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# Irmgard Flugge-Lotz

Irmgard Flügge-Lotz (1903-1974)

German mathematician and pioneer in aviation theory

Affiliation: Stanford University

“I wanted a life which would never be boring. That meant a life in which always new things would occur. I wanted a career in which I would always be happy, even if I were to remain unmarried.”

Irmgard Flügge-Lotz was a German mathematician and pioneer in aviation theory and the theory of discontinuous automatic control. She is particularly known for her advancements in the spanwise lift distribution of an airplane wing, known as the Lotz method, and the development of the on-off control.

## The Lotz method

Early on in her career, when working at the Aerodynamische Versuchsanstalt (AVA) in Göttingen, which was one of the most prominent aeronautical research institutions in Europe at the time, Irmgard Flügge-Lotzdeveloped a method for calculating the lift of a three-dimensional wing. Before she arrived at AVA, Ludwig Prandtl, a leading German aerodynamicist, had been unsuccessfully working on solving a differential equation for his lifting-line theory for the spanwise lift distribution of an airplane wing. Irmgard Flügge-Lotz was able to solve the equation and additionally developed a relatively simple method for practical use. The method became known as the Lotz method and became a standard technique used internationally.

## On-off control

Later in her career, Irmgard Flügge-Lotz also developed the theory of discontinuous or on-off control systems, the simplest form of feedback control. An on-off controller drives the manipulated variable from fully closed to fully open depending on the position of the controlled variable relative to the setpoint. A typical example of on-off control is temperature control in a domestic heating system. When the temperature is below the thermostat setpoint, the heating system is switched on, and when the temperature is above the setpoint, the heating switches off. There are many examples of discontinuous control systems in our house appliances, for example, fridges and freezers, ovens and water heaters. They also occur in some non-critical industrial appliances, where the error between the setpoint and plant output can vary with a relatively large amount,such as furnaces.

## Standford’s first female professor of engineering

In 1960, Irmgard Flügge-Lotz was appointed professor at Stanford University, making her the first female engineering professor at Stanford.

She received many honors and awards, including the Achievement Award by the Society of Women Engineers (1970) and an honorary doctorate of science by the University of Maryland (1973). She was also chosen by the American Institute of Aeronautics and Astronautics to give the prestigious annual Karman lecture in 1971.

In the citation from her honorary doctorate, evaluators wrote:

“Professor Flügge-Lotz has acted in a central role in the development of the aircraft industry in the Western world. Her contributions have spanned a lifetime during which she demonstrated, in a field dominated by men, the value and quality of a woman’s intuitive approach in searching for and discovering solutions to complex engineering problems. Her work manifests unusual personal dedication and native intelligence.”

## Background and life

### Early interest in engineering

Irmgard Flügge-Lotz was born in Hamelin, Germany in 1903. Already at an early age, she showed a great interest in engineering and construction. For many generations, her mother’s family had been involved in construction, and Irmgard Flügge-Lotz often visited construction sites with her uncle and attended matinee shows for technical films.

After graduating from a girls’ gymnasium in Hamburg in 1923, she entered Leibniz University in Hannover. She was encouraged by her mother to pursue technical subjects and chose to study mathematics and engineering. She was often the only woman in her class.

In 1927, she received her diploma but remained in Hannover to earn her doctorate in engineering. Her thesis was about the mathematical theory of heat conduction in circular cylinders. During this time, she also held a full-time job as a teaching assistant in practical mathematics and descriptive geometry.

### Career progress

Though it was difficult for a female to find a job in engineering, Irmgard Flügge-Lotz received two offers; one from the steel industry and one from the Aerodynamische Versuchsanstalt (AVA) in Göttingen. She chose the latter. It is said she was asked to devote half her time to clerical work, leaving only half for research. However, her career progressed well, and in 1938 she was appointed head of the Department of Theoretical Aerodynamics.

In 1938, Irmgard Flügge-Lotz married Wilhelm Flügge, a civil engineer. In the following year they moved to Berlin where Wilhelm Flügge had accepted a position at the Deutsche Versuchsanstalt für Luftfahrt (DVL). The leaders of DVL quickly became aware of the talent possessed by Irmgard Flügge-Lotz, and they offered her a position as a consultant on aerodynamics and flight dynamics.

In the spring of 1944, the destruction of Berlin had progressed so far that Irmgard and Wilhelm Flügge-Lotz moved with their departments to Saulgau, a small town in the hills of southern Germany. When Germany surrendered the war, the Flügges found themselves in the French occupation zone. In 1947, they accepted offers to join the newly established Office National d’Études et de Recherches Aéronautiques. They moved, with many of their co-workers, to Paris. Irmgard Flügge-Lotz served as a chief of a research group in aerodynamics and published papers in both automatic control theory and aerodynamics, discussing, for example, the problems arising from the increased speed of aircraft.

### The Stanford period

In 1948, the Flügges accepted offers to teach at Stanford University. Despite Irmgard Flügge-Lotz’s reputation in research, she had to take the relatively minor lecturer position while her husband became a professor due to the Stanford policy that spouses could not both hold a professional title in the same department.

However, Irmgard Flügge-Lotz immediately began accepting PhD students for aerodynamic theory research, and in the spring of 1949, she taught her first course in boundary layer theory. She worked hard, guided the research of a succession of PhD candidates, developed courses, and established a weekly fluid mechanics seminar where faculty and students met to discuss ideas. She published a number of papers, among other things, in numerical methods to solve boundary layer problems in fluid mechanics (which is important to predict and explain the turbulence between a moving liquid and a relatively stable solid), and made extensive advancements in finite difference methods (one of the methods used to solve differential equations that are difficult or impossible to solve analytically) and the use of computers. In 1953, she published the first textbook on discontinuous automatic control. Irmgard Flügge-Lotz was carrying on the duties of a full-time professor without official recognition. In 1960, Stanford finally appointed her as a full professor in engineering mechanics, aeronautics, and astronautics, and she became their first female professor of engineering.

Over time, her research efforts went increasingly into control theory. In 1968, she published her second book called “Discontinuous and optimal control”. That same year, she retired but continued to research satellite control systems, heat transfer, and high-speed vehicle drag. She published over fifty technical papers.