6 War, flight and computing

In the 20th century fluid mechanics became a science of national power. Turbines and engines powered new industries; aircraft turned the boundary layer and the vortex into matters of life and death; two world wars poured money into wind tunnels and rocket test stands; and the collapse of empires sent scientists across the world, carrying their schools with them. After 1945 the electronic computer, itself born from wartime needs, began to solve the equations that had resisted mathematicians for two centuries, and in doing so rediscovered chaos. This chapter follows those threads up to the present, including the rockets that, in the 2020s, carried Korea’s own launch vehicle into orbit.

New industries: turbines, oil and the automobile¶

At the end of the 19th century, steam engines with pistons gave way to turbines, which turn the energy of a fast jet directly into rotation. In Sweden, Gustaf de Laval built a small, very fast impulse steam turbine and, around 1888, introduced the converging–diverging nozzle that accelerates steam to supersonic speed, the same shape used in every rocket engine today. In Britain, Charles Parsons (1854–1931) developed the multi-stage reaction turbine (1884), which expands steam gradually through many rows of blades. In 1897, at the naval review for Queen Victoria’s Diamond Jubilee at Spithead, his small turbine-driven boat Turbinia raced through the lines of warships at more than 34 knots, faster than any ship in the fleet. Within a decade turbines powered battleships, ocean liners and electrical power stations. Parsons also met a new hydraulic problem: at high speed, the low pressure behind his propeller blades made the water boil into vapor bubbles that collapsed violently. He built one of the first cavitation tunnels to study the phenomenon (1895).

Oil, a fluid fuel easy to store, pump and burn, transformed transport. Rudolf Diesel patented his compression-ignition engine in 1893; Henry Ford’s Model T (1908) made the automobile a mass product; navies converted from coal to oil before the First World War. The flow of air and fuel through carburettors, valves and cylinders, and the cooling of engines, became fields of engineering in their own right, and the lightweight gasoline engine made powered flight possible.

Learning to fly¶

The modern science of flight began with George Cayley (1773–1857), who in 1799 engraved on a silver disc a design separating the functions of an aircraft: a fixed wing for lift, a tail for control and a separate system for propulsion. His paper On Aerial Navigation (1809–1810) set out the basic principles, and in 1853 one of his gliders carried a person (reportedly his coachman) across a small valley.

In Germany, Otto Lilienthal (1848–1896) studied bird flight and measured the forces on curved wings, publishing Der Vogelflug als Grundlage der Fliegekunst (Bird Flight as the Basis of Aviation, 1889). Between 1891 and 1896 he made around two thousand glides from a hill near Berlin, controlling his gliders by shifting his body. Photographs of his flights circulated around the world. He died after a crash in 1896.

The bicycle makers Wilbur and Orville Wright of Dayton, Ohio, read Lilienthal and found that his tables of lift did not match their own gliders. In 1901 they built a small wind tunnel and measured the forces on some two hundred wing models, and they solved the problem of control by twisting (warping) the wings to bank the aircraft. On December 17, 1903, at Kitty Hawk, North Carolina, their Flyer, driven by a light engine and propellers they designed themselves, made the first controlled, sustained powered flights. Only nine days earlier, Samuel Langley’s government-funded Aerodrome had plunged into the Potomac for the second time.

Lift and circulation¶

Why does a wing lift? In England, Frederick Lanchester (1868–1946) argued in the 1890s that a wing produces lift by setting up a circulation of air around it, and that the circulation must leave the wing tips as trailing vortices. His book Aerial Flight (1907) was hard to read and little understood. Independently, two mathematicians found the quantitative law: Martin Wilhelm Kutta in Germany (1902) and Nikolai Zhukovsky (Joukowski) in Russia (1906).

The theorem revealed the role of the vortex in flight. In an ideal fluid, d’Alembert’s paradox forbids drag, but not lift: a wing can lift by carrying a “bound vortex.” And by Helmholtz’s theorems (see Chapter 4), a vortex cannot end in the fluid, so the bound vortex must continue as two trailing vortices from the wing tips. Prandtl’s lifting-line theory (1918–1919) used this picture to calculate the lift of a finite wing and its induced drag, the price paid for lift by shedding trailing vortices, which is smallest for long, slender wings with an elliptical distribution of lift. The theory explained why gliders and long-range aircraft have long wings, and why the wingtip vortices of a large aircraft are a hazard to the one behind it.

Zhukovsky, the “father of Russian aviation,” built one of the first wind tunnels in Moscow, and in December 1918, in the middle of the Civil War, he founded the Central Aerohydrodynamic Institute (TsAGI), which became the center of Soviet aeronautics.

The vortex of war¶

The First World War (1914–1918) turned the aircraft from a curiosity into a weapon. Governments founded research establishments: the British Advisory Committee for Aeronautics (1909), the American National Advisory Committee for Aeronautics, NACA (1915), and an expanded Göttingen laboratory under Prandtl. Thick wing sections, of the kind studied at Göttingen, gave the Fokker fighters of 1918 better climb and handling; Hugo Junkers built the first all-metal aircraft (1915). By the end of the war, aircraft design had moved from craftsmanship to wind-tunnel testing and calculation.

