n 



form resistance. So long as no separation occurs, a lower limit for this 

 frictional form resistance can be estimated from Milllkan's formula for bodies 

 of revolution,^' vrtiich gives an increase of the order of 4 to 6 percent over 

 the corresponding plate values. A further effect is the change in the wetted 

 surface due to the changed attitude of the model and to the wave flow. The 

 latter is important for high Proude numbers only; ** it becomes decisive for 

 vessels with large hydrodynamic lift. 



b. Viscous normal or pressure resistance ; This resistance is caused 

 by the pressure changes due to viscosity, especially in the afterbody. It 

 includes separation effects and loss of pressure due to finite boundary thick- 

 ness. This definition is broader than "separation" or "eddy" resistance; the 

 addition "viscous" becomes necessary to avoid confusion with wave resistance 

 which can also be derived from pressure measurements. Frictional and normal 

 resistances— a and b above — can be separated by pressure measurements when 

 wave making is absent or negligible. 



Throughout this report the denotation "eddy resistance" will be used 

 in the same sense as viscous normal resistance. Sometimes the sum of friction- 

 al-form resistance plus viscous-pressure resistance is referred to as viscous- 

 form resistance; the adjective viscous should not be dropped.** 



c. Wave resistance : Items a and b give the total viscous drag. Wave 

 resistance can be computed as the difference between the total normal and the 

 viscous normal resistance, or between the total resistance and the total vis- 

 cous drag. Surface models and wholly submerged double models have been used 

 for this purpose under the assumption that for the same Reynolds number the 

 wave flow does not influence a and b.^' ^^>^^ One can dispense with the dou- 

 ble models if pressure measurements on large simple models admitting of high 

 Resmolds numbers are made at low Proude numbers giving a negligible wave pat- 

 tern, A more direct approach would be to calculate the resistance from actual 

 wave patterns (stereo-photogrammetric pictures) which, however, never has been 

 successfully tried. Most of these methods are suitable for research work 

 only. 



d. Spray or jet resistance ; This becomes important for very-high- 

 speed length ratios, such as are found in gliders and seaplanes. It must be 

 listed here as a surface effect sui generis which is not described by the the- 

 ory of surface waves; in fact its generation does not depend on gravity. In 

 normal vessels, sprays can be prevented by avoiding blunt surfaces normal to 

 the direction of advance. 



