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FROM BASEL TO ST. PE TERSBURG AERONAUTICAL AND SCIENTIFIC MILESTONES: AND 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 . 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 mechanics L. Prandtl and N. I. Zhukovsky created modern theory. aeronautical . Both scientists have given their names to Their successors were and fundamental equations, which are used today to scientists as well: the professors Chaplygin and Ackeret had made important contributions to demonstrate the () conservation aerospace science, development of transonic in and model the inviscid fluid flow. Both 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 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 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 while developing wave theory and human flying started only after 150 years passed kinetic theory of . since the creation of the first and fundamental In 1760 he also became engaged a lot with laws of ?”. It seems obvious that astronomy and, in particular, conducted the early flight was much more the undertaking of observations of Venus’ . 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. , , 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: 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 , 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 (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 and Mecanica (Mechanics) is the most important 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 . mathematics. In Russia he works a lot on his The other notable publications of Euler main scientific 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

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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 (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 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). x,y,z are the coordinates along the axes, which form a three-dimensional coordinate system used for the 4. Successors description of changes of properties within the fluid flow; u, v, w are the components of the fluid flow 4.1 Sergey Chaplygin (1869 – 1942) velocity vector V (3): u    V = v  (3)   w

D(e +V 2 2) ρ = −∇()pV (4) Dt where: e is the energy of the fluid flow. These equations are based on second Newton's law (5): d 2 x F = M m (5) dt 2 where: F is the force, which is applied to the body; M is the mass of the body;

Fig. 5: Sergei Chaplygin

4 FROM BASEL TO ST. PE TERSBURG

University was afterwards divided into a Chaplygin (shown in Fig. 5) was born in number of large independent Universities, Ranenburg (Ryazan province) in 1869. He which still exist today. graduated from Moscow University in 1890. In 1918 Chaplygin was invited by The Doctor thesis of Chaplygin, which he Zhukovsky to start work on the creation of defended 1902, About streams has TsAGI (Ts entralniy Aero gidrodinamicheskiy illustrated the possibility of reducing the general Institut). problem of stationary two-dimensional In 1924 he was elected as a corresponding isentropic movement of compressible gas to the member of the Russian Academy of Sciences solution of one linear partial differential and got full member status in 1929. equation (7). This publication was one of the In 1928-1931 Chaplygin was the Director founding works of gas dynamics. of TsAGI. ∂2 Φυ 2 ∂ 2 Φ ∂Φ In 1931-1941 Chaplygin was in charge of + +υ = 0 (7) ∂Θ2υ 2 ∂υ 2 ∂ υ the creation of TsAGI aerodynamics 1− c2 laboratories. In 1910 Chaplygin provided an analytical where: derivation for the Zhukovsky law formula (13): Θ is the angle between the fluid particle F=−ρ V ×Γ l velocity and x-axis; gas gas ∞ (13) υ is the fluid particle speed; where: F c is the speed of sound; lift is the lifting force; Φ is the function, which is defined by equation ρ is the density of the gas; (8): gas Φ=− + + V ∞ is the velocity of undisturbed uniform gas ϕx υx y υ y (8) gas where: flow; ϕ is the velocity potential, which is defined by Γ is the of gas flow velocity; equation (9): l is the length of the wing section, which is ∂Φ perpendicular to the plane that contains ϕ= −Φ − υ (9) ∂υ the profile cross-section. x, y are the coordinates of the fluid particle, Simultaneously with Zhukovsky himself which are calculated according to the Chaplygin proved that circulation Г in the system of equations (10): Zhukovsky law is uniquely determined by the  ∂Φ ∂Φsin Θ ∂Φ finiteness of the speed at the trailing edge of the x = =cos Θ − wing profile (this statement is now known as  ∂υ ∂ υ υ ∂Θ  x Zhukovsky – Chaplygin postulate).  (10) ∂Φ The postulate goes as follows: “Of all y = =sin Θ  ∂υ possible kinds of streamlining of a sharp trailing  y edge wing the only ones, which are υ, υ x y are the components of fluid particle implemented in nature, are those that provide velocity vector, which are calculated finite values of the trailing edge speed.” according to equations (11) and (12): In 1913 Chaplygin published one of the

υx = υ cos Θ (11) world’s first works in the finite span wing υ= υ sin Θ (12) theory. He made the emphasis on taking the tip y vortices into the account. From 1893 Chaplygin taught mechanical Chaplygin also attempted to derive the engineering and applied mathematics at several lifting force and induced drag formulas. The educational institutions including Moscow State results of his research were not confirmed by University. Zhukovsky experiments, but were afterwards In 1918-1919 Chaplygin was the first nd used in “Prandtl’s inductive theory”. Rector of the 2 Moscow State University. This

