NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS I9 



The approximation attainable when compressibility is thus left out 



S S . 



of account depends on the value of "^ . If is a small fraction, as 



it nearly always is with liquids, equation (7) is a satisfactory sub- 

 stitute for (6). The speed of sound in air under ordinary conditions 

 is of the order of iioo feet per second, or 750 miles per hour. For 



9 

 rifled projectiles ' , may be as high as 2.5 or even 3, so that equation 



(7) would be entirely misleading if used in studying projectile resist- 

 ances. But at the speeds which occur in aeronautics, with the excep- 

 tion of propeller tip speeds, the ratio „ is a sufficiently small fraction 



that the air acts nearly like an incompressible fluid, i. e., like a liquid 

 of the same density and viscosity ; and equation (7) may be used as a 

 sufficiently approximate substitute for the more general equation (6). 

 Equation (7) supplies the basis for the experimental investigation 

 of the aerodynamic problems which occur in connection with aero- 

 nautics and aviation by means of reduced scale methods. 



Restriction to Geometrically Similar Bodies 



Let us now confine our attention to a series of bodies of various 

 sizes but all of the same shape, and presented to the wind in the same 

 attitude. The bodies are geometrically similar, and any one may be 

 regarded as a reduced or enlarged model of any other. The ratios 

 r', /',.... are now constants, so that equation (7) assumes the 

 simpler form 



in which the form of the unknown function ^ of the single argument 



DS 



remains to be determined by experimenting on bodies of the 



given series. The nature of this function will depend on the shape 

 and attitude of the bodies but not on their size, if our disregard of 

 compressibility, leading from (6) to (7), was a justifiable approxi- 

 mation. 



The obvious procedure, in investigating xj/ by analyzing the results 



of experiments, is to plot observed values of f^^^^ against values of 



DS . ^ '^ 



— and draw a curve through the points thus obtained. If we are 



using air of constant density and viscosity the experiments may con- 



