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    The Davis Wing and the Problem of Airfoil Design Essay

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    Among the many important decisions confronting designers of an airplane is choice of shape for the fore-and-aft sections of the wing. During the 1930s most American designers made this choice from an extensive catalog of sections whose aerodynamic properties had been measured in the wind tunnels of the National Advisory Committee for Aeronautics. In 1938, however, one major company, the Consolidated Aircraft Corporation of San Diego, chose for its B-24 bomber a some what mysterious section devised by a lone inventor named David R. Davis. The choice depended on some unusual test results, unexplained at the time, from the wind tunnel at the California Institute of Tech nology. The B-24 went on to become the most numerous and one of the most successful bombers of World War II. The Davis section, after its moment in the sun, disappeared quiedy and with litde effect on the evolution of wing design. This situation, curious at the time and largely forgotten today, is an interesting sidelight in the history of aeronautics. More important for scholarly concerns, it provides a useful vehicle for studying engineering knowledge in relation to design. This article is a companion to three earlier studies in which I ex amined various aspects of engineering knowledge in the contexts successively of experimental research, theoretical analysis, and pro duction.1 The intermediate activity of design figured in all of these, but  not in a central way.

    The Davis episode appeared to offer an opportu nity to fill this gap. In view of the ambiguity surrounding Consoli dated^ choice, I hoped in particular to learn something about how uncertainties in knowledge affect and are affected by engineering design. Engineers frequently have to make decisions of great practical consequence in the face of incomplete and uncertain knowledge; it seemed likely that this necessity might have epistemological implica tions. At the same time, as an aeronautical engineer I was curious to see whether the unusual performance of the Davis section could be ex plained in light of subsequent understanding. In pursuit of this goal, a second and related theme emerged: how knowledge grows in relation to concrete demands from design.

    Design thus relates clearly to “the central problem of epistemology [which] has always been and still is the problem of the growth of knowledge.”2 Edw-in Layton has emphasized the multiple benefits for historians of “examining technology from the point of view of design.”’ Design, however, is not all of a kind; it involves many levels of activity in a typically hierarchical relationship. In the case of airplanes, the hierar chy proceeds downward, in the present instance, through project definition, overall airplane design, overall wing design, aerodynamic wing design, and, finally, wing-section design. At the last three levels, other elements appear besides the one noted (e.g., structural and mechanical wing design in the next to last), and the total design process goes on iteratively, up and down and horizontally, through the hierar chy. At the upper levels, even the form of the solution is frequently  uncertain beforehand. At the topmost level, the task of project defini tion, as the term implies, is to translate often ill-defined commercial or military needs into a concrete technical problem for the level below. Innovation of new devices and systems in any field of technology depends on the relatively unstructured conceptual activity at such upper levels. People outside engineering tend to think of design mostly in such terms.

    At the lower levels of the airplane-design hierarchy, where the greatest expenditure of engineering effort actually takes place, problems are normally well defined, and activity tends to be highly structured. In the choice of wing section at the bottommost level, the form of the solution had been established well before the 1930s, and the problem was one of specifics. Uncertainties arose main ly from the explicit knowledge on which designers depended.4 My two initial questions dictate the organization of w hat follows. The first section explores the design process at Consolidated, with emphasis on what was and was not known. This section shows the nature of uncertainties in aerodynamic knowledge in the 1930s. It also illustrates how an engineering design community functions in the face of uncer tainty at a given time. The second section then outlines the general history of airfoil design to determine w’here the Davis section belongs and to attempt to explain its performance. In so doing, we see how an engineering community acts to increase knowledge and reduce uncer tainty as time proceeds. The final section then enlarges on the themes of uncertainty and growth. We observe, among other things, that growth of knowledge and reduction of uncertainty in design are actively related, even when increased performance is not at issue.

