This paper was presented by the Executive Secretary at the twentieth anniversary convention of the Australian Institute of Navigation held in Sydney, New South Wales, on 10 and 11 October 1969.

In July this year two men landed on the Moon, certainly the most spectacular navigational achievement of mankind. It was a voyage backed by all the massive scientific resources of a modern industrial state, in which thousands of people were directly involved. The astronauts were a single link in a navigational loop employing a host of technologies.

Two hundred years previously James Cook had sailed on the first of his three great voyages, during which he discovered New Zealand and the coast of New South Wales. Cook was perhaps the most illustrious navigator of all times, even if perhaps he advanced the art more by force of character than by any specific contribution. When he started his voyages, the art of nautical astronomy was in its infancy. At their finish William Wales could comment, in 1788, that no officer who had been concerned with them ‘would not, whatever his real skill may be, feel ashamed to have it thought that he did not know how to observe for and compute the time at sea, though but a short time before these voyages…such a thing was scarcely ever heard of among seamen; and even first-rate astronomers doubted the probability of doing it with sufficient exactness’.

The introduction by an airline of a new aircraft type into passenger service, the inclusion of a new route in a world-wide network, or the adoption of new cruising flight levels, are preceded by extensive route analyses and flight planning studies. The known or expected performance characteristics of the aircraft are matched against statistics of wind velocity and ambient temperature, in order to derive estimates of sector times, fuel requirements and payload capacities. This paper refers to some of the sources of the meteorological data hitherto employed for this purpose and presents the results of a recent airline study of environmental conditions at Concorde cruising levels on a selection of routes.

Captain W. Burger and Captain A. G. Corbet in their general comment on the meeting of the Technical Committee in London, 16 April 1969, gave a curious and instructive hypothetical example of end-on encounter, a problem in navigation which they and others have found by experiments to have importance and practical difficulties. Their example is set in surface navigation at sea, and especially when using radar in fog. Two ships close with each other (in their example head-on and green-to-green), the two tracks being straight and parallel, and separated (in their example by half a mile). Should both ships stand on? My answer is affirmative, my argument difficult.

If one makes the fruitful assumption that neither ship in this example alters course or speed, and then tries to plot The Edge [ of regression of The (mutual) Line (of bearing)], he discovers that the result is not a non-singular parabola, but rather simply a fixed finite point, i.e. at best a degenerate parabola—yet clearly there can be no finite collision, and collision at infinity is an empty threat. What do plotters of The Edge make of this paradox? Here handbook summaries will not do.

In certain esoteric mathematical and computing circles there is, or used to be before the advent of the electronic computer, an interest in near-integral solutions of incommensurable problems. Apart from aesthetic considerations such solutions can have valuable applications in the checking of methods of computation; this is the excuse for the following note.

The investigation from which it arises was itself a by-product. As part of the British contribution to the new Sight Reduction Tables for Marine Navigation (H.O. 229 in U.S.A.; H.D. 605, in the United Kingdom) it was necessary to examine carefully each of the approximately 20 million figures in the six volumes; although the setting was computer-controlled and numerically checked, only visual examination could detect indistinct or broken figures. Such examination is extremely arduous and calls for great powers of concentration if its purpose is not to be wasted.

The note by J. W. Crosbie prompts the writer to the following comments. Lecky's Tables2 do not cover vertical angles below the geometrical horizon (zenith distance =90°), or, indeed, angles of less than 10’ above it. Crosbie's method, also, does not cater for angles below the geometrical horizon, though it could be adapted to do so. His extraordinary evolutions with the traverse tables, undertaken to avoid solving a quadratic equation by orthodox methods, are fascinating. Surely, a slide rule, with which the equation could be solved in a few seconds, is available in today's chartroom.

In this paper Commandant Oudet, who might well be called the architect of routing in the Dover Strait, discusses certain aspects of what has come to be known as the Sandettie problem, namely the emergence of a potential accident black spot at the north-eastern extremity of the one-way routes in the Strait. Various solutions are discussed, including the reversal of the direction of traffic flow in the Strait recently proposed by the Honourable Company of Master Mariners and supported by Trinity House. Commandant Oudet shows that this proposal, unless the direction of flow were reversed in adjoining traffic separation schemes, would have the effect of greatly increasing the number of crossings and encounters outside the Strait. ‘The remedy would be worse than the disease’, he concludes. ‘It would be better to abandon traffic separation altogether’.

