The twelfth Duke of Edinburgh Lecture was presented in London on 15 October 1986 at the Royal Geographical Society to the thirty-ninth Annual General Meeting of the Institute, the President in the Chair. The lecturer, the President said in his introductory remarks, was a geographical scholar who had devoted much of his time to the verification of early voyages by following the paths described in the often legendary accounts:the travels of Marco Polo in 1961 and later the voyages on which the present paper is based, of St Brendan, Sindbad and Jason. In 1976–7 in the medieval leather boat Brendan he followed a route from Ireland across the Atlantic described in the 8/9th century Navigatio. In 1980–81 in the Arabian boom Sohar he sailed over 6000 miles from Oman to Canton in a reconstruction of Sindbad's seven voyages described in One Thousand and One Nights, and finally in 1984 in Argo, a reconstructed Greek vessel of the 13th century B.C., his voyage took him from Greece through the Bosphorus to Georgia in the USSR, following the legendary path of Jason in search of the Golden Fleece. No-one could be better fitted to reflect on the human factor in early navigation.

Spacecraft which are sent on deep space missions to the planets must be accurately navigated in order to achieve the correct flight path. Navigation analysts use precise measurements and large computational software systems to determine a spacecraft's position throughout the mission and compute the velocity corrections for its guidance through space. When the spacecraft is launched into deep space on its voyage, it is impossible to know with great precision where it is headed. Imperfections in both the launch vehicle's terminal velocity and the uncertainty in the knowledge of the parameters which will affect the spacecraft trajectory contribute to errors in the predictions of the total flight path. Continuous navigation of the spacecraft achieves an ever-evolving prediction of its orbit from the reduction of radiometric and astrometric observations of the craft. Control of the spacecraft is achieved by computing and signalling to the craft a series of propulsive, velocity correction commands, which manoeuvre the craft to its desired course.

Practical navigation is far from an exact science because the navigator in his daily routine uses too many approximations which would be unacceptable in careful scientific work. These approximations will not be referred to in detail, or elaborated upon, since the matter is adequately dealt with in standard navigation manuals and textbooks. The laws that govern the distribution of random errors, however, their occurrence and frequency, will be discussed in this paper in terms of the theory of probability and mathematical statistics. The main objective will be the quantitative error analysis of random structures. We shall also formulate mathematical models and use them for computer simulations of practical navigation problems.

In the past, air traffic services (ATS) have been compared with vessel traffic services (VTS) in numerous articles, in particular from a technical and operational point of view. Generally emphasis has been laid on existing technical differences between air navigation and shipping, which in brief are related to the speed of aircraft and ships and the medium in which these craft move.

Mean relative collision risks for marine crossing encounters are derived from calculated encounter rates by the use of a two-part weighting function. The relative importance of the two parts is determined from data concerning the collisions which have taken place during the last few years. The method is applied to the crossing traffic in the English Channel to obtain the optimum crossing angles in both clear and restricted visibility.

In any maritime emergency where time elapses from the start of the incident to the arrival of rescue units it is necessary to establish the most probable survivor area. The procedure for establishing a most probable area is known as search area determination and requires the calculation of one position from another, known respectively as the datum point (DP) – the most probable position of survivors – and the last known position (LKP) – the incident position with recourse to the effects of tide and wind. Under the present manual methodology of the search and rescue planning system (USCG 1973), the DP is given an error treatment comprising drift initial position and search and rescue unit navigational (SRU) errors. Error calculations produce a search area radius (R) which is ‘boxed’ and referenced by four corner coordinates given in latitude and longitude.

A system which yields the automatic positioning of a ship from computer analysis of marine radar images of nearby coastlines has been tested on data from the survey vessel Maxwell while proceeding in and out of Halifax harbour. Differences between radar-determined position fixes and those obtained by a microwave navigation system with an error of the order i o m show little evidence of additional error when the origin of the radar images used as ‘reference map’ is within 500 m of the actual position. As the distance increases the accuracy slowly decreases.

Traditional receivers for the low-frequency, hyperbolic radio-navigation systems – Loran-C, Decca Navigator and Omega – are expensive and are operated manually. They either display position fixes in hyperbolic coordinates for plotting by hand on navigation charts printed with hyperbolic overlays or they plot tracks automatically, often on distorted charts. Recently, low-cost receivers have been developed for marine navigation which operate wholly or largely automatically and which display position measurements in geographical coordinates – latitude and longitude – or as headings and distances to waypoints which are entered by the navigator in geographical coordinates.

This paper reports on a study conducted during the academic year 1985–6 by Assistant Professor H. Hagiwara of the University of Mercantile Marine in Tokyo and Professor J. A. Spaans of Delft University of Technology.

Flight inspection is the means by which the performance of a navigation aid is measured to ensure that it is meeting the requirements of the operational procedures based upon it. It can involve laboratory-type measurements in an environment which is generally unstable and sometimes hostile. The first requirement is the position of the aircraft fixed to an accuracy commensurate with that implied by the operational specification of the navigational aid. A range of techniques for position fixing has been developed over the years. Where possible the technique should just meet the ‘one order better than’ criteria. The use of systems with accuracies significantly better will usually result in financial or logistic penalties.

Civil airways route structures are constructed around en-route and terminal navigation aids such as VOR, DME and ILS. Radio navaids do not always provide accurate information to aircraft and their performance can be seriously degraded by system drift, electronic interference and unrelated changes to the local environment such as man-made obstructions erected in the beam forming area. To ensure efficient and safe operation of air traffic control, ground-based aids must be commissioned and maintained to stringent specifications at all times. Consequently, regular airborne performance checks of all radio/radar navigation aids are essential, and since the most critical time of any flight is the approach and landing phase, the precision aids (PAR and ILS) are checked at regular intervals and with a greater positional accuracy than the general navigation aids.

Methods of calculating the course and the distance between two points from a knowledge of their latitudes and longitudes, or calculating the latitude and the longitude of the arrival point from the course and the distance from a known departure point, are called sailings. Middle-latitude sailing and Mercator sailing have been widely used.