Within the University of Wales Institute of Science and Technology, a general study of navigation has led to a review of error distributions which has now reached the stage at which comment on a wide front would be particularly welcome. The work has been undertaken by Wing Commander E. W. Anderson who, with the generous permission of Smiths Industries Limited, is writing a thesis for the Department of Maritime Studies, and by D. M. Ellis, Lecturer in Statistics in the Department of Mathematics. In the first half of this paper, Anderson emphasizes the distinction between distributions involving one item or identical items and those involving a number of items which, though nominally the same, are in fact diverse. In the second half of the paper (from Section 8 on), Ellis shows how the apparent variation of results that arise in practice may be unified into a simple inclusive pattern.

The first step was to investigate the distributions that arise in practice. It was decided that the pages of this Journal would make ideal witnesses because they provide a broad sample and are impartial. From these pages every distribution was extracted which involved more than fifty observations and whose pattern was not markedly skew. The distributions were transferred to log-linear graph paper so that the horizontal error scale was linear and the probability of each error was plotted on the vertical logarithmic scale.

During the past twenty-five years the aviation scene has progressed from one in which relatively small numbers of aircraft flew from point of origin to destination with the guidance afforded by very limited M/F range facilities and a great deal of individual navigational skill on the part of the operating crews. Air traffic control functioned only as a means of sorting out the order of take-off and landing. Moving forward to the present we see the already high density traffic serving the population centres of the world continuing to increase at a rate of around 10 per cent per annum. Both station referenced and self-contained navigational systems proliferate and control of traffic must be almost total if collision accidents are to be avoided. During the same time period aircraft speeds have increased threefold and necessitated a consequent improvement in the ability of the air traffic control service to react quickly and precisely to any conflict situations, either by detection in the strategic/planning case or resolution in the tactical frame by direct intervention before critical situations can develop.

In a procedural Air Traffic Control environment, navigation standards are related to separation standards because of the way they both affect the collision risk. The Air Traffic Studies division of the Mathematics Department at R.A.E. has developed methods of estimating the collision risk procedural systems and these provide rational grounds for decisions on separation standards. In a radar-monitored system navigation accuracy and separation standards both affect the workload of the controller on the ground and it is necessary to study these effects to ensure that he is not overloaded. In addition the problems of estimating the collision risk will become more complicated. I shall very briefly describe the mathematical theory of collision risk for parallel tracks. A fuller description has been published in the Journal.

This note complements the papers by White and Lloyd by commenting on some of the features of a preliminary statistical analysis of the N.A.T.C.S. data on track-keeping recently collected along Green I Airway near the Strumble VOR. All values quoted are illustrative only and have no firm validity at this time but they illustrate the numbers involved in determining acceptable separation standards for the lateral navigation case in a typical ‘continental’ environment.

This paper is intended to show those areas in which improved avionics could, in the relatively near future, contribute to overcoming the limitations described by Reich and Dickie. Sir Robert Cockburn has pointed out that present-day avionics is ‘decision-limited’ rather than ‘technology-limited’. If the present paper is to do more than reiterate a melancholy list of avionics solutions which are still unsuccessfully seeking suitable problems, it is essential to consider the constraints under which the airspace planners must operate, and the contribution which good electronic design might make to breaking the decision-taking bottleneck.

When flying at high latitudes the rapid convergence of Earth meridians makes it difficult to establish true heading at any particular instant. Magnetic compass stabilizing forces are weak and steering must normally be carried out using a directional gyro. The navigation problem is normally solved on the chart by using a ‘grid’ technique.

The possibilities of using the measurement of the ranges to a pair of satellites to give an observer his position have been extensively studied, and expressions giving latitude and longitude have been derived. These since they involve powers of the fourth order are somewhat cumbersome, but given the appropriate computer on his craft an observer at a known distance from the centre of the Earth can obtain track data by measuring the ranges and continuously calculating his position. Alternatively, he may measure the incremental changes in these quantities from their value at the starting point which avoids (if a synchronous time or frequency technique is used) the necessity for continual two-way exchange of signals between the craft and the satellite, but the real-time solution of relatively complicated equations still has to be done.

Instances of merchant ships beset in times of ice pressure in the Gulf of St. Lawrence were investigated to study the observed relationship between winds and ice pressure generation. The relative power of the ships reported beset was calculated in an attempt to relate ice pressure severity with ship performance. Most pressure episodes occurred during onshore winds or near the time of major wind shifts. Ice pressure intensity during onshore winds appeared to be related to wind strength and duration and distance from shore. The ‘Mouth of the Gaspé Passage’ area was anomalous.