    Consolidated, Aircraft and the Davis Profile

    In the summer of 1937, engineers at Consolidated (later Consoli dated Vultee and now the Convair Division of General Dynamics) were engaged in extensive design study of wing optimization for long-range naval patrol aircraft. Production for the navy of the company’s PBY two-engine flying boat, which in World War II would be built in larger numbers than any other water-based airplane, was nearing 100, and construction of the prototype XPB2Y-1 four-engine boat was well along. With the rapid advances taking place in airframe, engine, and propeller design, a potential market existed for still-higher  performance flying boats—not only for the navy but also for the growing intercontinental commercial service. At the same time, Reuben H. Fleet (1887-1975), founder and president of Consolidated, seems to have had his eye on sales to the Army Air Corps of long-range, land-based bombers. The Boeing B-17 was beginning to demonstrate what was possible w ith such airplanes. Some engineers at Consolidated already felt that the days of the flying boat would eventually be num bered and that the growth and even survival of the company required air corps as well as navy business. In the rapidly changing aeronautical world of the late 1930s, a study of wings for long-range aircraft could serve a complex of purposes.5 To define the shape of a w ing for construction, the aircraft designer must decide on the planform—that is, the outline of the wing when viewed from above—and on the profile of the fore-and-aft sections, referred to as an airfoil profile, airfoil section, or simply airfoilThe shape of the wing, in turn, determines its aerodynamic performance.

    Deci sions on shape must therefore be made with the desired performance in view, and this requires some method for evaluating the performance of different designs. For unswept wings of the sort used in the 1930s, aerodynamic performance can be calculated fairly accurately from theoretical ideas that reduce this problem also to one of planform and section. This reduction, which is an approximation aerodynamically, affords a number of simplifications. The most notable is that it allows  the aerodynamic drag to be treated as the sum of two parts, induced drag and profile drag, which have very different causes. For a given aerodynamic lift, the planform determines the magni tude of the induced drag. This drag supplies the work required to generate the energy of the continuously lengthening vortices that trail from the tip regions of any lifting wing of finite span. Induced drag is thus the price that must be paid for lift on such a wing.

    Theoretical calculation of induced drag docs not require consideration of the viscosity (or internal friction) of die airstream. The calculation, while complicated, is thus not insuperably difficult. Practical methods for general planforms were well developed by the mid-1930s.7 Profile drag, by contrast, is a property of the airfoil section. It depends on the shape of the section and is assumed to be the same as would exist on a hypothetical wing having that selfsame section over an infinite span. (In such a limiting case the tips, and hence the induced drag, vanish.) The profile drag is a funcdon of the viscosity of the airstream; unlike induced drag, which exists independendy of viscos ity, it would theoretically disappear if air were frictionless. Since cal culation of practical viscous flows was beyond the reach of theory in the 1930s (difficulties exist even today), profile drag and other aerody namic characteristics of airfoil sections had to be found by testing wings in a wind tunnel and subtracting out the calculated planform effects. Development of airfoils was thus largely an empirical activity. Such aerodynamic ideas, plus structural considerations, formed the basis for the Consolidated study.* As could be calculated from theory, induced drag decreases, other things being equal, as the planform is made longer and more slender. Increased bending of the longer wing under lift, however, requires a heavier structure and, if the additional weight is not to get out of hand, a thicker airfoil. But increases in thickness tend to increase profile drag, thus counteracting and possibly nullifying the reduction in induced drag.

    The optimum wing for a given flight condition thus requires a complicated trade-off between a number of conflicting requirements. In quest for their optimum, Con solidated engineers made calculations for numerous wings aimed at maximum possible flight range with as high a cruising speed as feasible. These included planforms with aspect ratio up to 12, an unusually  high value for the time. (Aspect ratio is the engineer’s measure of planform slenderness and is defined as the span of the wing divided by the average streamwise width—or chord.) Airfoil sections were chosen from the catalog of profiles and associated wind-tunnel data supplied by the National Advisory Committee for Aeronautics (NACA). As the Consolidated engineers well knew, however, optimization calculations of the sort described are approximations at best. The study therefore included evaluation of several of the most promising wings in the 1 О-foot wind tunnel at the Guggenheim Aeronautics Laboratory of the California Institute of Technology (usually called GAI.CIT).9 It was at this point that David Davis entered the picture. Davis (1894- 1972) was an entrepreneur and self-taught inventor and designer of the type common in the pioneering days of aviation but disappearing by the 1930s. He had learned to fly in Los Angeles in the early 1910s, and in 1920, with family money, became the partner and financial supporter of Donald Douglas in founding the Davis-Douglas Aircraft Company. This became the Douglas Aircraft Company when Davis withdrew a year later after helping design and flight test the first Douglas airplane, the Cloudster.

