INDUSTRIAL MATHEMATICS 287 



ested 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 inaccuracy 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 unable to get oflf the ground. 

 Mathematical methods have always been used in this phase of aircraft 

 design in so far as they were available. The standard technique is first to 

 design a part on the basis of calculated strength, then build and test it, 

 and if the tests do not agree with predictions, revise the design and build 

 and test the modified part. This process is continued as many times as 

 necessary to attain a satisfactory result. It is slow and expensive. The- 

 oretical methods are now reliable enough that the majority of structural 

 tests confirm predictions with sufficient accuracy to require no revision. 

 However, new problems constantly present themselves — the introduction of 

 pressurized cabins recently gave rise to several — and hence continual 

 mathematical study is required. A beginning has also been made in the 

 use of the principles of probability in setting up structural loading factors. 



(5) Flutter 



We have already commented upon the impracticability of studying 

 this phenomenon by any means other than the mathematical. The general 

 equations are complicated, and have only been solved by making important 

 simplifying assumptions. The results are serviceable for check purposes, 

 but need further elaboration. The importance of the problem increases 

 progressively as more efficient planes are designed, and the necessity for an 

 adequate mathematical theory is becoming critical. 



Future Prospects. It appears inevitable that from motives of economy 

 the industry will rely increasingly upon theoretical methods of design, 

 and that mathematics will play a larger part in the future than at present. 

 It is also probable that for competitive reasons the various companies 

 will supplement government research by fundamental studies of their own. 

 Furthermore, in view of the present fragmentary state of aerodynamic 

 theory, it would not be surprising if part of the research eflfort was devoted 

 to the improvement of the basic theory itself. 



The reliability of these predictions is, of course, conditioned by the 

 financial prospects of the industry. Just now, war orders are causing 

 abnormal inflation of earnings; when these cease, retrenchment will be 



