[**107**] THROUGHOUT most of
the war years, Harvey Allen was in charge of the Theoretical
Aerodynamics Section, reporting to Don Wood, who at first was Chief
of Research and later Chief of the Theoretical and Applied Research
Division. Harvey's staff included Walter Vincenti, Max Heaslet,
Gerald Nitzberg, Donald Graham, and, later, Milton Van Dyke. In the
early years, as has been noted, the pure theory of this group was
rather thoroughly mixed up with the reinforced concrete of design and
construction. Allen, in any case, was as much an experimentalist as a
theorist; thus it was not long before his brainchild, the 1- by 3
1/2-foot tunnel, became a part of his command. Nor was it surprising
when, in July 1945, a new High Speed Research Division was created
with Allen as Chief. Within the new Division were established a 1- by
3-Foot Tunnel Section under Vincenti and a 1- by 3 1/2-Foot Tunnel
Section under Graham. The Theoretical Aerodynamics Section, now
headed by the scholarly Dr. Max Heaslet, remained in Don Wood's
Division which itself had been augmented by a 12-Foot Tunnel Section
headed by Robert Crane.

Allen, a man of many loves,
** ^{1}** adapted quite readily to the requirements of his
various assignments. While occupied with design and experimentation,
he still managed to turn out one of the most outstanding and
generally useful theoretical papers produced by the Ames staff during
the war years. This was TR 833 (ref. A-8) entitled "General Theory of
Airfoil Sections Having Arbitrary Shape or Pressure Distribution."
Actually, Harvey had done much of the thinking for this report while
still at Langley, but the writing took place at Ames.

Allen's report, and much of the other theoretical research carried on during the early years at Ames, concerned that basic element of all airplanes, the airfoil or wing section. During the late 1930's, as earlier noted, NACA engineers at Langley had developed a new and more scientific method of designing airfoils. This method allowed designers, through....

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.....manipulation of pressure distribution, to achieve airfoil designs having low drag (extensive laminar flow) and high compressibility speeds. All one had to do was first to choose the desired pressure distribution and then to design an airfoil of the right shape to produce that distribution. But ah! there was the rub. How did one proceed from pressure distribution to airfoil shape? The designer was in the classic position of the lost traveler who, on inquiring of a native about the route, was told, after some cogitation, "You can't get there from here!"

Actually, in the case of the airfoil, there was a theoretical method of getting there from here but it was extremely laborious. It was like many other airfoil theories developed by mathematical purists. But Harvey was not a purist. His interests lay not in trying to build a mathematical Taj Mahal. He was much more interested in useful results than in the virgin beauty of his mathematical edifice. He was not above using approximations, reasonable assumptions, unique analogies, and special devices with the result that he often found working solutions to problems that had baffled more polished mathematicians. That is about what he did in the case of the airfoil problem. He developed a simple method for proceeding from an arbitrarily chosen pressure distribution to the physical shape of the airfoil that would produce that distribution. Allen's method was extremely helpful in the attack on the compressibility-effects problem which at that time was troubling Ames research people. The relevance of the method to the compressibility problem lies in the fact that pressures are a measure of the velocity in the local flow over an airfoil, and the velocity of sound in the local flow marks the beginning of the more severe compressibility effects.

The onset and intensity of compressibility
effects depended not only On the shape, or thickness distribution, of
the airfoil but also on its angle of attack and lift coefficient. The
airspeed or Mach number at which these [**109**] effects began to
appear was called the "critical speed" or "critical Mach number" and
much effort was spent in devising airfoils having high critical
speeds through a wide range of angle of attack. Analytical means for
predicting the critical Mach number of airfoils at different lift
coefficients, with and without flaps, were developed during this
period by Max Heaslet and Otway Pardee. The problem was also attacked
in the 1- by 3 1/2-foot tunnel where a systematic Investigation was
made of the pressure distribution over several NACA low-drag and
conventional (old style) airfoils. The latter study, made by Don
Graham, Gerald Nitzberg, and Robert Olson, is reported in TR 832
(ref. A-9) . Also undertaken in the 1-by 3 1/2-foot tunnel was a
program to determine the high-speed characteristics of a promising
group of NACA low-drag airfoils. This investigation was carried out
and reported by Milton Van Dyke and G. A. Wibbert.