The standard formulae, assuming a spherical Earth, for converting distance on a rhumb-line track into differences of latitude and longitude are:

where C is the course and α is known as the middle latitude. It is approximately the mean latitude when both points are on the same side of the equator; tables of the correction to be applied to the mean latitude to give the middle latitude are given in most collections of nautical tables.

Captain Giessler, who is now assistant to the director of the Auschuss für Funkortung (the German association concerned with radio navigation) was navigating officer of the Scharnhorst when that ship with the Gneisenau and Prinz Eugen broke through the English Channel in February 1942. It is thought that this account of the operation will interest many navigators, even though it is not entirely navigational in content.

Towards the end of 1941 the repairs to the battle-cruisers Schamhorst and Gneisenau, lying at Brest, and to the heavy cruiser Prinz Eugen were already so far advanced, in spite of continual very heavy air attacks, that a decision had to be made as to the further use of these forces.

For a number of years helicopter operations will mainly take place at operating altitudes between 500 and 2000 ft. Due to the inaccuracies of existing pressure altimeters vertical separation less than 1000 ft. cannot be applied and therefore maximum use will have to be made of lateral and longitudinal separation possibilities if the development of helicopter operations in high density areas is not to be impeded. As far as possible helicopter operations will be kept apart from fixed-wing traffic but this may be difficult to achieve in terminal areas where departing and arriving fixed-wing aircraft are at low altitude and the available airspace is restricted.

It is, therefore, essential that the navigational aid on which air traffic control base safe separation should be one which enables the helicopter pilot to adhere strictly to his pre-determined track and also provides him with an accurate measurement of progress along track. Quite apart from the air traffic control aspect, since the helicopter flies low, frequently in poor horizontal visibility and low cloud-base conditions, accurate track keeping is essential from the standpoint of avoiding obstructions or high ground in the vicinity of the route. Accurate and solid coverage over a wide area at low altitude is therefore an important requirement of any helicopter aid system, particularly in a high traffic density area such as western Europe.

The use of the Decca flight log is most simply illustrated by referring to an actual flight, in this case on a Viscount service out of London Airport.

Fig. 1, which is a section from the chart roll used on a recent service, shows the London Control Zone chart. Take-off was from runway 2 8 RIGHT on an IFR day and the outward bound clearance was Chertsey 2000 ft., Dunsfold 3000 ft. with a radar climb en route to Seaford. At the time when the pilots are fully occupied with after take-off drills, r.t. &c., and maximum concentration on instrument flying is necessary, a quick glance at the flight log is all that is necessary to check that the aircraft is on track. At this stage, in the event of radar failure, an accurate position of the aircraft can be passed to air traffic control at any time it is requested, and ‘flying well right of the centre line’ and subsequent resumption of track is easily effected.

Dectra (Decca Track/Range) is one of two British systems recommended at the March 1954. meeting of Com. Division of I.C.A.O. in Montreal for evaluation by interested States. Arrangements are now being made to commence proving trials of Dectra at the end of this year or possibly the beginning of 1957. The trials will be made under the auspices of the Ministry of Supply and Ministry of Transport and Civil Aviation in this country and with the support of the Department of Transport in Newfoundland. The system is primarily designed for the navigation of fast jet aircraft across the North Atlantic, a problem intensified by air traffic control when more than 100 aircraft are in the air at the same time on those routes. It is, however, likely to prove valuable for other similar applications. The trials installation will cover the main route Prestwick–Gander.

That a ship's captain may exercise supreme powers when at sea has been recognized since maritime laws were first formulated. But when Francis Drake summarily executed Thomas Doughty in Patagonia in 1578 there were serious misgivings at home, and the commanding officer of the next long distance expedition was hedged about with carefully thought out restrictions, and ordered, save ia the last resort, to bring any serious offender home as a prisoner. This voyage was organized and financed by the Earl of Leicester, Drake and a number of City merchants, its objective being to open up trade with the Far East by a voyage round the Cape. It had originally been intended to put Martin Frobisher in command, but for reasons unknown a gentleman and soldier of fortune, who had been with him on the second and third voyages to the Northwest Passage, Captain Edward Fenton, was substituted for Frobisher. This caused murmuring among the sailors who evidently thought poorly of him. And he did indeed turn out a weak, vacillating leader, though full of his own importance, so that the voyage was a failure, and two of his ships actually left him.