For marine traffic engineering, traffic surveys are most important and provide the fundamental materials necessary for harbour and fairway design, traffic control planning, &c. Such surveys cover numerous items, the main subjects being traffic volume, speed, distribution of ships' tracks, origin and destination and type of cargo. Since we have to deal with many vessels, handled by people with varying temperaments, knowledge and ability, observations usually show a wide scatter; the object is often to find some formula or rule to explain the phenomena, and traffic surveys are therefore apt to prove both expensive and time consuming. When, for example, Yamaguchi and others conducted a year long observation on traffic in the Akashi Channel in 1963 at least two members of the team stood watch for 24 × 365 hours in a hillside cottage making both visual and radar observations. Since then the survey has been extended to more than ten other straits well known for difficulties in manœuvring.

A marine traffic accident may be defined in the wider sense as a collision or stranding and in a narrow sense as a collision. Several reports are available on the causes of collisions and on the relation of collision frequency to such factors as location, weather and time; S. Fujii continuing Asai's work has shown that the ratio, R, between the number of vessels in collision and the number of vessels registered increases with the length of the vessel between perpendiculars. Shiobara gives a linear correlation between log R and log G with a slope of 0·5 and a correlation factor of 0·95, where G is the gross tonnage. In other words the collision frequency is proportional to L1.4. He further shows that R is almost proportional to L.

Traffic capacity is the capability of a waterway to deal with the traffic and when the traffic volume exceeds this limit traffic flow stops, as is often experienced on congested roads.

According to the U.S. Government Highway Capacity Manual the capacity of a highway with four or more lanes and free from conditions hindering smooth traffic flow has a maximum value of V/Ymin per lane, where V is the speed of a group of vehicles and Ymin is the average minimum separation of cars. Since Ymin is a function of V and increases rapidly and continuously with speed, there is a maximum value for V/Ymin which is a function of the speed. This is called basic capacity. Several examples of capacity together with the speeds of the transportation facilities are given in Table I.

By the North European Trade Axis is meant the trade route from Ushant and Land's End, up the English Channel, through the Dover Strait fanning out to serve eastern England, the north coast of continental Europe and leading to the Baltic Basin. Recent events in this area have left a feeling that some form of tightening of control is not only desirable, but is rapidly becoming imperative. There is a basic conflict between the two forms of shipping using the area: the local users who use the area more or less constantly, and the long-distance traders, usually much larger, which arrive in the area for a brief stay after a prolonged period at sea, which has usually been in good weather conditions. Frequently these latter ships have a very poor notion of the hornet's nest into which they are steaming when they arrive. The net result is all too often the same: the local users, with familiarity breeding contempt, wander about as they see fit, with scant regard for routing or the regulations; all too often the big ships arrive from sea with navigating staffs who are too confused, sometimes too ignorant—and sometimes too terrified—to do much more than blunder forward in a straight line hoping for the best. Quite obviously this is not a total picture, and there are large numbers of ships which navigate perfectly competently, but the minority of those which do not seem to be rising rapidly, and show every sign of continuing to increase.

In recent years attempts have been made to reduce the manpower requirements of merchant ships and, largely as a consequence of technological advances, some measure of success has been achieved. Indeed, there is now no technical obstacle which prevents the construction and operation of an unmanned ship. With this knowledge perhaps the time has come to reflect on the wisdom of excessive enthusiasm for technological innovation and to consider objectives.

A situation as presented in the article by Buzek/Wepster (24, 35) is hard to imagine in the quite different atmosphere of another international shipping operation, such as the Continental European river systems of Rhine and Danube.

Anneveld has shown that drift angle due to coriolis may be appreciable in the case of large vessels operating in the middle and higher latitudes. Unfortunately the hydrodynamic information on which he bases his equations is not complete, leading to a false idea of the magnitude of the effect at normal ship operating speeds.

The purpose of the descent and approach is to move the aircraft from the cruise to final approach while keeping within the proper envelopes of speed, acceleration, rate of descent, adherence to A.T.C. clearances, avoidance of bad weather and clearance from terrain and obstructions and other visible aircraft. Man carries out this task, at least until the ILS glide slope is captured. The methods used are not as thorough as the programme an electronic computer would need for this task. Perhaps men prefer to use common sense, but perhaps a high level of safety can only be achieved with thorough rules.

Gaussian logarithms are designed to facilitate finding the common logarithm of a sum or difference of two numbers whose common logarithms are known. The object of a table of Gaussian logarithms, sometimes known as Addition and Subtraction Logarithms, is to give log (a±b) by single entry when log a and log b are known.