Free Surface Effects tn Hull Propeller Interactton 
(momentum theory), the method of singularities (Lagally's theorem) 
for calculating forces on the hull and Havelock's method of images for 
a linearized treatment of the free surface. 
In recent years considerable effort has been put into the in- 
vestigation of potential and viscous effects in hull propeller interaction 
(see Bibliography). Especially in this country, Beveridge ina series 
of papers (1962, 63, 66, 68) has refined the technique of calculating the 
potential thrust deduction to a state of near perfection. At the same 
time, Hucho (1965, 68) in Germany has made significant contributions 
to our understanding of viscous effects. The wave effects, however, 
were persistently ignored for nearly thirty years since Dickmann(1939), 
until the fundamental treatise of Yamazaki (1967) revived interest in 
this subject and inspired the recent work of Nakatake (1967, 68) in 
Japan. 
Still far from resolving the complex issues at stake, Nakatake's 
papers are just added evidence of the same conviction that underlies 
the present study(which, incidentally, was initiated without knowledge 
of the Japanese effort), namely that the time is now ripe to make a 
fresh attempt at the further clarification of this admittedly difficult 
problem. This is due mainly to the following reasons : 
1) Major advances in the vortex theory of propellers now 
allow the use of a far more refined mathematical model of the propel- 
ler. 
2) The recently developed technique of wave profile measure- 
ment and analysis enables us to verify by (almost) direct measurement 
the wave effects predicted by analytical theory. 
3) The general availability of large electronic computers al- 
lows the use of more realistic singularity distributions for represent- 
ing the hull, the propeller and their images in the free surface. 
Beside the intrinsic interest of a fundamental problem in ship 
hydrodynamics, a recommendation by the Performance Committee of 
the International Towing Tank Conference 1966 for specific research 
in the basic problem area of hull propeller interaction - of which free 
surface effects are certainly the most intriguing aspect - as wellas 
the prospect of practical application to modern high speed craft with 
propellers operating at shallow or even partial submergence were 
further motivations for undertaking this research, 
1847 