Places where road traffic is particularly dangerous and congested are often referred to as accident black spots; and the term is beginning to be used in the same sense in a navigational context. At sea an excessive density traffic always involves danger, because it is impossible to build fly-overs, as on land, and so avoid crossings; all encounters and all crossings take place on the same plane.

The Admiralty Tide Tables give the utmost accuracy in tidal calculations, but at the cost of a number of tedious interpolations. Many seamen, particularly those in small vessels, would be willing to sacrifice some of this accuracy if they could have a simpler form of calculation. In any case meteorological effects, and the uncertainty of the time and height corrections for some of die smaller ports impose uncertainties which upset the apparent accuracy. In fact many yachtsmen do not use the Admiralty Tide Tables, but use tables in commercial almanacs, usually giving the times and heights of high water only.

Distance off by measuring the elevation of a mountain top above the horizon has been a popular means of finding position at sea ever since Captain Lecky published his famous tables. This popularity persists into the radar age because distance off can often be found from a vertical sextant angle long before a ship is within effective radar range of the coast. In view of this it is surprising that the standard textbooks on navigation give scant attention to this method and any seaman finding himself without Lecky's tables would find little guidance elsewhere.

Wing Commander E. W. Anderson in The Principles of Navigation indicates that the whole angle subtended by a mountain at a ship can be found by adding half the estimated distance off in miles to the visible angle in minutes, having first corrected this angle for dip and refraction. This can be proved by simple geometry by showing that the angle subtended by the part of a mountain hidden to an observer at sea-level is equal to half the distance off.

If Turner is right that ‘the underlying theory of the traditional approach (to rhumb-line sailing) is obscure’ and that there is a ‘lack of ready availability of a table of distances of parallels of latitude from the equator, it is certainly not the fault of this Journal which precisely 20 years earlier published a paper which gave:

1. The correct mathematical theory of rhumb-line sailing on an oblate spheroid.

2. The name ‘meridional distance’ to what Turner now calls the L(φ) function.

3. A table to reduce latitude to meridional distance.

4. A rule of thumb procedure to calculate rhumb-line distances correctly with no more labour than that which has always been used to do it wrongly.

5. A method (with table) for use on the spheroid when the track angle is nearly 90° and the method Turner discusses is impracticable.

6. A survey of methods and tables then current.

A student of navigation who refers to the standard textbooks will be confronted with a multiplicity of sailings which are said to include plane sailing, parallel sailing, middle or mid-latitude sailing, mean latitude sailing, traverse sailing, short distance sailing using rhumb-line formulae, mercator sailing, great-circle sailing, approximate great-circle sailing, composite sailing and composite greatcircle sailing. To the student it may seem a reasonable assumption that so many differently named sailings are based upon as many different ways of taking a ship from one position to another, which is of course a nonsense.

In a very interesting paper which appeared recently the author, Capitão Mário Gama of the Portuguese Merchant Navy, describes a direct method for computing position lines from star (or planet) observations.

The principal feature of Captain Gama's method is the systematic manner in which he arrives at an intercept to the extent, not only of saving time in sight reduction, but also in reducing the possibility of blundering.

The method employs the Computed Tables of Altitude and Azimuth (HD 486) and involves timing a series of star-sights, the ship making headway meanwhile, by means of a stop watch which is set at zero at a noted chronometer time shortly before the observations commence. The following example, given in the original paper, in reducing sights of Vega and Denebola observed during morning twilight of 25 Feb. 1959, in D.R. position Lat. 10°10′ S., Long. 73°48′ E., will serve to illustrate the method.

Captain P. A. Thompson's paper, Revised Rules for Preventing Collisions at Sea, in the January issue of the Journal should be discussed. I agree with him that ‘rules (the ones which are mainly based on the operational aspect of the collision problem, i.e. manœuvring rules) to cover every conceivable circumstance would be of such length as to be impracticable.’ However, in my opinion, rules based on the principles—the organic aspects—can cope practically because then the object of the rules is to define the collision problem and its solution so that use of the rules can be immediate, easy and effective. For example, by establishing a safety distance the passing operation would have to be carried out such that the miss distance would always be greater than the safety distance. Furthermore, by keeping the ship's range above the safety distance, one ensures that the entire operation is correctly carried out.

