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H.O. NO. 208 (HYDROGRAPHIC OFFICE PUBLICATION NO. 208). NAVIGATION TABLES FOR MARINERS AND AVIATORS. By Lieutenant Commander J. Y. Dreisonstok, U. S. Navy. Second edition. 1928. Washington. $.75.
Reviewed by Captain Radler de Aquino, Brazilian Navy.
“…the trouble required by the computer to learn the use of a table need scarcely be considered; the important matter is the time and labour saved by it after he has learned its use.—Encyclopedia Britannica, Eleventh Edition, 1911, Vol. XXVI, page 326. Article: “Table, Mathematical.”
Just back to Rio de Janeiro after a pleasant tour of duty on the Upper Paraguay River in command of our naval station and flotilla at Ladario, State of Matto Grosso, it was very gratifying to see a copy of H.O. No. 208, second edition, 1928.
Its neat appearance, clear type, fine paper, and handy size will make these tables very convenient for sea and air navigation, although the vertical arguments for latitude run only from 0° to 65° in Table I. This fact reduces their availability for other problems, such as star identification and course and distance in great-circle sailing and in radio position-finding.
To those who have dealings with this ever-interesting subject—navigation—(and this year the writer can claim thirty years at it) the principle and formulas of Dreisonstok’s method are pretty well known. With the unnecessary addition, as we will see later, of the log cosecants of the perpendicular a to three places and raised to 103 power to find Z" by means of C + D, the method contained in H.O. No. 208 is simply Bertin’s method (as described in 1913[1] by him and by Captain Isaias A. Newton[2]) in which the final corrections of the tabular h are replaced by Souillagouët’s method,[3] as modified by Ogura,[4] in 1919.
Those who are familiar with my tables will readily solve any problem along the lines of the methods contained in H.O. No. 208, as all the necessary data will be found in them,[5] it being unnecessary to compute C + D in order to find Z”.
Commander Dreisonstok has followed Lord Kelvin, Souillagouët, Delafon, Bertin, Obrecht, and Smart and Shearme when taking the auxiliary arcs b and B (my c and C), while Garcia Moansilla, Newton, Ogura, Weems, and others take my b and my C, which simplify the rules and precepts and render them mnemonical. Use of the tables is better understood if precepts are given:
The precepts for H.O. No. 208 would be as follows, using Dreisonstok’s notations:
These precepts, of course, can be reduced to two:
In the Brazilian Centenary Edition (London, 1924) and in the U. S. Naval Institute’s Edition (Annapolis, 1927) of my tables I gave a full description of Bertin’s method, and showed how they could be used advantageously. These descriptions, I believe, are the only ones that have appeared in the English language and probably account for Bertin’s methods and tables being so little known outside of France.
In comparing these precepts with those contained in my tables for Bertin’s method one can readily see that the use of my b and C transfers the case in which a supplement appears, to the case in which t is greater than 90° and the century-old rules for combining the auxiliary data (same name, t < 90°, subtract; other cases: t > 90° and contrary names, add) are readily accepted and understood.
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The typical example on the inside of the cover of H.O. No. 208 worked out according to Dreisonstok’s method by means of my 1924 edition, pages 95 and 122, would be as follows:
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Instead of using logarithms, Bertin finishes up as follows: with a = 52° and C = 59° we find h = 18°-29' and M = 56°-11'. The corrections for the odd minutes of a and of C (both always negative) are 2'.4 and 10'.5 which gives h = 18°-29' - 12'.9 = 18°-16'.1.
The 1927 edition could be used with great advantage and great accuracy by simply adding to it nine pages of my log sec table, contained in my 1912, 1917, 1918, and 1924 editions (latitude or declination tables from my New Log and Versine Altitude Tables, 1912, 1917, 1918, and 1924).
In going through H.O. No. 208 I have noticed quite a few differences in the values of A in Table I when comparing them with those in Ogura’s Tables. For L = 31° and t = 67° the value given is 21159 while the exact value is 211578. Ogura gives 21158.
