#### Theories of Flight - An Overview

During the centuries before the Wright brothers' first flight in 1903, physical scientists had developed a large body of theory concerning fluid flow. Much of their work had focused on understanding the flow of water, and incompressible fluid, and the science of fluid flow was originally called hydrodynamics. Only a small number of these researchers were interested in studying airflow, largely because human flight was believed to be impossible. Yet because air and water are both fluids, some important concepts for the science of aerodynamics came from studies of water.

The first of these was Bernoullli's Principle, which states that in a fluid in motion, as the fluid's velocity increases, the fluid's pressure decreases. Derived by Daniel Bernoulli during the 1730s from an examination of how water flowed out of tanks, this principle is often used (not entirely correctly) to explain how wings generate lift. Because of the way wings are shaped, air flowing across the top of the wing must move faster than the air across the wing's bottom. The lower air pressure on top of the wing generates a “suction” that lifts the airplane. Bernoulli's principle was an incomplete description of how lift works, but it was a beginning.

Bernoulli's student, Leonhard Euler, made what was probably the 18th century's most important contribution to 20th century aerodynamics, the Euler equations. During a 25-year period in St. Petersberg, Russia, Euler constructed a set of equations that accurately represent both compressible and incompressible flow of any fluid, as long as one can assume that the flow is inviscid—free of the effects of viscosity. Among other things, Euler's equations allow accurate calculation of lift (but not drag). The equations were published in a set of three papers during the 1750s and were well known to individuals interested in experimenting with flying machines later in that century, such as George Cayley. Unfortunately, neither Euler nor anyone else had able to solve the equations during the 18th or early 19th centuries. This did not stop theoreticians from continuing to seek yet more powerful analytic descriptions of fluid flows. The key issue missing from Euler's description of fluid motion was the problem of friction, or what modern aerodynamicists call skin drag. During the early 19th century, two mathematicians, Frenchman Louis Navier and Englishman George Stokes, independently arrived at a set of equations that were similar to Euler's but included friction's effects. Known as the Navier-Stokes equations, these were by far the most powerful equations of fluid motion, but they were unsolvable until the mid-20th century.

The unsolvability of the highly complex Euler and Navier-Stokes equations led to two consequences. The first was that theoreticians turned to trying to simplify the equations and arrive at approximate solutions representing specific cases. This effort led to other important theoretical innovations, such as Hermann von Helmholtz's concept of vortex filaments (1858), which in turn led to Frederick Lanchester's concept of circulatory flow (1894)and to the Kutta-Joukowski circulation theory of lift  (1906). (see fig)  The second consequence was that theoretical analysis played no role in the Wright brothers' achievement of powered flight in 1903. Instead, the Wrights relied upon experimentation to figure out what theory could not yet tell them.

Experimentation with airfoil shapes had its own long history. Researchers had devised two different instruments with which to conduct airfoil experiments. The earlier device was called a whirling arm, which spun an airfoil around in a circle in order to generate lift and drag data. The second instrument, the wind tunnel, became the primary tool for aerodynamic research during the first half of the 20th century. Invented by Francis Wendham in 1870, the wind tunnel was not initially well regarded as a scientific instrument. But that changed when the Wright brothers used one of their own design to demonstrate that data produced by numerous other respected and methodical researchers using the whirling arm was wrong. The discredited whirling arm vanished as a research tool after 1903, while a vast variety of wind tunnels sprang up across the western world.

After the Wrights' success, theory and theoreticians began to play a larger role in aeronautics. One major reason why was Ludwig Prandtl, who finally explained the two most important causes of drag in 1904. Prandtl argued that the fluid immediately adjacent to a surface was motionless, and that in a thin transitional region (the boundary layer), as one moved away from the surface the fluid velocity increased rapidly. At the edge of this boundary layer, the fluid velocity reached the full, frictionless velocity that researchers had been studying for the past two centuries. Thus the effects of friction, or skin drag, were confined to the boundary layer. Under certain circumstances, this boundary layer could separate, causing a dramatic decrease in lift and increase in drag. When this happens, the airfoil has stalled. Prandtl's boundary layer theory allowed various simplifications of the Navier-Stokes equations, which in turn permitted prediction of skin friction drag and the location of flow separation for simple shapes, like cones and plates. While Prandtl's boundary layer simplifications still did not make calculation of complex shapes possible, the boundary layer theory became very important to airfoil research during the 1920s.

