 In a series of publications beginning in 1947 with his Ph.D. thesis under Theodore von Kármán at the California Institute of Technology
, he developed a theory of supersonic flow called the area rule which strongly influenced the design of high-speed aircraft.His work also provided the first understanding of the behavior of delta wing aircraft flying just above the speed of sound.He followed his work in supersonic flow with groundbreaking studies in the late 1940s and early 1950s in hypersonic flow, which is considered to begin at about five times the speed of sound, or Mach 5.