Aerodynamics Summary

  • Last updated on November 10, 2022

The study of airflow over bodies.

Historical Aspects

In the late seventeenth century, English physicist Isaac Newton laid the foundations for not only modern mechanics and calculus but also fluid mechanics. Newton’s analysis of fluid flow considered air to be composed of individual particles that struck a body’s surface. This analysis was applied to determine the drag of an object in a moving fluid stream but gave poor results, because it did not account for the effect of the wing or body on the oncoming air. Interestingly, it later proved to be far more valuable in hypersonic flow analysis. Swiss mathematician Daniel Bernoulli and his father, Johann I, both published treatises in the 1740’s that greatly clarified the understanding of the behavior of fluid flows. Eighteenth century Swiss mathematician Leonhard Euler noted the problems with Newton’s model and proposed a more accurate formula for drag in 1755.

Subsequent aerodynamic theories developed in the 1800’s and early 1900’s were based on the works of Newton, Euler, and the Bernoullis. In 1894, British inventor Frederick William Lanchester developed a theory that could predict the aerodynamics of wings. However, Lanchester published this work many years later, in 1907. An acquaintance with Lanchester’s theory might have saved considerable effort for Orville and Wilbur Wright, who first flew a heavier-than-air craft in 1903. Instead, the Wrights gained an understanding of aerodynamics through numerous wind-tunnel experiments conducted in their homebuilt wind tunnel. Subsequent advances in aerodynamics are associated with individuals, including Max Munk, Adolf Busemann, Ludwig Prandtl, and Robert Jones, who developed the principles of aerodynamic analysis.

Aerodynamic Flight Regimes

Fluids comprise both gases and liquids. A major difference between a fluid and a solid is that a fluid deforms readily. The major distinction between a gas and liquid is that a liquid is difficult to compress. The atmosphere is a gas composed of 78 percent nitrogen, 20.9 percent oxygen, 0.9 percent argon, 0.03 percent carbon dioxide, and in very small quantities, neon, helium, krypton, hydrogen, xenon, ozone, and radon, based on their volume. The study of the behavior of a body immersed in a moving liquid is called hydrodynamics; in a moving gas, gas dynamics; and in air, aerodynamics.

Aerodynamics may be categorized as either low- or high-speed, depending on where the fluid behavior changes. A common demarcation is subsonic and supersonic flow, where the latter has airspeeds greater then the speed of sound. Transonic flow, where both sub- and supersonic flow may exist, is also usually treated as a distinct regime. Increasing airspeed sees supersonic flow evolving into hypersonic flow at about five times the speed of sound. Difficulty in the analysis of airflow has additionally resulted in airflows being divided into viscous flows and inviscid flows, in which the latter are assumed to have no viscosity and are generally much simpler to analyze. The basic principles underlying aircraft flight are well described assuming inviscid flow.


The flow of air over a body is governed by the so-called continuity equation and the momentum equations. These equations state that mass can be neither created nor destroyed and that the sum of the forces experienced by a body equals its rate of change of momentum, or its quantity of motion. Analysis of these equations applied to various flight problems laid the foundations of aerodynamics. As air flows over an airplane, the plane causes the air to change its velocity, which also leads to changes in the static pressure distribution over the aircraft. The static pressure is the pressure that is felt when moving at the speed of the airstream. The static pressure distribution causes forces and moments, or torques, over the aircraft. The equation that relates velocity and static pressure is referred to as Bernoulli’s principle.

Subsonic Airflow over Airfoils

The forces and moment that an aircraft experiences are affected by the air density, which in turn is affected by air pressure, temperature, and the amount of moisture in the air, as well as the speed and size of the airplane. As the aircraft flies through the air, it displaces air downward. By pushing the air down, the aircraft’s wings experience a reaction force that tends to push the airplane up, creating lift. The lift is defined as being perpendicular to the oncoming airstream. One may imagine the lift of a wing flying along a wave of high pressure to be somewhat like a surfer on a surfboard riding an ocean wave.

