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Pyotr Yakovlevich Ufimtsev (Russian: Пётр Я́ковлевич Уфи́мцев) (born 1931 in Altai Krai) is a Soviet/Russian physicist and mathematician, considered the seminal force behind modern stealth aircraft technology. In the 1960s he began developing equations for predicting the reflection of electromagnetic waves from simple two-dimensional shapes.[1]

Much of Ufimtsev's work was translated into English, and in the 1970s American Lockheed engineers began to expand upon some of his theories to create the concept of aircraft with reduced radar signatures.[2]


Ufimtsev was born into a peasant family in the village of Ust-Charysh Pristan, in the Altai region, of the former USSR (N 52.40, E 83.66). At the age of 3 his father was repressed by the regime and later died in a forced labor camp (GULAG system). In 1949 Ufimtsev finished school and entered the physics-math department at Almaty State University (now in Kazakhstan). Because of progressing myopia (nearsightedness) he had to move from Almaty to a specialized clinic located in Odessa city (now Ukraine). Later in 1952 he continued his studies at the Odessa State University. After graduating from university in 1954 he was invited to attend the Central Radio Institute (CNIRTI) in Moscow, where he specializes in electronic warfare.

Developing the mathematics

Ufimtsev became interested in describing the reflection of lasers while working in Moscow. He gained permission to do work on it after being advised that work was useless and would curtail his advancement. Because the work was considered of no military or economic value, Ufimtsev was allowed to publish his work internationally.[3]

A stealth engineer at Lockheed, Denys Overholser, had read the publication and realized that Ufimtsev had created the mathematical theory and tools to do finite analysis of radar reflection.[4] This discovery inspired and had a big role in the design of the first true stealth aircraft, the Lockheed F-117. Northrop also used Ufimtsev's work to program super computers to predict the radar reflection of the B-2 bomber.

In the 1960s Ufimtsev began developing a high-frequency asymptotic theory for predicting the scattering of electromagnetic waves from two-dimensional and three-dimensional objects. Among such objects were the finite size bodies of revolution (disk, finite cylinder with flat bases, finite cone, finite paraboloid, spherical segment, finite thin wire). This theory is now well known as the Physical Theory of Diffraction (PTD).

The first results of PTD were collected in the book: P.Ya. Ufimtsev, Method of Edge Waves in the Physical Theory of Diffraction, Soviet Radio, Moscow, 1962. In 1971 this book was translated into English with the same title by U.S. Air Force, Foreign Technology Division (National Air Intelligence Center ), Wright-Patterson AFB, OH, 1971. Technical Report AD 733203, Defense Technical Information Center of USA, Cameron Station, Alexandria, VA, 22304-6145, USA.

According to the following publications, this theory played a critical role in the design of American stealth-aircraft F-117 and B-2.[5][6][7]

See also the Forewords written by K. Mitzner to the books:

  • Ufimtsev, P.Ya. Theory of Edge Diffraction in Electromagnetics, Tech Science Press, Encino, California, 2003.
  • Ufimtsev, P.Ya. Fundamentals of the Physical Theory of Diffraction, Wiley & Sons, Inc., Hoboken, New Jersey, 2007.

In these two books, P.Ya. Ufimtsev presented the further development and application of PTD and its validation by the exact mathematical theory. In particular, a new version of PTD, based on the concept of elementary edge waves, is presented in his book Fundamentals of the Physical Theory of Diffraction (2007). With appropriate modifications the modern PTD can be utilized for the solution to many practical problems. Among them are the design of microwave antennas, mobile radio communication, construction of acoustic barriers to decrease a noise level, evaluation of radar cross sections for large objects[8] (tanks, ships, missiles, etc.).

Dr. Ufimtsev has been affiliated with a number of research and academic institutions, including the Institute of Radio Engineering and Electronics of the USSR Academy of Sciences (Moscow), Moscow Aviation Institute, the University of California (Los Angeles, Irvine) and most recently, the Moscow State University (Russia, 2007) and the Siena University (Italy, 2008). Currently he is a retiree and a consultant in the field of electromagnetics. Among his honors and awards are the USSR State Prize and the Leroy Randle Grumman Medal.[9]

Ufimtsev taught at the University of California, Los Angeles (UCLA), which is the same school that Ben Rich, developer of the F-117 "Stealth Fighter", studied for his graduate degree.


  • P. Ya. Ufimtsev, Theory of Edge Diffraction in Electromagnetics, Tech Science Press, Encino, California, 2003. ISBN 0-9657001-7-8
  • P. Ya. Ufimtsev, Fundamentals of the Physical Theory of Diffraction, Wiley & Sons, Inc., Hoboken, New Jersey, 2007. ISBN 0-470-09771-X
  • P. Ya. Ufimtsev, Method of Edge Waves in the Physical Theory of Diffraction, Soviet Radio, Moscow, 1962

See also


  1. Ufimtsev, P. Ya. (1971-09-07). "Method of Edge Waves in the Physical Theory of Diffraction". 
  2. Dwayne A. Day. "Stealth Technology". U.S. Centennial of Flight Commission. Retrieved 2009-01-15. 
  3. Larry Musa. "Physicist of the Week: Pyotr Ufimtsev". Retrieved 2009-01-15. 
  4. Patrick Kiger. "The F117A — A Secret History". Discovery Channel. Retrieved 2009-01-15. 
  5. Browne, M.W. "Two rival designers led the way to stealthy warplanes", New York Times, Sci. Times Sec., May 14, 1991.
  6. Browne, M.W. "Lockheed credits Soviet theory in design of F-117", Aviation Week Space Technology p. 27, December 1991.
  7. Rich, Ben and L. Janos, Skunk Works, Little Brown, Boston, 1994.
  8. J.M.L. Bernard, G. Pelosi, P.Ya. Ufimtsev, [Eds], "Radar Cross Section of Complex Objects," Annales des Telecommunications (Annals of Telecommunications), 50, 5-6, May–June 1995. 471-598 pp.
  9. "Ufimtsev, Pyotr Ya. / Fundamentals of the Physical Theory of Diffraction". Retrieved 2009-01-15. 

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