As in “Fluid-Dynamic Drag”, this first chapter is intended to be some introduction as to the physical principles involved in the flow of fluids, and about airplanes in particular: The chapter also presents necessary and/or useful information on conventional definitions and physical properties. In doing so, duplication of the “general” chapter in “Fluid-Dynamic Drag” (1) has been minimized.


During the last decade or so, interest and effort in the United States have largely been shifted from aeronautics to astronautics (from atmospheric to space flight). Except for the deeds of the Wright Brothers (17 December 1903), and their own experiences as airline passengers, not all of our aerospace engineers may know much about the art of aerodynamic airplane design.

Heavier Than Air. We will not bother you with Leonardo da Vinci (1452 to 1519) or the balloonists (since 1783), not to mention kites (which may be 1000’s of years old) or birds (22) at that. The most prominent among the “modern” aerodynamic experimenters was Otto Lilienthal (2,b). Between 1891 and 1896, he made some 2000 gliding flights, down the side of a hill. Samuel P. Langley (then Director of the Smithsonian Institution) flew a steam-powered model airplane in 1896; and one with a gasoline engine in 1903. During all this time, stabilizing tail surfaces were used; and it is the Frenchman Penaud, who is reported to have invented the elevator, and to have combined it with the control of a rudder in a “stick” (1872 or 1876). The Wright Brothers invented the аііегол, by warping the ends of their wings.

(1) Hoerner, "Fluid-Dynamic Drag". 1958 and 1965 Editions, published by the author

Aerodynamic Theory in modern form, may have begun with Newton (Professor of Mathematics, 1642 to 1727). However, the largest steps forward have been the concept of the limited boundary layer (1904) promoted by Ludwig Prandtl (1875 to 1953) and his induced-drag formulation (before 1918). An equally famous aerodynamic scientist was Theodore von Karman (1881 to 1962) particularly known for his work on turbulent skin friction and in gasdynamics (3,e). Others instrumental in the development of modern knowledge in the field of fluid dynamics, listed in (1) have been:

Will Froude (1810 to 1879) dynamic Froude similarity

Osborne Reynolds (1842 to 1912) similarity of viscous flow N. E. Joukovsky (1847 to 1921) airfoil-section theory

F. W. Lanchester (1868 to 1945) flight mechanics

Still others are acknowledged in (2,d).

Wind Tunnels. Experiments, by means of arms rotating models through thq air (Lilienthal) or by moving them through water (towing tanks) were undertaken before 1900. Then came a period, particularly characterized by Gustave Eiffel (1832 to 1923) where wind tunnels (6) were built and used to find empirical forces such as the lift of wings. Then, persons such as Prandtl and his many associates tried to analyze the potential flow around wings. Subsequently, hundreds of wind tunnels such as in (4,d) proved that the theories were not quite right. As a consequence, 1000’s of tunnel investigations were undertaken. In fact, full-scale tunnels were built, at least in France and in the United States (6,c), where real airplanes could be tested, to finally arrive at the truth of aerodynamic forces and moments. However, all tunnels are limited in size, speed, pressure, temperature, quality of the stream, or at least half of these parameters. Theory and/or empirical calibration, is therefore required to “correct” the findings obtained in wind tunnels:

(2) History of aerodynamic airplane development:

a) History of Flight, American Heritage (Simon A Schuster) 1962.

b) Lilienthal. “Vlgelflug als Grundlage der Fliegekunst", Ber­lin 1889.

c) Octave Charmte, “Progress in t h ing Machines". 1 894.

d) Hunsaker and Doolittle, To 195 8. NAC A La-.t Annual Rpt (1958).

a) Turbulence (6,g). The flow of air in a wind tunnel is more or less turbulent. The acoustic noise from the fan driving the stream of air, is already sufficient to precipitate turbulence in an otherwise laminar boundary layer, in particular around the nose of an airfoil section.

b) Stimulation of boundary layer turbulence (by stream turbulence or by surface roughness on the model ) is very often desirable to produce at least qualitatively, flow pattern and forces as at highter Reynolds numbers.

c) Induced Angle. Elaborate methods have been developed and “verified” to account for the influence of toe tunnel walls (or the absence of them) upon the induced angle of attack of wings.

d) Blockage. When placing an obstacle within a duct (such as the test section of a wind tunnel) a pressure drop necessarily develops, from a higher level (ahead of the model) to a lower level (behind the model). Not only drag, but also lift is thus affected.

