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Wallace d. Hayes
1918–2001
elected in 1975
“For contributions to the basic understanding of transonic and supersonic
flow, and the Hayes equivalence principle for hypersonic similitude.”
By roNald f. ProBsTeiN
Wallace deaN Hayes, an emeritus professor at
Princeton University and one of the world’s leading theoretical
aerodynamicists, whose numerous and fundamental
contributions to the theories of supersonic and hypersonic flow
and wave motion strongly influenced the design of aircraft at
supersonic speeds and missiles at hypersonic speeds, died on
March 2, 2001, at the age of 82.
Wally was born on september 4, 1918, in Beijing, china,
where his father worked as a civil engineer. He came to
the United states at the age of 10, settling in california. He
received all of his higher education at the california institute
of Technology, from which he was awarded a B.s. in physics,
with honor, in 1941, the professional degree ae.e. in 1943, and
a Ph.d. in aeronautics, magna cum laude, in 1947.
His early professional career began as a stress analyst
in 1939 with consolidated aircraft and continued during
World War ii as an aerodynamicist with North american
aviation. He joined the division of applied Mathematics at
Brown University in 1948, which he left in 1952 to become
science liaison officer at the U.S. Office of Naval Research in
london. returning to the states in 1954, he became a professor
at Princeton University in the department of aeronautical
151
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152 MeMorial TriBUTes
engineering, where he remained until his retirement in 1989.
He also taught for periods at other universities he visited,
including delft Technical University in Holland. What was
important about his teaching in Holland was that he learned
dutch and gave his lectures in dutch. a number of Wally’s
friends who lectured at delft after he did were upset with him
because they were all asked why they could not give their
lectures in dutch like Wally did.
in a series of papers beginning with his Ph.d. thesis,
“Linearized Supersonic Flow,” submitted to the California
institute of Technology and defended on New year’s day
1947, he developed the concepts of transonic and supersonic
area rules. although the world-famous aerodynamicist
Theodore von Karman was Wally’s thesis supervisor, he had
never seen his work until Wally turned in his thesis, at which
point he discussed the results with him. The rules define how
an airplane’s cross section should be designed to minimize the
drag that results from shock waves that develop locally when
a plane flies at speeds below but close to the speed of sound
and the shock waves that develop about the airplane above
the speed of sound. credit for the transonic area rule was not
accorded Wally but rather given to richard Whitcomb, who
independently but some five years after Wally’s presentation
of it discovered it while working at the National advisory
committee for aeronautics, which later became the National
aeronautics and space administration. This work resulted
in the “Coke-bottle” aircraft design in which the airplane’s
fuselage was indented from the wings inward by an amount
related to the area occupied by the wings from the fuselage to
the wingtips.
Wally has been given full credit for the related supersonic
area rule. The design concepts of his theoretical work were
applied to the Convair B-58 bomber, the world’s first operational
supersonic jet bomber, which went into production in 1959,
and to the concorde airliner, which went into service about 10
years later along with other supersonic aircraft of the period.
all supersonic aircraft incorporate the area rule considerations
in their design.
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Wallace d. Hayes
The contributions of Wally to hypersonic flow theory can
be traced to a series of about five basic papers, beginning with
the now classic pioneering note “On Hypersonic Similitude” 1
(published in 1947) and peaking with the books (written with
this author) Hypersonic Flow Theory2 (published in 1959) and
Hypersonic Flow Theory, Second Edition: Volume I: Inviscid Flows3
(published in 1966). These works have, among other things,
included the “Hayes equivalence principle,” which has led to
hypersonic similitudes that enable one to take the results of
one series of theoretical calculations or tests and apply them to
the analysis of an entire family of similar configurations. The
Hayes principle now includes generalizations to a broad class
of viscous and nonviscous (inviscid) flows.
Wally’s development of Newtonian flow theory provides the
starting point for almost all quantitative hypersonic flow theories.
This theory employs the fact that at hypersonic speeds the shock
wave enveloping the body lays close to the body surface, and
in this thin layer the gas density is very high compared to the
density in front of the shock. The shock wave has about the same
inclination as the body, there is no friction between the thin shock
layer and the surface, and the fluid density is essentially constant.
This theory served as the starting point of almost all calculations
in the hypersonic speed range, where experiment and detailed
theory are often limited. Without the theoretical concepts of
Hayes, the problems of design in the hypersonic speed range
would have been enormous because of the difficulties involved
in directly reproducing flow conditions in the laboratory.
No presentation of Wally Hayes’s contributions would be
complete without noting his brilliant studies on wave motion.
The first of these is his book Gasdynamic Discontinuities4
W. D. Hayes, 1947, “On hypersonic similitude,” Quarterly Applied Mathematics
1
5:105-106.
