Ernst Mach

Ernst Mach

Unraveling the Cosmic Connections of Physics and Aerodynamics

Author: Dr. Sandeep Mouvanal

Ernst Mach (1838-1916) was an influential Austrian physicist, philosopher, and scientist. Born on February 18, 1838, in Brno, Moravia (now in the Czech Republic), Mach pursued his education in physics and mathematics at the University of Vienna. He held various academic positions, including a professorship in physics at the University of Graz and later at Charles University in Prague [1].

Portrait of Ernst Mach, watercolor on paper (15 x 11″, Artist: Dr.Sandeep Mouvanal)

Ernst Mach’s noteworthy contributions to the fields of aerodynamics and fluid dynamics, particularly the Mach number and shock waves, have left a profound impact. However, his intellectual pursuits extended far beyond these areas. As a remarkable physicist and philosopher, Mach explored a wide range of disciplines, including the philosophy of science and the psychology of perception. His groundbreaking research on Mach’s principle had a significant influence on the development of Albert Einstein’s theory of general relativity, challenging conventional notions of mass and space. Additionally, his investigations into kinesthetic illusions, acoustics, and optical phenomena, such as Mach bands and Mach’s disc, demonstrated his inquisitive and innovative mindset. Ernst Mach’s legacy is truly multifaceted, inspiring generations of researchers in diverse fields and making a lasting imprint on the scientific community.

Some Important Contributions:

  1. Mach’s Principle: Proposed the revolutionary idea that an object’s inertial mass is influenced by the distribution of all other matter in the universe, challenging traditional notions of mass and space.
  2. Mach Number: Contributed significantly to aerodynamics by inspiring the concept of the “Mach number,” a dimensionless parameter crucial in understanding high-speed fluid dynamics and supersonic flight.
  3. Shock Waves: Pioneered research in the study of shock waves in fluid dynamics, shedding light on the behavior of compressible flows and their impact on aerodynamic structures.
  4. Philosophy of Science: Made influential contributions to the philosophy of science, advocating for empiricism and critical analysis of scientific theories.
  5. Psychology of Perception: Investigated the human mind’s mechanisms of perception, particularly the “Mach bands,” an optical illusion illustrating how our brains interpret light and color gradients.
  6. Mach Bands: Discovered the optical phenomenon of “Mach bands,” which reveal the non-linearities in human perception of light intensity along edges, contributing to our understanding of visual processing.
  7. Mach’s Disc: Invented the “Mach’s disc,” a rotating device that demonstrates the persistence of vision and color perception.
  8. Kinesthetic Illusion: Studied kinesthetic illusions, known as the “Mach effect,” which demonstrates discrepancies between visual and kinesthetic perceptions of motion.
  9. Acoustics: Made significant contributions to the field of acoustics, particularly in the study of supersonic motion and the nature of sound waves.
  10. Impact on Einstein’s Theory of General Relativity: His ideas on Mach’s principle had a profound influence on Albert Einstein’s development of the theory of general relativity, inspiring new concepts in the understanding of gravity and spacetime curvature.

Contribution to high-speed Aerodynamics

Ernst Mach’s seminal contributions to shock waves revolutionized the understanding of supersonic phenomena and fluid dynamics. In 1887, he conducted a groundbreaking experiment where he photographed a bullet traveling at supersonic speeds through a transparent medium. The resulting image, commonly referred to as the “Mach angle photograph,” revealed the formation of a distinct shock wave pattern characterized by a conical region of compressed air emanating from the bullet’s nose. This photograph provided a tangible visualization of shock wave behavior, highlighting the abrupt changes in pressure, density, and flow velocity associated with the bullet’s supersonic flight. Mach’s experimental work played a crucial role in elucidating the complex physics governing shock waves, and his findings have since become fundamental in numerous scientific disciplines, including aerodynamics, astrophysics, and high-speed propulsion systems. The Mach angle photograph remains an iconic representation of the intricate nature of shock waves, inspiring further research and advancements in the field.

Ernst Mach’s historic photograph (Mach angle photograph) of a bow shockwave around a supersonic bullet (Image source [2]

Mach Number and Shock Waves: In 1877, Mach introduced the concept of the Mach number, which quantifies an object’s velocity relative to the speed of sound in a medium. The Mach number (M) is defined as the ratio of the object’s speed (v) to the speed of sound (c) in the same medium: M = v / c. This dimensionless parameter plays a crucial role in determining whether an object is moving at subsonic, transonic, or supersonic speeds. Mach’s pioneering work laid the foundation for understanding the behavior of objects as they approach and exceed the speed of sound, which is crucial in the formation of shock waves.

Shock Wave Formation: Mach’s most famous experimental contribution to the study of shock waves was the “Mach angle photograph,” conducted in 1887. In this experiment, Mach captured an image of a bullet traveling at supersonic speeds through a transparent medium, typically a liquid. The photograph revealed the formation of a distinctive conical shock wave pattern surrounding the bullet’s nose. This breakthrough visual representation demonstrated the abrupt compression and steep density gradients formed when an object travels at supersonic velocities, leading to the formation of shock waves.

Mach Reflection: Building on his observations, Mach investigated the behavior of shock waves as they interacted with surfaces. He identified a phenomenon known as “Mach reflection,” which occurs when a shock wave impacts an inclined surface at an angle greater than a certain critical value. The shock wave reflects back from the surface and forms a complex pattern of multiple shock waves and expansion waves. This discovery contributed significantly to the understanding of shock wave reflections and their implications in various applications, including supersonic aerodynamics.

Mach Stem and Oblique Shock Waves: Mach also studied the behavior of shock waves when they encountered obstructions. He observed that when a shock wave encountered a wedge-shaped obstacle, it produced a distinctive diamond-shaped pattern, known as the Mach stem. This configuration represents the compression region formed by the merging of multiple shock waves. Mach’s research on oblique shock waves provided valuable insights into their properties and how they interact with solid surfaces.

Mach’s Influence on Aerodynamics: Mach’s work on shock waves and fluid dynamics had a profound impact on the development of aerodynamics and high-speed flight. His findings became essential in designing and understanding supersonic and hypersonic aircraft, as well as rockets and space exploration vehicles. The Mach number, in particular, remains a fundamental parameter in aerodynamics, helping engineers and scientists characterize and analyze the behavior of objects moving at high speeds through air and other fluids.


[1] “Ernst Mach” Wikipedia, Wikimedia Foundation, 11 Dec 2022,
[2] Anderson, J. “Research in supersonic flight and the breaking of the sound barrier.” Retrieved September 30 (2001): 2009.
[3] Blackmore, John T. Ernst Mach; his work, life, and influence. Univ of California Press, 1972.
[4] Baatz, Ursula. “Ernst Mach-The Scientist as a Buddhist?.” Ernst Mach—A Deeper Look: Documents and New Perspectives. Dordrecht: Springer Netherlands, 1992. 183-199.
[5] Reichenbach, H. “Contributions of Ernst Mach to fluid mechanics.” Annual Review of Fluid Mechanics 15.1 (1983): 1-29.


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