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Daniel Bernoulli and Leonhard Euler a Russian-Swiss Heritage

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Daniel Bernoulli and Leonhard Euler a Russian-Swiss Heritage FROM BASEL TO ST. PE TERSBURG AERONAUTICAL AND SCIENTIFIC MILESTONES: DANIEL BERNOULLI AND LEONHARD EULER A RUSSIAN-SWISS HERITAGE Georges Bridel* *ARBEITSGRUPPE FÜR LUFT- UND RAUMFAHRT (ALR Aerospace), Zürich, Switzerland Keywords : aerospace scientists, aviation history, foundations of aeronautics Abstract The early XVIII century presented famous The paper adduces some facts about the history scientists like, for example, Russian Mikhail of aeronautical sciences. The purpose is to Lomonosov and Swiss Horace-Bénédict de explore and compare the activity of various Saussure. generations of scientists, who made valuable Bernoulli and Euler must be seen in the contributions to the development of context of their tradition. It is a characteristic of aeronautical sciences during XVIII-XX the scientific and technical communities that centuries. there has always been an intense exchange of The paper aims to explore how the scope of information and continuous contacts between scientific activity of the outstanding researchers the individuals. In our aerospace community changed over time and which factors influenced such contacts are particularly important and their output. fruitful. ICAS is an example of lived practice. 1 International Scientific Lives – 2 Aeronautical Sciences – Way to a Broad Globalization in the Past Field of Activity The names “Bernoulli” and “Euler” are widely Following the traditions of Bernoulli and Euler, known in aeronautics and fluid mechanics L. Prandtl and N. I. Zhukovsky created modern theory. aeronautical science. Both scientists have given their names to Their successors were engineers and fundamental equations, which are used today to scientists as well: the professors Chaplygin and Ackeret had made important contributions to demonstrate the pressure (energy) conservation aerospace science, development of transonic in fluids and model the inviscid fluid flow. Both aerodynamics and management of aeronautical Bernoulli and Euler are of Swiss origin, from centers such as the large TsAGI and the small Basel. However, they have realized their Institute of Aerodynamics at the ETH in Zurich. scientific achievements in the scientific According to the size of the countries one was community of St. Petersburg. Their scientific life must be seen in the large and the other one was small, but both context of the time: the XVIII century laid down people were dedicated to progress of the basis of the intense and broad scientific aeronautics. development, which was succeeded in the XIX Chaplygin and Ackeret were active in theory as well as with experiments. Ackeret was century and beyond by an increasing number of internationally active whereas Chaplygin scientists. worked only in Russia. The similarities are striking, nevertheless. 1 GEORGES BRIDEL Nature and extension of the sciences Lomonosov has become the Professor of evolved enormously at all times. Lomonosov chemistry at St. Petersburg. This is the period and de Saussure were active in an extremely when he devotes a lot of attention to the wide field, which included many sciences as experimental activities. well as culture at the same time. In 1748 Lomonosov formulated the law of They were called “Universal-Gelehrte” or “conservation of matter”, which is regarded as “universal scholars”. Some specialization can one of his most famous postulates and reads as already be noticed with Bernoulli and Euler as follows: “All changes in nature are such that will be shown later on. Finally, Chaplygin and inasmuch is taken from one object insomuch is Ackeret have dedicated their efforts mostly to added to another. So, if the amount of matter aerospace, which was still a relatively small decreases in one place, it increases elsewhere. field of activity at that time. This universal law of nature embraces laws of Today, aeronautical science is extremely motion as well, for an object moving others by wide and the specialization is progressing as its own force in fact imparts to another object shown by the number of topics at the ICAS the force it loses.” Congresses and the authors involved. In 1750s Lomonosov devoted a lot of time Another interesting question is “Why to physics while developing wave theory and human flying started only after 150 years passed kinetic theory of gases. since the creation of the first and fundamental In 1760 he also became engaged a lot with laws of fluid mechanics?”. It seems obvious that astronomy and, in particular, conducted the early flight was much more the undertaking of observations of Venus’ atmosphere. courageous and practical people than of Lomonosov was famous for a multitude of scientists. Also the early ideas of human flight his talents, which included artistic traits besides (originating from Leonardo da Vinci) did not scientific expertise. He was famous both as a inspire to establish a bridge in between. chemist, physicist, astronomer, geographer, geologist, mosaicist and poet. 3 “Founding fathers” of aeronautical sciences. 