In cross section, the wing of an airplane is composed of an airfoil profile. The shape of the airfoil profile’s camber line, which is the line equidistant between the upper and lower surface of the airfoil, increases the lift generated at a given angle of attack if the airfoil has positive camber. Positive camber indicates that the leading edge and trailing edges, or the front and back of the airfoil, are curved down. If the airfoil has negative camber, the lift generated at a particular angle of attack is reduced compared to that of a flat airfoil with no camber. Consequently, positive camber or curvature of the camber line has the effect of increasing the lift by a constant amount for a given angle of attack, compared to a flat or symmetrical airfoil. The larger the camber of the airfoil, that is, its curvature, the greater the lift the airfoil will generate. This effect is most pronounced as the location of the maximum camber, or highest point of the airfoil, moves to the trailing edge, or back of the airfoil. The thickness of the airfoil, with reasonable accuracy, does not directly affect the lift the airfoil section generates, but it may affect the nature of the airfoil’s stall.

The shape of the airfoil profile and its thickness distribution have a profound effect on the nature of the airfoil’s stall. When an airfoil’s angle of attack is greater than approximately 12 degrees, the majority of airfoils will stall. This condition is due to the air’s viscosity and is caused by a disruption and separation of airflow over the airfoil’s upper surface. Stall causes lift to decrease as the airfoil’s angle of attack is increased. Flow separation also causes a large increase in drag, referred to as pressure drag. For very thin wings, or a flat plate, for example, the stall is quite moderate, and the loss of lift is gradual. For airfoils with a maximum thickness in the 9 percent range, where the maximum thickness of the airfoil divided by the length, or chord, of the airfoil is 0.09, the nature of the stall is quite sharp, and the loss of lift is dramatic. Thicker airfoil profiles, analogous to very thin airfoils, also have weak stalls, with a gradual loss of lift.

Numerous methods and devices have been developed to delay the stall of airfoils. These usually comprise a modification to the nose of the airfoil and typically involve pointing the nose down or extending it off the airfoil and rotating it down. These devices are referred to as leading-edge flaps, or slats. Some birds use a similar concept with a feather called the alula, which forms a slat and stops the bird’s wing from stalling. For a given angle of attack below stall, these leading-edge devices generally do not much change the lift of the airfoil. However, they do extend the lift range of the airfoil and can increase it up to 10 degrees beyond the typical stall angle. These types of devices can be seen, and often heard extending or retracting, on airliners extending from the front of the wing at takeoff or landing.

On modern aircraft, all components are streamlined, that is, smoothly blended. The importance of streamlining became evident in the 1920’s, when it was found that smoothly faired, or joined, bodies, such as aircraft wheels with aerodynamic fairing, had much lower drag than nonfaired bodies. The fairing allowed the air flowing over the wheel to conform smoothly to the surface. Without the fairing, air would separate off the wheel and form large turbulent eddies, or swirling motions, in the wake behind the wheel, greatly increasing drag. The effect of streamlining is to reduce the tendency of the flow to separate off the surface. This separation is caused by the viscosity of the air.

Theoretically, at low speed in an inviscid airstream, an airfoil does not suffer any drag. This condition is known as d’Alembert’s paradox, after eighteenth century French mathematician Jean le Rond d’Alembert, who calculated this apparent anomaly but was unable to explain it. The reason for the paradox was the exclusion of the effects of the air’s viscosity in d’Alembert’s calculations. Due to viscosity, airfoils experience a component of drag called skin friction drag. The skin friction is caused by the viscosity of the fluid layers near the airfoil surface. On the wing surface, the speed of the air is zero, a condition referred to as the no-slip condition. However, at some small distance above the airfoil surface, the airspeed reaches that which would occur if the flow were inviscid. The region between the surface and this point is referred to as the boundary layer. The nature and behavior of this boundary layer have a significant impact on the skin friction drag and stalling characteristics of the airfoil.

