Recent articles by R. Williams and others have indicated an interest in ‘loxodromic distances’, and have described methods of calculation on the spheroidal Earth. However, these methods are not directly suitable for simple hand-held calculators. The following, approximate, methods are therefore suggested.

This paper deals with the work of the International Hydrographic Organisation (IHO) during the last ten years towards the standardization of nautical charts. The work began with the devising of a regional scheme of medium- and large-scale sheets of the north-east Atlantic area, to be co-produced by member nations as contributions to an International (INT) set of charts. It subsequently became clear that, as well as the scheme, a detailed set of specifications would be necessary to secure uniformity of choice of symbols and abbreviations throughout the International series, and also in the various national chart series of which it would form a part.

The history of nautical chart standardization has recently been traced by Ritchie – gradual at first after the beginning of the International Hydrographic Bureau in 1921, and later speeding up when the International Hydrographic Conference of 1967 established a study which led to two series of INT charts on very small scales. After this the process gathered further speed with the successful establishment of the two bodies with whose work this paper is primarily concerned: the North Sea International Chart Commission (NSICC) in 1972 and the Chart Specifications (later Standardization) Committee (CSC) in 1977. The ten-nation NSICC, in drawing up the network of INT sheet-lines for its area, established the principles on which such schemes would be extended worldwide and also did extensive groundwork for the Chart Specifications of the IHO. These were completed for worldwide application by the seventeen-nation CSC.

Many vessels trading on North Atlantic routes are equipped with weather facsimile receiving devices of various types. Ship-masters engaged on regular voyages in this area are thus able to conduct their own passage planning using the information readily available from these intruments. The capital cost in relation to other ship operation costs is negligible; in US dollars (1983) it is likely to be of the order:

There would be no problem in planning a vessel's route across an ocean if it were possible to forecast with total accuracy the actual sea state existing for the duration of a voyage. Such an ideal circumstance does not yet exist and a method must thus be used which incorporates flexibility to modify a voyage plan as actual weather varies from the prognosis. This means that a subjective approach to storm avoidance may, on occasions, be preferable to the stringent demands of a least-time track. The obsession of routing agencies with the latter method may be one reason why weather routing has not achieved the success it perhaps deserves.

A ship may be damaged or delayed by the action of sea waves on her hull or structure. Hull form and ship dimensions are usually selected on the basis of calm-water performance, rather than for sustained sea-speed.

Real Admiral Ritchie, who retired on 1 September 1982 after ten years as President of the Directing Committee of the International Hydrographic Bureau in Monaco, here looks at the work of the International Hydrographic Organisation, more particularly in those areas which are of direct interest to the navigator.

In 1919 an International Hydrographic Conference was called in London at which representatives from the hydrographic services of twenty-four nations attended. After discussing at length cooperation in the fields of charting, Notices to Mariners, and the international exchange of hydrographic data, it was resolved to set up a permanent Bureau. The Conclusion to the Conference reads as follows:

The International Hydrographic Bureau whose formation is here suggested fulfils, in our opinion, an imperative need. Assuring a close and permanent association between the National Hydrographic Services, it allows of the cooperation of the efforts of all maritime Powers to furnish navigators with more perfect and up-to-date nautical documents. Without limiting in any way the liberty and initiative which should be retained by the Offices of the countries concerned, the new organisation will avoid unnecessary effort and wasteful expenditure; it will create amongst the surveyors of the different countries a fruitful rivalry and personal relations which are frequently of great value. We are convinced that its rôle will constantly increase in the future, and that its establishment will tend greatly to advance the Science of Hydrography.

The italics in the above statement are mine. These words still reflect the most important aim of the International Hydrographic Organisation over sixty years later.

In 1835 Gustave-Gaspard Coriolis proved that, if a ‘body’ travelling unaccelerated at a speed v is made to conform to a medium rotating at a rate w, it will be accelerated sideways at vw. Hence air travelling freely, if subjected to the rotation of the Earth's surface, will be accelerated at – 2vω sin ø, –ω sin ø being the rate at which the local surface rotates, with –ω the speed at which the Earth spins and ø the local latitude. (In the diagrams ω is presented as Ω).