    Davis was brought to Consolidated and introduced to Reuben Fleet by Walter Brookins (1889?-1953), the first civilian taught to fly by the Wright brothers and since 1930 Davis’s partner in the Davis-Brookins Aircraft Corporation of Los Angeles. Brookins’s wife had been acquainted with the then Major Fleet, an old-time flyer himself, when she was secretary to his commanding officer at McCook Field, Dayton, Ohio, in the early 1920s. Brookins thought Fleet might be approachable for that reason.10 The main and apparently soleasset of the Davis-Brookins company was a patent, filed in 1931 and issued in 1934, for a family of  airfoil shapes defined by mathematical equations of Davis’s devising.” With these equations, Davis claimed, he had arrived at airfoils of performance superior to others then in use, performance that made them especially suitable for long-range aircraft. Fleet’s initial reaction, like that of his chief engineer Isaac M. (Mac) Laddon (1894-1976), was naturally skeptical. Laddon’s engineers could see no physical basis for Davis’s equations, and the chance of a lone and professionally un trained inventor improving on the extensive research of the NACA must have seemed unlikely. Most of all, the equations in Davis’s patent contained two unspecified, assignable constants for which Consoli dated engineers would need values in order to draw and examine his airfoils, and Davis refused to divulge this information. He was not about to reveal his essential secret in the absence of some commitment from Fleet and Laddon. Davis proposed instead that he build a wind- tunnel model to the same planform and spanwise thickness distribu- tion as one of the Consolidated models but incorporating his own airfoil. He would then deliver this model, still without specifying the shape of its sections, to GALCIT for testing together with the Consoli dated models. All this was to be done at Consolidated’s expense.

    If Davis’s wing proved superior and Consolidated signed a license to use it, he would then supply the shape of the profile. (The Davis contribu tion was thus only the airfoil profile—not the entire wing, as some people have assumed. I have retained the misleading term “Davis wing” in my title and occasionally elsewhere because the episode has customarily been identified by that name.) On the basis of this pro posal, Fleet and Laddon decided to go ahead. Airfoil design was still largely empirical, and there was always the outside chance that Davis might be onto something. I f Consolidated engineers doubted that Davis’s equations had a valid basis in fluid mechanics, they were—as we shall see—apparently cor rect. Davis, however, seems to have thought otherwise. His patent of 1934 includes, without elaboration, the statement that “The equation was developed from formulas based on the mechanical action of a rotor having rotation and translation through a fluid and giving the Magnus effect.”’* (“Magnus effect” is the name given the lift experi- enced by a circular cylinder rotating about its axis and moving through a fluid.) Two accounts in the popular press of the early 1940s, based on interviews with the inventor, attempted to explain Davis’s reasoning by  (in effect) enlarging on the patent statement in terms of a translating and rotating wheel or radius arm. These explanations, however, are either physically dubious or downright nonsensical.

    The lack of physical basis for the equations is clear from brief hand-lettered notes, unsigned and undated but apparently formulated by Davis prior to the patent.” These begin with a statement about the Magnus effect like that in the patent. They then go at once, with no fluid-mechanical or other physical reasoning, to a purely geometrical procedure based on a translating-rotating circle (the Magnus-effect cylinder). Davis appears simply to have plotted the trajectory of a point on the cylinder and noticed that a loop in this curve had an airfoil like shape. He then devised a complicated and unlikely geometrical con struction to change this shape to something closer to a typical airfoil and translated this construction into equations by ordinary algebra and trigonometry. He gave no explanation of the reasoning behind his construction, which could not possibly have depended in any logical way on fluid mechanics. He also provided no theoretical rationale connecting the airfoil problem to the considerably different Magnus effect. Knowledge of that effect appears to have served simply to focus Davis’s attention onto the rotating cylinder, though he may well have thought this connection gave his work a more valid theoretical basis than was apparently the case.

    Although he thus derived inspiration from the Magnus effect, his procedure was essentially an exercise in geometry.” It must be admitted, however, that Davis’s equations are  themselves not at all simple or obvious. The construction on which they are based is also both ingenious and complex. Although his scheme had no valid basis in fluid mechanics, it could not have been devised without a good deal of menial effort of some sort.” Whatever the nature of his thinking, Davis, like others, had to resort to experiment for his airfoils’ performance. Since no wind tunnel was available, he improvised by borrowing a large Packard car from his friend Douglas Shearer, chief sound engineer at the Metro-Goldwyn Mayer studios and brother of the movie actress Norma Shearer. He then mounted a large flat board horizontally on top of the car, to isolate his model from the aerodynamic disturbances of the car body, and tested his airfoils cantilevered vertically above the board. The measure ments of the distribution of pressure at the surface of the airfoil were made by photographing an array of manometers in the car as it was driven at high speed (on lonely back roads in Southern California according to one source and with flanged wheels on an abandoned railroad in the desert according to another).