The 1920s also saw the beginning of research focused on what was called the compressibility problem. Because air is a compressible fluid, its behavior changes substantially at high speeds, above about 350 miles per hour (563 kilometers per hour). Airplanes could not yet go that fast, but propellers (which are also airfoils) did exceed that speed, especially at the propeller tips. Airplane designers began to notice that high-speed propellers were suffering large losses in efficiency, causing researchers to investigate. Frank Caldwell and Elisha Fales, of the U.S. Army Air Service, demonstrated in 1918 that at a critical speed (later renamed the critical Mach number) airfoils suffered dramatic increases in drag and decreases in lift. In 1926, Lyman Briggs and Hugh Dryden, in an experiment sponsored by the National Advisory Committee for Aeronautics (NACA), demonstrated that a dramatic increase in pressure occurred on the airfoil's top surface at the critical speed, indicating that the airflow was separating from the surface. Finally, the NACA's John Stack found the cause of this flow separation in 1934. Using a special camera, Stack was able to photograph the formation of shock waves above the airfoil's surface. As the figure shows, the shock wave was the termination of a pocket of supersonic flow caused by the air's acceleration over the airfoil. The shock wave, in turn, caused the boundary layer to separate, essentially stalling the airfoil.

Over the subsequent decades, several individuals found ways to delay and weaken shock wave formation to permit higher speeds. The first of these was Adolf Busemann's 1935 idea of swept wings, initially ignored but rediscovered in the 1940s by Robert T. Jones and now used on all modern jet airliners.  During the 1950s, NACA researcher Richard T. Whitcomb developed the transonic area rule, which showed that one could reduce shock strength by careful tailoring of an aircraft's shape. In the 1960s, Whitcomb also demonstrated that one could design an airfoil that could operate well above the critical Mach number without encountering severe flow separation—a supercritical wing.

Supersonics

Long before Whitcomb worked out the supercritical wing, however, the quest for higher performance had led the US Air Force to demand true supersonic aircraft. From the standpoint of aerodynamic theory, supersonics posed an easier problem. On a transonic aircraft, shockwaves formed on top of the wings, meaning that part of the wing had supersonic flow and part of it had subsonic flow—a very difficult problem to resolve mathematically. In supersonic flight, however, the shockwaves formed at the aircraft's leading edges, meaning that the entire airflow around the vehicle was supersonic. This eliminated a large source of complexity. During the 19th century and the first two decades of the 20th century, researchers Leonhard Euler, G.F.B. Riemann, William Rankine, Pierre Henry Hugoniot, Ernst Mach, John William Strutt (Lord Rayleigh), Ludwig Prandtl, and Theodor Meyer had developed a solid methodology for calculating the behavior of supersonic shockwaves. During the 1920s, Swiss scientist Jakob Ackeret, working in Prandtl's laboratory at Goettingen, succeeded in simplifying, this body of theory enough so that it could be used to calculate the lift and drag of supersonic airfoils. Supersonic theory thus preceded supersonic flight substantially.

The major challenge aerodynamicists faced in making supersonic flight reasonably efficient was in finding ways to reduce the one unique kind of drag supersonic aircraft experienced: wave drag. Sonic shock waves were really compression waves, which meant that the air behind the shock was at a higher pressure than the air in front of the shock. The higher pressure behind the shock was exerted directly on the aircraft's leading edges and tended to slow it down—in other words, the higher pressure produced more pressure drag. In 1932, again well before supersonic flight was possible, Hungarian scientist Theodore von Kármán developed a method to calculate wave drag on simple bodies. It could also be used on more complex shapes, but the calculations necessary quickly became overwhelming. Through the 1960s, wave drag calculations for complex aircraft shapes were so laborious they were rarely done. Instead, aerodynamicists involved in supersonic research primarily experimented with wind tunnel models until electronic digital computers powerful enough to do the calculations became available in the 1960s.

