NO. 3 LANGLEY MEMOIB ON ME< HANICAL FLIGHT 129 



work in aerodromics. On the recommendation of Dr. Thurston be engaged the 

 services of the writer, who assumed charge of the work in June, L898. 



While the method of " cut and try " had brought success in the models, and 

 was perhaps the only method by which they could have been successfully devel- 

 oped, it was thought that, with these models as a basis of design, much time 

 would be saved by making an analytical study of them as engineering structures, 

 and from the data thus obtained the proper proportions for the parts of the 

 larger machine could be calculated. 



Such an analytical study, however, revealed very little from which to make 

 calculations as to the strength necessary for the various parts of the large ma- 

 chine, but it did show very clearly that most of the parts were working under 

 stresses generally far above the elastic limit of the materials, and in many cases 

 the ultimate breaking strength was closely approached. Such a condition was 

 the natural outcome of the method by which these models had been developed — 

 all the various parts having been built at first of the least possible weight and, 

 when they proved too weak, strengthened until they would withstand the stresses 

 imposed on them. It is extremely doubtful if previous calculations as to the 

 strength necessary would have been of any assistance, in fact it is probable 

 that it would have been a distinct disadvantage and would have resulted in the 

 machines being entirely too heavy for flight. 



The exact strength which had been incorporated in the frames of the mod- 

 els was as unknown as was the exact amount of the stresses which they had been 

 made to withstand. Their static strength was easily determined by calculation, 

 but the stresses due to the live loads were incapable of exact determination 

 from the available data, for stresses produce strains, which in turn generally 

 cause distortions accompanied by greatly increased stresses. While exact data 

 were, therefore, lacking as to stresses and strengths in many of the important, 

 parts, yet the models furnished most important illustrations of unusual strength 

 for minimum weight, and a careful study of them showed many ways in which 

 increased strength could be obtained with decreased weight which could hardly 

 have been devised without these concrete examples. 



It was, however, by no means possible to build the large aerodrome within 

 the permissible limits of weight by simply increasing the various parts of the 

 models according to some predetermined function of the size of the whole. 



The fundamental difficulty is that inevitably, by the laws of geometry, 

 which are mere expressions of the properties of space, if a solid of any form is 

 magnified, the weight increases as the cube, while the surface increases only as 

 the square, of the linear dimensions. Successive generations of physicists and 

 mathematicians pointed out that while this " law of the cube " is of advantage 

 in the construction of balloons, yet it is a stumbling block that will prevent man 



13 