5 GEORGES BRIDEL

In 1919 Chaplygin offered a method of approximate integration of differential equations while proving an original inequality theorem (“Chaplygin theorem”). Chaplygin headed the group of scientists from TsAGI, who founded SibNIA in 1941, and died in Novosibirsk in 1942. Fig. 7: Visualization of supersonic stream 4.2 Jakob Ackeret (1898 – 1981) similar to the experiments which were carried out by , leading Ackeret to introduce the Mach-number for the relationship between speed of the projectile and the speed of sound [3]

The simplification of the non-linear Euler equations for inviscid flow finally led to the simple linear equations (14) and (15), which can be used for calculation of lift and drag coefficients in a supersonic flow for thin airfoils at small angles of attack: 4α C = 1/2 (14) l V 2 −1 ()gas ∞

Fig.6: Jakob Ackeret where: Cl is the lift coefficient; Ackeret (shown in Fig. 6) was born in Zurich, α is the angle of attack; V 2 Switzerland, in 1898. He received his diploma gas ∞ is the speed of undisturbed uniform flow. in mechanical engineering and a doctorate from f(α, t ) ETH Zurich (Swiss Federal Institute of C = (15) d 2 − 1/2 Technology) in 1920 where he worked as an ()Vgas ∞ 1 assistant of Professor Stodola. Since 1921 where: Ackeret worked on aerodynamic research and Cd is the drag coefficient; became a department head in Göttingen under fα, t is some function of the angle of attack the supervision of Professor L. Prandtl. ( ) Returning to Switzerland in 1927 Ackeret and body shape/thickness (the values of became chief at the Escher-Wyss this function and their distribution company and in 1930 he created the Institute of depend on the shape of the body) Aerodynamics at the ETH and habilitated as a At the ETH Ackeret designed, built and Professor there. operated the world’s first supersonic closed- Ackeret was one of the pioneers in the circuit wind tunnel (shown in Fig. 8), which was theoretical and experimental investigation of driven by one of the first multi-stage axial supersonic flow about airfoils and in wind compressors ever created. Such compressor tunnels. In 1925 he published the small permitted independent variation of the values of perturbation theory of supersonic flow of a Reynolds and Mach numbers. Soon afterwards a perfect gas over a thin airfoil, which is often similar wind tunnel was built according to described as "Ackeret Theory". Fig. 7 illustrates Ackeret’s design in Guidonia, Italy. This tunnel the experiments, which were carried out by was capable of attaining Mach 4. Ackeret Ackeret in this field. introduced the term “Mach number” at his inaugural lecture at the ETH in 1929, which was first published in the SBZ (Ref. 3).

6 FROM BASEL TO ST. PE TERSBURG

By the beginning of WW II Ackeret was Publishing House. 1986, The Chaplygin Equation, the leading European authority on supersonic General problem of two-dimensional stationary motion of compressible gas flows. [3] J. Ackeret, Schweizerische Bauzeitung Bd. 94 1929, Ackeret died in Küsnacht, Switzerland in Der Luftwiderstand bei sehr grossen 1981. Geschwindigkeiten. [4] N. Rott, Ann. Rev. Fluid Mech. 1985.17: 1-9 Jakob Ackeret and the History of the Mach Number [5] A. Flax, National Academy of Engineering of the USA, Memorial Tributes, Vol. 8 1996, Jakob Ackeret.

6 Contact Author Email Address

Georges Bridel, PhD, ALR Aerospace Project Development Group, Zurich

Fig. 8: The first closed-cycle supersonic wind tunnel at [email protected] the ETH in Zurich, 1934. www.alr-aerospace.ch

5 Conclusions The author expresses his thanks for support from M. Sc. Pavel V. Zhuravlev, Moscow. Advances in research and development are often made in parallel. This was shown above on the 7 Copyright Statement examples of some great scientists. These The authors confirm that they, and/or their company or scientists have sometimes worked organization, hold copyright on all of the original material independently and sometimes collaborated in included in this paper. The authors also confirm that they have obtained permission, from the copyright holder of close contact while attaining these results. any third party material included in this paper, to publish The early scientists were active in an it as part of their paper. The authors confirm that they extremely broad field: they worked and were give permission, or have obtained permission from the famous as scientists, artists, writers, poets. copyright holder of this paper, for the publication and With time progressing, the scientists distribution of this paper as part of the ICAS 2014 proceedings or as individual off-prints from the became more specialized in one area of physics proceedings. (e.g. fluid mechanics). They also very often worked as engineers (Ackeret) and stimulated designs or managed institutes directly (Chaplygin). Fundamentally, scientists needed an excellent environment (St. Petersburg) and continuous exchange of information and experience (Lomonosov, Bernoulli, Euler, Ackeret) to produce the appropriate results. ICAS always was and still remains in the tradition of such information exchange experience and environment.

References

[1] John D. Anderson jr. A History of Aerodynamics and its importance for Flying Machines, Cambridge University Press 1997 [2] L.D. Landau, E.M. Lifshits. . IV. Hydrodynamics. Moscow. Nauka

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