The boundary layer can either be laminar, turbulent, or transitional from laminar to turbulent. A laminar boundary layer is composed of air moving in orderly lines. A turbulent boundary layer has air moving close to the airfoil surface in swirling motions. A laminar boundary layer has far lower skin friction drag than the turbulent boundary layer; however, it is also more prone to separate from the airfoil surface. Thus, most airfoils have an initially laminar boundary layer that flows from the front of the airfoil back along the surface. At some point, the boundary layer transitions from laminar to turbulent and is typically turbulent from this point to the trailing edge of the airfoil. Boundary layer transition can be caused by disturbances of insects, ice crystals, high airspeeds, and roughness or imperfections on the airfoil surface. To improve performance at high angles of attack by keeping the boundary layer attached to the airfoil upper surface, an aircraft designer may choose to cause the boundary layer to transition from laminar to turbulent at some point on the airfoil. This may be achieved using small protuberances attached to the airfoil’s surface.

Ultra Low-Speed Flight

Efficient flight at very low speeds, such as those of slow-moving birds and insects, presents unique complications. Typical airfoil shapes do not generate much lift at these low airspeeds. The boundary layer at these low speeds is normally always laminar, and so easily separates off the airfoil surface. When this occurs, the lift of the airfoil decreases significantly and its drag increases. Insects and small birds such as hummingbirds use complicated wing motions to create lift at their low airspeeds. These insects and birds develop both so-called steady and unsteady lift, the latter of which is caused by the acceleration of the wing and its carefully performed motion through the air.

Subsonic Flow over Wings

If the wingspan of the aircraft were infinitely long and the air were assumed to have no viscosity, the wing would theoretically generate a lift force and a moment but no drag. However, aircraft do not have infinite wings, and thus an aircraft in steady cruise experiences lift and drag, as well as a pitching moment, which tends to move the aircraft nose up or down, and possibly either a side force, or yawing moment, which tends to displace the nose from side to side, or a rolling moment, which causes the aircraft to roll about its fuselage such that one wing is higher than the other. The lift of an airfoil is reduced when the airfoil is incorporated into a wing of finite length. The shorter the wingspan is relative to the chord of the wing, the less lift is generated. The largest losses of lift are near the wingtips.

On a finite-length wing, air from the lower surface of the wing tries to curl up around the wingtip to the upper surface, causing the formation of two tornado-like structures, known as wingtip vortices, that trail from both wingtips backward. These vortices possess high rotational speeds and pose a significant threat to other aircraft that may fly through them. These vortices require delays between takeoffs and landings of aircraft using the same runways at airports, in order that vortices may have time to weaken.

The component of drag due to the aircraft having a finite-length wing is called vortex drag. Generally, a wing’s vortex drag is independent of its span. Thus, wings with either a large or a short span will, to a first approximation, develop the same vortex drag. The larger-span wing will, however, generate far more lift, and thus the vortex drag will have a greater effect for short-span wings. To keep the amount of vortex drag low compared to the lift generated, a wing should have a large span. This is the reason why airliners have wings with large spans, and also the reason why gliders have narrow-chord, large-span wings.

Aircraft may have many different types of wing shapes that are dictated by the aircraft’s function. A glider flies at low speed but needs to generate a large amount of lift with little drag. As a result, glider wings have large spans but small chords. An airliner needs to fly efficiently but is limited in its wingspan by airport considerations. A large wingspan results in a heavy wing, which is required to support the wing structure. As a result, airliner wings have a large span but not as large as their chord.

