Nowacki H. Leonhard Euler and the theory of ships (794398), страница 2
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[10], Szabó[11], Mikhajlov[12], Calinger [13]. In addition several general textbooks on the history of fluidmechanics contain sections appreciating Euler’s contributions (e.g. in Calero [14],Darrigol [15]). The monograph by Ferreiro [16] on the history of ship science in the17th and 18th c.
also touches on many details of Euler’s life and work. The contents ofsuch available sources shall not be repeated here. Suffice it to acknowledge in gratitudethat I owe them much inspiration.Rather I just want to retrace here how it happened that Euler developed a predilectionfor subjects of the theory of ships, a preference that is not obvious for the son of anAlpine country, and how he consistently returned to his early maritime applicationinterests during many stations of his vita. Table I shows evidence that his relatedpublications appeared between 1727 and 1782. How did this lifelong affinity arise?Leonhard Euler was born in Basel, Switzerland on April 15, 1707 as the son of theSwiss reformed priest Paulus Euler and his wife Margarethe née Brucker. He attendeda Latin Grammar School in Basel at the age of 8 to 13, as was customary, and thenenrolled at Basel University in preparatory courses.
Here before he was age 15 he methis later mentor and patron Johann Bernoulli (1667-1748), one of the leading scientistsof this era in mathematics and mechanics , from whom he took courses in these twosubjects. Bernoulli very early recognized Euler’s eminent talent and invited him to takepart in the series of Saturday private meetings in his house which he held with his sonsand selected guests and where mathematical subjects were discussed, literature wasreviewed and problems were solved.
This is where Euler also got acquainted withJohann Bernoulli’s sons, in particular with Daniel Bernoulli (1700-1782), with whomhe developed a long lasting friendship. After completing his first degree in 1723 by theMagister examination, although Euler at his father’s urging then enrolled in the divinityfaculty, he continued intensively to concentrate on mathematical studies under JohannBernoulli, who much promoted him.Now it was essentially a coincidence that Johann Bernoulli had already for some timeconcerned himself with special questions of ship theory because he regarded this fieldas a promising area for applying the still new methods of infinitesimal calculus,developed-3-Table I: Euler’s Publications on Subjects of Ship TheoryEnestroemIndex No.E.4E.78E.94E.110/E.111E.116E.137E.150E.413E.415E.426Place inOperaOmnia,Seriesvol., p.TitleMeditationes super problemate nautico,quod illustrissima regia ParisiensisAcademia scientiarum proposuit(Thoughts on the Nautical Problem Posedby the Most Illustrious Royal ParisianAcademy of Sciences)Dissertation sur la meilleure constructiondu cabestan(Treatise on the Best Construction of theCapstan)De motu cymbarum remis propulsarum influviis(On the Motion of Barges Propelled byOars on Rivers)Scientia Navalis, seu tractatus deconstruendis ac dirigendis navibus(Ship Theory or Treatise on theConstruction and Steering of Ships)Mémoire sur la force des rames(Memorandum on the Force of Rudders)Examen artificii navis a principio motusinterno propellendi(Examination of the Thought to Propel AShip by the Principle of Internal Motion )Meditationes in quaestionemobservationibus temporis momentumdeterminandi(Thoughts on the Question of Determiningthe Momentum by Observation of Time)De promotione navium sine vi venti(On the Propulsion of Ships without theForce of Wind)Sur le roulis et le tangage(On Rolling and Pitching)Théorie complette de la construction et dela manœuvre des vaisseaux(Complete Theory of the Construction andManeuvering of Ships)-4-Manu- Publiscript cationDateDatePublicationPlaceII 20,1-3517271728ParisII 20,36-8217411745ParisII 20,83-10017381747St.PetersburgII 18/19,2 vols.17411749St.PetersburgII 20,101-12917471749BerlinII 20,130-1451747/17481750St.PetersburgII 20,130-14517471750ParisII 20,146-18917531771ParisII 21,1-3017591771Paris1781St.PetersburgII 21,80-2221778Table I: Euler’s Publications on Subjects of Ship Theory (cont.)EnestroemIndex No.E.520E.545TitleEssai d’une théorie de la résistancequ’éprouve la proue d’un vaisseau dansson mouvement(Attempt at a Theory of ResistanceReferring to the Forebody of a Ship in itsMotion)De vi fluminis ad naves sursum trahendasapplicanda(On the Force to Apply to Tow Shipsupriver)Place inOperaOmnia,Ser.,vol.,p.ManuscriptDateII 21,223-22917781781ParisII 21,230-24217801783St.PetersburgPubli- Publication cationDatePlaceby Newton and Leibniz.
Johann Bernoulli in a treatise as early as 1714 [17] had beenfirst to attempt to apply Newton’s impact theory of resistance (cf. below) to determinethe forces acting on a ship sailing before the wind, viz., both the hull resistance due tounderwater hydrodynamic forces and the thrust acting on the sails due to theaerodynamic effects of wind. He achieved this in a mathematically valid way byintegration of the fluid dynamic impact forces acting on their respective areas ofapplication. However the agreement of these predictions with empirical observation wasdisappointing, which was to be attributed to the inadequate premises stipulated inNewton’s impact theory for the determination of the resistance in water and air. Thesubject remained of intriguing interest to Bernoulli and met a fashion of his time whichfavored subjects aiming at improvements in the performance of technical systems suchas ships by means of scientific methods.When the Parisian Royal Academy of Sciences launched a prize contest in 1726 in orderto determine the optimal configuration, number and height of masts for sailing vesselpropulsion, Johann Bernoulli encouraged his student Leonhard Euler to submit acontribution.