Hypersonics

If the challenges of designing supersonic aircraft helped motivate aerodynamicists to adopt the digital computer as design tool, hypersonic vehicles sparked a new subdiscipline, aerothermodynamics. Hypersonic flight, traditionally defined as speeds above Mach 5, meant new problems for aerodynamicists, one of which was the role of heating. At high speeds, friction causes the surface of a vehicle to heat up. At Mach 6.7, the speed NASA's X-15 research aircraft reached in the early 1960s, temperatures exceed 1300° F (704° C). Vehicles returning from space hit the atmosphere at speeds above Mach 18, producing temperatures above those at the Sun's surface. This places enormous heat loads on vehicles that can destroy them if their aerodynamic characteristics are not very carefully chosen.

After World War II, as the United States began to develop rockets for use as weapons and for space flight, the need to design vehicles for heat began to supplant the need to design them for aerodynamic efficiency. The earliest, and simplest, example of how important heating is to hypersonic aircraft design was the late 1950s recognition that for vehicles re-entering the earth's atmosphere, aerodynamicists should deliberately chose aerodynamically inefficient shapes. H. Julian “Harvey” Allen of the NACA's Ames laboratory is generally credited with this realization. Engineers designing missiles in the 1940s and 1950s expected to copy the aerodynamics of artillery shells—cones flying point first—for the missiles' warheads. Allen proposed that this was exactly backward. Warheads could still be conical, but they should fly blunt-end first. Allen based his reasoning on the behavior of shock wave that formed in front of the vehicle. Shock waves dissipate energy, and the stronger the shock wave, the more energy it would dissipate away from the vehicle structure. A pointed vehicle would form a weak shockwave and therefore would experience maximum heating. A blunt vehicle would produce a much stronger shockwave, reducing the heat loading the vehicle had to withstand. In essence, Allen's blunt-body theory required aerodynamicists to discard their long-standing emphasis on aerodynamic efficiency and embrace deliberately inefficient shapes for hypersonic flight.

One unusual concept that emerged from the demands of hypersonic flight was the lifting body—an airplane without wings. In the United States, this idea was first proposed at the same 1958 NACA conference on High Speed Aerodynamics that witnessed presentation of the space capsule idea used by both the United States and Soviet Union for their space programs of the 1960s. A lifting body-based hypersonic vehicle would be shaped like a blunt half-cone, to mitigate heating, and would offer the benefit of maneuverability during landing, something the space capsule couldn't do. During the 1960s and 1970s, researchers at NASA's Dryden Flight Research Center flew a variety of lifting bodies to demonstrate the idea's feasibility, including the one prominently featured crashing at the beginning of a popular television series, The Six Million Dollar Man.

Finally, interest in hypersonic flight has led aerodynamicists to revisit the 19th century's theoretical achievements. Because the Navier-Stokes equations can handle heat-conductive air flows as well as viscous, compressible flows—at least they can if aerodynamicists can find solutions to them—they offer the hope of designing reasonably efficient hypersonic vehicles. During the late 1970s, a new subdiscipline in aerodynamics formed around the use of supercomputers to approximate solutions to the Navier-Stokes and Euler equations. Called computational fluid dynamics, or CFD, the practitioners of this discipline are turning the number-crunching power of supercomputers into a virtual wind tunnel able to fully analyze the aerodynamics of any vehicle, in any speed range.

Computational fluid dynamics is actually a very broad research program encompassing all of flight's speed ranges, from subsonic to re-entry, and because it is relatively recent, it is far from being a completed. But it promises to have its greatest impact on hypersonic flight due to the combination of inadequate test facilities and high design complexity. An example will help illustrate CFD's promise while also underscoring how far aerodynamicists have to go before hypersonic flight is well understood. During the 1980s, the US Air Force and the National Aeronautics and Space Administration ran a program to develop hypersonic vehicle that could replace the Space Shuttle, but would use air-breathing engines instead of rockets. In the early 1990s, however, it became clear that the development effort had been premature. Aerodynamicists did not know exactly how air would behave during a key part of the vehicle's flight. The CFD analysis had produced an answer, but due to the lack of test facilities no one knew whether the computer was correct. If the CFD analysis was wrong, even slightly, the vehicle would not achieve orbit. And at a cost of more than \$10 billion, failure due to a lack of basic knowledge was not acceptable to anyone. Hence NASA is currently trying to verify the computer's answer by flying a CFD-designed working model, the X-43A, atop a solid-fuel booster rocket. If the X-43A performs as CFD predicts it will, then aerodynamicists will be one significant step closer to one of aviation's ultimate goals, an airplane that can reach space.

--Eric Conway

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