Why do planes fly?

c.1010

1. Early 11th century

   The monk who forgot the tail

   Eilmer, a monk of Malmesbury Abbey in England, straps wings to his hands and feet, jumps from a tower and glides “more than the distance of a furlong” before crashing and breaking both legs. A chronicler of the same abbey records his diagnosis about a century later: he had forgotten to put a tail on the back.1William of Malmesbury, Gesta Regum Anglorum II §225 (c. 1125), translated by Lynn White Jr., Technology and Culture 2 (1961). The date of the jump is White’s inference. The Ibn Firnas story comes from al-Maqqari, who died in 1632. A similar story is told of Abbas ibn Firnas in 9th-century Córdoba, in a source written 750 years after the fact. In both tellings a missing tail gets the blame, which is a problem of stability, not of lift.

2. c. 1486–1505

   Leonardo turns the problem around

   

   Leonardo da Vinci fills notebooks with flying machines and, around 1505, a whole codex on the flight of birds. Two of his notes are startlingly modern. “An object offers as much resistance to the air as the air does to the object”, a glimpse of action and reaction two centuries before Newton. And moving an object through still air is the same as moving air past a still object, which is the principle every wind tunnel relies on.2Codex Atlanticus f. 381v-a (c. 1486–90), in J. P. Richter’s translation; the relative-motion note is f. 180r-a (1505). The Codex on the Flight of Birds (1505–06) is in the Biblioteca Reale, Turin.

3. 1687

   Newton’s particles

   

   In the Principia, Isaac Newton models a fluid as a stream of particles striking a body, which makes the force on a tilted surface depend on the square of the sine of its angle. It badly underestimates the lift at small angles. In 1891 Samuel Langley measured twenty times more lift at 5° than the formula allowed, and later historians blamed it for discouraging would-be aviators.3Newton, Principia (1687), Book II, Prop. XXXV (XXXIV in later editions). S. P. Langley, Experiments in Aerodynamics (1891), pp. 24–25. That the formula held back flight is widely asserted by historians but rarely pinned on anyone in particular.

4. 1738–1757

   Bernoulli’s equation, which is Euler’s

   Daniel Bernoulli’s Hydrodynamica (1738) links the pressure of moving water to its speed, but the tidy “Bernoulli equation” printed in every textbook isn’t in it. Leonhard Euler wrote it down in the 1750s, as part of the first complete equations of an ideal fluid. Hydrodynamica says nothing about wings: the only “wings” in it are the sails of windmills.4D. Bernoulli, Hydrodynamica (1738). L. Euler, “Principes généraux du mouvement des fluides”, Mémoires de l’Académie de Berlin 11 (1757). C. Truesdell (1953): the equation “was first written down by Euler”.

5. 1749–1768

   The paradox of the perfect fluid

   Jean le Rond d’Alembert works out that, at least in several cases, a body moving steadily through a perfectly frictionless fluid feels no resistance at all, which is plainly false. “A singular paradox,” he writes in 1768, “which I leave to the geometers to clear up.” The same theory also gives no lift, a puzzle that takes until the 1900s to resolve.5J. le R. d’Alembert, Opuscules mathématiques, vol. V (1768), p. 138: “paradoxe singulier que je laisse à éclaircir aux Géomètres”. He had met the result in 1749–52 and set it aside as contrary to experience.

6. 1799–1853

   Cayley invents the aeroplane

   

   George Cayley, a Yorkshire baronet, engraves a small silver disc. One side shows a fixed wing with a separate means of propulsion and a tail; the other shows the air’s force on a tilted surface split into lift and drag. Ten years later he states the whole problem in one line: “To make a surface support a given weight by the application of power to the resistance of air.” Around 1853, by a family account, one of his gliders carried a man across a small valley. Decades later his granddaughter recalled the pilot, Cayley’s coachman, climbing out to give notice: he had been “hired to drive and not to fly.”6The disc is in the Science Museum, London (object 1935-283). G. Cayley, “On Aerial Navigation”, Nicholson’s Journal of Natural Philosophy (1809–10). The coachman story rests on a recollection his granddaughter wrote down in 1921; who actually flew is disputed.

7. 1822–1845

   The equations that contain everything

   Claude-Louis Navier in Paris and George Gabriel Stokes in Cambridge independently add friction to Euler’s equations. The Navier–Stokes equations describe the flow around a wing in full detail, and they still do: every serious simulation of a wing is built on them. Their sheer completeness is part of the problem. They contain the answer without stating it. In an irony nobody planned, Navier also wrote, with two colleagues, an 1829 report for the French Academy that dismissed the idea of a man flying by flapping wings. It became a standard authority on flight for decades.7C.-L. Navier, read to the Académie des sciences on 18 March 1822. G. G. Stokes, read in Cambridge on 14 April 1845. The 1829 Académie report, by Navier with Gay-Lussac and Flourens, concerned human flight by flapping; Langley (1891) wrote that it “became a standard authority upon the theory of flight”.