3.2 Horace-Bénédict de Saussure (1740- 1799) 3.1 Mikhail-Vasilyevich Lomonosov (1711- 1765) Fig. 2: Horace-Bénédict de Saussure Fig. 1: Mikhail Lomonosov De Saussure (shown in Fig. 2) was born in Lomonosov (shown in Fig. 1) was born in Conches (Switzerland) in 1740. He defended his Denisovka village (Arkhangelsk province) in dissertation “Sur la Nature du Feu” at the 1711. He studied mineralogy and metallurgy in Académie in 1759. De Saussure published the Germany in Marburg and Freiburg. In 1745 book, which described his experience of 2 FROM BASEL TO ST. PE TERSBURG climbing the mountains, titled Les Voyages dans Bernoulli’s main scientific postulates les Alpes in 1779. In 1783 De Saussure include the concept of conservation of energy conducted the research on hygrometry and within the flow and relation between the measurement devices. In 1784 he met de variations of pressure and velocity, leading to Montgolfier and Pilâtre de Rozier in Lyon. In the well known Bernoulli equation (6). 1787 he conducted barometric measurements at the peak of Mont Blanc. 3.4 Leonhard Euler (1707-1783) De Saussure also carried out further geology studies and lightning conductor experiments. He developed such instruments as the anemometer, magnetometer and cyanometer. De Saussure extended his mountaineering activities and published even more accounts of his journeys. He also constructed the first solar oven. 3.3 Daniel Bernoulli (1700-1782) Fig. 4: Leonhard Euler Euler (shown in Fig. 4) was born in Basel in 1707. He studied at the University of Basel and had separate lessons in mathematics from Johann Bernoulli (the father of Daniel Bernoulli). By the offer of Daniel Bernoulli (after the death of his brother Nicolas), Euler moved to St. Petersburg in 1727 and took up a position at the Mathematics Department of the Imperial Russian Academy of Sciences. In 1733 he succeeded Daniel Bernoulli as the head of Fig. 3: Daniel Bernoulli mathematics department. In 1741 Euler moved to Berlin Academy. Bernoulli (shown in Fig. 3) was born in Euler published a lot of works, of which Groningen as a son in a family of physicists and Mecanica (Mechanics) is the most important mathematicians in 1700, soon after his birth the one for aerospace sciences. family went to Basel. Bernoulli studied In 1766 Euler decided to move back to St. medicine at the University of Basel, Heidelberg Petersburg where he lived until his death in and Strasbourg. He earned a PhD in anatomy 1783. and botany in 1721. In 1724 Bernoulli was Besides formulating the very famous honored by the Académie des sciences in Paris. Bernoulli equation, Euler was also the first Being a close friend of Euler, Bernoulli decided scientist to describe the equations of mechanics to go to St. Petersburg in 1725 as a Professor of of fluids without friction. mathematics. In Russia he works a lot on his The other notable publications of Euler main scientific work titled Hydrodynamica include the following: Principles of Motion of (Hydrodynamics) . After having some health Fluids (1752), General Principles of State of problems, Bernoulli returns to Basel in 1733 Equilibrium of Fluids (1753) and General where he successfully worked as a Professor of Principles of Motion of Fluids (1755). anatomy, botany and physics at the University Euler considered pressure as a point of Basel until his death in 1782. property that could vary from point to point 3 GEORGES BRIDEL throughout a fluid flow. He derived the xm is the coordinate of the axis, which coincides differential equation, which describes the with the direction of the body movement. connection between pressure and velocity for Euler integrated the differential equations inviscid flow. In particular Euler equations (1), (2) and (4) yielding the first derivation of describe the conservation of mass (1), impulse what we call Bernoulli‘s equation. Therefore the (2) and energy (4): credit for Bernoulli‘s equation (6) should be ∂ ρ + ∇ V = 0 shared by Euler. ()ρ (1) 1 2 1 2 ∂t p1 + 2 ρV1 = p2 + 2 ρV2 (6) where: where: ρ is the density of the fluid; p1, p2 are the values of pressure in points 1 and t is the time, which is used to describe the 2 along the fluid flow; changes in the fluid flow; V1, V2 are the values of fluid flow speed in ∇ is the Hamiltonian operator for the three- points 1 and 2. dimensional space; Further application of Bernoulli’s equation V is the speed of the fluid flow. was made first by Joseph Lagrange, who first Du ∂p published his fundamental work on analytical ρ = − mechanics in 1788. Pierre-Simon Laplace made Dt ∂x simplifications and approximations of the Dv ∂p ρ = − (2) mentioned above equation and published his Dt ∂y works in 1789. And, of course, Claude-Louis- Dw ∂p Marie-Henri Navier and George Stokes were the ρ = − Dt ∂z ones to adduce the full equation of motion of fluid substances with taking into account the where: friction and thus extending Euler’s equations p is the pressure in the fluid flow; (around 1840).
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