DURAND— MECHANICAL ASPECTS. 185 



The existence of a law of kinematic similitude assumes that for 

 any given set of operating conditions for the full-sized body there 

 will correspond a determinable set of conditions for the model and 

 that the results realized for the model may be transformed into 

 the results to be anticipated from the full-sized body by the applica- 

 tion of determinable ratios which will be some known function of 

 the relation between the two sets of conditions. 



It should be noted further that this relation assumes that all of 

 the conditions which may affect the result in question admit of 

 definite expression in terms of mechanics and of definite numerical 

 measurement in specific cases. This is not always possible espe- 

 cially with such factors as surface roughness or degree of turbulence. 



Again the special conditions which are required for the model 

 may be inconvenient or even impracticable as regards experimental 

 realization. 



These various conditions prevail in the case of air propellers. It 

 is well known that we are only able to realize a practicable applica- 

 tion of the law by neglecting the influence of the viscosity of the 

 medium. This of itself, with the air propeller working in an in- 

 definite medium and under loads and speeds which would permit the 

 neglect of the influence due to the compressibility of the air and of 

 the distortion due to thrust and centrifugal force, would make all 

 speeds corresponding. This is equivalent to a reduction of the 

 equation for the thrust of a propeller to the form 



T = KDH-. 



Hence with such a relation the model may be run at any speed 

 with the same percentage slip as for the full-sized propeller, and 

 from the observed value of the thrust we may derive the factor K. 

 The constant thus determined should then serve for any diameter so 

 long as the shape and slip remain the same as for the experimental 

 conditions. 



If, however, allowance is to be made for compressibility and for 

 distortion due to force loading, theory indicates, as is well known, 

 that the tip speeds of both model and full-sized propeller should be 

 the same. 



The form of corresponding speed relation usually adopted for air 



