84 smithsonian miscellaneous collections vol. 62 



2. Critical Speeds for Flat Disks in a Normal Wind 



The value of tests on the resistance of small models in a wind tun- 

 nel depends upon the precision with which such results may be 

 applied to larger models at different speeds. The resistance of thin 

 disks normal to the wind is not of great practical interest in aero- 

 nautics, but certain theoretical conclusions of general importance . 

 may be drawn from experiments with disks. 



The resistance of the air depends upon the density, viscosity, and 

 compressibility of the fluid. Except in gunnery, the velocities in 

 common use do not approach the velocity of sound in air, and hence 

 compressibility is neglected. 



Two well-defined types of flow are recognized. The first is the 

 so-called stream line flow in which the fluid flows around the body 

 in steady lines, closing in behind it feo that no turbulent wake 

 is formed. Such flow may be expected about a fish-shaped body at 

 low speeds. The second form is called the discontinuous or turbulent 

 flow, in which eddies are formed on the body and are carried down 

 stream as a turbulent wake. Such flow may be expected about bodies 

 of abrupt form moving at high speeds. 



If no eddies are formed, the resistance to motion is a viscous drag 

 depending on the viscosity of the fluid, a linear dimension, and the 

 velocity. 



With the formation of eddies, additional resistance is caused by 

 the energy lost in imparting kinetic energy to the fluid in the eddies. 

 It is observed that, in general, eddies are left behind and so represent 

 a loss of energy. The eddy making resistance should depend on the 

 kinetic energy imparted to the fluid and hence should vary as the 

 density, the square of the velocity, and the extent of the disturbance. 

 The latter should be proportional to the square of a linear dimension 

 of the body, or the cross-section of the wake. 



In any real case both viscous and eddy resistance are present. For 

 bodies of easy shape, the turbulence is not great and we should expect 

 viscosity to play an important part, and the resistance to vary less 

 rapidly than V^. 



However, for a thin disk with its face normal to the wind we 

 should expect eddy making to be violent and the resistance to vary 

 with the density of the air, area of face of disk, and square of velocity. 

 Under such conditions the viscous drag might be negligible. 



At very low speeds, if it be possible for the fluid to turn the corner 

 and close in behind the disk, eddy making may be so much reduced 