8. 1871–1884

   Wind tunnels, and the first argument about why

   Francis Wenham and John Browning build the first wind tunnel: a trunk eighteen inches square and ten or twelve feet long (accounts differ), blown by a steam-powered fan. Flat plates tilted at small angles lift far more than Newton’s formula allows. In 1884 Horatio Phillips patents curved “blades for deflecting air”; the patent’s official summary explains that “a vacuum is formed over the blades”. In 1896 Hiram Maxim objects that the air is really being thrown downward. That’s the Bernoulli-versus-Newton argument, years before the first powered flight.8Aeronautical Society of Great Britain, Sixth Annual Report (1871). H. Phillips, British Patent 13,768 (1884). H. Maxim, “Natural and Artificial Flight”, The Aeronautical Annual (1896).

9. 1891–1896

   The glider king

   

   Otto Lilienthal publishes Birdflight as the Basis of Aviation and then does what no theorist does: he jumps off hills, over two thousand times, with gliders of his own design. His tables of lift become the world’s best data. On 9 August 1896 a gust stalls his glider fifteen metres up. He dies in Berlin the next day.9O. Lilienthal, Der Vogelflug als Grundlage der Fliegekunst (1889). Otto Lilienthal Museum, Anklam. The words often given as his last, “Sacrifices must be made”, first appear in print in 1930, 34 years after his death.

10. 1896–1903

    The experts weigh in

    Lord Kelvin, the most celebrated physicist in Britain, declines to join the Aeronautical Society in 1896: “I have not the smallest molecule of faith in aerial navigation other than ballooning.” In October 1903 the astronomer Simon Newcomb explains why a flying machine could never land safely: “How is he ever going to stop?”10Kelvin to B. F. S. Baden-Powell, 8 December 1896. S. Newcomb, “The Outlook for the Flying Machine”, The Independent, 22 October 1903. Newcomb’s better-known claim that the impossibility had been demonstrated appears in his 1906 book, after the Wrights had flown; it is not in his 1901 or 1903 articles.

11. 9 October 1903

    One million to ten million years

    

    Samuel Langley’s Aerodrome, funded with $50,000 of government money, is catapulted off a houseboat on the Potomac and drops straight into the river. Two days later The New York Times sneers that a flying machine that really flies might be evolved by mathematicians and mechanicians “in from one million to ten million years”. Langley tries again on 8 December, with the same result.11“Flying Machines Which Do Not Fly”, The New York Times, 9 October 1903, p. 6, written in sarcasm after Langley’s first crash. Scan at archive.org. The Smithsonian’s museum now calls the Aerodrome “structurally weak and unsound”.

12. 17 December 1903

    Sixty-nine days later

    

    At Kill Devil Hills, North Carolina, Orville Wright lifts off at 10:35 in the morning into a gusty headwind of 20 to 27 mph. He stays up for about 12 seconds and covers 120 feet. By noon Wilbur flies for 59 seconds and 852 feet. John T. Daniels, a crewman from the nearby lifesaving station, snaps their camera just as the machine leaves its rail, taking the most famous photograph in aviation.12Orville Wright’s diary for 17 December 1903, and his account “How We Made the First Flight” (1913). The glass-plate negative of the photograph is in the Library of Congress.

    

    The Wrights didn’t get there with better theory. They had built a wind tunnel in 1901, after their gliders lifted barely a third of what the published tables promised, tried some two hundred wing shapes and measured nearly fifty systematically. The standard textbook constant for air pressure turned out to be about 50% too large. “Having set out with absolute faith in the existing scientific data,” they wrote, “we were driven to doubt one thing after another.”13W. Wright, “Some Aeronautical Experiments” (1901). O. and W. Wright, “The Wright Brothers’ Aeroplane”, The Century Magazine 76 (1908). The traditional coefficient of 0.005 came from a table John Smeaton printed in 1759; the Wrights measured about 0.0033.

13. 1894–1918

    Theory catches up

    Frederick Lanchester in England works out that a wing flies by making the air circulate around it, and that its tips must shed swirling vortices. The Physical Society of London rejects his paper in 1897. In Germany Martin Kutta (1902) calculates the lift of a curved plate by insisting that the flow leave its sharp edges smoothly. In Russia Nikolai Joukowski (1906) proves the general theorem tying lift to circulation. Ludwig Prandtl adds the thin, sticky boundary layer next to the surface (1904) and, in Göttingen, a complete theory of finite wings (1918–19). For more than a decade, British experts resisted the German circulation theory.14F. W. Lanchester, Aerodynamics (1907), §108. W. M. Kutta, Illustrirte Aëronautische Mittheilungen 6 (1902). N. Joukowski (1906). L. Prandtl (1904; 1918–19). D. Bloor, The Enigma of the Aerofoil (University of Chicago Press, 2011).