In a recent issue of Nature Sir Charles Goodeve gave an illuminating account of the value of operational research in war and described how, in peacetime, similar methods were being applied to problems of rail and road traffic. It is significant that he was unable to give examples of similar investigations into the flow of air traffic.

The Mercator chart has been used for navigational purposes for nearly four hundred years. Before Kramer devised his chart in 1569 navigators generally used a chart based on the simple cylindrical projection. The Cylindrical Orthomorphic projection devised by Kramer (or Mercator, as he is commonly called) revolutionized navigation and from that time has been the standard navigational chart for marine use. It was to be expected that, when the time came, air navigators would copy and perhaps modify the technique of the seaman. This was done, and today air navigators continue to use the Mercator chart. In many ways, however, it is not an ideal chart; it is now time to depart from this tradition and to use charts more suitable for air navigation. That this is possible has been shown by experimental flying in the Royal Air Force and by other countries, notably the United States and Canada.

The effect of instrument errors in the basic pressure pattern formula (I) has been discussed. Calculations have been based on a 150 n.m. distance interval between altitude determinations, and the permissible instrumental tolerances are wider if the length of this run is increased. A particular latitude of N. 50° has been assumed, but this involves no loss of generality since ageostrophic errors and those due to the latitude term in the formula are believed to be compensatory. In general, both ageostrophic errors and pressure altimeter errors increase together with altitude, and if instrumentation is adequate for 10,000 feet (the level for which the probable error of 3 knots holds good) it will be so at higher levels. It appears that satisfactory results may be obtained by using a Mk. VI radio altimeter together with a Mk. XIV Kolsmann pressure altimeter, and taking the mean of four observations of D at the beginning and end of the run.

Consol is the name now given to a navigational aid developed by the Germans during the war. A Consol beacon broadcasts on a medium frequency a pattern of dots and dashes, and by listening to this pattern on an ordinary ship or aircraft wireless receiver a navigator can determine his bearing from the beacon with a much greater accuracy than is possible with a D/F loop. The accuracy of the bearings obtained depends on the bearing of the observer from the beacon; it is greatest along a line called the normal of the beacon and decreases until it is zero along a line at right angles to the normal. The useful coverage with the existing type of beacon is about 280° out of 360°. With such a beacon the range over the North Atlantic is about 1200 n.m. by day and 1700 n.m. by night; the probable error on the normal is by day about ⅙° and by night (at ranges greater than 500 n.m.) about ½°.

As A preliminary to the discussion of the pre-determined Position Line, it will be advantageous to consider the system of working a Position Line on the Intercept method. Although this is well-known to navigators, a certain analogy exists between the two and it may be demonstrated quite simply.

The paper is divided into two parts. The development of ship-borne compasses is reviewed in Part I; in this section some of the difficulties due to bad siting, &c., are mentioned and certain solutions such as the use of repeating compasses and improved methods of correction are described. Part II surveys the development of the aircraft compass and shows how its phases of development have corresponded to those of the marine compass. Some recent forms of aircraft compass and methods of development are also described.

Pressure pattern flying embraces a number of air navigation techniques all of which have one common feature: they relate pressure distribution along an aircraft's flight path to that component of the wind which acts at right angles to the aircraft's heading. My intention is to give a brief outline of the theory underlying these techniques.

Wind is brought about by horizontal pressure differences in the earth's atmosphere. Air tends to move from an area of high pressure towards an area of low pressure under the influence of the pressure gradient force. The direction of its motion is, however, affected by the earth's rotation in space. Considering this rotation in the horizontal plane only, it is at a maximum at the poles and zero at a point on the equator. At any intermediate point of latitude ϕ, the speed of rotation in the horizontal plane is proportional to the sine of the latitude. In the northern hemisphere the rotation is anticlockwise; in the southern hemisphere it is clockwise with reference to outer space.

For many years past great efforts have been made to devise methods of obviating the necessity for making navigational calculations by logarithms, on the grounds that the logarithmic process is too slow for modern navigational purposes. For some such purposes it undoubtedly is; but all these short methods suffer from some disadvantage or other, and when the preliminaries (which generally involve calculating the hour angle) common to both are completed, the difference in time between completing the sight by inspection and interpolation, and by logarithms, is not so great. For this reason it seems possible that logarithms would still be considered preferable for a wider range of purposes than at present, were it not that most of the volumes of logarithms still commonly used for navigation are designed for more accurate calculations than are necessary or justifiable for the practice of navigation, and hence are unnecessarily cumbrous and slow in use.

Twenty years ago meteorological forecasting was necessary and important to aviation. A number of factors made it so, as a short review of flying conditions in those days will show.

