THE SCALE EFFECT RECONSIDERED
At the end of World War I, a British Design Panel had been formed to investigate stress and aerofoil performance.44 The Panel’s main concern soon came to focus on scale effect. At its second meeting, after a long discussion, the Panel concluded that the scale effect was important. The Panel decided to state its own opinion formally as soon as possible.45 An RAE group under Wood summarized the relevant experimental research on this subject.46 Wood’s preliminary report noted a considerable difference between full-scale and model data for lift, drag, and center of pressure. It was decided, however, to defer a final recommendation while awaiting the arrival of still more comprehensive data.
After a year of preparation, the RAE group submitted its conclusions on scale effect in February 1923.47 By then, Glauert was actively introducing German aerodynamic theory and the International Trials were taking place. The RAE report included Prandtl corrections to its research data. This application triggered a heated debate first with the Design Panel and then with the Aerodynamics subcommittee. Introducing the RAE report as a part of the general investigation into the scale effect, Panel Chairman William S. Farren highlighted this first use of Prandtl corrections by British researchers. Farren himself was not in favor of the correction, because he considered it scientifically more desirable to compare results of full-scale testing with those of wind tunnel testing modified only through “purely experimental corrections.” Before the meeting, he had consulted two Main Committee members on this matter, and reported their disapproval of the correction to his own Panel members.48 Farren clearly recognized that the question concerned a fundamental principle of experimental procedure.
In response to the Chairman’s comment, Wood stated that the Prandtl correction had already been confirmed by the International Trials and was regarded by the RAE as part of routine wind tunnel experiments. Glauert agreed with Wood, and cited as a parallel case those corrections due to the interference of wires, which had long been regarded as valid. But their arguments were not sufficiently persuasive. R. V. Southwell, Superintendent of the Aerodynamics Department of the NPL, contended that the Prandtl correction should have been applied in a different section of the report. Of the four sections of the RAE report, the first two dealt with results of full-scale and model experiments, the third with the comparison of these two results, and the last with some applications of Prandtl’s theory. He suggested that Prandtl corrections should have been used and discussed in Part 3 instead of Part 2. He added that the NPL would soon be in a position to confirm experimentally the values given for the correction.
The Design Panel deferred judgment on the validity of the application of the Prandtl correction.49 The Aerodynamics subcommittee discussed the matter the following month.50 Despite the Chairman’s initial comment that the application of the Prandtl correction was already standard practice at foreign laboratories, most members of the subcommittee disagreed with the manner of presentation employed by the RAE group. These scientists, including Bairstow, Farren, Jones, and Glazebrook were all emphatically of the opinion that it was undesirable to give figures to which “purely theoretical corrections” have applied. Corrections to raw data were sometimes made, they argued, but “such correction was based upon actual observations, and was not of the same nature as the Prandtl correction.” Southwell called attention to the fact that the application of the Prandtl correction was not yet standard practice at the NPL. He announced that their on-going experiment on a biplane in the four-foot wind tunnel could check the validity of this correction.
Lacking Glauert’s support, Wood’s argument in defense of the Prandtl correction was insufficient to persuade all these critics. He merely mentioned that the correction for tunnel walls was usually made in experiments on propellers. Finally, on the chairman’s motion, the following recommendation was approved: the general practice should be to give the actual results both in the form of figures and tables, while results to which the Prandtl correction had been applied could also be added at the discretion of the authors. Further discussion of the validity of the Prandtl correction was postponed until results were obtained from the NPL experiments.
Two months later, however, Southwell wrote to the ARC Secretary that the NPL was not yet in a position to provide decisive results. He asked that the Committee discuss this matter during the summer vacation so that the NPL staff could initiate the program promptly in the fall. Following his request, the Aerodynamics subcommittee decided to initiate two types of experimental investigations, both intended to test experimentally the accuracy of the Prandtl correction.51 The first experiment involved testing a model in both a four-foot and a seven-foot wind tunnel so as to determine the difference in results due to the interference of the tunnel walls. The second experiment was to visualize the air flow behind airfoils of different spans in order to determine to what extent Prandtl’s theory was “substantiated.”52
Based on the results of the NPL testing, Glauert submitted a report in November entitled “Experimental Tests of the Vortex Theory of Aerofoils.”53 The report concluded that the NPL results experimentally confirmed the accuracy of the Prandtl correction when applied to wind tunnel results on certain wings. The agreement between tests done in wind tunnels of different size when the Prandtl correction was applied was indeed much more striking than had been the case with the French results in the International Trials report. At the subcommittee meeting, these positive results impressed every member.
