Industrial Research 



285 



piessure concentration). The sources of these data, however, are 

 numerous and at times require complicated mathematics, as in 

 the calculation of thermodynamic properties from spectroscopic 

 data via quantum statistics. 



The situation is much less favorable in the calculation of the 

 rates' of chemical reactions. A semicmpirical method, based 

 on quantum mechanics, has been applied with a little success to 

 some of the simplest reactions taking place in the gas phase, but 

 virtually no progress has been made in the more important field 

 of heterogeneous reactions (reactions of gases on surfaces, for 

 example). We may say that no satisfactory mathematical theory 

 for such calculation e.xists at the present time. Some progress is 

 being made, but we are far from being able to predict a suitable 

 catalyst for any desired reaction. For the present we are happy 

 to be able to account for observations made on some simple 

 reactions. 



Future prospects: It is inconceivable that research in 

 the industry will not continue at at least its present level. 

 Hence more, rather than less, mathematical work will 

 probably be undertaken in prospecting and in refining. 

 A demand of moderate proportions should exist for able 

 mathematicians with a suitable background of geology 

 and classical physics for the geophysical work, and of 

 physical chemistry and molecular physics in the 

 chemical field. 



Aircraft manufacture.- — The aircraft industry also 

 consists of a number of independent units, and is 

 higlily competitive. It is a new industry m which 

 rapid technical development and rapid increase in size 

 has been the rule. It has depended primarily upon 

 govermnent-supported laboratories and, to a lesser 

 extent, upon the universities for its research, and has 

 busied itself with the exploitation of that research in 

 the advancement of aircraft design. No unit of the 

 industry has had or, for that matter, now has a research 

 laboratory, in the sense in which the words would be 

 used in older and larger businesses, but the beginnings 

 of research departments have appeared, and individual 

 researchers and research projects are clearly recognizable. 



Number of mathematicians: Some men in the engi- 

 neering departments of these companies should un- 

 doubtedly be classed as mathematicians, but it is 

 impossible to make even an approximate estimate of 

 their nimiber. It is possible, however, to cite pertinent 

 information which bears on the importance of mathe- 

 matics to the industry. 



The design of a modem 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 distri- 

 bution 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 companies, about 25 have mathematical 

 training beyond that usually obtained by engineers. 



and 10 or so of these arc 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. 



(/) Performance Uhat is, pay-load, range, speed, climbing rate etc.) 



In the past, forecasts of perfonnance 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) 



Tills is the principal objective in the aerodynamic 

 design of the wing. The technique of prediction rests 

 on two supports: wind tunnel experiments and airfoil 

 theory, by means of which experimental data are inter- 

 preted and apphed. For example, airfoil theory sug- 

 gests the shape of airfoil to avoid unfavorable pressure 

 distributions and is leading to improved wing sections. 

 This part of aircraft design is already higlily mathe- 

 matical, but a number of fundamental problems still 

 remain unsolved. For example, the theory is still 

 unable to predict stall, and too httle is known about 

 optimum shapes or about turbulence, though the 

 recently developed statistical theory of turbulence has 

 contributed to the understanding of the airflow over an 

 airplane and resulted directly in a decrease in airplane 

 drag and consequent improvement in performance. 



(S) 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 oscilla- 

 tions" 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 interested 

 are the behavior of an airplane when running on the 

 ground and the behavior of seaplanes when running 

 on the water (porpoising) . 



(4) Structural safety 



Very precise appraisal of structural strength is 

 required in aircraft design. In most industries inac- 

 curacy can be compensated by increased factors of 

 safety, but the pay-load of an airplane is so small a 

 proportion of its total weight that slight increases in 

 factors of safety would seriously reduce its carrying 

 power or even make it imable to get off the ground. 

 Mathematical methods have always been used in this 



