displayed. Directional command signals to the pilot and autopilot enable the track to be closely followed.

A short technical description of the computer is given and the expected errors and methods of correction are evaluated. Procedures for turning corners, making diversions, regaining track and flying holding patterns are given, together with the limitations or inaccuracies of the navigational information under these conditions.

The possibility of obtaining altitude as additional information from an airborne doppler navigation equipment is reviewed, and some of the design problems involved are discussed briefly. These relate to the form of modulation used for transmission, the aerial beam shape and the direction of the aerial beams.

It is concluded that an accuracy of ±5 per cent. ±2 ft. over the range of 10–100 ft. might be possible. The work is in an investigational stage, and no specific design is described.

This equipment was originally designed as a pilot aid to facilitate the use of maps on a route flight. It was used to such an extent that several different models have been developed which fall into the category of automatic navigation equipment. However, even the new concept is still an open-loop navigation device, the loop being closed through the pilot or navigator in the aircraft who reduces the accumulated position errors to zero by direct observations. In the most sophisticated form the roller map equipment is driven automatically according to aircraft ground-speed derived from doppler instrumentation and is equipped with an aural flight programme replay device to draw the pilot's attention to salient features of his flight route.

The title of this contribution is, in itself, misleading. All our navigation is planned and devised by human beings, whatever may be the degree of automaticity inherent in any particular system. The navigation of a space rocket is just as human as that of a Polynesian canoe, despite the absence of a working navigator going along ‘for the ride’. In considering the degree of automaticity desirable for a given navigational task we are really trying to decide how best to deploy the available human effort.