Almost all the long-range civil transport aircraft entering service during the next few years will be equipped with some form of instrument system. It is proposed to describe here some aspects of the developments which have been embodied in one such system, the Smiths Flight System, and to indicate its scope when applied to the operation of such aircraft.

Since the war the operation of a high-performance transport aircraft on congested and competitive routes has become an increasingly complicated process. With the advent of the gas turbine, cruising speeds have doubled, and at the same time there has been a tendency towards higher standards of economy and safety. The development of the air traffic control system has brought about a demand for greater precision in navigation, and in the most congested areas by far the greatest number of flights are conducted under instrument conditions. Meanwhile, aircraft have also become more complex, and the pilots themselves are often expected to monitor the operation of the controls and instrumentation associated with the engines, electrics and pressurization as well as carry out the navigation. This extra work has had to be undertaken without any relaxation of the general vigilance which constitutes good airmanship.

In the contribution under this heading to the Forum (Vol. IX, p. 348) Fig. 1 of Mr. P. G. Powell's note was misplaced. The figure results from the table given at the foot of p. 351 and indicates the approximation in the overall distribution to normal Gaussian laws.

Summary of a paper presented at a meeting of the Auschuss für Funkortung at Essen on 28 February 1956.

In any investigation of the accuracy of Decca fixes it is necessary to distinguish between systematic and random errors. Investigations are generally based on a comparison between a Decca fix and a fix obtained by some other method; because of the high accuracy of Decca the other method must in practice be a terrestrial fix. The investigation can be made by comparing the decometer readings with values calculated for the true position; or the Decca position may be compared directly with the true position. The first way gives the differences of the Decca observations in terms of percentages of a lane, and the second shows immediately the errors of the Decca fix. The second method includes the uncertainty caused by the siting of the Decca stations, that is by the angle of intersection of the Decca hyperbolae. The second method will be of more direct use to practical navigators while on the first will be based considerations of a theoretical and strictly technical nature.

In December 1940 some 500 captured allied seamen, including the author, were transferred from a German commerce raider to an ex-Norwegian tanker under the command of a German prize crew, with the original crew still aboard. The ship was in the Southern Indian Ocean—in about S. 32°, E. 70°—just cruising about aimlessly; apparently awaiting orders to proceed. The captured Chinese and Indian ratings were accommodated aft somewhere, the shipmasters and passengers were housed amidships; and the rest were forward.

This vessel was very effective for the purpose to which it was being put as it was easy to position machine guns to cover all ways of approaching the midship house; in particular the fore part of the bridge was a solid wall right up from the foredeck to the high dodgers. Nothing could be seen of those on watch and no bells were struck, so that the officer prisoners were denied the sight of anything which might help them to guess what was happening, and any sound to give them an idea of the passage of ship's time.

In June 1955, Canadian Pacific Airlines inaugurated a regular scheduled service between Vancouver and Amsterdam via the polar route. The Company had a wealth of northern experience which was of immense operational value on the polar route. In addition to its overseas services, C.P.A. has operated regular flights for many years to far northern parts of Canada and some of the group of companies which amalgamated to form C.P.A. in 1942 had arctic experience dating from the days when commercial aviation was in its infancy. One aspect of navigational experience which has helped its navigators on many occasions has been the map reading talents of the former bush pilots who show an astonishing ability to locate themselves visually over country which is mostly water, and where one lake looks much like every other lake.

Throughout the history of aircraft design, a trend that has remained quite constant up to the present time is the steady increase of wing loading with successive types. This feature with its consequent raising of stalling speed, and therefore landing and take-off distances, has resulted in techniques rather more scientific than those used in the early days of civil flying. With take-off distances of anything up to 6000 feet, the pilot in deciding whether a particular airfield is adequate for a given aircraft is no longer the sole arbiter; the rule of thumb must give way to the slide rule.

The pilot is, of course, still responsible for the safety of a particular operation, and to help him in this respect, performance information for his particular type of aircraft is supplied in graphic form with the safety factor already built in. It is the purpose of this paper to explain why and how this is done.

With modern sight reduction tables, new techniques of working out astronomical observations and the recent changes in the Abridged Nautical Almanac, it has been found that many of the hitherto necessary mathematical tables included in the majority of the nautical tables are now no longer used in the Royal Navy. An analysis in the Royal Navy's navigation school, H.M.S. Dryad, has revealed that only about a third of the tables in each of the three most used books of nautical tables, Burton's, Inman's and Norie's, are used in the Royal Navy.