These differences show that it is impossible to obtain in all cases “a precision within 0’.1,” as stated on Pilot Chart No. 2600 of the South Atlantic Ocean, June-July- August, 1929.
The process is like Souillagouët’s tabular and logarithmic, although the logarithms appear in disguise as whole numbers.
The arrangement of the arguments should have been given as Souillagouët did give originally in his Tables du Point Auxiliaire, 1891, and as adopted in my tables with the latitude or declination at the bottom of the pages and H.A. on the sides, as H.A. changes 360° in every 24h while L, in the same interval of time, changes in ships at sea at most 12°. Pages are only turned for a change of latitude.
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The typical example worked out by my 1927 edition, where all arcs are given to the nearest O'.1 (within 3") and h is always found within (O'.25) of its exact value, would run as follows:
In ordinary navigation at sea and in the air Dd = 0'.6 could be considered as 0' (zero) and M would not have to be found from a and b.
The whole calculation would reduce itself to:
The combination of b = 6° and LA = 31° to find C = 37° could be done mentally and the only calculation necessary would be to find the assumed longitude Ga from tG and tA
In the air a Dd as large as 10' could be considered as 0' (zero).
Of course my method first proposed in these Proceedings for December, 1908, can be used advantageously when the azimuth is smaller than 80° and the altitude difference h — hA can also be reduced to zero—a decided advantage—as no line of position has to be drawn.
In modern ships with gyro compasses and excellent magnetic compasses the perpendicular a or the page from which all data is picked out can be found immediately from h and Z, and at the same time as a position line is plotted, the gyro compass or the standard magnetic compass is checked and controlled. No D.R. position needs to be calculated.
Observations of azimuth are already used to a certain extent for finding a great circle, a curve or a straight line of azimuth[6], as improvements take place in gyro compasses and radio beacons.
This is really the only method which “eliminates logarithms and reduces numerical work to a minimum” and it should be of “great value to aviators as well as navigators of submarines and surface craft,” and its use should become “mandatory in planes and airships.”
As in all tables using sines, cosines, secants, and cosecants and their logarithms, Dreisonstok’s method becomes less dependable and less accurate as the celestial body approaches the meridian or the zenith when a whole degree of latitude cannot be used. Table I shows critical points when the latitudes are low and the hour angles approach 90°.
A slight description of Professor Souillagouët’s monumental work Table du Point Auxiliaire pour Trouver Rapidement la Hauteur et VAzimut Estimes, July, 1891, new and last edition at Toulouse, 1900, Imprimerie Douladoure-Privat, might not be out of place here. Although Sir William Thomson (Lord Kelvin) had employed twenty years before an auxiliary position from which Sumner or position lines were drawn, Souillagouët was the first to start from an auxiliary or assumed position by taking the latitude and also the hour angle to the nearest tabular values. He was also the first to drop the perpendicular KZ from the zenith Z upon the circle of declination AP. It was only in 1893 that Lieutenant R. Delafon,[7] following more closely Lord Kelvin’s tables, devised his method and introduced the values of angles PZK and AZK from which the azimuth PZA is found.
Souillagouët gave us in his Table du Point Auxiliaire three tables. In Table I are given the values of j and of log cos j' for every 15' of arc from L = 0° to L = 60° and for H.A. for every lm from 0h to 3h. From L = 60° to 67° 30' j and log cos j' arc given for every 30' of L and for every 2m of H.A. In Table II the values of j and log cos j' are given for every 30' of L up to 60° and for H.A. for every 2m from 3h to 6h. j is rounded up to the nearest 5" (five seconds of arc).
The basic formulas are as follows:
tan j =cot L cos t
sin j’ = cos L sin t
sin h = cos j'-cos (D— j)
naturally, the same as used in H.O. No. 208.
In Table III similar to Lord Kelvin’s tables j and j’ are given for every 30' not only for L or d, but also for t or Z.
