U.S. Centennial of Flight Commission home page


Boundary layer

Ludwig Prandtl was the first to realize that the relative magnitude of the inertial and viscous forces changed from a layer very near the surface to a region far from the surface.


Induced drag

Ludwig Prandtl worked with Max Munk to solve problems related to induced drag where vortices, or whirling motions of fluid, affect the pressure distribution over the wings.

The Work of Ludwig Prandtl

In the early decades of the 20th century, Ludwig Prandtl formulated several important aerodynamic theories. The most notable of these were his boundary layer, thin-airfoil, and lifting-line theories. He was also a teacher of many prominent aerodynamicists.

Ludwig Prandtl was born in Freising, Bavaria, in 1874. His father was a professor of engineering. His mother suffered from a lengthy illness and, as a result, the young Ludwig spent more time with his father, becoming interested in his father's physics and machinery books. His father also encouraged him to observe nature and think about his observations. This upbringing fostered the young Prandtl's interest in science and experimentation.

Prandtl began his formal scientific studies at the age of 20 in Munich, Germany, and graduated with a Ph.D. from the University of Munich within six years. His work at Munich had been in solid mechanics and his first job was as an engineer designing factory equipment. There, he entered the field of fluid mechanics when he had to design a suction device. After carrying out some experiments, he came up with a original device that worked well and used less power than the device that had been used.

Prandtl became a professor of mechanics at a technical school in Hannover, Germany, I 1901. There he developed his boundary layer theory and studied supersonic fluid flows through nozzles.

In 1904, he delivered a revolutionary paper to the Third International Mathematical Congress at Heidelberg, Germany. Titled “Ueber Flussigkeitsbewegung Bei Sehr Kleiner Reibung” (Fluid Flow in Very Little Friction), the paper described his boundary layer theory.

Prandtl's boundary layer theory contributed to an understanding of skin friction drag and how streamlining reduces the drag experienced by airplane wings and other moving bodies. Prandtl examined the drag that resulted from the friction that was created when a fluid such as air passed over an object's surface.

Prandtl determined that there was an extremely thin layer of fluid around a wing or airfoil that stuck to it because of friction. The friction caused this thin layer of fluid, called the boundary layer, to move, or flow, around the wing very slowly as if it were being dragged or pulled over the surface. The farther away from the wing's surface the layer of air was, the less it was affected by friction and the faster it moved until it reached the outer edges of the boundary layer, where the airflow was normal and the fluid moved at normal speed.

Prandtl also observed that flow separation was another possible result of friction. When a certain type of flow occurred, the boundary layer separated from the surface of the wing. This resulted in a region of slow-moving air behind the wing. This slow-moving air had lower pressure than the air flowing over the front of the wing. This change in pressure distribution around the wing resulted in a pressure drag toward the rear of the aircraft that much exceeded friction drag.

His 1904 paper raised Prandtl's prestige as an aerodynamicist. He became director of the Institute for Technical Physics at the University of Göttingen later in the year, where he worked with many outstanding students, creating the greatest aerodynamics research center of his time.

In the years that followed, Prandtl began work on calculating the effect of induced drag on lift. Induced drag is the drag created by the vortices that trail an aircraft from the tips of its wings. These vortices, or whirling motions of fluid, affect the pressure distribution over the wings and result in a force in the direction of drag. Hence, induced drag is a kind of pressure drag. He worked with Albert Betz and Max Munk for almost ten years to solve this problem. The result was his lifting line theory, which was published in 1918-1919. It enabled accurate calculations of induced drag and its effect on lift.

In England, Prandtl's lifting line theory is referred to as the Lanchester-Prandtl theory. This is because the English scientist Frederick Lanchester published the foundation for Prandtl's theory years earlier. In his 1907 book Aerodynamics, Lanchester had described his model for the vortices that occur behind wings during flight. Prandtl's model for his theory was similar to Lanchester's, although Prandtl claimed that he had not considered Lanchester's model when he had begun his work in 1911.

During World War I, Prandtl created his thin-airfoil theory that enabled the calculation of lift for thin, cambered airfoils. It is still used today. He later contributed to the Prandtl-Glauert rule for subsonic airflow that describes the compressibility effects of air at high speeds. Prandtl also made important advances in developing theories of supersonic flow and turbulence.

Prandtl worked with his student, Theodor Meyer, to develop the first theory for calculating the properties of shock and expansion waves in supersonic flow in 1908. In 1929, he worked with Adolf Busemann and created a method for designing a supersonic nozzle. Today, all supersonic wind-tunnel nozzles and rocket-engine nozzles are designed using the same method. Prandtl also developed a rule for correcting low-speed airfoil lift calculations that accounted for the way air compressed at high speeds. This became very useful during World War II as aircraft began approaching supersonic speeds.

In 1925 Prandtl became director of the Kaiser Wilhelm Institute for Flow Investigation at Göttingen. By the 1930s, he was known worldwide as the leader in the science of fluid dynamics, the study of the effect of fluid motion on objects. He continued his research in many areas, such as meteorology and structural mechanics. Prandtl also taught famous aerodynamicists such as Theodor von Kármán and Klaus Oswatitsch.

Ludwig Prandtl was a likeable man and an accomplished pianist. He worked at Göttingen until his death on August 15, 1953. His work and achievements in fluid dynamics resulted in equations that were easier to understand than others and are still used today in many areas of aerodynamics. It is for this reason that he is referred to as the father of modern aerodynamics.

—Dan Johnston


Anderson, Jr., John D. A History of Aerodynamics. Cambridge, England: Cambridge University Press, 1997.

Prandtl, Ludwig, Tietjens, O.G., and Hartjog, J. Applied Hydro and Aeromechanics. London, England: McGraw-Hill Book Company, Inc., 1934.

Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag, 1991.

“Ludwig Prandtl: Father of Aerodynamic Theory” http://www.allstar.fiu.edu/aero/prandtl.htm

“A Brief History of Hydrodynamics: Ludwig Prandtl” http://www.icase.edu/~luo/hydrodynamics.html

Educational Organization

Standard Designation  (where applicable

Content of Standard

International Technology Education Association

Standard 2

Students will develop an understanding of the core concepts of technology.

International Technology Education Association

Standard 10

Students will develop an understanding of the role of experimentation and research and development in problem solving.

American Association for the Advancement of Science


Students will develop an understanding of principles of scientific inquiry.