NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 23 



the edge and not dependent on the size of plate, it seems possible that 



some of the apparent discrepancies between = constant and „.. = 



variable may be due to the experimental results of various observers 

 having" been influenced by such critical phenomena, which were not, 

 however, sufificiently marked to attract attention. 



To decide whether an explanation of this sort is applicable would 

 require an experimental study of the forms of edge which have been 

 used ; for until the critical speeds for these edges — if they have any — 

 have been investigated, it is impossible to say whether the speeds at 

 which various experimenters have worked may have overlapped with 

 these critical ranges. Nothing more definite can be said, at present, 

 than that it is well to pay close attention to geometrical similarity ; 

 but it seems that a further experimental study of the resistance of 

 flat plates, undertaken with the foregoing possibilities in mind, might 

 lead to interesting results. 



Dynamical Similarity 



Let us suppose that we are confronted with a problem of design 

 which requires our knowing, in advance, the head resistance, at a pre- 

 scribed speed, of some body such as an air-ship which is too large 

 for direct experiment. The question is, how to get the desired infor- 

 mation from experiments on a small model which can be made at a 

 permissible cost. 



Returning to equation (9) or 



R=pD^S^(^,^^ (II) 



we notice that whatever be the form of 9, if its two arguments have 

 the same values during two different experiments on geometrically 

 similar bodies, the value of ^ itself will be the same in both experi- 

 ments. This observation leads to the notion of corresponding speeds 

 and dynamical similarity. 



Let us suppose that we require the resistance i? of a body of size D 

 at the speed S in a medium with the properties p, v, C; and that we 

 have a model of the size Dm, which can be run in a medium with the 

 properties pm, vm, Cm- Then if we run the model at a speed Sm, such 

 that 



^^jnSm=^^ and ^'« =^ (12) 



and observe the resistance Rm, we know by equation (11) that 



R pD^S^ , , 