W. d. Hayes and r. f. Probstein, Hypersonic Flow Theory (New york: academic
2
Press, 1959).
W. d. Hayes and r. f. Probstein, Hypersonic Flow Theory, Second Edition: Volume I:
3
Inviscid Flows (New york: academic Press, 1966). reprinted as Hypersonic Inviscid
Flow (Mineola, Ny: dover, 2004).
W. d. Hayes, Gasdynamic Discontinuities (Princeton, N.J.: Princeton University
4
Press, 1960).
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(published in 1960). in this study Wally clearly laid out the
subject of the physics of shock waves in a manner that is as
relevant today as when it was first published. Through visits
to the soviet Union in the early 1960s, Wally and this writer
became aware of the important russian book Physics of Shock
Waves and High-Temperature Hydrodynamic Phenomena5 by ya.
B. Zel’dovich and yu. P. raizer. We thought that this work
should be made available to american scientists, and our
translation and editing were done from a manuscript provided
by the authors of the then-forthcoming second edition. it was
published in 1966 in english at about the same time as the
second russian edition, which had incorporated many of the
edits and corrections of the english edition.
somewhat after publication of the Zel’dovich-raizer book,
Wally’s attention was drawn to the problem of sonic boom
resulting from the motion of an aircraft at supersonic speeds
through the atmosphere. His theory for the calculation of sonic
boom propagation in a stratified atmosphere has become the
model for all such calculations and the basis for minimizing its
effect. His general theory on the conservation of wave action
applies to the broad range of studies of progressive waves and
can be called foundational in the subject of wave studies.
among his honors Wally was elected to the National
academy of engineering in 1975. He was also elected a fellow
of the american academy of arts and sciences, the american
Physical society, and the american institute of aeronautics
and astronautics, which honored him in 1965 with its research
award. it is this writer’s view that these honors alone cannot
represent the depth and brilliance of Wally’s contributions,
which profoundly shaped our understanding of high-speed
flight that is now taken for granted but for which he laid the
trail.
Wally had many friends throughout the world, for he was
a very easy person to have as a friend. He had a wonderful
ya. B. Zel’dovich and yu. P. raizer, Physics of Shock Waves and High-Temperature
5
Hydrodynamic Phenomena, edited by W. d. Hayes and r. f. Probstein (New york:
academic Press, vol. i, 1966; vol. ii, 1967; corrected and reprinted by dover
Publications, Mineola, Ny, 2002).
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Wallace d. Hayes
sense of humor, he almost always had a smile on his face, and
he was interested in people. He was a glider pilot and small-
airplane flight instructor, and he had a love for the outdoors
and extreme sports, including mountaineering, ice climbing,
hiking, water sports, and skiing. Unfortunately, i did not
share his love for the outdoors and sports, although I did fly
and ski with him. However, i fall into the cautious category
when compared with Wally’s daunting approaches. i recall
one time when my wife irène and i were skiing with him in
switzerland, and he suggested we ski down from the top of
Piz Neir, the highest and steepest mountain in st. Moritz.
When we got off at the top of the lift, not a soul was to be seen
except the attendant whom Wally asked in german what the
skiing was like. after he answered, Wally turned to both of
us and said, “He says it’s not so bad.” For a moment he had
forgotten that irène understood german, and she whispered
in my ear that the attendant had responded that it was “very
dangerous.” our downhill speed that day exceeded anything
i had ever done before or since, and as i look back on it i have
never been certain just how we made it down. But that was
Wally; he savored the thrills and excitement of activities that
brought him to his limit, while at the same time his scientific
work was the product not just of his deep insights but also
of a caution that ensured every result could be justified or
seen from different approaches. There was no challenge either
physical or intellectual from which he would ever turn away.
His curiosity was unbounded and the depth to which he would
plumb an intellectual problem unlimited.
His daughter Judith wrote:
“My sisters and I remember our dad as an unusually
un-self-conscious, fun-loving person who enjoyed
camping, hiking, rock-climbing, snorkeling, canoeing,
both downhill and cross-country skiing, dancing,
traveling, and eating really fine or interesting food. We
are grateful that he shared these proclivities with us.
He was very loving, capable of truly unconditional love
for his kids. He was also a pretty bad procrastinator
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and absent-minded professor. But when he worked, he
focused like no one else we have ever met—we used to
have to shake him to get his attention away from his
work. Having been raised in california, he loved fruit
and made his own jams and jellies. His sense of wry,
dry and sometimes bawdy humor was almost always
in gear. We all feel fortunate to have had this playful,
adventurous, loving, and quirky man for a father.”
surviving family members are his three daughters,
carolyn g. Hayes, Judith l. Hayes, and Barbara d. Hayes; six
grandchildren; and his stepbrother, retired air force general
Peter d. Hayes. His former wife, laura Hayes Horbatt,
survived him for about a year and a half.
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