There are endless regulations concerning the speed and size of vehicles on our roads, but none that apply to vessels using our maritime routes, even though there is a regular increase, in step with technical advances, in both the size and speed of ships. For reasons of economy roads are narrow, and the necessity to avoid obstacles means that they have to be winding. No such considerations apply at sea; changes of direction are slight and widely spaced out, nor are there any ditches or hedges to limit the width of the routes that are used. Nevertheless, studies of maritime traffic have shown that overcrowding is becoming more and more pronounced on the busiest routes, and the present tendency to develop oneway routes is an implicit recognition of the fact that the remedies for such overcrowding on the roads and at sea have something in common. One-way traffic, for example, is derived from the Collision Regulations (Rule 25). It is worth examining what help the Regulations can give in solving problems raised by the size and speed of ships.

A continuing study of ship's bridge design and ship control conducted by the Defence Research Board of Canada has recognized that the conventional method of issuing and executing verbal orders contains inherent delay and is a possible source of error in ship control. As a partial solution to this problem, it was proposed that ‘the officer originating decisions to change the course and speed should implement these decisions himself through the direct control of helm and engines on the bridge’ (p. 21). It was further proposed that the direct controls be located on a console positioned at the front of the bridge on the centre-line of the ship.

The conventional location and arrangement of the bridge restricts visibility, however, in areas close to the ship, and this limited visibility from the bridge often causes manœuvring difficulties. In some instances, distances as great as 800 ft. ahead of the bow and 50 ft. abeam are ‘blind areas’. In most cases, areas aft on the centre-line cannot be seen at all. In an attempt to alleviate these problems, bridges have been extended to the sides of ships, or bridge wings provided so that much of the ship's side can be seen by the conning officer. With direct control from the centre-line and the use of a television system, bridge wings could possibly be eliminated, while still providing better close-in vision.

A ship will drift regardless of whether she is stopped or underway due to the action of the wind and sea. A knowledge of this movement is necessary in order to correct the course, to deduce the estimated position, for manœuvring at slow speeds and for search and rescue work. The causes of drift are the force of the wind on the upperworks, drift current whose strength depends on the wind, rolling which is caused by the action of sea and swell and, finally, ocean currents and tidal stream currents. To study the effect of wind on drift an experiment was carried out in which this effect was isolated from the other causes mentioned above.

A salmon drifter was used in which a gill-net was observed by radar from the time of the net being shot until it was hauled in. The net was then allowed to drift with the ship with the ocean current, the tidal stream current, the drift current and the wind and sea. The ship itself, however, was also subject to drift from the wind whereas the corner reflector on the net (which was several miles long) was not subject to this effect, the net acting as a sea anchor. It was thus possible to isolate the effect of wind drift.

Contour charts are of great value ‘providing’, as Hughes says, ‘the navigator with a quick and sure means of comparing the echo sound record he has just made with the variations in contour and so enabling him actually to plot his line of position by soundings’. But it is evident that the most useful method of using contour lines would be if the position lines based on them are plotted in the same way as every position line, i.e. by plotting the intersection of two or more of these lines. The object of this paper is to propose such a method.

It is possible to plot a contour-based position line by means of the sight line to one point of a contour line and its range, because if we draw (Fig. 1) from every point of contour line A, parallels of the same length to the sight line, all points at the other end of contour line define such a position line, which may be called a range-bearing (RB) position line. Better accuracy can be obtained by sextant, using a second sight line to the same or another contour line (Fig. 2), measuring the angle α between them—then we have a position line which may be called a two-range position line. When it is possible to measure the minimum range to a contour, the angular datum can be omitted, using the position line which may be called a mini-range position line.

A basic parameter of a ship's motion is its velocity, a knowledge of which is important to both seaman and ship designer. Often it is sufficient to know the ship's mean speed at given engine revolutions. Sometimes the knowledge of its instantaneous velocity may also be required.

Instantaneous velocity measurement is possible by means of a doppler radar. The radar is located on the ship and at a selected point of reference on shore, or on a buoy, a reflector is placed which strongly reflects the electromagnetic waves; the ship is then steered directly towards or away from the reflector. The radar emits a beam of electromagnetic waves directed toward the reflector. Due to the ship's motion in relation to the reflector, the received signal returned by the reflector is shifted in frequency from the transmitted frequency by a doppler frequency. This frequency is proportional to the instantaneous velocity. The mean velocity may be measured by counting the number of signal periods of doppler frequency. This number is the measure of the distance covered by the ship. Simultaneous measurement of the time enables the mean velocity over the given distance to be determined.