Souillagouët employed his Table III for finding the azimuth, and working out all the other problems depending upon a right angled spherical triangle.
Strange to say, in all modern tables based on Souillagouët’s method, except in Fuss’s[8] and Bertin’s, there is no reference to his name or to his monumental work.
On board the Brazilian battleship "Sao Paulo,”
Rio de Janeiro, November 11,1929
LA NAVIGATION AÉRIENNE TRANSATLANTIC. By Captain G. Voitoux, French Navy (Retired). Paris: Societe D’Editions Geographiques, etc., Maritimes et Coloniales. 1930.
Reviewed by Lieutenant Commander D. C. Ramsey, U. S. Navy
The author discusses in considerable detail the effect of wind and weather upon long-distance flights by aircraft and deals fully and comprehensively with the many varying conditions which may be encountered by pilots or navigators of planes embarking on easterly or westerly flights across the North Atlantic Ocean. Captain Voitoux makes use of weather data obtained during steamer crossings over a period of several years and it is interesting to compare his deduced figures of force and direction of the wind for the various seasons and latitudes with those which appear in graphic representation on the pilot charts of the upper air for the North Atlantic Ocean, first published by the Hydrographic Office in December, 1927.
While the author stresses the all-important elements of winds and storms and their effect upon an aerial transatlantic crossing, he does not neglect other factors which may compromise the success of such a flight. He points out, for example, the dangers of ice formation with its attending increase in weight of the plane structure and alteration of airfoil contours. He emphasizes the existing imperfections of those aircraft instruments which become vital accessories when low visibility sets in. In spite of the recognized limitations of planes and equipment he stresses as a most important point his belief that the failure of many of the attempts to cross the Atlantic by air may be laid at the door of personnel deficiencies.
It is believed to be the author’s thought, as translated from the original text, that the transoceanic flyer must have, aside from the indispensable qualifications of an airman, a thorough working knowledge of aerial celestial navigation and an equally sound knowledge of the science of meteorology. He points out the fallacy, before a crossing, of attempting through study and analysis of such weather data as may be available to draw up a finished plan for the entire flight. Such radical and unforeseen weather changes may occur over the Atlantic in the course of a 35- or 40-hour passage, that the aerial navigator is forced to discard his original data and fall back upon later information received by radio, or failing this, his own knowledge and resources to meet the emergencies of the moment. Unless he keeps an accurate running record of his true position such information as he may receive from a meteorological broadcasting center of the zones of high and low pressure and other weather data of interest can have but little value. Accuracy in navigation, therefore, is of paramount importance at all times during the flight. Insurance must be carried on such flights in the form of knowledge of the elements and their vicissitudes, skill in the application of the principles of navigation, and resourcefulness under conditions of trial and danger, otherwise in the opinion of the author an adventure of this kind at the present day can have, at best, a doubtful termination.
The author sets forth a series of observations pertaining to Atlantic weather which may be used to advantage by airmen in drawing up plans for an easterly or westerly crossing. Succinctly, these are as follows :
The northeast trades blow with more or less intensity below the twenty-fourth parallel throughout the year.
Winds which have 20 to 25 per cent frequency over the great circles between northern United States ports and the English Channel have but 2 to 3 per cent frequency at the Azores.
Winds increase in intensity with increase in latitude.
Winds over the North Atlantic having components directed towards the east are from two to three times more frequent than those directed towards the west. (This ratio will increase with increase in altitude).
Under normal circumstances northerly and southerly sets will balance out in the course of a crossing. It must follow that in an easterly crossing it is always desirable to keep to the southward of the centers of low-pressure areas and to the northward of the centers of the areas of high pressure. On a westerly flight the reverse is true.
The author holds that the effect of the wind on a plane in flight is more often disadvantageous than favorable. He points out the effect of winds blowing at right angles to the course, which, if compensated for, develop into retarding elements. This may be true, likewise, of winds of appreciable force blowing from certain compass points in excess of 90 degrees from the flight path. It is interesting to tie up these facts with the author’s contention that northerly and southerly sets usually balance out during an aerial crossing of the north Atlantic. With fair weather prevailing throughout the flight such a condition naturally would make it undesirable to attempt to hold to the true course at all times.