2. Coriolis also proved the converse formula from which, if air travels freely over the surface of the Earth, it will accelerate at + 2ω sin ø relative to the local rotating surface. This reversed Coriolis formula happens to be far more important than the original direct formula. It has been applied to long-range artillery, to aircraft using spirit-level sextants, to inertial navigation systems and to the ground tracking of space craft. It has also been applied to forecasting wind speeds.

3. We can handle the duality of Coriolis by a loop diagram as in Fig. 1. The central link shows the direct Coriolis acceleration produced when air travelling freely is forced to conform to the rotating surface of the Earth, The link to the left depicts the reversed Coriolis acceleration which applies to air travelling freely as seen from the local surface of the rotating Earth.

The term ‘portolan chart’ first occurs in Italy in the thirteenth century, not long after this aid to navigation came into general use on board ship. The Italian word portolano, however, can best be translated as ‘pilot book’ or ‘sailing directions’, a different aid to navigation of which one example survives from the fourth century b.c., and pilot books are indeed still published in modern form by all seafaring nations. References by Herodotus in the History make it probable that such documents already existed in his time, and under the name of periplus they continued up to the sixth century a.d.; after which they do not appear again until the golden age of navigation in Italy and Catalonia in the late Middle Ages, apart from some much simpler early medieval types. The portolano or periplus is a description of ports, with information required by the navigator concerning anchorages, dangers threatening landfall and the winds and weather over wider areas. Commercial information was sometimes included, obviously also a matter of interest to the mariner who could read, though it may be doubted if many of them then could.

Italian portolan charts exist from almost the same period as the portolani, both of them denoted by the same word compasso, but while the pilot books have their modern successors the charts were only produced up to the beginning of the seventeenth century and are not really the forerunners of the modern sea chart.

An announcement of Wing Commander Anderson's recent death appears on another page. Mr William's spirited criticism of Anderson's ‘Rotations in Navigation’, and by implication his more recent note on Coriolis (May 1983 issue), was of course written before the sad news was known. It is published here without modification (and in spite of the author's offer to withdraw it) as would undoubtedly have been Wing Commander Anderson's wish.

At the end of the last war Wing Commander E. W. Anderson was one of the most distinguished practising navigators in the Royal Air Force. ‘Andy’, as he is known to so many, has since become navigation's leading exegete through his work in this Institute, his articles, lectures and books. ‘Rotations in Navigation’, however, has got him in a flat spin. The reason why has wider implications worth examining.

Andy starts by suggesting that the difficulty of explaining Coriolis ‘may be due to the intellectual danger of trusting mathematics without making sure that the right circumstances surround the formulae which emerge’. This observation illustrates how well one can write English without saying what one means. Circumstances, right or wrong, cannot surround a formula although the statement a formula makes may be irrelevant to our circumstances. It is precisely because pure mathematics is the language, as Russell put it, ‘in which we do not know what we are talking about or care whether what we say about it is true’, that applied mathematics is the language in which we are obliged to say what we mean or be seen to use the language wrongly.

Two main concepts in mathematical modelling of ship encounters have been proposed by Davis. The first, the ‘domain’, was an adaptation of a concept originally introduced by Goodwin, who defined the domain as the ‘area about own-ship that a navigator wished to keep free with respect to ships and other stationary objects’. The second, the ‘arena’, conceived by Davis, is the area around the domain which when infringed causes the mariner to consider whether to make a collision-avoidance manoeuvre. Thus, in a computer model, when a vessel enters the arena the computer analyses the situation and, depending on the severity of the threat, makes a collision-avoidance manoeuvre.

Goodwin's domain was divided into three sectors corresponding to the ‘giveway’, the ‘stand-on’ and the ‘overtaking’ regions as defined by the relative velocity of approach. The domain was derived from radar films of ship tracks and records of radar simulator experiments. Davis smoothed the sectored domain to a circle with own-ship off-centred astern and to port, and the weighting of each of the sectors retained. Davis's domain had a solid theoretical grounding; the arena, however, was simply a larger version of the smoothed domain. Its size and position were obtained by means of a well-distributed questionnaire. It served its purpose in the model, but lacked any real validation.

One problem with the Davis arena was its inability automatically to take into account different velocities, both of own-ship and of targets.

