286 BELL SYSTEM TECHNICAL JOURNAL 



The design of a modern four-engine transport plane requires about 

 600,000 hours of engineering time up to the point where complete working 

 drawings have been prepared. About 100,000 hours are spent on mathe- 

 matical analysis of structures, performance, lift distribution and stability. 

 Most of this work is routine, but some is fundamental in character, as is 

 evident from several of the examples mentioned earlier in this report. 



Of 670 men in the engineering department of one of the larger com- 

 panies, about 25 have mathematical training beyond that usually obtained 

 by engineers, and 10 or so of these are using this advanced training to a 

 significant extent. 



Uses of Mathematics. In designing an airplane, five factors are of 

 particular importance. These may be used to indicate the directions 

 in which mathematical research may be expected. 



(1) Performance (that is, pay-load, range, speed, climbing rate, etc.) 



In the past, forecasts of performance have been based almost entirely 

 on empirical data. Mathematical methods of estimation are now being 

 developed from hydrodynamic theory, however, and are being used to an 

 increasingly greater extent. 



(2) Lift and Drag (i.e., the force variation over the wings) 



This is the principal objective in the aerodynamic design of the wing. 

 The technique of prediction rests on two supports: wind tunnel experi- 

 ments and airfoil theory, by means of which experimental data are inter- 

 preted and applied. For example, airfoil theory suggests the shape of 

 airfoil to avoid unfavorable pressure distributions and is leading to im- 

 proved wing sections. This part of aircraft design is already highly 

 mathematical, but a number of fundamental problems still remain unsolved. 

 For example, the theory is still unable to predict stall, and too little is 

 known about optimum shapes or about turbulence, though the recently 

 developed statistical theory of turbulence has contributed to the under- 

 standing of the airflow over an airplane and resulted directly in a decrease 

 in airplane drag and consequent improvement in performance. 



(3) Stability (inherent steadiness of motion) 



The stability of an airplane in flight is inherent in its aerodynamic 

 design and quite distinct from its control or maneuverability. The theory 

 of "small oscillations" has been successfully applied to rectilinear flight. 

 More recently the problem of predicting the response of an airplane to 

 control maneuvers has used the Heaviside operational calculus. Current 

 problems of dynamical stability in which applied mathematicians are inter- 