As aircraft fly faster and approach the speed of sound, the flow over the wing changes. Shock waves may appear on the wings, even though the aircraft is still flying subsonically. An airfoil accelerates the air flowing over its upper surface such that it may become locally supersonic. A shock wave is a very thin flow discontinuity that occurs in supersonic flow and causes the airflow through it to slow down significantly. Shock waves are accompanied by large increases in drag on the airplane and are thus undesirable. A way to delay the onset of shock waves on wings is to sweep the wings back, a commonly seen design on airliners, in which most wings have a sweep of about 20 to 30 degrees. This sweep effectively reduces the airspeed that causes the shock waves to form and so allows the plane to fly closer to the speed of sound, normally about 760 miles per hour at sea level. The speed of sound varies with the square root of the air’s temperature.

Supersonic Aerodynamics

When the airspeed is greater than the speed of sound, the airflow is said to be supersonic. Aircraft that are designed to fly supersonically have distinctive design features. At supersonic speed, a new component of drag, called wave drag, appears in addition to the vortex, pressure, and skin friction drag. The wave drag is usually caused by the presence of shock waves on the wing or airfoil. This drag component is sensitive to the thickness of the wing and the lift that the wing is generating and increases with both. To keep wave drag as low as possible, supersonic airplanes may have very thin wings, such as those seen on fighter aircraft, highly swept wings, or a combination of both.

The wing on the Concorde is an excellent example of a supersonic wing design. A popular wing planform shape is the delta, or triangular, wing, upon which the Concorde’s wing is based. The design requirements for efficient flight at supersonic speed and subsonic speed are contradictory. At low speeds, a large-span wing is desirable, whereas at high speeds, a highly swept wing is most effective. These requirements have led to the development of the so-called swing wing, seen on aircraft developed in the 1960’s and 1970’s, such as the European Panavia Tornado and the U.S. B-1 bomber. For low-speed flight, the wings sweep forward, whereas for high-speed flight, the wings sweep rearward. However, this design’s prohibitive cost and structural weight have generally hindered its widespread use.

A problem with wings designed for supersonic flight is that, due to their large sweep and small wingspans, they are poor lift generators. That is, they do not develop a large amount of lift for a particular angle of attack, which can pose serious difficulties when these aircraft either take off and land at very high speeds requiring long runways. One way to alleviate this problem is by designing the highly swept wing to have a sharp nose or leading edge. This design causes the airflow over the wing to form two tornado-like vortices that lie above the wing. These vortices may be clearly seen in photographs of the Concorde taking off or landing on humid days. These vortices greatly increase the lift of the wing, but they also significantly increase drag.

  • Anderson, J. D. Fundamentals of Aerodynamics. 3d ed. Boston: McGraw-Hill, 2001. An excellent, if mathematical, presentation of the foundations of aerodynamics. Subjects are treated in a thorough and logical manner.
  • Barnard, R. H., and D. R. Philpott. Aircraft Flight: A Description of the Physical Principles of Aircraft Flight. 2d ed. Harlow, Essex, England: Longman Scientific and Technical, 1994. A comprehensive and lucid explanation of the principles underlying airplane flight, in a nonmathematical formulation.
  • Kermode, A. C. Flight Without Formulae. 5th ed. Harlow, Essex, England: Longman Scientific and Technical, 1989. A clear and well-illustrated text that explains aircraft flight in a logical presentation.
  • Shevell, R. S. Fundamental of Flight. 2d ed. Englewood Cliffs, N.J.: Prentice Hall, 1989. A thorough introduction to both the aerodynamics and mechanics of airplane flight.
  • Wegener, P. P. What Makes Airplanes Fly?History, Science, and Applications of Aerodynamics. 2d ed. New York: Springer-Verlag, 1996. A somewhat technical presentation that traces the development of aircraft and aircraft technology.

Aeronautical engineering





Forces of flight

Heavier-than-air craft


Ludwig Prandtl

Supersonic aircraft

Wind tunnels

Wing designs

Wright brothers

Airplane manufacturers quickly realized that sleek, streamlined aircraft flew most efficiently. This P-51 Mustang, photographed in 1942, illustrates the principles of aerodynamic design.

(Library of Congress)
Categories: History