    Davis’s purpose was to search out the optimum airfoil from among the family obtained by altering the values assigned to the constants in his equations. After laboriously testing a number of airfoils in the years 1935 to 1937, he decided, however, that such procedure would require the rest of his life.” When Consolidated engineer George S. Schairer questioned him  about it later (after the company had learned the shape of the profile), Davis said he therefore “sat in a chair for three days considering the matter [of the value of the assignable constants) and concluded on theoretical grounds that plus one and minus one were best.”19 He did not say what the theoretical grounds were. I le then checked this airfoil out to his satisfaction on the Packard. This was the airfoil incorporated in the model he delivered to GALC1T. The comparative measurements at GALGIT, made in late August and early September of 1937, came as a shock to Professor Clark B. Millikan (1903-66) and his wind-tunnelstaff. In Millikan’s words from his report to Consolidated, “Certain of the results for the Davis wing are so striking that when they were first obtained, it was felt that some experimental error must have entered.” The Davis model and the Consolidated model that served for comparison (the latter with N АСА “21-series” sections) were therefore carefully remeasured to make certain their planforms agreed sufficiently (they did). The Davis model was then retested on two more occasions some weeks apart, with the three tests showing “practically perfect agreement.

    ” The Consolidated model, which according to Millikan had originally a poor surface finish, was polished to the same outstanding finish as the Davis model and also retested to see whether the results of the latter model could be duplicated. (Understanding was growing, though a few years would elapse before it became firm and widespread, that surface condition can have as much effect on airfoil performance as the shape of the airfoil itself.) The Consolidated model, however, still showed nothing unusual.*0 The most striking result for the Davis wing was in the relationship between lift and angle of attack (the angle of inclination of the wing relative to the airstream). Engineers measure this relationship by the lift-cun’e slope, defined as the increase in lift per degree increase in  angle of attack. To the consternation of the investigators, the Davis model gave an experimental slope practically equal to the value calcu lated from the usual theory of nonviscous (i.e., frictionless) flow.

    This finding caused concern because viscosity should, in principle, reduce the measured value below that given by theory. The expected rela tionship was recovered when Theodore von Kirm£n, director at GALCIT, pointed out that the generally used theory was an approxi mate one and that a more accurate nonviscous theory gave a comfort ably higher result. A question nevertheless remained: the measured slope for the Davis model was still from 7 to 13 percent higher than for the great majority of wings tested at GALCIT and 6 percent higher than the previous best. Millikan could offer no explanation for this difference. He could only surmise that the high value for the Davis model came from some peculiar and unspecified variation of viscous effects with angle of attack (a possibility 1 shall return to later). This uncertainty was of more academic than practical importance, however, since a slightly higher lift-curve slope has no great use for the aircraft designer. Of greater interest to Consolidated was the fact that the Davis model also showed a slightly lower minimum drag compared with the com pany’s design and a significantly lower increase in drag with increasing lift. As a result, the Davis model exhibited about 10 percent less drag at the lift required for long-range cruise. This potentially usef ul finding was tempered, however, by a notorious difficulty with wind-tunnel testing: because of “scale effects” associated with viscosity, results from a small model at relatively low speeds (as was the situation in the tests at GALCIT) cannot be extrapolated simply and reliably to the full-scale airplane at the speeds encountered in flight.

    On account of the un usually large aspect ratio and the limitation on span imposed by the 10-foot diameter of the tunnel, the average chord of the present models (the significant dimension for airfoil studies) was considerably less than customary at GALCIT. Millikan worried, therefore, whether the differences in performance might not be due more to reduced scale than to the difference in airfoil shape.*’ Reception of the results at Consolidated, at least at the level of Fleet and Laddon, was apparently less critical. (Debate must certainly have occurred within the engineering staff, but records from the Consoli dated days no longer exist at Convair.) In late September, three weeks after the tests, Fleet reported the development to Admiral Arthur B.

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