While all these considerations are of little or no consequence, within the range of smaller lift coefficients and larger tunnels, they can be problematic at higher coefficients (including CL)< ) and particularly in regard to the longitudinal (pitching) moment. [1] [2] [3]

High Reynolds Numbers. Researchers such as Eiffel and Prandtl started out with R’numbers (on wing chord) around 10 . We now have test results up to 107. In the quest for higher Reynolds numbers, the speeds of wind tunnels have been increased over the years (this leads to compressibility effects), the size has been increased up to 240 m2 (= 2500 ft2) test-cross-section area (which results in expensive and hard to manage facilities), and the tunnel pressure has been increased in a few installations (thus increasing the air density in the Reynolds number). The last method leads to a very interesting phenomenon. As pointed out in chapter V of “Fluid-Dynamic Drag”, the permissible surface roughness of the wing models to be investigated, is among others к ^ l/^>. So, for a tunnel pressure of 10 at (instead of one at) that size is only 1/10 of that in atmospheric air (provided that temperature and speed are the same). Besides the British Compressed Air Tunnel, an extreme example is or was the NACA’s Vari­able Density Tunnel. For a maximum pressure of 20 atmospheres, at a speed of 8 m/s (= 26 ft/sec) the maxi­mum permissible “sand” grain size is in the order of 0.01 mm. For comparison, this is between the optimum possi­ble painted, and the average paint-sprayed surface of air­planes. Of course, a metal surface can be polished down to a grain size of one micron (= 1/1000 of a mm). However, erosion by dust particles usually present in wind tunnels, can be expected to produce roughness much larger than one micron during the testing of a model. In fact, the tunnel discussed is no longer listed as active in (6,d). We are tempted to use the many published reults from that tunnel, however. In conclusion, a little better thinking can be more important than a lot of “fruitless air blowing” (quoted from Munk, J. Aeron Sci 1938 p 241). To say the least, test conditions have to be judged when using wind – tunnel results. One can also say that applied fluid dynam­ics is to some degree an art (rather than a science); and in the words of Philip von Doepp (Junker’s last chief aero- dynamicist), “the air is a beast”, meaning that we must always be prepared for an unexpected result.

Aviation. Since the days of Lilienthal and the Wright Brothers, aviation has grown from a possible 30 people involved, at one and the same time, to more than 30,000 members of the American Institute of Aeronautics and Astronautics alone. The number of employees of the big airplane (and space) companies may be above 100,000 each. The number of airplanes produced during WW II was in the order or 300,000. The number of passenger miles is now in excess of 40 billion per year. In the words C. S. Gross (Lockheed Aircraft Corporation) all this may only be the beginning of atmospheric aviation. It is possible that now after reaching the moon (and finding nothing there but clues as to the nature of the Universe), that technological interest will really return to safe and low cost mass transportation from New York to London or San Francisco as well as other nearby cities.

Mathematics. Ever since Newton (around 1700), mathe­matics have been a useful tool in the exploration of fluid dynamics. It must be said, however, that Newton’s theory of particle flow (although correct at the boundary of outer space, see chapter XIX of “Fluid-Dynamic Dreg”) was erroneous as far as atmospheric airplanes are con­cerned. This did not prevent civil engineers from applying results of that theory in building codes, for a period of 200 years. Contrary to the belief of many, Einstein was originally and primarily a physicist (with imagination). He had to learn and use mathematics, however, as a tool to bring order and system into his theories. Today we have computers speeding up the work not only of mathematics, but also of your supermarket. This book only uses h gh – school mathematics. The point is to encourage the de­signer of airplanes (and similar contraptions) to think in terms of force, power, moment, equilibrium, as the Wright Brothers, or men such as Ludwig Prandtl. did. Instead of depending on the results for computer studies, the engi­neer should in many cases study the problem and conduct the necessary simple calculations to obtain answers.. This is important as many of the computer programs are long and complex with only the initial programmer and the engineers involved able to understand the program, its limitations and results. By conducting his own calcula­tions and knowing the many assumptions and empirical data, the background necessary to apply the computer programs is obtained with a much better understanding of the results. The computer programs then become ex­tremely valuable and, with proper testing, lead to the best overall solution. In conclusion, a sound combination of analysis (mathematics), experience and experiment v/ill lead to the most satisfactory engineering results.

(5) The most important research reports come from:

a) National Advisory Committee for Aeronautics (since 1915).

b) National Aeronautics and Space Administration (since 1959).

c) British Aeronautical Research Council; Brit Info Service New York City. [4]

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