Nowacki H. Leonhard Euler and the theory of ships (794398)
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Leonhard Euler and the Theory of ShipsHorst Nowacki, BerlinAbstractOn April 15, 2007 the scientific world has commemorated Leonhard Euler’s 300thbirthday. Euler’s eminent work has become famous in many fields: Mathematics,mechanics, optics, acoustics, astronomy and geodesy, even in the theory of music. Thisarticle will recall his no less distinguished contributions to the founding of the moderntheory of ships.
These are not so widely known to the general professional public. Inlaying these foundations in ship theory like in other fields Euler was seeking “firstprinciples, generality, order and above all clarity”. This article will highlight thoseachievements for which we owe him our gratitude.There is no doubt that Leonhard Euler was one of the founders of the modern theory ofships. He raised many fundamental questions for the first time and through all phases ofhis professional lifetime devoted himself to subjects of ship theory. Thereby he gave aunique profile to this still nascent scientific discipline.
Many of his approaches havebeen of lasting, incisive influence on the structure of this field. Some of his ideas havebecome so much a matter of routine today that we have forgotten their descent fromEuler. This article will synoptically review Euler’s contributions to the foundation ofthis discipline, will correlate them with the stages of Euler’s own scientificdevelopment, embedded in the rich environment of scientific enlightenment in the 18thc., and will appreciate the value of his lasting aftereffects until today. The same examplewill serve to recognize the fertile field of tension always existing between Euler’sfundamental orientation and his desire to make contributions to practical applications,which has remained characteristic of ship theory to the present day. Without claimingcompleteness in detail this article aims at giving a coherent overview of Euler’sapproaches and objectives in this discipline. This synopsis will be presented primarilyfrom the viewpoint of engineering science in its current stage of development.1.
IntroductionLeonhard Euler (1707-1783) is famous for many brilliant scientific achievements inmathematics, in solid and fluid mechanics, as a physicist in optics and acoustics, inastronomy and geodesy, and even in the theory of music. Euler excelled also in theapplication of science to practical problems, which in our current awareness has beenrelegated to the background. One of his favorite application themes was also the theoryof ships, i.e., the application of the scientific principles of solid and fluid mechanics topractical and technical problems in the design, performance evaluation and in theoperation of ships. Euler throughout his scientific career devoted no small share of hisinvestigations and publications to such topics in the theory of ships.It is all the more surprising that Euler’s role in the foundation of modern ship theoryand the substance of his contributions are not widely known today, even amongspecialists who are working on matters of ship theory today.
In this regard the statementmade by the French geometer Taquet in the 17th c., referring to Archimedes, theclassical ancestor of ship theory, may also be applied to Leonhard Euler:“All praise him, few read him, all admire him, few understand him”.Many causes may have contributed to creating this gap in our historical memory.
First,Euler wrote the majority of his publications in Latin, the classical language of-1-Fig. 1: Leonhard Euler (1707-1783)Fig. 2: Pierre Bouguer (1698-1758)science at the Academies in his era, in particular also his principal opus on Ship Theory,the famous “Scientia Navalis”[1] (1749).
Thus the access thereto by practitioners ofshipbuilding must have been difficult, even during Euler’s lifetime. Until today thereexists no complete translation of “Scientia Navalis”, a two volume work of ca. 900pages, into a modern language. Second, it is true that he gave an analytical exposition ofthe subject in brilliant clarity of style, but he rarely ever concerned himself withnumerical examples for specific, built or designed ships. Third, he presumed from hisreader an understanding of the mathematical notation of analysis and of the methods ofinfinitesimal calculus, which was not widely spread in his days.
Thus his publicationson the theory of the ship became accessible and comprehensible to the general publiconly after a long delay. Nevertheless his influence in science was always well perceivedand even without many readers did reach those who later continued his work indeveloping ship theory, certainly no later than in the 19th c.Euler is not the only founder of the modern theory of ships. Among his contemporariesthe French scientist Pierre Bouguer (1698-1758), hydrographer, mathematician,geodesist, physicist and in particular also ship theoretician must be mentioned who hadplayed a similar eminent role in the 18th c.
Bouguer has by his principal opus “Traitédu Navire” [2] (1746), written in French, during his lifetime no doubt gained faster andmore direct influence on developments in practice, in particular since he was willingalso to furnish practical examples and numerical calculation methods. Bouguer andEuler both were first to use infinitesimal calculus as an approach to subjects of shiptheory. This is why I count both of them as founders of “modern” ship theory.
Theircontemporaries, especially during the second half of the 18th c., such as D’Alembert,Jorge Juan de Santacilia or Chapman, also made other, influential contributions to thefundamentals of the theory of ships. In this illustrious field Euler is eminent by his longrange impact on the whole field of ship theory which he founded on the first principlesof mechanics and to which he gave a systematic structure. This is why Euler’s role as afounder of ship theory will be particularly stressed in this article.In the following sections a chronological survey will be given first illustrating howtopics of ship theory accompanied Euler’s whole scientific career.
Then Euler’sindividual contributions are sorted by thematic aspects and are assigned to the mostimportant subtopics of ship theory: Hydrostatics and ship stability, resistance,propulsion, maneuvering and ship motions in rigid body degrees of freedom. His impacton the development of general fluid mechanics will be briefly recorded, too. Thisoverview will demonstrate the close interrelation between fundamentals and-2-applications in his work, and will illustrate on the other hand how even a brilliantscientist like Euler cannot offer all definitive solutions in one strike, but mustcontinuously learn by experience to achieve a mature form of his insights. Euleraccepted and succeeded in this lifelong learning process.In later literature Euler by some commentators, and not infrequently, was characterizedas a pure mathematician without motivation for practical applications.
I must dismisssuch views (cf. also Truesdell [3], Eckert [4]). Rather it is essentially demonstrated byhis contributions to the foundation of the theory of ships that his goal in this context wasto achieve practical success in applications by a well constructed physical foundation.This message will also be presented in this article.2. The Theory of Ships in Euler’s BiographyEuler’s biography is well known from multitudinous presentations (e.g. Fellmann [5]).His oeuvre has been very systematically documented and reprinted in his CollectedWorks (Opera Omnia Euleri [6]), although these comprehensive series have not yetbeen fully completed. In this collection his treatises dealing with the theory of ships arecontained, too (Series II, vols.
18-21). Table I gives an overview of Euler’scontributions to this subject area with reference to the Enestroem Index Nos. of hispublications. In these volumes generally very elaborate appreciations and interpretationsof his works are given. The following must be mentioned in particular in the context offluid mechanics and ship theory: Truesdell [3], Habicht [7, 8, 9]. Further in the samevein important summaries are given in: Burckhardt et al.
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