Why Johann Bernoulli did not participate in the contest himself, cannot beclearly stated. Perhaps he wanted to promote Euler and at the same time avoid the riskof laying open his cards to the competition? In any case it was in this way that Euler’sfirst treatise [18] on a subject of ship theory was initiated, which he submitted in 1727at the age of 20.Euler earned the recognition of a runner-up award (Grade: “Accessit”).
The first prizewent to Pierre Bouguer, the already better known French scientist, who had beenworking on the issue of ship masting for some time. It is futile to compare the merits ofthe two treatises today. For on the one hand the two authors started from very similarfundamental premises, in particular from Newton’s impact theory of resistance as wellas a precise knowledge of contemporary sail force theory, which had been intensivelyand controversially debated during the decades before the contest (Renau [19], Huygens[20]). On the other hand neither author yet achieved a satisfactory solution to theproblem.
Both suffered from deficits in the fundamentals of hydrostatics which wererequired for determining the equilibrium floating condition by trim and heel angle whenthe ship was displaced by wind loads. This issue was circumnavigated. Euler e.g.assumed the vessel to be fixed (or frozen in ice) temporarily in a heeled and trimmedcondition. It appears however that with respect to such weak assumptions the results ofthe prize contest and the knowledge achieved were not to the satisfaction of Euler atleast, perhaps not of Bouguer either. For both continued to work on the subject andcertainly had recognized the deficits in the fundamentals of ship hydrostatics.-5-In any event Euler by this experience had established a first closer acquaintance withsubjects of the mechanics of ships, had familiarized himself with the concepts of shipgeometry, sailing equipment and nautical topics and from then on maintained a lastinginterest in problems of ship theory as issues of applied mechanics and mathematicalanalysis.Still in 1727 Euler received an attractive offer from the Russian Imperial Academy ofSciences in St.
Petersburg, founded by Tsar Peter I in 1725. He was pleased to acceptthis offer, initially with a modest salary as a research fellow. He traveled by ship on theRhine from Basel to Mainz, from there by horse drawn coach to Lubeck where heembarked on a ship to cross the Baltic Sea to reach the Neva in St. Petersburg in June1727. He was scientifically quite successful right away and soon advanced to beappointed a full member of the Academy (1731) with responsibilities in physics, andespecially in mathematics and mechanics. His first St. Petersburg period extended from1727 to 1741.
During this time he also intensively dealt with topics in ship theory.This is attested first of all by the minutes and reports of the Academy, which in 1735assigned to Euler a review of a treatise submitted by La Croix on the transverse stabilityof the ship and, as his reply makes evident, found him well prepared to point out errorsin La Croix’ derivation and to provide the correct answer, at least for the simple shapeof a floating parallelepiped. Euler’s stability criterion from the beginning was a positiverestoring moment when the ship was inclined by a very small (infinitesimal) angle.
Ageneral solution for ships of arbitrary hull form was already in preparation in 1735.His reputation for outstanding knowledge in the theory of ships became well known atthe Academy, so in 1737 – probably at his prior request – he was commissioned by theAcademy to write a comprehensive treatise on the whole range of subjects in shiptheory. Therefrom resulted Euler’s most famous opus on this subject, the two volumetreatise Scientia Navalis. Euler’s manuscripts for this work were completed by 1741,but he failed to find a publisher for this voluminous, very specialized treatise in Latin sothat after very long delays this monumental work of early ship theory did not appearuntil 1749 in St.
Petersburg. (Pierre Bouguer’s “Traité du Navire” [2], a work ofcomparable significance, had been developed simultaneously and independently (see[21]), but was published in 1746 in Paris soon after Bouguer’s return from an Andeanscientific expedition conducted from 1735 to 1744 by the Parisian Academy [16]).After many scientifically fertile years in St. Petersburg Euler in view of a certainpolitical turmoil in Russia accepted an invitation by King Frederick II of Prussia tomove to Berlin in 1741, where he was involved in the foundation of the Royal Academyof Sciences (1745) and where he worked through 1766. During his Berlin years Euler,officially responsible for the class of mathematics, was active in many fields of scienceand remained very creative.
Fluid mechanics from these years owes him manyimportant, even today still fundamental results:--Euler’s equation of the motion of a fluid volume element (1752),The rejection of Newton’s impact theory of resistance, practised as „common rule“until that time (1753),The establishment of a new field theory of fluids, i.e., a continuum theory of fluidmechanics, based on the modern concepts of pressure and velocity, initially appliedto ideal fluids (1755),Beginnings of potential flow theory (1755),Considerations on fluid friction (1751).These fundamental results led to a new level of understanding of flow phenomena,furnished the exposition for a catalogue of questions for a large class of applications and-6-had lasting effects on the further development of fluid mechanics.
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