The fall of empires and the migration of scientists¶

The war destroyed four empires, Russian, Austro-Hungarian, German and Ottoman, and scattered their engineers. Igor Sikorsky, who had built the first four-engined aircraft in Russia (1913), left after the Revolution and founded his own company in the United States (1923), where he later developed practical helicopters. Theodore von Kármán, who had served in the Austro-Hungarian army’s aviation corps, briefly took part in the short-lived Hungarian revolutionary government of 1919 as an education official, returned to Aachen, and in 1930 accepted the direction of the Guggenheim Aeronautical Laboratory at the California Institute of Technology (GALCIT).

The Nazi seizure of power in 1933 drove out Jewish scientists and many others. The Göttingen school of mathematics was destroyed almost overnight; Richard Courant, Hermann Weyl, Emmy Noether and many others emigrated. Kármán, who was Jewish, stayed in the United States. Prandtl remained in Germany, where his institutes were greatly expanded for military research, and his record in this period, including letters in which he defended German policy to colleagues abroad, remains a subject of historical discussion. The migration brought the German traditions of aerodynamics and applied mathematics to the United States, which after 1945 became the center of the field.

The NACA meanwhile built a strong program of its own. Max Munk, a Prandtl student, designed its variable-density wind tunnel (1923), which reproduced the Reynolds numbers of full-size aircraft by testing models in compressed air; the NACA airfoil families of the 1930s were used around the world.

Liquidity and the Great Depression¶

The language of flow spread beyond physics. In economics, money and credit came to be described as liquid; markets have flows and circulation; crises begin when liquidity “dries up.” After the crash of 1929, the Great Depression showed what happens when money stops circulating. John Maynard Keynes’s General Theory of Employment, Interest and Money (1936) introduced liquidity preference, the desire of people to hold money rather than invest it, as a cause of persistent unemployment.

The analogy was made literal in 1949 by Bill Phillips, a New Zealand engineer turned economist at the London School of Economics, who built the MONIAC, a hydraulic computer of tanks, pipes and valves in which colored water represented the flow of money through the British economy: income, taxes, savings, investment and imports. Several machines were built for universities and central banks. Before electronic computers were widespread, water was used to simulate an economy.

The sound barrier and the jet engine¶

As aircraft became faster in the 1930s, the compressibility of air became important. At the 1935 Volta Conference in Rome on high-speed flight, Adolf Busemann proposed sweeping wings backward to delay the drag rise near the speed of sound; the idea was developed in secret in Germany and adopted widely after 1945. Kármán and his student Qian Xuesen derived the Kármán–Tsien rule (1939) for correcting pressures for compressibility.

The jet engine, a gas turbine driving air through a nozzle, was invented independently by Frank Whittle in Britain (patented 1930) and Hans von Ohain in Germany, whose engine powered the Heinkel He 178 on the first jet flight on August 27, 1939, days before the Second World War began. On October 14, 1947 Chuck Yeager flew the rocket-powered Bell X-1 faster than sound, demonstrating that the “sound barrier” could be crossed safely.

The politics of rockets¶

The rocket equation was published in 1903 by the Russian schoolteacher Konstantin Tsiolkovsky:

In the United States, Robert Goddard (1882–1945) published A Method of Reaching Extreme Altitudes (1919), was ridiculed by the New York Times for suggesting that a rocket could work in the vacuum of space (the paper printed a correction in 1969, as Apollo 11 flew to the Moon), and launched the first liquid-fueled rocket on March 16, 1926 in Auburn, Massachusetts. In Germany, Hermann Oberth’s book Die Rakete zu den Planetenräumen (The Rocket into Planetary Space, 1923) inspired an amateur rocket society. One of its young members, Wernher von Braun, joined the army’s rocket program in 1932. At Peenemünde on the Baltic, his team developed the A-4 ballistic missile, used from September 1944 as the V-2 against London and Antwerp. It was produced in underground factories by concentration camp prisoners, thousands of whom died; more people were killed building the V-2 than by its use as a weapon.

At Caltech, in 1936, a group of students and enthusiasts around Frank Malina, Jack Parsons and Qian Xuesen, under Kármán’s protection, began testing rocket motors in the Arroyo Seco near Pasadena. Their work produced jet-assisted take-off units for aircraft during the war and, in 1944, the Jet Propulsion Laboratory, which later built America’s first satellite, Explorer 1 (1958), and its planetary probes. At the end of the war, Kármán and Qian, in uniform, interviewed German scientists including Prandtl and von Braun. Von Braun and many of his team were brought to the United States, where they built the Saturn V rockets of the Apollo program. In the Soviet Union, Sergei Korolev, who had survived imprisonment in the Gulag (1938–1944), led the program that launched Sputnik on October 4, 1957 and Yuri Gagarin in 1961.