Captain Voitoux discusses the characteristics and types of aircraft best fitted to undertake a transatlantic voyage and emphasizes the importance of high cruising speeds. He favors, therefore, heavier-than-air craft rather than lighter-than-air craft for such operations and presents the following example to illustrate his point:
A rigid airship with a cruising radius of 7,500 miles at 100 miles an hour undertakes a westerly crossing of the Atlantic (3,750 miles), encounters head winds of 50 miles an hour average velocity and arrives at its destination with zero margin of safety in fuel, whereas a plane with a cruising radius of but 5,600 miles and a cruising speed of 180 miles per hour accomplishes the flight under the same adverse conditions with over two hours fuel left in its tanks. While the assumed performance data are somewhat fantastic, the advantage of high cruising speed is clearly demonstrated.
Captain Voitoux presents additional figures to show that a margin of safety of 1,250 miles in cruising endurance is not excessive for westerly flights in the high latitudes. This is supported by the statement that on an average of 20 days out of 100 winds of from 40 to 70 miles per hour velocity may be expected in the vicinity of the northern sea lanes followed by transatlantic steamers. It is also supported by the record of the flight of the British rigid airship R-34 from England to the United States via the northern route shortly after the war. It will be recalled that this vessel took departure with what was considered to be ample margin of safety in fuel and finally eased up to the mooring mast at Mitchell Field with dry tanks.
The author’s treatment of his subject is illuminating and interesting and his book particularly deserves the careful attention of those who contemplate aerial crossings of the Atlantic in the future.
[1] La table de Point Spherique ou Essai d’une Navigation sans Logarithmes, in the Revue Maritime et Coloniale for July, 1913, to January, 1914. See his Extrait de la Table de Point Spherique; Pour Calculer a la Mer Vite et sans Erreur: Rennes, Imprimierie Oberthur, 1918, and also his enlarged edition Tablette de Point Spherique; Meth- ode Generate de Calculs Nantiques, Simple, Rapide, Sure, Precise et Sans Logarithmes: Paris, 1919, Gauthier Villars et Cie.
[2] Novo Processo Rapido Para a Determinacao de Rectas de Altura, Applicavel is Taboas de Radler de Aquino e de Souillagouet. Lisboa, 1912. Reprinted from the Anais do Club Militar Naval de Lisboa, No. 3, 1912. See also Nos. 6, 7, and 8 of these annals for 1912 and No. 5 for 1913 for Newton’s modifications.
[3] Tables du Point Auxiliaire Pour Trouver Rapidement la Hauteur et YAzimut Estimes: Paris, 1891. Second and last edition, Toulouse, 1900.
[4] Shinkodo Hoikakuhyo (New Altitude and Azimuth Tables). Tokyo, 1920. Published by the Japanese Hydrographic Department. A new edition was published in English in 1924.
[5] The "Newest” Navigation and Aviation Altitude and Azimuth Tables for facilitating the determination of lines of position and geographical position at sea and in the air. The simplest and readiest in solution. Third electrotyped edition: London, 1924. Published by J. D. Potter, Admiralty agent for charts, etc., 145 Minories, E.C. 3. Price 20 shillings. The Altitude and Azimuth Tables are also contained in H.O. No. 200.
[6] See an article Curvas e Rectos do Azimuth no NavegacSo; Astronomica e Radiogomometrica. Reprinted from the Revista Maritima Brasileira, July, 1928, page 79.
[7] Methode Rapide pour Determiner les Droites et Courbes de Hauteur et Faire le Point. Paris: Berger Levrault et Cie. Editeurs.
[8] Tablitzi dlya Nakashdeniya Visott i Azimutoff. Typography of the Imperial Academy of Sciences. Saint Petersburg, 1901.