Since 1975 the Royal Netherlands Naval College has operated a bridge manoeuvring simulator for the training of naval officers and petty officers of the deck department. There is a strong relationship between training objectives and performance abilities of a simulator and the way the two match defines the cost effectiveness and the value of simulator training. The training objective being the result aimed at (for a professional watchkeeper) consists partially of a combination of training subjects (things to be learned at the simulator). During 1980 and 1981 R.Nl.N.C. conducted a survey on simulator training subjects by means of an inquiry amongst Royal Netherland's Navy and Merchant Navy officers, marine lecturers (all of Dutch origin) and members of the International Marine Simulator Forum (IMSF). The results form the subject of this note.

Van de Ree has provided a solution to what must be a fairly common problem in navigation. The problem may be stated as follows.

A ship on a rhumb-line course encounters head-winds and heavy seas requiring her to reduce speed. If she alters course, but does not change the rate of fuel consumption, her speed will be given by (a + b sin A), where A is the course change, a is the speed into the head sea and a + b is the speed in a beam sea. How far should the navigator alter course so that, after a given time, the ship will be nearer the destination than on any other course and, in addition, the labouring of the vessel will be reduced?

Van de Ree's trial-and-error solution assumed the destination to be initially 63 miles away, a = 12, b = 5, and the optimization period 1 hour. His solution was to alter course by 20(± 2·5)°. It is possible to obtain a general algebraic solution to this problem, but it requires differentiating complicated trigonometric functions and solving a complicated trigonometric equation, and so the algebraic solution is not practically useful. It is also possible to solve the problem graphically. This solution is by far the simplest one and would be recommended in place of either Van de Ree's laborious numerical solution, or the equally difficult algebraic solution.

However, one could question whether the chosen tactic is the appropriate one.

Efforts to determine the mean size of ship ‘domains’ from measurements of the distribution of ships in the vicinity of an individual ship have been made by several workers, particularly by Goodwin, who made extensive observations in the Sunk Lightship area of the North Sea. The work involved plotting the positions of vessels at time intervals of a few minutes to estimate the number of ships in an annulus about a central ship, or alternatively the number per unit area at various distances from a central ship. These figures were used to obtain distribution curves from which the average domain could be estimated. The work of Curtis and Barratt on the validation of simulator studies of passing manoeuvres in fog, in which the nearest point of approach of ship's tracks was determined, serves to illustrate an alternative method based on the distribution of the density of tracks. In both procedures use is made of the point at which the distribution function first returns to the value which would obtain if the distribution were uniform, that is, if ship domains were absent. Some doubts have been expressed as to the validity of using the position of the cross-over point as a measure of the average domain size, and also whether it would be more appropriate to employ the position of the maximum value of the functions.

Wing Commander Anderson, the author of The Principles of Navigation in which he emphasized the essential unity of philosophy which underlies all forms of navigation, has further developed this concept in two papers in this Journal published in 1980, ‘Navigational Measurements’ and ‘The Magic of Animal Navigation’ (Vol. 33, pp. 33 and 444). In the present paper he examines further in non-mathematical terms some of the difficulties met with in the analysis of rotations in navigation, including the effects of the Earth's rotation on its axis.

The ICA system which is now being considered by the Civil Aviation Administrations in the UK and the USA is based on a new height unit, the ‘millica’. Below an arbitrary fixed level (29000 ft) this unit is equal to 0.3 m; above that level it increases gradually, the rate of increase corresponding to the standard deviation of aircraft height from assigned cruising level. At 10 000 m the unit is equal to 0.325 m and 15 000 m to 0.477 m. In this way the ratio between the separation of cruising levels and the standard deviation of the departure from assigned level remains constant; that is to say, the safety margin is constant. At present, cruising levels up to 29 000 ft are separated by 1000 ft and above this level by 2000 ft, so that there are five cruising levels between 29000 and 39000 ft; in the new system there would be nine.

If δh is the height difference, δp the barometric pressure difference and p the mean atmospheric density in this interval, it is clear that δp = pδh and δh(1/p)δp. From this it follows that if δh is constant between adjacent flight levels the δp decreases with altitude and the vertical separation safety factor also decreases.

If, as has sometimes been suggested, δp remains constant between adjacent flight levels, then δh will increase with altitude and the safety factor will increase also.