Qian Xuesen (1911–2009), one of Kármán’s most brilliant students and a co-founder of JPL, was accused during the anti-communist campaigns of the early 1950s of communist sympathies, had his security clearance revoked in 1950, and was held under restrictions for five years. In 1955 he was deported to China, where he led the development of China’s ballistic missiles and space program. A US Navy official is reported to have said that he would rather shoot Qian than let him leave, because he was worth five divisions. The story is often told as an example of how politics, not only science, decides where knowledge flows.

From Richardson’s dream to the computer¶

During the First World War, Lewis Fry Richardson (see Chapter 5) calculated by hand, over many weeks, a six-hour forecast of the pressure change over central Europe, using the equations of fluid motion. His result, a pressure rise of about 145 hPa in six hours, was wildly wrong, mainly because of imbalances in the initial data. But in Weather Prediction by Numerical Process (1922) he imagined a “forecast factory” in which some 64,000 human computers, coordinated by a conductor, would calculate the weather faster than it happened.

The machine to realize the dream came from the war. ENIAC, the first general-purpose electronic computer, was built at the University of Pennsylvania (completed 1945) to calculate artillery firing tables, an old problem of fluid resistance going back to Robins and Euler (see Chapter 3). The mathematician John von Neumann (1903–1957), who had worked on shock waves and implosions for the atomic bomb at Los Alamos, saw that the computer could solve nonlinear problems in fluid dynamics that no analysis could reach, and chose weather forecasting as a showcase. In 1950 Jule Charney, Ragnar Fjørtoft and von Neumann made the first successful numerical weather forecasts on ENIAC, using a simplified equation that filtered out the fast waves that had ruined Richardson’s calculation. A 24-hour forecast took about 24 hours to compute.

Computational fluid dynamics (CFD) grew from these beginnings. Richard Courant, Kurt Friedrichs and Hans Lewy had already found in Göttingen (1928) the stability condition that limits the time step in such calculations (the CFL condition). At Los Alamos, Francis Harlow’s group developed the particle-in-cell (1955) and marker-and-cell (1965) methods; Sergei Godunov in Moscow (1959) created a method for shock waves; Joseph Smagorinsky (1963) introduced a sub-grid model for weather and climate simulations, the beginning of large-eddy simulation; and Steven Orszag and George Patterson (1972) made the first direct numerical simulation of turbulence. Today the Navier–Stokes equations are solved every day to design aircraft, cars, turbines, pumps, dams, spillways and to forecast floods and weather.

Chaos rediscovered¶

In 1961 Edward Lorenz (1917–2008), a meteorologist at MIT, was running a simple model of atmospheric convection on a small computer. Restarting a run from printed numbers rounded to three decimal places, he found that the new solution soon diverged completely from the old one. In 1963 he published Deterministic Nonperiodic Flow, showing that a system of only three equations, derived from a model of fluid convection, can have solutions that never repeat and are extremely sensitive to initial conditions, wandering on what was later called a strange attractor. In a 1972 talk he asked whether the flap of a butterfly’s wings in Brazil could set off a tornado in Texas.

Lorenz’s discovery, together with Poincaré’s earlier insight (see Chapter 5), set limits on the predictability of the weather, about two weeks for day-to-day detail, and led to ensemble forecasting. It also inspired the science of chaos in the 1970s and 1980s, which found universal routes to irregular behavior in dripping taps, convection cells and fluid flows between rotating cylinders. Heraclitus’s river, always changing yet always the same, had found a mathematical form.

Korea’s rocket: Nuri¶

The story of rocketry has a recent Korean chapter. For decades, bilateral missile guidelines agreed with the United States limited the range of Korean missiles and constrained the development of solid-fuel rockets; the last of these restrictions was lifted in May 2021. Korea developed its own space launch vehicle, Nuri (KSLV-II), a three-stage rocket powered by Korean-designed liquid-fueled engines: four engines of 75 metric tons of thrust in the first stage, one in the second stage, and a 7-metric-ton engine in the third. Its turbopumps, which drive kerosene and liquid oxygen into the combustion chambers at high pressure, are among the most demanding pieces of fluid machinery in any engine. The first launch, on October 21, 2021, reached the target altitude but the dummy satellite did not reach orbital velocity because the third stage shut down early. The second launch, on June 21, 2022, placed satellites in orbit, making Korea the seventh country to launch a satellite of more than one metric ton with its own rocket. A third launch in May 2023 deployed working satellites.

From Hero’s aeolipile to Nuri’s turbopumps, the problem has remained the same in essence: turning the energy of a fluid into controlled motion.

Summary¶

Turbines (de Laval, Parsons), oil and the automobile created new industries and new fluid problems such as cavitation.
The Wrights achieved controlled powered flight (1903); Kutta, Zhukovsky and Prandtl explained lift and induced drag through circulation and trailing vortices.
The world wars and the collapse of empires reorganized aeronautics around state laboratories and moved scientists across the world.
Rocketry, from Tsiolkovsky and Goddard to the V-2, JPL, Sputnik and Qian Xuesen, was shaped by politics as much as by science.
The computer, born from ballistics and weapons research, made numerical weather prediction and CFD possible; Lorenz rediscovered chaos in a model of convection.