This method makes possible the measurement of the instantaneous velocity and acceleration of the ship. Simultaneous observation of instantaneous velocity when measuring the mean velocity allows a measuring length along which the velocity of the ship reaches a steady value to be chosen and the maximum velocity to be measured.

The stick charts found in the Marshall Islands, of which some 20 or 30 are extant in museums throughout the world, have for long puzzled historians of navigation. In this paper, which is based on a more complete work, to be published elsewhere, the author examines the authenticity and meaning of these objects and concludes that they were mnemonic devices, of no great antiquity, to facilitate navigation and to train navigators.

An important consideration in the design of systems for human control is the difficulty of the task. An analytic measure of this subjective consideration is denned. The difficulty is a function of the lead factor which is an integrated measure of the amount of lead the human must produce. The theory together with experimental results imply that the performance function minimized by a human controller includes the amount of control as well as the amount of error. The difficulty is constrained by the capability, training and stress level of the operator. Remnant is accounted for by assuming that the operator generates additive noise as a function of the difficulty. The model is used to explain Bernotat's experimental results with prediction display.

This work was performed while the author was a guest professor at the Institut für Flugführung as part of the exchange programme between M.I.T. and the Technische Universität, Berlin.

As a general rule the navigational function is aimed at determining the position of the aircraft in order to resolve three types of problem:

(1) To subject the aircraft's flight path to an optimum trajectory calculated before departure or progressively adapted in course of flight to the circumstances encountered.

(2) To choose at each point of the selected flight path the flight system best adapted to the safety and economy of the flight.

(3) Taking into account the presence of other aircraft in the airspace, to know and make known the actual position and the information allowing provision to be made for future positions, so as to permit effective air traffic control.

Departures of the actual from the chosen flight path penalize the flight by a lowering of economy (in flying time or fuel consumption). It does not seem, however, that the problems raised from this point of view by S.S.T. are by nature or in difficulty any different from those which affect conventional aircraft. Taking into account the present-day precision of navigational aids there is every reason to believe that departures of the actual flight path from the optimum flight path will introduce a penalization which it is possible to ignore when compared with the penalization due to the inaccuracy of the knowledge of the elements (winds, temperatures, pressures) which have, in fact, served to determine this optimum flight path.

The S.S.T. simulation programme of the F.A.A., already in progress since May 1963, aims at determining system requirements both ground and air in the period 1970–75 and, as a future project, in the era 1975–80. In this context, air operations involving the following types of aircraft are under study:

(a) Current and future military aircraft with supersonic speed capabilities;

(b) Concorde-type operations;

(c) Mach 3 or mach 2.7 civil transport operations.

Since the start of the S.S.T. simulation programme, six studies have been undertaken, each of an average duration of 6 months.

From May 1964, a S.S.T. flight deck simulator (modified DC-8 simulator), located at the N.A.S.A. Research Center, was linked with the A.T.C. simulator at N.A.F.E.C., for communication of positional data (digital, including S.S.R.) and voice information, and thus formed part of the traffic sample under study, i.e. one aircraft among 108 others that can simultaneously be simulated at N.A.F.E.C.

Whilst previous exercises concentrated on terminal area (T.M.A.) requirements, the exercises in progress in July 1966 were designed to examine extended T.M.A. and en-route operations in the early 1970s, with Concorde and mach 3 or mach 2.7-type S.S.T.s flying in or through a mixed environment of subsonic traffic. Amongst other parameters, a variety of geographical zones, air traffic control centres, T.M.A. control units, route network configurations in the New York, Boston, Cleveland and California areas, were simulated with a view to determining the impact of specific regional terrain and traffic conditions.

It its early work, the Working Group decided to study amongst other subjects the problems of bringing the S.S.T. into a traffic control system; almost certainly there will be an effect on the flight profile of the S.S.T. and on the requirements for accuracy of the navigation. In the absence of special information on the characteristics and performance of the S.S.T., a study has been made of the trends in A.T.C. handling of terminal area traffic (T.M.A.). The term terminal area has been interpreted in its broader sense, that is to say the region in which present-day transport aircraft and a fortiori supersonic aircraft are not in the cruise phase but are either descending towards the destination airport or climbing from the departure airport. With this definition, the most important terminal areas (those in countries overflown by heavy traffic and in which there is a plenitude of radio navigation aids and control), have in practice the same limitations as the flight information regions in which they find themselves.

