Huang and von Kerezek 
INTRODUCTION 
Since the contribution of Froude about a century ago, total 
ship resistance has been assumed to be composed of two separate 
and independent parts: (1) frictional resistance, equal to the resis- 
tance of an equivalent plank or flat plate of the same wetted area and 
length as the ship, and (2) the remainder, called "residual" resis- 
tance. It has been a practical engineering solution to extrapolate the 
resistance measured on a model to that of a full-scale ship either 
(1) by assuming that the frictional resistance follows a Reynolds- 
number scaling law and that the residual resistance follows a Froude- 
number scaling law, or (2) by usinga form factor to distribute part 
of the residual resistance into viscous form drag. These phenomeno- 
logical assumptions have never allowed one to predict by pure analy- 
tical means the resistance of a ship. 
The prediction of total ship resistance depends on our 
ability to calculate the potential flow and turbulent boundary layer 
flow around ship hulls. The calculation of the potential flow not only 
provides the wave resistance, but also provides the "outer" flow for 
the boundary layer computation. At present, the potential flow about 
a given hull has been solved only approximately (e. g., Michell thin 
ship theory and slender ship theory). It is well known that thin ship 
theory fails for the flow around the bilges and on flat bottoms of 
ships, Lunde! , and slender ship theory overpredicts the effect of 
the waves, Tuck® . More accurate methods for predicting the poten- 
tial flow around surface ships are not available. We can, however, 
calculate the potentiai flow about deeply-submerged bodies and about 
ships at zero Froude number (e.g., the submerged ''double model"). 
This can be done accurately by the Douglas-Neumann~ computer pro- 
gram, and approximately by the slender-body computer program of 
Tuck and von Kerczek* . As will be demonstrated, this program 
yields an adequate approximation of streamlines and pressure dis- 
tributions on ''slender'' ships at very small Froude number for the 
boundary layer calculations. The calculation of the boundary-layer 
flow in the context of the submerged double model can serve to deve- 
lop and to test the boundary layer calculation methods. Furthermore, 
this computation may provide a good approximation of the boundary 
layer flow around a ship hull at low Froude number, especially in the 
vicinity of the shoulder and bilge. 
The present status of three-dimensional boundary layer 
calculation methods is somewhat better than the ship potential flow 
theory. Several computation methods have been developed recently : 
1964 