The paper by Captain J. P. Stewart in the July issue of the Journal, entitled as above, presents a wealth of evidence and argument for the obvious sense of designing marine radars in such a way that they can:

(a) present compass stabilized radar pictures in the natural ship's-head-up orientation. This avoids the mental stress of trying to correlate the radar view and the eye-ball view of the same situation when the two may be presented in completely different orientations;

and

(b) simultaneously allow true bearings of targets to be read off directly.

Although Admiral Ritchie does not agree, I still think that some significance does attach to the difference between the British Standard Nautical Mile and the International Mile. It is a matter of definition and is of vital importance to the young student beginning to study navigation. Unless basic definitions are clear and unambiguous continual difficulty arises which obscures practical considerations of the reliability of measurements that are made. Moreover, it is extremely unfortunate that the length of a minute of arc of a meridian was ever given the label ‘mile’—a standard of measurement of distance, or that anyone should ever have suggested measuring distance with a unit of variable length. The confusion that has been caused in the minds of student navigators over the years is enormous and the opportunity now exists for this source of confusion to be removed.

A Great deal has already been written about possible amendments to the Collision Regulations, but as there may be an international conference on the subject in 1972 the various schemes should be discussed as much as possible so that their advantages and disadvantages will be fully appreciated.

Criticism of the present Steering and Sailing Rules is mainly concerned with Rule 21. Disadvantages of this rule include the following:

(1) If a giving-way vessel on a crossing course takes no action the privileged vessel must not act until collision cannot be avoided by the giving-way vessel alone. By such time collision is likely to be inevitable.

(2) Small sailing vessels which may not easily be seen, especially at night, are required to maintain course and speed for large power-driven vessels.

(3) High-speed vessels such as hovercraft are required to maintain course and speed for low powered ships crossing from the port side.

(4) No provision is made for different types of hampered vessel approaching one another so as to involve risk of collision. If deep-draught vessels in certain areas are to be included in this category in the future the question of priorities may have to be considered.

When the danger of collision between vessels occurs, the proper interpretation of radar information will indicate that, with respect to the manœuvring rules, any avoiding action should always be positive. However, it is well known that radar information is not always properly interpreted. Misinterpretation may cause a situation to be assessed as ambiguous. This, in turn, may produce disagreement, on both vessels, about how the rules should be correctly applied. To solve this difficulty, some authors propose communication between the vessels. Others think the avoiding action of any vessel should automatically be such that the sight line rotates in the anti-clockwise direction. (The latter suggestion results in a port-to-port passing whilst the vessels cross with a port bearing from the aspect of the overtaking ship.) Complications may arise from either proposal.

The Trinity House and Honourable Company of Master Mariners would, of course, have much preferred to comment on Commandant Oudet's latest article in the same edition as the article appeared (Journal, 23, 371). However, as we could only be afforded a weekend in which to give a considered reply this was clearly impossible, bearing in mind the grave and far-reaching issues involved.

It is to be hoped that before the Collision Regulations are revised in any sense that affects the rights and obligations of sailing vessels, people with practical experience of navigation under sail will be consulted. It looks as though their advice will be needed.

One increasingly hears, for example, that under modern conditions steam should no longer be required to give way to sail. ‘It seems quite unreasonable now’—Captain Dickson, for instance, expresses it in the last number of the Journal (22, 448)—‘to expect in most cases that sailing vessels should be required to stand on for power-driven vessels’. But the reason a power-driven vessel is required to give way to sail is not some kind of old world courtesy, but that if there is no wind, the sailing vessel is immobilized: it cannot give way.

This country, and the marine industry in particular, is in the throes of a change that it has been decided shall be called metrication. It is evident from what is both written and spoken that not everyone is aware of what metrication means, that many people assume that it is simply a change from imperial units to metric units. However, what is really intended is the adoption of the S.I. system of units and this implies much more than just the use of metric dimensions. The two main points of the S.I. system are (i) that every dimension is measured in decimal multiples of a basic unit and (ii) that the system of units is a coherent one. The educational advantages of such a system are too well known to require restating here. Antagonists of change usually point out that time does not conform to condition (i) and while this is true, nevertheless the S.I. system will be a great improvement on our present one and the non-conformity of time should not be used as an excuse for other non-conformities.