Working Around Ignorance

The presence of such parameters points to another layer of engineering knowledge, or lack thereof. A striking feature of this episode is the extent to which the design process revolved around ignorance – more precisely, the recognition of ignorance and ways of compensating for and safeguarding against it. No one working on axial compressors and fans in that era knew what the flow inside a blade row was at any level of detail. It was not just that they could not calculate the detailed flow; they could not even measure it inside the rotating blade rows – only at their inlet and

outlet. Rolls-Royce’s way of dealing with this in the case of the bypass flow in the Conway was to use several stages with standard subsonic, low pressure-ratio airfoils whose “black-box” performance had been established empirically. Even though Pratt & Whitney knew that General Electric had achieved a 1.6 pressure-ratio in a single stage, they recognized that they did not know how to do this and opted for two stages. They too used pre-defined, pre-tested airfoils – in their case double­circular-arc airfoils that could be pushed to inlet Mach numbers of 1.15 and a little above. The boundaries of ignorance within P&W had been pushed back somewhat by the mid-1950s compared with those of Rolls-Royce two or three years earlier, but these boundaries still dictated the design.

The boundaries of GE’s ignorance had been pushed even further back, yet most of their design effort was still aimed primarily at compensating for what they did not know. They did not know how to control the effects of shocks, but they recognized that they could get away with not knowing this if they limited the tip Mach number to 1.25, safely below the 1.35 level where the losses had jumped in Klapproth’s NACA rotor. GE had no way of knowing the complicated three-dimensional flow inside their rotor blade row, but they knew they could get away with this so long as their calculated radial and axial velocity distributions were sufficiently similar in key respects to those of conventional airfoils and their diffusion factors remained below the established limiting values. The novel computer program they devised, besides giving them information about the velocity distributions, allowed them to work backwards from these distributions to plausible blade contours. Even so, as their tests showed, the actual flow departed non-trivially from their calculation. Yet they came sufficiently close to the actual flow in crucial respects, most notably the diflusion factor, to achieve a breakthrough in stage performance.

A related point about dealing with ignorance holds for the NACA compressor research program. Its aim was not one of obtaining detailed knowledge of the three­dimensional flow inside a blade row and how to control it. Rather, the aim was to find ways of achieving both consistent and superior designs without having to know the detailed flow. The cascade wind-tunnel tests gave black-box performance of two-dimensional airfoils, and the NACA design method provided ways of compensating for radial effects in using this two-dimensional performance. The transonic research program searched for ways of pushing the boundaries of ignorance back a little, and the supersonic program explored the possibility of pushing them back dramatically. The most striking example of compensating for ignorance, however, is the diffusion factor. The whole idea behind it was to employ quantities that could be measured, at the inlet and outlet of blade rows, to provide an approximation to a feature of the flow inside the blade row that generally could not be measured or calculated with confidence. The diffusion factor enabled higher pressure-ratio stages to be pursued without having to know more about the flow inside the blade row. The rule of thumb it gave for limiting blade loading defined a boundary of ignorance. Reasonable stages could be designed without mastery of the detailed flow inside the blade rows so long as the diffusion factor remained below its empirically determined critical value and velocity distributions did not depart radically from those of the past. The correlation of airfoil profile losses with the diffusion factor, together with a subsequently developed NACA model for calculating shock losses at higher Mach numbers87, allowed designers in the engine companies to live with their ignorance. Engineers do not need to know why some­thing works so long as they know how to stay safely within the bounds of their ignorance and still produce competitive designs.

These practices differ markedly from Vincenti’s characterization of uncertainty in engineering, where engineers usually “did not know as much as they thought they did,” and sometimes “didn’t even know what they didn’t know.”88 In our case, engineers knew rather acccurately what they did not know and hence endeavored specifically to work around the boundaries of their ignorance. Nonetheless, their work is well described by Vincenti’s observation that such work often serves “to free engineering from the limitations of science.”89 Although physicists had established the equations of motion for fluid flow more than a century earlier, these equations remained intractable even for flows enormously simpler than those in compressor and fan stages. Engineers could turn to physics for simplified, approximate reformulations of these equations, but engineering judgment then became crucial in deciding which features of the flow could be ignored or represented grossly by an empirically-based model.90 Experiments could be carried out in wind tunnels and measurements could be made on full stages, but again judgment and ingenuity were indispensable in drawing conclusions from data that designers could use. The shortage of science fostered an engineering practice epitomized by the following recommendation, made not in the early 1950s, but in 1978: “No compressor designer should overlook the possibility or underestimate the advantages of scaling an existing compressor geometry of known performance to meet his current design goals.”91 Even when existing designs could not be so used, they served as starting points for incremental advances. The continuous improvement achieved in axial fan and compressor design in the period covered in this paper, and subsequently, has not come from being better able to exploit scientific knowledge of fluid flow, but rather from sophisticated aspects of engineering practice aimed at defining, surmounting, and hence shifting, boundaries of ignorance.

We have shown how the development of turbofan engines, a technology with significant technical preconditions and precedents, emerged out of a disparate, but rich set of experiments and designs, working with knowledge of fluid flow very close to its boundaries of uncertainty. How well do the historical phenomena in this analysis apply to engineering epistemology in general? This question can be reformulated: is the role of uncertainty in engineering design exaggerated when one examines cutting-edge aerodynamics, where the physics of turbulence, that paradigm of poorly-understood phenomena, so dominate? Isn’t design in other contexts a more “certain” endeavor? Anecdotal evidence suggests otherwise. A prominent computer scientist and algorithm designer, when recently asked this question, responded emphatically in the negative. Any number of parameters in computer systems, from network behavior to algorithmic complexity, display similar phenomena. We understand, after all, how any individual Newtonian air particle behaves, just as we understand individual transistors. Their sum totals, however, exhibit behaviors currently beyond “the limitations of science.” It is at this boundary, we argue, literally at the border of complexity, that engineering begins.