DIMENSIONAL RELATIONSHIPS 

 FOR FLYING ANIMALS 



By CRAWFORD H. GREENEWALT 

 President, E. I. du Pont de Nemours & Co. 



For a dimensionally similar series of objects, animate or inanimate, 

 a volume or a mass will be proportional to the cube, a surface to the 

 square, of a linear dimension. If Alice, then, after sipping from the 

 bottle labeled "Drink me," were reduced to one-third of her normal 

 height, her surface would be one-ninth, her weight one twenty- seventh, 

 of its original value. Or if we should plot Alice's weight and that of 

 many other little girls, large and small, against let us say the length of 

 their arms, we should find in logarithmic coordinates a straight line 

 whose slope is 3, or in mathematical terms 



W = cl^ 

 where W is weight, / is length of arm, and c a constant of proportion- 

 ality. 



For cats or for mice the result should be the same with, however, a 

 different value for c, meaning simply that cats or mice are dimension- 

 ally similar within their families but not with each other, or for that 

 matter with little girls. 



BODY WEIGHT AND WING LENGTH 



We turn now to figure 1 (all figures follow page 7), on which is 

 plotted total weight against wing length for the entire array of flying 

 animals. We see that for body weights ranging from less than 1 to more 

 than 10 million milligrams, weight is roughly proportional to the cube 

 of the wing length. 



Insects show a much greater "scatter" than birds, evidence I sup- 

 pose of nature's versatility in designing many models of animate air- 

 craft at the lower end of the scale. The highest values of wing length 

 per unit weight are found for the dragonflies and damselflies, for cer- 

 tain butterflies, and for such insect specialties as the craneflies and 

 mosquitoes. Except for the dragonflies, these are rather poor fliers 

 with low wing-beat rates. Lowest relative wing lengths are for the 



SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 144, NO. 2 



1 