Yet some reservations continued to be expressed. G. I. Taylor questioned the scientific grounds of this confirmation, asking whether the effect was due to circulation or to the eddying of air around the airfoil. Taylor was asked by the chairman to discuss this matter with the NPL staff.54 The next month, Taylor submitted a paper dealing with this question and with Glauert’s treatment of Prandtl’s circulation theory.55 At the beginning of Glauert’s paper, Glauert had mentioned experimental confirmation very briefly. He cited the measurement of air flow around an airfoil at the NPL, showing that the circulation around the airfoil was independent of the area of the chosen contour; its value was very close to the theoretical value. In discussing this argument, Taylor pointed out in his report that if the contour was selected in a special way, the experimental results cited by Glauert would be obtained no matter whether resulting from the circulatory flow or the discontinuous stream flow. The observed results, therefore, could not be taken as confirmation of the physical hypothesis of Prandtl’s theory. As Taylor stated, his discussion was intended to “see how far evidence of this kind may be taken as confirmatory of Prandtl’s theory,” and added that his comments were “very probably well known to followers of the work of the Prandtl school.”56
After Taylor’s brief comment at the Aerodynamics subcommittee meeting, Bairstow and Horace Lamb expressed their own doubts, stating that they were not certain that the corrections calculated by the Prandtl theory were really accurate. They therefore considered it undesirable to change the method of presentation of wind tunnel results decided upon at the July meeting. Wood responded by referring to analogous corrections which were made for experiments of propellers and airships in wind tunnels of different sizes. Bairstow then made a proposal on the manner of presentation, which was seconded by Lamb. According to this proposal, the following method should be followed:
1. The numerical results of wind tunnel tests should be presented without the Prandtl correction.
2. A statement should be made as to the amount of the Prandtl correction.
3. The diagrams should be drawn from the results obtained after applying the Prandtl correction.57
Farren and Jones, both faculty members at Cambridge University’s Aeronautical Department, suggested that the proposal be amended so that instead of the old method as prescribed in the first term, the numerical results would be presented in a form to which the Prandtl correction was already applied. Farren and Jones thus changed their view on the Prandtl correction, and came to side with Wood and Glauert. Bairstow then slightly modified their proposal so that numerical results without the Prandtl correction were presented together with additional columns containing the same results with the Prandtl correction applied.
The result of the vote was very close, seven to six in favor of Farren’s and Jones’s amendment. The Aerodynamics subcommittee thus agreed to recommend to the Main Committee the following method of presentation:
The authors of reports describing wind tunnel tests should present their results… in a form after the Prandtl correction was applied. A statement would also need to be added as to the amount of the Prandtl correction.58 Glauert’s report was approved for publication.
Shortly afterwards, the Design Panel convened to discuss what manner of presentation it would use for its final report on scale effect. Southwell expressed his strong opinion on “the necessity for dispelling any impression that the Committee thought scale effect should be zero.”59 It was obvious to every Committee member that the statement was a criticism of the previous report of the “Scale Effect” subcommittee and of Bairstow, who had insisted on the insignificance of the scale effect as well as the inclusion of an explicit statement on such evaluation in its final report. Following Southwell’s suggestion, the Design Panel decided to include a brief history of the problem in its final report, pointing out that the application of the Prandtl correction caused “a marked improvement in agreement” between full-scale and wind tunnel tests.60 The controversy over the scale effect was finally settled.
A few years later, the Scale Effect Panel was formed. This time, the scale effect was not enclosed in quotation marks. Ironically, Bairstow was selected for its chairman.61 The task assigned to the panel was twofold: to study the scale effect as well as to examine the advantages of the use of a variable-density wind tunnel. This new type of wind tunnel had been developed by the NACA to reduce the scale effect.62 The tunnel was placed inside an air tight tank to create an aerodynamic condition with the same Reynolds number as in full-scale flight. The construction of this wind tunnel was based on the realization that the scale effect was now a significant factor to be taken into account. The panel was unanimous in recommending the construction of this new wind tunnel, and submitted the conclusion that it be constructed as a project for the program of 1928-29.63 The Main Committee sanctioned the project.