30 



QUANTITATIVE ANALYSIS OP RESISTANCE TEST DATA 



WITH AND WITHOUT STIMULATION 



The resistance test of a model provides a relationship between the 

 total measured resistance R. and the towing speed U. As is well known the 

 model towing speed is determined so that the Froude number, U/VgT7, is the same 

 in model and prototype dimensions. Froude 1 s basic assumption as used today 

 may be stated: 



isu 2 ' fsu 2 fsu 2 [1U] 



C t = C r + C f [14a] 



where R, is the total resistance, 



R is the so-called residuary resistance, 



R f is the frictional resistance of the model, 



p is the mass density of the fluid, 



g is the acceleration due to gravity, and 



C, ,C ,C f are the corresponding resistance coefficients. 



In order to scale the residuary resistance the model must be towed at the same 

 Froude number,* whereas to scale the frictional resistance the model must be 

 towed at the same Reynolds number. This incompatible situation is circum- 

 vented by assuming that the frictional resistance of model and prototype may 

 be calculated from the empirical laws for the frictional resistance of flat 

 planks having the same wetted surface and towed at the same Reynolds numbers . 

 A summary of the experimental and theoretical work in regard to flat-plate re- 

 sistance has been given by Davidson. 13 The details of the method used at the 

 Model Basin are reported in Reference 12. 



Although the use of a device to stimulate turbulence represents an 

 effort to make the flow about the model similar to that about the prototype, 

 the stimulator itself may introduce additional forces or modify the flow to 

 produce effects on the drag of the model which are undesirable. A sand strip 



♦Actually, Froude's assumption is an oversimplification because the residuary resistance as calcu- 

 lated involves quantities which are not independent of the Reynolds number. The residuary resistance 

 is the sum of the wave resistance, the viscous pressure drag and the additional frictional forces which 

 arise from the curvature of the form and the surface roughness. Each of these terms is dependent more 

 or less on the model Reynolds number. 



