THE PRANDTL CORRECTION

Ludwig Prandtl’s laboratory at Gottingen did not participate in this large “international” project. Nevertheless, Prandtl’s theory of interference effects played a crucial role. The British learned about it from the report of the French tests for the International Trials.38 Compared with British results, the French results gave lower values for lift coefficients but close values for drag coefficients and the center of pressure. More importantly, the report revealed that the French used very different testing procedures from the British, particularly in their employment of the Prandtl correction for the aerodynamic interference due to wind tunnel walls.

The Prandtl correction derived from Prandtl’s concept of the trailing vortex.39 Prandtl’s aerodynamic theory posited that the lift of the airplane was due to the circulation of the air flow around its wings. This airflow produced trailing vortices, which stretched out behind the tips of the wings. These vortices, in turn, produced “induced drag,” which retarded the movement of the airfoil through the air stream. Inside a closed space like a wind tunnel, these trailing vortices were more deformed and more condensed than in the open air because of the existence of the tunnel wall. Prandtl’s theory could derive the effect of their deformation and quantitatively determine the difference in induced drag in full-scale and small-scale testing. All these theoretical discussions were then being introduced to the British aeronautical community through Glauert’s technical reports.40

In their report, the French gave results without this theoretical correction, since they had been requested to do so for the purpose of comparison with the results of other laboratories. But the French representatives emphatically recommended use of the Prandtl correction, stating that its application to raw data was a normal procedure for all their tests, especially for those made for aircraft constructors.41 In its conclusion, this interim report gave the results to which the Prandtl correction had been applied. The application of the Prandtl correction did not necessarily give uniformly better agreement between the French and the British results nor between the two French results, but it gave an agreement between the two French results on lift coefficient.

The French investigators’ confident reliance on the Prandtl correction surprised the British. In March 1923, after this report was prepared, ARC Secretary Nayler and another British official, R. J. Goodman Crouch, were sent to the French laboratories at St. Cyr and Auteuil. Both of them discussed with French representatives the Prandtl correction as well as French methods of testing in general. The representatives of both laboratories told Nayler that they considered the Prandtl correction very accurate and hoped to see the comparison between the British and the French testing results after the Prandtl correction was applied.42 Another French engineer told Crouch that the French had compared the results at the Gottingen laboratory with their own by constructing and using models of the size given in German reports, and that the results of this comparison conformed closely.

With all this information, Crouch suggested in his report to the Aerodynamics subcommittee that these test results should be reported to the Main Committee so that they could again discuss the possibility of the Gottingen laboratory participating in the International Trials.43 The report encouraged the investigators at Famborough to recommend strongly the adoption of Prandtl’s theory. In discussions at meetings of the Design Panel, the Aerodynamics subcommittee, and the Main Committee, Wood and Glauert argued for the use of the Prandtl correction and of his theory in general. However, they were still unable to persuade their British colleagues.