The parallel cursor and disc. In the Royal Navy manœuvring problems are normally worked out on the Battenburg Course Indicator which gives a mechanical solution of the speed/distance triangle (Fig. 1). A similar device for direct use on the PPI face can be made by engraving parallel lines on the rotatable PPI mask and attaching two perspex vector arms to the centre. Although developed primarily for manœuvring purposes this idea can be put to several purely navigational uses and from it have sprung two valuable adjuncts to the PPI: the parallel cursor and the fixed plotting surface (or disc).

Captain Wylie's paper on ‘The Region of Collision’ raises some interesting points but if one accepts the view that graphing of some sort is not wholly ‘academic’ the writer feels that there is an alternative graph which Captain Wylie has not mentioned and is worth considering.

As Captain Wylie has shown, the time-distance plot gives very little useful information except that it does keep prominently in mind the distance between the two vessels. The time-bearing plot is much more informative as to the element of danger present in the situation but if the time-bearing is the only plot kept then the fact that it shows no distance between the vessels is a serious disadvantage. The writer suggests that it might be worthwhile considering the advantages of plotting change of bearing against distance between the vessels, especially if this is done on a graph having precomputed curves for various minimum separations between the vessels. The sort of graph obtained is illustrated in Fig. 1 which shows a family of curves for vessels maintaining steady courses and passing at minimum separations of ½, 1 and 1½ miles, curves A, B and C respectively, on the assumption that plotting is begun from the point where the vessels are four miles apart.

Yacht and other small-boat navigators must often wonder what error in a d.f. loop reading on a radiobeacon may be due to heel. The error is in fact quite small, the maximum for a 25° angle of heel being 2°.8 when the bearing is quadrantal to the boat's heading, i.e. when the relative bearing is 45°, 135°, 225° or 315°. When the relative bearing is 0, 90°, 180° or 270°, i.e. when the beacon is ahead or astern or abeam, the error is nil.

Table I gives corrections to the nearest ½ degree, to be applied to the relative bearing of a beacon for 15° and 25° of heel. It makes no difference whether the boat is heeled towards or away from the beacon.

Professor Taylor contends that the expression used to describe a course of action so simple as to leave no room for mistakes is plain sailing; that this is nautical in origin in that it derives from a simple or plain system of navigation based upon the use of a simple or plain (manifestly foolproof) chart; that this system of navigation was known originally as plain (simple) sailing—which expression she traces back to Richard Norwood's Doctrine of Plaine and Sphericall Triangles of 1631, and that it was sophisticated into plane sailing in the eighteenth century in the belief—which she holds to be erroneous—that the expression described a form of navigation based upon the use of a plane or flat chart on which the Earth was drawn as if the Earth and oceans lay in one horizontal plane area and not upon the surface of a sphere or, more accurately, ellipsoid; and, finally, that the Admiralty Navigation Manual is in error in teaching mariners that ‘to regard certain small triangles as plane… gives rise to the expression plane sailing, which is popularly referred to as if plane were spelt plain and the sailing free from difficulty’.

If a ‘sailing’ is defined as a means of finding by calculation, tables or construction, either: (a) the course and distance from one place to another, or (b) the position of arrival after making a given course and distance from a given position, then what is commonly known as ‘plane sailing’ is not in this sense, a sailing at all. ‘Plane’ or ‘Plain’ sailing according to modern as well as early usage involves the arguments, distance, d. lat., departuie and course angle, and in order to solve the problems (a) or (b), d. long., and either meridional d. lat. or ‘middle’ (not ‘mean’) latitude must enter the solution.

In Lieutenant-Commander Waters' paper ‘The Development of the English and the Dutchman's Log' (this Journal, 9, 70) there is an illustration (Fig. 1, p. 73) of the English log, reproduced from Champlain's Les Voyages de la Nouvelle France Occidentale. The device illustrated, though no doubt correct in intention, could not have performed the function stated, namely, of floating ‘vertically in the water presenting its full face to the ship's wake' (p. 74). This raises the suspicion that Champlain had not examined the log minutely enough, if at all, or at least had failed to instruct his draughtsman properly.