The weather was then the dominant factor in training. The wingloading of training aircraft was then so light that a sudden variation of only 10 m.p.h. in the wind made a practice landing hazardous. Both pupil and instructor therefore anxiously awaited the weather forecast. The wind forecast was equally important to the transport pilot of 1928 when a headwind of 60 m.p.h. was likely to prevent his reaching a destination only 200 miles away.

It is the present usage by the National Physical Laboratory and the Trade to give, on its Certificate, the ‘constant’ (graduation and centring) errors of a sextant only at stated points on the scale. If these errors are of a magnitude which is worth while applying as a correction, this usage is not quite what the user requires. The N.P.L. Class A Test, issued for instruments reading directly to 10″ (or o′·2 in the case of decimal subdivision) allows combined graduation and centring error up to 40″ or 4 scale divisions of the micrometer or vernier; the Class B Test for instruments graduated to 20″ permits such error up to 2′ or 6 scale divisions. Thus, even with instruments that pass these tests, it may be worth the marine navigator's while to apply the error as a correction. What he wants to know, however, are the limits of such errors as are worth his while to apply. In other words, he requires a Critical Table of Corrections, of the type used in the Air Almanac and in certain mathematical tables by L. J. Comrie, by whom, it is understood, the method was introduced.

The navigational problem. In order to find out how an aircraft is tracking with respect to the ground, we can either obtain information from data accurately placed with respect to the ground, or assess the horizontal movement of the air masses through which the aircraft is flying and combine this motion with that of the aircraft through the air. To determine the track we require accurate knowledge of the aircraft's heading and of the drift, which is the effect of the beam component of the wind. Along any given course line the navigator can make a series of drift observations, usually visual and therefore requiring downward visibility, and estimate the departure from the course line by averaging such observations to obtain the integrated effect of the drift. Since the sole purpose of drift observation is to estimate the departure of an aircraft from a given course line, a method of obtaining this total departure from a single observation or pair of observations, under any visibility conditions, is of considerable value. Again, if it is possible to estimate before flight the total integrated effect of drift for the whole flight, and our object is merely to fly to reach our destination, then the necessity of taking drifts during flight will be obviated.

During the cruise of H.M.S. Van Kinsbergen, of the Royal Netherlands Navy, with 92 midshipmen on board (of whom 66 were Executive Branch), as may be expected, a great many sights were taken. Very often the ship's position was obtained by bearings shortly before the star observations were made; in this way the DR position was known and the accuracy of the sights could be determined.

The preceding papers indicate that the theory of pressure pattern flying assumes that the wind satisfies the conditions imposed by the geostrophic wind equation and that the atmospheric pressure distribution is not changing. These conditions are not satisfied in the atmosphere, and the errors caused by their non-fulfilment are discussed in the following paragraphs.

Effect of departures of wind from geostrophic. The geostrophic wind equation is derived on the assumption that the wind blows uniformly without acceleration and without friction. These conditions are never satisfied in the atmosphere, nevertheless the practising meteorologist has found that the geostrophic wind represents a useful approximation to the true wind. There are certain exceptions of which the most important are in low latitudes and at levels below 2000 feet.

When astronomical sights have been reduced by means of tables calculated for a fixed equinox, it is necessary to make a correction for the precession that has occurred since the date for which the tables were calculated. In the Astronomical Navigation Tables this correction is applied to each intercept separately. It is, however, possible to apply the correction once only to the fix obtained. This would probably be simpler, particularly with such tables as the Experimental Air Navigation Tables and H.O.249.

On page 179 of the first volume of the Journal, Commander J. Middendorp, R.N.N.R., discusses the effect on the observed altitude that arises when the sextant is tilted out of the vertical plane, and concludes that the error is a maximum for altitudes in the region of 45; it seems to me that the conclusion is incorrect. I have no quarrel with Commander Middendorp's mathematics, but with his fundamental hypothesis, which is that when a sextant is tilted it is rotated about the line of sight to the star. I believe on the contrary that a sextant tilt is a rotation approximately around a horizontal axis.

Since the inauguration of the B.O.A.C. Return Ferry Service, the principles of pressure pattern flying have been followed on the North Atlantic as regards flight planning. In co-operation with the forecaster the practice developed of working out a number of flight plans to achieve the shortest possible flight time, and eventually it became possible to select the most favourable route with a reasonable degree of precision.

The advent of the radar altimeter furthered development of the pressure position line theory which I believe was first propounded by R.A.E., Farnborough, and has since been elaborately garnished and enthusiastically tested by our American friends during recent years. The words ‘altimetry’ and ‘aerologation’ have been added to our generally common language to cover flight techniques that might perhaps be more simply described as ‘pressure comparison navigation.’