AIR TRANSPORT — ^DURAND 515 



the weight of the plane in contradistinction to the amount of useful 

 load which it can carry. We may now refer to the aggregate weight 

 of the structural elements of the plane simply as the weight of the 

 structure. With these conventions, then, weight of plane equals 

 weight of structure plus weight of power plant, and the total lift 

 must equal weight of the structure, plus weight of power plant, plus 

 the useful load. 



Let us now turn to the relation between weight of structure and 

 wing area. We have seen that gross lift, other things being equal, 

 will increase with the area — that is, with the square of a linear dimen- 

 sion. Now it is an inescapable consequence of the laws of structural 

 mechanics that, for wing structures carrying the same load per unit 

 of area and with the same geometry of design and materials of con- 

 struction, the dimensions of all structural elements must vary in the 

 same ratio as that for the over-all dimensions. This means, for ex- 

 ample, that if the over-all dimensions were increased twofold, the 

 wing area would be increased fourfold, whereas the volume and 

 hence the weight of all structural elements would be increased eight- 

 fold. This is often referred to as the square-cube law, implying, as 

 it does, that with increase in over-all dimension, the lift will increase 

 with the square of the linear dimension and the weight of the structure 

 with the cube. According to this law, then, with increase in size, the 

 weight will increase at a much faster rate than the lift, and, unless 

 some escape is found, this excess weight would soon absorb the differ- 

 ence between the total lift and the weight of the plane and thus reduce 

 the useful load to zero. The law is inexorable under the conditions 

 stated, and in the early years of airplane development, led to proph- 

 ecies of sharp limitation in the increase in size of airplane structures. 

 The ways and means whereby the consequences of this law have been 

 evaded form one of the most brilliant achievements in the develop- 

 ment of airplane design and construction. I must take only the time 

 to indicate them in briefest outline. They comprise, first, more effi- 

 cient methods of design whereby the material employed is more effec- 

 tively distributed with reference to the loads to be carried; second, 

 improved materials of construction; third, improved aerodynamic 

 design whereby for the same power, increased speed may be obtained, 

 and with increased speed, increased lift with the same wing area. 



There is a further factor which helps in the same direction. The 

 structure of the plane, under certain conditions, as we have seen, 

 would be subject to this square-cube law. The power plant would 

 not be so subject. Power is related primarily to surface or, broadly, 

 to wing area. For the same speed, therefore, the power required 

 will increase with the wing area, or as the square of the linear 

 dimension rather than as the cube. One part of the weight of the 



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