If we try to look ahead ten years to the period from 1965 to 1975, it is precisely in this period, in the countries overflown by heavy traffic, that the instruments and systems which have been recently devised and experimentally used to meet the problems of subsonic traffic control will, in fact, become operational. With these points in mind the following notes refer to the possible evolution of traffic control in the future.

The publication of a new impression of Professor E. G. R. Taylor's first volume of Mathematical Practioners so soon after the appearance of her second volume makes it a particularly appropriate time to take stock and consider the next steps. Despite various criticisms, some of which will be discussed below, all reviewers agree that her volumes mark a great advance in this field and will be of ‘immense service to scholars’. Our debt to the author is all the greater when we realize that these books followed on a whole series of standard works in her own subject of geography, and that she was neither a mathematician nor a bibliographer. The best tribute to Professor Taylor is to continue the work recorded in these two volumes, but there are few who have the detailed knowledge and expertise to follow her in such a wide field. This article will, for example, offer little comment on instrument-makers who form such a large section of her practitioners and who left records of their work in museums and private hands all over the country; here we shall be much more concerned with the written work, with the bibliography of the subject.

Reviewers of her volumes have found it difficult to define the practitioners of whom she wrote and to decide in what sense they differ from mathematicians in the normally accepted sense of this country or overseas.

Newton'sPrincipia contains a neglected passage, which is nevertheless the true source of inertial navigation, occurring in De Motu Corporum Liber Primus, toward the end of ‘Sect. X. De Motu Corporum in Superficiebus datis, deg; Funipendulorum Motu reciproco’ as ‘Corol. 2’ to Prop. LIII. Prob. XXXV. Concessis figurarum curvilinearum Quadraturis, invenire vires quibus corpora in datis curvis lineis Oscillationes semper Isochronas peragent’. The corollary reads in the first edition:

‘Corol. 2. Igitur in Horologiis, si vires a Machina in Pendulum ad motum conservandum impressae ita cum vi gravitatis componi possint, ut vis tota deorsum semper sit ut linea quae oritur applicando rectangulum sub arcu TR & radio AR, ad sinum TN, Oscillationes omnes erunt Isochronae’.

This text shows only one or two very minor changes in the second and third editions, but the two extra drawings added in the third edition are helpful. Cajori, in a readily available publication quite adequate for reference here, gives these drawings, and his version of Motte's translation reads:

‘Cor. II. And therefore in clocks, if forces are impressed by some machine upon the pendulum which continues the motion, and so compounded with the force of gravity that the whole force tending downwards will be always as a line which is obtained by dividing the product of the arc TR and the radius AR, by the sine TN, then all the oscillations will become isochronous.’

Having studied marine statistics for a number of years, especially those concerning casualties at sea and in particular collisions between ships, the opening paragraph of the Traffic Separation Working Group's report (this Journal, 19, 4) is, to say the least, lacking confirmatory evidence on two counts.

I refer to the general statements which allege that:

(i) ‘The main risk at sea today arises not as it used to from stranding and shipwreck, but from collision’.

(ii) ‘In the open sea, where nearly 30 per cent of all collisions occur…’

As both include the words ‘at sea’ or ‘open sea’ it is not unreasonable to suppose that they imply freedom to manœuvre under own power unhampered by depth of water or similar navigational restriction.

This being so, and not an irrational definition of the area of concern to the Working Party, what are the facts and how exactly do casualties at sea compare with those in other areas of marine interest throughout the world.

To find the right answer to the global problem is not easy and there are no short cuts, such as for example making a sample analysis in a limited area where traffic density is high, in order to arrive at fairly large numbers which are then used to deduce the statistical probability applicable to all areas.

In the Working Group Report (19, 411) a mistake in the figure quoted (page 415 , paragraph 5) for the number of collisions analysed in Appendix I (2648 not 2748) results in minor corrections to a number of the figures quoted in the first two pages of Appendix I. These in no way affect the arguments put forward. On page 415 of the Journal (page 5 of the separately published version) paragraph 5 , lines 1 and 2, should now read:

‘An analysis of some 2648 collisions selected randomly (Appendix I) showed that 70 per cent occurred in port areas and 30 per cent at sea.’